OpenBLAS/lapack-netlib/SRC/cheevr.c

/* 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__10 = 10;
static integer c__1 = 1;
static integer c__2 = 2;
static integer c__3 = 3;
static integer c__4 = 4;
static integer c_n1 = -1;

/* > \brief <b> CHEEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE mat
rices</b> */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download CHEEVR + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cheevr.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cheevr.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cheevr.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE CHEEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, */
/*                          ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, */
/*                          RWORK, LRWORK, IWORK, LIWORK, INFO ) */

/*       CHARACTER          JOBZ, RANGE, UPLO */
/*       INTEGER            IL, INFO, IU, LDA, LDZ, LIWORK, LRWORK, LWORK, */
/*      $                   M, N */
/*       REAL               ABSTOL, VL, VU */
/*       INTEGER            ISUPPZ( * ), IWORK( * ) */
/*       REAL               RWORK( * ), W( * ) */
/*       COMPLEX            A( LDA, * ), WORK( * ), Z( LDZ, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > CHEEVR computes selected eigenvalues and, optionally, eigenvectors */
/* > of a complex Hermitian matrix A.  Eigenvalues and eigenvectors can */
/* > be selected by specifying either a range of values or a range of */
/* > indices for the desired eigenvalues. */
/* > */
/* > CHEEVR first reduces the matrix A to tridiagonal form T with a call */
/* > to CHETRD.  Then, whenever possible, CHEEVR calls CSTEMR to compute */
/* > the eigenspectrum using Relatively Robust Representations.  CSTEMR */
/* > computes eigenvalues by the dqds algorithm, while orthogonal */
/* > eigenvectors are computed from various "good" L D L^T representations */
/* > (also known as Relatively Robust Representations). Gram-Schmidt */
/* > orthogonalization is avoided as far as possible. More specifically, */
/* > the various steps of the algorithm are as follows. */
/* > */
/* > For each unreduced block (submatrix) of T, */
/* >    (a) Compute T - sigma I  = L D L^T, so that L and D */
/* >        define all the wanted eigenvalues to high relative accuracy. */
/* >        This means that small relative changes in the entries of D and L */
/* >        cause only small relative changes in the eigenvalues and */
/* >        eigenvectors. The standard (unfactored) representation of the */
/* >        tridiagonal matrix T does not have this property in general. */
/* >    (b) Compute the eigenvalues to suitable accuracy. */
/* >        If the eigenvectors are desired, the algorithm attains full */
/* >        accuracy of the computed eigenvalues only right before */
/* >        the corresponding vectors have to be computed, see steps c) and d). */
/* >    (c) For each cluster of close eigenvalues, select a new */
/* >        shift close to the cluster, find a new factorization, and refine */
/* >        the shifted eigenvalues to suitable accuracy. */
/* >    (d) For each eigenvalue with a large enough relative separation compute */
/* >        the corresponding eigenvector by forming a rank revealing twisted */
/* >        factorization. Go back to (c) for any clusters that remain. */
/* > */
/* > The desired accuracy of the output can be specified by the input */
/* > parameter ABSTOL. */
/* > */
/* > For more details, see DSTEMR's documentation and: */
/* > - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations */
/* >   to compute orthogonal eigenvectors of symmetric tridiagonal matrices," */
/* >   Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. */
/* > - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and */
/* >   Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, */
/* >   2004.  Also LAPACK Working Note 154. */
/* > - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric */
/* >   tridiagonal eigenvalue/eigenvector problem", */
/* >   Computer Science Division Technical Report No. UCB/CSD-97-971, */
/* >   UC Berkeley, May 1997. */
/* > */
/* > */
/* > Note 1 : CHEEVR calls CSTEMR when the full spectrum is requested */
/* > on machines which conform to the ieee-754 floating point standard. */
/* > CHEEVR calls SSTEBZ and CSTEIN on non-ieee machines and */
/* > when partial spectrum requests are made. */
/* > */
/* > Normal execution of CSTEMR may create NaNs and infinities and */
/* > hence may abort due to a floating point exception in environments */
/* > which do not handle NaNs and infinities in the ieee standard default */
/* > manner. */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] JOBZ */
/* > \verbatim */
/* >          JOBZ is CHARACTER*1 */
/* >          = 'N':  Compute eigenvalues only; */
/* >          = 'V':  Compute eigenvalues and eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] RANGE */
/* > \verbatim */
/* >          RANGE is CHARACTER*1 */
/* >          = 'A': all eigenvalues will be found. */
/* >          = 'V': all eigenvalues in the half-open interval (VL,VU] */
/* >                 will be found. */
/* >          = 'I': the IL-th through IU-th eigenvalues will be found. */
/* >          For RANGE = 'V' or 'I' and IU - IL < N - 1, SSTEBZ and */
/* >          CSTEIN are called */
/* > \endverbatim */
/* > */
/* > \param[in] UPLO */
/* > \verbatim */
/* >          UPLO is CHARACTER*1 */
/* >          = 'U':  Upper triangle of A is stored; */
/* >          = 'L':  Lower triangle of A is stored. */
/* > \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 Hermitian matrix A.  If UPLO = 'U', the */
/* >          leading N-by-N upper triangular part of A contains the */
/* >          upper triangular part of the matrix A.  If UPLO = 'L', */
/* >          the leading N-by-N lower triangular part of A contains */
/* >          the lower triangular part of the matrix A. */
/* >          On exit, the lower triangle (if UPLO='L') or the upper */
/* >          triangle (if UPLO='U') of A, including the diagonal, is */
/* >          destroyed. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] VL */
/* > \verbatim */
/* >          VL is REAL */
/* >          If RANGE='V', the lower bound of the interval to */
/* >          be searched for eigenvalues. VL < VU. */
/* >          Not referenced if RANGE = 'A' or 'I'. */
/* > \endverbatim */
/* > */
/* > \param[in] VU */
/* > \verbatim */
/* >          VU is REAL */
/* >          If RANGE='V', the upper bound of the interval to */
/* >          be searched for eigenvalues. VL < VU. */
/* >          Not referenced if RANGE = 'A' or 'I'. */
/* > \endverbatim */
/* > */
/* > \param[in] IL */
/* > \verbatim */
/* >          IL is INTEGER */
/* >          If RANGE='I', the index of the */
/* >          smallest eigenvalue to be returned. */
/* >          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
/* >          Not referenced if RANGE = 'A' or 'V'. */
/* > \endverbatim */
/* > */
/* > \param[in] IU */
/* > \verbatim */
/* >          IU is INTEGER */
/* >          If RANGE='I', the index of the */
/* >          largest eigenvalue to be returned. */
/* >          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
/* >          Not referenced if RANGE = 'A' or 'V'. */
/* > \endverbatim */
/* > */
/* > \param[in] ABSTOL */
/* > \verbatim */
/* >          ABSTOL is REAL */
/* >          The absolute error tolerance for the eigenvalues. */
/* >          An approximate eigenvalue is accepted as converged */
/* >          when it is determined to lie in an interval [a,b] */
/* >          of width less than or equal to */
/* > */
/* >                  ABSTOL + EPS *   f2cmax( |a|,|b| ) , */
/* > */
/* >          where EPS is the machine precision.  If ABSTOL is less than */
/* >          or equal to zero, then  EPS*|T|  will be used in its place, */
/* >          where |T| is the 1-norm of the tridiagonal matrix obtained */
/* >          by reducing A to tridiagonal form. */
/* > */
/* >          See "Computing Small Singular Values of Bidiagonal Matrices */
/* >          with Guaranteed High Relative Accuracy," by Demmel and */
/* >          Kahan, LAPACK Working Note #3. */
/* > */
/* >          If high relative accuracy is important, set ABSTOL to */
/* >          SLAMCH( 'Safe minimum' ).  Doing so will guarantee that */
/* >          eigenvalues are computed to high relative accuracy when */
/* >          possible in future releases.  The current code does not */
/* >          make any guarantees about high relative accuracy, but */
/* >          future releases will. See J. Barlow and J. Demmel, */
/* >          "Computing Accurate Eigensystems of Scaled Diagonally */
/* >          Dominant Matrices", LAPACK Working Note #7, for a discussion */
/* >          of which matrices define their eigenvalues to high relative */
/* >          accuracy. */
/* > \endverbatim */
/* > */
/* > \param[out] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The total number of eigenvalues found.  0 <= M <= N. */
/* >          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* >          W is REAL array, dimension (N) */
/* >          The first M elements contain the selected eigenvalues in */
/* >          ascending order. */
/* > \endverbatim */
/* > */
/* > \param[out] Z */
/* > \verbatim */
/* >          Z is COMPLEX array, dimension (LDZ, f2cmax(1,M)) */
/* >          If JOBZ = 'V', then if INFO = 0, the first M columns of Z */
/* >          contain the orthonormal eigenvectors of the matrix A */
/* >          corresponding to the selected eigenvalues, with the i-th */
/* >          column of Z holding the eigenvector associated with W(i). */
/* >          If JOBZ = 'N', then Z is not referenced. */
/* >          Note: the user must ensure that at least f2cmax(1,M) columns are */
/* >          supplied in the array Z; if RANGE = 'V', the exact value of M */
/* >          is not known in advance and an upper bound must be used. */
/* > \endverbatim */
/* > */
/* > \param[in] LDZ */
/* > \verbatim */
/* >          LDZ is INTEGER */
/* >          The leading dimension of the array Z.  LDZ >= 1, and if */
/* >          JOBZ = 'V', LDZ >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] ISUPPZ */
/* > \verbatim */
/* >          ISUPPZ is INTEGER array, dimension ( 2*f2cmax(1,M) ) */
/* >          The support of the eigenvectors in Z, i.e., the indices */
/* >          indicating the nonzero elements in Z. The i-th eigenvector */
/* >          is nonzero only in elements ISUPPZ( 2*i-1 ) through */
/* >          ISUPPZ( 2*i ). This is an output of CSTEMR (tridiagonal */
/* >          matrix). The support of the eigenvectors of A is typically */
/* >          1:N because of the unitary transformations applied by CUNMTR. */
/* >          Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 */
/* > \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(1,2*N). */
/* >          For optimal efficiency, LWORK >= (NB+1)*N, */
/* >          where NB is the f2cmax of the blocksize for CHETRD and for */
/* >          CUNMTR as returned by ILAENV. */
/* > */
/* >          If LWORK = -1, then a workspace query is assumed; the routine */
/* >          only calculates the optimal sizes of the WORK, RWORK and */
/* >          IWORK arrays, returns these values as the first entries of */
/* >          the WORK, RWORK and IWORK arrays, and no error message */
/* >          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* >          RWORK is REAL array, dimension (MAX(1,LRWORK)) */
/* >          On exit, if INFO = 0, RWORK(1) returns the optimal */
/* >          (and minimal) LRWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LRWORK */
/* > \verbatim */
/* >          LRWORK is INTEGER */
/* >          The length of the array RWORK.  LRWORK >= f2cmax(1,24*N). */
/* > */
/* >          If LRWORK = -1, then a workspace query is assumed; the */
/* >          routine only calculates the optimal sizes of the WORK, RWORK */
/* >          and IWORK arrays, returns these values as the first entries */
/* >          of the WORK, RWORK and IWORK arrays, and no error message */
/* >          related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
/* >          On exit, if INFO = 0, IWORK(1) returns the optimal */
/* >          (and minimal) LIWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LIWORK */
/* > \verbatim */
/* >          LIWORK is INTEGER */
/* >          The dimension of the array IWORK.  LIWORK >= f2cmax(1,10*N). */
/* > */
/* >          If LIWORK = -1, then a workspace query is assumed; the */
/* >          routine only calculates the optimal sizes of the WORK, RWORK */
/* >          and IWORK arrays, returns these values as the first entries */
/* >          of the WORK, RWORK and IWORK arrays, and no error message */
/* >          related to LWORK or LRWORK or LIWORK 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:  Internal error */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \date June 2016 */

/* > \ingroup complexHEeigen */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >     Inderjit Dhillon, IBM Almaden, USA \n */
/* >     Osni Marques, LBNL/NERSC, USA \n */
/* >     Ken Stanley, Computer Science Division, University of */
/* >       California at Berkeley, USA \n */
/* >     Jason Riedy, Computer Science Division, University of */
/* >       California at Berkeley, USA \n */
/* > */
/*  ===================================================================== */
/* Subroutine */ int cheevr_(char *jobz, char *range, char *uplo, integer *n, 
	complex *a, integer *lda, real *vl, real *vu, integer *il, integer *
	iu, real *abstol, integer *m, real *w, complex *z__, integer *ldz, 
	integer *isuppz, complex *work, integer *lwork, real *rwork, integer *
	lrwork, integer *iwork, integer *liwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2;
    real r__1, r__2;

    /* Local variables */
    real anrm;
    integer imax;
    real rmin, rmax;
    logical test;
    integer itmp1, i__, j, indrd, indre;
    real sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    char order[1];
    integer indwk;
    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
	    complex *, integer *);
    integer lwmin;
    logical lower;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *);
    logical wantz;
    integer nb, jj;
    logical alleig, indeig;
    integer iscale, ieeeok, indibl, indrdd, indifl, indree;
    logical valeig;
    extern real slamch_(char *);
    extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer 
	    *, real *, real *, complex *, complex *, integer *, integer *), csscal_(integer *, real *, complex *, integer *);
    real safmin;
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    real abstll, bignum;
    integer indtau, indisp;
    extern /* Subroutine */ int cstein_(integer *, real *, real *, integer *, 
	    real *, integer *, integer *, complex *, integer *, real *, 
	    integer *, integer *, integer *);
    integer indiwo, indwkn;
    extern real clansy_(char *, char *, integer *, complex *, integer *, real 
	    *);
    extern /* Subroutine */ int cstemr_(char *, char *, integer *, real *, 
	    real *, real *, real *, integer *, integer *, integer *, real *, 
	    complex *, integer *, integer *, integer *, logical *, real *, 
	    integer *, integer *, integer *, integer *);
    integer indrwk, liwmin;
    logical tryrac;
    extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *);
    integer lrwmin, llwrkn, llwork, nsplit;
    real smlnum;
    extern /* Subroutine */ int cunmtr_(char *, char *, char *, integer *, 
	    integer *, complex *, integer *, complex *, complex *, integer *, 
	    complex *, integer *, integer *), sstebz_(
	    char *, char *, integer *, real *, real *, integer *, integer *, 
	    real *, real *, real *, integer *, integer *, real *, integer *, 
	    integer *, real *, integer *, integer *);
    logical lquery;
    integer lwkopt;
    real eps, vll, vuu;
    integer llrwork;
    real tmp1;


/*  -- 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 parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --w;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --isuppz;
    --work;
    --rwork;
    --iwork;

    /* Function Body */
    ieeeok = ilaenv_(&c__10, "CHEEVR", "N", &c__1, &c__2, &c__3, &c__4, (
	    ftnlen)6, (ftnlen)1);

    lower = lsame_(uplo, "L");
    wantz = lsame_(jobz, "V");
    alleig = lsame_(range, "A");
    valeig = lsame_(range, "V");
    indeig = lsame_(range, "I");

    lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;

/* Computing MAX */
    i__1 = 1, i__2 = *n * 24;
    lrwmin = f2cmax(i__1,i__2);
/* Computing MAX */
    i__1 = 1, i__2 = *n * 10;
    liwmin = f2cmax(i__1,i__2);
/* Computing MAX */
    i__1 = 1, i__2 = *n << 1;
    lwmin = f2cmax(i__1,i__2);

    *info = 0;
    if (! (wantz || lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (alleig || valeig || indeig)) {
	*info = -2;
    } else if (! (lower || lsame_(uplo, "U"))) {
	*info = -3;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < f2cmax(1,*n)) {
	*info = -6;
    } else {
	if (valeig) {
	    if (*n > 0 && *vu <= *vl) {
		*info = -8;
	    }
	} else if (indeig) {
	    if (*il < 1 || *il > f2cmax(1,*n)) {
		*info = -9;
	    } else if (*iu < f2cmin(*n,*il) || *iu > *n) {
		*info = -10;
	    }
	}
    }
    if (*info == 0) {
	if (*ldz < 1 || wantz && *ldz < *n) {
	    *info = -15;
	}
    }

    if (*info == 0) {
	nb = ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
		 (ftnlen)1);
/* Computing MAX */
	i__1 = nb, i__2 = ilaenv_(&c__1, "CUNMTR", uplo, n, &c_n1, &c_n1, &
		c_n1, (ftnlen)6, (ftnlen)1);
	nb = f2cmax(i__1,i__2);
/* Computing MAX */
	i__1 = (nb + 1) * *n;
	lwkopt = f2cmax(i__1,lwmin);
	work[1].r = (real) lwkopt, work[1].i = 0.f;
	rwork[1] = (real) lrwmin;
	iwork[1] = liwmin;

	if (*lwork < lwmin && ! lquery) {
	    *info = -18;
	} else if (*lrwork < lrwmin && ! lquery) {
	    *info = -20;
	} else if (*liwork < liwmin && ! lquery) {
	    *info = -22;
	}
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("CHEEVR", &i__1, (ftnlen)6);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    *m = 0;
    if (*n == 0) {
	work[1].r = 1.f, work[1].i = 0.f;
	return 0;
    }

    if (*n == 1) {
	work[1].r = 2.f, work[1].i = 0.f;
	if (alleig || indeig) {
	    *m = 1;
	    i__1 = a_dim1 + 1;
	    w[1] = a[i__1].r;
	} else {
	    i__1 = a_dim1 + 1;
	    i__2 = a_dim1 + 1;
	    if (*vl < a[i__1].r && *vu >= a[i__2].r) {
		*m = 1;
		i__1 = a_dim1 + 1;
		w[1] = a[i__1].r;
	    }
	}
	if (wantz) {
	    i__1 = z_dim1 + 1;
	    z__[i__1].r = 1.f, z__[i__1].i = 0.f;
	    isuppz[1] = 1;
	    isuppz[2] = 1;
	}
	return 0;
    }

/*     Get machine constants. */

    safmin = slamch_("Safe minimum");
    eps = slamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1.f / smlnum;
    rmin = sqrt(smlnum);
/* Computing MIN */
    r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin));
    rmax = f2cmin(r__1,r__2);

/*     Scale matrix to allowable range, if necessary. */

    iscale = 0;
    abstll = *abstol;
    if (valeig) {
	vll = *vl;
	vuu = *vu;
    }
    anrm = clansy_("M", uplo, n, &a[a_offset], lda, &rwork[1]);
    if (anrm > 0.f && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	if (lower) {
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		i__2 = *n - j + 1;
		csscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1);
/* L10: */
	    }
	} else {
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		csscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1);
/* L20: */
	    }
	}
	if (*abstol > 0.f) {
	    abstll = *abstol * sigma;
	}
	if (valeig) {
	    vll = *vl * sigma;
	    vuu = *vu * sigma;
	}
    }
/*     Initialize indices into workspaces.  Note: The IWORK indices are */
/*     used only if SSTERF or CSTEMR fail. */
/*     WORK(INDTAU:INDTAU+N-1) stores the complex scalar factors of the */
/*     elementary reflectors used in CHETRD. */
    indtau = 1;
/*     INDWK is the starting offset of the remaining complex workspace, */
/*     and LLWORK is the remaining complex workspace size. */
    indwk = indtau + *n;
    llwork = *lwork - indwk + 1;
/*     RWORK(INDRD:INDRD+N-1) stores the real tridiagonal's diagonal */
/*     entries. */
    indrd = 1;
/*     RWORK(INDRE:INDRE+N-1) stores the off-diagonal entries of the */
/*     tridiagonal matrix from CHETRD. */
    indre = indrd + *n;
/*     RWORK(INDRDD:INDRDD+N-1) is a copy of the diagonal entries over */
/*     -written by CSTEMR (the SSTERF path copies the diagonal to W). */
    indrdd = indre + *n;
/*     RWORK(INDREE:INDREE+N-1) is a copy of the off-diagonal entries over */
/*     -written while computing the eigenvalues in SSTERF and CSTEMR. */
    indree = indrdd + *n;
/*     INDRWK is the starting offset of the left-over real workspace, and */
/*     LLRWORK is the remaining workspace size. */
    indrwk = indree + *n;
    llrwork = *lrwork - indrwk + 1;
/*     IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in SSTEBZ and */
/*     stores the block indices of each of the M<=N eigenvalues. */
    indibl = 1;
/*     IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in SSTEBZ and */
/*     stores the starting and finishing indices of each block. */
    indisp = indibl + *n;
/*     IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors */
/*     that corresponding to eigenvectors that fail to converge in */
/*     SSTEIN.  This information is discarded; if any fail, the driver */
/*     returns INFO > 0. */
    indifl = indisp + *n;
/*     INDIWO is the offset of the remaining integer workspace. */
    indiwo = indifl + *n;

/*     Call CHETRD to reduce Hermitian matrix to tridiagonal form. */

    chetrd_(uplo, n, &a[a_offset], lda, &rwork[indrd], &rwork[indre], &work[
	    indtau], &work[indwk], &llwork, &iinfo);

/*     If all eigenvalues are desired */
/*     then call SSTERF or CSTEMR and CUNMTR. */

    test = FALSE_;
    if (indeig) {
	if (*il == 1 && *iu == *n) {
	    test = TRUE_;
	}
    }
    if ((alleig || test) && ieeeok == 1) {
	if (! wantz) {
	    scopy_(n, &rwork[indrd], &c__1, &w[1], &c__1);
	    i__1 = *n - 1;
	    scopy_(&i__1, &rwork[indre], &c__1, &rwork[indree], &c__1);
	    ssterf_(n, &w[1], &rwork[indree], info);
	} else {
	    i__1 = *n - 1;
	    scopy_(&i__1, &rwork[indre], &c__1, &rwork[indree], &c__1);
	    scopy_(n, &rwork[indrd], &c__1, &rwork[indrdd], &c__1);

	    if (*abstol <= *n * 2.f * eps) {
		tryrac = TRUE_;
	    } else {
		tryrac = FALSE_;
	    }
	    cstemr_(jobz, "A", n, &rwork[indrdd], &rwork[indree], vl, vu, il, 
		    iu, m, &w[1], &z__[z_offset], ldz, n, &isuppz[1], &tryrac,
		     &rwork[indrwk], &llrwork, &iwork[1], liwork, info);

/*           Apply unitary matrix used in reduction to tridiagonal */
/*           form to eigenvectors returned by CSTEMR. */

	    if (wantz && *info == 0) {
		indwkn = indwk;
		llwrkn = *lwork - indwkn + 1;
		cunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau]
			, &z__[z_offset], ldz, &work[indwkn], &llwrkn, &iinfo);
	    }
	}


	if (*info == 0) {
	    *m = *n;
	    goto L30;
	}
	*info = 0;
    }

/*     Otherwise, call SSTEBZ and, if eigenvectors are desired, CSTEIN. */
/*     Also call SSTEBZ and CSTEIN if CSTEMR fails. */

    if (wantz) {
	*(unsigned char *)order = 'B';
    } else {
	*(unsigned char *)order = 'E';
    }
    sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &rwork[indrd], &
	    rwork[indre], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &
	    rwork[indrwk], &iwork[indiwo], info);

    if (wantz) {
	cstein_(n, &rwork[indrd], &rwork[indre], m, &w[1], &iwork[indibl], &
		iwork[indisp], &z__[z_offset], ldz, &rwork[indrwk], &iwork[
		indiwo], &iwork[indifl], info);

/*        Apply unitary matrix used in reduction to tridiagonal */
/*        form to eigenvectors returned by CSTEIN. */

	indwkn = indwk;
	llwrkn = *lwork - indwkn + 1;
	cunmtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau], &z__[
		z_offset], ldz, &work[indwkn], &llwrkn, &iinfo);
    }

/*     If matrix was scaled, then rescale eigenvalues appropriately. */

L30:
    if (iscale == 1) {
	if (*info == 0) {
	    imax = *m;
	} else {
	    imax = *info - 1;
	}
	r__1 = 1.f / sigma;
	sscal_(&imax, &r__1, &w[1], &c__1);
    }

/*     If eigenvalues are not in order, then sort them, along with */
/*     eigenvectors. */

    if (wantz) {
	i__1 = *m - 1;
	for (j = 1; j <= i__1; ++j) {
	    i__ = 0;
	    tmp1 = w[j];
	    i__2 = *m;
	    for (jj = j + 1; jj <= i__2; ++jj) {
		if (w[jj] < tmp1) {
		    i__ = jj;
		    tmp1 = w[jj];
		}
/* L40: */
	    }

	    if (i__ != 0) {
		itmp1 = iwork[indibl + i__ - 1];
		w[i__] = w[j];
		iwork[indibl + i__ - 1] = iwork[indibl + j - 1];
		w[j] = tmp1;
		iwork[indibl + j - 1] = itmp1;
		cswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1],
			 &c__1);
	    }
/* L50: */
	}
    }

/*     Set WORK(1) to optimal workspace size. */

    work[1].r = (real) lwkopt, work[1].i = 0.f;
    rwork[1] = (real) lrwmin;
    iwork[1] = liwmin;

    return 0;

/*     End of CHEEVR */

} /* cheevr_ */