Add C versions as fallback

lapack-netlib/SRC/cgbcon.c

@@ -0,0 +1,742 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* > \brief \b CGBCON */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGBCON + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbcon.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbcon.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbcon.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, */
+/*                          WORK, RWORK, INFO ) */
+
+/*       CHARACTER          NORM */
+/*       INTEGER            INFO, KL, KU, LDAB, N */
+/*       REAL               ANORM, RCOND */
+/*       INTEGER            IPIV( * ) */
+/*       REAL               RWORK( * ) */
+/*       COMPLEX            AB( LDAB, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGBCON estimates the reciprocal of the condition number of a complex */
+/* > general band matrix A, in either the 1-norm or the infinity-norm, */
+/* > using the LU factorization computed by CGBTRF. */
+/* > */
+/* > An estimate is obtained for norm(inv(A)), and the reciprocal of the */
+/* > condition number is computed as */
+/* >    RCOND = 1 / ( norm(A) * norm(inv(A)) ). */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] NORM */
+/* > \verbatim */
+/* >          NORM is CHARACTER*1 */
+/* >          Specifies whether the 1-norm condition number or the */
+/* >          infinity-norm condition number is required: */
+/* >          = '1' or 'O':  1-norm; */
+/* >          = 'I':         Infinity-norm. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KL */
+/* > \verbatim */
+/* >          KL is INTEGER */
+/* >          The number of subdiagonals within the band of A.  KL >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KU */
+/* > \verbatim */
+/* >          KU is INTEGER */
+/* >          The number of superdiagonals within the band of A.  KU >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] AB */
+/* > \verbatim */
+/* >          AB is COMPLEX array, dimension (LDAB,N) */
+/* >          Details of the LU factorization of the band matrix A, as */
+/* >          computed by CGBTRF.  U is stored as an upper triangular band */
+/* >          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
+/* >          the multipliers used during the factorization are stored in */
+/* >          rows KL+KU+2 to 2*KL+KU+1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDAB */
+/* > \verbatim */
+/* >          LDAB is INTEGER */
+/* >          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (N) */
+/* >          The pivot indices; for 1 <= i <= N, row i of the matrix was */
+/* >          interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] ANORM */
+/* > \verbatim */
+/* >          ANORM is REAL */
+/* >          If NORM = '1' or 'O', the 1-norm of the original matrix A. */
+/* >          If NORM = 'I', the infinity-norm of the original matrix A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RCOND */
+/* > \verbatim */
+/* >          RCOND is REAL */
+/* >          The reciprocal of the condition number of the matrix A, */
+/* >          computed as RCOND = 1/(norm(A) * norm(inv(A))). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (2*N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RWORK */
+/* > \verbatim */
+/* >          RWORK is REAL array, dimension (N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGBcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgbcon_(char *norm, integer *n, integer *kl, integer *ku,
+	 complex *ab, integer *ldab, integer *ipiv, real *anorm, real *rcond, 
+	complex *work, real *rwork, integer *info)
+{
+    /* System generated locals */
+    integer ab_dim1, ab_offset, i__1, i__2, i__3;
+    real r__1, r__2;
+    complex q__1, q__2;
+
+    /* Local variables */
+    integer kase, kase1, j;
+    complex t;
+    real scale;
+    extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer 
+	    *, complex *, integer *);
+    extern logical lsame_(char *, char *);
+    integer isave[3];
+    extern /* Subroutine */ int caxpy_(integer *, complex *, complex *, 
+	    integer *, complex *, integer *);
+    logical lnoti;
+    extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real 
+	    *, integer *, integer *);
+    integer kd, lm, jp, ix;
+    extern integer icamax_(integer *, complex *, integer *);
+    extern real slamch_(char *);
+    extern /* Subroutine */ int clatbs_(char *, char *, char *, char *, 
+	    integer *, integer *, complex *, integer *, complex *, real *, 
+	    real *, integer *), xerbla_(char *
+	    , integer *, ftnlen);
+    real ainvnm;
+    extern /* Subroutine */ int csrscl_(integer *, real *, complex *, integer 
+	    *);
+    logical onenrm;
+    char normin[1];
+    real smlnum;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    ab_dim1 = *ldab;
+    ab_offset = 1 + ab_dim1 * 1;
+    ab -= ab_offset;
+    --ipiv;
+    --work;
+    --rwork;
+
+    /* Function Body */
+    *info = 0;
+    onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
+    if (! onenrm && ! lsame_(norm, "I")) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*kl < 0) {
+	*info = -3;
+    } else if (*ku < 0) {
+	*info = -4;
+    } else if (*ldab < (*kl << 1) + *ku + 1) {
+	*info = -6;
+    } else if (*anorm < 0.f) {
+	*info = -8;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGBCON", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    *rcond = 0.f;
+    if (*n == 0) {
+	*rcond = 1.f;
+	return 0;
+    } else if (*anorm == 0.f) {
+	return 0;
+    }
+
+    smlnum = slamch_("Safe minimum");
+
+/*     Estimate the norm of inv(A). */
+
+    ainvnm = 0.f;
+    *(unsigned char *)normin = 'N';
+    if (onenrm) {
+	kase1 = 1;
+    } else {
+	kase1 = 2;
+    }
+    kd = *kl + *ku + 1;
+    lnoti = *kl > 0;
+    kase = 0;
+L10:
+    clacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
+    if (kase != 0) {
+	if (kase == kase1) {
+
+/*           Multiply by inv(L). */
+
+	    if (lnoti) {
+		i__1 = *n - 1;
+		for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+		    i__2 = *kl, i__3 = *n - j;
+		    lm = f2cmin(i__2,i__3);
+		    jp = ipiv[j];
+		    i__2 = jp;
+		    t.r = work[i__2].r, t.i = work[i__2].i;
+		    if (jp != j) {
+			i__2 = jp;
+			i__3 = j;
+			work[i__2].r = work[i__3].r, work[i__2].i = work[i__3]
+				.i;
+			i__2 = j;
+			work[i__2].r = t.r, work[i__2].i = t.i;
+		    }
+		    q__1.r = -t.r, q__1.i = -t.i;
+		    caxpy_(&lm, &q__1, &ab[kd + 1 + j * ab_dim1], &c__1, &
+			    work[j + 1], &c__1);
+/* L20: */
+		}
+	    }
+
+/*           Multiply by inv(U). */
+
+	    i__1 = *kl + *ku;
+	    clatbs_("Upper", "No transpose", "Non-unit", normin, n, &i__1, &
+		    ab[ab_offset], ldab, &work[1], &scale, &rwork[1], info);
+	} else {
+
+/*           Multiply by inv(U**H). */
+
+	    i__1 = *kl + *ku;
+	    clatbs_("Upper", "Conjugate transpose", "Non-unit", normin, n, &
+		    i__1, &ab[ab_offset], ldab, &work[1], &scale, &rwork[1], 
+		    info);
+
+/*           Multiply by inv(L**H). */
+
+	    if (lnoti) {
+		for (j = *n - 1; j >= 1; --j) {
+/* Computing MIN */
+		    i__1 = *kl, i__2 = *n - j;
+		    lm = f2cmin(i__1,i__2);
+		    i__1 = j;
+		    i__2 = j;
+		    cdotc_(&q__2, &lm, &ab[kd + 1 + j * ab_dim1], &c__1, &
+			    work[j + 1], &c__1);
+		    q__1.r = work[i__2].r - q__2.r, q__1.i = work[i__2].i - 
+			    q__2.i;
+		    work[i__1].r = q__1.r, work[i__1].i = q__1.i;
+		    jp = ipiv[j];
+		    if (jp != j) {
+			i__1 = jp;
+			t.r = work[i__1].r, t.i = work[i__1].i;
+			i__1 = jp;
+			i__2 = j;
+			work[i__1].r = work[i__2].r, work[i__1].i = work[i__2]
+				.i;
+			i__1 = j;
+			work[i__1].r = t.r, work[i__1].i = t.i;
+		    }
+/* L30: */
+		}
+	    }
+	}
+
+/*        Divide X by 1/SCALE if doing so will not cause overflow. */
+
+	*(unsigned char *)normin = 'Y';
+	if (scale != 1.f) {
+	    ix = icamax_(n, &work[1], &c__1);
+	    i__1 = ix;
+	    if (scale < ((r__1 = work[i__1].r, abs(r__1)) + (r__2 = r_imag(&
+		    work[ix]), abs(r__2))) * smlnum || scale == 0.f) {
+		goto L40;
+	    }
+	    csrscl_(n, &scale, &work[1], &c__1);
+	}
+	goto L10;
+    }
+
+/*     Compute the estimate of the reciprocal condition number. */
+
+    if (ainvnm != 0.f) {
+	*rcond = 1.f / ainvnm / *anorm;
+    }
+
+L40:
+    return 0;
+
+/*     End of CGBCON */
+
+} /* cgbcon_ */
+

lapack-netlib/SRC/cgbequ.c

@@ -0,0 +1,767 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGBEQU */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGBEQU + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbequ.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbequ.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbequ.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, */
+/*                          AMAX, INFO ) */
+
+/*       INTEGER            INFO, KL, KU, LDAB, M, N */
+/*       REAL               AMAX, COLCND, ROWCND */
+/*       REAL               C( * ), R( * ) */
+/*       COMPLEX            AB( LDAB, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGBEQU computes row and column scalings intended to equilibrate an */
+/* > M-by-N band matrix A and reduce its condition number.  R returns the */
+/* > row scale factors and C the column scale factors, chosen to try to */
+/* > make the largest element in each row and column of the matrix B with */
+/* > elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1. */
+/* > */
+/* > R(i) and C(j) are restricted to be between SMLNUM = smallest safe */
+/* > number and BIGNUM = largest safe number.  Use of these scaling */
+/* > factors is not guaranteed to reduce the condition number of A but */
+/* > works well in practice. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KL */
+/* > \verbatim */
+/* >          KL is INTEGER */
+/* >          The number of subdiagonals within the band of A.  KL >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KU */
+/* > \verbatim */
+/* >          KU is INTEGER */
+/* >          The number of superdiagonals within the band of A.  KU >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] AB */
+/* > \verbatim */
+/* >          AB is COMPLEX array, dimension (LDAB,N) */
+/* >          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th */
+/* >          column of A is stored in the j-th column of the array AB as */
+/* >          follows: */
+/* >          AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(m,j+kl). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDAB */
+/* > \verbatim */
+/* >          LDAB is INTEGER */
+/* >          The leading dimension of the array AB.  LDAB >= KL+KU+1. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] R */
+/* > \verbatim */
+/* >          R is REAL array, dimension (M) */
+/* >          If INFO = 0, or INFO > M, R contains the row scale factors */
+/* >          for A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] C */
+/* > \verbatim */
+/* >          C is REAL array, dimension (N) */
+/* >          If INFO = 0, C contains the column scale factors for A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] ROWCND */
+/* > \verbatim */
+/* >          ROWCND is REAL */
+/* >          If INFO = 0 or INFO > M, ROWCND contains the ratio of the */
+/* >          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and */
+/* >          AMAX is neither too large nor too small, it is not worth */
+/* >          scaling by R. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] COLCND */
+/* > \verbatim */
+/* >          COLCND is REAL */
+/* >          If INFO = 0, COLCND contains the ratio of the smallest */
+/* >          C(i) to the largest C(i).  If COLCND >= 0.1, it is not */
+/* >          worth scaling by C. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] AMAX */
+/* > \verbatim */
+/* >          AMAX is REAL */
+/* >          Absolute value of largest matrix element.  If AMAX is very */
+/* >          close to overflow or very close to underflow, the matrix */
+/* >          should be scaled. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO = i, and i is */
+/* >                <= M:  the i-th row of A is exactly zero */
+/* >                >  M:  the (i-M)-th column of A is exactly zero */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGBcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgbequ_(integer *m, integer *n, integer *kl, integer *ku,
+	 complex *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real 
+	*colcnd, real *amax, integer *info)
+{
+    /* System generated locals */
+    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
+    real r__1, r__2, r__3, r__4;
+
+    /* Local variables */
+    integer i__, j;
+    real rcmin, rcmax;
+    integer kd;
+    extern real slamch_(char *);
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    real bignum, smlnum;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters */
+
+    /* Parameter adjustments */
+    ab_dim1 = *ldab;
+    ab_offset = 1 + ab_dim1 * 1;
+    ab -= ab_offset;
+    --r__;
+    --c__;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*kl < 0) {
+	*info = -3;
+    } else if (*ku < 0) {
+	*info = -4;
+    } else if (*ldab < *kl + *ku + 1) {
+	*info = -6;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGBEQU", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*m == 0 || *n == 0) {
+	*rowcnd = 1.f;
+	*colcnd = 1.f;
+	*amax = 0.f;
+	return 0;
+    }
+
+/*     Get machine constants. */
+
+    smlnum = slamch_("S");
+    bignum = 1.f / smlnum;
+
+/*     Compute row scale factors. */
+
+    i__1 = *m;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	r__[i__] = 0.f;
+/* L10: */
+    }
+
+/*     Find the maximum element in each row. */
+
+    kd = *ku + 1;
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+/* Computing MAX */
+	i__2 = j - *ku;
+/* Computing MIN */
+	i__4 = j + *kl;
+	i__3 = f2cmin(i__4,*m);
+	for (i__ = f2cmax(i__2,1); i__ <= i__3; ++i__) {
+/* Computing MAX */
+	    i__2 = kd + i__ - j + j * ab_dim1;
+	    r__3 = r__[i__], r__4 = (r__1 = ab[i__2].r, abs(r__1)) + (r__2 = 
+		    r_imag(&ab[kd + i__ - j + j * ab_dim1]), abs(r__2));
+	    r__[i__] = f2cmax(r__3,r__4);
+/* L20: */
+	}
+/* L30: */
+    }
+
+/*     Find the maximum and minimum scale factors. */
+
+    rcmin = bignum;
+    rcmax = 0.f;
+    i__1 = *m;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+/* Computing MAX */
+	r__1 = rcmax, r__2 = r__[i__];
+	rcmax = f2cmax(r__1,r__2);
+/* Computing MIN */
+	r__1 = rcmin, r__2 = r__[i__];
+	rcmin = f2cmin(r__1,r__2);
+/* L40: */
+    }
+    *amax = rcmax;
+
+    if (rcmin == 0.f) {
+
+/*        Find the first zero scale factor and return an error code. */
+
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    if (r__[i__] == 0.f) {
+		*info = i__;
+		return 0;
+	    }
+/* L50: */
+	}
+    } else {
+
+/*        Invert the scale factors. */
+
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+/* Computing MIN */
+/* Computing MAX */
+	    r__2 = r__[i__];
+	    r__1 = f2cmax(r__2,smlnum);
+	    r__[i__] = 1.f / f2cmin(r__1,bignum);
+/* L60: */
+	}
+
+/*        Compute ROWCND = f2cmin(R(I)) / f2cmax(R(I)) */
+
+	*rowcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
+    }
+
+/*     Compute column scale factors */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	c__[j] = 0.f;
+/* L70: */
+    }
+
+/*     Find the maximum element in each column, */
+/*     assuming the row scaling computed above. */
+
+    kd = *ku + 1;
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+/* Computing MAX */
+	i__3 = j - *ku;
+/* Computing MIN */
+	i__4 = j + *kl;
+	i__2 = f2cmin(i__4,*m);
+	for (i__ = f2cmax(i__3,1); i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    i__3 = kd + i__ - j + j * ab_dim1;
+	    r__3 = c__[j], r__4 = ((r__1 = ab[i__3].r, abs(r__1)) + (r__2 = 
+		    r_imag(&ab[kd + i__ - j + j * ab_dim1]), abs(r__2))) * 
+		    r__[i__];
+	    c__[j] = f2cmax(r__3,r__4);
+/* L80: */
+	}
+/* L90: */
+    }
+
+/*     Find the maximum and minimum scale factors. */
+
+    rcmin = bignum;
+    rcmax = 0.f;
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+	r__1 = rcmin, r__2 = c__[j];
+	rcmin = f2cmin(r__1,r__2);
+/* Computing MAX */
+	r__1 = rcmax, r__2 = c__[j];
+	rcmax = f2cmax(r__1,r__2);
+/* L100: */
+    }
+
+    if (rcmin == 0.f) {
+
+/*        Find the first zero scale factor and return an error code. */
+
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    if (c__[j] == 0.f) {
+		*info = *m + j;
+		return 0;
+	    }
+/* L110: */
+	}
+    } else {
+
+/*        Invert the scale factors. */
+
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+/* Computing MAX */
+	    r__2 = c__[j];
+	    r__1 = f2cmax(r__2,smlnum);
+	    c__[j] = 1.f / f2cmin(r__1,bignum);
+/* L120: */
+	}
+
+/*        Compute COLCND = f2cmin(C(J)) / f2cmax(C(J)) */
+
+	*colcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
+    }
+
+    return 0;
+
+/*     End of CGBEQU */
+
+} /* cgbequ_ */
+

lapack-netlib/SRC/cgbequb.c

@@ -0,0 +1,786 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGBEQUB */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGBEQUB + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbequb
+.f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbequb
+.f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbequb
+.f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, */
+/*                           AMAX, INFO ) */
+
+/*       INTEGER            INFO, KL, KU, LDAB, M, N */
+/*       REAL               AMAX, COLCND, ROWCND */
+/*       REAL               C( * ), R( * ) */
+/*       COMPLEX            AB( LDAB, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGBEQUB computes row and column scalings intended to equilibrate an */
+/* > M-by-N matrix A and reduce its condition number.  R returns the row */
+/* > scale factors and C the column scale factors, chosen to try to make */
+/* > the largest element in each row and column of the matrix B with */
+/* > elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most */
+/* > the radix. */
+/* > */
+/* > R(i) and C(j) are restricted to be a power of the radix between */
+/* > SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use */
+/* > of these scaling factors is not guaranteed to reduce the condition */
+/* > number of A but works well in practice. */
+/* > */
+/* > This routine differs from CGEEQU by restricting the scaling factors */
+/* > to a power of the radix.  Barring over- and underflow, scaling by */
+/* > these factors introduces no additional rounding errors.  However, the */
+/* > scaled entries' magnitudes are no longer approximately 1 but lie */
+/* > between sqrt(radix) and 1/sqrt(radix). */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KL */
+/* > \verbatim */
+/* >          KL is INTEGER */
+/* >          The number of subdiagonals within the band of A.  KL >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KU */
+/* > \verbatim */
+/* >          KU is INTEGER */
+/* >          The number of superdiagonals within the band of A.  KU >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] AB */
+/* > \verbatim */
+/* >          AB is COMPLEX array, dimension (LDAB,N) */
+/* >          On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */
+/* >          The j-th column of A is stored in the j-th column of the */
+/* >          array AB as follows: */
+/* >          AB(KU+1+i-j,j) = A(i,j) for f2cmax(1,j-KU)<=i<=f2cmin(N,j+kl) */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDAB */
+/* > \verbatim */
+/* >          LDAB is INTEGER */
+/* >          The leading dimension of the array A.  LDAB >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] R */
+/* > \verbatim */
+/* >          R is REAL array, dimension (M) */
+/* >          If INFO = 0 or INFO > M, R contains the row scale factors */
+/* >          for A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] C */
+/* > \verbatim */
+/* >          C is REAL array, dimension (N) */
+/* >          If INFO = 0,  C contains the column scale factors for A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] ROWCND */
+/* > \verbatim */
+/* >          ROWCND is REAL */
+/* >          If INFO = 0 or INFO > M, ROWCND contains the ratio of the */
+/* >          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and */
+/* >          AMAX is neither too large nor too small, it is not worth */
+/* >          scaling by R. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] COLCND */
+/* > \verbatim */
+/* >          COLCND is REAL */
+/* >          If INFO = 0, COLCND contains the ratio of the smallest */
+/* >          C(i) to the largest C(i).  If COLCND >= 0.1, it is not */
+/* >          worth scaling by C. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] AMAX */
+/* > \verbatim */
+/* >          AMAX is REAL */
+/* >          Absolute value of largest matrix element.  If AMAX is very */
+/* >          close to overflow or very close to underflow, the matrix */
+/* >          should be scaled. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO = i,  and i is */
+/* >                <= M:  the i-th row of A is exactly zero */
+/* >                >  M:  the (i-M)-th column of A is exactly zero */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2016 */
+
+/* > \ingroup complexGBcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgbequb_(integer *m, integer *n, integer *kl, integer *
+	ku, complex *ab, integer *ldab, real *r__, real *c__, real *rowcnd, 
+	real *colcnd, real *amax, integer *info)
+{
+    /* System generated locals */
+    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
+    real r__1, r__2, r__3, r__4;
+
+    /* Local variables */
+    integer i__, j;
+    real radix, rcmin, rcmax;
+    integer kd;
+    extern real slamch_(char *);
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    real bignum, logrdx, smlnum;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    ab_dim1 = *ldab;
+    ab_offset = 1 + ab_dim1 * 1;
+    ab -= ab_offset;
+    --r__;
+    --c__;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*kl < 0) {
+	*info = -3;
+    } else if (*ku < 0) {
+	*info = -4;
+    } else if (*ldab < *kl + *ku + 1) {
+	*info = -6;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGBEQUB", &i__1, (ftnlen)7);
+	return 0;
+    }
+
+/*     Quick return if possible. */
+
+    if (*m == 0 || *n == 0) {
+	*rowcnd = 1.f;
+	*colcnd = 1.f;
+	*amax = 0.f;
+	return 0;
+    }
+
+/*     Get machine constants.  Assume SMLNUM is a power of the radix. */
+
+    smlnum = slamch_("S");
+    bignum = 1.f / smlnum;
+    radix = slamch_("B");
+    logrdx = log(radix);
+
+/*     Compute row scale factors. */
+
+    i__1 = *m;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	r__[i__] = 0.f;
+/* L10: */
+    }
+
+/*     Find the maximum element in each row. */
+
+    kd = *ku + 1;
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+/* Computing MAX */
+	i__2 = j - *ku;
+/* Computing MIN */
+	i__4 = j + *kl;
+	i__3 = f2cmin(i__4,*m);
+	for (i__ = f2cmax(i__2,1); i__ <= i__3; ++i__) {
+/* Computing MAX */
+	    i__2 = kd + i__ - j + j * ab_dim1;
+	    r__3 = r__[i__], r__4 = (r__1 = ab[i__2].r, abs(r__1)) + (r__2 = 
+		    r_imag(&ab[kd + i__ - j + j * ab_dim1]), abs(r__2));
+	    r__[i__] = f2cmax(r__3,r__4);
+/* L20: */
+	}
+/* L30: */
+    }
+    i__1 = *m;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	if (r__[i__] > 0.f) {
+	    i__3 = (integer) (log(r__[i__]) / logrdx);
+	    r__[i__] = pow_ri(&radix, &i__3);
+	}
+    }
+
+/*     Find the maximum and minimum scale factors. */
+
+    rcmin = bignum;
+    rcmax = 0.f;
+    i__1 = *m;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+/* Computing MAX */
+	r__1 = rcmax, r__2 = r__[i__];
+	rcmax = f2cmax(r__1,r__2);
+/* Computing MIN */
+	r__1 = rcmin, r__2 = r__[i__];
+	rcmin = f2cmin(r__1,r__2);
+/* L40: */
+    }
+    *amax = rcmax;
+
+    if (rcmin == 0.f) {
+
+/*        Find the first zero scale factor and return an error code. */
+
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    if (r__[i__] == 0.f) {
+		*info = i__;
+		return 0;
+	    }
+/* L50: */
+	}
+    } else {
+
+/*        Invert the scale factors. */
+
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+/* Computing MIN */
+/* Computing MAX */
+	    r__2 = r__[i__];
+	    r__1 = f2cmax(r__2,smlnum);
+	    r__[i__] = 1.f / f2cmin(r__1,bignum);
+/* L60: */
+	}
+
+/*        Compute ROWCND = f2cmin(R(I)) / f2cmax(R(I)). */
+
+	*rowcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
+    }
+
+/*     Compute column scale factors. */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	c__[j] = 0.f;
+/* L70: */
+    }
+
+/*     Find the maximum element in each column, */
+/*     assuming the row scaling computed above. */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+/* Computing MAX */
+	i__3 = j - *ku;
+/* Computing MIN */
+	i__4 = j + *kl;
+	i__2 = f2cmin(i__4,*m);
+	for (i__ = f2cmax(i__3,1); i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    i__3 = kd + i__ - j + j * ab_dim1;
+	    r__3 = c__[j], r__4 = ((r__1 = ab[i__3].r, abs(r__1)) + (r__2 = 
+		    r_imag(&ab[kd + i__ - j + j * ab_dim1]), abs(r__2))) * 
+		    r__[i__];
+	    c__[j] = f2cmax(r__3,r__4);
+/* L80: */
+	}
+	if (c__[j] > 0.f) {
+	    i__2 = (integer) (log(c__[j]) / logrdx);
+	    c__[j] = pow_ri(&radix, &i__2);
+	}
+/* L90: */
+    }
+
+/*     Find the maximum and minimum scale factors. */
+
+    rcmin = bignum;
+    rcmax = 0.f;
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+	r__1 = rcmin, r__2 = c__[j];
+	rcmin = f2cmin(r__1,r__2);
+/* Computing MAX */
+	r__1 = rcmax, r__2 = c__[j];
+	rcmax = f2cmax(r__1,r__2);
+/* L100: */
+    }
+
+    if (rcmin == 0.f) {
+
+/*        Find the first zero scale factor and return an error code. */
+
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    if (c__[j] == 0.f) {
+		*info = *m + j;
+		return 0;
+	    }
+/* L110: */
+	}
+    } else {
+
+/*        Invert the scale factors. */
+
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+/* Computing MAX */
+	    r__2 = c__[j];
+	    r__1 = f2cmax(r__2,smlnum);
+	    c__[j] = 1.f / f2cmin(r__1,bignum);
+/* L120: */
+	}
+
+/*        Compute COLCND = f2cmin(C(J)) / f2cmax(C(J)). */
+
+	*colcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
+    }
+
+    return 0;
+
+/*     End of CGBEQUB */
+
+} /* cgbequb_ */
+

lapack-netlib/SRC/cgbrfs.c

@@ -0,0 +1,950 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+
+/* > \brief \b CGBRFS */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGBRFS + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbrfs.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbrfs.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbrfs.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, */
+/*                          IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, */
+/*                          INFO ) */
+
+/*       CHARACTER          TRANS */
+/*       INTEGER            INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS */
+/*       INTEGER            IPIV( * ) */
+/*       REAL               BERR( * ), FERR( * ), RWORK( * ) */
+/*       COMPLEX            AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), */
+/*      $                   WORK( * ), X( LDX, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGBRFS improves the computed solution to a system of linear */
+/* > equations when the coefficient matrix is banded, and provides */
+/* > error bounds and backward error estimates for the solution. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] TRANS */
+/* > \verbatim */
+/* >          TRANS is CHARACTER*1 */
+/* >          Specifies the form of the system of equations: */
+/* >          = 'N':  A * X = B     (No transpose) */
+/* >          = 'T':  A**T * X = B  (Transpose) */
+/* >          = 'C':  A**H * X = B  (Conjugate transpose) */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KL */
+/* > \verbatim */
+/* >          KL is INTEGER */
+/* >          The number of subdiagonals within the band of A.  KL >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KU */
+/* > \verbatim */
+/* >          KU is INTEGER */
+/* >          The number of superdiagonals within the band of A.  KU >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NRHS */
+/* > \verbatim */
+/* >          NRHS is INTEGER */
+/* >          The number of right hand sides, i.e., the number of columns */
+/* >          of the matrices B and X.  NRHS >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] AB */
+/* > \verbatim */
+/* >          AB is COMPLEX array, dimension (LDAB,N) */
+/* >          The original band matrix A, stored in rows 1 to KL+KU+1. */
+/* >          The j-th column of A is stored in the j-th column of the */
+/* >          array AB as follows: */
+/* >          AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(n,j+kl). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDAB */
+/* > \verbatim */
+/* >          LDAB is INTEGER */
+/* >          The leading dimension of the array AB.  LDAB >= KL+KU+1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] AFB */
+/* > \verbatim */
+/* >          AFB is COMPLEX array, dimension (LDAFB,N) */
+/* >          Details of the LU factorization of the band matrix A, as */
+/* >          computed by CGBTRF.  U is stored as an upper triangular band */
+/* >          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
+/* >          the multipliers used during the factorization are stored in */
+/* >          rows KL+KU+2 to 2*KL+KU+1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDAFB */
+/* > \verbatim */
+/* >          LDAFB is INTEGER */
+/* >          The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (N) */
+/* >          The pivot indices from CGBTRF; for 1<=i<=N, row i of the */
+/* >          matrix was interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] B */
+/* > \verbatim */
+/* >          B is COMPLEX array, dimension (LDB,NRHS) */
+/* >          The right hand side matrix B. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDB */
+/* > \verbatim */
+/* >          LDB is INTEGER */
+/* >          The leading dimension of the array B.  LDB >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] X */
+/* > \verbatim */
+/* >          X is COMPLEX array, dimension (LDX,NRHS) */
+/* >          On entry, the solution matrix X, as computed by CGBTRS. */
+/* >          On exit, the improved solution matrix X. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDX */
+/* > \verbatim */
+/* >          LDX is INTEGER */
+/* >          The leading dimension of the array X.  LDX >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] FERR */
+/* > \verbatim */
+/* >          FERR is REAL array, dimension (NRHS) */
+/* >          The estimated forward error bound for each solution vector */
+/* >          X(j) (the j-th column of the solution matrix X). */
+/* >          If XTRUE is the true solution corresponding to X(j), FERR(j) */
+/* >          is an estimated upper bound for the magnitude of the largest */
+/* >          element in (X(j) - XTRUE) divided by the magnitude of the */
+/* >          largest element in X(j).  The estimate is as reliable as */
+/* >          the estimate for RCOND, and is almost always a slight */
+/* >          overestimate of the true error. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] BERR */
+/* > \verbatim */
+/* >          BERR is REAL array, dimension (NRHS) */
+/* >          The componentwise relative backward error of each solution */
+/* >          vector X(j) (i.e., the smallest relative change in */
+/* >          any element of A or B that makes X(j) an exact solution). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (2*N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RWORK */
+/* > \verbatim */
+/* >          RWORK is REAL array, dimension (N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/* > \par Internal Parameters: */
+/*  ========================= */
+/* > */
+/* > \verbatim */
+/* >  ITMAX is the maximum number of steps of iterative refinement. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGBcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgbrfs_(char *trans, integer *n, integer *kl, integer *
+	ku, integer *nrhs, complex *ab, integer *ldab, complex *afb, integer *
+	ldafb, integer *ipiv, complex *b, integer *ldb, complex *x, integer *
+	ldx, real *ferr, real *berr, complex *work, real *rwork, integer *
+	info)
+{
+    /* System generated locals */
+    integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, 
+	    x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
+    real r__1, r__2, r__3, r__4;
+    complex q__1;
+
+    /* Local variables */
+    integer kase;
+    real safe1, safe2;
+    integer i__, j, k;
+    real s;
+    extern /* Subroutine */ int cgbmv_(char *, integer *, integer *, integer *
+	    , integer *, complex *, complex *, integer *, complex *, integer *
+	    , complex *, complex *, integer *);
+    extern logical lsame_(char *, char *);
+    integer isave[3];
+    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
+	    complex *, integer *), caxpy_(integer *, complex *, complex *, 
+	    integer *, complex *, integer *);
+    integer count;
+    extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real 
+	    *, integer *, integer *);
+    integer kk;
+    real xk;
+    extern real slamch_(char *);
+    integer nz;
+    real safmin;
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), cgbtrs_(
+	    char *, integer *, integer *, integer *, integer *, complex *, 
+	    integer *, integer *, complex *, integer *, integer *);
+    logical notran;
+    char transn[1], transt[1];
+    real lstres, eps;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    ab_dim1 = *ldab;
+    ab_offset = 1 + ab_dim1 * 1;
+    ab -= ab_offset;
+    afb_dim1 = *ldafb;
+    afb_offset = 1 + afb_dim1 * 1;
+    afb -= afb_offset;
+    --ipiv;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1 * 1;
+    b -= b_offset;
+    x_dim1 = *ldx;
+    x_offset = 1 + x_dim1 * 1;
+    x -= x_offset;
+    --ferr;
+    --berr;
+    --work;
+    --rwork;
+
+    /* Function Body */
+    *info = 0;
+    notran = lsame_(trans, "N");
+    if (! notran && ! lsame_(trans, "T") && ! lsame_(
+	    trans, "C")) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*kl < 0) {
+	*info = -3;
+    } else if (*ku < 0) {
+	*info = -4;
+    } else if (*nrhs < 0) {
+	*info = -5;
+    } else if (*ldab < *kl + *ku + 1) {
+	*info = -7;
+    } else if (*ldafb < (*kl << 1) + *ku + 1) {
+	*info = -9;
+    } else if (*ldb < f2cmax(1,*n)) {
+	*info = -12;
+    } else if (*ldx < f2cmax(1,*n)) {
+	*info = -14;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGBRFS", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0 || *nrhs == 0) {
+	i__1 = *nrhs;
+	for (j = 1; j <= i__1; ++j) {
+	    ferr[j] = 0.f;
+	    berr[j] = 0.f;
+/* L10: */
+	}
+	return 0;
+    }
+
+    if (notran) {
+	*(unsigned char *)transn = 'N';
+	*(unsigned char *)transt = 'C';
+    } else {
+	*(unsigned char *)transn = 'C';
+	*(unsigned char *)transt = 'N';
+    }
+
+/*     NZ = maximum number of nonzero elements in each row of A, plus 1 */
+
+/* Computing MIN */
+    i__1 = *kl + *ku + 2, i__2 = *n + 1;
+    nz = f2cmin(i__1,i__2);
+    eps = slamch_("Epsilon");
+    safmin = slamch_("Safe minimum");
+    safe1 = nz * safmin;
+    safe2 = safe1 / eps;
+
+/*     Do for each right hand side */
+
+    i__1 = *nrhs;
+    for (j = 1; j <= i__1; ++j) {
+
+	count = 1;
+	lstres = 3.f;
+L20:
+
+/*        Loop until stopping criterion is satisfied. */
+
+/*        Compute residual R = B - op(A) * X, */
+/*        where op(A) = A, A**T, or A**H, depending on TRANS. */
+
+	ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
+	q__1.r = -1.f, q__1.i = 0.f;
+	cgbmv_(trans, n, n, kl, ku, &q__1, &ab[ab_offset], ldab, &x[j * 
+		x_dim1 + 1], &c__1, &c_b1, &work[1], &c__1);
+
+/*        Compute componentwise relative backward error from formula */
+
+/*        f2cmax(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) ) */
+
+/*        where abs(Z) is the componentwise absolute value of the matrix */
+/*        or vector Z.  If the i-th component of the denominator is less */
+/*        than SAFE2, then SAFE1 is added to the i-th components of the */
+/*        numerator and denominator before dividing. */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    i__3 = i__ + j * b_dim1;
+	    rwork[i__] = (r__1 = b[i__3].r, abs(r__1)) + (r__2 = r_imag(&b[
+		    i__ + j * b_dim1]), abs(r__2));
+/* L30: */
+	}
+
+/*        Compute abs(op(A))*abs(X) + abs(B). */
+
+	if (notran) {
+	    i__2 = *n;
+	    for (k = 1; k <= i__2; ++k) {
+		kk = *ku + 1 - k;
+		i__3 = k + j * x_dim1;
+		xk = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[k + j *
+			 x_dim1]), abs(r__2));
+/* Computing MAX */
+		i__3 = 1, i__4 = k - *ku;
+/* Computing MIN */
+		i__6 = *n, i__7 = k + *kl;
+		i__5 = f2cmin(i__6,i__7);
+		for (i__ = f2cmax(i__3,i__4); i__ <= i__5; ++i__) {
+		    i__3 = kk + i__ + k * ab_dim1;
+		    rwork[i__] += ((r__1 = ab[i__3].r, abs(r__1)) + (r__2 = 
+			    r_imag(&ab[kk + i__ + k * ab_dim1]), abs(r__2))) *
+			     xk;
+/* L40: */
+		}
+/* L50: */
+	    }
+	} else {
+	    i__2 = *n;
+	    for (k = 1; k <= i__2; ++k) {
+		s = 0.f;
+		kk = *ku + 1 - k;
+/* Computing MAX */
+		i__5 = 1, i__3 = k - *ku;
+/* Computing MIN */
+		i__6 = *n, i__7 = k + *kl;
+		i__4 = f2cmin(i__6,i__7);
+		for (i__ = f2cmax(i__5,i__3); i__ <= i__4; ++i__) {
+		    i__5 = kk + i__ + k * ab_dim1;
+		    i__3 = i__ + j * x_dim1;
+		    s += ((r__1 = ab[i__5].r, abs(r__1)) + (r__2 = r_imag(&ab[
+			    kk + i__ + k * ab_dim1]), abs(r__2))) * ((r__3 = 
+			    x[i__3].r, abs(r__3)) + (r__4 = r_imag(&x[i__ + j 
+			    * x_dim1]), abs(r__4)));
+/* L60: */
+		}
+		rwork[k] += s;
+/* L70: */
+	    }
+	}
+	s = 0.f;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (rwork[i__] > safe2) {
+/* Computing MAX */
+		i__4 = i__;
+		r__3 = s, r__4 = ((r__1 = work[i__4].r, abs(r__1)) + (r__2 = 
+			r_imag(&work[i__]), abs(r__2))) / rwork[i__];
+		s = f2cmax(r__3,r__4);
+	    } else {
+/* Computing MAX */
+		i__4 = i__;
+		r__3 = s, r__4 = ((r__1 = work[i__4].r, abs(r__1)) + (r__2 = 
+			r_imag(&work[i__]), abs(r__2)) + safe1) / (rwork[i__] 
+			+ safe1);
+		s = f2cmax(r__3,r__4);
+	    }
+/* L80: */
+	}
+	berr[j] = s;
+
+/*        Test stopping criterion. Continue iterating if */
+/*           1) The residual BERR(J) is larger than machine epsilon, and */
+/*           2) BERR(J) decreased by at least a factor of 2 during the */
+/*              last iteration, and */
+/*           3) At most ITMAX iterations tried. */
+
+	if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
+
+/*           Update solution and try again. */
+
+	    cgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1]
+		    , &work[1], n, info);
+	    caxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
+	    lstres = berr[j];
+	    ++count;
+	    goto L20;
+	}
+
+/*        Bound error from formula */
+
+/*        norm(X - XTRUE) / norm(X) .le. FERR = */
+/*        norm( abs(inv(op(A)))* */
+/*           ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X) */
+
+/*        where */
+/*          norm(Z) is the magnitude of the largest component of Z */
+/*          inv(op(A)) is the inverse of op(A) */
+/*          abs(Z) is the componentwise absolute value of the matrix or */
+/*             vector Z */
+/*          NZ is the maximum number of nonzeros in any row of A, plus 1 */
+/*          EPS is machine epsilon */
+
+/*        The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B)) */
+/*        is incremented by SAFE1 if the i-th component of */
+/*        abs(op(A))*abs(X) + abs(B) is less than SAFE2. */
+
+/*        Use CLACN2 to estimate the infinity-norm of the matrix */
+/*           inv(op(A)) * diag(W), */
+/*        where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (rwork[i__] > safe2) {
+		i__4 = i__;
+		rwork[i__] = (r__1 = work[i__4].r, abs(r__1)) + (r__2 = 
+			r_imag(&work[i__]), abs(r__2)) + nz * eps * rwork[i__]
+			;
+	    } else {
+		i__4 = i__;
+		rwork[i__] = (r__1 = work[i__4].r, abs(r__1)) + (r__2 = 
+			r_imag(&work[i__]), abs(r__2)) + nz * eps * rwork[i__]
+			 + safe1;
+	    }
+/* L90: */
+	}
+
+	kase = 0;
+L100:
+	clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
+	if (kase != 0) {
+	    if (kase == 1) {
+
+/*              Multiply by diag(W)*inv(op(A)**H). */
+
+		cgbtrs_(transt, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
+			ipiv[1], &work[1], n, info);
+		i__2 = *n;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    i__4 = i__;
+		    i__5 = i__;
+		    i__3 = i__;
+		    q__1.r = rwork[i__5] * work[i__3].r, q__1.i = rwork[i__5] 
+			    * work[i__3].i;
+		    work[i__4].r = q__1.r, work[i__4].i = q__1.i;
+/* L110: */
+		}
+	    } else {
+
+/*              Multiply by inv(op(A))*diag(W). */
+
+		i__2 = *n;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    i__4 = i__;
+		    i__5 = i__;
+		    i__3 = i__;
+		    q__1.r = rwork[i__5] * work[i__3].r, q__1.i = rwork[i__5] 
+			    * work[i__3].i;
+		    work[i__4].r = q__1.r, work[i__4].i = q__1.i;
+/* L120: */
+		}
+		cgbtrs_(transn, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
+			ipiv[1], &work[1], n, info);
+	    }
+	    goto L100;
+	}
+
+/*        Normalize error. */
+
+	lstres = 0.f;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    i__4 = i__ + j * x_dim1;
+	    r__3 = lstres, r__4 = (r__1 = x[i__4].r, abs(r__1)) + (r__2 = 
+		    r_imag(&x[i__ + j * x_dim1]), abs(r__2));
+	    lstres = f2cmax(r__3,r__4);
+/* L130: */
+	}
+	if (lstres != 0.f) {
+	    ferr[j] /= lstres;
+	}
+
+/* L140: */
+    }
+
+    return 0;
+
+/*     End of CGBRFS */
+
+} /* cgbrfs_ */
+

lapack-netlib/SRC/cgbrfsx.c

@@ -0,0 +1,381 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif

lapack-netlib/SRC/cgbsv.c

@@ -0,0 +1,622 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief <b> CGBSV computes the solution to system of linear equations A * X = B for GB matrices</b> (simpl
+e driver) */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGBSV + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbsv.f
+"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbsv.f
+"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbsv.f
+"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) */
+
+/*       INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS */
+/*       INTEGER            IPIV( * ) */
+/*       COMPLEX            AB( LDAB, * ), B( LDB, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGBSV computes the solution to a complex system of linear equations */
+/* > A * X = B, where A is a band matrix of order N with KL subdiagonals */
+/* > and KU superdiagonals, and X and B are N-by-NRHS matrices. */
+/* > */
+/* > The LU decomposition with partial pivoting and row interchanges is */
+/* > used to factor A as A = L * U, where L is a product of permutation */
+/* > and unit lower triangular matrices with KL subdiagonals, and U is */
+/* > upper triangular with KL+KU superdiagonals.  The factored form of A */
+/* > is then used to solve the system of equations A * X = B. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of linear equations, i.e., the order of the */
+/* >          matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KL */
+/* > \verbatim */
+/* >          KL is INTEGER */
+/* >          The number of subdiagonals within the band of A.  KL >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KU */
+/* > \verbatim */
+/* >          KU is INTEGER */
+/* >          The number of superdiagonals within the band of A.  KU >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NRHS */
+/* > \verbatim */
+/* >          NRHS is INTEGER */
+/* >          The number of right hand sides, i.e., the number of columns */
+/* >          of the matrix B.  NRHS >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] AB */
+/* > \verbatim */
+/* >          AB is COMPLEX array, dimension (LDAB,N) */
+/* >          On entry, the matrix A in band storage, in rows KL+1 to */
+/* >          2*KL+KU+1; rows 1 to KL of the array need not be set. */
+/* >          The j-th column of A is stored in the j-th column of the */
+/* >          array AB as follows: */
+/* >          AB(KL+KU+1+i-j,j) = A(i,j) for f2cmax(1,j-KU)<=i<=f2cmin(N,j+KL) */
+/* >          On exit, details of the factorization: U is stored as an */
+/* >          upper triangular band matrix with KL+KU superdiagonals in */
+/* >          rows 1 to KL+KU+1, and the multipliers used during the */
+/* >          factorization are stored in rows KL+KU+2 to 2*KL+KU+1. */
+/* >          See below for further details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDAB */
+/* > \verbatim */
+/* >          LDAB is INTEGER */
+/* >          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (N) */
+/* >          The pivot indices that define the permutation matrix P; */
+/* >          row i of the matrix was interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] B */
+/* > \verbatim */
+/* >          B is COMPLEX array, dimension (LDB,NRHS) */
+/* >          On entry, the N-by-NRHS right hand side matrix B. */
+/* >          On exit, if INFO = 0, the N-by-NRHS solution matrix X. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDB */
+/* > \verbatim */
+/* >          LDB is INTEGER */
+/* >          The leading dimension of the array B.  LDB >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO = i, U(i,i) is exactly zero.  The factorization */
+/* >                has been completed, but the factor U is exactly */
+/* >                singular, and the solution has not been computed. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGBsolve */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The band storage scheme is illustrated by the following example, when */
+/* >  M = N = 6, KL = 2, KU = 1: */
+/* > */
+/* >  On entry:                       On exit: */
+/* > */
+/* >      *    *    *    +    +    +       *    *    *   u14  u25  u36 */
+/* >      *    *    +    +    +    +       *    *   u13  u24  u35  u46 */
+/* >      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56 */
+/* >     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66 */
+/* >     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   * */
+/* >     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    * */
+/* > */
+/* >  Array elements marked * are not used by the routine; elements marked */
+/* >  + need not be set on entry, but are required by the routine to store */
+/* >  elements of U because of fill-in resulting from the row interchanges. */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgbsv_(integer *n, integer *kl, integer *ku, integer *
+	nrhs, complex *ab, integer *ldab, integer *ipiv, complex *b, integer *
+	ldb, integer *info)
+{
+    /* System generated locals */
+    integer ab_dim1, ab_offset, b_dim1, b_offset, i__1;
+
+    /* Local variables */
+    extern /* Subroutine */ int cgbtrf_(integer *, integer *, integer *, 
+	    integer *, complex *, integer *, integer *, integer *), xerbla_(
+	    char *, integer *, ftnlen), cgbtrs_(char *, integer *, integer *, 
+	    integer *, integer *, complex *, integer *, integer *, complex *, 
+	    integer *, integer *);
+
+
+/*  -- LAPACK driver routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    ab_dim1 = *ldab;
+    ab_offset = 1 + ab_dim1 * 1;
+    ab -= ab_offset;
+    --ipiv;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1 * 1;
+    b -= b_offset;
+
+    /* Function Body */
+    *info = 0;
+    if (*n < 0) {
+	*info = -1;
+    } else if (*kl < 0) {
+	*info = -2;
+    } else if (*ku < 0) {
+	*info = -3;
+    } else if (*nrhs < 0) {
+	*info = -4;
+    } else if (*ldab < (*kl << 1) + *ku + 1) {
+	*info = -6;
+    } else if (*ldb < f2cmax(*n,1)) {
+	*info = -9;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGBSV ", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Compute the LU factorization of the band matrix A. */
+
+    cgbtrf_(n, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info);
+    if (*info == 0) {
+
+/*        Solve the system A*X = B, overwriting B with X. */
+
+	cgbtrs_("No transpose", n, kl, ku, nrhs, &ab[ab_offset], ldab, &ipiv[
+		1], &b[b_offset], ldb, info);
+    }
+    return 0;
+
+/*     End of CGBSV */
+
+} /* cgbsv_ */
+

lapack-netlib/SRC/cgbtf2.c

@@ -0,0 +1,699 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+
+/* > \brief \b CGBTF2 computes the LU factorization of a general band matrix using the unblocked version of th
+e algorithm. */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGBTF2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbtf2.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbtf2.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbtf2.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO ) */
+
+/*       INTEGER            INFO, KL, KU, LDAB, M, N */
+/*       INTEGER            IPIV( * ) */
+/*       COMPLEX            AB( LDAB, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGBTF2 computes an LU factorization of a complex m-by-n band matrix */
+/* > A using partial pivoting with row interchanges. */
+/* > */
+/* > This is the unblocked version of the algorithm, calling Level 2 BLAS. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KL */
+/* > \verbatim */
+/* >          KL is INTEGER */
+/* >          The number of subdiagonals within the band of A.  KL >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KU */
+/* > \verbatim */
+/* >          KU is INTEGER */
+/* >          The number of superdiagonals within the band of A.  KU >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] AB */
+/* > \verbatim */
+/* >          AB is COMPLEX array, dimension (LDAB,N) */
+/* >          On entry, the matrix A in band storage, in rows KL+1 to */
+/* >          2*KL+KU+1; rows 1 to KL of the array need not be set. */
+/* >          The j-th column of A is stored in the j-th column of the */
+/* >          array AB as follows: */
+/* >          AB(kl+ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(m,j+kl) */
+/* > */
+/* >          On exit, details of the factorization: U is stored as an */
+/* >          upper triangular band matrix with KL+KU superdiagonals in */
+/* >          rows 1 to KL+KU+1, and the multipliers used during the */
+/* >          factorization are stored in rows KL+KU+2 to 2*KL+KU+1. */
+/* >          See below for further details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDAB */
+/* > \verbatim */
+/* >          LDAB is INTEGER */
+/* >          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (f2cmin(M,N)) */
+/* >          The pivot indices; for 1 <= i <= f2cmin(M,N), row i of the */
+/* >          matrix was interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0: if INFO = +i, U(i,i) is exactly zero. The factorization */
+/* >               has been completed, but the factor U is exactly */
+/* >               singular, and division by zero will occur if it is used */
+/* >               to solve a system of equations. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGBcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The band storage scheme is illustrated by the following example, when */
+/* >  M = N = 6, KL = 2, KU = 1: */
+/* > */
+/* >  On entry:                       On exit: */
+/* > */
+/* >      *    *    *    +    +    +       *    *    *   u14  u25  u36 */
+/* >      *    *    +    +    +    +       *    *   u13  u24  u35  u46 */
+/* >      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56 */
+/* >     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66 */
+/* >     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   * */
+/* >     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    * */
+/* > */
+/* >  Array elements marked * are not used by the routine; elements marked */
+/* >  + need not be set on entry, but are required by the routine to store */
+/* >  elements of U, because of fill-in resulting from the row */
+/* >  interchanges. */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgbtf2_(integer *m, integer *n, integer *kl, integer *ku,
+	 complex *ab, integer *ldab, integer *ipiv, integer *info)
+{
+    /* System generated locals */
+    integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, j;
+    extern /* Subroutine */ int cscal_(integer *, complex *, complex *, 
+	    integer *), cgeru_(integer *, integer *, complex *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *), cswap_(
+	    integer *, complex *, integer *, complex *, integer *);
+    integer km, jp, ju, kv;
+    extern integer icamax_(integer *, complex *, integer *);
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     KV is the number of superdiagonals in the factor U, allowing for */
+/*     fill-in. */
+
+    /* Parameter adjustments */
+    ab_dim1 = *ldab;
+    ab_offset = 1 + ab_dim1 * 1;
+    ab -= ab_offset;
+    --ipiv;
+
+    /* Function Body */
+    kv = *ku + *kl;
+
+/*     Test the input parameters. */
+
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*kl < 0) {
+	*info = -3;
+    } else if (*ku < 0) {
+	*info = -4;
+    } else if (*ldab < *kl + kv + 1) {
+	*info = -6;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGBTF2", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*m == 0 || *n == 0) {
+	return 0;
+    }
+
+/*     Gaussian elimination with partial pivoting */
+
+/*     Set fill-in elements in columns KU+2 to KV to zero. */
+
+    i__1 = f2cmin(kv,*n);
+    for (j = *ku + 2; j <= i__1; ++j) {
+	i__2 = *kl;
+	for (i__ = kv - j + 2; i__ <= i__2; ++i__) {
+	    i__3 = i__ + j * ab_dim1;
+	    ab[i__3].r = 0.f, ab[i__3].i = 0.f;
+/* L10: */
+	}
+/* L20: */
+    }
+
+/*     JU is the index of the last column affected by the current stage */
+/*     of the factorization. */
+
+    ju = 1;
+
+    i__1 = f2cmin(*m,*n);
+    for (j = 1; j <= i__1; ++j) {
+
+/*        Set fill-in elements in column J+KV to zero. */
+
+	if (j + kv <= *n) {
+	    i__2 = *kl;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		i__3 = i__ + (j + kv) * ab_dim1;
+		ab[i__3].r = 0.f, ab[i__3].i = 0.f;
+/* L30: */
+	    }
+	}
+
+/*        Find pivot and test for singularity. KM is the number of */
+/*        subdiagonal elements in the current column. */
+
+/* Computing MIN */
+	i__2 = *kl, i__3 = *m - j;
+	km = f2cmin(i__2,i__3);
+	i__2 = km + 1;
+	jp = icamax_(&i__2, &ab[kv + 1 + j * ab_dim1], &c__1);
+	ipiv[j] = jp + j - 1;
+	i__2 = kv + jp + j * ab_dim1;
+	if (ab[i__2].r != 0.f || ab[i__2].i != 0.f) {
+/* Computing MAX */
+/* Computing MIN */
+	    i__4 = j + *ku + jp - 1;
+	    i__2 = ju, i__3 = f2cmin(i__4,*n);
+	    ju = f2cmax(i__2,i__3);
+
+/*           Apply interchange to columns J to JU. */
+
+	    if (jp != 1) {
+		i__2 = ju - j + 1;
+		i__3 = *ldab - 1;
+		i__4 = *ldab - 1;
+		cswap_(&i__2, &ab[kv + jp + j * ab_dim1], &i__3, &ab[kv + 1 + 
+			j * ab_dim1], &i__4);
+	    }
+	    if (km > 0) {
+
+/*              Compute multipliers. */
+
+		c_div(&q__1, &c_b1, &ab[kv + 1 + j * ab_dim1]);
+		cscal_(&km, &q__1, &ab[kv + 2 + j * ab_dim1], &c__1);
+
+/*              Update trailing submatrix within the band. */
+
+		if (ju > j) {
+		    i__2 = ju - j;
+		    q__1.r = -1.f, q__1.i = 0.f;
+		    i__3 = *ldab - 1;
+		    i__4 = *ldab - 1;
+		    cgeru_(&km, &i__2, &q__1, &ab[kv + 2 + j * ab_dim1], &
+			    c__1, &ab[kv + (j + 1) * ab_dim1], &i__3, &ab[kv 
+			    + 1 + (j + 1) * ab_dim1], &i__4);
+		}
+	    }
+	} else {
+
+/*           If pivot is zero, set INFO to the index of the pivot */
+/*           unless a zero pivot has already been found. */
+
+	    if (*info == 0) {
+		*info = j;
+	    }
+	}
+/* L40: */
+    }
+    return 0;
+
+/*     End of CGBTF2 */
+
+} /* cgbtf2_ */
+

lapack-netlib/SRC/cgbtrs.c

@@ -0,0 +1,723 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+
+/* > \brief \b CGBTRS */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGBTRS + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbtrs.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbtrs.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbtrs.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, */
+/*                          INFO ) */
+
+/*       CHARACTER          TRANS */
+/*       INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS */
+/*       INTEGER            IPIV( * ) */
+/*       COMPLEX            AB( LDAB, * ), B( LDB, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGBTRS solves a system of linear equations */
+/* >    A * X = B,  A**T * X = B,  or  A**H * X = B */
+/* > with a general band matrix A using the LU factorization computed */
+/* > by CGBTRF. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] TRANS */
+/* > \verbatim */
+/* >          TRANS is CHARACTER*1 */
+/* >          Specifies the form of the system of equations. */
+/* >          = 'N':  A * X = B     (No transpose) */
+/* >          = 'T':  A**T * X = B  (Transpose) */
+/* >          = 'C':  A**H * X = B  (Conjugate transpose) */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KL */
+/* > \verbatim */
+/* >          KL is INTEGER */
+/* >          The number of subdiagonals within the band of A.  KL >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] KU */
+/* > \verbatim */
+/* >          KU is INTEGER */
+/* >          The number of superdiagonals within the band of A.  KU >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NRHS */
+/* > \verbatim */
+/* >          NRHS is INTEGER */
+/* >          The number of right hand sides, i.e., the number of columns */
+/* >          of the matrix B.  NRHS >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] AB */
+/* > \verbatim */
+/* >          AB is COMPLEX array, dimension (LDAB,N) */
+/* >          Details of the LU factorization of the band matrix A, as */
+/* >          computed by CGBTRF.  U is stored as an upper triangular band */
+/* >          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
+/* >          the multipliers used during the factorization are stored in */
+/* >          rows KL+KU+2 to 2*KL+KU+1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDAB */
+/* > \verbatim */
+/* >          LDAB is INTEGER */
+/* >          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (N) */
+/* >          The pivot indices; for 1 <= i <= N, row i of the matrix was */
+/* >          interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] B */
+/* > \verbatim */
+/* >          B is COMPLEX array, dimension (LDB,NRHS) */
+/* >          On entry, the right hand side matrix B. */
+/* >          On exit, the solution matrix X. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDB */
+/* > \verbatim */
+/* >          LDB is INTEGER */
+/* >          The leading dimension of the array B.  LDB >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGBcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgbtrs_(char *trans, integer *n, integer *kl, integer *
+	ku, integer *nrhs, complex *ab, integer *ldab, integer *ipiv, complex 
+	*b, integer *ldb, integer *info)
+{
+    /* System generated locals */
+    integer ab_dim1, ab_offset, b_dim1, b_offset, i__1, i__2, i__3;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, j, l;
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
+	    , complex *, integer *, complex *, integer *, complex *, complex *
+	    , integer *), cgeru_(integer *, integer *, complex *, 
+	    complex *, integer *, complex *, integer *, complex *, integer *),
+	     cswap_(integer *, complex *, integer *, complex *, integer *), 
+	    ctbsv_(char *, char *, char *, integer *, integer *, complex *, 
+	    integer *, complex *, integer *);
+    logical lnoti;
+    integer kd, lm;
+    extern /* Subroutine */ int clacgv_(integer *, complex *, integer *), 
+	    xerbla_(char *, integer *, ftnlen);
+    logical notran;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    ab_dim1 = *ldab;
+    ab_offset = 1 + ab_dim1 * 1;
+    ab -= ab_offset;
+    --ipiv;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1 * 1;
+    b -= b_offset;
+
+    /* Function Body */
+    *info = 0;
+    notran = lsame_(trans, "N");
+    if (! notran && ! lsame_(trans, "T") && ! lsame_(
+	    trans, "C")) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*kl < 0) {
+	*info = -3;
+    } else if (*ku < 0) {
+	*info = -4;
+    } else if (*nrhs < 0) {
+	*info = -5;
+    } else if (*ldab < (*kl << 1) + *ku + 1) {
+	*info = -7;
+    } else if (*ldb < f2cmax(1,*n)) {
+	*info = -10;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGBTRS", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0 || *nrhs == 0) {
+	return 0;
+    }
+
+    kd = *ku + *kl + 1;
+    lnoti = *kl > 0;
+
+    if (notran) {
+
+/*        Solve  A*X = B. */
+
+/*        Solve L*X = B, overwriting B with X. */
+
+/*        L is represented as a product of permutations and unit lower */
+/*        triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1), */
+/*        where each transformation L(i) is a rank-one modification of */
+/*        the identity matrix. */
+
+	if (lnoti) {
+	    i__1 = *n - 1;
+	    for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+		i__2 = *kl, i__3 = *n - j;
+		lm = f2cmin(i__2,i__3);
+		l = ipiv[j];
+		if (l != j) {
+		    cswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb);
+		}
+		q__1.r = -1.f, q__1.i = 0.f;
+		cgeru_(&lm, nrhs, &q__1, &ab[kd + 1 + j * ab_dim1], &c__1, &b[
+			j + b_dim1], ldb, &b[j + 1 + b_dim1], ldb);
+/* L10: */
+	    }
+	}
+
+	i__1 = *nrhs;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+
+/*           Solve U*X = B, overwriting B with X. */
+
+	    i__2 = *kl + *ku;
+	    ctbsv_("Upper", "No transpose", "Non-unit", n, &i__2, &ab[
+		    ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1);
+/* L20: */
+	}
+
+    } else if (lsame_(trans, "T")) {
+
+/*        Solve A**T * X = B. */
+
+	i__1 = *nrhs;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+
+/*           Solve U**T * X = B, overwriting B with X. */
+
+	    i__2 = *kl + *ku;
+	    ctbsv_("Upper", "Transpose", "Non-unit", n, &i__2, &ab[ab_offset],
+		     ldab, &b[i__ * b_dim1 + 1], &c__1);
+/* L30: */
+	}
+
+/*        Solve L**T * X = B, overwriting B with X. */
+
+	if (lnoti) {
+	    for (j = *n - 1; j >= 1; --j) {
+/* Computing MIN */
+		i__1 = *kl, i__2 = *n - j;
+		lm = f2cmin(i__1,i__2);
+		q__1.r = -1.f, q__1.i = 0.f;
+		cgemv_("Transpose", &lm, nrhs, &q__1, &b[j + 1 + b_dim1], ldb,
+			 &ab[kd + 1 + j * ab_dim1], &c__1, &c_b1, &b[j + 
+			b_dim1], ldb);
+		l = ipiv[j];
+		if (l != j) {
+		    cswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb);
+		}
+/* L40: */
+	    }
+	}
+
+    } else {
+
+/*        Solve A**H * X = B. */
+
+	i__1 = *nrhs;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+
+/*           Solve U**H * X = B, overwriting B with X. */
+
+	    i__2 = *kl + *ku;
+	    ctbsv_("Upper", "Conjugate transpose", "Non-unit", n, &i__2, &ab[
+		    ab_offset], ldab, &b[i__ * b_dim1 + 1], &c__1);
+/* L50: */
+	}
+
+/*        Solve L**H * X = B, overwriting B with X. */
+
+	if (lnoti) {
+	    for (j = *n - 1; j >= 1; --j) {
+/* Computing MIN */
+		i__1 = *kl, i__2 = *n - j;
+		lm = f2cmin(i__1,i__2);
+		clacgv_(nrhs, &b[j + b_dim1], ldb);
+		q__1.r = -1.f, q__1.i = 0.f;
+		cgemv_("Conjugate transpose", &lm, nrhs, &q__1, &b[j + 1 + 
+			b_dim1], ldb, &ab[kd + 1 + j * ab_dim1], &c__1, &c_b1,
+			 &b[j + b_dim1], ldb);
+		clacgv_(nrhs, &b[j + b_dim1], ldb);
+		l = ipiv[j];
+		if (l != j) {
+		    cswap_(nrhs, &b[l + b_dim1], ldb, &b[j + b_dim1], ldb);
+		}
+/* L60: */
+	    }
+	}
+    }
+    return 0;
+
+/*     End of CGBTRS */
+
+} /* cgbtrs_ */
+

lapack-netlib/SRC/cgebak.c

@@ -0,0 +1,675 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGEBAK */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEBAK + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgebak.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgebak.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgebak.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, */
+/*                          INFO ) */
+
+/*       CHARACTER          JOB, SIDE */
+/*       INTEGER            IHI, ILO, INFO, LDV, M, N */
+/*       REAL               SCALE( * ) */
+/*       COMPLEX            V( LDV, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEBAK forms the right or left eigenvectors of a complex general */
+/* > matrix by backward transformation on the computed eigenvectors of the */
+/* > balanced matrix output by CGEBAL. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] JOB */
+/* > \verbatim */
+/* >          JOB is CHARACTER*1 */
+/* >          Specifies the type of backward transformation required: */
+/* >          = 'N': do nothing, return immediately; */
+/* >          = 'P': do backward transformation for permutation only; */
+/* >          = 'S': do backward transformation for scaling only; */
+/* >          = 'B': do backward transformations for both permutation and */
+/* >                 scaling. */
+/* >          JOB must be the same as the argument JOB supplied to CGEBAL. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] SIDE */
+/* > \verbatim */
+/* >          SIDE is CHARACTER*1 */
+/* >          = 'R':  V contains right eigenvectors; */
+/* >          = 'L':  V contains left eigenvectors. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of rows of the matrix V.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] ILO */
+/* > \verbatim */
+/* >          ILO is INTEGER */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IHI */
+/* > \verbatim */
+/* >          IHI is INTEGER */
+/* >          The integers ILO and IHI determined by CGEBAL. */
+/* >          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] SCALE */
+/* > \verbatim */
+/* >          SCALE is REAL array, dimension (N) */
+/* >          Details of the permutation and scaling factors, as returned */
+/* >          by CGEBAL. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of columns of the matrix V.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] V */
+/* > \verbatim */
+/* >          V is COMPLEX array, dimension (LDV,M) */
+/* >          On entry, the matrix of right or left eigenvectors to be */
+/* >          transformed, as returned by CHSEIN or CTREVC. */
+/* >          On exit, V is overwritten by the transformed eigenvectors. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDV */
+/* > \verbatim */
+/* >          LDV is INTEGER */
+/* >          The leading dimension of the array V. LDV >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgebak_(char *job, char *side, integer *n, integer *ilo, 
+	integer *ihi, real *scale, integer *m, complex *v, integer *ldv, 
+	integer *info)
+{
+    /* System generated locals */
+    integer v_dim1, v_offset, i__1;
+
+    /* Local variables */
+    integer i__, k;
+    real s;
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
+	    complex *, integer *);
+    logical leftv;
+    integer ii;
+    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
+	    *), xerbla_(char *, integer *, ftnlen);
+    logical rightv;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Decode and Test the input parameters */
+
+    /* Parameter adjustments */
+    --scale;
+    v_dim1 = *ldv;
+    v_offset = 1 + v_dim1 * 1;
+    v -= v_offset;
+
+    /* Function Body */
+    rightv = lsame_(side, "R");
+    leftv = lsame_(side, "L");
+
+    *info = 0;
+    if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S") 
+	    && ! lsame_(job, "B")) {
+	*info = -1;
+    } else if (! rightv && ! leftv) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -3;
+    } else if (*ilo < 1 || *ilo > f2cmax(1,*n)) {
+	*info = -4;
+    } else if (*ihi < f2cmin(*ilo,*n) || *ihi > *n) {
+	*info = -5;
+    } else if (*m < 0) {
+	*info = -7;
+    } else if (*ldv < f2cmax(1,*n)) {
+	*info = -9;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEBAK", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+    if (*m == 0) {
+	return 0;
+    }
+    if (lsame_(job, "N")) {
+	return 0;
+    }
+
+    if (*ilo == *ihi) {
+	goto L30;
+    }
+
+/*     Backward balance */
+
+    if (lsame_(job, "S") || lsame_(job, "B")) {
+
+	if (rightv) {
+	    i__1 = *ihi;
+	    for (i__ = *ilo; i__ <= i__1; ++i__) {
+		s = scale[i__];
+		csscal_(m, &s, &v[i__ + v_dim1], ldv);
+/* L10: */
+	    }
+	}
+
+	if (leftv) {
+	    i__1 = *ihi;
+	    for (i__ = *ilo; i__ <= i__1; ++i__) {
+		s = 1.f / scale[i__];
+		csscal_(m, &s, &v[i__ + v_dim1], ldv);
+/* L20: */
+	    }
+	}
+
+    }
+
+/*     Backward permutation */
+
+/*     For  I = ILO-1 step -1 until 1, */
+/*              IHI+1 step 1 until N do -- */
+
+L30:
+    if (lsame_(job, "P") || lsame_(job, "B")) {
+	if (rightv) {
+	    i__1 = *n;
+	    for (ii = 1; ii <= i__1; ++ii) {
+		i__ = ii;
+		if (i__ >= *ilo && i__ <= *ihi) {
+		    goto L40;
+		}
+		if (i__ < *ilo) {
+		    i__ = *ilo - ii;
+		}
+		k = scale[i__];
+		if (k == i__) {
+		    goto L40;
+		}
+		cswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
+L40:
+		;
+	    }
+	}
+
+	if (leftv) {
+	    i__1 = *n;
+	    for (ii = 1; ii <= i__1; ++ii) {
+		i__ = ii;
+		if (i__ >= *ilo && i__ <= *ihi) {
+		    goto L50;
+		}
+		if (i__ < *ilo) {
+		    i__ = *ilo - ii;
+		}
+		k = scale[i__];
+		if (k == i__) {
+		    goto L50;
+		}
+		cswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
+L50:
+		;
+	    }
+	}
+    }
+
+    return 0;
+
+/*     End of CGEBAK */
+
+} /* cgebak_ */
+

lapack-netlib/SRC/cgebal.c

@@ -0,0 +1,843 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* > \brief \b CGEBAL */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEBAL + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgebal.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgebal.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgebal.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO ) */
+
+/*       CHARACTER          JOB */
+/*       INTEGER            IHI, ILO, INFO, LDA, N */
+/*       REAL               SCALE( * ) */
+/*       COMPLEX            A( LDA, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEBAL balances a general complex matrix A.  This involves, first, */
+/* > permuting A by a similarity transformation to isolate eigenvalues */
+/* > in the first 1 to ILO-1 and last IHI+1 to N elements on the */
+/* > diagonal; and second, applying a diagonal similarity transformation */
+/* > to rows and columns ILO to IHI to make the rows and columns as */
+/* > close in norm as possible.  Both steps are optional. */
+/* > */
+/* > Balancing may reduce the 1-norm of the matrix, and improve the */
+/* > accuracy of the computed eigenvalues and/or eigenvectors. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] JOB */
+/* > \verbatim */
+/* >          JOB is CHARACTER*1 */
+/* >          Specifies the operations to be performed on A: */
+/* >          = 'N':  none:  simply set ILO = 1, IHI = N, SCALE(I) = 1.0 */
+/* >                  for i = 1,...,N; */
+/* >          = 'P':  permute only; */
+/* >          = 'S':  scale only; */
+/* >          = 'B':  both permute and scale. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the input matrix A. */
+/* >          On exit,  A is overwritten by the balanced matrix. */
+/* >          If JOB = 'N', A is not referenced. */
+/* >          See Further Details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] ILO */
+/* > \verbatim */
+/* >          ILO is INTEGER */
+/* > \endverbatim */
+/* > \param[out] IHI */
+/* > \verbatim */
+/* >          IHI is INTEGER */
+/* >          ILO and IHI are set to integers such that on exit */
+/* >          A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N. */
+/* >          If JOB = 'N' or 'S', ILO = 1 and IHI = N. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] SCALE */
+/* > \verbatim */
+/* >          SCALE is REAL array, dimension (N) */
+/* >          Details of the permutations and scaling factors applied to */
+/* >          A.  If P(j) is the index of the row and column interchanged */
+/* >          with row and column j and D(j) is the scaling factor */
+/* >          applied to row and column j, then */
+/* >          SCALE(j) = P(j)    for j = 1,...,ILO-1 */
+/* >                   = D(j)    for j = ILO,...,IHI */
+/* >                   = P(j)    for j = IHI+1,...,N. */
+/* >          The order in which the interchanges are made is N to IHI+1, */
+/* >          then 1 to ILO-1. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit. */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The permutations consist of row and column interchanges which put */
+/* >  the matrix in the form */
+/* > */
+/* >             ( T1   X   Y  ) */
+/* >     P A P = (  0   B   Z  ) */
+/* >             (  0   0   T2 ) */
+/* > */
+/* >  where T1 and T2 are upper triangular matrices whose eigenvalues lie */
+/* >  along the diagonal.  The column indices ILO and IHI mark the starting */
+/* >  and ending columns of the submatrix B. Balancing consists of applying */
+/* >  a diagonal similarity transformation inv(D) * B * D to make the */
+/* >  1-norms of each row of B and its corresponding column nearly equal. */
+/* >  The output matrix is */
+/* > */
+/* >     ( T1     X*D          Y    ) */
+/* >     (  0  inv(D)*B*D  inv(D)*Z ). */
+/* >     (  0      0           T2   ) */
+/* > */
+/* >  Information about the permutations P and the diagonal matrix D is */
+/* >  returned in the vector SCALE. */
+/* > */
+/* >  This subroutine is based on the EISPACK routine CBAL. */
+/* > */
+/* >  Modified by Tzu-Yi Chen, Computer Science Division, University of */
+/* >    California at Berkeley, USA */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgebal_(char *job, integer *n, complex *a, integer *lda, 
+	integer *ilo, integer *ihi, real *scale, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+    real r__1, r__2;
+
+    /* Local variables */
+    integer iexc;
+    real c__, f, g;
+    integer i__, j, k, l, m;
+    real r__, s;
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
+	    complex *, integer *);
+    real sfmin1, sfmin2, sfmax1, sfmax2, ca;
+    extern real scnrm2_(integer *, complex *, integer *);
+    real ra;
+    extern integer icamax_(integer *, complex *, integer *);
+    extern real slamch_(char *);
+    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
+	    *), xerbla_(char *, integer *, ftnlen);
+    extern logical sisnan_(real *);
+    logical noconv;
+    integer ica, ira;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --scale;
+
+    /* Function Body */
+    *info = 0;
+    if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S") 
+	    && ! lsame_(job, "B")) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEBAL", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+    k = 1;
+    l = *n;
+
+    if (*n == 0) {
+	goto L210;
+    }
+
+    if (lsame_(job, "N")) {
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    scale[i__] = 1.f;
+/* L10: */
+	}
+	goto L210;
+    }
+
+    if (lsame_(job, "S")) {
+	goto L120;
+    }
+
+/*     Permutation to isolate eigenvalues if possible */
+
+    goto L50;
+
+/*     Row and column exchange. */
+
+L20:
+    scale[m] = (real) j;
+    if (j == m) {
+	goto L30;
+    }
+
+    cswap_(&l, &a[j * a_dim1 + 1], &c__1, &a[m * a_dim1 + 1], &c__1);
+    i__1 = *n - k + 1;
+    cswap_(&i__1, &a[j + k * a_dim1], lda, &a[m + k * a_dim1], lda);
+
+L30:
+    switch (iexc) {
+	case 1:  goto L40;
+	case 2:  goto L80;
+    }
+
+/*     Search for rows isolating an eigenvalue and push them down. */
+
+L40:
+    if (l == 1) {
+	goto L210;
+    }
+    --l;
+
+L50:
+    for (j = l; j >= 1; --j) {
+
+	i__1 = l;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    if (i__ == j) {
+		goto L60;
+	    }
+	    i__2 = j + i__ * a_dim1;
+	    if (a[i__2].r != 0.f || r_imag(&a[j + i__ * a_dim1]) != 0.f) {
+		goto L70;
+	    }
+L60:
+	    ;
+	}
+
+	m = l;
+	iexc = 1;
+	goto L20;
+L70:
+	;
+    }
+
+    goto L90;
+
+/*     Search for columns isolating an eigenvalue and push them left. */
+
+L80:
+    ++k;
+
+L90:
+    i__1 = l;
+    for (j = k; j <= i__1; ++j) {
+
+	i__2 = l;
+	for (i__ = k; i__ <= i__2; ++i__) {
+	    if (i__ == j) {
+		goto L100;
+	    }
+	    i__3 = i__ + j * a_dim1;
+	    if (a[i__3].r != 0.f || r_imag(&a[i__ + j * a_dim1]) != 0.f) {
+		goto L110;
+	    }
+L100:
+	    ;
+	}
+
+	m = k;
+	iexc = 2;
+	goto L20;
+L110:
+	;
+    }
+
+L120:
+    i__1 = l;
+    for (i__ = k; i__ <= i__1; ++i__) {
+	scale[i__] = 1.f;
+/* L130: */
+    }
+
+    if (lsame_(job, "P")) {
+	goto L210;
+    }
+
+/*     Balance the submatrix in rows K to L. */
+
+/*     Iterative loop for norm reduction */
+
+    sfmin1 = slamch_("S") / slamch_("P");
+    sfmax1 = 1.f / sfmin1;
+    sfmin2 = sfmin1 * 2.f;
+    sfmax2 = 1.f / sfmin2;
+L140:
+    noconv = FALSE_;
+
+    i__1 = l;
+    for (i__ = k; i__ <= i__1; ++i__) {
+
+	i__2 = l - k + 1;
+	c__ = scnrm2_(&i__2, &a[k + i__ * a_dim1], &c__1);
+	i__2 = l - k + 1;
+	r__ = scnrm2_(&i__2, &a[i__ + k * a_dim1], lda);
+	ica = icamax_(&l, &a[i__ * a_dim1 + 1], &c__1);
+	ca = c_abs(&a[ica + i__ * a_dim1]);
+	i__2 = *n - k + 1;
+	ira = icamax_(&i__2, &a[i__ + k * a_dim1], lda);
+	ra = c_abs(&a[i__ + (ira + k - 1) * a_dim1]);
+
+/*        Guard against zero C or R due to underflow. */
+
+	if (c__ == 0.f || r__ == 0.f) {
+	    goto L200;
+	}
+	g = r__ / 2.f;
+	f = 1.f;
+	s = c__ + r__;
+L160:
+/* Computing MAX */
+	r__1 = f2cmax(f,c__);
+/* Computing MIN */
+	r__2 = f2cmin(r__,g);
+	if (c__ >= g || f2cmax(r__1,ca) >= sfmax2 || f2cmin(r__2,ra) <= sfmin2) {
+	    goto L170;
+	}
+	r__1 = c__ + f + ca + r__ + g + ra;
+	if (sisnan_(&r__1)) {
+
+/*           Exit if NaN to avoid infinite loop */
+
+	    *info = -3;
+	    i__2 = -(*info);
+	    xerbla_("CGEBAL", &i__2, (ftnlen)6);
+	    return 0;
+	}
+	f *= 2.f;
+	c__ *= 2.f;
+	ca *= 2.f;
+	r__ /= 2.f;
+	g /= 2.f;
+	ra /= 2.f;
+	goto L160;
+
+L170:
+	g = c__ / 2.f;
+L180:
+/* Computing MIN */
+	r__1 = f2cmin(f,c__), r__1 = f2cmin(r__1,g);
+	if (g < r__ || f2cmax(r__,ra) >= sfmax2 || f2cmin(r__1,ca) <= sfmin2) {
+	    goto L190;
+	}
+	f /= 2.f;
+	c__ /= 2.f;
+	g /= 2.f;
+	ca /= 2.f;
+	r__ *= 2.f;
+	ra *= 2.f;
+	goto L180;
+
+/*        Now balance. */
+
+L190:
+	if (c__ + r__ >= s * .95f) {
+	    goto L200;
+	}
+	if (f < 1.f && scale[i__] < 1.f) {
+	    if (f * scale[i__] <= sfmin1) {
+		goto L200;
+	    }
+	}
+	if (f > 1.f && scale[i__] > 1.f) {
+	    if (scale[i__] >= sfmax1 / f) {
+		goto L200;
+	    }
+	}
+	g = 1.f / f;
+	scale[i__] *= f;
+	noconv = TRUE_;
+
+	i__2 = *n - k + 1;
+	csscal_(&i__2, &g, &a[i__ + k * a_dim1], lda);
+	csscal_(&l, &f, &a[i__ * a_dim1 + 1], &c__1);
+
+L200:
+	;
+    }
+
+    if (noconv) {
+	goto L140;
+    }
+
+L210:
+    *ilo = k;
+    *ihi = l;
+
+    return 0;
+
+/*     End of CGEBAL */
+
+} /* cgebal_ */
+

lapack-netlib/SRC/cgebd2.c

@@ -0,0 +1,784 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* > \brief \b CGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm. */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEBD2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgebd2.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgebd2.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgebd2.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       REAL               D( * ), E( * ) */
+/*       COMPLEX            A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEBD2 reduces a complex general m by n matrix A to upper or lower */
+/* > real bidiagonal form B by a unitary transformation: Q**H * A * P = B. */
+/* > */
+/* > If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows in the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns in the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the m by n general matrix to be reduced. */
+/* >          On exit, */
+/* >          if m >= n, the diagonal and the first superdiagonal are */
+/* >            overwritten with the upper bidiagonal matrix B; the */
+/* >            elements below the diagonal, with the array TAUQ, represent */
+/* >            the unitary matrix Q as a product of elementary */
+/* >            reflectors, and the elements above the first superdiagonal, */
+/* >            with the array TAUP, represent the unitary matrix P as */
+/* >            a product of elementary reflectors; */
+/* >          if m < n, the diagonal and the first subdiagonal are */
+/* >            overwritten with the lower bidiagonal matrix B; the */
+/* >            elements below the first subdiagonal, with the array TAUQ, */
+/* >            represent the unitary matrix Q as a product of */
+/* >            elementary reflectors, and the elements above the diagonal, */
+/* >            with the array TAUP, represent the unitary matrix P as */
+/* >            a product of elementary reflectors. */
+/* >          See Further Details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] D */
+/* > \verbatim */
+/* >          D is REAL array, dimension (f2cmin(M,N)) */
+/* >          The diagonal elements of the bidiagonal matrix B: */
+/* >          D(i) = A(i,i). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] E */
+/* > \verbatim */
+/* >          E is REAL array, dimension (f2cmin(M,N)-1) */
+/* >          The off-diagonal elements of the bidiagonal matrix B: */
+/* >          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */
+/* >          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAUQ */
+/* > \verbatim */
+/* >          TAUQ is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors which */
+/* >          represent the unitary matrix Q. See Further Details. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAUP */
+/* > \verbatim */
+/* >          TAUP is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors which */
+/* >          represent the unitary matrix P. See Further Details. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (f2cmax(M,N)) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2017 */
+
+/* > \ingroup complexGEcomputational */
+/* @precisions normal c -> s d z */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrices Q and P are represented as products of elementary */
+/* >  reflectors: */
+/* > */
+/* >  If m >= n, */
+/* > */
+/* >     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1) */
+/* > */
+/* >  Each H(i) and G(i) has the form: */
+/* > */
+/* >     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H */
+/* > */
+/* >  where tauq and taup are complex scalars, and v and u are complex */
+/* >  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in */
+/* >  A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in */
+/* >  A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
+/* > */
+/* >  If m < n, */
+/* > */
+/* >     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m) */
+/* > */
+/* >  Each H(i) and G(i) has the form: */
+/* > */
+/* >     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H */
+/* > */
+/* >  where tauq and taup are complex scalars, v and u are complex vectors; */
+/* >  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */
+/* >  u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */
+/* >  tauq is stored in TAUQ(i) and taup in TAUP(i). */
+/* > */
+/* >  The contents of A on exit are illustrated by the following examples: */
+/* > */
+/* >  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n): */
+/* > */
+/* >    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 ) */
+/* >    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 ) */
+/* >    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 ) */
+/* >    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 ) */
+/* >    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 ) */
+/* >    (  v1  v2  v3  v4  v5 ) */
+/* > */
+/* >  where d and e denote diagonal and off-diagonal elements of B, vi */
+/* >  denotes an element of the vector defining H(i), and ui an element of */
+/* >  the vector defining G(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgebd2_(integer *m, integer *n, complex *a, integer *lda,
+	 real *d__, real *e, complex *tauq, complex *taup, complex *work, 
+	integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+    complex q__1;
+
+    /* Local variables */
+    integer i__;
+    complex alpha;
+    extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex *
+	    , integer *, complex *, complex *, integer *, complex *), 
+	    clarfg_(integer *, complex *, complex *, integer *, complex *), 
+	    clacgv_(integer *, complex *, integer *), xerbla_(char *, integer 
+	    *, ftnlen);
+
+
+/*  -- LAPACK computational routine (version 3.7.1) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2017 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --d__;
+    --e;
+    --tauq;
+    --taup;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info < 0) {
+	i__1 = -(*info);
+	xerbla_("CGEBD2", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+    if (*m >= *n) {
+
+/*        Reduce to upper bidiagonal form */
+
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+
+/*           Generate elementary reflector H(i) to annihilate A(i+1:m,i) */
+
+	    i__2 = i__ + i__ * a_dim1;
+	    alpha.r = a[i__2].r, alpha.i = a[i__2].i;
+	    i__2 = *m - i__ + 1;
+/* Computing MIN */
+	    i__3 = i__ + 1;
+	    clarfg_(&i__2, &alpha, &a[f2cmin(i__3,*m) + i__ * a_dim1], &c__1, &
+		    tauq[i__]);
+	    i__2 = i__;
+	    d__[i__2] = alpha.r;
+	    i__2 = i__ + i__ * a_dim1;
+	    a[i__2].r = 1.f, a[i__2].i = 0.f;
+
+/*           Apply H(i)**H to A(i:m,i+1:n) from the left */
+
+	    if (i__ < *n) {
+		i__2 = *m - i__ + 1;
+		i__3 = *n - i__;
+		r_cnjg(&q__1, &tauq[i__]);
+		clarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &
+			q__1, &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]);
+	    }
+	    i__2 = i__ + i__ * a_dim1;
+	    i__3 = i__;
+	    a[i__2].r = d__[i__3], a[i__2].i = 0.f;
+
+	    if (i__ < *n) {
+
+/*              Generate elementary reflector G(i) to annihilate */
+/*              A(i,i+2:n) */
+
+		i__2 = *n - i__;
+		clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
+		i__2 = i__ + (i__ + 1) * a_dim1;
+		alpha.r = a[i__2].r, alpha.i = a[i__2].i;
+		i__2 = *n - i__;
+/* Computing MIN */
+		i__3 = i__ + 2;
+		clarfg_(&i__2, &alpha, &a[i__ + f2cmin(i__3,*n) * a_dim1], lda, &
+			taup[i__]);
+		i__2 = i__;
+		e[i__2] = alpha.r;
+		i__2 = i__ + (i__ + 1) * a_dim1;
+		a[i__2].r = 1.f, a[i__2].i = 0.f;
+
+/*              Apply G(i) to A(i+1:m,i+1:n) from the right */
+
+		i__2 = *m - i__;
+		i__3 = *n - i__;
+		clarf_("Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], 
+			lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], 
+			lda, &work[1]);
+		i__2 = *n - i__;
+		clacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda);
+		i__2 = i__ + (i__ + 1) * a_dim1;
+		i__3 = i__;
+		a[i__2].r = e[i__3], a[i__2].i = 0.f;
+	    } else {
+		i__2 = i__;
+		taup[i__2].r = 0.f, taup[i__2].i = 0.f;
+	    }
+/* L10: */
+	}
+    } else {
+
+/*        Reduce to lower bidiagonal form */
+
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+
+/*           Generate elementary reflector G(i) to annihilate A(i,i+1:n) */
+
+	    i__2 = *n - i__ + 1;
+	    clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
+	    i__2 = i__ + i__ * a_dim1;
+	    alpha.r = a[i__2].r, alpha.i = a[i__2].i;
+	    i__2 = *n - i__ + 1;
+/* Computing MIN */
+	    i__3 = i__ + 1;
+	    clarfg_(&i__2, &alpha, &a[i__ + f2cmin(i__3,*n) * a_dim1], lda, &
+		    taup[i__]);
+	    i__2 = i__;
+	    d__[i__2] = alpha.r;
+	    i__2 = i__ + i__ * a_dim1;
+	    a[i__2].r = 1.f, a[i__2].i = 0.f;
+
+/*           Apply G(i) to A(i+1:m,i:n) from the right */
+
+	    if (i__ < *m) {
+		i__2 = *m - i__;
+		i__3 = *n - i__ + 1;
+		clarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &
+			taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]);
+	    }
+	    i__2 = *n - i__ + 1;
+	    clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
+	    i__2 = i__ + i__ * a_dim1;
+	    i__3 = i__;
+	    a[i__2].r = d__[i__3], a[i__2].i = 0.f;
+
+	    if (i__ < *m) {
+
+/*              Generate elementary reflector H(i) to annihilate */
+/*              A(i+2:m,i) */
+
+		i__2 = i__ + 1 + i__ * a_dim1;
+		alpha.r = a[i__2].r, alpha.i = a[i__2].i;
+		i__2 = *m - i__;
+/* Computing MIN */
+		i__3 = i__ + 2;
+		clarfg_(&i__2, &alpha, &a[f2cmin(i__3,*m) + i__ * a_dim1], &c__1,
+			 &tauq[i__]);
+		i__2 = i__;
+		e[i__2] = alpha.r;
+		i__2 = i__ + 1 + i__ * a_dim1;
+		a[i__2].r = 1.f, a[i__2].i = 0.f;
+
+/*              Apply H(i)**H to A(i+1:m,i+1:n) from the left */
+
+		i__2 = *m - i__;
+		i__3 = *n - i__;
+		r_cnjg(&q__1, &tauq[i__]);
+		clarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &
+			c__1, &q__1, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, &
+			work[1]);
+		i__2 = i__ + 1 + i__ * a_dim1;
+		i__3 = i__;
+		a[i__2].r = e[i__3], a[i__2].i = 0.f;
+	    } else {
+		i__2 = i__;
+		tauq[i__2].r = 0.f, tauq[i__2].i = 0.f;
+	    }
+/* L20: */
+	}
+    }
+    return 0;
+
+/*     End of CGEBD2 */
+
+} /* cgebd2_ */
+

lapack-netlib/SRC/cgebrd.c

@@ -0,0 +1,798 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__3 = 3;
+static integer c__2 = 2;
+
+/* > \brief \b CGEBRD */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEBRD + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgebrd.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgebrd.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgebrd.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, */
+/*                          INFO ) */
+
+/*       INTEGER            INFO, LDA, LWORK, M, N */
+/*       REAL               D( * ), E( * ) */
+/*       COMPLEX            A( LDA, * ), TAUP( * ), TAUQ( * ), */
+/*      $                   WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEBRD reduces a general complex M-by-N matrix A to upper or lower */
+/* > bidiagonal form B by a unitary transformation: Q**H * A * P = B. */
+/* > */
+/* > If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows in the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns in the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N general matrix to be reduced. */
+/* >          On exit, */
+/* >          if m >= n, the diagonal and the first superdiagonal are */
+/* >            overwritten with the upper bidiagonal matrix B; the */
+/* >            elements below the diagonal, with the array TAUQ, represent */
+/* >            the unitary matrix Q as a product of elementary */
+/* >            reflectors, and the elements above the first superdiagonal, */
+/* >            with the array TAUP, represent the unitary matrix P as */
+/* >            a product of elementary reflectors; */
+/* >          if m < n, the diagonal and the first subdiagonal are */
+/* >            overwritten with the lower bidiagonal matrix B; the */
+/* >            elements below the first subdiagonal, with the array TAUQ, */
+/* >            represent the unitary matrix Q as a product of */
+/* >            elementary reflectors, and the elements above the diagonal, */
+/* >            with the array TAUP, represent the unitary matrix P as */
+/* >            a product of elementary reflectors. */
+/* >          See Further Details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] D */
+/* > \verbatim */
+/* >          D is REAL array, dimension (f2cmin(M,N)) */
+/* >          The diagonal elements of the bidiagonal matrix B: */
+/* >          D(i) = A(i,i). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] E */
+/* > \verbatim */
+/* >          E is REAL array, dimension (f2cmin(M,N)-1) */
+/* >          The off-diagonal elements of the bidiagonal matrix B: */
+/* >          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */
+/* >          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAUQ */
+/* > \verbatim */
+/* >          TAUQ is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors which */
+/* >          represent the unitary matrix Q. See Further Details. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAUP */
+/* > \verbatim */
+/* >          TAUP is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors which */
+/* >          represent the unitary matrix P. See Further Details. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The length of the array WORK.  LWORK >= f2cmax(1,M,N). */
+/* >          For optimum performance LWORK >= (M+N)*NB, where NB */
+/* >          is the optimal blocksize. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit. */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date November 2017 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrices Q and P are represented as products of elementary */
+/* >  reflectors: */
+/* > */
+/* >  If m >= n, */
+/* > */
+/* >     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1) */
+/* > */
+/* >  Each H(i) and G(i) has the form: */
+/* > */
+/* >     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H */
+/* > */
+/* >  where tauq and taup are complex scalars, and v and u are complex */
+/* >  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in */
+/* >  A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in */
+/* >  A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
+/* > */
+/* >  If m < n, */
+/* > */
+/* >     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m) */
+/* > */
+/* >  Each H(i) and G(i) has the form: */
+/* > */
+/* >     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H */
+/* > */
+/* >  where tauq and taup are complex scalars, and v and u are complex */
+/* >  vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in */
+/* >  A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in */
+/* >  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */
+/* > */
+/* >  The contents of A on exit are illustrated by the following examples: */
+/* > */
+/* >  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n): */
+/* > */
+/* >    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 ) */
+/* >    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 ) */
+/* >    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 ) */
+/* >    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 ) */
+/* >    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 ) */
+/* >    (  v1  v2  v3  v4  v5 ) */
+/* > */
+/* >  where d and e denote diagonal and off-diagonal elements of B, vi */
+/* >  denotes an element of the vector defining H(i), and ui an element of */
+/* >  the vector defining G(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgebrd_(integer *m, integer *n, complex *a, integer *lda,
+	 real *d__, real *e, complex *tauq, complex *taup, complex *work, 
+	integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
+    real r__1;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, j;
+    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
+	    integer *, complex *, complex *, integer *, complex *, integer *, 
+	    complex *, complex *, integer *);
+    integer nbmin, iinfo, minmn;
+    extern /* Subroutine */ int cgebd2_(integer *, integer *, complex *, 
+	    integer *, real *, real *, complex *, complex *, complex *, 
+	    integer *);
+    integer nb;
+    extern /* Subroutine */ int clabrd_(integer *, integer *, integer *, 
+	    complex *, integer *, real *, real *, complex *, complex *, 
+	    complex *, integer *, complex *, integer *);
+    integer nx, ws;
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    integer ldwrkx, ldwrky, lwkopt;
+    logical lquery;
+
+
+/*  -- LAPACK computational routine (version 3.8.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     November 2017 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --d__;
+    --e;
+    --tauq;
+    --taup;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+/* Computing MAX */
+    i__1 = 1, i__2 = ilaenv_(&c__1, "CGEBRD", " ", m, n, &c_n1, &c_n1, (
+	    ftnlen)6, (ftnlen)1);
+    nb = f2cmax(i__1,i__2);
+    lwkopt = (*m + *n) * nb;
+    r__1 = (real) lwkopt;
+    work[1].r = r__1, work[1].i = 0.f;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    } else /* if(complicated condition) */ {
+/* Computing MAX */
+	i__1 = f2cmax(1,*m);
+	if (*lwork < f2cmax(i__1,*n) && ! lquery) {
+	    *info = -10;
+	}
+    }
+    if (*info < 0) {
+	i__1 = -(*info);
+	xerbla_("CGEBRD", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    minmn = f2cmin(*m,*n);
+    if (minmn == 0) {
+	work[1].r = 1.f, work[1].i = 0.f;
+	return 0;
+    }
+
+    ws = f2cmax(*m,*n);
+    ldwrkx = *m;
+    ldwrky = *n;
+
+    if (nb > 1 && nb < minmn) {
+
+/*        Set the crossover point NX. */
+
+/* Computing MAX */
+	i__1 = nb, i__2 = ilaenv_(&c__3, "CGEBRD", " ", m, n, &c_n1, &c_n1, (
+		ftnlen)6, (ftnlen)1);
+	nx = f2cmax(i__1,i__2);
+
+/*        Determine when to switch from blocked to unblocked code. */
+
+	if (nx < minmn) {
+	    ws = (*m + *n) * nb;
+	    if (*lwork < ws) {
+
+/*              Not enough work space for the optimal NB, consider using */
+/*              a smaller block size. */
+
+		nbmin = ilaenv_(&c__2, "CGEBRD", " ", m, n, &c_n1, &c_n1, (
+			ftnlen)6, (ftnlen)1);
+		if (*lwork >= (*m + *n) * nbmin) {
+		    nb = *lwork / (*m + *n);
+		} else {
+		    nb = 1;
+		    nx = minmn;
+		}
+	    }
+	}
+    } else {
+	nx = minmn;
+    }
+
+    i__1 = minmn - nx;
+    i__2 = nb;
+    for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+
+/*        Reduce rows and columns i:i+ib-1 to bidiagonal form and return */
+/*        the matrices X and Y which are needed to update the unreduced */
+/*        part of the matrix */
+
+	i__3 = *m - i__ + 1;
+	i__4 = *n - i__ + 1;
+	clabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[
+		i__], &tauq[i__], &taup[i__], &work[1], &ldwrkx, &work[ldwrkx 
+		* nb + 1], &ldwrky);
+
+/*        Update the trailing submatrix A(i+ib:m,i+ib:n), using */
+/*        an update of the form  A := A - V*Y**H - X*U**H */
+
+	i__3 = *m - i__ - nb + 1;
+	i__4 = *n - i__ - nb + 1;
+	q__1.r = -1.f, q__1.i = 0.f;
+	cgemm_("No transpose", "Conjugate transpose", &i__3, &i__4, &nb, &
+		q__1, &a[i__ + nb + i__ * a_dim1], lda, &work[ldwrkx * nb + 
+		nb + 1], &ldwrky, &c_b1, &a[i__ + nb + (i__ + nb) * a_dim1], 
+		lda);
+	i__3 = *m - i__ - nb + 1;
+	i__4 = *n - i__ - nb + 1;
+	q__1.r = -1.f, q__1.i = 0.f;
+	cgemm_("No transpose", "No transpose", &i__3, &i__4, &nb, &q__1, &
+		work[nb + 1], &ldwrkx, &a[i__ + (i__ + nb) * a_dim1], lda, &
+		c_b1, &a[i__ + nb + (i__ + nb) * a_dim1], lda);
+
+/*        Copy diagonal and off-diagonal elements of B back into A */
+
+	if (*m >= *n) {
+	    i__3 = i__ + nb - 1;
+	    for (j = i__; j <= i__3; ++j) {
+		i__4 = j + j * a_dim1;
+		i__5 = j;
+		a[i__4].r = d__[i__5], a[i__4].i = 0.f;
+		i__4 = j + (j + 1) * a_dim1;
+		i__5 = j;
+		a[i__4].r = e[i__5], a[i__4].i = 0.f;
+/* L10: */
+	    }
+	} else {
+	    i__3 = i__ + nb - 1;
+	    for (j = i__; j <= i__3; ++j) {
+		i__4 = j + j * a_dim1;
+		i__5 = j;
+		a[i__4].r = d__[i__5], a[i__4].i = 0.f;
+		i__4 = j + 1 + j * a_dim1;
+		i__5 = j;
+		a[i__4].r = e[i__5], a[i__4].i = 0.f;
+/* L20: */
+	    }
+	}
+/* L30: */
+    }
+
+/*     Use unblocked code to reduce the remainder of the matrix */
+
+    i__2 = *m - i__ + 1;
+    i__1 = *n - i__ + 1;
+    cgebd2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], &
+	    tauq[i__], &taup[i__], &work[1], &iinfo);
+    work[1].r = (real) ws, work[1].i = 0.f;
+    return 0;
+
+/*     End of CGEBRD */
+
+} /* cgebrd_ */
+

lapack-netlib/SRC/cgecon.c

@@ -0,0 +1,658 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* > \brief \b CGECON */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGECON + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgecon.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgecon.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgecon.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK, */
+/*                          INFO ) */
+
+/*       CHARACTER          NORM */
+/*       INTEGER            INFO, LDA, N */
+/*       REAL               ANORM, RCOND */
+/*       REAL               RWORK( * ) */
+/*       COMPLEX            A( LDA, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGECON estimates the reciprocal of the condition number of a general */
+/* > complex matrix A, in either the 1-norm or the infinity-norm, using */
+/* > the LU factorization computed by CGETRF. */
+/* > */
+/* > An estimate is obtained for norm(inv(A)), and the reciprocal of the */
+/* > condition number is computed as */
+/* >    RCOND = 1 / ( norm(A) * norm(inv(A)) ). */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] NORM */
+/* > \verbatim */
+/* >          NORM is CHARACTER*1 */
+/* >          Specifies whether the 1-norm condition number or the */
+/* >          infinity-norm condition number is required: */
+/* >          = '1' or 'O':  1-norm; */
+/* >          = 'I':         Infinity-norm. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          The factors L and U from the factorization A = P*L*U */
+/* >          as computed by CGETRF. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] ANORM */
+/* > \verbatim */
+/* >          ANORM is REAL */
+/* >          If NORM = '1' or 'O', the 1-norm of the original matrix A. */
+/* >          If NORM = 'I', the infinity-norm of the original matrix A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RCOND */
+/* > \verbatim */
+/* >          RCOND is REAL */
+/* >          The reciprocal of the condition number of the matrix A, */
+/* >          computed as RCOND = 1/(norm(A) * norm(inv(A))). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (2*N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RWORK */
+/* > \verbatim */
+/* >          RWORK is REAL array, dimension (2*N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgecon_(char *norm, integer *n, complex *a, integer *lda,
+	 real *anorm, real *rcond, complex *work, real *rwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1;
+    real r__1, r__2;
+
+    /* Local variables */
+    integer kase, kase1;
+    real scale;
+    extern logical lsame_(char *, char *);
+    integer isave[3];
+    extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real 
+	    *, integer *, integer *);
+    real sl;
+    integer ix;
+    extern integer icamax_(integer *, complex *, integer *);
+    extern real slamch_(char *);
+    real su;
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    real ainvnm;
+    extern /* Subroutine */ int clatrs_(char *, char *, char *, char *, 
+	    integer *, complex *, integer *, complex *, real *, real *, 
+	    integer *), csrscl_(integer *, 
+	    real *, complex *, integer *);
+    logical onenrm;
+    char normin[1];
+    real smlnum;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --work;
+    --rwork;
+
+    /* Function Body */
+    *info = 0;
+    onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
+    if (! onenrm && ! lsame_(norm, "I")) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -4;
+    } else if (*anorm < 0.f) {
+	*info = -5;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGECON", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    *rcond = 0.f;
+    if (*n == 0) {
+	*rcond = 1.f;
+	return 0;
+    } else if (*anorm == 0.f) {
+	return 0;
+    }
+
+    smlnum = slamch_("Safe minimum");
+
+/*     Estimate the norm of inv(A). */
+
+    ainvnm = 0.f;
+    *(unsigned char *)normin = 'N';
+    if (onenrm) {
+	kase1 = 1;
+    } else {
+	kase1 = 2;
+    }
+    kase = 0;
+L10:
+    clacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
+    if (kase != 0) {
+	if (kase == kase1) {
+
+/*           Multiply by inv(L). */
+
+	    clatrs_("Lower", "No transpose", "Unit", normin, n, &a[a_offset], 
+		    lda, &work[1], &sl, &rwork[1], info);
+
+/*           Multiply by inv(U). */
+
+	    clatrs_("Upper", "No transpose", "Non-unit", normin, n, &a[
+		    a_offset], lda, &work[1], &su, &rwork[*n + 1], info);
+	} else {
+
+/*           Multiply by inv(U**H). */
+
+	    clatrs_("Upper", "Conjugate transpose", "Non-unit", normin, n, &a[
+		    a_offset], lda, &work[1], &su, &rwork[*n + 1], info);
+
+/*           Multiply by inv(L**H). */
+
+	    clatrs_("Lower", "Conjugate transpose", "Unit", normin, n, &a[
+		    a_offset], lda, &work[1], &sl, &rwork[1], info);
+	}
+
+/*        Divide X by 1/(SL*SU) if doing so will not cause overflow. */
+
+	scale = sl * su;
+	*(unsigned char *)normin = 'Y';
+	if (scale != 1.f) {
+	    ix = icamax_(n, &work[1], &c__1);
+	    i__1 = ix;
+	    if (scale < ((r__1 = work[i__1].r, abs(r__1)) + (r__2 = r_imag(&
+		    work[ix]), abs(r__2))) * smlnum || scale == 0.f) {
+		goto L20;
+	    }
+	    csrscl_(n, &scale, &work[1], &c__1);
+	}
+	goto L10;
+    }
+
+/*     Compute the estimate of the reciprocal condition number. */
+
+    if (ainvnm != 0.f) {
+	*rcond = 1.f / ainvnm / *anorm;
+    }
+
+L20:
+    return 0;
+
+/*     End of CGECON */
+
+} /* cgecon_ */
+

lapack-netlib/SRC/cgeequ.c

@@ -0,0 +1,737 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGEEQU */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEEQU + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeequ.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeequ.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeequ.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, */
+/*                          INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       REAL               AMAX, COLCND, ROWCND */
+/*       REAL               C( * ), R( * ) */
+/*       COMPLEX            A( LDA, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEEQU computes row and column scalings intended to equilibrate an */
+/* > M-by-N matrix A and reduce its condition number.  R returns the row */
+/* > scale factors and C the column scale factors, chosen to try to make */
+/* > the largest element in each row and column of the matrix B with */
+/* > elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1. */
+/* > */
+/* > R(i) and C(j) are restricted to be between SMLNUM = smallest safe */
+/* > number and BIGNUM = largest safe number.  Use of these scaling */
+/* > factors is not guaranteed to reduce the condition number of A but */
+/* > works well in practice. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          The M-by-N matrix whose equilibration factors are */
+/* >          to be computed. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] R */
+/* > \verbatim */
+/* >          R is REAL array, dimension (M) */
+/* >          If INFO = 0 or INFO > M, R contains the row scale factors */
+/* >          for A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] C */
+/* > \verbatim */
+/* >          C is REAL array, dimension (N) */
+/* >          If INFO = 0,  C contains the column scale factors for A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] ROWCND */
+/* > \verbatim */
+/* >          ROWCND is REAL */
+/* >          If INFO = 0 or INFO > M, ROWCND contains the ratio of the */
+/* >          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and */
+/* >          AMAX is neither too large nor too small, it is not worth */
+/* >          scaling by R. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] COLCND */
+/* > \verbatim */
+/* >          COLCND is REAL */
+/* >          If INFO = 0, COLCND contains the ratio of the smallest */
+/* >          C(i) to the largest C(i).  If COLCND >= 0.1, it is not */
+/* >          worth scaling by C. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] AMAX */
+/* > \verbatim */
+/* >          AMAX is REAL */
+/* >          Absolute value of largest matrix element.  If AMAX is very */
+/* >          close to overflow or very close to underflow, the matrix */
+/* >          should be scaled. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO = i,  and i is */
+/* >                <= M:  the i-th row of A is exactly zero */
+/* >                >  M:  the (i-M)-th column of A is exactly zero */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgeequ_(integer *m, integer *n, complex *a, integer *lda,
+	 real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, 
+	integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+    real r__1, r__2, r__3, r__4;
+
+    /* Local variables */
+    integer i__, j;
+    real rcmin, rcmax;
+    extern real slamch_(char *);
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    real bignum, smlnum;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --r__;
+    --c__;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEEQU", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*m == 0 || *n == 0) {
+	*rowcnd = 1.f;
+	*colcnd = 1.f;
+	*amax = 0.f;
+	return 0;
+    }
+
+/*     Get machine constants. */
+
+    smlnum = slamch_("S");
+    bignum = 1.f / smlnum;
+
+/*     Compute row scale factors. */
+
+    i__1 = *m;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	r__[i__] = 0.f;
+/* L10: */
+    }
+
+/*     Find the maximum element in each row. */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	i__2 = *m;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    i__3 = i__ + j * a_dim1;
+	    r__3 = r__[i__], r__4 = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = 
+		    r_imag(&a[i__ + j * a_dim1]), abs(r__2));
+	    r__[i__] = f2cmax(r__3,r__4);
+/* L20: */
+	}
+/* L30: */
+    }
+
+/*     Find the maximum and minimum scale factors. */
+
+    rcmin = bignum;
+    rcmax = 0.f;
+    i__1 = *m;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+/* Computing MAX */
+	r__1 = rcmax, r__2 = r__[i__];
+	rcmax = f2cmax(r__1,r__2);
+/* Computing MIN */
+	r__1 = rcmin, r__2 = r__[i__];
+	rcmin = f2cmin(r__1,r__2);
+/* L40: */
+    }
+    *amax = rcmax;
+
+    if (rcmin == 0.f) {
+
+/*        Find the first zero scale factor and return an error code. */
+
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    if (r__[i__] == 0.f) {
+		*info = i__;
+		return 0;
+	    }
+/* L50: */
+	}
+    } else {
+
+/*        Invert the scale factors. */
+
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+/* Computing MIN */
+/* Computing MAX */
+	    r__2 = r__[i__];
+	    r__1 = f2cmax(r__2,smlnum);
+	    r__[i__] = 1.f / f2cmin(r__1,bignum);
+/* L60: */
+	}
+
+/*        Compute ROWCND = f2cmin(R(I)) / f2cmax(R(I)) */
+
+	*rowcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
+    }
+
+/*     Compute column scale factors */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	c__[j] = 0.f;
+/* L70: */
+    }
+
+/*     Find the maximum element in each column, */
+/*     assuming the row scaling computed above. */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	i__2 = *m;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    i__3 = i__ + j * a_dim1;
+	    r__3 = c__[j], r__4 = ((r__1 = a[i__3].r, abs(r__1)) + (r__2 = 
+		    r_imag(&a[i__ + j * a_dim1]), abs(r__2))) * r__[i__];
+	    c__[j] = f2cmax(r__3,r__4);
+/* L80: */
+	}
+/* L90: */
+    }
+
+/*     Find the maximum and minimum scale factors. */
+
+    rcmin = bignum;
+    rcmax = 0.f;
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+	r__1 = rcmin, r__2 = c__[j];
+	rcmin = f2cmin(r__1,r__2);
+/* Computing MAX */
+	r__1 = rcmax, r__2 = c__[j];
+	rcmax = f2cmax(r__1,r__2);
+/* L100: */
+    }
+
+    if (rcmin == 0.f) {
+
+/*        Find the first zero scale factor and return an error code. */
+
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    if (c__[j] == 0.f) {
+		*info = *m + j;
+		return 0;
+	    }
+/* L110: */
+	}
+    } else {
+
+/*        Invert the scale factors. */
+
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+/* Computing MAX */
+	    r__2 = c__[j];
+	    r__1 = f2cmax(r__2,smlnum);
+	    c__[j] = 1.f / f2cmin(r__1,bignum);
+/* L120: */
+	}
+
+/*        Compute COLCND = f2cmin(C(J)) / f2cmax(C(J)) */
+
+	*colcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
+    }
+
+    return 0;
+
+/*     End of CGEEQU */
+
+} /* cgeequ_ */
+

lapack-netlib/SRC/cgeequb.c

@@ -0,0 +1,757 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGEEQUB */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEEQUB + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeequb
+.f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeequb
+.f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeequb
+.f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEEQUB( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, */
+/*                           INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       REAL               AMAX, COLCND, ROWCND */
+/*       REAL               C( * ), R( * ) */
+/*       COMPLEX            A( LDA, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEEQUB computes row and column scalings intended to equilibrate an */
+/* > M-by-N matrix A and reduce its condition number.  R returns the row */
+/* > scale factors and C the column scale factors, chosen to try to make */
+/* > the largest element in each row and column of the matrix B with */
+/* > elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most */
+/* > the radix. */
+/* > */
+/* > R(i) and C(j) are restricted to be a power of the radix between */
+/* > SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use */
+/* > of these scaling factors is not guaranteed to reduce the condition */
+/* > number of A but works well in practice. */
+/* > */
+/* > This routine differs from CGEEQU by restricting the scaling factors */
+/* > to a power of the radix.  Barring over- and underflow, scaling by */
+/* > these factors introduces no additional rounding errors.  However, the */
+/* > scaled entries' magnitudes are no longer approximately 1 but lie */
+/* > between sqrt(radix) and 1/sqrt(radix). */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          The M-by-N matrix whose equilibration factors are */
+/* >          to be computed. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] R */
+/* > \verbatim */
+/* >          R is REAL array, dimension (M) */
+/* >          If INFO = 0 or INFO > M, R contains the row scale factors */
+/* >          for A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] C */
+/* > \verbatim */
+/* >          C is REAL array, dimension (N) */
+/* >          If INFO = 0,  C contains the column scale factors for A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] ROWCND */
+/* > \verbatim */
+/* >          ROWCND is REAL */
+/* >          If INFO = 0 or INFO > M, ROWCND contains the ratio of the */
+/* >          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and */
+/* >          AMAX is neither too large nor too small, it is not worth */
+/* >          scaling by R. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] COLCND */
+/* > \verbatim */
+/* >          COLCND is REAL */
+/* >          If INFO = 0, COLCND contains the ratio of the smallest */
+/* >          C(i) to the largest C(i).  If COLCND >= 0.1, it is not */
+/* >          worth scaling by C. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] AMAX */
+/* > \verbatim */
+/* >          AMAX is REAL */
+/* >          Absolute value of largest matrix element.  If AMAX is very */
+/* >          close to overflow or very close to underflow, the matrix */
+/* >          should be scaled. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO = i,  and i is */
+/* >                <= M:  the i-th row of A is exactly zero */
+/* >                >  M:  the (i-M)-th column of A is exactly zero */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgeequb_(integer *m, integer *n, complex *a, integer *
+	lda, real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, 
+	integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+    real r__1, r__2, r__3, r__4;
+
+    /* Local variables */
+    integer i__, j;
+    real radix, rcmin, rcmax;
+    extern real slamch_(char *);
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    real bignum, logrdx, smlnum;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --r__;
+    --c__;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEEQUB", &i__1, (ftnlen)7);
+	return 0;
+    }
+
+/*     Quick return if possible. */
+
+    if (*m == 0 || *n == 0) {
+	*rowcnd = 1.f;
+	*colcnd = 1.f;
+	*amax = 0.f;
+	return 0;
+    }
+
+/*     Get machine constants.  Assume SMLNUM is a power of the radix. */
+
+    smlnum = slamch_("S");
+    bignum = 1.f / smlnum;
+    radix = slamch_("B");
+    logrdx = log(radix);
+
+/*     Compute row scale factors. */
+
+    i__1 = *m;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	r__[i__] = 0.f;
+/* L10: */
+    }
+
+/*     Find the maximum element in each row. */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	i__2 = *m;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    i__3 = i__ + j * a_dim1;
+	    r__3 = r__[i__], r__4 = (r__1 = a[i__3].r, abs(r__1)) + (r__2 = 
+		    r_imag(&a[i__ + j * a_dim1]), abs(r__2));
+	    r__[i__] = f2cmax(r__3,r__4);
+/* L20: */
+	}
+/* L30: */
+    }
+    i__1 = *m;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	if (r__[i__] > 0.f) {
+	    i__2 = (integer) (log(r__[i__]) / logrdx);
+	    r__[i__] = pow_ri(&radix, &i__2);
+	}
+    }
+
+/*     Find the maximum and minimum scale factors. */
+
+    rcmin = bignum;
+    rcmax = 0.f;
+    i__1 = *m;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+/* Computing MAX */
+	r__1 = rcmax, r__2 = r__[i__];
+	rcmax = f2cmax(r__1,r__2);
+/* Computing MIN */
+	r__1 = rcmin, r__2 = r__[i__];
+	rcmin = f2cmin(r__1,r__2);
+/* L40: */
+    }
+    *amax = rcmax;
+
+    if (rcmin == 0.f) {
+
+/*        Find the first zero scale factor and return an error code. */
+
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    if (r__[i__] == 0.f) {
+		*info = i__;
+		return 0;
+	    }
+/* L50: */
+	}
+    } else {
+
+/*        Invert the scale factors. */
+
+	i__1 = *m;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+/* Computing MIN */
+/* Computing MAX */
+	    r__2 = r__[i__];
+	    r__1 = f2cmax(r__2,smlnum);
+	    r__[i__] = 1.f / f2cmin(r__1,bignum);
+/* L60: */
+	}
+
+/*        Compute ROWCND = f2cmin(R(I)) / f2cmax(R(I)). */
+
+	*rowcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
+    }
+
+/*     Compute column scale factors. */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	c__[j] = 0.f;
+/* L70: */
+    }
+
+/*     Find the maximum element in each column, */
+/*     assuming the row scaling computed above. */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	i__2 = *m;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    i__3 = i__ + j * a_dim1;
+	    r__3 = c__[j], r__4 = ((r__1 = a[i__3].r, abs(r__1)) + (r__2 = 
+		    r_imag(&a[i__ + j * a_dim1]), abs(r__2))) * r__[i__];
+	    c__[j] = f2cmax(r__3,r__4);
+/* L80: */
+	}
+	if (c__[j] > 0.f) {
+	    i__2 = (integer) (log(c__[j]) / logrdx);
+	    c__[j] = pow_ri(&radix, &i__2);
+	}
+/* L90: */
+    }
+
+/*     Find the maximum and minimum scale factors. */
+
+    rcmin = bignum;
+    rcmax = 0.f;
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+	r__1 = rcmin, r__2 = c__[j];
+	rcmin = f2cmin(r__1,r__2);
+/* Computing MAX */
+	r__1 = rcmax, r__2 = c__[j];
+	rcmax = f2cmax(r__1,r__2);
+/* L100: */
+    }
+
+    if (rcmin == 0.f) {
+
+/*        Find the first zero scale factor and return an error code. */
+
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+	    if (c__[j] == 0.f) {
+		*info = *m + j;
+		return 0;
+	    }
+/* L110: */
+	}
+    } else {
+
+/*        Invert the scale factors. */
+
+	i__1 = *n;
+	for (j = 1; j <= i__1; ++j) {
+/* Computing MIN */
+/* Computing MAX */
+	    r__2 = c__[j];
+	    r__1 = f2cmax(r__2,smlnum);
+	    c__[j] = 1.f / f2cmin(r__1,bignum);
+/* L120: */
+	}
+
+/*        Compute COLCND = f2cmin(C(J)) / f2cmax(C(J)). */
+
+	*colcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
+    }
+
+    return 0;
+
+/*     End of CGEEQUB */
+
+} /* cgeequb_ */
+

lapack-netlib/SRC/cgees.c

@@ -0,0 +1,855 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c__0 = 0;
+static integer c_n1 = -1;
+
+/* > \brief <b> CGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors f
+or GE matrices</b> */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEES + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgees.f
+"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgees.f
+"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgees.f
+"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEES( JOBVS, SORT, SELECT, N, A, LDA, SDIM, W, VS, */
+/*                         LDVS, WORK, LWORK, RWORK, BWORK, INFO ) */
+
+/*       CHARACTER          JOBVS, SORT */
+/*       INTEGER            INFO, LDA, LDVS, LWORK, N, SDIM */
+/*       LOGICAL            BWORK( * ) */
+/*       REAL               RWORK( * ) */
+/*       COMPLEX            A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * ) */
+/*       LOGICAL            SELECT */
+/*       EXTERNAL           SELECT */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEES computes for an N-by-N complex nonsymmetric matrix A, the */
+/* > eigenvalues, the Schur form T, and, optionally, the matrix of Schur */
+/* > vectors Z.  This gives the Schur factorization A = Z*T*(Z**H). */
+/* > */
+/* > Optionally, it also orders the eigenvalues on the diagonal of the */
+/* > Schur form so that selected eigenvalues are at the top left. */
+/* > The leading columns of Z then form an orthonormal basis for the */
+/* > invariant subspace corresponding to the selected eigenvalues. */
+/* > */
+/* > A complex matrix is in Schur form if it is upper triangular. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] JOBVS */
+/* > \verbatim */
+/* >          JOBVS is CHARACTER*1 */
+/* >          = 'N': Schur vectors are not computed; */
+/* >          = 'V': Schur vectors are computed. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] SORT */
+/* > \verbatim */
+/* >          SORT is CHARACTER*1 */
+/* >          Specifies whether or not to order the eigenvalues on the */
+/* >          diagonal of the Schur form. */
+/* >          = 'N': Eigenvalues are not ordered: */
+/* >          = 'S': Eigenvalues are ordered (see SELECT). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] SELECT */
+/* > \verbatim */
+/* >          SELECT is a LOGICAL FUNCTION of one COMPLEX argument */
+/* >          SELECT must be declared EXTERNAL in the calling subroutine. */
+/* >          If SORT = 'S', SELECT is used to select eigenvalues to order */
+/* >          to the top left of the Schur form. */
+/* >          IF SORT = 'N', SELECT is not referenced. */
+/* >          The eigenvalue W(j) is selected if SELECT(W(j)) is true. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A. N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the N-by-N matrix A. */
+/* >          On exit, A has been overwritten by its Schur form T. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] SDIM */
+/* > \verbatim */
+/* >          SDIM is INTEGER */
+/* >          If SORT = 'N', SDIM = 0. */
+/* >          If SORT = 'S', SDIM = number of eigenvalues for which */
+/* >                         SELECT is true. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] W */
+/* > \verbatim */
+/* >          W is COMPLEX array, dimension (N) */
+/* >          W contains the computed eigenvalues, in the same order that */
+/* >          they appear on the diagonal of the output Schur form T. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] VS */
+/* > \verbatim */
+/* >          VS is COMPLEX array, dimension (LDVS,N) */
+/* >          If JOBVS = 'V', VS contains the unitary matrix Z of Schur */
+/* >          vectors. */
+/* >          If JOBVS = 'N', VS is not referenced. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDVS */
+/* > \verbatim */
+/* >          LDVS is INTEGER */
+/* >          The leading dimension of the array VS.  LDVS >= 1; if */
+/* >          JOBVS = 'V', LDVS >= N. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,2*N). */
+/* >          For good performance, LWORK must generally be larger. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RWORK */
+/* > \verbatim */
+/* >          RWORK is REAL array, dimension (N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] BWORK */
+/* > \verbatim */
+/* >          BWORK is LOGICAL array, dimension (N) */
+/* >          Not referenced if SORT = 'N'. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value. */
+/* >          > 0: if INFO = i, and i is */
+/* >               <= N:  the QR algorithm failed to compute all the */
+/* >                      eigenvalues; elements 1:ILO-1 and i+1:N of W */
+/* >                      contain those eigenvalues which have converged; */
+/* >                      if JOBVS = 'V', VS contains the matrix which */
+/* >                      reduces A to its partially converged Schur form. */
+/* >               = N+1: the eigenvalues could not be reordered because */
+/* >                      some eigenvalues were too close to separate (the */
+/* >                      problem is very ill-conditioned); */
+/* >               = N+2: after reordering, roundoff changed values of */
+/* >                      some complex eigenvalues so that leading */
+/* >                      eigenvalues in the Schur form no longer satisfy */
+/* >                      SELECT = .TRUE..  This could also be caused by */
+/* >                      underflow due to scaling. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEeigen */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgees_(char *jobvs, char *sort, L_fp select, integer *n, 
+	complex *a, integer *lda, integer *sdim, complex *w, complex *vs, 
+	integer *ldvs, complex *work, integer *lwork, real *rwork, logical *
+	bwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2;
+
+    /* Local variables */
+    integer ibal;
+    real anrm;
+    integer ierr, itau, iwrk, i__;
+    real s;
+    integer icond, ieval;
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
+	    complex *, integer *), cgebak_(char *, char *, integer *, integer 
+	    *, integer *, real *, integer *, complex *, integer *, integer *), cgebal_(char *, integer *, complex *, integer *, 
+	    integer *, integer *, real *, integer *), slabad_(real *, 
+	    real *);
+    logical scalea;
+    extern real clange_(char *, integer *, integer *, complex *, integer *, 
+	    real *);
+    real cscale;
+    extern /* Subroutine */ int cgehrd_(integer *, integer *, integer *, 
+	    complex *, integer *, complex *, complex *, integer *, integer *),
+	     clascl_(char *, integer *, integer *, real *, real *, integer *, 
+	    integer *, complex *, integer *, integer *);
+    extern real slamch_(char *);
+    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
+	    *, integer *, complex *, integer *), xerbla_(char *, 
+	    integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    real bignum;
+    extern /* Subroutine */ int chseqr_(char *, char *, integer *, integer *, 
+	    integer *, complex *, integer *, complex *, complex *, integer *, 
+	    complex *, integer *, integer *), cunghr_(integer 
+	    *, integer *, integer *, complex *, integer *, complex *, complex 
+	    *, integer *, integer *), ctrsen_(char *, char *, logical *, 
+	    integer *, complex *, integer *, complex *, integer *, complex *, 
+	    integer *, real *, real *, complex *, integer *, integer *);
+    integer minwrk, maxwrk;
+    real smlnum;
+    integer hswork;
+    logical wantst, lquery, wantvs;
+    integer ihi, ilo;
+    real dum[1], eps, sep;
+
+
+/*  -- LAPACK driver routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --w;
+    vs_dim1 = *ldvs;
+    vs_offset = 1 + vs_dim1 * 1;
+    vs -= vs_offset;
+    --work;
+    --rwork;
+    --bwork;
+
+    /* Function Body */
+    *info = 0;
+    lquery = *lwork == -1;
+    wantvs = lsame_(jobvs, "V");
+    wantst = lsame_(sort, "S");
+    if (! wantvs && ! lsame_(jobvs, "N")) {
+	*info = -1;
+    } else if (! wantst && ! lsame_(sort, "N")) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -4;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -6;
+    } else if (*ldvs < 1 || wantvs && *ldvs < *n) {
+	*info = -10;
+    }
+
+/*     Compute workspace */
+/*      (Note: Comments in the code beginning "Workspace:" describe the */
+/*       minimal amount of workspace needed at that point in the code, */
+/*       as well as the preferred amount for good performance. */
+/*       CWorkspace refers to complex workspace, and RWorkspace to real */
+/*       workspace. NB refers to the optimal block size for the */
+/*       immediately following subroutine, as returned by ILAENV. */
+/*       HSWORK refers to the workspace preferred by CHSEQR, as */
+/*       calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
+/*       the worst case.) */
+
+    if (*info == 0) {
+	if (*n == 0) {
+	    minwrk = 1;
+	    maxwrk = 1;
+	} else {
+	    maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &
+		    c__0, (ftnlen)6, (ftnlen)1);
+	    minwrk = *n << 1;
+
+	    chseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &w[1], &vs[
+		    vs_offset], ldvs, &work[1], &c_n1, &ieval);
+	    hswork = work[1].r;
+
+	    if (! wantvs) {
+		maxwrk = f2cmax(maxwrk,hswork);
+	    } else {
+/* Computing MAX */
+		i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
+			 " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
+		maxwrk = f2cmax(i__1,i__2);
+		maxwrk = f2cmax(maxwrk,hswork);
+	    }
+	}
+	work[1].r = (real) maxwrk, work[1].i = 0.f;
+
+	if (*lwork < minwrk && ! lquery) {
+	    *info = -12;
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEES ", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	*sdim = 0;
+	return 0;
+    }
+
+/*     Get machine constants */
+
+    eps = slamch_("P");
+    smlnum = slamch_("S");
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+    smlnum = sqrt(smlnum) / eps;
+    bignum = 1.f / smlnum;
+
+/*     Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
+
+    anrm = clange_("M", n, n, &a[a_offset], lda, dum);
+    scalea = FALSE_;
+    if (anrm > 0.f && anrm < smlnum) {
+	scalea = TRUE_;
+	cscale = smlnum;
+    } else if (anrm > bignum) {
+	scalea = TRUE_;
+	cscale = bignum;
+    }
+    if (scalea) {
+	clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
+		ierr);
+    }
+
+/*     Permute the matrix to make it more nearly triangular */
+/*     (CWorkspace: none) */
+/*     (RWorkspace: need N) */
+
+    ibal = 1;
+    cgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);
+
+/*     Reduce to upper Hessenberg form */
+/*     (CWorkspace: need 2*N, prefer N+N*NB) */
+/*     (RWorkspace: none) */
+
+    itau = 1;
+    iwrk = *n + itau;
+    i__1 = *lwork - iwrk + 1;
+    cgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
+	     &ierr);
+
+    if (wantvs) {
+
+/*        Copy Householder vectors to VS */
+
+	clacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
+		;
+
+/*        Generate unitary matrix in VS */
+/*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
+/*        (RWorkspace: none) */
+
+	i__1 = *lwork - iwrk + 1;
+	cunghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
+		 &i__1, &ierr);
+    }
+
+    *sdim = 0;
+
+/*     Perform QR iteration, accumulating Schur vectors in VS if desired */
+/*     (CWorkspace: need 1, prefer HSWORK (see comments) ) */
+/*     (RWorkspace: none) */
+
+    iwrk = itau;
+    i__1 = *lwork - iwrk + 1;
+    chseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vs[
+	    vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
+    if (ieval > 0) {
+	*info = ieval;
+    }
+
+/*     Sort eigenvalues if desired */
+
+    if (wantst && *info == 0) {
+	if (scalea) {
+	    clascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
+		    ierr);
+	}
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    bwork[i__] = (*select)(&w[i__]);
+/* L10: */
+	}
+
+/*        Reorder eigenvalues and transform Schur vectors */
+/*        (CWorkspace: none) */
+/*        (RWorkspace: none) */
+
+	i__1 = *lwork - iwrk + 1;
+	ctrsen_("N", jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset], 
+		ldvs, &w[1], sdim, &s, &sep, &work[iwrk], &i__1, &icond);
+    }
+
+    if (wantvs) {
+
+/*        Undo balancing */
+/*        (CWorkspace: none) */
+/*        (RWorkspace: need N) */
+
+	cgebak_("P", "R", n, &ilo, &ihi, &rwork[ibal], n, &vs[vs_offset], 
+		ldvs, &ierr);
+    }
+
+    if (scalea) {
+
+/*        Undo scaling for the Schur form of A */
+
+	clascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
+		ierr);
+	i__1 = *lda + 1;
+	ccopy_(n, &a[a_offset], &i__1, &w[1], &c__1);
+    }
+
+    work[1].r = (real) maxwrk, work[1].i = 0.f;
+    return 0;
+
+/*     End of CGEES */
+
+} /* cgees_ */
+

lapack-netlib/SRC/cgeesx.c

@@ -0,0 +1,937 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c__0 = 0;
+static integer c_n1 = -1;
+
+/* > \brief <b> CGEESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors 
+for GE matrices</b> */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEESX + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeesx.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeesx.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeesx.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, W, */
+/*                          VS, LDVS, RCONDE, RCONDV, WORK, LWORK, RWORK, */
+/*                          BWORK, INFO ) */
+
+/*       CHARACTER          JOBVS, SENSE, SORT */
+/*       INTEGER            INFO, LDA, LDVS, LWORK, N, SDIM */
+/*       REAL               RCONDE, RCONDV */
+/*       LOGICAL            BWORK( * ) */
+/*       REAL               RWORK( * ) */
+/*       COMPLEX            A( LDA, * ), VS( LDVS, * ), W( * ), WORK( * ) */
+/*       LOGICAL            SELECT */
+/*       EXTERNAL           SELECT */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEESX computes for an N-by-N complex nonsymmetric matrix A, the */
+/* > eigenvalues, the Schur form T, and, optionally, the matrix of Schur */
+/* > vectors Z.  This gives the Schur factorization A = Z*T*(Z**H). */
+/* > */
+/* > Optionally, it also orders the eigenvalues on the diagonal of the */
+/* > Schur form so that selected eigenvalues are at the top left; */
+/* > computes a reciprocal condition number for the average of the */
+/* > selected eigenvalues (RCONDE); and computes a reciprocal condition */
+/* > number for the right invariant subspace corresponding to the */
+/* > selected eigenvalues (RCONDV).  The leading columns of Z form an */
+/* > orthonormal basis for this invariant subspace. */
+/* > */
+/* > For further explanation of the reciprocal condition numbers RCONDE */
+/* > and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where */
+/* > these quantities are called s and sep respectively). */
+/* > */
+/* > A complex matrix is in Schur form if it is upper triangular. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] JOBVS */
+/* > \verbatim */
+/* >          JOBVS is CHARACTER*1 */
+/* >          = 'N': Schur vectors are not computed; */
+/* >          = 'V': Schur vectors are computed. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] SORT */
+/* > \verbatim */
+/* >          SORT is CHARACTER*1 */
+/* >          Specifies whether or not to order the eigenvalues on the */
+/* >          diagonal of the Schur form. */
+/* >          = 'N': Eigenvalues are not ordered; */
+/* >          = 'S': Eigenvalues are ordered (see SELECT). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] SELECT */
+/* > \verbatim */
+/* >          SELECT is a LOGICAL FUNCTION of one COMPLEX argument */
+/* >          SELECT must be declared EXTERNAL in the calling subroutine. */
+/* >          If SORT = 'S', SELECT is used to select eigenvalues to order */
+/* >          to the top left of the Schur form. */
+/* >          If SORT = 'N', SELECT is not referenced. */
+/* >          An eigenvalue W(j) is selected if SELECT(W(j)) is true. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] SENSE */
+/* > \verbatim */
+/* >          SENSE is CHARACTER*1 */
+/* >          Determines which reciprocal condition numbers are computed. */
+/* >          = 'N': None are computed; */
+/* >          = 'E': Computed for average of selected eigenvalues only; */
+/* >          = 'V': Computed for selected right invariant subspace only; */
+/* >          = 'B': Computed for both. */
+/* >          If SENSE = 'E', 'V' or 'B', SORT must equal 'S'. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A. N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA, N) */
+/* >          On entry, the N-by-N matrix A. */
+/* >          On exit, A is overwritten by its Schur form T. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] SDIM */
+/* > \verbatim */
+/* >          SDIM is INTEGER */
+/* >          If SORT = 'N', SDIM = 0. */
+/* >          If SORT = 'S', SDIM = number of eigenvalues for which */
+/* >                         SELECT is true. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] W */
+/* > \verbatim */
+/* >          W is COMPLEX array, dimension (N) */
+/* >          W contains the computed eigenvalues, in the same order */
+/* >          that they appear on the diagonal of the output Schur form T. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] VS */
+/* > \verbatim */
+/* >          VS is COMPLEX array, dimension (LDVS,N) */
+/* >          If JOBVS = 'V', VS contains the unitary matrix Z of Schur */
+/* >          vectors. */
+/* >          If JOBVS = 'N', VS is not referenced. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDVS */
+/* > \verbatim */
+/* >          LDVS is INTEGER */
+/* >          The leading dimension of the array VS.  LDVS >= 1, and if */
+/* >          JOBVS = 'V', LDVS >= N. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RCONDE */
+/* > \verbatim */
+/* >          RCONDE is REAL */
+/* >          If SENSE = 'E' or 'B', RCONDE contains the reciprocal */
+/* >          condition number for the average of the selected eigenvalues. */
+/* >          Not referenced if SENSE = 'N' or 'V'. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RCONDV */
+/* > \verbatim */
+/* >          RCONDV is REAL */
+/* >          If SENSE = 'V' or 'B', RCONDV contains the reciprocal */
+/* >          condition number for the selected right invariant subspace. */
+/* >          Not referenced if SENSE = 'N' or 'E'. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,2*N). */
+/* >          Also, if SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM), */
+/* >          where SDIM is the number of selected eigenvalues computed by */
+/* >          this routine.  Note that 2*SDIM*(N-SDIM) <= N*N/2. Note also */
+/* >          that an error is only returned if LWORK < f2cmax(1,2*N), but if */
+/* >          SENSE = 'E' or 'V' or 'B' this may not be large enough. */
+/* >          For good performance, LWORK must generally be larger. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates upper bound on the optimal size of the */
+/* >          array WORK, returns this value as the first entry of the WORK */
+/* >          array, and no error message related to LWORK is issued by */
+/* >          XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RWORK */
+/* > \verbatim */
+/* >          RWORK is REAL array, dimension (N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] BWORK */
+/* > \verbatim */
+/* >          BWORK is LOGICAL array, dimension (N) */
+/* >          Not referenced if SORT = 'N'. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value. */
+/* >          > 0: if INFO = i, and i is */
+/* >             <= N: the QR algorithm failed to compute all the */
+/* >                   eigenvalues; elements 1:ILO-1 and i+1:N of W */
+/* >                   contain those eigenvalues which have converged; if */
+/* >                   JOBVS = 'V', VS contains the transformation which */
+/* >                   reduces A to its partially converged Schur form. */
+/* >             = N+1: the eigenvalues could not be reordered because some */
+/* >                   eigenvalues were too close to separate (the problem */
+/* >                   is very ill-conditioned); */
+/* >             = N+2: after reordering, roundoff changed values of some */
+/* >                   complex eigenvalues so that leading eigenvalues in */
+/* >                   the Schur form no longer satisfy SELECT=.TRUE.  This */
+/* >                   could also be caused by underflow due to scaling. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2016 */
+
+/* > \ingroup complexGEeigen */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgeesx_(char *jobvs, char *sort, L_fp select, char *
+	sense, integer *n, complex *a, integer *lda, integer *sdim, complex *
+	w, complex *vs, integer *ldvs, real *rconde, real *rcondv, complex *
+	work, integer *lwork, real *rwork, logical *bwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2;
+
+    /* Local variables */
+    integer ibal;
+    real anrm;
+    integer ierr, itau, iwrk, lwrk, i__, icond, ieval;
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
+	    complex *, integer *), cgebak_(char *, char *, integer *, integer 
+	    *, integer *, real *, integer *, complex *, integer *, integer *), cgebal_(char *, integer *, complex *, integer *, 
+	    integer *, integer *, real *, integer *), slabad_(real *, 
+	    real *);
+    logical scalea;
+    extern real clange_(char *, integer *, integer *, complex *, integer *, 
+	    real *);
+    real cscale;
+    extern /* Subroutine */ int cgehrd_(integer *, integer *, integer *, 
+	    complex *, integer *, complex *, complex *, integer *, integer *),
+	     clascl_(char *, integer *, integer *, real *, real *, integer *, 
+	    integer *, complex *, integer *, integer *);
+    extern real slamch_(char *);
+    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
+	    *, integer *, complex *, integer *), xerbla_(char *, 
+	    integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    real bignum;
+    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
+	    real *, integer *, integer *, real *, integer *, integer *), chseqr_(char *, char *, integer *, integer *, integer *, 
+	    complex *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *, integer *), cunghr_(integer *, integer 
+	    *, integer *, complex *, integer *, complex *, complex *, integer 
+	    *, integer *);
+    logical wantsb;
+    extern /* Subroutine */ int ctrsen_(char *, char *, logical *, integer *, 
+	    complex *, integer *, complex *, integer *, complex *, integer *, 
+	    real *, real *, complex *, integer *, integer *);
+    logical wantse;
+    integer minwrk, maxwrk;
+    logical wantsn;
+    real smlnum;
+    integer hswork;
+    logical wantst, lquery, wantsv, wantvs;
+    integer ihi, ilo;
+    real dum[1], eps;
+
+
+/*  -- LAPACK driver routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --w;
+    vs_dim1 = *ldvs;
+    vs_offset = 1 + vs_dim1 * 1;
+    vs -= vs_offset;
+    --work;
+    --rwork;
+    --bwork;
+
+    /* Function Body */
+    *info = 0;
+    wantvs = lsame_(jobvs, "V");
+    wantst = lsame_(sort, "S");
+    wantsn = lsame_(sense, "N");
+    wantse = lsame_(sense, "E");
+    wantsv = lsame_(sense, "V");
+    wantsb = lsame_(sense, "B");
+    lquery = *lwork == -1;
+
+    if (! wantvs && ! lsame_(jobvs, "N")) {
+	*info = -1;
+    } else if (! wantst && ! lsame_(sort, "N")) {
+	*info = -2;
+    } else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && ! 
+	    wantsn) {
+	*info = -4;
+    } else if (*n < 0) {
+	*info = -5;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -7;
+    } else if (*ldvs < 1 || wantvs && *ldvs < *n) {
+	*info = -11;
+    }
+
+/*     Compute workspace */
+/*      (Note: Comments in the code beginning "Workspace:" describe the */
+/*       minimal amount of real workspace needed at that point in the */
+/*       code, as well as the preferred amount for good performance. */
+/*       CWorkspace refers to complex workspace, and RWorkspace to real */
+/*       workspace. NB refers to the optimal block size for the */
+/*       immediately following subroutine, as returned by ILAENV. */
+/*       HSWORK refers to the workspace preferred by CHSEQR, as */
+/*       calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
+/*       the worst case. */
+/*       If SENSE = 'E', 'V' or 'B', then the amount of workspace needed */
+/*       depends on SDIM, which is computed by the routine CTRSEN later */
+/*       in the code.) */
+
+    if (*info == 0) {
+	if (*n == 0) {
+	    minwrk = 1;
+	    lwrk = 1;
+	} else {
+	    maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &
+		    c__0, (ftnlen)6, (ftnlen)1);
+	    minwrk = *n << 1;
+
+	    chseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &w[1], &vs[
+		    vs_offset], ldvs, &work[1], &c_n1, &ieval);
+	    hswork = work[1].r;
+
+	    if (! wantvs) {
+		maxwrk = f2cmax(maxwrk,hswork);
+	    } else {
+/* Computing MAX */
+		i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
+			 " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
+		maxwrk = f2cmax(i__1,i__2);
+		maxwrk = f2cmax(maxwrk,hswork);
+	    }
+	    lwrk = maxwrk;
+	    if (! wantsn) {
+/* Computing MAX */
+		i__1 = lwrk, i__2 = *n * *n / 2;
+		lwrk = f2cmax(i__1,i__2);
+	    }
+	}
+	work[1].r = (real) lwrk, work[1].i = 0.f;
+
+	if (*lwork < minwrk && ! lquery) {
+	    *info = -15;
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEESX", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	*sdim = 0;
+	return 0;
+    }
+
+/*     Get machine constants */
+
+    eps = slamch_("P");
+    smlnum = slamch_("S");
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+    smlnum = sqrt(smlnum) / eps;
+    bignum = 1.f / smlnum;
+
+/*     Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
+
+    anrm = clange_("M", n, n, &a[a_offset], lda, dum);
+    scalea = FALSE_;
+    if (anrm > 0.f && anrm < smlnum) {
+	scalea = TRUE_;
+	cscale = smlnum;
+    } else if (anrm > bignum) {
+	scalea = TRUE_;
+	cscale = bignum;
+    }
+    if (scalea) {
+	clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
+		ierr);
+    }
+
+
+/*     Permute the matrix to make it more nearly triangular */
+/*     (CWorkspace: none) */
+/*     (RWorkspace: need N) */
+
+    ibal = 1;
+    cgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);
+
+/*     Reduce to upper Hessenberg form */
+/*     (CWorkspace: need 2*N, prefer N+N*NB) */
+/*     (RWorkspace: none) */
+
+    itau = 1;
+    iwrk = *n + itau;
+    i__1 = *lwork - iwrk + 1;
+    cgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
+	     &ierr);
+
+    if (wantvs) {
+
+/*        Copy Householder vectors to VS */
+
+	clacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
+		;
+
+/*        Generate unitary matrix in VS */
+/*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
+/*        (RWorkspace: none) */
+
+	i__1 = *lwork - iwrk + 1;
+	cunghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
+		 &i__1, &ierr);
+    }
+
+    *sdim = 0;
+
+/*     Perform QR iteration, accumulating Schur vectors in VS if desired */
+/*     (CWorkspace: need 1, prefer HSWORK (see comments) ) */
+/*     (RWorkspace: none) */
+
+    iwrk = itau;
+    i__1 = *lwork - iwrk + 1;
+    chseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vs[
+	    vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
+    if (ieval > 0) {
+	*info = ieval;
+    }
+
+/*     Sort eigenvalues if desired */
+
+    if (wantst && *info == 0) {
+	if (scalea) {
+	    clascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
+		    ierr);
+	}
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    bwork[i__] = (*select)(&w[i__]);
+/* L10: */
+	}
+
+/*        Reorder eigenvalues, transform Schur vectors, and compute */
+/*        reciprocal condition numbers */
+/*        (CWorkspace: if SENSE is not 'N', need 2*SDIM*(N-SDIM) */
+/*                     otherwise, need none ) */
+/*        (RWorkspace: none) */
+
+	i__1 = *lwork - iwrk + 1;
+	ctrsen_(sense, jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
+		 ldvs, &w[1], sdim, rconde, rcondv, &work[iwrk], &i__1, &
+		icond);
+	if (! wantsn) {
+/* Computing MAX */
+	    i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
+	    maxwrk = f2cmax(i__1,i__2);
+	}
+	if (icond == -14) {
+
+/*           Not enough complex workspace */
+
+	    *info = -15;
+	}
+    }
+
+    if (wantvs) {
+
+/*        Undo balancing */
+/*        (CWorkspace: none) */
+/*        (RWorkspace: need N) */
+
+	cgebak_("P", "R", n, &ilo, &ihi, &rwork[ibal], n, &vs[vs_offset], 
+		ldvs, &ierr);
+    }
+
+    if (scalea) {
+
+/*        Undo scaling for the Schur form of A */
+
+	clascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
+		ierr);
+	i__1 = *lda + 1;
+	ccopy_(n, &a[a_offset], &i__1, &w[1], &c__1);
+	if ((wantsv || wantsb) && *info == 0) {
+	    dum[0] = *rcondv;
+	    slascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &
+		    c__1, &ierr);
+	    *rcondv = dum[0];
+	}
+    }
+
+    work[1].r = (real) maxwrk, work[1].i = 0.f;
+    return 0;
+
+/*     End of CGEESX */
+
+} /* cgeesx_ */
+

lapack-netlib/SRC/cgeev.c

@@ -0,0 +1,994 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c__0 = 0;
+static integer c_n1 = -1;
+
+/* > \brief <b> CGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matr
+ices</b> */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEEV + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeev.f
+"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeev.f
+"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeev.f
+"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, */
+/*                         WORK, LWORK, RWORK, INFO ) */
+
+/*       CHARACTER          JOBVL, JOBVR */
+/*       INTEGER            INFO, LDA, LDVL, LDVR, LWORK, N */
+/*       REAL   RWORK( * ) */
+/*       COMPLEX         A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), */
+/*      $                   W( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEEV computes for an N-by-N complex nonsymmetric matrix A, the */
+/* > eigenvalues and, optionally, the left and/or right eigenvectors. */
+/* > */
+/* > The right eigenvector v(j) of A satisfies */
+/* >                  A * v(j) = lambda(j) * v(j) */
+/* > where lambda(j) is its eigenvalue. */
+/* > The left eigenvector u(j) of A satisfies */
+/* >               u(j)**H * A = lambda(j) * u(j)**H */
+/* > where u(j)**H denotes the conjugate transpose of u(j). */
+/* > */
+/* > The computed eigenvectors are normalized to have Euclidean norm */
+/* > equal to 1 and largest component real. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] JOBVL */
+/* > \verbatim */
+/* >          JOBVL is CHARACTER*1 */
+/* >          = 'N': left eigenvectors of A are not computed; */
+/* >          = 'V': left eigenvectors of are computed. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] JOBVR */
+/* > \verbatim */
+/* >          JOBVR is CHARACTER*1 */
+/* >          = 'N': right eigenvectors of A are not computed; */
+/* >          = 'V': right eigenvectors of A are computed. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A. N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the N-by-N matrix A. */
+/* >          On exit, A has been overwritten. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] W */
+/* > \verbatim */
+/* >          W is COMPLEX array, dimension (N) */
+/* >          W contains the computed eigenvalues. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] VL */
+/* > \verbatim */
+/* >          VL is COMPLEX array, dimension (LDVL,N) */
+/* >          If JOBVL = 'V', the left eigenvectors u(j) are stored one */
+/* >          after another in the columns of VL, in the same order */
+/* >          as their eigenvalues. */
+/* >          If JOBVL = 'N', VL is not referenced. */
+/* >          u(j) = VL(:,j), the j-th column of VL. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDVL */
+/* > \verbatim */
+/* >          LDVL is INTEGER */
+/* >          The leading dimension of the array VL.  LDVL >= 1; if */
+/* >          JOBVL = 'V', LDVL >= N. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] VR */
+/* > \verbatim */
+/* >          VR is COMPLEX array, dimension (LDVR,N) */
+/* >          If JOBVR = 'V', the right eigenvectors v(j) are stored one */
+/* >          after another in the columns of VR, in the same order */
+/* >          as their eigenvalues. */
+/* >          If JOBVR = 'N', VR is not referenced. */
+/* >          v(j) = VR(:,j), the j-th column of VR. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDVR */
+/* > \verbatim */
+/* >          LDVR is INTEGER */
+/* >          The leading dimension of the array VR.  LDVR >= 1; if */
+/* >          JOBVR = 'V', LDVR >= N. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,2*N). */
+/* >          For good performance, LWORK must generally be larger. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RWORK */
+/* > \verbatim */
+/* >          RWORK is REAL array, dimension (2*N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
+/* >          > 0:  if INFO = i, the QR algorithm failed to compute all the */
+/* >                eigenvalues, and no eigenvectors have been computed; */
+/* >                elements i+1:N of W contain eigenvalues which have */
+/* >                converged. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2016 */
+
+/*  @generated from zgeev.f, fortran z -> c, Tue Apr 19 01:47:44 2016 */
+
+/* > \ingroup complexGEeigen */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgeev_(char *jobvl, char *jobvr, integer *n, complex *a, 
+	integer *lda, complex *w, complex *vl, integer *ldvl, complex *vr, 
+	integer *ldvr, complex *work, integer *lwork, real *rwork, integer *
+	info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, 
+	    i__2, i__3;
+    real r__1, r__2;
+    complex q__1, q__2;
+
+    /* Local variables */
+    integer ibal;
+    char side[1];
+    real anrm;
+    integer ierr, itau, iwrk, nout, i__, k;
+    extern /* Subroutine */ int cscal_(integer *, complex *, complex *, 
+	    integer *);
+    extern logical lsame_(char *, char *);
+    extern real scnrm2_(integer *, complex *, integer *);
+    extern /* Subroutine */ int cgebak_(char *, char *, integer *, integer *, 
+	    integer *, real *, integer *, complex *, integer *, integer *), cgebal_(char *, integer *, complex *, integer *, 
+	    integer *, integer *, real *, integer *), slabad_(real *, 
+	    real *);
+    logical scalea;
+    extern real clange_(char *, integer *, integer *, complex *, integer *, 
+	    real *);
+    real cscale;
+    extern /* Subroutine */ int cgehrd_(integer *, integer *, integer *, 
+	    complex *, integer *, complex *, complex *, integer *, integer *),
+	     clascl_(char *, integer *, integer *, real *, real *, integer *, 
+	    integer *, complex *, integer *, integer *);
+    extern real slamch_(char *);
+    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
+	    *), clacpy_(char *, integer *, integer *, complex *, integer *, 
+	    complex *, integer *), xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    logical select[1];
+    real bignum;
+    extern integer isamax_(integer *, real *, integer *);
+    extern /* Subroutine */ int chseqr_(char *, char *, integer *, integer *, 
+	    integer *, complex *, integer *, complex *, complex *, integer *, 
+	    complex *, integer *, integer *), cunghr_(integer 
+	    *, integer *, integer *, complex *, integer *, complex *, complex 
+	    *, integer *, integer *);
+    integer minwrk, maxwrk;
+    logical wantvl;
+    real smlnum;
+    integer hswork, irwork;
+    logical lquery, wantvr;
+    extern /* Subroutine */ int ctrevc3_(char *, char *, logical *, integer *,
+	     complex *, integer *, complex *, integer *, complex *, integer *,
+	     integer *, integer *, complex *, integer *, real *, integer *, 
+	    integer *);
+    integer ihi;
+    real scl;
+    integer ilo;
+    real dum[1], eps;
+    complex tmp;
+    integer lwork_trevc__;
+
+
+/*  -- LAPACK driver routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --w;
+    vl_dim1 = *ldvl;
+    vl_offset = 1 + vl_dim1 * 1;
+    vl -= vl_offset;
+    vr_dim1 = *ldvr;
+    vr_offset = 1 + vr_dim1 * 1;
+    vr -= vr_offset;
+    --work;
+    --rwork;
+
+    /* Function Body */
+    *info = 0;
+    lquery = *lwork == -1;
+    wantvl = lsame_(jobvl, "V");
+    wantvr = lsame_(jobvr, "V");
+    if (! wantvl && ! lsame_(jobvl, "N")) {
+	*info = -1;
+    } else if (! wantvr && ! lsame_(jobvr, "N")) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -3;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -5;
+    } else if (*ldvl < 1 || wantvl && *ldvl < *n) {
+	*info = -8;
+    } else if (*ldvr < 1 || wantvr && *ldvr < *n) {
+	*info = -10;
+    }
+
+/*     Compute workspace */
+/*      (Note: Comments in the code beginning "Workspace:" describe the */
+/*       minimal amount of workspace needed at that point in the code, */
+/*       as well as the preferred amount for good performance. */
+/*       CWorkspace refers to complex workspace, and RWorkspace to real */
+/*       workspace. NB refers to the optimal block size for the */
+/*       immediately following subroutine, as returned by ILAENV. */
+/*       HSWORK refers to the workspace preferred by CHSEQR, as */
+/*       calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
+/*       the worst case.) */
+
+    if (*info == 0) {
+	if (*n == 0) {
+	    minwrk = 1;
+	    maxwrk = 1;
+	} else {
+	    maxwrk = *n + *n * ilaenv_(&c__1, "CGEHRD", " ", n, &c__1, n, &
+		    c__0, (ftnlen)6, (ftnlen)1);
+	    minwrk = *n << 1;
+	    if (wantvl) {
+/* Computing MAX */
+		i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
+			 " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
+		maxwrk = f2cmax(i__1,i__2);
+		ctrevc3_("L", "B", select, n, &a[a_offset], lda, &vl[
+			vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, &
+			work[1], &c_n1, &rwork[1], &c_n1, &ierr);
+		lwork_trevc__ = (integer) work[1].r;
+/* Computing MAX */
+		i__1 = maxwrk, i__2 = *n + lwork_trevc__;
+		maxwrk = f2cmax(i__1,i__2);
+		chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[
+			vl_offset], ldvl, &work[1], &c_n1, info);
+	    } else if (wantvr) {
+/* Computing MAX */
+		i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "CUNGHR",
+			 " ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
+		maxwrk = f2cmax(i__1,i__2);
+		ctrevc3_("R", "B", select, n, &a[a_offset], lda, &vl[
+			vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, &
+			work[1], &c_n1, &rwork[1], &c_n1, &ierr);
+		lwork_trevc__ = (integer) work[1].r;
+/* Computing MAX */
+		i__1 = maxwrk, i__2 = *n + lwork_trevc__;
+		maxwrk = f2cmax(i__1,i__2);
+		chseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[
+			vr_offset], ldvr, &work[1], &c_n1, info);
+	    } else {
+		chseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[
+			vr_offset], ldvr, &work[1], &c_n1, info);
+	    }
+	    hswork = (integer) work[1].r;
+/* Computing MAX */
+	    i__1 = f2cmax(maxwrk,hswork);
+	    maxwrk = f2cmax(i__1,minwrk);
+	}
+	work[1].r = (real) maxwrk, work[1].i = 0.f;
+
+	if (*lwork < minwrk && ! lquery) {
+	    *info = -12;
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEEV ", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+
+/*     Get machine constants */
+
+    eps = slamch_("P");
+    smlnum = slamch_("S");
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+    smlnum = sqrt(smlnum) / eps;
+    bignum = 1.f / smlnum;
+
+/*     Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
+
+    anrm = clange_("M", n, n, &a[a_offset], lda, dum);
+    scalea = FALSE_;
+    if (anrm > 0.f && anrm < smlnum) {
+	scalea = TRUE_;
+	cscale = smlnum;
+    } else if (anrm > bignum) {
+	scalea = TRUE_;
+	cscale = bignum;
+    }
+    if (scalea) {
+	clascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
+		ierr);
+    }
+
+/*     Balance the matrix */
+/*     (CWorkspace: none) */
+/*     (RWorkspace: need N) */
+
+    ibal = 1;
+    cgebal_("B", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);
+
+/*     Reduce to upper Hessenberg form */
+/*     (CWorkspace: need 2*N, prefer N+N*NB) */
+/*     (RWorkspace: none) */
+
+    itau = 1;
+    iwrk = itau + *n;
+    i__1 = *lwork - iwrk + 1;
+    cgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
+	     &ierr);
+
+    if (wantvl) {
+
+/*        Want left eigenvectors */
+/*        Copy Householder vectors to VL */
+
+	*(unsigned char *)side = 'L';
+	clacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
+		;
+
+/*        Generate unitary matrix in VL */
+/*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
+/*        (RWorkspace: none) */
+
+	i__1 = *lwork - iwrk + 1;
+	cunghr_(n, &ilo, &ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk],
+		 &i__1, &ierr);
+
+/*        Perform QR iteration, accumulating Schur vectors in VL */
+/*        (CWorkspace: need 1, prefer HSWORK (see comments) ) */
+/*        (RWorkspace: none) */
+
+	iwrk = itau;
+	i__1 = *lwork - iwrk + 1;
+	chseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vl[
+		vl_offset], ldvl, &work[iwrk], &i__1, info);
+
+	if (wantvr) {
+
+/*           Want left and right eigenvectors */
+/*           Copy Schur vectors to VR */
+
+	    *(unsigned char *)side = 'B';
+	    clacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
+	}
+
+    } else if (wantvr) {
+
+/*        Want right eigenvectors */
+/*        Copy Householder vectors to VR */
+
+	*(unsigned char *)side = 'R';
+	clacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
+		;
+
+/*        Generate unitary matrix in VR */
+/*        (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
+/*        (RWorkspace: none) */
+
+	i__1 = *lwork - iwrk + 1;
+	cunghr_(n, &ilo, &ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk],
+		 &i__1, &ierr);
+
+/*        Perform QR iteration, accumulating Schur vectors in VR */
+/*        (CWorkspace: need 1, prefer HSWORK (see comments) ) */
+/*        (RWorkspace: none) */
+
+	iwrk = itau;
+	i__1 = *lwork - iwrk + 1;
+	chseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vr[
+		vr_offset], ldvr, &work[iwrk], &i__1, info);
+
+    } else {
+
+/*        Compute eigenvalues only */
+/*        (CWorkspace: need 1, prefer HSWORK (see comments) ) */
+/*        (RWorkspace: none) */
+
+	iwrk = itau;
+	i__1 = *lwork - iwrk + 1;
+	chseqr_("E", "N", n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vr[
+		vr_offset], ldvr, &work[iwrk], &i__1, info);
+    }
+
+/*     If INFO .NE. 0 from CHSEQR, then quit */
+
+    if (*info != 0) {
+	goto L50;
+    }
+
+    if (wantvl || wantvr) {
+
+/*        Compute left and/or right eigenvectors */
+/*        (CWorkspace: need 2*N, prefer N + 2*N*NB) */
+/*        (RWorkspace: need 2*N) */
+
+	irwork = ibal + *n;
+	i__1 = *lwork - iwrk + 1;
+	ctrevc3_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], 
+		ldvl, &vr[vr_offset], ldvr, n, &nout, &work[iwrk], &i__1, &
+		rwork[irwork], n, &ierr);
+    }
+
+    if (wantvl) {
+
+/*        Undo balancing of left eigenvectors */
+/*        (CWorkspace: none) */
+/*        (RWorkspace: need N) */
+
+	cgebak_("B", "L", n, &ilo, &ihi, &rwork[ibal], n, &vl[vl_offset], 
+		ldvl, &ierr);
+
+/*        Normalize left eigenvectors and make largest component real */
+
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    scl = 1.f / scnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
+	    csscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
+	    i__2 = *n;
+	    for (k = 1; k <= i__2; ++k) {
+		i__3 = k + i__ * vl_dim1;
+/* Computing 2nd power */
+		r__1 = vl[i__3].r;
+/* Computing 2nd power */
+		r__2 = r_imag(&vl[k + i__ * vl_dim1]);
+		rwork[irwork + k - 1] = r__1 * r__1 + r__2 * r__2;
+/* L10: */
+	    }
+	    k = isamax_(n, &rwork[irwork], &c__1);
+	    r_cnjg(&q__2, &vl[k + i__ * vl_dim1]);
+	    r__1 = sqrt(rwork[irwork + k - 1]);
+	    q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
+	    tmp.r = q__1.r, tmp.i = q__1.i;
+	    cscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
+	    i__2 = k + i__ * vl_dim1;
+	    i__3 = k + i__ * vl_dim1;
+	    r__1 = vl[i__3].r;
+	    q__1.r = r__1, q__1.i = 0.f;
+	    vl[i__2].r = q__1.r, vl[i__2].i = q__1.i;
+/* L20: */
+	}
+    }
+
+    if (wantvr) {
+
+/*        Undo balancing of right eigenvectors */
+/*        (CWorkspace: none) */
+/*        (RWorkspace: need N) */
+
+	cgebak_("B", "R", n, &ilo, &ihi, &rwork[ibal], n, &vr[vr_offset], 
+		ldvr, &ierr);
+
+/*        Normalize right eigenvectors and make largest component real */
+
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    scl = 1.f / scnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
+	    csscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
+	    i__2 = *n;
+	    for (k = 1; k <= i__2; ++k) {
+		i__3 = k + i__ * vr_dim1;
+/* Computing 2nd power */
+		r__1 = vr[i__3].r;
+/* Computing 2nd power */
+		r__2 = r_imag(&vr[k + i__ * vr_dim1]);
+		rwork[irwork + k - 1] = r__1 * r__1 + r__2 * r__2;
+/* L30: */
+	    }
+	    k = isamax_(n, &rwork[irwork], &c__1);
+	    r_cnjg(&q__2, &vr[k + i__ * vr_dim1]);
+	    r__1 = sqrt(rwork[irwork + k - 1]);
+	    q__1.r = q__2.r / r__1, q__1.i = q__2.i / r__1;
+	    tmp.r = q__1.r, tmp.i = q__1.i;
+	    cscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
+	    i__2 = k + i__ * vr_dim1;
+	    i__3 = k + i__ * vr_dim1;
+	    r__1 = vr[i__3].r;
+	    q__1.r = r__1, q__1.i = 0.f;
+	    vr[i__2].r = q__1.r, vr[i__2].i = q__1.i;
+/* L40: */
+	}
+    }
+
+/*     Undo scaling if necessary */
+
+L50:
+    if (scalea) {
+	i__1 = *n - *info;
+/* Computing MAX */
+	i__3 = *n - *info;
+	i__2 = f2cmax(i__3,1);
+	clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1]
+		, &i__2, &ierr);
+	if (*info > 0) {
+	    i__1 = ilo - 1;
+	    clascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n,
+		     &ierr);
+	}
+    }
+
+    work[1].r = (real) maxwrk, work[1].i = 0.f;
+    return 0;
+
+/*     End of CGEEV */
+
+} /* cgeev_ */
+

lapack-netlib/SRC/cgehd2.c

@@ -0,0 +1,632 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* > \brief \b CGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm. 
+*/
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEHD2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgehd2.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgehd2.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgehd2.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO ) */
+
+/*       INTEGER            IHI, ILO, INFO, LDA, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEHD2 reduces a complex general matrix A to upper Hessenberg form H */
+/* > by a unitary similarity transformation:  Q**H * A * Q = H . */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] ILO */
+/* > \verbatim */
+/* >          ILO is INTEGER */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IHI */
+/* > \verbatim */
+/* >          IHI is INTEGER */
+/* > */
+/* >          It is assumed that A is already upper triangular in rows */
+/* >          and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
+/* >          set by a previous call to CGEBAL; otherwise they should be */
+/* >          set to 1 and N respectively. See Further Details. */
+/* >          1 <= ILO <= IHI <= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the n by n general matrix to be reduced. */
+/* >          On exit, the upper triangle and the first subdiagonal of A */
+/* >          are overwritten with the upper Hessenberg matrix H, and the */
+/* >          elements below the first subdiagonal, with the array TAU, */
+/* >          represent the unitary matrix Q as a product of elementary */
+/* >          reflectors. See Further Details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (N-1) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of (ihi-ilo) elementary */
+/* >  reflectors */
+/* > */
+/* >     Q = H(ilo) H(ilo+1) . . . H(ihi-1). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on */
+/* >  exit in A(i+2:ihi,i), and tau in TAU(i). */
+/* > */
+/* >  The contents of A are illustrated by the following example, with */
+/* >  n = 7, ilo = 2 and ihi = 6: */
+/* > */
+/* >  on entry,                        on exit, */
+/* > */
+/* >  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a ) */
+/* >  (     a   a   a   a   a   a )    (      a   h   h   h   h   a ) */
+/* >  (     a   a   a   a   a   a )    (      h   h   h   h   h   h ) */
+/* >  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h ) */
+/* >  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h ) */
+/* >  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h ) */
+/* >  (                         a )    (                          a ) */
+/* > */
+/* >  where a denotes an element of the original matrix A, h denotes a */
+/* >  modified element of the upper Hessenberg matrix H, and vi denotes an */
+/* >  element of the vector defining H(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgehd2_(integer *n, integer *ilo, integer *ihi, complex *
+	a, integer *lda, complex *tau, complex *work, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+    complex q__1;
+
+    /* Local variables */
+    integer i__;
+    complex alpha;
+    extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex *
+	    , integer *, complex *, complex *, integer *, complex *), 
+	    clarfg_(integer *, complex *, complex *, integer *, complex *), 
+	    xerbla_(char *, integer *, ftnlen);
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    if (*n < 0) {
+	*info = -1;
+    } else if (*ilo < 1 || *ilo > f2cmax(1,*n)) {
+	*info = -2;
+    } else if (*ihi < f2cmin(*ilo,*n) || *ihi > *n) {
+	*info = -3;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -5;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEHD2", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+    i__1 = *ihi - 1;
+    for (i__ = *ilo; i__ <= i__1; ++i__) {
+
+/*        Compute elementary reflector H(i) to annihilate A(i+2:ihi,i) */
+
+	i__2 = i__ + 1 + i__ * a_dim1;
+	alpha.r = a[i__2].r, alpha.i = a[i__2].i;
+	i__2 = *ihi - i__;
+/* Computing MIN */
+	i__3 = i__ + 2;
+	clarfg_(&i__2, &alpha, &a[f2cmin(i__3,*n) + i__ * a_dim1], &c__1, &tau[
+		i__]);
+	i__2 = i__ + 1 + i__ * a_dim1;
+	a[i__2].r = 1.f, a[i__2].i = 0.f;
+
+/*        Apply H(i) to A(1:ihi,i+1:ihi) from the right */
+
+	i__2 = *ihi - i__;
+	clarf_("Right", ihi, &i__2, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
+		i__], &a[(i__ + 1) * a_dim1 + 1], lda, &work[1]);
+
+/*        Apply H(i)**H to A(i+1:ihi,i+1:n) from the left */
+
+	i__2 = *ihi - i__;
+	i__3 = *n - i__;
+	r_cnjg(&q__1, &tau[i__]);
+	clarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &c__1, &q__1,
+		 &a[i__ + 1 + (i__ + 1) * a_dim1], lda, &work[1]);
+
+	i__2 = i__ + 1 + i__ * a_dim1;
+	a[i__2].r = alpha.r, a[i__2].i = alpha.i;
+/* L10: */
+    }
+
+    return 0;
+
+/*     End of CGEHD2 */
+
+} /* cgehd2_ */
+

lapack-netlib/SRC/cgehrd.c

@@ -0,0 +1,796 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b2 = {1.f,0.f};
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__3 = 3;
+static integer c__2 = 2;
+static integer c__65 = 65;
+
+/* > \brief \b CGEHRD */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEHRD + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgehrd.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgehrd.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgehrd.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) */
+
+/*       INTEGER            IHI, ILO, INFO, LDA, LWORK, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEHRD reduces a complex general matrix A to upper Hessenberg form H by */
+/* > an unitary similarity transformation:  Q**H * A * Q = H . */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] ILO */
+/* > \verbatim */
+/* >          ILO is INTEGER */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IHI */
+/* > \verbatim */
+/* >          IHI is INTEGER */
+/* > */
+/* >          It is assumed that A is already upper triangular in rows */
+/* >          and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
+/* >          set by a previous call to CGEBAL; otherwise they should be */
+/* >          set to 1 and N respectively. See Further Details. */
+/* >          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the N-by-N general matrix to be reduced. */
+/* >          On exit, the upper triangle and the first subdiagonal of A */
+/* >          are overwritten with the upper Hessenberg matrix H, and the */
+/* >          elements below the first subdiagonal, with the array TAU, */
+/* >          represent the unitary matrix Q as a product of elementary */
+/* >          reflectors. See Further Details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (N-1) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to */
+/* >          zero. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (LWORK) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The length of the array WORK.  LWORK >= f2cmax(1,N). */
+/* >          For good performance, LWORK should generally be larger. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of (ihi-ilo) elementary */
+/* >  reflectors */
+/* > */
+/* >     Q = H(ilo) H(ilo+1) . . . H(ihi-1). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on */
+/* >  exit in A(i+2:ihi,i), and tau in TAU(i). */
+/* > */
+/* >  The contents of A are illustrated by the following example, with */
+/* >  n = 7, ilo = 2 and ihi = 6: */
+/* > */
+/* >  on entry,                        on exit, */
+/* > */
+/* >  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a ) */
+/* >  (     a   a   a   a   a   a )    (      a   h   h   h   h   a ) */
+/* >  (     a   a   a   a   a   a )    (      h   h   h   h   h   h ) */
+/* >  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h ) */
+/* >  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h ) */
+/* >  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h ) */
+/* >  (                         a )    (                          a ) */
+/* > */
+/* >  where a denotes an element of the original matrix A, h denotes a */
+/* >  modified element of the upper Hessenberg matrix H, and vi denotes an */
+/* >  element of the vector defining H(i). */
+/* > */
+/* >  This file is a slight modification of LAPACK-3.0's DGEHRD */
+/* >  subroutine incorporating improvements proposed by Quintana-Orti and */
+/* >  Van de Geijn (2006). (See DLAHR2.) */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgehrd_(integer *n, integer *ilo, integer *ihi, complex *
+	a, integer *lda, complex *tau, complex *work, integer *lwork, integer 
+	*info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, j;
+    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
+	    integer *, complex *, complex *, integer *, complex *, integer *, 
+	    complex *, complex *, integer *);
+    integer nbmin, iinfo;
+    extern /* Subroutine */ int ctrmm_(char *, char *, char *, char *, 
+	    integer *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *), caxpy_(integer *, 
+	    complex *, complex *, integer *, complex *, integer *), cgehd2_(
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    complex *, integer *), clahr2_(integer *, integer *, integer *, 
+	    complex *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *);
+    integer ib;
+    complex ei;
+    integer nb, nh;
+    extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, 
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *);
+    integer nx;
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    integer ldwork, lwkopt;
+    logical lquery;
+    integer iwt;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    lquery = *lwork == -1;
+    if (*n < 0) {
+	*info = -1;
+    } else if (*ilo < 1 || *ilo > f2cmax(1,*n)) {
+	*info = -2;
+    } else if (*ihi < f2cmin(*ilo,*n) || *ihi > *n) {
+	*info = -3;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -5;
+    } else if (*lwork < f2cmax(1,*n) && ! lquery) {
+	*info = -8;
+    }
+
+    if (*info == 0) {
+
+/*        Compute the workspace requirements */
+
+/* Computing MIN */
+	i__1 = 64, i__2 = ilaenv_(&c__1, "CGEHRD", " ", n, ilo, ihi, &c_n1, (
+		ftnlen)6, (ftnlen)1);
+	nb = f2cmin(i__1,i__2);
+	lwkopt = *n * nb + 4160;
+	work[1].r = (real) lwkopt, work[1].i = 0.f;
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEHRD", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
+
+    i__1 = *ilo - 1;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	i__2 = i__;
+	tau[i__2].r = 0.f, tau[i__2].i = 0.f;
+/* L10: */
+    }
+    i__1 = *n - 1;
+    for (i__ = f2cmax(1,*ihi); i__ <= i__1; ++i__) {
+	i__2 = i__;
+	tau[i__2].r = 0.f, tau[i__2].i = 0.f;
+/* L20: */
+    }
+
+/*     Quick return if possible */
+
+    nh = *ihi - *ilo + 1;
+    if (nh <= 1) {
+	work[1].r = 1.f, work[1].i = 0.f;
+	return 0;
+    }
+
+/*     Determine the block size */
+
+/* Computing MIN */
+    i__1 = 64, i__2 = ilaenv_(&c__1, "CGEHRD", " ", n, ilo, ihi, &c_n1, (
+	    ftnlen)6, (ftnlen)1);
+    nb = f2cmin(i__1,i__2);
+    nbmin = 2;
+    if (nb > 1 && nb < nh) {
+
+/*        Determine when to cross over from blocked to unblocked code */
+/*        (last block is always handled by unblocked code) */
+
+/* Computing MAX */
+	i__1 = nb, i__2 = ilaenv_(&c__3, "CGEHRD", " ", n, ilo, ihi, &c_n1, (
+		ftnlen)6, (ftnlen)1);
+	nx = f2cmax(i__1,i__2);
+	if (nx < nh) {
+
+/*           Determine if workspace is large enough for blocked code */
+
+	    if (*lwork < *n * nb + 4160) {
+
+/*              Not enough workspace to use optimal NB:  determine the */
+/*              minimum value of NB, and reduce NB or force use of */
+/*              unblocked code */
+
+/* Computing MAX */
+		i__1 = 2, i__2 = ilaenv_(&c__2, "CGEHRD", " ", n, ilo, ihi, &
+			c_n1, (ftnlen)6, (ftnlen)1);
+		nbmin = f2cmax(i__1,i__2);
+		if (*lwork >= *n * nbmin + 4160) {
+		    nb = (*lwork - 4160) / *n;
+		} else {
+		    nb = 1;
+		}
+	    }
+	}
+    }
+    ldwork = *n;
+
+    if (nb < nbmin || nb >= nh) {
+
+/*        Use unblocked code below */
+
+	i__ = *ilo;
+
+    } else {
+
+/*        Use blocked code */
+
+	iwt = *n * nb + 1;
+	i__1 = *ihi - 1 - nx;
+	i__2 = nb;
+	for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+/* Computing MIN */
+	    i__3 = nb, i__4 = *ihi - i__;
+	    ib = f2cmin(i__3,i__4);
+
+/*           Reduce columns i:i+ib-1 to Hessenberg form, returning the */
+/*           matrices V and T of the block reflector H = I - V*T*V**H */
+/*           which performs the reduction, and also the matrix Y = A*V*T */
+
+	    clahr2_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], &
+		    work[iwt], &c__65, &work[1], &ldwork);
+
+/*           Apply the block reflector H to A(1:ihi,i+ib:ihi) from the */
+/*           right, computing  A := A - Y * V**H. V(i+ib,ib-1) must be set */
+/*           to 1 */
+
+	    i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
+	    ei.r = a[i__3].r, ei.i = a[i__3].i;
+	    i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
+	    a[i__3].r = 1.f, a[i__3].i = 0.f;
+	    i__3 = *ihi - i__ - ib + 1;
+	    q__1.r = -1.f, q__1.i = 0.f;
+	    cgemm_("No transpose", "Conjugate transpose", ihi, &i__3, &ib, &
+		    q__1, &work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda,
+		     &c_b2, &a[(i__ + ib) * a_dim1 + 1], lda);
+	    i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
+	    a[i__3].r = ei.r, a[i__3].i = ei.i;
+
+/*           Apply the block reflector H to A(1:i,i+1:i+ib-1) from the */
+/*           right */
+
+	    i__3 = ib - 1;
+	    ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", &i__, &
+		    i__3, &c_b2, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], &
+		    ldwork);
+	    i__3 = ib - 2;
+	    for (j = 0; j <= i__3; ++j) {
+		q__1.r = -1.f, q__1.i = 0.f;
+		caxpy_(&i__, &q__1, &work[ldwork * j + 1], &c__1, &a[(i__ + j 
+			+ 1) * a_dim1 + 1], &c__1);
+/* L30: */
+	    }
+
+/*           Apply the block reflector H to A(i+1:ihi,i+ib:n) from the */
+/*           left */
+
+	    i__3 = *ihi - i__;
+	    i__4 = *n - i__ - ib + 1;
+	    clarfb_("Left", "Conjugate transpose", "Forward", "Columnwise", &
+		    i__3, &i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, &work[
+		    iwt], &c__65, &a[i__ + 1 + (i__ + ib) * a_dim1], lda, &
+		    work[1], &ldwork);
+/* L40: */
+	}
+    }
+
+/*     Use unblocked code to reduce the rest of the matrix */
+
+    cgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
+    work[1].r = (real) lwkopt, work[1].i = 0.f;
+
+    return 0;
+
+/*     End of CGEHRD */
+
+} /* cgehrd_ */
+

lapack-netlib/SRC/cgelq.c

@@ -0,0 +1,745 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__2 = 2;
+
+/* > \brief \b CGELQ */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK, */
+/*                         INFO ) */
+
+/*       INTEGER           INFO, LDA, M, N, TSIZE, LWORK */
+/*       COMPLEX           A( LDA, * ), T( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGELQ computes an LQ factorization of a complex M-by-N matrix A: */
+/* > */
+/* >    A = ( L 0 ) *  Q */
+/* > */
+/* > where: */
+/* > */
+/* >    Q is a N-by-N orthogonal matrix; */
+/* >    L is a lower-triangular M-by-M matrix; */
+/* >    0 is a M-by-(N-M) zero matrix, if M < N. */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, the elements on and below the diagonal of the array */
+/* >          contain the M-by-f2cmin(M,N) lower trapezoidal matrix L */
+/* >          (L is lower triangular if M <= N); */
+/* >          the elements above the diagonal are used to store part of the */
+/* >          data structure to represent Q. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (MAX(5,TSIZE)) */
+/* >          On exit, if INFO = 0, T(1) returns optimal (or either minimal */
+/* >          or optimal, if query is assumed) TSIZE. See TSIZE for details. */
+/* >          Remaining T contains part of the data structure used to represent Q. */
+/* >          If one wants to apply or construct Q, then one needs to keep T */
+/* >          (in addition to A) and pass it to further subroutines. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] TSIZE */
+/* > \verbatim */
+/* >          TSIZE is INTEGER */
+/* >          If TSIZE >= 5, the dimension of the array T. */
+/* >          If TSIZE = -1 or -2, then a workspace query is assumed. The routine */
+/* >          only calculates the sizes of the T and WORK arrays, returns these */
+/* >          values as the first entries of the T and WORK arrays, and no error */
+/* >          message related to T or WORK is issued by XERBLA. */
+/* >          If TSIZE = -1, the routine calculates optimal size of T for the */
+/* >          optimum performance and returns this value in T(1). */
+/* >          If TSIZE = -2, the routine calculates minimal size of T and */
+/* >          returns this value in T(1). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          (workspace) COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal */
+/* >          or optimal, if query was assumed) LWORK. */
+/* >          See LWORK for details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK. */
+/* >          If LWORK = -1 or -2, then a workspace query is assumed. The routine */
+/* >          only calculates the sizes of the T and WORK arrays, returns these */
+/* >          values as the first entries of the T and WORK arrays, and no error */
+/* >          message related to T or WORK is issued by XERBLA. */
+/* >          If LWORK = -1, the routine calculates optimal size of WORK for the */
+/* >          optimal performance and returns this value in WORK(1). */
+/* >          If LWORK = -2, the routine calculates minimal size of WORK and */
+/* >          returns this value in WORK(1). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \par Further Details */
+/*  ==================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* > The goal of the interface is to give maximum freedom to the developers for */
+/* > creating any LQ factorization algorithm they wish. The triangular */
+/* > (trapezoidal) L has to be stored in the lower part of A. The lower part of A */
+/* > and the array T can be used to store any relevant information for applying or */
+/* > constructing the Q factor. The WORK array can safely be discarded after exit. */
+/* > */
+/* > Caution: One should not expect the sizes of T and WORK to be the same from one */
+/* > LAPACK implementation to the other, or even from one execution to the other. */
+/* > A workspace query (for T and WORK) is needed at each execution. However, */
+/* > for a given execution, the size of T and WORK are fixed and will not change */
+/* > from one query to the next. */
+/* > */
+/* > \endverbatim */
+/* > */
+/* > \par Further Details particular to this LAPACK implementation: */
+/*  ============================================================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* > These details are particular for this LAPACK implementation. Users should not */
+/* > take them for granted. These details may change in the future, and are not likely */
+/* > true for another LAPACK implementation. These details are relevant if one wants */
+/* > to try to understand the code. They are not part of the interface. */
+/* > */
+/* > In this version, */
+/* > */
+/* >          T(2): row block size (MB) */
+/* >          T(3): column block size (NB) */
+/* >          T(6:TSIZE): data structure needed for Q, computed by */
+/* >                           CLASWLQ or CGELQT */
+/* > */
+/* >  Depending on the matrix dimensions M and N, and row and column */
+/* >  block sizes MB and NB returned by ILAENV, CGELQ will use either */
+/* >  CLASWLQ (if the matrix is short-and-wide) or CGELQT to compute */
+/* >  the LQ factorization. */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgelq_(integer *m, integer *n, complex *a, integer *lda, 
+	complex *t, integer *tsize, complex *work, integer *lwork, integer *
+	info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2;
+
+    /* Local variables */
+    logical mint, minw;
+    integer lwmin, lwreq, lwopt, mb, nb, nblcks;
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    extern /* Subroutine */ int cgelqt_(integer *, integer *, integer *, 
+	    complex *, integer *, complex *, integer *, complex *, integer *);
+    logical lminws, lquery;
+    integer mintsz;
+    extern /* Subroutine */ int claswlq_(integer *, integer *, integer *, 
+	    integer *, complex *, integer *, complex *, integer *, complex *, 
+	    integer *, integer *);
+
+
+/*  -- LAPACK computational routine (version 3.9.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. -- */
+/*     November 2019 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --t;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+
+    lquery = *tsize == -1 || *tsize == -2 || *lwork == -1 || *lwork == -2;
+
+    mint = FALSE_;
+    minw = FALSE_;
+    if (*tsize == -2 || *lwork == -2) {
+	if (*tsize != -1) {
+	    mint = TRUE_;
+	}
+	if (*lwork != -1) {
+	    minw = TRUE_;
+	}
+    }
+
+/*     Determine the block size */
+
+    if (f2cmin(*m,*n) > 0) {
+	mb = ilaenv_(&c__1, "CGELQ ", " ", m, n, &c__1, &c_n1, (ftnlen)6, (
+		ftnlen)1);
+	nb = ilaenv_(&c__1, "CGELQ ", " ", m, n, &c__2, &c_n1, (ftnlen)6, (
+		ftnlen)1);
+    } else {
+	mb = 1;
+	nb = *n;
+    }
+    if (mb > f2cmin(*m,*n) || mb < 1) {
+	mb = 1;
+    }
+    if (nb > *n || nb <= *m) {
+	nb = *n;
+    }
+    mintsz = *m + 5;
+    if (nb > *m && *n > *m) {
+	if ((*n - *m) % (nb - *m) == 0) {
+	    nblcks = (*n - *m) / (nb - *m);
+	} else {
+	    nblcks = (*n - *m) / (nb - *m) + 1;
+	}
+    } else {
+	nblcks = 1;
+    }
+
+/*     Determine if the workspace size satisfies minimal size */
+
+    if (*n <= *m || nb <= *m || nb >= *n) {
+	lwmin = f2cmax(1,*n);
+/* Computing MAX */
+	i__1 = 1, i__2 = mb * *n;
+	lwopt = f2cmax(i__1,i__2);
+    } else {
+	lwmin = f2cmax(1,*m);
+/* Computing MAX */
+	i__1 = 1, i__2 = mb * *m;
+	lwopt = f2cmax(i__1,i__2);
+    }
+    lminws = FALSE_;
+/* Computing MAX */
+    i__1 = 1, i__2 = mb * *m * nblcks + 5;
+    if ((*tsize < f2cmax(i__1,i__2) || *lwork < lwopt) && *lwork >= lwmin && *
+	    tsize >= mintsz && ! lquery) {
+/* Computing MAX */
+	i__1 = 1, i__2 = mb * *m * nblcks + 5;
+	if (*tsize < f2cmax(i__1,i__2)) {
+	    lminws = TRUE_;
+	    mb = 1;
+	    nb = *n;
+	}
+	if (*lwork < lwopt) {
+	    lminws = TRUE_;
+	    mb = 1;
+	}
+    }
+    if (*n <= *m || nb <= *m || nb >= *n) {
+/* Computing MAX */
+	i__1 = 1, i__2 = mb * *n;
+	lwreq = f2cmax(i__1,i__2);
+    } else {
+/* Computing MAX */
+	i__1 = 1, i__2 = mb * *m;
+	lwreq = f2cmax(i__1,i__2);
+    }
+
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    } else /* if(complicated condition) */ {
+/* Computing MAX */
+	i__1 = 1, i__2 = mb * *m * nblcks + 5;
+	if (*tsize < f2cmax(i__1,i__2) && ! lquery && ! lminws) {
+	    *info = -6;
+	} else if (*lwork < lwreq && ! lquery && ! lminws) {
+	    *info = -8;
+	}
+    }
+
+    if (*info == 0) {
+	if (mint) {
+	    t[1].r = (real) mintsz, t[1].i = 0.f;
+	} else {
+	    i__1 = mb * *m * nblcks + 5;
+	    t[1].r = (real) i__1, t[1].i = 0.f;
+	}
+	t[2].r = (real) mb, t[2].i = 0.f;
+	t[3].r = (real) nb, t[3].i = 0.f;
+	if (minw) {
+	    work[1].r = (real) lwmin, work[1].i = 0.f;
+	} else {
+	    work[1].r = (real) lwreq, work[1].i = 0.f;
+	}
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGELQ", &i__1, (ftnlen)5);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (f2cmin(*m,*n) == 0) {
+	return 0;
+    }
+
+/*     The LQ Decomposition */
+
+    if (*n <= *m || nb <= *m || nb >= *n) {
+	cgelqt_(m, n, &mb, &a[a_offset], lda, &t[6], &mb, &work[1], info);
+    } else {
+	claswlq_(m, n, &mb, &nb, &a[a_offset], lda, &t[6], &mb, &work[1], 
+		lwork, info);
+    }
+
+    work[1].r = (real) lwreq, work[1].i = 0.f;
+
+    return 0;
+
+/*     End of CGELQ */
+
+} /* cgelq_ */
+

lapack-netlib/SRC/cgelq2.c

@@ -0,0 +1,605 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorit
+hm. */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGELQ2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgelq2.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgelq2.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgelq2.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGELQ2( M, N, A, LDA, TAU, WORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGELQ2 computes an LQ factorization of a complex m-by-n matrix A: */
+/* > */
+/* >    A = ( L 0 ) *  Q */
+/* > */
+/* > where: */
+/* > */
+/* >    Q is a n-by-n orthogonal matrix; */
+/* >    L is an lower-triangular m-by-m matrix; */
+/* >    0 is a m-by-(n-m) zero matrix, if m < n. */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the m by n matrix A. */
+/* >          On exit, the elements on and below the diagonal of the array */
+/* >          contain the m by f2cmin(m,n) lower trapezoidal matrix L (L is */
+/* >          lower triangular if m <= n); the elements above the diagonal, */
+/* >          with the array TAU, represent the unitary matrix Q as a */
+/* >          product of elementary reflectors (see Further Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (M) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date November 2019 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(k)**H . . . H(2)**H H(1)**H, where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in */
+/* >  A(i,i+1:n), and tau in TAU(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgelq2_(integer *m, integer *n, complex *a, integer *lda,
+	 complex *tau, complex *work, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+
+    /* Local variables */
+    integer i__, k;
+    complex alpha;
+    extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex *
+	    , integer *, complex *, complex *, integer *, complex *), 
+	    clarfg_(integer *, complex *, complex *, integer *, complex *), 
+	    clacgv_(integer *, complex *, integer *), xerbla_(char *, integer 
+	    *, ftnlen);
+
+
+/*  -- LAPACK computational routine (version 3.9.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     November 2019 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGELQ2", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+    k = f2cmin(*m,*n);
+
+    i__1 = k;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+
+/*        Generate elementary reflector H(i) to annihilate A(i,i+1:n) */
+
+	i__2 = *n - i__ + 1;
+	clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
+	i__2 = i__ + i__ * a_dim1;
+	alpha.r = a[i__2].r, alpha.i = a[i__2].i;
+	i__2 = *n - i__ + 1;
+/* Computing MIN */
+	i__3 = i__ + 1;
+	clarfg_(&i__2, &alpha, &a[i__ + f2cmin(i__3,*n) * a_dim1], lda, &tau[i__]
+		);
+	if (i__ < *m) {
+
+/*           Apply H(i) to A(i+1:m,i:n) from the right */
+
+	    i__2 = i__ + i__ * a_dim1;
+	    a[i__2].r = 1.f, a[i__2].i = 0.f;
+	    i__2 = *m - i__;
+	    i__3 = *n - i__ + 1;
+	    clarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[
+		    i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]);
+	}
+	i__2 = i__ + i__ * a_dim1;
+	a[i__2].r = alpha.r, a[i__2].i = alpha.i;
+	i__2 = *n - i__ + 1;
+	clacgv_(&i__2, &a[i__ + i__ * a_dim1], lda);
+/* L10: */
+    }
+    return 0;
+
+/*     End of CGELQ2 */
+
+} /* cgelq2_ */
+

lapack-netlib/SRC/cgelqf.c

@@ -0,0 +1,699 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__3 = 3;
+static integer c__2 = 2;
+
+/* > \brief \b CGELQF */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGELQF + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgelqf.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgelqf.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgelqf.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, LWORK, M, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGELQF computes an LQ factorization of a complex M-by-N matrix A: */
+/* > */
+/* >    A = ( L 0 ) *  Q */
+/* > */
+/* > where: */
+/* > */
+/* >    Q is a N-by-N orthogonal matrix; */
+/* >    L is an lower-triangular M-by-M matrix; */
+/* >    0 is a M-by-(N-M) zero matrix, if M < N. */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, the elements on and below the diagonal of the array */
+/* >          contain the m-by-f2cmin(m,n) lower trapezoidal matrix L (L is */
+/* >          lower triangular if m <= n); the elements above the diagonal, */
+/* >          with the array TAU, represent the unitary matrix Q as a */
+/* >          product of elementary reflectors (see Further Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,M). */
+/* >          For optimum performance LWORK >= M*NB, where NB is the */
+/* >          optimal blocksize. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date November 2019 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(k)**H . . . H(2)**H H(1)**H, where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in */
+/* >  A(i,i+1:n), and tau in TAU(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgelqf_(integer *m, integer *n, complex *a, integer *lda,
+	 complex *tau, complex *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+
+    /* Local variables */
+    integer i__, k, nbmin, iinfo;
+    extern /* Subroutine */ int cgelq2_(integer *, integer *, complex *, 
+	    integer *, complex *, complex *, integer *);
+    integer ib, nb;
+    extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, 
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *);
+    integer nx;
+    extern /* Subroutine */ int clarft_(char *, char *, integer *, integer *, 
+	    complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    integer ldwork, lwkopt;
+    logical lquery;
+    integer iws;
+
+
+/*  -- LAPACK computational routine (version 3.9.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     November 2019 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    nb = ilaenv_(&c__1, "CGELQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
+	    1);
+    lwkopt = *m * nb;
+    work[1].r = (real) lwkopt, work[1].i = 0.f;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    } else if (*lwork < f2cmax(1,*m) && ! lquery) {
+	*info = -7;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGELQF", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    k = f2cmin(*m,*n);
+    if (k == 0) {
+	work[1].r = 1.f, work[1].i = 0.f;
+	return 0;
+    }
+
+    nbmin = 2;
+    nx = 0;
+    iws = *m;
+    if (nb > 1 && nb < k) {
+
+/*        Determine when to cross over from blocked to unblocked code. */
+
+/* Computing MAX */
+	i__1 = 0, i__2 = ilaenv_(&c__3, "CGELQF", " ", m, n, &c_n1, &c_n1, (
+		ftnlen)6, (ftnlen)1);
+	nx = f2cmax(i__1,i__2);
+	if (nx < k) {
+
+/*           Determine if workspace is large enough for blocked code. */
+
+	    ldwork = *m;
+	    iws = ldwork * nb;
+	    if (*lwork < iws) {
+
+/*              Not enough workspace to use optimal NB:  reduce NB and */
+/*              determine the minimum value of NB. */
+
+		nb = *lwork / ldwork;
+/* Computing MAX */
+		i__1 = 2, i__2 = ilaenv_(&c__2, "CGELQF", " ", m, n, &c_n1, &
+			c_n1, (ftnlen)6, (ftnlen)1);
+		nbmin = f2cmax(i__1,i__2);
+	    }
+	}
+    }
+
+    if (nb >= nbmin && nb < k && nx < k) {
+
+/*        Use blocked code initially */
+
+	i__1 = k - nx;
+	i__2 = nb;
+	for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+/* Computing MIN */
+	    i__3 = k - i__ + 1;
+	    ib = f2cmin(i__3,nb);
+
+/*           Compute the LQ factorization of the current block */
+/*           A(i:i+ib-1,i:n) */
+
+	    i__3 = *n - i__ + 1;
+	    cgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
+		    1], &iinfo);
+	    if (i__ + ib <= *m) {
+
+/*              Form the triangular factor of the block reflector */
+/*              H = H(i) H(i+1) . . . H(i+ib-1) */
+
+		i__3 = *n - i__ + 1;
+		clarft_("Forward", "Rowwise", &i__3, &ib, &a[i__ + i__ * 
+			a_dim1], lda, &tau[i__], &work[1], &ldwork);
+
+/*              Apply H to A(i+ib:m,i:n) from the right */
+
+		i__3 = *m - i__ - ib + 1;
+		i__4 = *n - i__ + 1;
+		clarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3, 
+			&i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &
+			ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + 
+			1], &ldwork);
+	    }
+/* L10: */
+	}
+    } else {
+	i__ = 1;
+    }
+
+/*     Use unblocked code to factor the last or only block. */
+
+    if (i__ <= k) {
+	i__2 = *m - i__ + 1;
+	i__1 = *n - i__ + 1;
+	cgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
+		, &iinfo);
+    }
+
+    work[1].r = (real) iws, work[1].i = 0.f;
+    return 0;
+
+/*     End of CGELQF */
+
+} /* cgelqf_ */
+

lapack-netlib/SRC/cgelqt.c

@@ -0,0 +1,601 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGELQT */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGELQT( M, N, MB, A, LDA, T, LDT, WORK, INFO ) */
+
+/*       INTEGER INFO, LDA, LDT, M, N, MB */
+/*       COMPLEX A( LDA, * ), T( LDT, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGELQT computes a blocked LQ factorization of a complex M-by-N matrix A */
+/* > using the compact WY representation of Q. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] MB */
+/* > \verbatim */
+/* >          MB is INTEGER */
+/* >          The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, the elements on and below the diagonal of the array */
+/* >          contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is */
+/* >          lower triangular if M <= N); the elements above the diagonal */
+/* >          are the rows of V. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (LDT,MIN(M,N)) */
+/* >          The upper triangular block reflectors stored in compact form */
+/* >          as a sequence of upper triangular blocks.  See below */
+/* >          for further details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDT */
+/* > \verbatim */
+/* >          LDT is INTEGER */
+/* >          The leading dimension of the array T.  LDT >= MB. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MB*N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2017 */
+
+/* > \ingroup doubleGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix V stores the elementary reflectors H(i) in the i-th row */
+/* >  above the diagonal. For example, if M=5 and N=3, the matrix V is */
+/* > */
+/* >               V = (  1  v1 v1 v1 v1 ) */
+/* >                   (     1  v2 v2 v2 ) */
+/* >                   (         1 v3 v3 ) */
+/* > */
+/* > */
+/* >  where the vi's represent the vectors which define H(i), which are returned */
+/* >  in the matrix A.  The 1's along the diagonal of V are not stored in A. */
+/* >  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/MB), where each */
+/* >  block is of order MB except for the last block, which is of order */
+/* >  IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block */
+/* >  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB */
+/* >  for the last block) T's are stored in the MB-by-K matrix T as */
+/* > */
+/* >               T = (T1 T2 ... TB). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgelqt_(integer *m, integer *n, integer *mb, complex *a, 
+	integer *lda, complex *t, integer *ldt, complex *work, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4, i__5;
+
+    /* Local variables */
+    integer i__, k, iinfo, ib;
+    extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, 
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *, ftnlen), 
+	    cgelqt3_(integer *, integer *, complex *, integer *, complex *, 
+	    integer *, integer *);
+
+
+/*  -- LAPACK computational routine (version 3.7.1) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2017 */
+
+
+/* ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1 * 1;
+    t -= t_offset;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*mb < 1 || *mb > f2cmin(*m,*n) && f2cmin(*m,*n) > 0) {
+	*info = -3;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -5;
+    } else if (*ldt < *mb) {
+	*info = -7;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGELQT", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    k = f2cmin(*m,*n);
+    if (k == 0) {
+	return 0;
+    }
+
+/*     Blocked loop of length K */
+
+    i__1 = k;
+    i__2 = *mb;
+    for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+/* Computing MIN */
+	i__3 = k - i__ + 1;
+	ib = f2cmin(i__3,*mb);
+
+/*     Compute the LQ factorization of the current block A(I:M,I:I+IB-1) */
+
+	i__3 = *n - i__ + 1;
+	cgelqt3_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &t[i__ * t_dim1 + 1]
+		, ldt, &iinfo);
+	if (i__ + ib <= *m) {
+
+/*     Update by applying H**T to A(I:M,I+IB:N) from the right */
+
+	    i__3 = *m - i__ - ib + 1;
+	    i__4 = *n - i__ + 1;
+	    i__5 = *m - i__ - ib + 1;
+	    clarfb_("R", "N", "F", "R", &i__3, &i__4, &ib, &a[i__ + i__ * 
+		    a_dim1], lda, &t[i__ * t_dim1 + 1], ldt, &a[i__ + ib + 
+		    i__ * a_dim1], lda, &work[1], &i__5);
+	}
+    }
+    return 0;
+
+/*     End of CGELQT */
+
+} /* cgelqt_ */
+

lapack-netlib/SRC/cgelqt3.c

@@ -0,0 +1,676 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+
+/* > \brief \b CGELQT3 */
+
+/*  Definition: */
+/*  =========== */
+
+/*        SUBROUTINE CGELQT3( M, N, A, LDA, T, LDT, INFO ) */
+
+/*       INTEGER   INFO, LDA, M, N, LDT */
+/*       COMPLEX   A( LDA, * ), T( LDT, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGELQT3 recursively computes a LQ factorization of a complex M-by-N */
+/* > matrix A, using the compact WY representation of Q. */
+/* > */
+/* > Based on the algorithm of Elmroth and Gustavson, */
+/* > IBM J. Res. Develop. Vol 44 No. 4 July 2000. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M =< N. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the real M-by-N matrix A.  On exit, the elements on and */
+/* >          below the diagonal contain the N-by-N lower triangular matrix L; the */
+/* >          elements above the diagonal are the rows of V.  See below for */
+/* >          further details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (LDT,N) */
+/* >          The N-by-N upper triangular factor of the block reflector. */
+/* >          The elements on and above the diagonal contain the block */
+/* >          reflector T; the elements below the diagonal are not used. */
+/* >          See below for further details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDT */
+/* > \verbatim */
+/* >          LDT is INTEGER */
+/* >          The leading dimension of the array T.  LDT >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date November 2017 */
+
+/* > \ingroup doubleGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix V stores the elementary reflectors H(i) in the i-th row */
+/* >  above the diagonal. For example, if M=5 and N=3, the matrix V is */
+/* > */
+/* >               V = (  1  v1 v1 v1 v1 ) */
+/* >                   (     1  v2 v2 v2 ) */
+/* >                   (     1  v3 v3 v3 ) */
+/* > */
+/* > */
+/* >  where the vi's represent the vectors which define H(i), which are returned */
+/* >  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The */
+/* >  block reflector H is then given by */
+/* > */
+/* >               H = I - V * T * V**T */
+/* > */
+/* >  where V**T is the transpose of V. */
+/* > */
+/* >  For details of the algorithm, see Elmroth and Gustavson (cited above). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgelqt3_(integer *m, integer *n, complex *a, integer *
+	lda, complex *t, integer *ldt, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4, i__5;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, j;
+    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
+	    integer *, complex *, complex *, integer *, complex *, integer *, 
+	    complex *, complex *, integer *);
+    integer iinfo;
+    extern /* Subroutine */ int ctrmm_(char *, char *, char *, char *, 
+	    integer *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *);
+    integer i1, j1, m1, m2;
+    extern /* Subroutine */ int clarfg_(integer *, complex *, complex *, 
+	    integer *, complex *), xerbla_(char *, integer *, ftnlen);
+
+
+/*  -- LAPACK computational routine (version 3.8.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     November 2017 */
+
+
+/*  ===================================================================== */
+
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1 * 1;
+    t -= t_offset;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < *m) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    } else if (*ldt < f2cmax(1,*m)) {
+	*info = -6;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGELQT3", &i__1, (ftnlen)7);
+	return 0;
+    }
+
+    if (*m == 1) {
+
+/*        Compute Householder transform when N=1 */
+
+	clarfg_(n, &a[a_offset], &a[f2cmin(2,*n) * a_dim1 + 1], lda, &t[t_offset]
+		);
+	i__1 = t_dim1 + 1;
+	r_cnjg(&q__1, &t[t_dim1 + 1]);
+	t[i__1].r = q__1.r, t[i__1].i = q__1.i;
+
+    } else {
+
+/*        Otherwise, split A into blocks... */
+
+	m1 = *m / 2;
+	m2 = *m - m1;
+/* Computing MIN */
+	i__1 = m1 + 1;
+	i1 = f2cmin(i__1,*m);
+/* Computing MIN */
+	i__1 = *m + 1;
+	j1 = f2cmin(i__1,*n);
+
+/*        Compute A(1:M1,1:N) <- (Y1,R1,T1), where Q1 = I - Y1 T1 Y1^H */
+
+	cgelqt3_(&m1, n, &a[a_offset], lda, &t[t_offset], ldt, &iinfo);
+
+/*        Compute A(J1:M,1:N) =  A(J1:M,1:N) Q1^H [workspace: T(1:N1,J1:N)] */
+
+	i__1 = m2;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    i__2 = m1;
+	    for (j = 1; j <= i__2; ++j) {
+		i__3 = i__ + m1 + j * t_dim1;
+		i__4 = i__ + m1 + j * a_dim1;
+		t[i__3].r = a[i__4].r, t[i__3].i = a[i__4].i;
+	    }
+	}
+	ctrmm_("R", "U", "C", "U", &m2, &m1, &c_b1, &a[a_offset], lda, &t[i1 
+		+ t_dim1], ldt);
+
+	i__1 = *n - m1;
+	cgemm_("N", "C", &m2, &m1, &i__1, &c_b1, &a[i1 + i1 * a_dim1], lda, &
+		a[i1 * a_dim1 + 1], lda, &c_b1, &t[i1 + t_dim1], ldt);
+
+	ctrmm_("R", "U", "N", "N", &m2, &m1, &c_b1, &t[t_offset], ldt, &t[i1 
+		+ t_dim1], ldt);
+
+	i__1 = *n - m1;
+	q__1.r = -1.f, q__1.i = 0.f;
+	cgemm_("N", "N", &m2, &i__1, &m1, &q__1, &t[i1 + t_dim1], ldt, &a[i1 *
+		 a_dim1 + 1], lda, &c_b1, &a[i1 + i1 * a_dim1], lda);
+
+	ctrmm_("R", "U", "N", "U", &m2, &m1, &c_b1, &a[a_offset], lda, &t[i1 
+		+ t_dim1], ldt);
+
+	i__1 = m2;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    i__2 = m1;
+	    for (j = 1; j <= i__2; ++j) {
+		i__3 = i__ + m1 + j * a_dim1;
+		i__4 = i__ + m1 + j * a_dim1;
+		i__5 = i__ + m1 + j * t_dim1;
+		q__1.r = a[i__4].r - t[i__5].r, q__1.i = a[i__4].i - t[i__5]
+			.i;
+		a[i__3].r = q__1.r, a[i__3].i = q__1.i;
+		i__3 = i__ + m1 + j * t_dim1;
+		t[i__3].r = 0.f, t[i__3].i = 0.f;
+	    }
+	}
+
+/*        Compute A(J1:M,J1:N) <- (Y2,R2,T2) where Q2 = I - Y2 T2 Y2^H */
+
+	i__1 = *n - m1;
+	cgelqt3_(&m2, &i__1, &a[i1 + i1 * a_dim1], lda, &t[i1 + i1 * t_dim1], 
+		ldt, &iinfo);
+
+/*        Compute T3 = T(J1:N1,1:N) = -T1 Y1^H Y2 T2 */
+
+	i__1 = m2;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    i__2 = m1;
+	    for (j = 1; j <= i__2; ++j) {
+		i__3 = j + (i__ + m1) * t_dim1;
+		i__4 = j + (i__ + m1) * a_dim1;
+		t[i__3].r = a[i__4].r, t[i__3].i = a[i__4].i;
+	    }
+	}
+
+	ctrmm_("R", "U", "C", "U", &m1, &m2, &c_b1, &a[i1 + i1 * a_dim1], lda,
+		 &t[i1 * t_dim1 + 1], ldt);
+
+	i__1 = *n - *m;
+	cgemm_("N", "C", &m1, &m2, &i__1, &c_b1, &a[j1 * a_dim1 + 1], lda, &a[
+		i1 + j1 * a_dim1], lda, &c_b1, &t[i1 * t_dim1 + 1], ldt);
+
+	q__1.r = -1.f, q__1.i = 0.f;
+	ctrmm_("L", "U", "N", "N", &m1, &m2, &q__1, &t[t_offset], ldt, &t[i1 *
+		 t_dim1 + 1], ldt)
+		;
+
+	ctrmm_("R", "U", "N", "N", &m1, &m2, &c_b1, &t[i1 + i1 * t_dim1], ldt,
+		 &t[i1 * t_dim1 + 1], ldt);
+
+
+
+/*        Y = (Y1,Y2); L = [ L1            0  ];  T = [T1 T3] */
+/*                         [ A(1:N1,J1:N)  L2 ]       [ 0 T2] */
+
+    }
+
+    return 0;
+
+/*     End of CGELQT3 */
+
+} /* cgelqt3_ */
+

lapack-netlib/SRC/cgels.c

@@ -0,0 +1,961 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {0.f,0.f};
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__0 = 0;
+
+/* > \brief <b> CGELS solves overdetermined or underdetermined systems for GE matrices</b> */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGELS + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgels.f
+"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgels.f
+"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgels.f
+"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, */
+/*                         INFO ) */
+
+/*       CHARACTER          TRANS */
+/*       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS */
+/*       COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGELS solves overdetermined or underdetermined complex linear systems */
+/* > involving an M-by-N matrix A, or its conjugate-transpose, using a QR */
+/* > or LQ factorization of A.  It is assumed that A has full rank. */
+/* > */
+/* > The following options are provided: */
+/* > */
+/* > 1. If TRANS = 'N' and m >= n:  find the least squares solution of */
+/* >    an overdetermined system, i.e., solve the least squares problem */
+/* >                 minimize || B - A*X ||. */
+/* > */
+/* > 2. If TRANS = 'N' and m < n:  find the minimum norm solution of */
+/* >    an underdetermined system A * X = B. */
+/* > */
+/* > 3. If TRANS = 'C' and m >= n:  find the minimum norm solution of */
+/* >    an underdetermined system A**H * X = B. */
+/* > */
+/* > 4. If TRANS = 'C' and m < n:  find the least squares solution of */
+/* >    an overdetermined system, i.e., solve the least squares problem */
+/* >                 minimize || B - A**H * X ||. */
+/* > */
+/* > Several right hand side vectors b and solution vectors x can be */
+/* > handled in a single call; they are stored as the columns of the */
+/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
+/* > matrix X. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] TRANS */
+/* > \verbatim */
+/* >          TRANS is CHARACTER*1 */
+/* >          = 'N': the linear system involves A; */
+/* >          = 'C': the linear system involves A**H. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NRHS */
+/* > \verbatim */
+/* >          NRHS is INTEGER */
+/* >          The number of right hand sides, i.e., the number of */
+/* >          columns of the matrices B and X. NRHS >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >            if M >= N, A is overwritten by details of its QR */
+/* >                       factorization as returned by CGEQRF; */
+/* >            if M <  N, A is overwritten by details of its LQ */
+/* >                       factorization as returned by CGELQF. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] B */
+/* > \verbatim */
+/* >          B is COMPLEX array, dimension (LDB,NRHS) */
+/* >          On entry, the matrix B of right hand side vectors, stored */
+/* >          columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS */
+/* >          if TRANS = 'C'. */
+/* >          On exit, if INFO = 0, B is overwritten by the solution */
+/* >          vectors, stored columnwise: */
+/* >          if TRANS = 'N' and m >= n, rows 1 to n of B contain the least */
+/* >          squares solution vectors; the residual sum of squares for the */
+/* >          solution in each column is given by the sum of squares of the */
+/* >          modulus of elements N+1 to M in that column; */
+/* >          if TRANS = 'N' and m < n, rows 1 to N of B contain the */
+/* >          minimum norm solution vectors; */
+/* >          if TRANS = 'C' and m >= n, rows 1 to M of B contain the */
+/* >          minimum norm solution vectors; */
+/* >          if TRANS = 'C' and m < n, rows 1 to M of B contain the */
+/* >          least squares solution vectors; the residual sum of squares */
+/* >          for the solution in each column is given by the sum of */
+/* >          squares of the modulus of elements M+1 to N in that column. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDB */
+/* > \verbatim */
+/* >          LDB is INTEGER */
+/* >          The leading dimension of the array B. LDB >= MAX(1,M,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK. */
+/* >          LWORK >= f2cmax( 1, MN + f2cmax( MN, NRHS ) ). */
+/* >          For optimal performance, */
+/* >          LWORK >= f2cmax( 1, MN + f2cmax( MN, NRHS )*NB ). */
+/* >          where MN = f2cmin(M,N) and NB is the optimum block size. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO =  i, the i-th diagonal element of the */
+/* >                triangular factor of A is zero, so that A does not have */
+/* >                full rank; the least squares solution could not be */
+/* >                computed. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEsolve */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgels_(char *trans, integer *m, integer *n, integer *
+	nrhs, complex *a, integer *lda, complex *b, integer *ldb, complex *
+	work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
+    real r__1;
+
+    /* Local variables */
+    real anrm, bnrm;
+    integer brow;
+    logical tpsd;
+    integer i__, j, iascl, ibscl;
+    extern logical lsame_(char *, char *);
+    integer wsize;
+    real rwork[1];
+    integer nb;
+    extern /* Subroutine */ int slabad_(real *, real *);
+    extern real clange_(char *, integer *, integer *, complex *, integer *, 
+	    real *);
+    integer mn;
+    extern /* Subroutine */ int cgelqf_(integer *, integer *, complex *, 
+	    integer *, complex *, complex *, integer *, integer *), clascl_(
+	    char *, integer *, integer *, real *, real *, integer *, integer *
+	    , complex *, integer *, integer *);
+    extern real slamch_(char *);
+    extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *, 
+	    integer *, complex *, complex *, integer *, integer *), claset_(
+	    char *, integer *, integer *, complex *, complex *, complex *, 
+	    integer *), xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    integer scllen;
+    real bignum;
+    extern /* Subroutine */ int cunmlq_(char *, char *, integer *, integer *, 
+	    integer *, complex *, integer *, complex *, complex *, integer *, 
+	    complex *, integer *, integer *), cunmqr_(char *, 
+	    char *, integer *, integer *, integer *, complex *, integer *, 
+	    complex *, complex *, integer *, complex *, integer *, integer *);
+    real smlnum;
+    logical lquery;
+    extern /* Subroutine */ int ctrtrs_(char *, char *, char *, integer *, 
+	    integer *, complex *, integer *, complex *, integer *, integer *);
+
+
+/*  -- LAPACK driver routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1 * 1;
+    b -= b_offset;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    mn = f2cmin(*m,*n);
+    lquery = *lwork == -1;
+    if (! (lsame_(trans, "N") || lsame_(trans, "C"))) {
+	*info = -1;
+    } else if (*m < 0) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -3;
+    } else if (*nrhs < 0) {
+	*info = -4;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -6;
+    } else /* if(complicated condition) */ {
+/* Computing MAX */
+	i__1 = f2cmax(1,*m);
+	if (*ldb < f2cmax(i__1,*n)) {
+	    *info = -8;
+	} else /* if(complicated condition) */ {
+/* Computing MAX */
+	    i__1 = 1, i__2 = mn + f2cmax(mn,*nrhs);
+	    if (*lwork < f2cmax(i__1,i__2) && ! lquery) {
+		*info = -10;
+	    }
+	}
+    }
+
+/*     Figure out optimal block size */
+
+    if (*info == 0 || *info == -10) {
+
+	tpsd = TRUE_;
+	if (lsame_(trans, "N")) {
+	    tpsd = FALSE_;
+	}
+
+	if (*m >= *n) {
+	    nb = ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, 
+		    (ftnlen)1);
+	    if (tpsd) {
+/* Computing MAX */
+		i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMQR", "LN", m, nrhs, n, &
+			c_n1, (ftnlen)6, (ftnlen)2);
+		nb = f2cmax(i__1,i__2);
+	    } else {
+/* Computing MAX */
+		i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMQR", "LC", m, nrhs, n, &
+			c_n1, (ftnlen)6, (ftnlen)2);
+		nb = f2cmax(i__1,i__2);
+	    }
+	} else {
+	    nb = ilaenv_(&c__1, "CGELQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, 
+		    (ftnlen)1);
+	    if (tpsd) {
+/* Computing MAX */
+		i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMLQ", "LC", n, nrhs, m, &
+			c_n1, (ftnlen)6, (ftnlen)2);
+		nb = f2cmax(i__1,i__2);
+	    } else {
+/* Computing MAX */
+		i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMLQ", "LN", n, nrhs, m, &
+			c_n1, (ftnlen)6, (ftnlen)2);
+		nb = f2cmax(i__1,i__2);
+	    }
+	}
+
+/* Computing MAX */
+	i__1 = 1, i__2 = mn + f2cmax(mn,*nrhs) * nb;
+	wsize = f2cmax(i__1,i__2);
+	r__1 = (real) wsize;
+	work[1].r = r__1, work[1].i = 0.f;
+
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGELS ", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+/* Computing MIN */
+    i__1 = f2cmin(*m,*n);
+    if (f2cmin(i__1,*nrhs) == 0) {
+	i__1 = f2cmax(*m,*n);
+	claset_("Full", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
+	return 0;
+    }
+
+/*     Get machine parameters */
+
+    smlnum = slamch_("S") / slamch_("P");
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+
+/*     Scale A, B if f2cmax element outside range [SMLNUM,BIGNUM] */
+
+    anrm = clange_("M", m, n, &a[a_offset], lda, rwork);
+    iascl = 0;
+    if (anrm > 0.f && anrm < smlnum) {
+
+/*        Scale matrix norm up to SMLNUM */
+
+	clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
+		info);
+	iascl = 1;
+    } else if (anrm > bignum) {
+
+/*        Scale matrix norm down to BIGNUM */
+
+	clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
+		info);
+	iascl = 2;
+    } else if (anrm == 0.f) {
+
+/*        Matrix all zero. Return zero solution. */
+
+	i__1 = f2cmax(*m,*n);
+	claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
+	goto L50;
+    }
+
+    brow = *m;
+    if (tpsd) {
+	brow = *n;
+    }
+    bnrm = clange_("M", &brow, nrhs, &b[b_offset], ldb, rwork);
+    ibscl = 0;
+    if (bnrm > 0.f && bnrm < smlnum) {
+
+/*        Scale matrix norm up to SMLNUM */
+
+	clascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, nrhs, &b[b_offset], 
+		ldb, info);
+	ibscl = 1;
+    } else if (bnrm > bignum) {
+
+/*        Scale matrix norm down to BIGNUM */
+
+	clascl_("G", &c__0, &c__0, &bnrm, &bignum, &brow, nrhs, &b[b_offset], 
+		ldb, info);
+	ibscl = 2;
+    }
+
+    if (*m >= *n) {
+
+/*        compute QR factorization of A */
+
+	i__1 = *lwork - mn;
+	cgeqrf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
+		;
+
+/*        workspace at least N, optimally N*NB */
+
+	if (! tpsd) {
+
+/*           Least-Squares Problem f2cmin || A * X - B || */
+
+/*           B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS) */
+
+	    i__1 = *lwork - mn;
+	    cunmqr_("Left", "Conjugate transpose", m, nrhs, n, &a[a_offset], 
+		    lda, &work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, 
+		    info);
+
+/*           workspace at least NRHS, optimally NRHS*NB */
+
+/*           B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */
+
+	    ctrtrs_("Upper", "No transpose", "Non-unit", n, nrhs, &a[a_offset]
+		    , lda, &b[b_offset], ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+	    scllen = *n;
+
+	} else {
+
+/*           Underdetermined system of equations A**T * X = B */
+
+/*           B(1:N,1:NRHS) := inv(R**H) * B(1:N,1:NRHS) */
+
+	    ctrtrs_("Upper", "Conjugate transpose", "Non-unit", n, nrhs, &a[
+		    a_offset], lda, &b[b_offset], ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+/*           B(N+1:M,1:NRHS) = ZERO */
+
+	    i__1 = *nrhs;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = *n + 1; i__ <= i__2; ++i__) {
+		    i__3 = i__ + j * b_dim1;
+		    b[i__3].r = 0.f, b[i__3].i = 0.f;
+/* L10: */
+		}
+/* L20: */
+	    }
+
+/*           B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */
+
+	    i__1 = *lwork - mn;
+	    cunmqr_("Left", "No transpose", m, nrhs, n, &a[a_offset], lda, &
+		    work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
+
+/*           workspace at least NRHS, optimally NRHS*NB */
+
+	    scllen = *m;
+
+	}
+
+    } else {
+
+/*        Compute LQ factorization of A */
+
+	i__1 = *lwork - mn;
+	cgelqf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
+		;
+
+/*        workspace at least M, optimally M*NB. */
+
+	if (! tpsd) {
+
+/*           underdetermined system of equations A * X = B */
+
+/*           B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */
+
+	    ctrtrs_("Lower", "No transpose", "Non-unit", m, nrhs, &a[a_offset]
+		    , lda, &b[b_offset], ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+/*           B(M+1:N,1:NRHS) = 0 */
+
+	    i__1 = *nrhs;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *n;
+		for (i__ = *m + 1; i__ <= i__2; ++i__) {
+		    i__3 = i__ + j * b_dim1;
+		    b[i__3].r = 0.f, b[i__3].i = 0.f;
+/* L30: */
+		}
+/* L40: */
+	    }
+
+/*           B(1:N,1:NRHS) := Q(1:N,:)**H * B(1:M,1:NRHS) */
+
+	    i__1 = *lwork - mn;
+	    cunmlq_("Left", "Conjugate transpose", n, nrhs, m, &a[a_offset], 
+		    lda, &work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, 
+		    info);
+
+/*           workspace at least NRHS, optimally NRHS*NB */
+
+	    scllen = *n;
+
+	} else {
+
+/*           overdetermined system f2cmin || A**H * X - B || */
+
+/*           B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */
+
+	    i__1 = *lwork - mn;
+	    cunmlq_("Left", "No transpose", n, nrhs, m, &a[a_offset], lda, &
+		    work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
+
+/*           workspace at least NRHS, optimally NRHS*NB */
+
+/*           B(1:M,1:NRHS) := inv(L**H) * B(1:M,1:NRHS) */
+
+	    ctrtrs_("Lower", "Conjugate transpose", "Non-unit", m, nrhs, &a[
+		    a_offset], lda, &b[b_offset], ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+	    scllen = *m;
+
+	}
+
+    }
+
+/*     Undo scaling */
+
+    if (iascl == 1) {
+	clascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
+		, ldb, info);
+    } else if (iascl == 2) {
+	clascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
+		, ldb, info);
+    }
+    if (ibscl == 1) {
+	clascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
+		, ldb, info);
+    } else if (ibscl == 2) {
+	clascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
+		, ldb, info);
+    }
+
+L50:
+    r__1 = (real) wsize;
+    work[1].r = r__1, work[1].i = 0.f;
+
+    return 0;
+
+/*     End of CGELS */
+
+} /* cgels_ */
+

lapack-netlib/SRC/cgelsy.c

@@ -0,0 +1,966 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {0.f,0.f};
+static complex c_b2 = {1.f,0.f};
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__0 = 0;
+static integer c__2 = 2;
+
+/* > \brief <b> CGELSY solves overdetermined or underdetermined systems for GE matrices</b> */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGELSY + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgelsy.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgelsy.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgelsy.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, */
+/*                          WORK, LWORK, RWORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */
+/*       REAL               RCOND */
+/*       INTEGER            JPVT( * ) */
+/*       REAL               RWORK( * ) */
+/*       COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGELSY computes the minimum-norm solution to a complex linear least */
+/* > squares problem: */
+/* >     minimize || A * X - B || */
+/* > using a complete orthogonal factorization of A.  A is an M-by-N */
+/* > matrix which may be rank-deficient. */
+/* > */
+/* > Several right hand side vectors b and solution vectors x can be */
+/* > handled in a single call; they are stored as the columns of the */
+/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
+/* > matrix X. */
+/* > */
+/* > The routine first computes a QR factorization with column pivoting: */
+/* >     A * P = Q * [ R11 R12 ] */
+/* >                 [  0  R22 ] */
+/* > with R11 defined as the largest leading submatrix whose estimated */
+/* > condition number is less than 1/RCOND.  The order of R11, RANK, */
+/* > is the effective rank of A. */
+/* > */
+/* > Then, R22 is considered to be negligible, and R12 is annihilated */
+/* > by unitary transformations from the right, arriving at the */
+/* > complete orthogonal factorization: */
+/* >    A * P = Q * [ T11 0 ] * Z */
+/* >                [  0  0 ] */
+/* > The minimum-norm solution is then */
+/* >    X = P * Z**H [ inv(T11)*Q1**H*B ] */
+/* >                 [        0         ] */
+/* > where Q1 consists of the first RANK columns of Q. */
+/* > */
+/* > This routine is basically identical to the original xGELSX except */
+/* > three differences: */
+/* >   o The permutation of matrix B (the right hand side) is faster and */
+/* >     more simple. */
+/* >   o The call to the subroutine xGEQPF has been substituted by the */
+/* >     the call to the subroutine xGEQP3. This subroutine is a Blas-3 */
+/* >     version of the QR factorization with column pivoting. */
+/* >   o Matrix B (the right hand side) is updated with Blas-3. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NRHS */
+/* > \verbatim */
+/* >          NRHS is INTEGER */
+/* >          The number of right hand sides, i.e., the number of */
+/* >          columns of matrices B and X. NRHS >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, A has been overwritten by details of its */
+/* >          complete orthogonal factorization. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] B */
+/* > \verbatim */
+/* >          B is COMPLEX array, dimension (LDB,NRHS) */
+/* >          On entry, the M-by-NRHS right hand side matrix B. */
+/* >          On exit, the N-by-NRHS solution matrix X. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDB */
+/* > \verbatim */
+/* >          LDB is INTEGER */
+/* >          The leading dimension of the array B. LDB >= f2cmax(1,M,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] JPVT */
+/* > \verbatim */
+/* >          JPVT is INTEGER array, dimension (N) */
+/* >          On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted */
+/* >          to the front of AP, otherwise column i is a free column. */
+/* >          On exit, if JPVT(i) = k, then the i-th column of A*P */
+/* >          was the k-th column of A. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] RCOND */
+/* > \verbatim */
+/* >          RCOND is REAL */
+/* >          RCOND is used to determine the effective rank of A, which */
+/* >          is defined as the order of the largest leading triangular */
+/* >          submatrix R11 in the QR factorization with pivoting of A, */
+/* >          whose estimated condition number < 1/RCOND. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RANK */
+/* > \verbatim */
+/* >          RANK is INTEGER */
+/* >          The effective rank of A, i.e., the order of the submatrix */
+/* >          R11.  This is the same as the order of the submatrix T11 */
+/* >          in the complete orthogonal factorization of A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK. */
+/* >          The unblocked strategy requires that: */
+/* >            LWORK >= MN + MAX( 2*MN, N+1, MN+NRHS ) */
+/* >          where MN = f2cmin(M,N). */
+/* >          The block algorithm requires that: */
+/* >            LWORK >= MN + MAX( 2*MN, NB*(N+1), MN+MN*NB, MN+NB*NRHS ) */
+/* >          where NB is an upper bound on the blocksize returned */
+/* >          by ILAENV for the routines CGEQP3, CTZRZF, CTZRQF, CUNMQR, */
+/* >          and CUNMRZ. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RWORK */
+/* > \verbatim */
+/* >          RWORK is REAL array, dimension (2*N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEsolve */
+
+/* > \par Contributors: */
+/*  ================== */
+/* > */
+/* >    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA \n */
+/* >    E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n */
+/* >    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgelsy_(integer *m, integer *n, integer *nrhs, complex *
+	a, integer *lda, complex *b, integer *ldb, integer *jpvt, real *rcond,
+	 integer *rank, complex *work, integer *lwork, real *rwork, integer *
+	info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
+    real r__1, r__2;
+    complex q__1;
+
+    /* Local variables */
+    real anrm, bnrm, smin, smax;
+    integer i__, j, iascl, ibscl;
+    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
+	    complex *, integer *);
+    integer ismin, ismax;
+    complex c1, c2;
+    extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
+	    integer *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *), claic1_(integer *, 
+	    integer *, complex *, real *, complex *, complex *, real *, 
+	    complex *, complex *);
+    real wsize;
+    complex s1, s2;
+    extern /* Subroutine */ int cgeqp3_(integer *, integer *, complex *, 
+	    integer *, integer *, complex *, complex *, integer *, real *, 
+	    integer *);
+    integer nb;
+    extern /* Subroutine */ int slabad_(real *, real *);
+    extern real clange_(char *, integer *, integer *, complex *, integer *, 
+	    real *);
+    integer mn;
+    extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, 
+	    real *, integer *, integer *, complex *, integer *, integer *);
+    extern real slamch_(char *);
+    extern /* Subroutine */ int claset_(char *, integer *, integer *, complex 
+	    *, complex *, complex *, integer *), xerbla_(char *, 
+	    integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    real bignum;
+    integer nb1, nb2, nb3, nb4;
+    extern /* Subroutine */ int cunmqr_(char *, char *, integer *, integer *, 
+	    integer *, complex *, integer *, complex *, complex *, integer *, 
+	    complex *, integer *, integer *);
+    real sminpr, smaxpr, smlnum;
+    extern /* Subroutine */ int cunmrz_(char *, char *, integer *, integer *, 
+	    integer *, integer *, complex *, integer *, complex *, complex *, 
+	    integer *, complex *, integer *, integer *);
+    integer lwkopt;
+    logical lquery;
+    extern /* Subroutine */ int ctzrzf_(integer *, integer *, complex *, 
+	    integer *, complex *, complex *, integer *, integer *);
+
+
+/*  -- LAPACK driver routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1 * 1;
+    b -= b_offset;
+    --jpvt;
+    --work;
+    --rwork;
+
+    /* Function Body */
+    mn = f2cmin(*m,*n);
+    ismin = mn + 1;
+    ismax = (mn << 1) + 1;
+
+/*     Test the input arguments. */
+
+    *info = 0;
+    nb1 = ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
+	    ftnlen)1);
+    nb2 = ilaenv_(&c__1, "CGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
+	    ftnlen)1);
+    nb3 = ilaenv_(&c__1, "CUNMQR", " ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)
+	    1);
+    nb4 = ilaenv_(&c__1, "CUNMRQ", " ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)
+	    1);
+/* Computing MAX */
+    i__1 = f2cmax(nb1,nb2), i__1 = f2cmax(i__1,nb3);
+    nb = f2cmax(i__1,nb4);
+/* Computing MAX */
+    i__1 = 1, i__2 = mn + (*n << 1) + nb * (*n + 1), i__1 = f2cmax(i__1,i__2), 
+	    i__2 = (mn << 1) + nb * *nrhs;
+    lwkopt = f2cmax(i__1,i__2);
+    q__1.r = (real) lwkopt, q__1.i = 0.f;
+    work[1].r = q__1.r, work[1].i = q__1.i;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*nrhs < 0) {
+	*info = -3;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -5;
+    } else /* if(complicated condition) */ {
+/* Computing MAX */
+	i__1 = f2cmax(1,*m);
+	if (*ldb < f2cmax(i__1,*n)) {
+	    *info = -7;
+	} else /* if(complicated condition) */ {
+/* Computing MAX */
+	    i__1 = mn << 1, i__2 = *n + 1, i__1 = f2cmax(i__1,i__2), i__2 = mn + 
+		    *nrhs;
+	    if (*lwork < mn + f2cmax(i__1,i__2) && ! lquery) {
+		*info = -12;
+	    }
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGELSY", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+/* Computing MIN */
+    i__1 = f2cmin(*m,*n);
+    if (f2cmin(i__1,*nrhs) == 0) {
+	*rank = 0;
+	return 0;
+    }
+
+/*     Get machine parameters */
+
+    smlnum = slamch_("S") / slamch_("P");
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+
+/*     Scale A, B if f2cmax entries outside range [SMLNUM,BIGNUM] */
+
+    anrm = clange_("M", m, n, &a[a_offset], lda, &rwork[1]);
+    iascl = 0;
+    if (anrm > 0.f && anrm < smlnum) {
+
+/*        Scale matrix norm up to SMLNUM */
+
+	clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
+		info);
+	iascl = 1;
+    } else if (anrm > bignum) {
+
+/*        Scale matrix norm down to BIGNUM */
+
+	clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
+		info);
+	iascl = 2;
+    } else if (anrm == 0.f) {
+
+/*        Matrix all zero. Return zero solution. */
+
+	i__1 = f2cmax(*m,*n);
+	claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
+	*rank = 0;
+	goto L70;
+    }
+
+    bnrm = clange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1]);
+    ibscl = 0;
+    if (bnrm > 0.f && bnrm < smlnum) {
+
+/*        Scale matrix norm up to SMLNUM */
+
+	clascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
+		 info);
+	ibscl = 1;
+    } else if (bnrm > bignum) {
+
+/*        Scale matrix norm down to BIGNUM */
+
+	clascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
+		 info);
+	ibscl = 2;
+    }
+
+/*     Compute QR factorization with column pivoting of A: */
+/*        A * P = Q * R */
+
+    i__1 = *lwork - mn;
+    cgeqp3_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], &i__1,
+	     &rwork[1], info);
+    i__1 = mn + 1;
+    wsize = mn + work[i__1].r;
+
+/*     complex workspace: MN+NB*(N+1). real workspace 2*N. */
+/*     Details of Householder rotations stored in WORK(1:MN). */
+
+/*     Determine RANK using incremental condition estimation */
+
+    i__1 = ismin;
+    work[i__1].r = 1.f, work[i__1].i = 0.f;
+    i__1 = ismax;
+    work[i__1].r = 1.f, work[i__1].i = 0.f;
+    smax = c_abs(&a[a_dim1 + 1]);
+    smin = smax;
+    if (c_abs(&a[a_dim1 + 1]) == 0.f) {
+	*rank = 0;
+	i__1 = f2cmax(*m,*n);
+	claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
+	goto L70;
+    } else {
+	*rank = 1;
+    }
+
+L10:
+    if (*rank < mn) {
+	i__ = *rank + 1;
+	claic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[
+		i__ + i__ * a_dim1], &sminpr, &s1, &c1);
+	claic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[
+		i__ + i__ * a_dim1], &smaxpr, &s2, &c2);
+
+	if (smaxpr * *rcond <= sminpr) {
+	    i__1 = *rank;
+	    for (i__ = 1; i__ <= i__1; ++i__) {
+		i__2 = ismin + i__ - 1;
+		i__3 = ismin + i__ - 1;
+		q__1.r = s1.r * work[i__3].r - s1.i * work[i__3].i, q__1.i = 
+			s1.r * work[i__3].i + s1.i * work[i__3].r;
+		work[i__2].r = q__1.r, work[i__2].i = q__1.i;
+		i__2 = ismax + i__ - 1;
+		i__3 = ismax + i__ - 1;
+		q__1.r = s2.r * work[i__3].r - s2.i * work[i__3].i, q__1.i = 
+			s2.r * work[i__3].i + s2.i * work[i__3].r;
+		work[i__2].r = q__1.r, work[i__2].i = q__1.i;
+/* L20: */
+	    }
+	    i__1 = ismin + *rank;
+	    work[i__1].r = c1.r, work[i__1].i = c1.i;
+	    i__1 = ismax + *rank;
+	    work[i__1].r = c2.r, work[i__1].i = c2.i;
+	    smin = sminpr;
+	    smax = smaxpr;
+	    ++(*rank);
+	    goto L10;
+	}
+    }
+
+/*     complex workspace: 3*MN. */
+
+/*     Logically partition R = [ R11 R12 ] */
+/*                             [  0  R22 ] */
+/*     where R11 = R(1:RANK,1:RANK) */
+
+/*     [R11,R12] = [ T11, 0 ] * Y */
+
+    if (*rank < *n) {
+	i__1 = *lwork - (mn << 1);
+	ctzrzf_(rank, n, &a[a_offset], lda, &work[mn + 1], &work[(mn << 1) + 
+		1], &i__1, info);
+    }
+
+/*     complex workspace: 2*MN. */
+/*     Details of Householder rotations stored in WORK(MN+1:2*MN) */
+
+/*     B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS) */
+
+    i__1 = *lwork - (mn << 1);
+    cunmqr_("Left", "Conjugate transpose", m, nrhs, &mn, &a[a_offset], lda, &
+	    work[1], &b[b_offset], ldb, &work[(mn << 1) + 1], &i__1, info);
+/* Computing MAX */
+    i__1 = (mn << 1) + 1;
+    r__1 = wsize, r__2 = (mn << 1) + work[i__1].r;
+    wsize = f2cmax(r__1,r__2);
+
+/*     complex workspace: 2*MN+NB*NRHS. */
+
+/*     B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
+
+    ctrsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b2, &a[
+	    a_offset], lda, &b[b_offset], ldb);
+
+    i__1 = *nrhs;
+    for (j = 1; j <= i__1; ++j) {
+	i__2 = *n;
+	for (i__ = *rank + 1; i__ <= i__2; ++i__) {
+	    i__3 = i__ + j * b_dim1;
+	    b[i__3].r = 0.f, b[i__3].i = 0.f;
+/* L30: */
+	}
+/* L40: */
+    }
+
+/*     B(1:N,1:NRHS) := Y**H * B(1:N,1:NRHS) */
+
+    if (*rank < *n) {
+	i__1 = *n - *rank;
+	i__2 = *lwork - (mn << 1);
+	cunmrz_("Left", "Conjugate transpose", n, nrhs, rank, &i__1, &a[
+		a_offset], lda, &work[mn + 1], &b[b_offset], ldb, &work[(mn <<
+		 1) + 1], &i__2, info);
+    }
+
+/*     complex workspace: 2*MN+NRHS. */
+
+/*     B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
+
+    i__1 = *nrhs;
+    for (j = 1; j <= i__1; ++j) {
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    i__3 = jpvt[i__];
+	    i__4 = i__ + j * b_dim1;
+	    work[i__3].r = b[i__4].r, work[i__3].i = b[i__4].i;
+/* L50: */
+	}
+	ccopy_(n, &work[1], &c__1, &b[j * b_dim1 + 1], &c__1);
+/* L60: */
+    }
+
+/*     complex workspace: N. */
+
+/*     Undo scaling */
+
+    if (iascl == 1) {
+	clascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
+		 info);
+	clascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset], 
+		lda, info);
+    } else if (iascl == 2) {
+	clascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
+		 info);
+	clascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset], 
+		lda, info);
+    }
+    if (ibscl == 1) {
+	clascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
+		 info);
+    } else if (ibscl == 2) {
+	clascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
+		 info);
+    }
+
+L70:
+    q__1.r = (real) lwkopt, q__1.i = 0.f;
+    work[1].r = q__1.r, work[1].i = q__1.i;
+
+    return 0;
+
+/*     End of CGELSY */
+
+} /* cgelsy_ */
+

lapack-netlib/SRC/cgemlq.c

@@ -0,0 +1,686 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGEMLQ */
+
+/*  Definition: */
+/*  =========== */
+
+/*      SUBROUTINE CGEMLQ( SIDE, TRANS, M, N, K, A, LDA, T, */
+/*     $                   TSIZE, C, LDC, WORK, LWORK, INFO ) */
+
+
+/*     CHARACTER         SIDE, TRANS */
+/*     INTEGER           INFO, LDA, M, N, K, LDT, TSIZE, LWORK, LDC */
+/*     COMPLEX           A( LDA, * ), T( * ), C(LDC, * ), WORK( * ) */
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* >     CGEMLQ overwrites the general real M-by-N matrix C with */
+/* > */
+/* >                      SIDE = 'L'     SIDE = 'R' */
+/* >      TRANS = 'N':      Q * C          C * Q */
+/* >      TRANS = 'C':      Q**H * C       C * Q**H */
+/* >      where Q is a complex unitary matrix defined as the product */
+/* >      of blocked elementary reflectors computed by short wide */
+/* >      LQ factorization (CGELQ) */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] SIDE */
+/* > \verbatim */
+/* >          SIDE is CHARACTER*1 */
+/* >          = 'L': apply Q or Q**T from the Left; */
+/* >          = 'R': apply Q or Q**T from the Right. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] TRANS */
+/* > \verbatim */
+/* >          TRANS is CHARACTER*1 */
+/* >          = 'N':  No transpose, apply Q; */
+/* >          = 'T':  Transpose, apply Q**T. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >=0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix C. N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] K */
+/* > \verbatim */
+/* >          K is INTEGER */
+/* >          The number of elementary reflectors whose product defines */
+/* >          the matrix Q. */
+/* >          If SIDE = 'L', M >= K >= 0; */
+/* >          if SIDE = 'R', N >= K >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension */
+/* >                               (LDA,M) if SIDE = 'L', */
+/* >                               (LDA,N) if SIDE = 'R' */
+/* >          Part of the data structure to represent Q as returned by CGELQ. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A. LDA >= f2cmax(1,K). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (MAX(5,TSIZE)). */
+/* >          Part of the data structure to represent Q as returned by CGELQ. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] TSIZE */
+/* > \verbatim */
+/* >          TSIZE is INTEGER */
+/* >          The dimension of the array T. TSIZE >= 5. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] C */
+/* > \verbatim */
+/* >          C is COMPLEX array, dimension (LDC,N) */
+/* >          On entry, the M-by-N matrix C. */
+/* >          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDC */
+/* > \verbatim */
+/* >          LDC is INTEGER */
+/* >          The leading dimension of the array C. LDC >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >         (workspace) COMPLEX array, dimension (MAX(1,LWORK)) */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK. */
+/* >          If LWORK = -1, then a workspace query is assumed. The routine */
+/* >          only calculates the size of the WORK array, returns this */
+/* >          value as WORK(1), and no error message related to WORK */
+/* >          is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \par Further Details */
+/*  ==================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* > These details are particular for this LAPACK implementation. Users should not */
+/* > take them for granted. These details may change in the future, and are not likely */
+/* > true for another LAPACK implementation. These details are relevant if one wants */
+/* > to try to understand the code. They are not part of the interface. */
+/* > */
+/* > In this version, */
+/* > */
+/* >          T(2): row block size (MB) */
+/* >          T(3): column block size (NB) */
+/* >          T(6:TSIZE): data structure needed for Q, computed by */
+/* >                           CLASWQR or CGELQT */
+/* > */
+/* >  Depending on the matrix dimensions M and N, and row and column */
+/* >  block sizes MB and NB returned by ILAENV, CGELQ will use either */
+/* >  CLASWLQ (if the matrix is wide-and-short) or CGELQT to compute */
+/* >  the LQ factorization. */
+/* >  This version of CGEMLQ will use either CLAMSWLQ or CGEMLQT to */
+/* >  multiply matrix Q by another matrix. */
+/* >  Further Details in CLAMSWLQ or CGEMLQT. */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgemlq_(char *side, char *trans, integer *m, integer *n, 
+	integer *k, complex *a, integer *lda, complex *t, integer *tsize, 
+	complex *c__, integer *ldc, complex *work, integer *lwork, integer *
+	info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, c_dim1, c_offset, i__1;
+    real r__1;
+
+    /* Local variables */
+    logical left, tran;
+    extern /* Subroutine */ int clamswlq_(char *, char *, integer *, integer *
+	    , integer *, integer *, integer *, complex *, integer *, complex *
+	    , integer *, complex *, integer *, complex *, integer *, integer *
+	    );
+    extern logical lsame_(char *, char *);
+    logical right;
+    integer mb, nb, mn, lw, nblcks;
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    logical notran, lquery;
+    extern /* Subroutine */ int cgemlqt_(char *, char *, integer *, integer *,
+	     integer *, integer *, complex *, integer *, complex *, integer *,
+	     complex *, integer *, complex *, integer *);
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/* ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --t;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1 * 1;
+    c__ -= c_offset;
+    --work;
+
+    /* Function Body */
+    lquery = *lwork == -1;
+    notran = lsame_(trans, "N");
+    tran = lsame_(trans, "C");
+    left = lsame_(side, "L");
+    right = lsame_(side, "R");
+
+    mb = (integer) t[2].r;
+    nb = (integer) t[3].r;
+    if (left) {
+	lw = *n * mb;
+	mn = *m;
+    } else {
+	lw = *m * mb;
+	mn = *n;
+    }
+
+    if (nb > *k && mn > *k) {
+	if ((mn - *k) % (nb - *k) == 0) {
+	    nblcks = (mn - *k) / (nb - *k);
+	} else {
+	    nblcks = (mn - *k) / (nb - *k) + 1;
+	}
+    } else {
+	nblcks = 1;
+    }
+
+    *info = 0;
+    if (! left && ! right) {
+	*info = -1;
+    } else if (! tran && ! notran) {
+	*info = -2;
+    } else if (*m < 0) {
+	*info = -3;
+    } else if (*n < 0) {
+	*info = -4;
+    } else if (*k < 0 || *k > mn) {
+	*info = -5;
+    } else if (*lda < f2cmax(1,*k)) {
+	*info = -7;
+    } else if (*tsize < 5) {
+	*info = -9;
+    } else if (*ldc < f2cmax(1,*m)) {
+	*info = -11;
+    } else if (*lwork < f2cmax(1,lw) && ! lquery) {
+	*info = -13;
+    }
+
+    if (*info == 0) {
+	r__1 = (real) lw;
+	work[1].r = r__1, work[1].i = 0.f;
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEMLQ", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+/* Computing MIN */
+    i__1 = f2cmin(*m,*n);
+    if (f2cmin(i__1,*k) == 0) {
+	return 0;
+    }
+
+/* Computing MAX */
+    i__1 = f2cmax(*m,*n);
+    if (left && *m <= *k || right && *n <= *k || nb <= *k || nb >= f2cmax(i__1,*
+	    k)) {
+	cgemlqt_(side, trans, m, n, k, &mb, &a[a_offset], lda, &t[6], &mb, &
+		c__[c_offset], ldc, &work[1], info);
+    } else {
+	clamswlq_(side, trans, m, n, k, &mb, &nb, &a[a_offset], lda, &t[6], &
+		mb, &c__[c_offset], ldc, &work[1], lwork, info);
+    }
+
+    r__1 = (real) lw;
+    work[1].r = r__1, work[1].i = 0.f;
+
+    return 0;
+
+/*     End of CGEMLQ */
+
+} /* cgemlq_ */
+

lapack-netlib/SRC/cgemlqt.c

@@ -0,0 +1,687 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGEMLQT */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEMLQT( SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, */
+/*                          C, LDC, WORK, INFO ) */
+
+/*       CHARACTER SIDE, TRANS */
+/*       INTEGER   INFO, K, LDV, LDC, M, N, MB, LDT */
+/*       COMPLEX V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEMLQT overwrites the general real M-by-N matrix C with */
+/* > */
+/* >                 SIDE = 'L'     SIDE = 'R' */
+/* > TRANS = 'N':      Q C            C Q */
+/* > TRANS = 'C':   Q**H C            C Q**H */
+/* > */
+/* > where Q is a complex orthogonal matrix defined as the product of K */
+/* > elementary reflectors: */
+/* > */
+/* >       Q = H(1) H(2) . . . H(K) = I - V T V**H */
+/* > */
+/* > generated using the compact WY representation as returned by CGELQT. */
+/* > */
+/* > Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] SIDE */
+/* > \verbatim */
+/* >          SIDE is CHARACTER*1 */
+/* >          = 'L': apply Q or Q**H from the Left; */
+/* >          = 'R': apply Q or Q**H from the Right. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] TRANS */
+/* > \verbatim */
+/* >          TRANS is CHARACTER*1 */
+/* >          = 'N':  No transpose, apply Q; */
+/* >          = 'C':  Transpose, apply Q**H. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix C. M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix C. N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] K */
+/* > \verbatim */
+/* >          K is INTEGER */
+/* >          The number of elementary reflectors whose product defines */
+/* >          the matrix Q. */
+/* >          If SIDE = 'L', M >= K >= 0; */
+/* >          if SIDE = 'R', N >= K >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] MB */
+/* > \verbatim */
+/* >          MB is INTEGER */
+/* >          The block size used for the storage of T.  K >= MB >= 1. */
+/* >          This must be the same value of MB used to generate T */
+/* >          in DGELQT. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] V */
+/* > \verbatim */
+/* >          V is COMPLEX array, dimension */
+/* >                               (LDV,M) if SIDE = 'L', */
+/* >                               (LDV,N) if SIDE = 'R' */
+/* >          The i-th row must contain the vector which defines the */
+/* >          elementary reflector H(i), for i = 1,2,...,k, as returned by */
+/* >          DGELQT in the first K rows of its array argument A. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDV */
+/* > \verbatim */
+/* >          LDV is INTEGER */
+/* >          The leading dimension of the array V. LDV >= f2cmax(1,K). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (LDT,K) */
+/* >          The upper triangular factors of the block reflectors */
+/* >          as returned by DGELQT, stored as a MB-by-K matrix. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDT */
+/* > \verbatim */
+/* >          LDT is INTEGER */
+/* >          The leading dimension of the array T.  LDT >= MB. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] C */
+/* > \verbatim */
+/* >          C is COMPLEX array, dimension (LDC,N) */
+/* >          On entry, the M-by-N matrix C. */
+/* >          On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDC */
+/* > \verbatim */
+/* >          LDC is INTEGER */
+/* >          The leading dimension of the array C. LDC >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array. The dimension of */
+/* >          WORK is N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date November 2017 */
+
+/* > \ingroup doubleGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgemlqt_(char *side, char *trans, integer *m, integer *n,
+	 integer *k, integer *mb, complex *v, integer *ldv, complex *t, 
+	integer *ldt, complex *c__, integer *ldc, complex *work, integer *
+	info)
+{
+    /* System generated locals */
+    integer v_dim1, v_offset, c_dim1, c_offset, t_dim1, t_offset, i__1, i__2, 
+	    i__3, i__4;
+
+    /* Local variables */
+    logical left, tran;
+    integer i__;
+    extern logical lsame_(char *, char *);
+    logical right;
+    integer ib, kf;
+    extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, 
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *, ftnlen);
+    logical notran;
+    integer ldwork;
+
+
+/*  -- LAPACK computational routine (version 3.8.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     November 2017 */
+
+
+/*  ===================================================================== */
+
+
+
+    /* Parameter adjustments */
+    v_dim1 = *ldv;
+    v_offset = 1 + v_dim1 * 1;
+    v -= v_offset;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1 * 1;
+    t -= t_offset;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1 * 1;
+    c__ -= c_offset;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    left = lsame_(side, "L");
+    right = lsame_(side, "R");
+    tran = lsame_(trans, "C");
+    notran = lsame_(trans, "N");
+
+    if (left) {
+	ldwork = f2cmax(1,*n);
+    } else if (right) {
+	ldwork = f2cmax(1,*m);
+    }
+    if (! left && ! right) {
+	*info = -1;
+    } else if (! tran && ! notran) {
+	*info = -2;
+    } else if (*m < 0) {
+	*info = -3;
+    } else if (*n < 0) {
+	*info = -4;
+    } else if (*k < 0) {
+	*info = -5;
+    } else if (*mb < 1 || *mb > *k && *k > 0) {
+	*info = -6;
+    } else if (*ldv < f2cmax(1,*k)) {
+	*info = -8;
+    } else if (*ldt < *mb) {
+	*info = -10;
+    } else if (*ldc < f2cmax(1,*m)) {
+	*info = -12;
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEMLQT", &i__1, (ftnlen)7);
+	return 0;
+    }
+
+
+    if (*m == 0 || *n == 0 || *k == 0) {
+	return 0;
+    }
+
+    if (left && notran) {
+
+	i__1 = *k;
+	i__2 = *mb;
+	for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+/* Computing MIN */
+	    i__3 = *mb, i__4 = *k - i__ + 1;
+	    ib = f2cmin(i__3,i__4);
+	    i__3 = *m - i__ + 1;
+	    clarfb_("L", "C", "F", "R", &i__3, n, &ib, &v[i__ + i__ * v_dim1],
+		     ldv, &t[i__ * t_dim1 + 1], ldt, &c__[i__ + c_dim1], ldc, 
+		    &work[1], &ldwork);
+	}
+
+    } else if (right && tran) {
+
+	i__2 = *k;
+	i__1 = *mb;
+	for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
+/* Computing MIN */
+	    i__3 = *mb, i__4 = *k - i__ + 1;
+	    ib = f2cmin(i__3,i__4);
+	    i__3 = *n - i__ + 1;
+	    clarfb_("R", "N", "F", "R", m, &i__3, &ib, &v[i__ + i__ * v_dim1],
+		     ldv, &t[i__ * t_dim1 + 1], ldt, &c__[i__ * c_dim1 + 1], 
+		    ldc, &work[1], &ldwork);
+	}
+
+    } else if (left && tran) {
+
+	kf = (*k - 1) / *mb * *mb + 1;
+	i__1 = -(*mb);
+	for (i__ = kf; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
+/* Computing MIN */
+	    i__2 = *mb, i__3 = *k - i__ + 1;
+	    ib = f2cmin(i__2,i__3);
+	    i__2 = *m - i__ + 1;
+	    clarfb_("L", "N", "F", "R", &i__2, n, &ib, &v[i__ + i__ * v_dim1],
+		     ldv, &t[i__ * t_dim1 + 1], ldt, &c__[i__ + c_dim1], ldc, 
+		    &work[1], &ldwork);
+	}
+
+    } else if (right && notran) {
+
+	kf = (*k - 1) / *mb * *mb + 1;
+	i__1 = -(*mb);
+	for (i__ = kf; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
+/* Computing MIN */
+	    i__2 = *mb, i__3 = *k - i__ + 1;
+	    ib = f2cmin(i__2,i__3);
+	    i__2 = *n - i__ + 1;
+	    clarfb_("R", "C", "F", "R", m, &i__2, &ib, &v[i__ + i__ * v_dim1],
+		     ldv, &t[i__ * t_dim1 + 1], ldt, &c__[i__ * c_dim1 + 1], 
+		    ldc, &work[1], &ldwork);
+	}
+
+    }
+
+    return 0;
+
+/*     End of CGEMLQT */
+
+} /* cgemlqt_ */
+

lapack-netlib/SRC/cgemqr.c

@@ -0,0 +1,685 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGEMQR */
+
+/*  Definition: */
+/*  =========== */
+
+/*      SUBROUTINE CGEMQR( SIDE, TRANS, M, N, K, A, LDA, T, */
+/*     $                   TSIZE, C, LDC, WORK, LWORK, INFO ) */
+
+
+/*     CHARACTER         SIDE, TRANS */
+/*     INTEGER           INFO, LDA, M, N, K, LDT, TSIZE, LWORK, LDC */
+/*     COMPLEX           A( LDA, * ), T( * ), C( LDC, * ), WORK( * ) */
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEMQR overwrites the general real M-by-N matrix C with */
+/* > */
+/* >                      SIDE = 'L'     SIDE = 'R' */
+/* >      TRANS = 'N':      Q * C          C * Q */
+/* >      TRANS = 'T':      Q**H * C       C * Q**H */
+/* > */
+/* > where Q is a complex unitary matrix defined as the product */
+/* > of blocked elementary reflectors computed by tall skinny */
+/* > QR factorization (CGEQR) */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] SIDE */
+/* > \verbatim */
+/* >          SIDE is CHARACTER*1 */
+/* >          = 'L': apply Q or Q**T from the Left; */
+/* >          = 'R': apply Q or Q**T from the Right. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] TRANS */
+/* > \verbatim */
+/* >          TRANS is CHARACTER*1 */
+/* >          = 'N':  No transpose, apply Q; */
+/* >          = 'T':  Transpose, apply Q**T. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >=0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix C. N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] K */
+/* > \verbatim */
+/* >          K is INTEGER */
+/* >          The number of elementary reflectors whose product defines */
+/* >          the matrix Q. */
+/* >          If SIDE = 'L', M >= K >= 0; */
+/* >          if SIDE = 'R', N >= K >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,K) */
+/* >          Part of the data structure to represent Q as returned by CGEQR. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A. */
+/* >          If SIDE = 'L', LDA >= f2cmax(1,M); */
+/* >          if SIDE = 'R', LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (MAX(5,TSIZE)). */
+/* >          Part of the data structure to represent Q as returned by CGEQR. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] TSIZE */
+/* > \verbatim */
+/* >          TSIZE is INTEGER */
+/* >          The dimension of the array T. TSIZE >= 5. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] C */
+/* > \verbatim */
+/* >          C is COMPLEX array, dimension (LDC,N) */
+/* >          On entry, the M-by-N matrix C. */
+/* >          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDC */
+/* > \verbatim */
+/* >          LDC is INTEGER */
+/* >          The leading dimension of the array C. LDC >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >         (workspace) COMPLEX array, dimension (MAX(1,LWORK)) */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK. */
+/* >          If LWORK = -1, then a workspace query is assumed. The routine */
+/* >          only calculates the size of the WORK array, returns this */
+/* >          value as WORK(1), and no error message related to WORK */
+/* >          is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \par Further Details */
+/*  ==================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* > These details are particular for this LAPACK implementation. Users should not */
+/* > take them for granted. These details may change in the future, and are not likely */
+/* > true for another LAPACK implementation. These details are relevant if one wants */
+/* > to try to understand the code. They are not part of the interface. */
+/* > */
+/* > In this version, */
+/* > */
+/* >          T(2): row block size (MB) */
+/* >          T(3): column block size (NB) */
+/* >          T(6:TSIZE): data structure needed for Q, computed by */
+/* >                           CLATSQR or CGEQRT */
+/* > */
+/* >  Depending on the matrix dimensions M and N, and row and column */
+/* >  block sizes MB and NB returned by ILAENV, CGEQR will use either */
+/* >  CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute */
+/* >  the QR factorization. */
+/* >  This version of CGEMQR will use either CLAMTSQR or CGEMQRT to */
+/* >  multiply matrix Q by another matrix. */
+/* >  Further Details in CLAMTSQR or CGEMQRT. */
+/* > */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgemqr_(char *side, char *trans, integer *m, integer *n, 
+	integer *k, complex *a, integer *lda, complex *t, integer *tsize, 
+	complex *c__, integer *ldc, complex *work, integer *lwork, integer *
+	info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, c_dim1, c_offset, i__1;
+
+    /* Local variables */
+    logical left, tran;
+    extern /* Subroutine */ int clamtsqr_(char *, char *, integer *, integer *
+	    , integer *, integer *, integer *, complex *, integer *, complex *
+	    , integer *, complex *, integer *, complex *, integer *, integer *
+	    );
+    extern logical lsame_(char *, char *);
+    logical right;
+    integer mb, nb, mn, lw, nblcks;
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    logical notran, lquery;
+    extern /* Subroutine */ int cgemqrt_(char *, char *, integer *, integer *,
+	     integer *, integer *, complex *, integer *, complex *, integer *,
+	     complex *, integer *, complex *, integer *);
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/* ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --t;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1 * 1;
+    c__ -= c_offset;
+    --work;
+
+    /* Function Body */
+    lquery = *lwork == -1;
+    notran = lsame_(trans, "N");
+    tran = lsame_(trans, "C");
+    left = lsame_(side, "L");
+    right = lsame_(side, "R");
+
+    mb = (integer) t[2].r;
+    nb = (integer) t[3].r;
+    if (left) {
+	lw = *n * nb;
+	mn = *m;
+    } else {
+	lw = mb * nb;
+	mn = *n;
+    }
+
+    if (mb > *k && mn > *k) {
+	if ((mn - *k) % (mb - *k) == 0) {
+	    nblcks = (mn - *k) / (mb - *k);
+	} else {
+	    nblcks = (mn - *k) / (mb - *k) + 1;
+	}
+    } else {
+	nblcks = 1;
+    }
+
+    *info = 0;
+    if (! left && ! right) {
+	*info = -1;
+    } else if (! tran && ! notran) {
+	*info = -2;
+    } else if (*m < 0) {
+	*info = -3;
+    } else if (*n < 0) {
+	*info = -4;
+    } else if (*k < 0 || *k > mn) {
+	*info = -5;
+    } else if (*lda < f2cmax(1,mn)) {
+	*info = -7;
+    } else if (*tsize < 5) {
+	*info = -9;
+    } else if (*ldc < f2cmax(1,*m)) {
+	*info = -11;
+    } else if (*lwork < f2cmax(1,lw) && ! lquery) {
+	*info = -13;
+    }
+
+    if (*info == 0) {
+	work[1].r = (real) lw, work[1].i = 0.f;
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEMQR", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+/* Computing MIN */
+    i__1 = f2cmin(*m,*n);
+    if (f2cmin(i__1,*k) == 0) {
+	return 0;
+    }
+
+/* Computing MAX */
+    i__1 = f2cmax(*m,*n);
+    if (left && *m <= *k || right && *n <= *k || mb <= *k || mb >= f2cmax(i__1,*
+	    k)) {
+	cgemqrt_(side, trans, m, n, k, &nb, &a[a_offset], lda, &t[6], &nb, &
+		c__[c_offset], ldc, &work[1], info);
+    } else {
+	clamtsqr_(side, trans, m, n, k, &mb, &nb, &a[a_offset], lda, &t[6], &
+		nb, &c__[c_offset], ldc, &work[1], lwork, info);
+    }
+
+    work[1].r = (real) lw, work[1].i = 0.f;
+
+    return 0;
+
+/*     End of CGEMQR */
+
+} /* cgemqr_ */
+

lapack-netlib/SRC/cgemqrt.c

@@ -0,0 +1,707 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGEMQRT */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEMQRT + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgemqrt
+.f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgemqrt
+.f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgemqrt
+.f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEMQRT( SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, */
+/*                          C, LDC, WORK, INFO ) */
+
+/*       CHARACTER SIDE, TRANS */
+/*       INTEGER   INFO, K, LDV, LDC, M, N, NB, LDT */
+/*       COMPLEX   V( LDV, * ), C( LDC, * ), T( LDT, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEMQRT overwrites the general complex M-by-N matrix C with */
+/* > */
+/* >                 SIDE = 'L'     SIDE = 'R' */
+/* > TRANS = 'N':      Q C            C Q */
+/* > TRANS = 'C':    Q**H C            C Q**H */
+/* > */
+/* > where Q is a complex orthogonal matrix defined as the product of K */
+/* > elementary reflectors: */
+/* > */
+/* >       Q = H(1) H(2) . . . H(K) = I - V T V**H */
+/* > */
+/* > generated using the compact WY representation as returned by CGEQRT. */
+/* > */
+/* > Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] SIDE */
+/* > \verbatim */
+/* >          SIDE is CHARACTER*1 */
+/* >          = 'L': apply Q or Q**H from the Left; */
+/* >          = 'R': apply Q or Q**H from the Right. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] TRANS */
+/* > \verbatim */
+/* >          TRANS is CHARACTER*1 */
+/* >          = 'N':  No transpose, apply Q; */
+/* >          = 'C':  Transpose, apply Q**H. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix C. M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix C. N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] K */
+/* > \verbatim */
+/* >          K is INTEGER */
+/* >          The number of elementary reflectors whose product defines */
+/* >          the matrix Q. */
+/* >          If SIDE = 'L', M >= K >= 0; */
+/* >          if SIDE = 'R', N >= K >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NB */
+/* > \verbatim */
+/* >          NB is INTEGER */
+/* >          The block size used for the storage of T.  K >= NB >= 1. */
+/* >          This must be the same value of NB used to generate T */
+/* >          in CGEQRT. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] V */
+/* > \verbatim */
+/* >          V is COMPLEX array, dimension (LDV,K) */
+/* >          The i-th column must contain the vector which defines the */
+/* >          elementary reflector H(i), for i = 1,2,...,k, as returned by */
+/* >          CGEQRT in the first K columns of its array argument A. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDV */
+/* > \verbatim */
+/* >          LDV is INTEGER */
+/* >          The leading dimension of the array V. */
+/* >          If SIDE = 'L', LDA >= f2cmax(1,M); */
+/* >          if SIDE = 'R', LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (LDT,K) */
+/* >          The upper triangular factors of the block reflectors */
+/* >          as returned by CGEQRT, stored as a NB-by-N matrix. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDT */
+/* > \verbatim */
+/* >          LDT is INTEGER */
+/* >          The leading dimension of the array T.  LDT >= NB. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] C */
+/* > \verbatim */
+/* >          C is COMPLEX array, dimension (LDC,N) */
+/* >          On entry, the M-by-N matrix C. */
+/* >          On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDC */
+/* > \verbatim */
+/* >          LDC is INTEGER */
+/* >          The leading dimension of the array C. LDC >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array. The dimension of WORK is */
+/* >           N*NB if SIDE = 'L', or  M*NB if SIDE = 'R'. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgemqrt_(char *side, char *trans, integer *m, integer *n,
+	 integer *k, integer *nb, complex *v, integer *ldv, complex *t, 
+	integer *ldt, complex *c__, integer *ldc, complex *work, integer *
+	info)
+{
+    /* System generated locals */
+    integer v_dim1, v_offset, c_dim1, c_offset, t_dim1, t_offset, i__1, i__2, 
+	    i__3, i__4;
+
+    /* Local variables */
+    logical left, tran;
+    integer i__, q;
+    extern logical lsame_(char *, char *);
+    logical right;
+    integer ib, kf;
+    extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, 
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *, ftnlen);
+    logical notran;
+    integer ldwork;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+
+    /* Parameter adjustments */
+    v_dim1 = *ldv;
+    v_offset = 1 + v_dim1 * 1;
+    v -= v_offset;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1 * 1;
+    t -= t_offset;
+    c_dim1 = *ldc;
+    c_offset = 1 + c_dim1 * 1;
+    c__ -= c_offset;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    left = lsame_(side, "L");
+    right = lsame_(side, "R");
+    tran = lsame_(trans, "C");
+    notran = lsame_(trans, "N");
+
+    if (left) {
+	ldwork = f2cmax(1,*n);
+	q = *m;
+    } else if (right) {
+	ldwork = f2cmax(1,*m);
+	q = *n;
+    }
+    if (! left && ! right) {
+	*info = -1;
+    } else if (! tran && ! notran) {
+	*info = -2;
+    } else if (*m < 0) {
+	*info = -3;
+    } else if (*n < 0) {
+	*info = -4;
+    } else if (*k < 0 || *k > q) {
+	*info = -5;
+    } else if (*nb < 1 || *nb > *k && *k > 0) {
+	*info = -6;
+    } else if (*ldv < f2cmax(1,q)) {
+	*info = -8;
+    } else if (*ldt < *nb) {
+	*info = -10;
+    } else if (*ldc < f2cmax(1,*m)) {
+	*info = -12;
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEMQRT", &i__1, (ftnlen)7);
+	return 0;
+    }
+
+
+    if (*m == 0 || *n == 0 || *k == 0) {
+	return 0;
+    }
+
+    if (left && tran) {
+
+	i__1 = *k;
+	i__2 = *nb;
+	for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+/* Computing MIN */
+	    i__3 = *nb, i__4 = *k - i__ + 1;
+	    ib = f2cmin(i__3,i__4);
+	    i__3 = *m - i__ + 1;
+	    clarfb_("L", "C", "F", "C", &i__3, n, &ib, &v[i__ + i__ * v_dim1],
+		     ldv, &t[i__ * t_dim1 + 1], ldt, &c__[i__ + c_dim1], ldc, 
+		    &work[1], &ldwork);
+	}
+
+    } else if (right && notran) {
+
+	i__2 = *k;
+	i__1 = *nb;
+	for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
+/* Computing MIN */
+	    i__3 = *nb, i__4 = *k - i__ + 1;
+	    ib = f2cmin(i__3,i__4);
+	    i__3 = *n - i__ + 1;
+	    clarfb_("R", "N", "F", "C", m, &i__3, &ib, &v[i__ + i__ * v_dim1],
+		     ldv, &t[i__ * t_dim1 + 1], ldt, &c__[i__ * c_dim1 + 1], 
+		    ldc, &work[1], &ldwork);
+	}
+
+    } else if (left && notran) {
+
+	kf = (*k - 1) / *nb * *nb + 1;
+	i__1 = -(*nb);
+	for (i__ = kf; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
+/* Computing MIN */
+	    i__2 = *nb, i__3 = *k - i__ + 1;
+	    ib = f2cmin(i__2,i__3);
+	    i__2 = *m - i__ + 1;
+	    clarfb_("L", "N", "F", "C", &i__2, n, &ib, &v[i__ + i__ * v_dim1],
+		     ldv, &t[i__ * t_dim1 + 1], ldt, &c__[i__ + c_dim1], ldc, 
+		    &work[1], &ldwork);
+	}
+
+    } else if (right && tran) {
+
+	kf = (*k - 1) / *nb * *nb + 1;
+	i__1 = -(*nb);
+	for (i__ = kf; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
+/* Computing MIN */
+	    i__2 = *nb, i__3 = *k - i__ + 1;
+	    ib = f2cmin(i__2,i__3);
+	    i__2 = *n - i__ + 1;
+	    clarfb_("R", "C", "F", "C", m, &i__2, &ib, &v[i__ + i__ * v_dim1],
+		     ldv, &t[i__ * t_dim1 + 1], ldt, &c__[i__ * c_dim1 + 1], 
+		    ldc, &work[1], &ldwork);
+	}
+
+    }
+
+    return 0;
+
+/*     End of CGEMQRT */
+
+} /* cgemqrt_ */
+

lapack-netlib/SRC/cgeql2.c

@@ -0,0 +1,596 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* > \brief \b CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorit
+hm. */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEQL2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeql2.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeql2.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeql2.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEQL2( M, N, A, LDA, TAU, WORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQL2 computes a QL factorization of a complex m by n matrix A: */
+/* > A = Q * L. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the m by n matrix A. */
+/* >          On exit, if m >= n, the lower triangle of the subarray */
+/* >          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L; */
+/* >          if m <= n, the elements on and below the (n-m)-th */
+/* >          superdiagonal contain the m by n lower trapezoidal matrix L; */
+/* >          the remaining elements, with the array TAU, represent the */
+/* >          unitary matrix Q as a product of elementary reflectors */
+/* >          (see Further Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(k) . . . H(2) H(1), where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in */
+/* >  A(1:m-k+i-1,n-k+i), and tau in TAU(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeql2_(integer *m, integer *n, complex *a, integer *lda,
+	 complex *tau, complex *work, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, k;
+    complex alpha;
+    extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex *
+	    , integer *, complex *, complex *, integer *, complex *), 
+	    clarfg_(integer *, complex *, complex *, integer *, complex *), 
+	    xerbla_(char *, integer *, ftnlen);
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQL2", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+    k = f2cmin(*m,*n);
+
+    for (i__ = k; i__ >= 1; --i__) {
+
+/*        Generate elementary reflector H(i) to annihilate */
+/*        A(1:m-k+i-1,n-k+i) */
+
+	i__1 = *m - k + i__ + (*n - k + i__) * a_dim1;
+	alpha.r = a[i__1].r, alpha.i = a[i__1].i;
+	i__1 = *m - k + i__;
+	clarfg_(&i__1, &alpha, &a[(*n - k + i__) * a_dim1 + 1], &c__1, &tau[
+		i__]);
+
+/*        Apply H(i)**H to A(1:m-k+i,1:n-k+i-1) from the left */
+
+	i__1 = *m - k + i__ + (*n - k + i__) * a_dim1;
+	a[i__1].r = 1.f, a[i__1].i = 0.f;
+	i__1 = *m - k + i__;
+	i__2 = *n - k + i__ - 1;
+	r_cnjg(&q__1, &tau[i__]);
+	clarf_("Left", &i__1, &i__2, &a[(*n - k + i__) * a_dim1 + 1], &c__1, &
+		q__1, &a[a_offset], lda, &work[1]);
+	i__1 = *m - k + i__ + (*n - k + i__) * a_dim1;
+	a[i__1].r = alpha.r, a[i__1].i = alpha.i;
+/* L10: */
+    }
+    return 0;
+
+/*     End of CGEQL2 */
+
+} /* cgeql2_ */
+

lapack-netlib/SRC/cgeqlf.c

@@ -0,0 +1,710 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__3 = 3;
+static integer c__2 = 2;
+
+/* > \brief \b CGEQLF */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEQLF + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqlf.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqlf.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqlf.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, LWORK, M, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQLF computes a QL factorization of a complex M-by-N matrix A: */
+/* > A = Q * L. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, */
+/* >          if m >= n, the lower triangle of the subarray */
+/* >          A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L; */
+/* >          if m <= n, the elements on and below the (n-m)-th */
+/* >          superdiagonal contain the M-by-N lower trapezoidal matrix L; */
+/* >          the remaining elements, with the array TAU, represent the */
+/* >          unitary matrix Q as a product of elementary reflectors */
+/* >          (see Further Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,N). */
+/* >          For optimum performance LWORK >= N*NB, where NB is */
+/* >          the optimal blocksize. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(k) . . . H(2) H(1), where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in */
+/* >  A(1:m-k+i-1,n-k+i), and tau in TAU(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeqlf_(integer *m, integer *n, complex *a, integer *lda,
+	 complex *tau, complex *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+
+    /* Local variables */
+    integer i__, k, nbmin, iinfo;
+    extern /* Subroutine */ int cgeql2_(integer *, integer *, complex *, 
+	    integer *, complex *, complex *, integer *);
+    integer ib, nb, ki, kk;
+    extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, 
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *);
+    integer mu, nu, nx;
+    extern /* Subroutine */ int clarft_(char *, char *, integer *, integer *, 
+	    complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    integer ldwork, lwkopt;
+    logical lquery;
+    integer iws;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+
+    if (*info == 0) {
+	k = f2cmin(*m,*n);
+	if (k == 0) {
+	    lwkopt = 1;
+	} else {
+	    nb = ilaenv_(&c__1, "CGEQLF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, 
+		    (ftnlen)1);
+	    lwkopt = *n * nb;
+	}
+	work[1].r = (real) lwkopt, work[1].i = 0.f;
+
+	if (*lwork < f2cmax(1,*n) && ! lquery) {
+	    *info = -7;
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQLF", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (k == 0) {
+	return 0;
+    }
+
+    nbmin = 2;
+    nx = 1;
+    iws = *n;
+    if (nb > 1 && nb < k) {
+
+/*        Determine when to cross over from blocked to unblocked code. */
+
+/* Computing MAX */
+	i__1 = 0, i__2 = ilaenv_(&c__3, "CGEQLF", " ", m, n, &c_n1, &c_n1, (
+		ftnlen)6, (ftnlen)1);
+	nx = f2cmax(i__1,i__2);
+	if (nx < k) {
+
+/*           Determine if workspace is large enough for blocked code. */
+
+	    ldwork = *n;
+	    iws = ldwork * nb;
+	    if (*lwork < iws) {
+
+/*              Not enough workspace to use optimal NB:  reduce NB and */
+/*              determine the minimum value of NB. */
+
+		nb = *lwork / ldwork;
+/* Computing MAX */
+		i__1 = 2, i__2 = ilaenv_(&c__2, "CGEQLF", " ", m, n, &c_n1, &
+			c_n1, (ftnlen)6, (ftnlen)1);
+		nbmin = f2cmax(i__1,i__2);
+	    }
+	}
+    }
+
+    if (nb >= nbmin && nb < k && nx < k) {
+
+/*        Use blocked code initially. */
+/*        The last kk columns are handled by the block method. */
+
+	ki = (k - nx - 1) / nb * nb;
+/* Computing MIN */
+	i__1 = k, i__2 = ki + nb;
+	kk = f2cmin(i__1,i__2);
+
+	i__1 = k - kk + 1;
+	i__2 = -nb;
+	for (i__ = k - kk + ki + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ 
+		+= i__2) {
+/* Computing MIN */
+	    i__3 = k - i__ + 1;
+	    ib = f2cmin(i__3,nb);
+
+/*           Compute the QL factorization of the current block */
+/*           A(1:m-k+i+ib-1,n-k+i:n-k+i+ib-1) */
+
+	    i__3 = *m - k + i__ + ib - 1;
+	    cgeql2_(&i__3, &ib, &a[(*n - k + i__) * a_dim1 + 1], lda, &tau[
+		    i__], &work[1], &iinfo);
+	    if (*n - k + i__ > 1) {
+
+/*              Form the triangular factor of the block reflector */
+/*              H = H(i+ib-1) . . . H(i+1) H(i) */
+
+		i__3 = *m - k + i__ + ib - 1;
+		clarft_("Backward", "Columnwise", &i__3, &ib, &a[(*n - k + 
+			i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork);
+
+/*              Apply H**H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */
+
+		i__3 = *m - k + i__ + ib - 1;
+		i__4 = *n - k + i__ - 1;
+		clarfb_("Left", "Conjugate transpose", "Backward", "Columnwi"
+			"se", &i__3, &i__4, &ib, &a[(*n - k + i__) * a_dim1 + 
+			1], lda, &work[1], &ldwork, &a[a_offset], lda, &work[
+			ib + 1], &ldwork);
+	    }
+/* L10: */
+	}
+	mu = *m - k + i__ + nb - 1;
+	nu = *n - k + i__ + nb - 1;
+    } else {
+	mu = *m;
+	nu = *n;
+    }
+
+/*     Use unblocked code to factor the last or only block */
+
+    if (mu > 0 && nu > 0) {
+	cgeql2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
+    }
+
+    work[1].r = (real) iws, work[1].i = 0.f;
+    return 0;
+
+/*     End of CGEQLF */
+
+} /* cgeqlf_ */
+

lapack-netlib/SRC/cgeqp3.c

@@ -0,0 +1,805 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__3 = 3;
+static integer c__2 = 2;
+
+/* > \brief \b CGEQP3 */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEQP3 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqp3.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqp3.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqp3.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, */
+/*                          INFO ) */
+
+/*       INTEGER            INFO, LDA, LWORK, M, N */
+/*       INTEGER            JPVT( * ) */
+/*       REAL               RWORK( * ) */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQP3 computes a QR factorization with column pivoting of a */
+/* > matrix A:  A*P = Q*R  using Level 3 BLAS. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A. M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, the upper triangle of the array contains the */
+/* >          f2cmin(M,N)-by-N upper trapezoidal matrix R; the elements below */
+/* >          the diagonal, together with the array TAU, represent the */
+/* >          unitary matrix Q as a product of f2cmin(M,N) elementary */
+/* >          reflectors. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A. LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] JPVT */
+/* > \verbatim */
+/* >          JPVT is INTEGER array, dimension (N) */
+/* >          On entry, if JPVT(J).ne.0, the J-th column of A is permuted */
+/* >          to the front of A*P (a leading column); if JPVT(J)=0, */
+/* >          the J-th column of A is a free column. */
+/* >          On exit, if JPVT(J)=K, then the J-th column of A*P was the */
+/* >          the K-th column of A. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO=0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK. LWORK >= N+1. */
+/* >          For optimal performance LWORK >= ( N+1 )*NB, where NB */
+/* >          is the optimal blocksize. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RWORK */
+/* > \verbatim */
+/* >          RWORK is REAL array, dimension (2*N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit. */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(1) H(2) . . . H(k), where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a real/complex vector */
+/* >  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in */
+/* >  A(i+1:m,i), and tau in TAU(i). */
+/* > \endverbatim */
+
+/* > \par Contributors: */
+/*  ================== */
+/* > */
+/* >    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
+/* >    X. Sun, Computer Science Dept., Duke University, USA */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeqp3_(integer *m, integer *n, complex *a, integer *lda,
+	 integer *jpvt, complex *tau, complex *work, integer *lwork, real *
+	rwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+    complex q__1;
+
+    /* Local variables */
+    integer nfxd, j, nbmin;
+    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
+	    complex *, integer *);
+    integer minmn, minws;
+    extern /* Subroutine */ int claqp2_(integer *, integer *, integer *, 
+	    complex *, integer *, integer *, complex *, real *, real *, 
+	    complex *);
+    extern real scnrm2_(integer *, complex *, integer *);
+    integer jb, na, nb, sm, sn, nx;
+    extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *, 
+	    integer *, complex *, complex *, integer *, integer *), xerbla_(
+	    char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    extern /* Subroutine */ int claqps_(integer *, integer *, integer *, 
+	    integer *, integer *, complex *, integer *, integer *, complex *, 
+	    real *, real *, complex *, complex *, integer *);
+    integer topbmn, sminmn;
+    extern /* Subroutine */ int cunmqr_(char *, char *, integer *, integer *, 
+	    integer *, complex *, integer *, complex *, complex *, integer *, 
+	    complex *, integer *, integer *);
+    integer lwkopt;
+    logical lquery;
+    integer fjb, iws;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test input arguments */
+/*  ==================== */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --jpvt;
+    --tau;
+    --work;
+    --rwork;
+
+    /* Function Body */
+    *info = 0;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+
+    if (*info == 0) {
+	minmn = f2cmin(*m,*n);
+	if (minmn == 0) {
+	    iws = 1;
+	    lwkopt = 1;
+	} else {
+	    iws = *n + 1;
+	    nb = ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, 
+		    (ftnlen)1);
+	    lwkopt = (*n + 1) * nb;
+	}
+	q__1.r = (real) lwkopt, q__1.i = 0.f;
+	work[1].r = q__1.r, work[1].i = q__1.i;
+
+	if (*lwork < iws && ! lquery) {
+	    *info = -8;
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQP3", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Move initial columns up front. */
+
+    nfxd = 1;
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	if (jpvt[j] != 0) {
+	    if (j != nfxd) {
+		cswap_(m, &a[j * a_dim1 + 1], &c__1, &a[nfxd * a_dim1 + 1], &
+			c__1);
+		jpvt[j] = jpvt[nfxd];
+		jpvt[nfxd] = j;
+	    } else {
+		jpvt[j] = j;
+	    }
+	    ++nfxd;
+	} else {
+	    jpvt[j] = j;
+	}
+/* L10: */
+    }
+    --nfxd;
+
+/*     Factorize fixed columns */
+/*  ======================= */
+
+/*     Compute the QR factorization of fixed columns and update */
+/*     remaining columns. */
+
+    if (nfxd > 0) {
+	na = f2cmin(*m,nfxd);
+/* CC      CALL CGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) */
+	cgeqrf_(m, &na, &a[a_offset], lda, &tau[1], &work[1], lwork, info);
+/* Computing MAX */
+	i__1 = iws, i__2 = (integer) work[1].r;
+	iws = f2cmax(i__1,i__2);
+	if (na < *n) {
+/* CC         CALL CUNM2R( 'Left', 'Conjugate Transpose', M, N-NA, */
+/* CC  $                   NA, A, LDA, TAU, A( 1, NA+1 ), LDA, WORK, */
+/* CC  $                   INFO ) */
+	    i__1 = *n - na;
+	    cunmqr_("Left", "Conjugate Transpose", m, &i__1, &na, &a[a_offset]
+		    , lda, &tau[1], &a[(na + 1) * a_dim1 + 1], lda, &work[1], 
+		    lwork, info);
+/* Computing MAX */
+	    i__1 = iws, i__2 = (integer) work[1].r;
+	    iws = f2cmax(i__1,i__2);
+	}
+    }
+
+/*     Factorize free columns */
+/*  ====================== */
+
+    if (nfxd < minmn) {
+
+	sm = *m - nfxd;
+	sn = *n - nfxd;
+	sminmn = minmn - nfxd;
+
+/*        Determine the block size. */
+
+	nb = ilaenv_(&c__1, "CGEQRF", " ", &sm, &sn, &c_n1, &c_n1, (ftnlen)6, 
+		(ftnlen)1);
+	nbmin = 2;
+	nx = 0;
+
+	if (nb > 1 && nb < sminmn) {
+
+/*           Determine when to cross over from blocked to unblocked code. */
+
+/* Computing MAX */
+	    i__1 = 0, i__2 = ilaenv_(&c__3, "CGEQRF", " ", &sm, &sn, &c_n1, &
+		    c_n1, (ftnlen)6, (ftnlen)1);
+	    nx = f2cmax(i__1,i__2);
+
+
+	    if (nx < sminmn) {
+
+/*              Determine if workspace is large enough for blocked code. */
+
+		minws = (sn + 1) * nb;
+		iws = f2cmax(iws,minws);
+		if (*lwork < minws) {
+
+/*                 Not enough workspace to use optimal NB: Reduce NB and */
+/*                 determine the minimum value of NB. */
+
+		    nb = *lwork / (sn + 1);
+/* Computing MAX */
+		    i__1 = 2, i__2 = ilaenv_(&c__2, "CGEQRF", " ", &sm, &sn, &
+			    c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
+		    nbmin = f2cmax(i__1,i__2);
+
+
+		}
+	    }
+	}
+
+/*        Initialize partial column norms. The first N elements of work */
+/*        store the exact column norms. */
+
+	i__1 = *n;
+	for (j = nfxd + 1; j <= i__1; ++j) {
+	    rwork[j] = scnrm2_(&sm, &a[nfxd + 1 + j * a_dim1], &c__1);
+	    rwork[*n + j] = rwork[j];
+/* L20: */
+	}
+
+	if (nb >= nbmin && nb < sminmn && nx < sminmn) {
+
+/*           Use blocked code initially. */
+
+	    j = nfxd + 1;
+
+/*           Compute factorization: while loop. */
+
+
+	    topbmn = minmn - nx;
+L30:
+	    if (j <= topbmn) {
+/* Computing MIN */
+		i__1 = nb, i__2 = topbmn - j + 1;
+		jb = f2cmin(i__1,i__2);
+
+/*              Factorize JB columns among columns J:N. */
+
+		i__1 = *n - j + 1;
+		i__2 = j - 1;
+		i__3 = *n - j + 1;
+		claqps_(m, &i__1, &i__2, &jb, &fjb, &a[j * a_dim1 + 1], lda, &
+			jpvt[j], &tau[j], &rwork[j], &rwork[*n + j], &work[1],
+			 &work[jb + 1], &i__3);
+
+		j += fjb;
+		goto L30;
+	    }
+	} else {
+	    j = nfxd + 1;
+	}
+
+/*        Use unblocked code to factor the last or only block. */
+
+
+	if (j <= minmn) {
+	    i__1 = *n - j + 1;
+	    i__2 = j - 1;
+	    claqp2_(m, &i__1, &i__2, &a[j * a_dim1 + 1], lda, &jpvt[j], &tau[
+		    j], &rwork[j], &rwork[*n + j], &work[1]);
+	}
+
+    }
+
+    q__1.r = (real) lwkopt, q__1.i = 0.f;
+    work[1].r = q__1.r, work[1].i = q__1.i;
+    return 0;
+
+/*     End of CGEQP3 */
+
+} /* cgeqp3_ */
+

lapack-netlib/SRC/cgeqr.c

@@ -0,0 +1,738 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__2 = 2;
+
+/* > \brief \b CGEQR */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK, */
+/*                         INFO ) */
+
+/*       INTEGER           INFO, LDA, M, N, TSIZE, LWORK */
+/*       COMPLEX           A( LDA, * ), T( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQR computes a QR factorization of a complex M-by-N matrix A: */
+/* > */
+/* >    A = Q * ( R ), */
+/* >            ( 0 ) */
+/* > */
+/* > where: */
+/* > */
+/* >    Q is a M-by-M orthogonal matrix; */
+/* >    R is an upper-triangular N-by-N matrix; */
+/* >    0 is a (M-N)-by-N zero matrix, if M > N. */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, the elements on and above the diagonal of the array */
+/* >          contain the f2cmin(M,N)-by-N upper trapezoidal matrix R */
+/* >          (R is upper triangular if M >= N); */
+/* >          the elements below the diagonal are used to store part of the */
+/* >          data structure to represent Q. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (MAX(5,TSIZE)) */
+/* >          On exit, if INFO = 0, T(1) returns optimal (or either minimal */
+/* >          or optimal, if query is assumed) TSIZE. See TSIZE for details. */
+/* >          Remaining T contains part of the data structure used to represent Q. */
+/* >          If one wants to apply or construct Q, then one needs to keep T */
+/* >          (in addition to A) and pass it to further subroutines. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] TSIZE */
+/* > \verbatim */
+/* >          TSIZE is INTEGER */
+/* >          If TSIZE >= 5, the dimension of the array T. */
+/* >          If TSIZE = -1 or -2, then a workspace query is assumed. The routine */
+/* >          only calculates the sizes of the T and WORK arrays, returns these */
+/* >          values as the first entries of the T and WORK arrays, and no error */
+/* >          message related to T or WORK is issued by XERBLA. */
+/* >          If TSIZE = -1, the routine calculates optimal size of T for the */
+/* >          optimum performance and returns this value in T(1). */
+/* >          If TSIZE = -2, the routine calculates minimal size of T and */
+/* >          returns this value in T(1). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          (workspace) COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal */
+/* >          or optimal, if query was assumed) LWORK. */
+/* >          See LWORK for details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK. */
+/* >          If LWORK = -1 or -2, then a workspace query is assumed. The routine */
+/* >          only calculates the sizes of the T and WORK arrays, returns these */
+/* >          values as the first entries of the T and WORK arrays, and no error */
+/* >          message related to T or WORK is issued by XERBLA. */
+/* >          If LWORK = -1, the routine calculates optimal size of WORK for the */
+/* >          optimal performance and returns this value in WORK(1). */
+/* >          If LWORK = -2, the routine calculates minimal size of WORK and */
+/* >          returns this value in WORK(1). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \par Further Details */
+/*  ==================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* > The goal of the interface is to give maximum freedom to the developers for */
+/* > creating any QR factorization algorithm they wish. The triangular */
+/* > (trapezoidal) R has to be stored in the upper part of A. The lower part of A */
+/* > and the array T can be used to store any relevant information for applying or */
+/* > constructing the Q factor. The WORK array can safely be discarded after exit. */
+/* > */
+/* > Caution: One should not expect the sizes of T and WORK to be the same from one */
+/* > LAPACK implementation to the other, or even from one execution to the other. */
+/* > A workspace query (for T and WORK) is needed at each execution. However, */
+/* > for a given execution, the size of T and WORK are fixed and will not change */
+/* > from one query to the next. */
+/* > */
+/* > \endverbatim */
+/* > */
+/* > \par Further Details particular to this LAPACK implementation: */
+/*  ============================================================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* > These details are particular for this LAPACK implementation. Users should not */
+/* > take them for granted. These details may change in the future, and are not likely */
+/* > true for another LAPACK implementation. These details are relevant if one wants */
+/* > to try to understand the code. They are not part of the interface. */
+/* > */
+/* > In this version, */
+/* > */
+/* >          T(2): row block size (MB) */
+/* >          T(3): column block size (NB) */
+/* >          T(6:TSIZE): data structure needed for Q, computed by */
+/* >                           CLATSQR or CGEQRT */
+/* > */
+/* >  Depending on the matrix dimensions M and N, and row and column */
+/* >  block sizes MB and NB returned by ILAENV, CGEQR will use either */
+/* >  CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute */
+/* >  the QR factorization. */
+/* > */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeqr_(integer *m, integer *n, complex *a, integer *lda, 
+	complex *t, integer *tsize, complex *work, integer *lwork, integer *
+	info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+
+    /* Local variables */
+    logical mint, minw;
+    integer mb, nb, nblcks;
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    extern /* Subroutine */ int cgeqrt_(integer *, integer *, integer *, 
+	    complex *, integer *, complex *, integer *, complex *, integer *);
+    logical lminws, lquery;
+    integer mintsz;
+    extern /* Subroutine */ int clatsqr_(integer *, integer *, integer *, 
+	    integer *, complex *, integer *, complex *, integer *, complex *, 
+	    integer *, integer *);
+
+
+/*  -- LAPACK computational routine (version 3.9.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. -- */
+/*     November 2019 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --t;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+
+    lquery = *tsize == -1 || *tsize == -2 || *lwork == -1 || *lwork == -2;
+
+    mint = FALSE_;
+    minw = FALSE_;
+    if (*tsize == -2 || *lwork == -2) {
+	if (*tsize != -1) {
+	    mint = TRUE_;
+	}
+	if (*lwork != -1) {
+	    minw = TRUE_;
+	}
+    }
+
+/*     Determine the block size */
+
+    if (f2cmin(*m,*n) > 0) {
+	mb = ilaenv_(&c__1, "CGEQR ", " ", m, n, &c__1, &c_n1, (ftnlen)6, (
+		ftnlen)1);
+	nb = ilaenv_(&c__1, "CGEQR ", " ", m, n, &c__2, &c_n1, (ftnlen)6, (
+		ftnlen)1);
+    } else {
+	mb = *m;
+	nb = 1;
+    }
+    if (mb > *m || mb <= *n) {
+	mb = *m;
+    }
+    if (nb > f2cmin(*m,*n) || nb < 1) {
+	nb = 1;
+    }
+    mintsz = *n + 5;
+    if (mb > *n && *m > *n) {
+	if ((*m - *n) % (mb - *n) == 0) {
+	    nblcks = (*m - *n) / (mb - *n);
+	} else {
+	    nblcks = (*m - *n) / (mb - *n) + 1;
+	}
+    } else {
+	nblcks = 1;
+    }
+
+/*     Determine if the workspace size satisfies minimal size */
+
+    lminws = FALSE_;
+/* Computing MAX */
+    i__1 = 1, i__2 = nb * *n * nblcks + 5;
+    if ((*tsize < f2cmax(i__1,i__2) || *lwork < nb * *n) && *lwork >= *n && *
+	    tsize >= mintsz && ! lquery) {
+/* Computing MAX */
+	i__1 = 1, i__2 = nb * *n * nblcks + 5;
+	if (*tsize < f2cmax(i__1,i__2)) {
+	    lminws = TRUE_;
+	    nb = 1;
+	    mb = *m;
+	}
+	if (*lwork < nb * *n) {
+	    lminws = TRUE_;
+	    nb = 1;
+	}
+    }
+
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    } else /* if(complicated condition) */ {
+/* Computing MAX */
+	i__1 = 1, i__2 = nb * *n * nblcks + 5;
+	if (*tsize < f2cmax(i__1,i__2) && ! lquery && ! lminws) {
+	    *info = -6;
+	} else /* if(complicated condition) */ {
+/* Computing MAX */
+	    i__1 = 1, i__2 = *n * nb;
+	    if (*lwork < f2cmax(i__1,i__2) && ! lquery && ! lminws) {
+		*info = -8;
+	    }
+	}
+    }
+
+    if (*info == 0) {
+	if (mint) {
+	    t[1].r = (real) mintsz, t[1].i = 0.f;
+	} else {
+	    i__1 = nb * *n * nblcks + 5;
+	    t[1].r = (real) i__1, t[1].i = 0.f;
+	}
+	t[2].r = (real) mb, t[2].i = 0.f;
+	t[3].r = (real) nb, t[3].i = 0.f;
+	if (minw) {
+	    i__1 = f2cmax(1,*n);
+	    work[1].r = (real) i__1, work[1].i = 0.f;
+	} else {
+/* Computing MAX */
+	    i__2 = 1, i__3 = nb * *n;
+	    i__1 = f2cmax(i__2,i__3);
+	    work[1].r = (real) i__1, work[1].i = 0.f;
+	}
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQR", &i__1, (ftnlen)5);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (f2cmin(*m,*n) == 0) {
+	return 0;
+    }
+
+/*     The QR Decomposition */
+
+    if (*m <= *n || mb <= *n || mb >= *m) {
+	cgeqrt_(m, n, &nb, &a[a_offset], lda, &t[6], &nb, &work[1], info);
+    } else {
+	clatsqr_(m, n, &mb, &nb, &a[a_offset], lda, &t[6], &nb, &work[1], 
+		lwork, info);
+    }
+
+/* Computing MAX */
+    i__2 = 1, i__3 = nb * *n;
+    i__1 = f2cmax(i__2,i__3);
+    work[1].r = (real) i__1, work[1].i = 0.f;
+
+    return 0;
+
+/*     End of CGEQR */
+
+} /* cgeqr_ */
+

lapack-netlib/SRC/cgeqr2.c

@@ -0,0 +1,607 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* > \brief \b CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorit
+hm. */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEQR2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqr2.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqr2.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqr2.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEQR2( M, N, A, LDA, TAU, WORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQR2 computes a QR factorization of a complex m-by-n matrix A: */
+/* > */
+/* >    A = Q * ( R ), */
+/* >            ( 0 ) */
+/* > */
+/* > where: */
+/* > */
+/* >    Q is a m-by-m orthogonal matrix; */
+/* >    R is an upper-triangular n-by-n matrix; */
+/* >    0 is a (m-n)-by-n zero matrix, if m > n. */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the m by n matrix A. */
+/* >          On exit, the elements on and above the diagonal of the array */
+/* >          contain the f2cmin(m,n) by n upper trapezoidal matrix R (R is */
+/* >          upper triangular if m >= n); the elements below the diagonal, */
+/* >          with the array TAU, represent the unitary matrix Q as a */
+/* >          product of elementary reflectors (see Further Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date November 2019 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(1) H(2) . . . H(k), where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */
+/* >  and tau in TAU(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeqr2_(integer *m, integer *n, complex *a, integer *lda,
+	 complex *tau, complex *work, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, k;
+    complex alpha;
+    extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex *
+	    , integer *, complex *, complex *, integer *, complex *), 
+	    clarfg_(integer *, complex *, complex *, integer *, complex *), 
+	    xerbla_(char *, integer *, ftnlen);
+
+
+/*  -- LAPACK computational routine (version 3.9.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     November 2019 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQR2", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+    k = f2cmin(*m,*n);
+
+    i__1 = k;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+
+/*        Generate elementary reflector H(i) to annihilate A(i+1:m,i) */
+
+	i__2 = *m - i__ + 1;
+/* Computing MIN */
+	i__3 = i__ + 1;
+	clarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[f2cmin(i__3,*m) + i__ * a_dim1]
+		, &c__1, &tau[i__]);
+	if (i__ < *n) {
+
+/*           Apply H(i)**H to A(i:m,i+1:n) from the left */
+
+	    i__2 = i__ + i__ * a_dim1;
+	    alpha.r = a[i__2].r, alpha.i = a[i__2].i;
+	    i__2 = i__ + i__ * a_dim1;
+	    a[i__2].r = 1.f, a[i__2].i = 0.f;
+	    i__2 = *m - i__ + 1;
+	    i__3 = *n - i__;
+	    r_cnjg(&q__1, &tau[i__]);
+	    clarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &q__1,
+		     &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]);
+	    i__2 = i__ + i__ * a_dim1;
+	    a[i__2].r = alpha.r, a[i__2].i = alpha.i;
+	}
+/* L10: */
+    }
+    return 0;
+
+/*     End of CGEQR2 */
+
+} /* cgeqr2_ */
+

lapack-netlib/SRC/cgeqr2p.c

@@ -0,0 +1,611 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* > \brief \b CGEQR2P computes the QR factorization of a general rectangular matrix with non-negative diagona
+l elements using an unblocked algorithm. */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEQR2P + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqr2p
+.f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqr2p
+.f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqr2p
+.f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEQR2P( M, N, A, LDA, TAU, WORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQR2P computes a QR factorization of a complex m-by-n matrix A: */
+/* > */
+/* >    A = Q * ( R ), */
+/* >            ( 0 ) */
+/* > */
+/* > where: */
+/* > */
+/* >    Q is a m-by-m orthogonal matrix; */
+/* >    R is an upper-triangular n-by-n matrix with nonnegative diagonal */
+/* >    entries; */
+/* >    0 is a (m-n)-by-n zero matrix, if m > n. */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the m by n matrix A. */
+/* >          On exit, the elements on and above the diagonal of the array */
+/* >          contain the f2cmin(m,n) by n upper trapezoidal matrix R (R is */
+/* >          upper triangular if m >= n). The diagonal entries of R are */
+/* >          real and nonnegative; the elements below the diagonal, */
+/* >          with the array TAU, represent the unitary matrix Q as a */
+/* >          product of elementary reflectors (see Further Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date November 2019 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(1) H(2) . . . H(k), where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */
+/* >  and tau in TAU(i). */
+/* > */
+/* > See Lapack Working Note 203 for details */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeqr2p_(integer *m, integer *n, complex *a, integer *
+	lda, complex *tau, complex *work, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, k;
+    complex alpha;
+    extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex *
+	    , integer *, complex *, complex *, integer *, complex *), 
+	    xerbla_(char *, integer *, ftnlen), clarfgp_(integer *, complex *,
+	     complex *, integer *, complex *);
+
+
+/*  -- LAPACK computational routine (version 3.9.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     November 2019 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQR2P", &i__1, (ftnlen)7);
+	return 0;
+    }
+
+    k = f2cmin(*m,*n);
+
+    i__1 = k;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+
+/*        Generate elementary reflector H(i) to annihilate A(i+1:m,i) */
+
+	i__2 = *m - i__ + 1;
+/* Computing MIN */
+	i__3 = i__ + 1;
+	clarfgp_(&i__2, &a[i__ + i__ * a_dim1], &a[f2cmin(i__3,*m) + i__ * 
+		a_dim1], &c__1, &tau[i__]);
+	if (i__ < *n) {
+
+/*           Apply H(i)**H to A(i:m,i+1:n) from the left */
+
+	    i__2 = i__ + i__ * a_dim1;
+	    alpha.r = a[i__2].r, alpha.i = a[i__2].i;
+	    i__2 = i__ + i__ * a_dim1;
+	    a[i__2].r = 1.f, a[i__2].i = 0.f;
+	    i__2 = *m - i__ + 1;
+	    i__3 = *n - i__;
+	    r_cnjg(&q__1, &tau[i__]);
+	    clarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &q__1,
+		     &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]);
+	    i__2 = i__ + i__ * a_dim1;
+	    a[i__2].r = alpha.r, a[i__2].i = alpha.i;
+	}
+/* L10: */
+    }
+    return 0;
+
+/*     End of CGEQR2P */
+
+} /* cgeqr2p_ */
+

lapack-netlib/SRC/cgeqrf.c

@@ -0,0 +1,701 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__3 = 3;
+static integer c__2 = 2;
+
+/* > \brief \b CGEQRF */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEQRF + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqrf.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqrf.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqrf.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, LWORK, M, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQRF computes a QR factorization of a complex M-by-N matrix A: */
+/* > */
+/* >    A = Q * ( R ), */
+/* >            ( 0 ) */
+/* > */
+/* > where: */
+/* > */
+/* >    Q is a M-by-M orthogonal matrix; */
+/* >    R is an upper-triangular N-by-N matrix; */
+/* >    0 is a (M-N)-by-N zero matrix, if M > N. */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, the elements on and above the diagonal of the array */
+/* >          contain the f2cmin(M,N)-by-N upper trapezoidal matrix R (R is */
+/* >          upper triangular if m >= n); the elements below the diagonal, */
+/* >          with the array TAU, represent the unitary matrix Q as a */
+/* >          product of f2cmin(m,n) elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,N). */
+/* >          For optimum performance LWORK >= N*NB, where NB is */
+/* >          the optimal blocksize. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date November 2019 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(1) H(2) . . . H(k), where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */
+/* >  and tau in TAU(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeqrf_(integer *m, integer *n, complex *a, integer *lda,
+	 complex *tau, complex *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+
+    /* Local variables */
+    integer i__, k, nbmin, iinfo;
+    extern /* Subroutine */ int cgeqr2_(integer *, integer *, complex *, 
+	    integer *, complex *, complex *, integer *);
+    integer ib, nb;
+    extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, 
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *);
+    integer nx;
+    extern /* Subroutine */ int clarft_(char *, char *, integer *, integer *, 
+	    complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    integer ldwork, lwkopt;
+    logical lquery;
+    integer iws;
+
+
+/*  -- LAPACK computational routine (version 3.9.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     November 2019 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    nb = ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
+	    1);
+    lwkopt = *n * nb;
+    work[1].r = (real) lwkopt, work[1].i = 0.f;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    } else if (*lwork < f2cmax(1,*n) && ! lquery) {
+	*info = -7;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQRF", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    k = f2cmin(*m,*n);
+    if (k == 0) {
+	work[1].r = 1.f, work[1].i = 0.f;
+	return 0;
+    }
+
+    nbmin = 2;
+    nx = 0;
+    iws = *n;
+    if (nb > 1 && nb < k) {
+
+/*        Determine when to cross over from blocked to unblocked code. */
+
+/* Computing MAX */
+	i__1 = 0, i__2 = ilaenv_(&c__3, "CGEQRF", " ", m, n, &c_n1, &c_n1, (
+		ftnlen)6, (ftnlen)1);
+	nx = f2cmax(i__1,i__2);
+	if (nx < k) {
+
+/*           Determine if workspace is large enough for blocked code. */
+
+	    ldwork = *n;
+	    iws = ldwork * nb;
+	    if (*lwork < iws) {
+
+/*              Not enough workspace to use optimal NB:  reduce NB and */
+/*              determine the minimum value of NB. */
+
+		nb = *lwork / ldwork;
+/* Computing MAX */
+		i__1 = 2, i__2 = ilaenv_(&c__2, "CGEQRF", " ", m, n, &c_n1, &
+			c_n1, (ftnlen)6, (ftnlen)1);
+		nbmin = f2cmax(i__1,i__2);
+	    }
+	}
+    }
+
+    if (nb >= nbmin && nb < k && nx < k) {
+
+/*        Use blocked code initially */
+
+	i__1 = k - nx;
+	i__2 = nb;
+	for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+/* Computing MIN */
+	    i__3 = k - i__ + 1;
+	    ib = f2cmin(i__3,nb);
+
+/*           Compute the QR factorization of the current block */
+/*           A(i:m,i:i+ib-1) */
+
+	    i__3 = *m - i__ + 1;
+	    cgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
+		    1], &iinfo);
+	    if (i__ + ib <= *n) {
+
+/*              Form the triangular factor of the block reflector */
+/*              H = H(i) H(i+1) . . . H(i+ib-1) */
+
+		i__3 = *m - i__ + 1;
+		clarft_("Forward", "Columnwise", &i__3, &ib, &a[i__ + i__ * 
+			a_dim1], lda, &tau[i__], &work[1], &ldwork);
+
+/*              Apply H**H to A(i:m,i+ib:n) from the left */
+
+		i__3 = *m - i__ + 1;
+		i__4 = *n - i__ - ib + 1;
+		clarfb_("Left", "Conjugate transpose", "Forward", "Columnwise"
+			, &i__3, &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &
+			work[1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, 
+			&work[ib + 1], &ldwork);
+	    }
+/* L10: */
+	}
+    } else {
+	i__ = 1;
+    }
+
+/*     Use unblocked code to factor the last or only block. */
+
+    if (i__ <= k) {
+	i__2 = *m - i__ + 1;
+	i__1 = *n - i__ + 1;
+	cgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
+		, &iinfo);
+    }
+
+    work[1].r = (real) iws, work[1].i = 0.f;
+    return 0;
+
+/*     End of CGEQRF */
+
+} /* cgeqrf_ */
+

lapack-netlib/SRC/cgeqrfp.c

@@ -0,0 +1,704 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__3 = 3;
+static integer c__2 = 2;
+
+/* > \brief \b CGEQRFP */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEQRFP + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqrfp
+.f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqrfp
+.f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqrfp
+.f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, LWORK, M, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQR2P computes a QR factorization of a complex M-by-N matrix A: */
+/* > */
+/* >    A = Q * ( R ), */
+/* >            ( 0 ) */
+/* > */
+/* > where: */
+/* > */
+/* >    Q is a M-by-M orthogonal matrix; */
+/* >    R is an upper-triangular N-by-N matrix with nonnegative diagonal */
+/* >    entries; */
+/* >    0 is a (M-N)-by-N zero matrix, if M > N. */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, the elements on and above the diagonal of the array */
+/* >          contain the f2cmin(M,N)-by-N upper trapezoidal matrix R (R is */
+/* >          upper triangular if m >= n). The diagonal entries of R */
+/* >          are real and nonnegative; the elements below the diagonal, */
+/* >          with the array TAU, represent the unitary matrix Q as a */
+/* >          product of f2cmin(m,n) elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,N). */
+/* >          For optimum performance LWORK >= N*NB, where NB is */
+/* >          the optimal blocksize. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date November 2019 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(1) H(2) . . . H(k), where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */
+/* >  and tau in TAU(i). */
+/* > */
+/* > See Lapack Working Note 203 for details */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeqrfp_(integer *m, integer *n, complex *a, integer *
+	lda, complex *tau, complex *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+
+    /* Local variables */
+    integer i__, k, nbmin, iinfo, ib, nb;
+    extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, 
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *);
+    integer nx;
+    extern /* Subroutine */ int clarft_(char *, char *, integer *, integer *, 
+	    complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    integer ldwork, lwkopt;
+    logical lquery;
+    extern /* Subroutine */ int cgeqr2p_(integer *, integer *, complex *, 
+	    integer *, complex *, complex *, integer *);
+    integer iws;
+
+
+/*  -- LAPACK computational routine (version 3.9.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     November 2019 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    nb = ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
+	    1);
+    lwkopt = *n * nb;
+    work[1].r = (real) lwkopt, work[1].i = 0.f;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    } else if (*lwork < f2cmax(1,*n) && ! lquery) {
+	*info = -7;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQRFP", &i__1, (ftnlen)7);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    k = f2cmin(*m,*n);
+    if (k == 0) {
+	work[1].r = 1.f, work[1].i = 0.f;
+	return 0;
+    }
+
+    nbmin = 2;
+    nx = 0;
+    iws = *n;
+    if (nb > 1 && nb < k) {
+
+/*        Determine when to cross over from blocked to unblocked code. */
+
+/* Computing MAX */
+	i__1 = 0, i__2 = ilaenv_(&c__3, "CGEQRF", " ", m, n, &c_n1, &c_n1, (
+		ftnlen)6, (ftnlen)1);
+	nx = f2cmax(i__1,i__2);
+	if (nx < k) {
+
+/*           Determine if workspace is large enough for blocked code. */
+
+	    ldwork = *n;
+	    iws = ldwork * nb;
+	    if (*lwork < iws) {
+
+/*              Not enough workspace to use optimal NB:  reduce NB and */
+/*              determine the minimum value of NB. */
+
+		nb = *lwork / ldwork;
+/* Computing MAX */
+		i__1 = 2, i__2 = ilaenv_(&c__2, "CGEQRF", " ", m, n, &c_n1, &
+			c_n1, (ftnlen)6, (ftnlen)1);
+		nbmin = f2cmax(i__1,i__2);
+	    }
+	}
+    }
+
+    if (nb >= nbmin && nb < k && nx < k) {
+
+/*        Use blocked code initially */
+
+	i__1 = k - nx;
+	i__2 = nb;
+	for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+/* Computing MIN */
+	    i__3 = k - i__ + 1;
+	    ib = f2cmin(i__3,nb);
+
+/*           Compute the QR factorization of the current block */
+/*           A(i:m,i:i+ib-1) */
+
+	    i__3 = *m - i__ + 1;
+	    cgeqr2p_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
+		    work[1], &iinfo);
+	    if (i__ + ib <= *n) {
+
+/*              Form the triangular factor of the block reflector */
+/*              H = H(i) H(i+1) . . . H(i+ib-1) */
+
+		i__3 = *m - i__ + 1;
+		clarft_("Forward", "Columnwise", &i__3, &ib, &a[i__ + i__ * 
+			a_dim1], lda, &tau[i__], &work[1], &ldwork);
+
+/*              Apply H**H to A(i:m,i+ib:n) from the left */
+
+		i__3 = *m - i__ + 1;
+		i__4 = *n - i__ - ib + 1;
+		clarfb_("Left", "Conjugate transpose", "Forward", "Columnwise"
+			, &i__3, &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &
+			work[1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, 
+			&work[ib + 1], &ldwork);
+	    }
+/* L10: */
+	}
+    } else {
+	i__ = 1;
+    }
+
+/*     Use unblocked code to factor the last or only block. */
+
+    if (i__ <= k) {
+	i__2 = *m - i__ + 1;
+	i__1 = *n - i__ + 1;
+	cgeqr2p_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
+		1], &iinfo);
+    }
+
+    work[1].r = (real) iws, work[1].i = 0.f;
+    return 0;
+
+/*     End of CGEQRFP */
+
+} /* cgeqrfp_ */
+

lapack-netlib/SRC/cgeqrt.c

@@ -0,0 +1,628 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGEQRT */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEQRT + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqrt.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqrt.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqrt.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEQRT( M, N, NB, A, LDA, T, LDT, WORK, INFO ) */
+
+/*       INTEGER INFO, LDA, LDT, M, N, NB */
+/*       COMPLEX A( LDA, * ), T( LDT, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQRT computes a blocked QR factorization of a complex M-by-N matrix A */
+/* > using the compact WY representation of Q. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NB */
+/* > \verbatim */
+/* >          NB is INTEGER */
+/* >          The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, the elements on and above the diagonal of the array */
+/* >          contain the f2cmin(M,N)-by-N upper trapezoidal matrix R (R is */
+/* >          upper triangular if M >= N); the elements below the diagonal */
+/* >          are the columns of V. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (LDT,MIN(M,N)) */
+/* >          The upper triangular block reflectors stored in compact form */
+/* >          as a sequence of upper triangular blocks.  See below */
+/* >          for further details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDT */
+/* > \verbatim */
+/* >          LDT is INTEGER */
+/* >          The leading dimension of the array T.  LDT >= NB. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (NB*N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2017 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix V stores the elementary reflectors H(i) in the i-th column */
+/* >  below the diagonal. For example, if M=5 and N=3, the matrix V is */
+/* > */
+/* >               V = (  1       ) */
+/* >                   ( v1  1    ) */
+/* >                   ( v1 v2  1 ) */
+/* >                   ( v1 v2 v3 ) */
+/* >                   ( v1 v2 v3 ) */
+/* > */
+/* >  where the vi's represent the vectors which define H(i), which are returned */
+/* >  in the matrix A.  The 1's along the diagonal of V are not stored in A. */
+/* > */
+/* >  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each */
+/* >  block is of order NB except for the last block, which is of order */
+/* >  IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block */
+/* >  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB */
+/* >  for the last block) T's are stored in the NB-by-K matrix T as */
+/* > */
+/* >               T = (T1 T2 ... TB). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeqrt_(integer *m, integer *n, integer *nb, complex *a, 
+	integer *lda, complex *t, integer *ldt, complex *work, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4, i__5;
+
+    /* Local variables */
+    integer i__, k, iinfo, ib;
+    extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, 
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *, ftnlen), 
+	    cgeqrt2_(integer *, integer *, complex *, integer *, complex *, 
+	    integer *, integer *), cgeqrt3_(integer *, integer *, complex *, 
+	    integer *, complex *, integer *, integer *);
+
+
+/*  -- LAPACK computational routine (version 3.7.1) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2017 */
+
+
+/* ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1 * 1;
+    t -= t_offset;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*nb < 1 || *nb > f2cmin(*m,*n) && f2cmin(*m,*n) > 0) {
+	*info = -3;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -5;
+    } else if (*ldt < *nb) {
+	*info = -7;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQRT", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    k = f2cmin(*m,*n);
+    if (k == 0) {
+	return 0;
+    }
+
+/*     Blocked loop of length K */
+
+    i__1 = k;
+    i__2 = *nb;
+    for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+/* Computing MIN */
+	i__3 = k - i__ + 1;
+	ib = f2cmin(i__3,*nb);
+
+/*     Compute the QR factorization of the current block A(I:M,I:I+IB-1) */
+
+	if (TRUE_) {
+	    i__3 = *m - i__ + 1;
+	    cgeqrt3_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &t[i__ * t_dim1 
+		    + 1], ldt, &iinfo);
+	} else {
+	    i__3 = *m - i__ + 1;
+	    cgeqrt2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &t[i__ * t_dim1 
+		    + 1], ldt, &iinfo);
+	}
+	if (i__ + ib <= *n) {
+
+/*     Update by applying H**H to A(I:M,I+IB:N) from the left */
+
+	    i__3 = *m - i__ + 1;
+	    i__4 = *n - i__ - ib + 1;
+	    i__5 = *n - i__ - ib + 1;
+	    clarfb_("L", "C", "F", "C", &i__3, &i__4, &ib, &a[i__ + i__ * 
+		    a_dim1], lda, &t[i__ * t_dim1 + 1], ldt, &a[i__ + (i__ + 
+		    ib) * a_dim1], lda, &work[1], &i__5);
+	}
+    }
+    return 0;
+
+/*     End of CGEQRT */
+
+} /* cgeqrt_ */
+

lapack-netlib/SRC/cgeqrt2.c

@@ -0,0 +1,659 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static complex c_b2 = {0.f,0.f};
+static integer c__1 = 1;
+
+/* > \brief \b CGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY re
+presentation of Q. */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEQRT2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqrt2
+.f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqrt2
+.f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqrt2
+.f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGEQRT2( M, N, A, LDA, T, LDT, INFO ) */
+
+/*       INTEGER   INFO, LDA, LDT, M, N */
+/*       COMPLEX   A( LDA, * ), T( LDT, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQRT2 computes a QR factorization of a complex M-by-N matrix A, */
+/* > using the compact WY representation of Q. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= N. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the complex M-by-N matrix A.  On exit, the elements on and */
+/* >          above the diagonal contain the N-by-N upper triangular matrix R; the */
+/* >          elements below the diagonal are the columns of V.  See below for */
+/* >          further details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (LDT,N) */
+/* >          The N-by-N upper triangular factor of the block reflector. */
+/* >          The elements on and above the diagonal contain the block */
+/* >          reflector T; the elements below the diagonal are not used. */
+/* >          See below for further details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDT */
+/* > \verbatim */
+/* >          LDT is INTEGER */
+/* >          The leading dimension of the array T.  LDT >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix V stores the elementary reflectors H(i) in the i-th column */
+/* >  below the diagonal. For example, if M=5 and N=3, the matrix V is */
+/* > */
+/* >               V = (  1       ) */
+/* >                   ( v1  1    ) */
+/* >                   ( v1 v2  1 ) */
+/* >                   ( v1 v2 v3 ) */
+/* >                   ( v1 v2 v3 ) */
+/* > */
+/* >  where the vi's represent the vectors which define H(i), which are returned */
+/* >  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The */
+/* >  block reflector H is then given by */
+/* > */
+/* >               H = I - V * T * V**H */
+/* > */
+/* >  where V**H is the conjugate transpose of V. */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeqrt2_(integer *m, integer *n, complex *a, integer *
+	lda, complex *t, integer *ldt, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3;
+    complex q__1, q__2;
+
+    /* Local variables */
+    integer i__, k;
+    extern /* Subroutine */ int cgerc_(integer *, integer *, complex *, 
+	    complex *, integer *, complex *, integer *, complex *, integer *);
+    complex alpha;
+    extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
+	    , complex *, integer *, complex *, integer *, complex *, complex *
+	    , integer *), ctrmv_(char *, char *, char *, integer *, 
+	    complex *, integer *, complex *, integer *), clarfg_(integer *, complex *, complex *, integer *, 
+	    complex *), xerbla_(char *, integer *, ftnlen);
+    complex aii;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1 * 1;
+    t -= t_offset;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    } else if (*ldt < f2cmax(1,*n)) {
+	*info = -6;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQRT2", &i__1, (ftnlen)7);
+	return 0;
+    }
+
+    k = f2cmin(*m,*n);
+
+    i__1 = k;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+
+/*        Generate elem. refl. H(i) to annihilate A(i+1:m,i), tau(I) -> T(I,1) */
+
+	i__2 = *m - i__ + 1;
+/* Computing MIN */
+	i__3 = i__ + 1;
+	clarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[f2cmin(i__3,*m) + i__ * a_dim1]
+		, &c__1, &t[i__ + t_dim1]);
+	if (i__ < *n) {
+
+/*           Apply H(i) to A(I:M,I+1:N) from the left */
+
+	    i__2 = i__ + i__ * a_dim1;
+	    aii.r = a[i__2].r, aii.i = a[i__2].i;
+	    i__2 = i__ + i__ * a_dim1;
+	    a[i__2].r = 1.f, a[i__2].i = 0.f;
+
+/*           W(1:N-I) := A(I:M,I+1:N)**H * A(I:M,I) [W = T(:,N)] */
+
+	    i__2 = *m - i__ + 1;
+	    i__3 = *n - i__;
+	    cgemv_("C", &i__2, &i__3, &c_b1, &a[i__ + (i__ + 1) * a_dim1], 
+		    lda, &a[i__ + i__ * a_dim1], &c__1, &c_b2, &t[*n * t_dim1 
+		    + 1], &c__1);
+
+/*           A(I:M,I+1:N) = A(I:m,I+1:N) + alpha*A(I:M,I)*W(1:N-1)**H */
+
+	    r_cnjg(&q__2, &t[i__ + t_dim1]);
+	    q__1.r = -q__2.r, q__1.i = -q__2.i;
+	    alpha.r = q__1.r, alpha.i = q__1.i;
+	    i__2 = *m - i__ + 1;
+	    i__3 = *n - i__;
+	    cgerc_(&i__2, &i__3, &alpha, &a[i__ + i__ * a_dim1], &c__1, &t[*n 
+		    * t_dim1 + 1], &c__1, &a[i__ + (i__ + 1) * a_dim1], lda);
+	    i__2 = i__ + i__ * a_dim1;
+	    a[i__2].r = aii.r, a[i__2].i = aii.i;
+	}
+    }
+
+    i__1 = *n;
+    for (i__ = 2; i__ <= i__1; ++i__) {
+	i__2 = i__ + i__ * a_dim1;
+	aii.r = a[i__2].r, aii.i = a[i__2].i;
+	i__2 = i__ + i__ * a_dim1;
+	a[i__2].r = 1.f, a[i__2].i = 0.f;
+
+/*        T(1:I-1,I) := alpha * A(I:M,1:I-1)**H * A(I:M,I) */
+
+	i__2 = i__ + t_dim1;
+	q__1.r = -t[i__2].r, q__1.i = -t[i__2].i;
+	alpha.r = q__1.r, alpha.i = q__1.i;
+	i__2 = *m - i__ + 1;
+	i__3 = i__ - 1;
+	cgemv_("C", &i__2, &i__3, &alpha, &a[i__ + a_dim1], lda, &a[i__ + i__ 
+		* a_dim1], &c__1, &c_b2, &t[i__ * t_dim1 + 1], &c__1);
+	i__2 = i__ + i__ * a_dim1;
+	a[i__2].r = aii.r, a[i__2].i = aii.i;
+
+/*        T(1:I-1,I) := T(1:I-1,1:I-1) * T(1:I-1,I) */
+
+	i__2 = i__ - 1;
+	ctrmv_("U", "N", "N", &i__2, &t[t_offset], ldt, &t[i__ * t_dim1 + 1], 
+		&c__1);
+
+/*           T(I,I) = tau(I) */
+
+	i__2 = i__ + i__ * t_dim1;
+	i__3 = i__ + t_dim1;
+	t[i__2].r = t[i__3].r, t[i__2].i = t[i__3].i;
+	i__2 = i__ + t_dim1;
+	t[i__2].r = 0.f, t[i__2].i = 0.f;
+    }
+
+/*     End of CGEQRT2 */
+
+    return 0;
+} /* cgeqrt2_ */
+

lapack-netlib/SRC/cgeqrt3.c

@@ -0,0 +1,693 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+
+/* > \brief <b> CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the 
+compact WY representation of Q. </b> */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGEQRT3 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgeqrt3
+.f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgeqrt3
+.f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgeqrt3
+.f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*        SUBROUTINE CGEQRT3( M, N, A, LDA, T, LDT, INFO ) */
+
+/*       INTEGER   INFO, LDA, M, N, LDT */
+/*       COMPLEX   A( LDA, * ), T( LDT, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A, */
+/* > using the compact WY representation of Q. */
+/* > */
+/* > Based on the algorithm of Elmroth and Gustavson, */
+/* > IBM J. Res. Develop. Vol 44 No. 4 July 2000. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= N. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the complex M-by-N matrix A.  On exit, the elements on and */
+/* >          above the diagonal contain the N-by-N upper triangular matrix R; the */
+/* >          elements below the diagonal are the columns of V.  See below for */
+/* >          further details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (LDT,N) */
+/* >          The N-by-N upper triangular factor of the block reflector. */
+/* >          The elements on and above the diagonal contain the block */
+/* >          reflector T; the elements below the diagonal are not used. */
+/* >          See below for further details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDT */
+/* > \verbatim */
+/* >          LDT is INTEGER */
+/* >          The leading dimension of the array T.  LDT >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix V stores the elementary reflectors H(i) in the i-th column */
+/* >  below the diagonal. For example, if M=5 and N=3, the matrix V is */
+/* > */
+/* >               V = (  1       ) */
+/* >                   ( v1  1    ) */
+/* >                   ( v1 v2  1 ) */
+/* >                   ( v1 v2 v3 ) */
+/* >                   ( v1 v2 v3 ) */
+/* > */
+/* >  where the vi's represent the vectors which define H(i), which are returned */
+/* >  in the matrix A.  The 1's along the diagonal of V are not stored in A.  The */
+/* >  block reflector H is then given by */
+/* > */
+/* >               H = I - V * T * V**H */
+/* > */
+/* >  where V**H is the conjugate transpose of V. */
+/* > */
+/* >  For details of the algorithm, see Elmroth and Gustavson (cited above). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgeqrt3_(integer *m, integer *n, complex *a, integer *
+	lda, complex *t, integer *ldt, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4, i__5;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, j;
+    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
+	    integer *, complex *, complex *, integer *, complex *, integer *, 
+	    complex *, complex *, integer *);
+    integer iinfo;
+    extern /* Subroutine */ int ctrmm_(char *, char *, char *, char *, 
+	    integer *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *);
+    integer i1, j1, n1, n2;
+    extern /* Subroutine */ int clarfg_(integer *, complex *, complex *, 
+	    integer *, complex *), xerbla_(char *, integer *, ftnlen);
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2016 */
+
+
+/*  ===================================================================== */
+
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1 * 1;
+    t -= t_offset;
+
+    /* Function Body */
+    *info = 0;
+    if (*n < 0) {
+	*info = -2;
+    } else if (*m < *n) {
+	*info = -1;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    } else if (*ldt < f2cmax(1,*n)) {
+	*info = -6;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGEQRT3", &i__1, (ftnlen)7);
+	return 0;
+    }
+
+    if (*n == 1) {
+
+/*        Compute Householder transform when N=1 */
+
+	clarfg_(m, &a[a_dim1 + 1], &a[f2cmin(2,*m) + a_dim1], &c__1, &t[t_dim1 + 
+		1]);
+
+    } else {
+
+/*        Otherwise, split A into blocks... */
+
+	n1 = *n / 2;
+	n2 = *n - n1;
+/* Computing MIN */
+	i__1 = n1 + 1;
+	j1 = f2cmin(i__1,*n);
+/* Computing MIN */
+	i__1 = *n + 1;
+	i1 = f2cmin(i__1,*m);
+
+/*        Compute A(1:M,1:N1) <- (Y1,R1,T1), where Q1 = I - Y1 T1 Y1**H */
+
+	cgeqrt3_(m, &n1, &a[a_offset], lda, &t[t_offset], ldt, &iinfo);
+
+/*        Compute A(1:M,J1:N) = Q1**H A(1:M,J1:N) [workspace: T(1:N1,J1:N)] */
+
+	i__1 = n2;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = n1;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		i__3 = i__ + (j + n1) * t_dim1;
+		i__4 = i__ + (j + n1) * a_dim1;
+		t[i__3].r = a[i__4].r, t[i__3].i = a[i__4].i;
+	    }
+	}
+	ctrmm_("L", "L", "C", "U", &n1, &n2, &c_b1, &a[a_offset], lda, &t[j1 *
+		 t_dim1 + 1], ldt)
+		;
+
+	i__1 = *m - n1;
+	cgemm_("C", "N", &n1, &n2, &i__1, &c_b1, &a[j1 + a_dim1], lda, &a[j1 
+		+ j1 * a_dim1], lda, &c_b1, &t[j1 * t_dim1 + 1], ldt);
+
+	ctrmm_("L", "U", "C", "N", &n1, &n2, &c_b1, &t[t_offset], ldt, &t[j1 *
+		 t_dim1 + 1], ldt)
+		;
+
+	i__1 = *m - n1;
+	q__1.r = -1.f, q__1.i = 0.f;
+	cgemm_("N", "N", &i__1, &n2, &n1, &q__1, &a[j1 + a_dim1], lda, &t[j1 *
+		 t_dim1 + 1], ldt, &c_b1, &a[j1 + j1 * a_dim1], lda);
+
+	ctrmm_("L", "L", "N", "U", &n1, &n2, &c_b1, &a[a_offset], lda, &t[j1 *
+		 t_dim1 + 1], ldt)
+		;
+
+	i__1 = n2;
+	for (j = 1; j <= i__1; ++j) {
+	    i__2 = n1;
+	    for (i__ = 1; i__ <= i__2; ++i__) {
+		i__3 = i__ + (j + n1) * a_dim1;
+		i__4 = i__ + (j + n1) * a_dim1;
+		i__5 = i__ + (j + n1) * t_dim1;
+		q__1.r = a[i__4].r - t[i__5].r, q__1.i = a[i__4].i - t[i__5]
+			.i;
+		a[i__3].r = q__1.r, a[i__3].i = q__1.i;
+	    }
+	}
+
+/*        Compute A(J1:M,J1:N) <- (Y2,R2,T2) where Q2 = I - Y2 T2 Y2**H */
+
+	i__1 = *m - n1;
+	cgeqrt3_(&i__1, &n2, &a[j1 + j1 * a_dim1], lda, &t[j1 + j1 * t_dim1], 
+		ldt, &iinfo);
+
+/*        Compute T3 = T(1:N1,J1:N) = -T1 Y1**H Y2 T2 */
+
+	i__1 = n1;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    i__2 = n2;
+	    for (j = 1; j <= i__2; ++j) {
+		i__3 = i__ + (j + n1) * t_dim1;
+		r_cnjg(&q__1, &a[j + n1 + i__ * a_dim1]);
+		t[i__3].r = q__1.r, t[i__3].i = q__1.i;
+	    }
+	}
+
+	ctrmm_("R", "L", "N", "U", &n1, &n2, &c_b1, &a[j1 + j1 * a_dim1], lda,
+		 &t[j1 * t_dim1 + 1], ldt);
+
+	i__1 = *m - *n;
+	cgemm_("C", "N", &n1, &n2, &i__1, &c_b1, &a[i1 + a_dim1], lda, &a[i1 
+		+ j1 * a_dim1], lda, &c_b1, &t[j1 * t_dim1 + 1], ldt);
+
+	q__1.r = -1.f, q__1.i = 0.f;
+	ctrmm_("L", "U", "N", "N", &n1, &n2, &q__1, &t[t_offset], ldt, &t[j1 *
+		 t_dim1 + 1], ldt)
+		;
+
+	ctrmm_("R", "U", "N", "N", &n1, &n2, &c_b1, &t[j1 + j1 * t_dim1], ldt,
+		 &t[j1 * t_dim1 + 1], ldt);
+
+/*        Y = (Y1,Y2); R = [ R1  A(1:N1,J1:N) ];  T = [T1 T3] */
+/*                         [  0        R2     ]       [ 0 T2] */
+
+    }
+
+    return 0;
+
+/*     End of CGEQRT3 */
+
+} /* cgeqrt3_ */
+

lapack-netlib/SRC/cgerfs.c

@@ -0,0 +1,912 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+
+/* > \brief \b CGERFS */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGERFS + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgerfs.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgerfs.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgerfs.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGERFS( TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, */
+/*                          X, LDX, FERR, BERR, WORK, RWORK, INFO ) */
+
+/*       CHARACTER          TRANS */
+/*       INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS */
+/*       INTEGER            IPIV( * ) */
+/*       REAL               BERR( * ), FERR( * ), RWORK( * ) */
+/*       COMPLEX            A( LDA, * ), AF( LDAF, * ), B( LDB, * ), */
+/*      $                   WORK( * ), X( LDX, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGERFS improves the computed solution to a system of linear */
+/* > equations and provides error bounds and backward error estimates for */
+/* > the solution. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] TRANS */
+/* > \verbatim */
+/* >          TRANS is CHARACTER*1 */
+/* >          Specifies the form of the system of equations: */
+/* >          = 'N':  A * X = B     (No transpose) */
+/* >          = 'T':  A**T * X = B  (Transpose) */
+/* >          = 'C':  A**H * X = B  (Conjugate transpose) */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NRHS */
+/* > \verbatim */
+/* >          NRHS is INTEGER */
+/* >          The number of right hand sides, i.e., the number of columns */
+/* >          of the matrices B and X.  NRHS >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          The original N-by-N matrix A. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] AF */
+/* > \verbatim */
+/* >          AF is COMPLEX array, dimension (LDAF,N) */
+/* >          The factors L and U from the factorization A = P*L*U */
+/* >          as computed by CGETRF. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDAF */
+/* > \verbatim */
+/* >          LDAF is INTEGER */
+/* >          The leading dimension of the array AF.  LDAF >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (N) */
+/* >          The pivot indices from CGETRF; for 1<=i<=N, row i of the */
+/* >          matrix was interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] B */
+/* > \verbatim */
+/* >          B is COMPLEX array, dimension (LDB,NRHS) */
+/* >          The right hand side matrix B. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDB */
+/* > \verbatim */
+/* >          LDB is INTEGER */
+/* >          The leading dimension of the array B.  LDB >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] X */
+/* > \verbatim */
+/* >          X is COMPLEX array, dimension (LDX,NRHS) */
+/* >          On entry, the solution matrix X, as computed by CGETRS. */
+/* >          On exit, the improved solution matrix X. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDX */
+/* > \verbatim */
+/* >          LDX is INTEGER */
+/* >          The leading dimension of the array X.  LDX >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] FERR */
+/* > \verbatim */
+/* >          FERR is REAL array, dimension (NRHS) */
+/* >          The estimated forward error bound for each solution vector */
+/* >          X(j) (the j-th column of the solution matrix X). */
+/* >          If XTRUE is the true solution corresponding to X(j), FERR(j) */
+/* >          is an estimated upper bound for the magnitude of the largest */
+/* >          element in (X(j) - XTRUE) divided by the magnitude of the */
+/* >          largest element in X(j).  The estimate is as reliable as */
+/* >          the estimate for RCOND, and is almost always a slight */
+/* >          overestimate of the true error. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] BERR */
+/* > \verbatim */
+/* >          BERR is REAL array, dimension (NRHS) */
+/* >          The componentwise relative backward error of each solution */
+/* >          vector X(j) (i.e., the smallest relative change in */
+/* >          any element of A or B that makes X(j) an exact solution). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (2*N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] RWORK */
+/* > \verbatim */
+/* >          RWORK is REAL array, dimension (N) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/* > \par Internal Parameters: */
+/*  ========================= */
+/* > */
+/* > \verbatim */
+/* >  ITMAX is the maximum number of steps of iterative refinement. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgerfs_(char *trans, integer *n, integer *nrhs, complex *
+	a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex *
+	b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr, 
+	complex *work, real *rwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, 
+	    x_offset, i__1, i__2, i__3, i__4, i__5;
+    real r__1, r__2, r__3, r__4;
+    complex q__1;
+
+    /* Local variables */
+    integer kase;
+    real safe1, safe2;
+    integer i__, j, k;
+    real s;
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
+	    , complex *, integer *, complex *, integer *, complex *, complex *
+	    , integer *);
+    integer isave[3];
+    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
+	    complex *, integer *), caxpy_(integer *, complex *, complex *, 
+	    integer *, complex *, integer *);
+    integer count;
+    extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real 
+	    *, integer *, integer *);
+    real xk;
+    extern real slamch_(char *);
+    integer nz;
+    real safmin;
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), cgetrs_(
+	    char *, integer *, integer *, complex *, integer *, integer *, 
+	    complex *, integer *, integer *);
+    logical notran;
+    char transn[1], transt[1];
+    real lstres, eps;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    af_dim1 = *ldaf;
+    af_offset = 1 + af_dim1 * 1;
+    af -= af_offset;
+    --ipiv;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1 * 1;
+    b -= b_offset;
+    x_dim1 = *ldx;
+    x_offset = 1 + x_dim1 * 1;
+    x -= x_offset;
+    --ferr;
+    --berr;
+    --work;
+    --rwork;
+
+    /* Function Body */
+    *info = 0;
+    notran = lsame_(trans, "N");
+    if (! notran && ! lsame_(trans, "T") && ! lsame_(
+	    trans, "C")) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*nrhs < 0) {
+	*info = -3;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -5;
+    } else if (*ldaf < f2cmax(1,*n)) {
+	*info = -7;
+    } else if (*ldb < f2cmax(1,*n)) {
+	*info = -10;
+    } else if (*ldx < f2cmax(1,*n)) {
+	*info = -12;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGERFS", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0 || *nrhs == 0) {
+	i__1 = *nrhs;
+	for (j = 1; j <= i__1; ++j) {
+	    ferr[j] = 0.f;
+	    berr[j] = 0.f;
+/* L10: */
+	}
+	return 0;
+    }
+
+    if (notran) {
+	*(unsigned char *)transn = 'N';
+	*(unsigned char *)transt = 'C';
+    } else {
+	*(unsigned char *)transn = 'C';
+	*(unsigned char *)transt = 'N';
+    }
+
+/*     NZ = maximum number of nonzero elements in each row of A, plus 1 */
+
+    nz = *n + 1;
+    eps = slamch_("Epsilon");
+    safmin = slamch_("Safe minimum");
+    safe1 = nz * safmin;
+    safe2 = safe1 / eps;
+
+/*     Do for each right hand side */
+
+    i__1 = *nrhs;
+    for (j = 1; j <= i__1; ++j) {
+
+	count = 1;
+	lstres = 3.f;
+L20:
+
+/*        Loop until stopping criterion is satisfied. */
+
+/*        Compute residual R = B - op(A) * X, */
+/*        where op(A) = A, A**T, or A**H, depending on TRANS. */
+
+	ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
+	q__1.r = -1.f, q__1.i = 0.f;
+	cgemv_(trans, n, n, &q__1, &a[a_offset], lda, &x[j * x_dim1 + 1], &
+		c__1, &c_b1, &work[1], &c__1);
+
+/*        Compute componentwise relative backward error from formula */
+
+/*        f2cmax(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) ) */
+
+/*        where abs(Z) is the componentwise absolute value of the matrix */
+/*        or vector Z.  If the i-th component of the denominator is less */
+/*        than SAFE2, then SAFE1 is added to the i-th components of the */
+/*        numerator and denominator before dividing. */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    i__3 = i__ + j * b_dim1;
+	    rwork[i__] = (r__1 = b[i__3].r, abs(r__1)) + (r__2 = r_imag(&b[
+		    i__ + j * b_dim1]), abs(r__2));
+/* L30: */
+	}
+
+/*        Compute abs(op(A))*abs(X) + abs(B). */
+
+	if (notran) {
+	    i__2 = *n;
+	    for (k = 1; k <= i__2; ++k) {
+		i__3 = k + j * x_dim1;
+		xk = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[k + j *
+			 x_dim1]), abs(r__2));
+		i__3 = *n;
+		for (i__ = 1; i__ <= i__3; ++i__) {
+		    i__4 = i__ + k * a_dim1;
+		    rwork[i__] += ((r__1 = a[i__4].r, abs(r__1)) + (r__2 = 
+			    r_imag(&a[i__ + k * a_dim1]), abs(r__2))) * xk;
+/* L40: */
+		}
+/* L50: */
+	    }
+	} else {
+	    i__2 = *n;
+	    for (k = 1; k <= i__2; ++k) {
+		s = 0.f;
+		i__3 = *n;
+		for (i__ = 1; i__ <= i__3; ++i__) {
+		    i__4 = i__ + k * a_dim1;
+		    i__5 = i__ + j * x_dim1;
+		    s += ((r__1 = a[i__4].r, abs(r__1)) + (r__2 = r_imag(&a[
+			    i__ + k * a_dim1]), abs(r__2))) * ((r__3 = x[i__5]
+			    .r, abs(r__3)) + (r__4 = r_imag(&x[i__ + j * 
+			    x_dim1]), abs(r__4)));
+/* L60: */
+		}
+		rwork[k] += s;
+/* L70: */
+	    }
+	}
+	s = 0.f;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (rwork[i__] > safe2) {
+/* Computing MAX */
+		i__3 = i__;
+		r__3 = s, r__4 = ((r__1 = work[i__3].r, abs(r__1)) + (r__2 = 
+			r_imag(&work[i__]), abs(r__2))) / rwork[i__];
+		s = f2cmax(r__3,r__4);
+	    } else {
+/* Computing MAX */
+		i__3 = i__;
+		r__3 = s, r__4 = ((r__1 = work[i__3].r, abs(r__1)) + (r__2 = 
+			r_imag(&work[i__]), abs(r__2)) + safe1) / (rwork[i__] 
+			+ safe1);
+		s = f2cmax(r__3,r__4);
+	    }
+/* L80: */
+	}
+	berr[j] = s;
+
+/*        Test stopping criterion. Continue iterating if */
+/*           1) The residual BERR(J) is larger than machine epsilon, and */
+/*           2) BERR(J) decreased by at least a factor of 2 during the */
+/*              last iteration, and */
+/*           3) At most ITMAX iterations tried. */
+
+	if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
+
+/*           Update solution and try again. */
+
+	    cgetrs_(trans, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[1],
+		     n, info);
+	    caxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
+	    lstres = berr[j];
+	    ++count;
+	    goto L20;
+	}
+
+/*        Bound error from formula */
+
+/*        norm(X - XTRUE) / norm(X) .le. FERR = */
+/*        norm( abs(inv(op(A)))* */
+/*           ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X) */
+
+/*        where */
+/*          norm(Z) is the magnitude of the largest component of Z */
+/*          inv(op(A)) is the inverse of op(A) */
+/*          abs(Z) is the componentwise absolute value of the matrix or */
+/*             vector Z */
+/*          NZ is the maximum number of nonzeros in any row of A, plus 1 */
+/*          EPS is machine epsilon */
+
+/*        The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B)) */
+/*        is incremented by SAFE1 if the i-th component of */
+/*        abs(op(A))*abs(X) + abs(B) is less than SAFE2. */
+
+/*        Use CLACN2 to estimate the infinity-norm of the matrix */
+/*           inv(op(A)) * diag(W), */
+/*        where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
+
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+	    if (rwork[i__] > safe2) {
+		i__3 = i__;
+		rwork[i__] = (r__1 = work[i__3].r, abs(r__1)) + (r__2 = 
+			r_imag(&work[i__]), abs(r__2)) + nz * eps * rwork[i__]
+			;
+	    } else {
+		i__3 = i__;
+		rwork[i__] = (r__1 = work[i__3].r, abs(r__1)) + (r__2 = 
+			r_imag(&work[i__]), abs(r__2)) + nz * eps * rwork[i__]
+			 + safe1;
+	    }
+/* L90: */
+	}
+
+	kase = 0;
+L100:
+	clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
+	if (kase != 0) {
+	    if (kase == 1) {
+
+/*              Multiply by diag(W)*inv(op(A)**H). */
+
+		cgetrs_(transt, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &
+			work[1], n, info);
+		i__2 = *n;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    i__3 = i__;
+		    i__4 = i__;
+		    i__5 = i__;
+		    q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4] 
+			    * work[i__5].i;
+		    work[i__3].r = q__1.r, work[i__3].i = q__1.i;
+/* L110: */
+		}
+	    } else {
+
+/*              Multiply by inv(op(A))*diag(W). */
+
+		i__2 = *n;
+		for (i__ = 1; i__ <= i__2; ++i__) {
+		    i__3 = i__;
+		    i__4 = i__;
+		    i__5 = i__;
+		    q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4] 
+			    * work[i__5].i;
+		    work[i__3].r = q__1.r, work[i__3].i = q__1.i;
+/* L120: */
+		}
+		cgetrs_(transn, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &
+			work[1], n, info);
+	    }
+	    goto L100;
+	}
+
+/*        Normalize error. */
+
+	lstres = 0.f;
+	i__2 = *n;
+	for (i__ = 1; i__ <= i__2; ++i__) {
+/* Computing MAX */
+	    i__3 = i__ + j * x_dim1;
+	    r__3 = lstres, r__4 = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = 
+		    r_imag(&x[i__ + j * x_dim1]), abs(r__2));
+	    lstres = f2cmax(r__3,r__4);
+/* L130: */
+	}
+	if (lstres != 0.f) {
+	    ferr[j] /= lstres;
+	}
+
+/* L140: */
+    }
+
+    return 0;
+
+/*     End of CGERFS */
+
+} /* cgerfs_ */
+

lapack-netlib/SRC/cgerfsx.c

@@ -0,0 +1,381 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif

lapack-netlib/SRC/cgerq2.c

@@ -0,0 +1,594 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorit
+hm. */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGERQ2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgerq2.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgerq2.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgerq2.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGERQ2 computes an RQ factorization of a complex m by n matrix A: */
+/* > A = R * Q. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the m by n matrix A. */
+/* >          On exit, if m <= n, the upper triangle of the subarray */
+/* >          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; */
+/* >          if m >= n, the elements on and above the (m-n)-th subdiagonal */
+/* >          contain the m by n upper trapezoidal matrix R; the remaining */
+/* >          elements, with the array TAU, represent the unitary matrix */
+/* >          Q as a product of elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (M) */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(1)**H H(2)**H . . . H(k)**H, where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on */
+/* >  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgerq2_(integer *m, integer *n, complex *a, integer *lda,
+	 complex *tau, complex *work, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2;
+
+    /* Local variables */
+    integer i__, k;
+    complex alpha;
+    extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex *
+	    , integer *, complex *, complex *, integer *, complex *), 
+	    clarfg_(integer *, complex *, complex *, integer *, complex *), 
+	    clacgv_(integer *, complex *, integer *), xerbla_(char *, integer 
+	    *, ftnlen);
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGERQ2", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+    k = f2cmin(*m,*n);
+
+    for (i__ = k; i__ >= 1; --i__) {
+
+/*        Generate elementary reflector H(i) to annihilate */
+/*        A(m-k+i,1:n-k+i-1) */
+
+	i__1 = *n - k + i__;
+	clacgv_(&i__1, &a[*m - k + i__ + a_dim1], lda);
+	i__1 = *m - k + i__ + (*n - k + i__) * a_dim1;
+	alpha.r = a[i__1].r, alpha.i = a[i__1].i;
+	i__1 = *n - k + i__;
+	clarfg_(&i__1, &alpha, &a[*m - k + i__ + a_dim1], lda, &tau[i__]);
+
+/*        Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right */
+
+	i__1 = *m - k + i__ + (*n - k + i__) * a_dim1;
+	a[i__1].r = 1.f, a[i__1].i = 0.f;
+	i__1 = *m - k + i__ - 1;
+	i__2 = *n - k + i__;
+	clarf_("Right", &i__1, &i__2, &a[*m - k + i__ + a_dim1], lda, &tau[
+		i__], &a[a_offset], lda, &work[1]);
+	i__1 = *m - k + i__ + (*n - k + i__) * a_dim1;
+	a[i__1].r = alpha.r, a[i__1].i = alpha.i;
+	i__1 = *n - k + i__ - 1;
+	clacgv_(&i__1, &a[*m - k + i__ + a_dim1], lda);
+/* L10: */
+    }
+    return 0;
+
+/*     End of CGERQ2 */
+
+} /* cgerq2_ */
+

lapack-netlib/SRC/cgerqf.c

@@ -0,0 +1,709 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__3 = 3;
+static integer c__2 = 2;
+
+/* > \brief \b CGERQF */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGERQF + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgerqf.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgerqf.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgerqf.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, LWORK, M, N */
+/*       COMPLEX            A( LDA, * ), TAU( * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGERQF computes an RQ factorization of a complex M-by-N matrix A: */
+/* > A = R * Q. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, */
+/* >          if m <= n, the upper triangle of the subarray */
+/* >          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; */
+/* >          if m >= n, the elements on and above the (m-n)-th subdiagonal */
+/* >          contain the M-by-N upper trapezoidal matrix R; */
+/* >          the remaining elements, with the array TAU, represent the */
+/* >          unitary matrix Q as a product of f2cmin(m,n) elementary */
+/* >          reflectors (see Further Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] TAU */
+/* > \verbatim */
+/* >          TAU is COMPLEX array, dimension (f2cmin(M,N)) */
+/* >          The scalar factors of the elementary reflectors (see Further */
+/* >          Details). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,M). */
+/* >          For optimum performance LWORK >= M*NB, where NB is */
+/* >          the optimal blocksize. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  The matrix Q is represented as a product of elementary reflectors */
+/* > */
+/* >     Q = H(1)**H H(2)**H . . . H(k)**H, where k = f2cmin(m,n). */
+/* > */
+/* >  Each H(i) has the form */
+/* > */
+/* >     H(i) = I - tau * v * v**H */
+/* > */
+/* >  where tau is a complex scalar, and v is a complex vector with */
+/* >  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on */
+/* >  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgerqf_(integer *m, integer *n, complex *a, integer *lda,
+	 complex *tau, complex *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+
+    /* Local variables */
+    integer i__, k, nbmin, iinfo;
+    extern /* Subroutine */ int cgerq2_(integer *, integer *, complex *, 
+	    integer *, complex *, complex *, integer *);
+    integer ib, nb, ki, kk;
+    extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, 
+	    integer *, integer *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *);
+    integer mu, nu, nx;
+    extern /* Subroutine */ int clarft_(char *, char *, integer *, integer *, 
+	    complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    integer ldwork, lwkopt;
+    logical lquery;
+    integer iws;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --tau;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+
+    if (*info == 0) {
+	k = f2cmin(*m,*n);
+	if (k == 0) {
+	    lwkopt = 1;
+	} else {
+	    nb = ilaenv_(&c__1, "CGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, 
+		    (ftnlen)1);
+	    lwkopt = *m * nb;
+	}
+	work[1].r = (real) lwkopt, work[1].i = 0.f;
+
+	if (*lwork < f2cmax(1,*m) && ! lquery) {
+	    *info = -7;
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGERQF", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (k == 0) {
+	return 0;
+    }
+
+    nbmin = 2;
+    nx = 1;
+    iws = *m;
+    if (nb > 1 && nb < k) {
+
+/*        Determine when to cross over from blocked to unblocked code. */
+
+/* Computing MAX */
+	i__1 = 0, i__2 = ilaenv_(&c__3, "CGERQF", " ", m, n, &c_n1, &c_n1, (
+		ftnlen)6, (ftnlen)1);
+	nx = f2cmax(i__1,i__2);
+	if (nx < k) {
+
+/*           Determine if workspace is large enough for blocked code. */
+
+	    ldwork = *m;
+	    iws = ldwork * nb;
+	    if (*lwork < iws) {
+
+/*              Not enough workspace to use optimal NB:  reduce NB and */
+/*              determine the minimum value of NB. */
+
+		nb = *lwork / ldwork;
+/* Computing MAX */
+		i__1 = 2, i__2 = ilaenv_(&c__2, "CGERQF", " ", m, n, &c_n1, &
+			c_n1, (ftnlen)6, (ftnlen)1);
+		nbmin = f2cmax(i__1,i__2);
+	    }
+	}
+    }
+
+    if (nb >= nbmin && nb < k && nx < k) {
+
+/*        Use blocked code initially. */
+/*        The last kk rows are handled by the block method. */
+
+	ki = (k - nx - 1) / nb * nb;
+/* Computing MIN */
+	i__1 = k, i__2 = ki + nb;
+	kk = f2cmin(i__1,i__2);
+
+	i__1 = k - kk + 1;
+	i__2 = -nb;
+	for (i__ = k - kk + ki + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ 
+		+= i__2) {
+/* Computing MIN */
+	    i__3 = k - i__ + 1;
+	    ib = f2cmin(i__3,nb);
+
+/*           Compute the RQ factorization of the current block */
+/*           A(m-k+i:m-k+i+ib-1,1:n-k+i+ib-1) */
+
+	    i__3 = *n - k + i__ + ib - 1;
+	    cgerq2_(&ib, &i__3, &a[*m - k + i__ + a_dim1], lda, &tau[i__], &
+		    work[1], &iinfo);
+	    if (*m - k + i__ > 1) {
+
+/*              Form the triangular factor of the block reflector */
+/*              H = H(i+ib-1) . . . H(i+1) H(i) */
+
+		i__3 = *n - k + i__ + ib - 1;
+		clarft_("Backward", "Rowwise", &i__3, &ib, &a[*m - k + i__ + 
+			a_dim1], lda, &tau[i__], &work[1], &ldwork);
+
+/*              Apply H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right */
+
+		i__3 = *m - k + i__ - 1;
+		i__4 = *n - k + i__ + ib - 1;
+		clarfb_("Right", "No transpose", "Backward", "Rowwise", &i__3,
+			 &i__4, &ib, &a[*m - k + i__ + a_dim1], lda, &work[1],
+			 &ldwork, &a[a_offset], lda, &work[ib + 1], &ldwork);
+	    }
+/* L10: */
+	}
+	mu = *m - k + i__ + nb - 1;
+	nu = *n - k + i__ + nb - 1;
+    } else {
+	mu = *m;
+	nu = *n;
+    }
+
+/*     Use unblocked code to factor the last or only block */
+
+    if (mu > 0 && nu > 0) {
+	cgerq2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
+    }
+
+    work[1].r = (real) iws, work[1].i = 0.f;
+    return 0;
+
+/*     End of CGERQF */
+
+} /* cgerqf_ */
+

lapack-netlib/SRC/cgesc2.c

@@ -0,0 +1,629 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static complex c_b13 = {1.f,0.f};
+static integer c_n1 = -1;
+
+/* > \brief \b CGESC2 solves a system of linear equations using the LU factorization with complete pivoting co
+mputed by sgetc2. */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGESC2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgesc2.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgesc2.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgesc2.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE ) */
+
+/*       INTEGER            LDA, N */
+/*       REAL               SCALE */
+/*       INTEGER            IPIV( * ), JPIV( * ) */
+/*       COMPLEX            A( LDA, * ), RHS( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGESC2 solves a system of linear equations */
+/* > */
+/* >           A * X = scale* RHS */
+/* > */
+/* > with a general N-by-N matrix A using the LU factorization with */
+/* > complete pivoting computed by CGETC2. */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA, N) */
+/* >          On entry, the  LU part of the factorization of the n-by-n */
+/* >          matrix A computed by CGETC2:  A = P * L * U * Q */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1, N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] RHS */
+/* > \verbatim */
+/* >          RHS is COMPLEX array, dimension N. */
+/* >          On entry, the right hand side vector b. */
+/* >          On exit, the solution vector X. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (N). */
+/* >          The pivot indices; for 1 <= i <= N, row i of the */
+/* >          matrix has been interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] JPIV */
+/* > \verbatim */
+/* >          JPIV is INTEGER array, dimension (N). */
+/* >          The pivot indices; for 1 <= j <= N, column j of the */
+/* >          matrix has been interchanged with column JPIV(j). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] SCALE */
+/* > \verbatim */
+/* >          SCALE is REAL */
+/* >           On exit, SCALE contains the scale factor. SCALE is chosen */
+/* >           0 <= SCALE <= 1 to prevent overflow in the solution. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEauxiliary */
+
+/* > \par Contributors: */
+/*  ================== */
+/* > */
+/* >     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
+/* >     Umea University, S-901 87 Umea, Sweden. */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgesc2_(integer *n, complex *a, integer *lda, complex *
+	rhs, integer *ipiv, integer *jpiv, real *scale)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
+    real r__1;
+    complex q__1, q__2, q__3;
+
+    /* Local variables */
+    complex temp;
+    integer i__, j;
+    extern /* Subroutine */ int cscal_(integer *, complex *, complex *, 
+	    integer *), slabad_(real *, real *);
+    extern integer icamax_(integer *, complex *, integer *);
+    extern real slamch_(char *);
+    real bignum;
+    extern /* Subroutine */ int claswp_(integer *, complex *, integer *, 
+	    integer *, integer *, integer *, integer *);
+    real smlnum, eps;
+
+
+/*  -- LAPACK auxiliary routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Set constant to control overflow */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --rhs;
+    --ipiv;
+    --jpiv;
+
+    /* Function Body */
+    eps = slamch_("P");
+    smlnum = slamch_("S") / eps;
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+
+/*     Apply permutations IPIV to RHS */
+
+    i__1 = *n - 1;
+    claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &ipiv[1], &c__1);
+
+/*     Solve for L part */
+
+    i__1 = *n - 1;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	i__2 = *n;
+	for (j = i__ + 1; j <= i__2; ++j) {
+	    i__3 = j;
+	    i__4 = j;
+	    i__5 = j + i__ * a_dim1;
+	    i__6 = i__;
+	    q__2.r = a[i__5].r * rhs[i__6].r - a[i__5].i * rhs[i__6].i, 
+		    q__2.i = a[i__5].r * rhs[i__6].i + a[i__5].i * rhs[i__6]
+		    .r;
+	    q__1.r = rhs[i__4].r - q__2.r, q__1.i = rhs[i__4].i - q__2.i;
+	    rhs[i__3].r = q__1.r, rhs[i__3].i = q__1.i;
+/* L10: */
+	}
+/* L20: */
+    }
+
+/*     Solve for U part */
+
+    *scale = 1.f;
+
+/*     Check for scaling */
+
+    i__ = icamax_(n, &rhs[1], &c__1);
+    if (smlnum * 2.f * c_abs(&rhs[i__]) > c_abs(&a[*n + *n * a_dim1])) {
+	r__1 = c_abs(&rhs[i__]);
+	q__1.r = .5f / r__1, q__1.i = 0.f / r__1;
+	temp.r = q__1.r, temp.i = q__1.i;
+	cscal_(n, &temp, &rhs[1], &c__1);
+	*scale *= temp.r;
+    }
+    for (i__ = *n; i__ >= 1; --i__) {
+	c_div(&q__1, &c_b13, &a[i__ + i__ * a_dim1]);
+	temp.r = q__1.r, temp.i = q__1.i;
+	i__1 = i__;
+	i__2 = i__;
+	q__1.r = rhs[i__2].r * temp.r - rhs[i__2].i * temp.i, q__1.i = rhs[
+		i__2].r * temp.i + rhs[i__2].i * temp.r;
+	rhs[i__1].r = q__1.r, rhs[i__1].i = q__1.i;
+	i__1 = *n;
+	for (j = i__ + 1; j <= i__1; ++j) {
+	    i__2 = i__;
+	    i__3 = i__;
+	    i__4 = j;
+	    i__5 = i__ + j * a_dim1;
+	    q__3.r = a[i__5].r * temp.r - a[i__5].i * temp.i, q__3.i = a[i__5]
+		    .r * temp.i + a[i__5].i * temp.r;
+	    q__2.r = rhs[i__4].r * q__3.r - rhs[i__4].i * q__3.i, q__2.i = 
+		    rhs[i__4].r * q__3.i + rhs[i__4].i * q__3.r;
+	    q__1.r = rhs[i__3].r - q__2.r, q__1.i = rhs[i__3].i - q__2.i;
+	    rhs[i__2].r = q__1.r, rhs[i__2].i = q__1.i;
+/* L30: */
+	}
+/* L40: */
+    }
+
+/*     Apply permutations JPIV to the solution (RHS) */
+
+    i__1 = *n - 1;
+    claswp_(&c__1, &rhs[1], lda, &c__1, &i__1, &jpiv[1], &c_n1);
+    return 0;
+
+/*     End of CGESC2 */
+
+} /* cgesc2_ */
+

lapack-netlib/SRC/cgesv.c

@@ -0,0 +1,575 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief <b> CGESV computes the solution to system of linear equations A * X = B for GE matrices (simple dr
+iver) </b> */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGESV + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgesv.f
+"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgesv.f
+"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgesv.f
+"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) */
+
+/*       INTEGER            INFO, LDA, LDB, N, NRHS */
+/*       INTEGER            IPIV( * ) */
+/*       COMPLEX            A( LDA, * ), B( LDB, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGESV computes the solution to a complex system of linear equations */
+/* >    A * X = B, */
+/* > where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */
+/* > */
+/* > The LU decomposition with partial pivoting and row interchanges is */
+/* > used to factor A as */
+/* >    A = P * L * U, */
+/* > where P is a permutation matrix, L is unit lower triangular, and U is */
+/* > upper triangular.  The factored form of A is then used to solve the */
+/* > system of equations A * X = B. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of linear equations, i.e., the order of the */
+/* >          matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NRHS */
+/* > \verbatim */
+/* >          NRHS is INTEGER */
+/* >          The number of right hand sides, i.e., the number of columns */
+/* >          of the matrix B.  NRHS >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the N-by-N coefficient matrix A. */
+/* >          On exit, the factors L and U from the factorization */
+/* >          A = P*L*U; the unit diagonal elements of L are not stored. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (N) */
+/* >          The pivot indices that define the permutation matrix P; */
+/* >          row i of the matrix was interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] B */
+/* > \verbatim */
+/* >          B is COMPLEX array, dimension (LDB,NRHS) */
+/* >          On entry, the N-by-NRHS matrix of right hand side matrix B. */
+/* >          On exit, if INFO = 0, the N-by-NRHS solution matrix X. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDB */
+/* > \verbatim */
+/* >          LDB is INTEGER */
+/* >          The leading dimension of the array B.  LDB >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO = i, U(i,i) is exactly zero.  The factorization */
+/* >                has been completed, but the factor U is exactly */
+/* >                singular, so the solution could not be computed. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2017 */
+
+/* > \ingroup complexGEsolve */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgesv_(integer *n, integer *nrhs, complex *a, integer *
+	lda, integer *ipiv, complex *b, integer *ldb, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, i__1;
+
+    /* Local variables */
+    extern /* Subroutine */ int cgetrf_(integer *, integer *, complex *, 
+	    integer *, integer *, integer *), xerbla_(char *, integer *, ftnlen), cgetrs_(char *, integer *, integer *, complex *, integer 
+	    *, integer *, complex *, integer *, integer *);
+
+
+/*  -- LAPACK driver routine (version 3.7.1) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2017 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --ipiv;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1 * 1;
+    b -= b_offset;
+
+    /* Function Body */
+    *info = 0;
+    if (*n < 0) {
+	*info = -1;
+    } else if (*nrhs < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -4;
+    } else if (*ldb < f2cmax(1,*n)) {
+	*info = -7;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGESV ", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Compute the LU factorization of A. */
+
+    cgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info);
+    if (*info == 0) {
+
+/*        Solve the system A*X = B, overwriting B with X. */
+
+	cgetrs_("No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[
+		b_offset], ldb, info);
+    }
+    return 0;
+
+/*     End of CGESV */
+
+} /* cgesv_ */
+

lapack-netlib/SRC/cgetc2.c

@@ -0,0 +1,654 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static complex c_b10 = {-1.f,0.f};
+
+/* > \brief \b CGETC2 computes the LU factorization with complete pivoting of the general n-by-n matrix. */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGETC2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgetc2.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgetc2.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgetc2.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGETC2( N, A, LDA, IPIV, JPIV, INFO ) */
+
+/*       INTEGER            INFO, LDA, N */
+/*       INTEGER            IPIV( * ), JPIV( * ) */
+/*       COMPLEX            A( LDA, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGETC2 computes an LU factorization, using complete pivoting, of the */
+/* > n-by-n matrix A. The factorization has the form A = P * L * U * Q, */
+/* > where P and Q are permutation matrices, L is lower triangular with */
+/* > unit diagonal elements and U is upper triangular. */
+/* > */
+/* > This is a level 1 BLAS version of the algorithm. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A. N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA, N) */
+/* >          On entry, the n-by-n matrix to be factored. */
+/* >          On exit, the factors L and U from the factorization */
+/* >          A = P*L*U*Q; the unit diagonal elements of L are not stored. */
+/* >          If U(k, k) appears to be less than SMIN, U(k, k) is given the */
+/* >          value of SMIN, giving a nonsingular perturbed system. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1, N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (N). */
+/* >          The pivot indices; for 1 <= i <= N, row i of the */
+/* >          matrix has been interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] JPIV */
+/* > \verbatim */
+/* >          JPIV is INTEGER array, dimension (N). */
+/* >          The pivot indices; for 1 <= j <= N, column j of the */
+/* >          matrix has been interchanged with column JPIV(j). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >           = 0: successful exit */
+/* >           > 0: if INFO = k, U(k, k) is likely to produce overflow if */
+/* >                one tries to solve for x in Ax = b. So U is perturbed */
+/* >                to avoid the overflow. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2016 */
+
+/* > \ingroup complexGEauxiliary */
+
+/* > \par Contributors: */
+/*  ================== */
+/* > */
+/* >     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
+/* >     Umea University, S-901 87 Umea, Sweden. */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgetc2_(integer *n, complex *a, integer *lda, integer *
+	ipiv, integer *jpiv, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+    real r__1;
+    complex q__1;
+
+    /* Local variables */
+    real smin, xmax;
+    integer i__, j;
+    extern /* Subroutine */ int cgeru_(integer *, integer *, complex *, 
+	    complex *, integer *, complex *, integer *, complex *, integer *),
+	     cswap_(integer *, complex *, integer *, complex *, integer *), 
+	    slabad_(real *, real *);
+    integer ip, jp;
+    extern real slamch_(char *);
+    real bignum, smlnum, eps;
+    integer ipv, jpv;
+
+
+/*  -- LAPACK auxiliary routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2016 */
+
+
+/*  ===================================================================== */
+
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --ipiv;
+    --jpiv;
+
+    /* Function Body */
+    *info = 0;
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+
+/*     Set constants to control overflow */
+
+    eps = slamch_("P");
+    smlnum = slamch_("S") / eps;
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+
+/*     Handle the case N=1 by itself */
+
+    if (*n == 1) {
+	ipiv[1] = 1;
+	jpiv[1] = 1;
+	if (c_abs(&a[a_dim1 + 1]) < smlnum) {
+	    *info = 1;
+	    i__1 = a_dim1 + 1;
+	    q__1.r = smlnum, q__1.i = 0.f;
+	    a[i__1].r = q__1.r, a[i__1].i = q__1.i;
+	}
+	return 0;
+    }
+
+/*     Factorize A using complete pivoting. */
+/*     Set pivots less than SMIN to SMIN */
+
+    i__1 = *n - 1;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+
+/*        Find f2cmax element in matrix A */
+
+	xmax = 0.f;
+	i__2 = *n;
+	for (ip = i__; ip <= i__2; ++ip) {
+	    i__3 = *n;
+	    for (jp = i__; jp <= i__3; ++jp) {
+		if (c_abs(&a[ip + jp * a_dim1]) >= xmax) {
+		    xmax = c_abs(&a[ip + jp * a_dim1]);
+		    ipv = ip;
+		    jpv = jp;
+		}
+/* L10: */
+	    }
+/* L20: */
+	}
+	if (i__ == 1) {
+/* Computing MAX */
+	    r__1 = eps * xmax;
+	    smin = f2cmax(r__1,smlnum);
+	}
+
+/*        Swap rows */
+
+	if (ipv != i__) {
+	    cswap_(n, &a[ipv + a_dim1], lda, &a[i__ + a_dim1], lda);
+	}
+	ipiv[i__] = ipv;
+
+/*        Swap columns */
+
+	if (jpv != i__) {
+	    cswap_(n, &a[jpv * a_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &
+		    c__1);
+	}
+	jpiv[i__] = jpv;
+
+/*        Check for singularity */
+
+	if (c_abs(&a[i__ + i__ * a_dim1]) < smin) {
+	    *info = i__;
+	    i__2 = i__ + i__ * a_dim1;
+	    q__1.r = smin, q__1.i = 0.f;
+	    a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+	}
+	i__2 = *n;
+	for (j = i__ + 1; j <= i__2; ++j) {
+	    i__3 = j + i__ * a_dim1;
+	    c_div(&q__1, &a[j + i__ * a_dim1], &a[i__ + i__ * a_dim1]);
+	    a[i__3].r = q__1.r, a[i__3].i = q__1.i;
+/* L30: */
+	}
+	i__2 = *n - i__;
+	i__3 = *n - i__;
+	cgeru_(&i__2, &i__3, &c_b10, &a[i__ + 1 + i__ * a_dim1], &c__1, &a[
+		i__ + (i__ + 1) * a_dim1], lda, &a[i__ + 1 + (i__ + 1) * 
+		a_dim1], lda);
+/* L40: */
+    }
+
+    if (c_abs(&a[*n + *n * a_dim1]) < smin) {
+	*info = *n;
+	i__1 = *n + *n * a_dim1;
+	q__1.r = smin, q__1.i = 0.f;
+	a[i__1].r = q__1.r, a[i__1].i = q__1.i;
+    }
+
+/*     Set last pivots to N */
+
+    ipiv[*n] = *n;
+    jpiv[*n] = *n;
+
+    return 0;
+
+/*     End of CGETC2 */
+
+} /* cgetc2_ */
+

lapack-netlib/SRC/cgetf2.c

@@ -0,0 +1,624 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+
+/* > \brief \b CGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row
+ interchanges (unblocked algorithm). */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGETF2 + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgetf2.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgetf2.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgetf2.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGETF2( M, N, A, LDA, IPIV, INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       INTEGER            IPIV( * ) */
+/*       COMPLEX            A( LDA, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGETF2 computes an LU factorization of a general m-by-n matrix A */
+/* > using partial pivoting with row interchanges. */
+/* > */
+/* > The factorization has the form */
+/* >    A = P * L * U */
+/* > where P is a permutation matrix, L is lower triangular with unit */
+/* > diagonal elements (lower trapezoidal if m > n), and U is upper */
+/* > triangular (upper trapezoidal if m < n). */
+/* > */
+/* > This is the right-looking Level 2 BLAS version of the algorithm. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the m by n matrix to be factored. */
+/* >          On exit, the factors L and U from the factorization */
+/* >          A = P*L*U; the unit diagonal elements of L are not stored. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (f2cmin(M,N)) */
+/* >          The pivot indices; for 1 <= i <= f2cmin(M,N), row i of the */
+/* >          matrix was interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0: successful exit */
+/* >          < 0: if INFO = -k, the k-th argument had an illegal value */
+/* >          > 0: if INFO = k, U(k,k) is exactly zero. The factorization */
+/* >               has been completed, but the factor U is exactly */
+/* >               singular, and division by zero will occur if it is used */
+/* >               to solve a system of equations. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgetf2_(integer *m, integer *n, complex *a, integer *lda,
+	 integer *ipiv, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, j;
+    extern /* Subroutine */ int cscal_(integer *, complex *, complex *, 
+	    integer *), cgeru_(integer *, integer *, complex *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *);
+    real sfmin;
+    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
+	    complex *, integer *);
+    integer jp;
+    extern integer icamax_(integer *, complex *, integer *);
+    extern real slamch_(char *);
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --ipiv;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGETF2", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*m == 0 || *n == 0) {
+	return 0;
+    }
+
+/*     Compute machine safe minimum */
+
+    sfmin = slamch_("S");
+
+    i__1 = f2cmin(*m,*n);
+    for (j = 1; j <= i__1; ++j) {
+
+/*        Find pivot and test for singularity. */
+
+	i__2 = *m - j + 1;
+	jp = j - 1 + icamax_(&i__2, &a[j + j * a_dim1], &c__1);
+	ipiv[j] = jp;
+	i__2 = jp + j * a_dim1;
+	if (a[i__2].r != 0.f || a[i__2].i != 0.f) {
+
+/*           Apply the interchange to columns 1:N. */
+
+	    if (jp != j) {
+		cswap_(n, &a[j + a_dim1], lda, &a[jp + a_dim1], lda);
+	    }
+
+/*           Compute elements J+1:M of J-th column. */
+
+	    if (j < *m) {
+		if (c_abs(&a[j + j * a_dim1]) >= sfmin) {
+		    i__2 = *m - j;
+		    c_div(&q__1, &c_b1, &a[j + j * a_dim1]);
+		    cscal_(&i__2, &q__1, &a[j + 1 + j * a_dim1], &c__1);
+		} else {
+		    i__2 = *m - j;
+		    for (i__ = 1; i__ <= i__2; ++i__) {
+			i__3 = j + i__ + j * a_dim1;
+			c_div(&q__1, &a[j + i__ + j * a_dim1], &a[j + j * 
+				a_dim1]);
+			a[i__3].r = q__1.r, a[i__3].i = q__1.i;
+/* L20: */
+		    }
+		}
+	    }
+
+	} else if (*info == 0) {
+
+	    *info = j;
+	}
+
+	if (j < f2cmin(*m,*n)) {
+
+/*           Update trailing submatrix. */
+
+	    i__2 = *m - j;
+	    i__3 = *n - j;
+	    q__1.r = -1.f, q__1.i = 0.f;
+	    cgeru_(&i__2, &i__3, &q__1, &a[j + 1 + j * a_dim1], &c__1, &a[j + 
+		    (j + 1) * a_dim1], lda, &a[j + 1 + (j + 1) * a_dim1], lda)
+		    ;
+	}
+/* L10: */
+    }
+    return 0;
+
+/*     End of CGETF2 */
+
+} /* cgetf2_ */
+

lapack-netlib/SRC/cgetrf.c

@@ -0,0 +1,646 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+static integer c_n1 = -1;
+
+/* > \brief \b CGETRF */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGETRF + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgetrf.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgetrf.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgetrf.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGETRF( M, N, A, LDA, IPIV, INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       INTEGER            IPIV( * ) */
+/*       COMPLEX            A( LDA, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGETRF computes an LU factorization of a general M-by-N matrix A */
+/* > using partial pivoting with row interchanges. */
+/* > */
+/* > The factorization has the form */
+/* >    A = P * L * U */
+/* > where P is a permutation matrix, L is lower triangular with unit */
+/* > diagonal elements (lower trapezoidal if m > n), and U is upper */
+/* > triangular (upper trapezoidal if m < n). */
+/* > */
+/* > This is the right-looking Level 3 BLAS version of the algorithm. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix to be factored. */
+/* >          On exit, the factors L and U from the factorization */
+/* >          A = P*L*U; the unit diagonal elements of L are not stored. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (f2cmin(M,N)) */
+/* >          The pivot indices; for 1 <= i <= f2cmin(M,N), row i of the */
+/* >          matrix was interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization */
+/* >                has been completed, but the factor U is exactly */
+/* >                singular, and division by zero will occur if it is used */
+/* >                to solve a system of equations. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgetrf_(integer *m, integer *n, complex *a, integer *lda,
+	 integer *ipiv, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, j;
+    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
+	    integer *, complex *, complex *, integer *, complex *, integer *, 
+	    complex *, complex *, integer *);
+    integer iinfo;
+    extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
+	    integer *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *);
+    integer jb, nb;
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    extern /* Subroutine */ int claswp_(integer *, complex *, integer *, 
+	    integer *, integer *, integer *, integer *), cgetrf2_(integer *, 
+	    integer *, complex *, integer *, integer *, integer *);
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --ipiv;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGETRF", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*m == 0 || *n == 0) {
+	return 0;
+    }
+
+/*     Determine the block size for this environment. */
+
+    nb = ilaenv_(&c__1, "CGETRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
+	    1);
+    if (nb <= 1 || nb >= f2cmin(*m,*n)) {
+
+/*        Use unblocked code. */
+
+	cgetrf2_(m, n, &a[a_offset], lda, &ipiv[1], info);
+    } else {
+
+/*        Use blocked code. */
+
+	i__1 = f2cmin(*m,*n);
+	i__2 = nb;
+	for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
+/* Computing MIN */
+	    i__3 = f2cmin(*m,*n) - j + 1;
+	    jb = f2cmin(i__3,nb);
+
+/*           Factor diagonal and subdiagonal blocks and test for exact */
+/*           singularity. */
+
+	    i__3 = *m - j + 1;
+	    cgetrf2_(&i__3, &jb, &a[j + j * a_dim1], lda, &ipiv[j], &iinfo);
+
+/*           Adjust INFO and the pivot indices. */
+
+	    if (*info == 0 && iinfo > 0) {
+		*info = iinfo + j - 1;
+	    }
+/* Computing MIN */
+	    i__4 = *m, i__5 = j + jb - 1;
+	    i__3 = f2cmin(i__4,i__5);
+	    for (i__ = j; i__ <= i__3; ++i__) {
+		ipiv[i__] = j - 1 + ipiv[i__];
+/* L10: */
+	    }
+
+/*           Apply interchanges to columns 1:J-1. */
+
+	    i__3 = j - 1;
+	    i__4 = j + jb - 1;
+	    claswp_(&i__3, &a[a_offset], lda, &j, &i__4, &ipiv[1], &c__1);
+
+	    if (j + jb <= *n) {
+
+/*              Apply interchanges to columns J+JB:N. */
+
+		i__3 = *n - j - jb + 1;
+		i__4 = j + jb - 1;
+		claswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, &
+			ipiv[1], &c__1);
+
+/*              Compute block row of U. */
+
+		i__3 = *n - j - jb + 1;
+		ctrsm_("Left", "Lower", "No transpose", "Unit", &jb, &i__3, &
+			c_b1, &a[j + j * a_dim1], lda, &a[j + (j + jb) * 
+			a_dim1], lda);
+		if (j + jb <= *m) {
+
+/*                 Update trailing submatrix. */
+
+		    i__3 = *m - j - jb + 1;
+		    i__4 = *n - j - jb + 1;
+		    q__1.r = -1.f, q__1.i = 0.f;
+		    cgemm_("No transpose", "No transpose", &i__3, &i__4, &jb, 
+			    &q__1, &a[j + jb + j * a_dim1], lda, &a[j + (j + 
+			    jb) * a_dim1], lda, &c_b1, &a[j + jb + (j + jb) * 
+			    a_dim1], lda);
+		}
+	    }
+/* L20: */
+	}
+    }
+    return 0;
+
+/*     End of CGETRF */
+
+} /* cgetrf_ */
+

lapack-netlib/SRC/cgetrf2.c

@@ -0,0 +1,691 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+
+/* > \brief \b CGETRF2 */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/*  Definition: */
+/*  =========== */
+
+/*        SUBROUTINE CGETRF2( M, N, A, LDA, IPIV, INFO ) */
+
+/*       INTEGER            INFO, LDA, M, N */
+/*       INTEGER            IPIV( * ) */
+/*       COMPLEX            A( LDA, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGETRF2 computes an LU factorization of a general M-by-N matrix A */
+/* > using partial pivoting with row interchanges. */
+/* > */
+/* > The factorization has the form */
+/* >    A = P * L * U */
+/* > where P is a permutation matrix, L is lower triangular with unit */
+/* > diagonal elements (lower trapezoidal if m > n), and U is upper */
+/* > triangular (upper trapezoidal if m < n). */
+/* > */
+/* > This is the recursive version of the algorithm. It divides */
+/* > the matrix into four submatrices: */
+/* > */
+/* >        [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2 */
+/* >    A = [ -----|----- ]  with n1 = f2cmin(m,n)/2 */
+/* >        [  A21 | A22  ]       n2 = n-n1 */
+/* > */
+/* >                                       [ A11 ] */
+/* > The subroutine calls itself to factor [ --- ], */
+/* >                                       [ A12 ] */
+/* >                 [ A12 ] */
+/* > do the swaps on [ --- ], solve A12, update A22, */
+/* >                 [ A22 ] */
+/* > */
+/* > then calls itself to factor A22 and do the swaps on A21. */
+/* > */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix to be factored. */
+/* >          On exit, the factors L and U from the factorization */
+/* >          A = P*L*U; the unit diagonal elements of L are not stored. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (f2cmin(M,N)) */
+/* >          The pivot indices; for 1 <= i <= f2cmin(M,N), row i of the */
+/* >          matrix was interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization */
+/* >                has been completed, but the factor U is exactly */
+/* >                singular, and division by zero will occur if it is used */
+/* >                to solve a system of equations. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgetrf2_(integer *m, integer *n, complex *a, integer *
+	lda, integer *ipiv, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2;
+    complex q__1;
+
+    /* Local variables */
+    complex temp;
+    integer i__;
+    extern /* Subroutine */ int cscal_(integer *, complex *, complex *, 
+	    integer *), cgemm_(char *, char *, integer *, integer *, integer *
+	    , complex *, complex *, integer *, complex *, integer *, complex *
+	    , complex *, integer *);
+    integer iinfo;
+    real sfmin;
+    extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
+	    integer *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *);
+    integer n1, n2;
+    extern integer icamax_(integer *, complex *, integer *);
+    extern real slamch_(char *);
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), claswp_(
+	    integer *, complex *, integer *, integer *, integer *, integer *, 
+	    integer *);
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --ipiv;
+
+    /* Function Body */
+    *info = 0;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -4;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGETRF2", &i__1, (ftnlen)7);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*m == 0 || *n == 0) {
+	return 0;
+    }
+    if (*m == 1) {
+
+/*        Use unblocked code for one row case */
+/*        Just need to handle IPIV and INFO */
+
+	ipiv[1] = 1;
+	i__1 = a_dim1 + 1;
+	if (a[i__1].r == 0.f && a[i__1].i == 0.f) {
+	    *info = 1;
+	}
+
+    } else if (*n == 1) {
+
+/*        Use unblocked code for one column case */
+
+
+/*        Compute machine safe minimum */
+
+	sfmin = slamch_("S");
+
+/*        Find pivot and test for singularity */
+
+	i__ = icamax_(m, &a[a_dim1 + 1], &c__1);
+	ipiv[1] = i__;
+	i__1 = i__ + a_dim1;
+	if (a[i__1].r != 0.f || a[i__1].i != 0.f) {
+
+/*           Apply the interchange */
+
+	    if (i__ != 1) {
+		i__1 = a_dim1 + 1;
+		temp.r = a[i__1].r, temp.i = a[i__1].i;
+		i__1 = a_dim1 + 1;
+		i__2 = i__ + a_dim1;
+		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
+		i__1 = i__ + a_dim1;
+		a[i__1].r = temp.r, a[i__1].i = temp.i;
+	    }
+
+/*           Compute elements 2:M of the column */
+
+	    if (c_abs(&a[a_dim1 + 1]) >= sfmin) {
+		i__1 = *m - 1;
+		c_div(&q__1, &c_b1, &a[a_dim1 + 1]);
+		cscal_(&i__1, &q__1, &a[a_dim1 + 2], &c__1);
+	    } else {
+		i__1 = *m - 1;
+		for (i__ = 1; i__ <= i__1; ++i__) {
+		    i__2 = i__ + 1 + a_dim1;
+		    c_div(&q__1, &a[i__ + 1 + a_dim1], &a[a_dim1 + 1]);
+		    a[i__2].r = q__1.r, a[i__2].i = q__1.i;
+/* L10: */
+		}
+	    }
+
+	} else {
+	    *info = 1;
+	}
+
+    } else {
+
+/*        Use recursive code */
+
+	n1 = f2cmin(*m,*n) / 2;
+	n2 = *n - n1;
+
+/*               [ A11 ] */
+/*        Factor [ --- ] */
+/*               [ A21 ] */
+
+	cgetrf2_(m, &n1, &a[a_offset], lda, &ipiv[1], &iinfo);
+	if (*info == 0 && iinfo > 0) {
+	    *info = iinfo;
+	}
+
+/*                              [ A12 ] */
+/*        Apply interchanges to [ --- ] */
+/*                              [ A22 ] */
+
+	claswp_(&n2, &a[(n1 + 1) * a_dim1 + 1], lda, &c__1, &n1, &ipiv[1], &
+		c__1);
+
+/*        Solve A12 */
+
+	ctrsm_("L", "L", "N", "U", &n1, &n2, &c_b1, &a[a_offset], lda, &a[(n1 
+		+ 1) * a_dim1 + 1], lda);
+
+/*        Update A22 */
+
+	i__1 = *m - n1;
+	q__1.r = -1.f, q__1.i = 0.f;
+	cgemm_("N", "N", &i__1, &n2, &n1, &q__1, &a[n1 + 1 + a_dim1], lda, &a[
+		(n1 + 1) * a_dim1 + 1], lda, &c_b1, &a[n1 + 1 + (n1 + 1) * 
+		a_dim1], lda);
+
+/*        Factor A22 */
+
+	i__1 = *m - n1;
+	cgetrf2_(&i__1, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &ipiv[n1 + 
+		1], &iinfo);
+
+/*        Adjust INFO and the pivot indices */
+
+	if (*info == 0 && iinfo > 0) {
+	    *info = iinfo + n1;
+	}
+	i__1 = f2cmin(*m,*n);
+	for (i__ = n1 + 1; i__ <= i__1; ++i__) {
+	    ipiv[i__] += n1;
+/* L20: */
+	}
+
+/*        Apply interchanges to A21 */
+
+	i__1 = n1 + 1;
+	i__2 = f2cmin(*m,*n);
+	claswp_(&n1, &a[a_dim1 + 1], lda, &i__1, &i__2, &ipiv[1], &c__1);
+
+    }
+    return 0;
+
+/*     End of CGETRF2 */
+
+} /* cgetrf2_ */
+

lapack-netlib/SRC/cgetri.c

@@ -0,0 +1,701 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b2 = {1.f,0.f};
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__2 = 2;
+
+/* > \brief \b CGETRI */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGETRI + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgetri.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgetri.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgetri.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) */
+
+/*       INTEGER            INFO, LDA, LWORK, N */
+/*       INTEGER            IPIV( * ) */
+/*       COMPLEX            A( LDA, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGETRI computes the inverse of a matrix using the LU factorization */
+/* > computed by CGETRF. */
+/* > */
+/* > This method inverts U and then computes inv(A) by solving the system */
+/* > inv(A)*L = inv(U) for inv(A). */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the factors L and U from the factorization */
+/* >          A = P*L*U as computed by CGETRF. */
+/* >          On exit, if INFO = 0, the inverse of the original matrix A. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (N) */
+/* >          The pivot indices from CGETRF; for 1<=i<=N, row i of the */
+/* >          matrix was interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO=0, then WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK.  LWORK >= f2cmax(1,N). */
+/* >          For optimal performance LWORK >= N*NB, where NB is */
+/* >          the optimal blocksize returned by ILAENV. */
+/* > */
+/* >          If LWORK = -1, then a workspace query is assumed; the routine */
+/* >          only calculates the optimal size of the WORK array, returns */
+/* >          this value as the first entry of the WORK array, and no error */
+/* >          message related to LWORK is issued by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is */
+/* >                singular and its inverse could not be computed. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgetri_(integer *n, complex *a, integer *lda, integer *
+	ipiv, complex *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
+    complex q__1;
+
+    /* Local variables */
+    integer i__, j;
+    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
+	    integer *, complex *, complex *, integer *, complex *, integer *, 
+	    complex *, complex *, integer *), cgemv_(char *, 
+	    integer *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *, complex *, complex *, integer *);
+    integer nbmin;
+    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
+	    complex *, integer *), ctrsm_(char *, char *, char *, char *, 
+	    integer *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *);
+    integer jb, nb, jj, jp, nn;
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *, ftnlen, ftnlen);
+    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
+    integer ldwork;
+    extern /* Subroutine */ int ctrtri_(char *, char *, integer *, complex *, 
+	    integer *, integer *);
+    integer lwkopt;
+    logical lquery;
+    integer iws;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --ipiv;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    nb = ilaenv_(&c__1, "CGETRI", " ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
+	    ftnlen)1);
+    lwkopt = *n * nb;
+    work[1].r = (real) lwkopt, work[1].i = 0.f;
+    lquery = *lwork == -1;
+    if (*n < 0) {
+	*info = -1;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -3;
+    } else if (*lwork < f2cmax(1,*n) && ! lquery) {
+	*info = -6;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGETRI", &i__1, (ftnlen)6);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+
+/*     Form inv(U).  If INFO > 0 from CTRTRI, then U is singular, */
+/*     and the inverse is not computed. */
+
+    ctrtri_("Upper", "Non-unit", n, &a[a_offset], lda, info);
+    if (*info > 0) {
+	return 0;
+    }
+
+    nbmin = 2;
+    ldwork = *n;
+    if (nb > 1 && nb < *n) {
+/* Computing MAX */
+	i__1 = ldwork * nb;
+	iws = f2cmax(i__1,1);
+	if (*lwork < iws) {
+	    nb = *lwork / ldwork;
+/* Computing MAX */
+	    i__1 = 2, i__2 = ilaenv_(&c__2, "CGETRI", " ", n, &c_n1, &c_n1, &
+		    c_n1, (ftnlen)6, (ftnlen)1);
+	    nbmin = f2cmax(i__1,i__2);
+	}
+    } else {
+	iws = *n;
+    }
+
+/*     Solve the equation inv(A)*L = inv(U) for inv(A). */
+
+    if (nb < nbmin || nb >= *n) {
+
+/*        Use unblocked code. */
+
+	for (j = *n; j >= 1; --j) {
+
+/*           Copy current column of L to WORK and replace with zeros. */
+
+	    i__1 = *n;
+	    for (i__ = j + 1; i__ <= i__1; ++i__) {
+		i__2 = i__;
+		i__3 = i__ + j * a_dim1;
+		work[i__2].r = a[i__3].r, work[i__2].i = a[i__3].i;
+		i__2 = i__ + j * a_dim1;
+		a[i__2].r = 0.f, a[i__2].i = 0.f;
+/* L10: */
+	    }
+
+/*           Compute current column of inv(A). */
+
+	    if (j < *n) {
+		i__1 = *n - j;
+		q__1.r = -1.f, q__1.i = 0.f;
+		cgemv_("No transpose", n, &i__1, &q__1, &a[(j + 1) * a_dim1 + 
+			1], lda, &work[j + 1], &c__1, &c_b2, &a[j * a_dim1 + 
+			1], &c__1);
+	    }
+/* L20: */
+	}
+    } else {
+
+/*        Use blocked code. */
+
+	nn = (*n - 1) / nb * nb + 1;
+	i__1 = -nb;
+	for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) {
+/* Computing MIN */
+	    i__2 = nb, i__3 = *n - j + 1;
+	    jb = f2cmin(i__2,i__3);
+
+/*           Copy current block column of L to WORK and replace with */
+/*           zeros. */
+
+	    i__2 = j + jb - 1;
+	    for (jj = j; jj <= i__2; ++jj) {
+		i__3 = *n;
+		for (i__ = jj + 1; i__ <= i__3; ++i__) {
+		    i__4 = i__ + (jj - j) * ldwork;
+		    i__5 = i__ + jj * a_dim1;
+		    work[i__4].r = a[i__5].r, work[i__4].i = a[i__5].i;
+		    i__4 = i__ + jj * a_dim1;
+		    a[i__4].r = 0.f, a[i__4].i = 0.f;
+/* L30: */
+		}
+/* L40: */
+	    }
+
+/*           Compute current block column of inv(A). */
+
+	    if (j + jb <= *n) {
+		i__2 = *n - j - jb + 1;
+		q__1.r = -1.f, q__1.i = 0.f;
+		cgemm_("No transpose", "No transpose", n, &jb, &i__2, &q__1, &
+			a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], &ldwork,
+			 &c_b2, &a[j * a_dim1 + 1], lda);
+	    }
+	    ctrsm_("Right", "Lower", "No transpose", "Unit", n, &jb, &c_b2, &
+		    work[j], &ldwork, &a[j * a_dim1 + 1], lda);
+/* L50: */
+	}
+    }
+
+/*     Apply column interchanges. */
+
+    for (j = *n - 1; j >= 1; --j) {
+	jp = ipiv[j];
+	if (jp != j) {
+	    cswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1);
+	}
+/* L60: */
+    }
+
+    work[1].r = (real) iws, work[1].i = 0.f;
+    return 0;
+
+/*     End of CGETRI */
+
+} /* cgetri_ */
+

lapack-netlib/SRC/cgetrs.c

@@ -0,0 +1,620 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {1.f,0.f};
+static integer c__1 = 1;
+static integer c_n1 = -1;
+
+/* > \brief \b CGETRS */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGETRS + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgetrs.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgetrs.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgetrs.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) */
+
+/*       CHARACTER          TRANS */
+/*       INTEGER            INFO, LDA, LDB, N, NRHS */
+/*       INTEGER            IPIV( * ) */
+/*       COMPLEX            A( LDA, * ), B( LDB, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGETRS solves a system of linear equations */
+/* >    A * X = B,  A**T * X = B,  or  A**H * X = B */
+/* > with a general N-by-N matrix A using the LU factorization computed */
+/* > by CGETRF. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] TRANS */
+/* > \verbatim */
+/* >          TRANS is CHARACTER*1 */
+/* >          Specifies the form of the system of equations: */
+/* >          = 'N':  A * X = B     (No transpose) */
+/* >          = 'T':  A**T * X = B  (Transpose) */
+/* >          = 'C':  A**H * X = B  (Conjugate transpose) */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The order of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NRHS */
+/* > \verbatim */
+/* >          NRHS is INTEGER */
+/* >          The number of right hand sides, i.e., the number of columns */
+/* >          of the matrix B.  NRHS >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          The factors L and U from the factorization A = P*L*U */
+/* >          as computed by CGETRF. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IPIV */
+/* > \verbatim */
+/* >          IPIV is INTEGER array, dimension (N) */
+/* >          The pivot indices from CGETRF; for 1<=i<=N, row i of the */
+/* >          matrix was interchanged with row IPIV(i). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] B */
+/* > \verbatim */
+/* >          B is COMPLEX array, dimension (LDB,NRHS) */
+/* >          On entry, the right hand side matrix B. */
+/* >          On exit, the solution matrix X. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDB */
+/* > \verbatim */
+/* >          LDB is INTEGER */
+/* >          The leading dimension of the array B.  LDB >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGEcomputational */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgetrs_(char *trans, integer *n, integer *nrhs, complex *
+	a, integer *lda, integer *ipiv, complex *b, integer *ldb, integer *
+	info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, i__1;
+
+    /* Local variables */
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *, 
+	    integer *, integer *, complex *, complex *, integer *, complex *, 
+	    integer *), xerbla_(char *, 
+	    integer *, ftnlen), claswp_(integer *, complex *, integer *, 
+	    integer *, integer *, integer *, integer *);
+    logical notran;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    --ipiv;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1 * 1;
+    b -= b_offset;
+
+    /* Function Body */
+    *info = 0;
+    notran = lsame_(trans, "N");
+    if (! notran && ! lsame_(trans, "T") && ! lsame_(
+	    trans, "C")) {
+	*info = -1;
+    } else if (*n < 0) {
+	*info = -2;
+    } else if (*nrhs < 0) {
+	*info = -3;
+    } else if (*lda < f2cmax(1,*n)) {
+	*info = -5;
+    } else if (*ldb < f2cmax(1,*n)) {
+	*info = -8;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGETRS", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0 || *nrhs == 0) {
+	return 0;
+    }
+
+    if (notran) {
+
+/*        Solve A * X = B. */
+
+/*        Apply row interchanges to the right hand sides. */
+
+	claswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c__1);
+
+/*        Solve L*X = B, overwriting B with X. */
+
+	ctrsm_("Left", "Lower", "No transpose", "Unit", n, nrhs, &c_b1, &a[
+		a_offset], lda, &b[b_offset], ldb);
+
+/*        Solve U*X = B, overwriting B with X. */
+
+	ctrsm_("Left", "Upper", "No transpose", "Non-unit", n, nrhs, &c_b1, &
+		a[a_offset], lda, &b[b_offset], ldb);
+    } else {
+
+/*        Solve A**T * X = B  or A**H * X = B. */
+
+/*        Solve U**T *X = B or U**H *X = B, overwriting B with X. */
+
+	ctrsm_("Left", "Upper", trans, "Non-unit", n, nrhs, &c_b1, &a[
+		a_offset], lda, &b[b_offset], ldb);
+
+/*        Solve L**T *X = B, or L**H *X = B overwriting B with X. */
+
+	ctrsm_("Left", "Lower", trans, "Unit", n, nrhs, &c_b1, &a[a_offset], 
+		lda, &b[b_offset], ldb);
+
+/*        Apply row interchanges to the solution vectors. */
+
+	claswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c_n1);
+    }
+
+    return 0;
+
+/*     End of CGETRS */
+
+} /* cgetrs_ */
+

lapack-netlib/SRC/cgetsls.c

@@ -0,0 +1,939 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static complex c_b1 = {0.f,0.f};
+static integer c_n1 = -1;
+static integer c_n2 = -2;
+static integer c__0 = 0;
+
+/* > \brief \b CGETSLS */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGETSLS( TRANS, M, N, NRHS, A, LDA, B, LDB, */
+/*     $                     WORK, LWORK, INFO ) */
+
+/*       CHARACTER          TRANS */
+/*       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS */
+/*       COMPLEX            A( LDA, * ), B( LDB, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGETSLS solves overdetermined or underdetermined complex linear systems */
+/* > involving an M-by-N matrix A, using a tall skinny QR or short wide LQ */
+/* > factorization of A.  It is assumed that A has full rank. */
+/* > */
+/* > */
+/* > */
+/* > The following options are provided: */
+/* > */
+/* > 1. If TRANS = 'N' and m >= n:  find the least squares solution of */
+/* >    an overdetermined system, i.e., solve the least squares problem */
+/* >                 minimize || B - A*X ||. */
+/* > */
+/* > 2. If TRANS = 'N' and m < n:  find the minimum norm solution of */
+/* >    an underdetermined system A * X = B. */
+/* > */
+/* > 3. If TRANS = 'C' and m >= n:  find the minimum norm solution of */
+/* >    an undetermined system A**T * X = B. */
+/* > */
+/* > 4. If TRANS = 'C' and m < n:  find the least squares solution of */
+/* >    an overdetermined system, i.e., solve the least squares problem */
+/* >                 minimize || B - A**T * X ||. */
+/* > */
+/* > Several right hand side vectors b and solution vectors x can be */
+/* > handled in a single call; they are stored as the columns of the */
+/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
+/* > matrix X. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] TRANS */
+/* > \verbatim */
+/* >          TRANS is CHARACTER*1 */
+/* >          = 'N': the linear system involves A; */
+/* >          = 'C': the linear system involves A**H. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NRHS */
+/* > \verbatim */
+/* >          NRHS is INTEGER */
+/* >          The number of right hand sides, i.e., the number of */
+/* >          columns of the matrices B and X. NRHS >=0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX array, dimension (LDA,N) */
+/* >          On entry, the M-by-N matrix A. */
+/* >          On exit, */
+/* >          A is overwritten by details of its QR or LQ */
+/* >          factorization as returned by CGEQR or CGELQ. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] B */
+/* > \verbatim */
+/* >          B is COMPLEX array, dimension (LDB,NRHS) */
+/* >          On entry, the matrix B of right hand side vectors, stored */
+/* >          columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS */
+/* >          if TRANS = 'C'. */
+/* >          On exit, if INFO = 0, B is overwritten by the solution */
+/* >          vectors, stored columnwise: */
+/* >          if TRANS = 'N' and m >= n, rows 1 to n of B contain the least */
+/* >          squares solution vectors. */
+/* >          if TRANS = 'N' and m < n, rows 1 to N of B contain the */
+/* >          minimum norm solution vectors; */
+/* >          if TRANS = 'C' and m >= n, rows 1 to M of B contain the */
+/* >          minimum norm solution vectors; */
+/* >          if TRANS = 'C' and m < n, rows 1 to M of B contain the */
+/* >          least squares solution vectors. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDB */
+/* > \verbatim */
+/* >          LDB is INTEGER */
+/* >          The leading dimension of the array B. LDB >= MAX(1,M,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          (workspace) COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal */
+/* >          or optimal, if query was assumed) LWORK. */
+/* >          See LWORK for details. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          LWORK is INTEGER */
+/* >          The dimension of the array WORK. */
+/* >          If LWORK = -1 or -2, then a workspace query is assumed. */
+/* >          If LWORK = -1, the routine calculates optimal size of WORK for the */
+/* >          optimal performance and returns this value in WORK(1). */
+/* >          If LWORK = -2, the routine calculates minimal size of WORK and */
+/* >          returns this value in WORK(1). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* >          > 0:  if INFO =  i, the i-th diagonal element of the */
+/* >                triangular factor of A is zero, so that A does not have */
+/* >                full rank; the least squares solution could not be */
+/* >                computed. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date June 2017 */
+
+/* > \ingroup complexGEsolve */
+
+/*  ===================================================================== */
+/* Subroutine */ int cgetsls_(char *trans, integer *m, integer *n, integer *
+	nrhs, complex *a, integer *lda, complex *b, integer *ldb, complex *
+	work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
+    real r__1;
+
+    /* Local variables */
+    real anrm, bnrm;
+    logical tran;
+    integer brow, tszm, tszo, info2, i__, j, iascl, ibscl;
+    extern /* Subroutine */ int cgelq_(integer *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *, integer *);
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int cgeqr_(integer *, integer *, complex *, 
+	    integer *, complex *, integer *, complex *, integer *, integer *);
+    integer minmn, maxmn;
+    complex workq[1];
+    extern /* Subroutine */ int slabad_(real *, real *);
+    extern real clange_(char *, integer *, integer *, complex *, integer *, 
+	    real *);
+    extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, 
+	    real *, integer *, integer *, complex *, integer *, integer *);
+    complex tq[5];
+    extern real slamch_(char *);
+    extern /* Subroutine */ int cgemlq_(char *, char *, integer *, integer *, 
+	    integer *, complex *, integer *, complex *, integer *, complex *, 
+	    integer *, complex *, integer *, integer *), 
+	    claset_(char *, integer *, integer *, complex *, complex *, 
+	    complex *, integer *), xerbla_(char *, integer *, ftnlen),
+	     cgemqr_(char *, char *, integer *, integer *, integer *, complex 
+	    *, integer *, complex *, integer *, complex *, integer *, complex 
+	    *, integer *, integer *);
+    integer scllen;
+    real bignum, smlnum;
+    integer wsizem, wsizeo;
+    logical lquery;
+    extern /* Subroutine */ int ctrtrs_(char *, char *, char *, integer *, 
+	    integer *, complex *, integer *, complex *, integer *, integer *);
+    integer lw1, lw2, mnk;
+    real dum[1];
+    integer lwm, lwo;
+
+
+/*  -- LAPACK driver routine (version 3.7.1) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     June 2017 */
+
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    b_dim1 = *ldb;
+    b_offset = 1 + b_dim1 * 1;
+    b -= b_offset;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    minmn = f2cmin(*m,*n);
+    maxmn = f2cmax(*m,*n);
+    mnk = f2cmax(minmn,*nrhs);
+    tran = lsame_(trans, "C");
+
+    lquery = *lwork == -1 || *lwork == -2;
+    if (! (lsame_(trans, "N") || lsame_(trans, "C"))) {
+	*info = -1;
+    } else if (*m < 0) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -3;
+    } else if (*nrhs < 0) {
+	*info = -4;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -6;
+    } else /* if(complicated condition) */ {
+/* Computing MAX */
+	i__1 = f2cmax(1,*m);
+	if (*ldb < f2cmax(i__1,*n)) {
+	    *info = -8;
+	}
+    }
+
+    if (*info == 0) {
+
+/*     Determine the block size and minimum LWORK */
+
+	if (*m >= *n) {
+	    cgeqr_(m, n, &a[a_offset], lda, tq, &c_n1, workq, &c_n1, &info2);
+	    tszo = (integer) tq[0].r;
+	    lwo = (integer) workq[0].r;
+	    cgemqr_("L", trans, m, nrhs, n, &a[a_offset], lda, tq, &tszo, &b[
+		    b_offset], ldb, workq, &c_n1, &info2);
+/* Computing MAX */
+	    i__1 = lwo, i__2 = (integer) workq[0].r;
+	    lwo = f2cmax(i__1,i__2);
+	    cgeqr_(m, n, &a[a_offset], lda, tq, &c_n2, workq, &c_n2, &info2);
+	    tszm = (integer) tq[0].r;
+	    lwm = (integer) workq[0].r;
+	    cgemqr_("L", trans, m, nrhs, n, &a[a_offset], lda, tq, &tszm, &b[
+		    b_offset], ldb, workq, &c_n1, &info2);
+/* Computing MAX */
+	    i__1 = lwm, i__2 = (integer) workq[0].r;
+	    lwm = f2cmax(i__1,i__2);
+	    wsizeo = tszo + lwo;
+	    wsizem = tszm + lwm;
+	} else {
+	    cgelq_(m, n, &a[a_offset], lda, tq, &c_n1, workq, &c_n1, &info2);
+	    tszo = (integer) tq[0].r;
+	    lwo = (integer) workq[0].r;
+	    cgemlq_("L", trans, n, nrhs, m, &a[a_offset], lda, tq, &tszo, &b[
+		    b_offset], ldb, workq, &c_n1, &info2);
+/* Computing MAX */
+	    i__1 = lwo, i__2 = (integer) workq[0].r;
+	    lwo = f2cmax(i__1,i__2);
+	    cgelq_(m, n, &a[a_offset], lda, tq, &c_n2, workq, &c_n2, &info2);
+	    tszm = (integer) tq[0].r;
+	    lwm = (integer) workq[0].r;
+	    cgemlq_("L", trans, n, nrhs, m, &a[a_offset], lda, tq, &tszm, &b[
+		    b_offset], ldb, workq, &c_n1, &info2);
+/* Computing MAX */
+	    i__1 = lwm, i__2 = (integer) workq[0].r;
+	    lwm = f2cmax(i__1,i__2);
+	    wsizeo = tszo + lwo;
+	    wsizem = tszm + lwm;
+	}
+
+	if (*lwork < wsizem && ! lquery) {
+	    *info = -10;
+	}
+
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGETSLS", &i__1, (ftnlen)7);
+	r__1 = (real) wsizeo;
+	work[1].r = r__1, work[1].i = 0.f;
+	return 0;
+    }
+    if (lquery) {
+	if (*lwork == -1) {
+	    r__1 = (real) wsizeo;
+	    work[1].r = r__1, work[1].i = 0.f;
+	}
+	if (*lwork == -2) {
+	    r__1 = (real) wsizem;
+	    work[1].r = r__1, work[1].i = 0.f;
+	}
+	return 0;
+    }
+    if (*lwork < wsizeo) {
+	lw1 = tszm;
+	lw2 = lwm;
+    } else {
+	lw1 = tszo;
+	lw2 = lwo;
+    }
+
+/*     Quick return if possible */
+
+/* Computing MIN */
+    i__1 = f2cmin(*m,*n);
+    if (f2cmin(i__1,*nrhs) == 0) {
+	i__1 = f2cmax(*m,*n);
+	claset_("FULL", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
+	return 0;
+    }
+
+/*     Get machine parameters */
+
+    smlnum = slamch_("S") / slamch_("P");
+    bignum = 1.f / smlnum;
+    slabad_(&smlnum, &bignum);
+
+/*     Scale A, B if f2cmax element outside range [SMLNUM,BIGNUM] */
+
+    anrm = clange_("M", m, n, &a[a_offset], lda, dum);
+    iascl = 0;
+    if (anrm > 0.f && anrm < smlnum) {
+
+/*        Scale matrix norm up to SMLNUM */
+
+	clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, 
+		info);
+	iascl = 1;
+    } else if (anrm > bignum) {
+
+/*        Scale matrix norm down to BIGNUM */
+
+	clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, 
+		info);
+	iascl = 2;
+    } else if (anrm == 0.f) {
+
+/*        Matrix all zero. Return zero solution. */
+
+	claset_("F", &maxmn, nrhs, &c_b1, &c_b1, &b[b_offset], ldb)
+		;
+	goto L50;
+    }
+
+    brow = *m;
+    if (tran) {
+	brow = *n;
+    }
+    bnrm = clange_("M", &brow, nrhs, &b[b_offset], ldb, dum);
+    ibscl = 0;
+    if (bnrm > 0.f && bnrm < smlnum) {
+
+/*        Scale matrix norm up to SMLNUM */
+
+	clascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, nrhs, &b[b_offset], 
+		ldb, info);
+	ibscl = 1;
+    } else if (bnrm > bignum) {
+
+/*        Scale matrix norm down to BIGNUM */
+
+	clascl_("G", &c__0, &c__0, &bnrm, &bignum, &brow, nrhs, &b[b_offset], 
+		ldb, info);
+	ibscl = 2;
+    }
+
+    if (*m >= *n) {
+
+/*        compute QR factorization of A */
+
+	cgeqr_(m, n, &a[a_offset], lda, &work[lw2 + 1], &lw1, &work[1], &lw2, 
+		info);
+	if (! tran) {
+
+/*           Least-Squares Problem f2cmin || A * X - B || */
+
+/*           B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS) */
+
+	    cgemqr_("L", "C", m, nrhs, n, &a[a_offset], lda, &work[lw2 + 1], &
+		    lw1, &b[b_offset], ldb, &work[1], &lw2, info);
+
+/*           B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */
+
+	    ctrtrs_("U", "N", "N", n, nrhs, &a[a_offset], lda, &b[b_offset], 
+		    ldb, info);
+	    if (*info > 0) {
+		return 0;
+	    }
+	    scllen = *n;
+	} else {
+
+/*           Overdetermined system of equations A**T * X = B */
+
+/*           B(1:N,1:NRHS) := inv(R**T) * B(1:N,1:NRHS) */
+
+	    ctrtrs_("U", "C", "N", n, nrhs, &a[a_offset], lda, &b[b_offset], 
+		    ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+/*           B(N+1:M,1:NRHS) = CZERO */
+
+	    i__1 = *nrhs;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *m;
+		for (i__ = *n + 1; i__ <= i__2; ++i__) {
+		    i__3 = i__ + j * b_dim1;
+		    b[i__3].r = 0.f, b[i__3].i = 0.f;
+/* L10: */
+		}
+/* L20: */
+	    }
+
+/*           B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */
+
+	    cgemqr_("L", "N", m, nrhs, n, &a[a_offset], lda, &work[lw2 + 1], &
+		    lw1, &b[b_offset], ldb, &work[1], &lw2, info);
+
+	    scllen = *m;
+
+	}
+
+    } else {
+
+/*        Compute LQ factorization of A */
+
+	cgelq_(m, n, &a[a_offset], lda, &work[lw2 + 1], &lw1, &work[1], &lw2, 
+		info);
+
+/*        workspace at least M, optimally M*NB. */
+
+	if (! tran) {
+
+/*           underdetermined system of equations A * X = B */
+
+/*           B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */
+
+	    ctrtrs_("L", "N", "N", m, nrhs, &a[a_offset], lda, &b[b_offset], 
+		    ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+/*           B(M+1:N,1:NRHS) = 0 */
+
+	    i__1 = *nrhs;
+	    for (j = 1; j <= i__1; ++j) {
+		i__2 = *n;
+		for (i__ = *m + 1; i__ <= i__2; ++i__) {
+		    i__3 = i__ + j * b_dim1;
+		    b[i__3].r = 0.f, b[i__3].i = 0.f;
+/* L30: */
+		}
+/* L40: */
+	    }
+
+/*           B(1:N,1:NRHS) := Q(1:N,:)**T * B(1:M,1:NRHS) */
+
+	    cgemlq_("L", "C", n, nrhs, m, &a[a_offset], lda, &work[lw2 + 1], &
+		    lw1, &b[b_offset], ldb, &work[1], &lw2, info);
+
+/*           workspace at least NRHS, optimally NRHS*NB */
+
+	    scllen = *n;
+
+	} else {
+
+/*           overdetermined system f2cmin || A**T * X - B || */
+
+/*           B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */
+
+	    cgemlq_("L", "N", n, nrhs, m, &a[a_offset], lda, &work[lw2 + 1], &
+		    lw1, &b[b_offset], ldb, &work[1], &lw2, info);
+
+/*           workspace at least NRHS, optimally NRHS*NB */
+
+/*           B(1:M,1:NRHS) := inv(L**T) * B(1:M,1:NRHS) */
+
+	    ctrtrs_("L", "C", "N", m, nrhs, &a[a_offset], lda, &b[b_offset], 
+		    ldb, info);
+
+	    if (*info > 0) {
+		return 0;
+	    }
+
+	    scllen = *m;
+
+	}
+
+    }
+
+/*     Undo scaling */
+
+    if (iascl == 1) {
+	clascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
+		, ldb, info);
+    } else if (iascl == 2) {
+	clascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
+		, ldb, info);
+    }
+    if (ibscl == 1) {
+	clascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
+		, ldb, info);
+    } else if (ibscl == 2) {
+	clascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
+		, ldb, info);
+    }
+
+L50:
+    r__1 = (real) (tszo + lwo);
+    work[1].r = r__1, work[1].i = 0.f;
+    return 0;
+
+/*     End of ZGETSLS */
+
+} /* cgetsls_ */
+

lapack-netlib/SRC/cgetsqrhrt.c

@@ -0,0 +1,779 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* > \brief \b CGETSQRHRT */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGETSQRHRT + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgetsqr
+hrt.f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgetsqr
+hrt.f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgetsqr
+hrt.f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGETSQRHRT( M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK, */
+/*      $                       LWORK, INFO ) */
+/*       IMPLICIT NONE */
+
+/*       INTEGER           INFO, LDA, LDT, LWORK, M, N, NB1, NB2, MB1 */
+/*       COMPLEX*16        A( LDA, * ), T( LDT, * ), WORK( * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGETSQRHRT computes a NB2-sized column blocked QR-factorization */
+/* > of a complex M-by-N matrix A with M >= N, */
+/* > */
+/* >    A = Q * R. */
+/* > */
+/* > The routine uses internally a NB1-sized column blocked and MB1-sized */
+/* > row blocked TSQR-factorization and perfors the reconstruction */
+/* > of the Householder vectors from the TSQR output. The routine also */
+/* > converts the R_tsqr factor from the TSQR-factorization output into */
+/* > the R factor that corresponds to the Householder QR-factorization, */
+/* > */
+/* >    A = Q_tsqr * R_tsqr = Q * R. */
+/* > */
+/* > The output Q and R factors are stored in the same format as in CGEQRT */
+/* > (Q is in blocked compact WY-representation). See the documentation */
+/* > of CGEQRT for more details on the format. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of rows of the matrix A.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of columns of the matrix A. M >= N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] MB1 */
+/* > \verbatim */
+/* >          MB1 is INTEGER */
+/* >          The row block size to be used in the blocked TSQR. */
+/* >          MB1 > N. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NB1 */
+/* > \verbatim */
+/* >          NB1 is INTEGER */
+/* >          The column block size to be used in the blocked TSQR. */
+/* >          N >= NB1 >= 1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] NB2 */
+/* > \verbatim */
+/* >          NB2 is INTEGER */
+/* >          The block size to be used in the blocked QR that is */
+/* >          output. NB2 >= 1. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] A */
+/* > \verbatim */
+/* >          A is COMPLEX*16 array, dimension (LDA,N) */
+/* > */
+/* >          On entry: an M-by-N matrix A. */
+/* > */
+/* >          On exit: */
+/* >           a) the elements on and above the diagonal */
+/* >              of the array contain the N-by-N upper-triangular */
+/* >              matrix R corresponding to the Householder QR; */
+/* >           b) the elements below the diagonal represent Q by */
+/* >              the columns of blocked V (compact WY-representation). */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDA */
+/* > \verbatim */
+/* >          LDA is INTEGER */
+/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] T */
+/* > \verbatim */
+/* >          T is COMPLEX array, dimension (LDT,N)) */
+/* >          The upper triangular block reflectors stored in compact form */
+/* >          as a sequence of upper triangular blocks. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDT */
+/* > \verbatim */
+/* >          LDT is INTEGER */
+/* >          The leading dimension of the array T.  LDT >= NB2. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] WORK */
+/* > \verbatim */
+/* >          (workspace) COMPLEX array, dimension (MAX(1,LWORK)) */
+/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LWORK */
+/* > \verbatim */
+/* >          The dimension of the array WORK. */
+/* >          LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), */
+/* >          where */
+/* >             NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)), */
+/* >             NB1LOCAL = MIN(NB1,N). */
+/* >             LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL, */
+/* >             LW1 = NB1LOCAL * N, */
+/* >             LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ), */
+/* >          If LWORK = -1, then a workspace query is assumed. */
+/* >          The routine only calculates the optimal size of the WORK */
+/* >          array, returns this value as the first entry of the WORK */
+/* >          array, and no error message related to LWORK is issued */
+/* >          by XERBLA. */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \ingroup comlpexOTHERcomputational */
+
+/* > \par Contributors: */
+/*  ================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* > November 2020, Igor Kozachenko, */
+/* >                Computer Science Division, */
+/* >                University of California, Berkeley */
+/* > */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cgetsqrhrt_(integer *m, integer *n, integer *mb1, 
+	integer *nb1, integer *nb2, complex *a, integer *lda, complex *t, 
+	integer *ldt, complex *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4;
+    real r__1, r__2, r__3;
+    complex q__1, q__2;
+
+    /* Local variables */
+    integer ldwt, lworkopt, i__, j;
+    extern /* Subroutine */ int cungtsqr_row_(integer *, integer *, integer *
+	    , integer *, complex *, integer *, complex *, integer *, complex *
+	    , integer *, integer *);
+    integer iinfo;
+    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
+	    complex *, integer *), cunhr_col_(integer *, integer *, integer *
+	    , complex *, integer *, complex *, integer *, complex *, integer *
+	    ), xerbla_(char *, integer *, ftnlen);
+    logical lquery;
+    integer lw1, lw2, num_all_row_blocks__, lwt;
+    extern /* Subroutine */ int clatsqr_(integer *, integer *, integer *, 
+	    integer *, complex *, integer *, complex *, integer *, complex *, 
+	    integer *, integer *);
+    integer nb1local, nb2local;
+
+
+/*  -- LAPACK computational routine -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input arguments */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1 * 1;
+    a -= a_offset;
+    t_dim1 = *ldt;
+    t_offset = 1 + t_dim1 * 1;
+    t -= t_offset;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    lquery = *lwork == -1;
+    if (*m < 0) {
+	*info = -1;
+    } else if (*n < 0 || *m < *n) {
+	*info = -2;
+    } else if (*mb1 <= *n) {
+	*info = -3;
+    } else if (*nb1 < 1) {
+	*info = -4;
+    } else if (*nb2 < 1) {
+	*info = -5;
+    } else if (*lda < f2cmax(1,*m)) {
+	*info = -7;
+    } else /* if(complicated condition) */ {
+/* Computing MAX */
+	i__1 = 1, i__2 = f2cmin(*nb2,*n);
+	if (*ldt < f2cmax(i__1,i__2)) {
+	    *info = -9;
+	} else {
+
+/*        Test the input LWORK for the dimension of the array WORK. */
+/*        This workspace is used to store array: */
+/*        a) Matrix T and WORK for CLATSQR; */
+/*        b) N-by-N upper-triangular factor R_tsqr; */
+/*        c) Matrix T and array WORK for CUNGTSQR_ROW; */
+/*        d) Diagonal D for CUNHR_COL. */
+
+	    if (*lwork < *n * *n + 1 && ! lquery) {
+		*info = -11;
+	    } else {
+
+/*           Set block size for column blocks */
+
+		nb1local = f2cmin(*nb1,*n);
+
+/* Computing MAX */
+		r__3 = (real) (*m - *n) / (real) (*mb1 - *n) + .5f;
+		r__1 = 1.f, r__2 = r_int(&r__3);
+		num_all_row_blocks__ = f2cmax(r__1,r__2);
+
+/*           Length and leading dimension of WORK array to place */
+/*           T array in TSQR. */
+
+		lwt = num_all_row_blocks__ * *n * nb1local;
+		ldwt = nb1local;
+
+/*           Length of TSQR work array */
+
+		lw1 = nb1local * *n;
+
+/*           Length of CUNGTSQR_ROW work array. */
+
+/* Computing MAX */
+		i__1 = nb1local, i__2 = *n - nb1local;
+		lw2 = nb1local * f2cmax(i__1,i__2);
+
+/* Computing MAX */
+/* Computing MAX */
+		i__3 = lwt + *n * *n + lw2, i__4 = lwt + *n * *n + *n;
+		i__1 = lwt + lw1, i__2 = f2cmax(i__3,i__4);
+		lworkopt = f2cmax(i__1,i__2);
+
+		if (*lwork < f2cmax(1,lworkopt) && ! lquery) {
+		    *info = -11;
+		}
+
+	    }
+	}
+    }
+
+/*     Handle error in the input parameters and return workspace query. */
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGETSQRHRT", &i__1, (ftnlen)10);
+	return 0;
+    } else if (lquery) {
+	q__1.r = (real) lworkopt, q__1.i = 0.f;
+	work[1].r = q__1.r, work[1].i = q__1.i;
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (f2cmin(*m,*n) == 0) {
+	q__1.r = (real) lworkopt, q__1.i = 0.f;
+	work[1].r = q__1.r, work[1].i = q__1.i;
+	return 0;
+    }
+
+    nb2local = f2cmin(*nb2,*n);
+
+
+/*     (1) Perform TSQR-factorization of the M-by-N matrix A. */
+
+    clatsqr_(m, n, mb1, &nb1local, &a[a_offset], lda, &work[1], &ldwt, &work[
+	    lwt + 1], &lw1, &iinfo);
+
+/*     (2) Copy the factor R_tsqr stored in the upper-triangular part */
+/*         of A into the square matrix in the work array */
+/*         WORK(LWT+1:LWT+N*N) column-by-column. */
+
+    i__1 = *n;
+    for (j = 1; j <= i__1; ++j) {
+	ccopy_(&j, &a[j * a_dim1 + 1], &c__1, &work[lwt + *n * (j - 1) + 1], &
+		c__1);
+    }
+
+/*     (3) Generate a M-by-N matrix Q with orthonormal columns from */
+/*     the result stored below the diagonal in the array A in place. */
+
+    cungtsqr_row_(m, n, mb1, &nb1local, &a[a_offset], lda, &work[1], &ldwt, &
+	    work[lwt + *n * *n + 1], &lw2, &iinfo);
+
+/*     (4) Perform the reconstruction of Householder vectors from */
+/*     the matrix Q (stored in A) in place. */
+
+    cunhr_col_(m, n, &nb2local, &a[a_offset], lda, &t[t_offset], ldt, &work[
+	    lwt + *n * *n + 1], &iinfo);
+
+/*     (5) Copy the factor R_tsqr stored in the square matrix in the */
+/*     work array WORK(LWT+1:LWT+N*N) into the upper-triangular */
+/*     part of A. */
+
+/*     (6) Compute from R_tsqr the factor R_hr corresponding to */
+/*     the reconstructed Householder vectors, i.e. R_hr = S * R_tsqr. */
+/*     This multiplication by the sign matrix S on the left means */
+/*     changing the sign of I-th row of the matrix R_tsqr according */
+/*     to sign of the I-th diagonal element DIAG(I) of the matrix S. */
+/*     DIAG is stored in WORK( LWT+N*N+1 ) from the CUNHR_COL output. */
+
+/*     (5) and (6) can be combined in a single loop, so the rows in A */
+/*     are accessed only once. */
+
+    i__1 = *n;
+    for (i__ = 1; i__ <= i__1; ++i__) {
+	i__2 = lwt + *n * *n + i__;
+	q__1.r = -1.f, q__1.i = 0.f;
+	if (work[i__2].r == q__1.r && work[i__2].i == q__1.i) {
+	    i__2 = *n;
+	    for (j = i__; j <= i__2; ++j) {
+		i__3 = i__ + j * a_dim1;
+		q__2.r = -1.f, q__2.i = 0.f;
+		i__4 = lwt + *n * (j - 1) + i__;
+		q__1.r = q__2.r * work[i__4].r - q__2.i * work[i__4].i, 
+			q__1.i = q__2.r * work[i__4].i + q__2.i * work[i__4]
+			.r;
+		a[i__3].r = q__1.r, a[i__3].i = q__1.i;
+	    }
+	} else {
+	    i__2 = *n - i__ + 1;
+	    ccopy_(&i__2, &work[lwt + *n * (i__ - 1) + i__], n, &a[i__ + i__ *
+		     a_dim1], lda);
+	}
+    }
+
+    q__1.r = (real) lworkopt, q__1.i = 0.f;
+    work[1].r = q__1.r, work[1].i = q__1.i;
+    return 0;
+
+/*     End of CGETSQRHRT */
+
+} /* cgetsqrhrt_ */
+

lapack-netlib/SRC/cggbak.c

@@ -0,0 +1,721 @@
+/* f2c.h  --  Standard Fortran to C header file */
+
+/**  barf  [ba:rf]  2.  "He suggested using FORTRAN, and everybody barfed."
+
+	- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
+
+#ifndef F2C_INCLUDE
+#define F2C_INCLUDE
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+#include <complex.h>
+#ifdef complex
+#undef complex
+#endif
+#ifdef I
+#undef I
+#endif
+
+typedef int integer;
+typedef unsigned int uinteger;
+typedef char *address;
+typedef short int shortint;
+typedef float real;
+typedef double doublereal;
+typedef struct { real r, i; } complex;
+typedef struct { doublereal r, i; } doublecomplex;
+static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
+static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
+static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
+#define pCf(z) (*_pCf(z))
+#define pCd(z) (*_pCd(z))
+typedef int logical;
+typedef short int shortlogical;
+typedef char logical1;
+typedef char integer1;
+
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+/* Extern is for use with -E */
+#ifndef Extern
+#define Extern extern
+#endif
+
+/* I/O stuff */
+
+typedef int flag;
+typedef int ftnlen;
+typedef int ftnint;
+
+/*external read, write*/
+typedef struct
+{	flag cierr;
+	ftnint ciunit;
+	flag ciend;
+	char *cifmt;
+	ftnint cirec;
+} cilist;
+
+/*internal read, write*/
+typedef struct
+{	flag icierr;
+	char *iciunit;
+	flag iciend;
+	char *icifmt;
+	ftnint icirlen;
+	ftnint icirnum;
+} icilist;
+
+/*open*/
+typedef struct
+{	flag oerr;
+	ftnint ounit;
+	char *ofnm;
+	ftnlen ofnmlen;
+	char *osta;
+	char *oacc;
+	char *ofm;
+	ftnint orl;
+	char *oblnk;
+} olist;
+
+/*close*/
+typedef struct
+{	flag cerr;
+	ftnint cunit;
+	char *csta;
+} cllist;
+
+/*rewind, backspace, endfile*/
+typedef struct
+{	flag aerr;
+	ftnint aunit;
+} alist;
+
+/* inquire */
+typedef struct
+{	flag inerr;
+	ftnint inunit;
+	char *infile;
+	ftnlen infilen;
+	ftnint	*inex;	/*parameters in standard's order*/
+	ftnint	*inopen;
+	ftnint	*innum;
+	ftnint	*innamed;
+	char	*inname;
+	ftnlen	innamlen;
+	char	*inacc;
+	ftnlen	inacclen;
+	char	*inseq;
+	ftnlen	inseqlen;
+	char 	*indir;
+	ftnlen	indirlen;
+	char	*infmt;
+	ftnlen	infmtlen;
+	char	*inform;
+	ftnint	informlen;
+	char	*inunf;
+	ftnlen	inunflen;
+	ftnint	*inrecl;
+	ftnint	*innrec;
+	char	*inblank;
+	ftnlen	inblanklen;
+} inlist;
+
+#define VOID void
+
+union Multitype {	/* for multiple entry points */
+	integer1 g;
+	shortint h;
+	integer i;
+	/* longint j; */
+	real r;
+	doublereal d;
+	complex c;
+	doublecomplex z;
+	};
+
+typedef union Multitype Multitype;
+
+struct Vardesc {	/* for Namelist */
+	char *name;
+	char *addr;
+	ftnlen *dims;
+	int  type;
+	};
+typedef struct Vardesc Vardesc;
+
+struct Namelist {
+	char *name;
+	Vardesc **vars;
+	int nvars;
+	};
+typedef struct Namelist Namelist;
+
+#define abs(x) ((x) >= 0 ? (x) : -(x))
+#define dabs(x) (fabs(x))
+#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
+#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
+#define dmin(a,b) (f2cmin(a,b))
+#define dmax(a,b) (f2cmax(a,b))
+#define bit_test(a,b)	((a) >> (b) & 1)
+#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
+#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))
+
+#define abort_() { sig_die("Fortran abort routine called", 1); }
+#define c_abs(z) (cabsf(Cf(z)))
+#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
+#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
+#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
+#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
+#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
+#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
+//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
+#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
+#define d_abs(x) (fabs(*(x)))
+#define d_acos(x) (acos(*(x)))
+#define d_asin(x) (asin(*(x)))
+#define d_atan(x) (atan(*(x)))
+#define d_atn2(x, y) (atan2(*(x),*(y)))
+#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
+#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
+#define d_cos(x) (cos(*(x)))
+#define d_cosh(x) (cosh(*(x)))
+#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
+#define d_exp(x) (exp(*(x)))
+#define d_imag(z) (cimag(Cd(z)))
+#define r_imag(z) (cimag(Cf(z)))
+#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
+#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
+#define d_log(x) (log(*(x)))
+#define d_mod(x, y) (fmod(*(x), *(y)))
+#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
+#define d_nint(x) u_nint(*(x))
+#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
+#define d_sign(a,b) u_sign(*(a),*(b))
+#define r_sign(a,b) u_sign(*(a),*(b))
+#define d_sin(x) (sin(*(x)))
+#define d_sinh(x) (sinh(*(x)))
+#define d_sqrt(x) (sqrt(*(x)))
+#define d_tan(x) (tan(*(x)))
+#define d_tanh(x) (tanh(*(x)))
+#define i_abs(x) abs(*(x))
+#define i_dnnt(x) ((integer)u_nint(*(x)))
+#define i_len(s, n) (n)
+#define i_nint(x) ((integer)u_nint(*(x)))
+#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
+#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
+#define pow_si(B,E) spow_ui(*(B),*(E))
+#define pow_ri(B,E) spow_ui(*(B),*(E))
+#define pow_di(B,E) dpow_ui(*(B),*(E))
+#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
+#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
+#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
+#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
+#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
+#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
+#define sig_die(s, kill) { exit(1); }
+#define s_stop(s, n) {exit(0);}
+static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
+#define z_abs(z) (cabs(Cd(z)))
+#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
+#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
+#define myexit_() break;
+#define mycycle() continue;
+#define myceiling(w) {ceil(w)}
+#define myhuge(w) {HUGE_VAL}
+//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
+#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
+
+/* procedure parameter types for -A and -C++ */
+
+#define F2C_proc_par_types 1
+#ifdef __cplusplus
+typedef logical (*L_fp)(...);
+#else
+typedef logical (*L_fp)();
+#endif
+
+static float spow_ui(float x, integer n) {
+	float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static double dpow_ui(double x, integer n) {
+	double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex float cpow_ui(_Complex float x, integer n) {
+	_Complex float pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static _Complex double zpow_ui(_Complex double x, integer n) {
+	_Complex double pow=1.0; unsigned long int u;
+	if(n != 0) {
+		if(n < 0) n = -n, x = 1/x;
+		for(u = n; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer pow_ii(integer x, integer n) {
+	integer pow; unsigned long int u;
+	if (n <= 0) {
+		if (n == 0 || x == 1) pow = 1;
+		else if (x != -1) pow = x == 0 ? 1/x : 0;
+		else n = -n;
+	}
+	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
+		u = n;
+		for(pow = 1; ; ) {
+			if(u & 01) pow *= x;
+			if(u >>= 1) x *= x;
+			else break;
+		}
+	}
+	return pow;
+}
+static integer dmaxloc_(double *w, integer s, integer e, integer *n)
+{
+	double m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static integer smaxloc_(float *w, integer s, integer e, integer *n)
+{
+	float m; integer i, mi;
+	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
+		if (w[i-1]>m) mi=i ,m=w[i-1];
+	return mi-s+1;
+}
+static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}	
+static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex float zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i]) * Cf(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
+		}
+	}
+	pCf(z) = zdotc;
+}
+static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
+	integer n = *n_, incx = *incx_, incy = *incy_, i;
+	_Complex double zdotc = 0.0;
+	if (incx == 1 && incy == 1) {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i]) * Cd(&y[i]);
+		}
+	} else {
+		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
+			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
+		}
+	}
+	pCd(z) = zdotc;
+}
+#endif
+/*  -- translated by f2c (version 20000121).
+   You must link the resulting object file with the libraries:
+	-lf2c -lm   (in that order)
+*/
+
+
+
+/* > \brief \b CGGBAK */
+
+/*  =========== DOCUMENTATION =========== */
+
+/* Online html documentation available at */
+/*            http://www.netlib.org/lapack/explore-html/ */
+
+/* > \htmlonly */
+/* > Download CGGBAK + dependencies */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cggbak.
+f"> */
+/* > [TGZ]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cggbak.
+f"> */
+/* > [ZIP]</a> */
+/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cggbak.
+f"> */
+/* > [TXT]</a> */
+/* > \endhtmlonly */
+
+/*  Definition: */
+/*  =========== */
+
+/*       SUBROUTINE CGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V, */
+/*                          LDV, INFO ) */
+
+/*       CHARACTER          JOB, SIDE */
+/*       INTEGER            IHI, ILO, INFO, LDV, M, N */
+/*       REAL               LSCALE( * ), RSCALE( * ) */
+/*       COMPLEX            V( LDV, * ) */
+
+
+/* > \par Purpose: */
+/*  ============= */
+/* > */
+/* > \verbatim */
+/* > */
+/* > CGGBAK forms the right or left eigenvectors of a complex generalized */
+/* > eigenvalue problem A*x = lambda*B*x, by backward transformation on */
+/* > the computed eigenvectors of the balanced pair of matrices output by */
+/* > CGGBAL. */
+/* > \endverbatim */
+
+/*  Arguments: */
+/*  ========== */
+
+/* > \param[in] JOB */
+/* > \verbatim */
+/* >          JOB is CHARACTER*1 */
+/* >          Specifies the type of backward transformation required: */
+/* >          = 'N':  do nothing, return immediately; */
+/* >          = 'P':  do backward transformation for permutation only; */
+/* >          = 'S':  do backward transformation for scaling only; */
+/* >          = 'B':  do backward transformations for both permutation and */
+/* >                  scaling. */
+/* >          JOB must be the same as the argument JOB supplied to CGGBAL. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] SIDE */
+/* > \verbatim */
+/* >          SIDE is CHARACTER*1 */
+/* >          = 'R':  V contains right eigenvectors; */
+/* >          = 'L':  V contains left eigenvectors. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] N */
+/* > \verbatim */
+/* >          N is INTEGER */
+/* >          The number of rows of the matrix V.  N >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] ILO */
+/* > \verbatim */
+/* >          ILO is INTEGER */
+/* > \endverbatim */
+/* > */
+/* > \param[in] IHI */
+/* > \verbatim */
+/* >          IHI is INTEGER */
+/* >          The integers ILO and IHI determined by CGGBAL. */
+/* >          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LSCALE */
+/* > \verbatim */
+/* >          LSCALE is REAL array, dimension (N) */
+/* >          Details of the permutations and/or scaling factors applied */
+/* >          to the left side of A and B, as returned by CGGBAL. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] RSCALE */
+/* > \verbatim */
+/* >          RSCALE is REAL array, dimension (N) */
+/* >          Details of the permutations and/or scaling factors applied */
+/* >          to the right side of A and B, as returned by CGGBAL. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] M */
+/* > \verbatim */
+/* >          M is INTEGER */
+/* >          The number of columns of the matrix V.  M >= 0. */
+/* > \endverbatim */
+/* > */
+/* > \param[in,out] V */
+/* > \verbatim */
+/* >          V is COMPLEX array, dimension (LDV,M) */
+/* >          On entry, the matrix of right or left eigenvectors to be */
+/* >          transformed, as returned by CTGEVC. */
+/* >          On exit, V is overwritten by the transformed eigenvectors. */
+/* > \endverbatim */
+/* > */
+/* > \param[in] LDV */
+/* > \verbatim */
+/* >          LDV is INTEGER */
+/* >          The leading dimension of the matrix V. LDV >= f2cmax(1,N). */
+/* > \endverbatim */
+/* > */
+/* > \param[out] INFO */
+/* > \verbatim */
+/* >          INFO is INTEGER */
+/* >          = 0:  successful exit. */
+/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
+/* > \endverbatim */
+
+/*  Authors: */
+/*  ======== */
+
+/* > \author Univ. of Tennessee */
+/* > \author Univ. of California Berkeley */
+/* > \author Univ. of Colorado Denver */
+/* > \author NAG Ltd. */
+
+/* > \date December 2016 */
+
+/* > \ingroup complexGBcomputational */
+
+/* > \par Further Details: */
+/*  ===================== */
+/* > */
+/* > \verbatim */
+/* > */
+/* >  See R.C. Ward, Balancing the generalized eigenvalue problem, */
+/* >                 SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. */
+/* > \endverbatim */
+/* > */
+/*  ===================================================================== */
+/* Subroutine */ int cggbak_(char *job, char *side, integer *n, integer *ilo, 
+	integer *ihi, real *lscale, real *rscale, integer *m, complex *v, 
+	integer *ldv, integer *info)
+{
+    /* System generated locals */
+    integer v_dim1, v_offset, i__1;
+
+    /* Local variables */
+    integer i__, k;
+    extern logical lsame_(char *, char *);
+    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
+	    complex *, integer *);
+    logical leftv;
+    extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer 
+	    *), xerbla_(char *, integer *, ftnlen);
+    logical rightv;
+
+
+/*  -- LAPACK computational routine (version 3.7.0) -- */
+/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
+/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
+/*     December 2016 */
+
+
+/*  ===================================================================== */
+
+
+/*     Test the input parameters */
+
+    /* Parameter adjustments */
+    --lscale;
+    --rscale;
+    v_dim1 = *ldv;
+    v_offset = 1 + v_dim1 * 1;
+    v -= v_offset;
+
+    /* Function Body */
+    rightv = lsame_(side, "R");
+    leftv = lsame_(side, "L");
+
+    *info = 0;
+    if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S") 
+	    && ! lsame_(job, "B")) {
+	*info = -1;
+    } else if (! rightv && ! leftv) {
+	*info = -2;
+    } else if (*n < 0) {
+	*info = -3;
+    } else if (*ilo < 1) {
+	*info = -4;
+    } else if (*n == 0 && *ihi == 0 && *ilo != 1) {
+	*info = -4;
+    } else if (*n > 0 && (*ihi < *ilo || *ihi > f2cmax(1,*n))) {
+	*info = -5;
+    } else if (*n == 0 && *ilo == 1 && *ihi != 0) {
+	*info = -5;
+    } else if (*m < 0) {
+	*info = -8;
+    } else if (*ldv < f2cmax(1,*n)) {
+	*info = -10;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("CGGBAK", &i__1, (ftnlen)6);
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+    if (*m == 0) {
+	return 0;
+    }
+    if (lsame_(job, "N")) {
+	return 0;
+    }
+
+    if (*ilo == *ihi) {
+	goto L30;
+    }
+
+/*     Backward balance */
+
+    if (lsame_(job, "S") || lsame_(job, "B")) {
+
+/*        Backward transformation on right eigenvectors */
+
+	if (rightv) {
+	    i__1 = *ihi;
+	    for (i__ = *ilo; i__ <= i__1; ++i__) {
+		csscal_(m, &rscale[i__], &v[i__ + v_dim1], ldv);
+/* L10: */
+	    }
+	}
+
+/*        Backward transformation on left eigenvectors */
+
+	if (leftv) {
+	    i__1 = *ihi;
+	    for (i__ = *ilo; i__ <= i__1; ++i__) {
+		csscal_(m, &lscale[i__], &v[i__ + v_dim1], ldv);
+/* L20: */
+	    }
+	}
+    }
+
+/*     Backward permutation */
+
+L30:
+    if (lsame_(job, "P") || lsame_(job, "B")) {
+
+/*        Backward permutation on right eigenvectors */
+
+	if (rightv) {
+	    if (*ilo == 1) {
+		goto L50;
+	    }
+	    for (i__ = *ilo - 1; i__ >= 1; --i__) {
+		k = rscale[i__];
+		if (k == i__) {
+		    goto L40;
+		}
+		cswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
+L40:
+		;
+	    }
+
+L50:
+	    if (*ihi == *n) {
+		goto L70;
+	    }
+	    i__1 = *n;
+	    for (i__ = *ihi + 1; i__ <= i__1; ++i__) {
+		k = rscale[i__];
+		if (k == i__) {
+		    goto L60;
+		}
+		cswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
+L60:
+		;
+	    }
+	}
+
+/*        Backward permutation on left eigenvectors */
+
+L70:
+	if (leftv) {
+	    if (*ilo == 1) {
+		goto L90;
+	    }
+	    for (i__ = *ilo - 1; i__ >= 1; --i__) {
+		k = lscale[i__];
+		if (k == i__) {
+		    goto L80;
+		}
+		cswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
+L80:
+		;
+	    }
+
+L90:
+	    if (*ihi == *n) {
+		goto L110;
+	    }
+	    i__1 = *n;
+	    for (i__ = *ihi + 1; i__ <= i__1; ++i__) {
+		k = lscale[i__];
+		if (k == i__) {
+		    goto L100;
+		}
+		cswap_(m, &v[i__ + v_dim1], ldv, &v[k + v_dim1], ldv);
+L100:
+		;
+	    }
+	}
+    }
+
+L110:
+
+    return 0;
+
+/*     End of CGGBAK */
+
+} /* cggbak_ */
+