OpenBLAS/lapack-netlib/SRC/slasda.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__0 = 0;
static real c_b11 = 0.f;
static real c_b12 = 1.f;
static integer c__1 = 1;
static integer c__2 = 2;

/* > \brief \b SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with d
iagonal d and off-diagonal e. Used by sbdsdc. */

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

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

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

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

/*       SUBROUTINE SLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, */
/*                          DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, */
/*                          PERM, GIVNUM, C, S, WORK, IWORK, INFO ) */

/*       INTEGER            ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE */
/*       INTEGER            GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */
/*      $                   K( * ), PERM( LDGCOL, * ) */
/*       REAL               C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), */
/*      $                   E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), */
/*      $                   S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), */
/*      $                   Z( LDU, * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > Using a divide and conquer approach, SLASDA computes the singular */
/* > value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */
/* > B with diagonal D and offdiagonal E, where M = N + SQRE. The */
/* > algorithm computes the singular values in the SVD B = U * S * VT. */
/* > The orthogonal matrices U and VT are optionally computed in */
/* > compact form. */
/* > */
/* > A related subroutine, SLASD0, computes the singular values and */
/* > the singular vectors in explicit form. */
/* > \endverbatim */

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

/* > \param[in] ICOMPQ */
/* > \verbatim */
/* >          ICOMPQ is INTEGER */
/* >         Specifies whether singular vectors are to be computed */
/* >         in compact form, as follows */
/* >         = 0: Compute singular values only. */
/* >         = 1: Compute singular vectors of upper bidiagonal */
/* >              matrix in compact form. */
/* > \endverbatim */
/* > */
/* > \param[in] SMLSIZ */
/* > \verbatim */
/* >          SMLSIZ is INTEGER */
/* >         The maximum size of the subproblems at the bottom of the */
/* >         computation tree. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >         The row dimension of the upper bidiagonal matrix. This is */
/* >         also the dimension of the main diagonal array D. */
/* > \endverbatim */
/* > */
/* > \param[in] SQRE */
/* > \verbatim */
/* >          SQRE is INTEGER */
/* >         Specifies the column dimension of the bidiagonal matrix. */
/* >         = 0: The bidiagonal matrix has column dimension M = N; */
/* >         = 1: The bidiagonal matrix has column dimension M = N + 1. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* >          D is REAL array, dimension ( N ) */
/* >         On entry D contains the main diagonal of the bidiagonal */
/* >         matrix. On exit D, if INFO = 0, contains its singular values. */
/* > \endverbatim */
/* > */
/* > \param[in] E */
/* > \verbatim */
/* >          E is REAL array, dimension ( M-1 ) */
/* >         Contains the subdiagonal entries of the bidiagonal matrix. */
/* >         On exit, E has been destroyed. */
/* > \endverbatim */
/* > */
/* > \param[out] U */
/* > \verbatim */
/* >          U is REAL array, */
/* >         dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */
/* >         if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left */
/* >         singular vector matrices of all subproblems at the bottom */
/* >         level. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* >          LDU is INTEGER, LDU = > N. */
/* >         The leading dimension of arrays U, VT, DIFL, DIFR, POLES, */
/* >         GIVNUM, and Z. */
/* > \endverbatim */
/* > */
/* > \param[out] VT */
/* > \verbatim */
/* >          VT is REAL array, */
/* >         dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */
/* >         if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right */
/* >         singular vector matrices of all subproblems at the bottom */
/* >         level. */
/* > \endverbatim */
/* > */
/* > \param[out] K */
/* > \verbatim */
/* >          K is INTEGER array, dimension ( N ) */
/* >         if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */
/* >         If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */
/* >         secular equation on the computation tree. */
/* > \endverbatim */
/* > */
/* > \param[out] DIFL */
/* > \verbatim */
/* >          DIFL is REAL array, dimension ( LDU, NLVL ), */
/* >         where NLVL = floor(log_2 (N/SMLSIZ))). */
/* > \endverbatim */
/* > */
/* > \param[out] DIFR */
/* > \verbatim */
/* >          DIFR is REAL array, */
/* >                  dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and */
/* >                  dimension ( N ) if ICOMPQ = 0. */
/* >         If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */
/* >         record distances between singular values on the I-th */
/* >         level and singular values on the (I -1)-th level, and */
/* >         DIFR(1:N, 2 * I ) contains the normalizing factors for */
/* >         the right singular vector matrix. See SLASD8 for details. */
/* > \endverbatim */
/* > */
/* > \param[out] Z */
/* > \verbatim */
/* >          Z is REAL array, */
/* >                  dimension ( LDU, NLVL ) if ICOMPQ = 1 and */
/* >                  dimension ( N ) if ICOMPQ = 0. */
/* >         The first K elements of Z(1, I) contain the components of */
/* >         the deflation-adjusted updating row vector for subproblems */
/* >         on the I-th level. */
/* > \endverbatim */
/* > */
/* > \param[out] POLES */
/* > \verbatim */
/* >          POLES is REAL array, */
/* >         dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */
/* >         if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */
/* >         POLES(1, 2*I) contain  the new and old singular values */
/* >         involved in the secular equations on the I-th level. */
/* > \endverbatim */
/* > */
/* > \param[out] GIVPTR */
/* > \verbatim */
/* >          GIVPTR is INTEGER array, */
/* >         dimension ( N ) if ICOMPQ = 1, and not referenced if */
/* >         ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */
/* >         the number of Givens rotations performed on the I-th */
/* >         problem on the computation tree. */
/* > \endverbatim */
/* > */
/* > \param[out] GIVCOL */
/* > \verbatim */
/* >          GIVCOL is INTEGER array, */
/* >         dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */
/* >         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
/* >         GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations */
/* >         of Givens rotations performed on the I-th level on the */
/* >         computation tree. */
/* > \endverbatim */
/* > */
/* > \param[in] LDGCOL */
/* > \verbatim */
/* >          LDGCOL is INTEGER, LDGCOL = > N. */
/* >         The leading dimension of arrays GIVCOL and PERM. */
/* > \endverbatim */
/* > */
/* > \param[out] PERM */
/* > \verbatim */
/* >          PERM is INTEGER array, dimension ( LDGCOL, NLVL ) */
/* >         if ICOMPQ = 1, and not referenced */
/* >         if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */
/* >         permutations done on the I-th level of the computation tree. */
/* > \endverbatim */
/* > */
/* > \param[out] GIVNUM */
/* > \verbatim */
/* >          GIVNUM is REAL array, */
/* >         dimension ( LDU,  2 * NLVL ) if ICOMPQ = 1, and not */
/* >         referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
/* >         GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */
/* >         values of Givens rotations performed on the I-th level on */
/* >         the computation tree. */
/* > \endverbatim */
/* > */
/* > \param[out] C */
/* > \verbatim */
/* >          C is REAL array, */
/* >         dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */
/* >         If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */
/* >         C( I ) contains the C-value of a Givens rotation related to */
/* >         the right null space of the I-th subproblem. */
/* > \endverbatim */
/* > */
/* > \param[out] S */
/* > \verbatim */
/* >          S is REAL array, dimension ( N ) if */
/* >         ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */
/* >         and the I-th subproblem is not square, on exit, S( I ) */
/* >         contains the S-value of a Givens rotation related to */
/* >         the right null space of the I-th subproblem. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL array, dimension */
/* >         (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (7*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 = 1, a singular value did not converge */
/* > \endverbatim */

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

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

/* > \date December 2016 */

/* > \ingroup OTHERauxiliary */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >     Ming Gu and Huan Ren, Computer Science Division, University of */
/* >     California at Berkeley, USA */
/* > */
/*  ===================================================================== */
/* Subroutine */ int slasda_(integer *icompq, integer *smlsiz, integer *n, 
	integer *sqre, real *d__, real *e, real *u, integer *ldu, real *vt, 
	integer *k, real *difl, real *difr, real *z__, real *poles, integer *
	givptr, integer *givcol, integer *ldgcol, integer *perm, real *givnum,
	 real *c__, real *s, real *work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, 
	    difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, 
	    poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, 
	    z_dim1, z_offset, i__1, i__2;

    /* Local variables */
    real beta;
    integer idxq, nlvl, i__, j, m;
    real alpha;
    integer inode, ndiml, ndimr, idxqi, itemp, sqrei, i1;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
	    integer *), slasd6_(integer *, integer *, integer *, integer *, 
	    real *, real *, real *, real *, real *, integer *, integer *, 
	    integer *, integer *, integer *, real *, integer *, real *, real *
	    , real *, real *, integer *, real *, real *, real *, integer *, 
	    integer *);
    integer ic, nwork1, lf, nd, nwork2, ll, nl, vf, nr, vl;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slasdq_(
	    char *, integer *, integer *, integer *, integer *, integer *, 
	    real *, real *, real *, integer *, real *, integer *, real *, 
	    integer *, real *, integer *), slasdt_(integer *, integer 
	    *, integer *, integer *, integer *, integer *, integer *), 
	    slaset_(char *, integer *, integer *, real *, real *, real *, 
	    integer *);
    integer im1, smlszp, ncc, nlf, nrf, vfi, iwk, vli, lvl, nru, ndb1, nlp1, 
	    lvl2, nrp1;


/*  -- 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 */


/*  ===================================================================== */


/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    --e;
    givnum_dim1 = *ldu;
    givnum_offset = 1 + givnum_dim1 * 1;
    givnum -= givnum_offset;
    poles_dim1 = *ldu;
    poles_offset = 1 + poles_dim1 * 1;
    poles -= poles_offset;
    z_dim1 = *ldu;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    difr_dim1 = *ldu;
    difr_offset = 1 + difr_dim1 * 1;
    difr -= difr_offset;
    difl_dim1 = *ldu;
    difl_offset = 1 + difl_dim1 * 1;
    difl -= difl_offset;
    vt_dim1 = *ldu;
    vt_offset = 1 + vt_dim1 * 1;
    vt -= vt_offset;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1 * 1;
    u -= u_offset;
    --k;
    --givptr;
    perm_dim1 = *ldgcol;
    perm_offset = 1 + perm_dim1 * 1;
    perm -= perm_offset;
    givcol_dim1 = *ldgcol;
    givcol_offset = 1 + givcol_dim1 * 1;
    givcol -= givcol_offset;
    --c__;
    --s;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;

    if (*icompq < 0 || *icompq > 1) {
	*info = -1;
    } else if (*smlsiz < 3) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*sqre < 0 || *sqre > 1) {
	*info = -4;
    } else if (*ldu < *n + *sqre) {
	*info = -8;
    } else if (*ldgcol < *n) {
	*info = -17;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SLASDA", &i__1, (ftnlen)6);
	return 0;
    }

    m = *n + *sqre;

/*     If the input matrix is too small, call SLASDQ to find the SVD. */

    if (*n <= *smlsiz) {
	if (*icompq == 0) {
	    slasdq_("U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[
		    vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, &
		    work[1], info);
	} else {
	    slasdq_("U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset]
		    , ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1], 
		    info);
	}
	return 0;
    }

/*     Book-keeping and  set up the computation tree. */

    inode = 1;
    ndiml = inode + *n;
    ndimr = ndiml + *n;
    idxq = ndimr + *n;
    iwk = idxq + *n;

    ncc = 0;
    nru = 0;

    smlszp = *smlsiz + 1;
    vf = 1;
    vl = vf + m;
    nwork1 = vl + m;
    nwork2 = nwork1 + smlszp * smlszp;

    slasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], 
	    smlsiz);

/*     for the nodes on bottom level of the tree, solve */
/*     their subproblems by SLASDQ. */

    ndb1 = (nd + 1) / 2;
    i__1 = nd;
    for (i__ = ndb1; i__ <= i__1; ++i__) {

/*        IC : center row of each node */
/*        NL : number of rows of left  subproblem */
/*        NR : number of rows of right subproblem */
/*        NLF: starting row of the left   subproblem */
/*        NRF: starting row of the right  subproblem */

	i1 = i__ - 1;
	ic = iwork[inode + i1];
	nl = iwork[ndiml + i1];
	nlp1 = nl + 1;
	nr = iwork[ndimr + i1];
	nlf = ic - nl;
	nrf = ic + 1;
	idxqi = idxq + nlf - 2;
	vfi = vf + nlf - 1;
	vli = vl + nlf - 1;
	sqrei = 1;
	if (*icompq == 0) {
	    slaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
	    slasdq_("U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], &
		    work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2], 
		    &nl, &work[nwork2], info);
	    itemp = nwork1 + nl * smlszp;
	    scopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1);
	    scopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1);
	} else {
	    slaset_("A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu);
	    slaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1], 
		    ldu);
	    slasdq_("U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], &
		    vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf + 
		    u_dim1], ldu, &work[nwork1], info);
	    scopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1);
	    scopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1)
		    ;
	}
	if (*info != 0) {
	    return 0;
	}
	i__2 = nl;
	for (j = 1; j <= i__2; ++j) {
	    iwork[idxqi + j] = j;
/* L10: */
	}
	if (i__ == nd && *sqre == 0) {
	    sqrei = 0;
	} else {
	    sqrei = 1;
	}
	idxqi += nlp1;
	vfi += nlp1;
	vli += nlp1;
	nrp1 = nr + sqrei;
	if (*icompq == 0) {
	    slaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
	    slasdq_("U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], &
		    work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2], 
		    &nr, &work[nwork2], info);
	    itemp = nwork1 + (nrp1 - 1) * smlszp;
	    scopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1);
	    scopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1);
	} else {
	    slaset_("A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu);
	    slaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1], 
		    ldu);
	    slasdq_("U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], &
		    vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf + 
		    u_dim1], ldu, &work[nwork1], info);
	    scopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1);
	    scopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1)
		    ;
	}
	if (*info != 0) {
	    return 0;
	}
	i__2 = nr;
	for (j = 1; j <= i__2; ++j) {
	    iwork[idxqi + j] = j;
/* L20: */
	}
/* L30: */
    }

/*     Now conquer each subproblem bottom-up. */

    j = pow_ii(&c__2, &nlvl);
    for (lvl = nlvl; lvl >= 1; --lvl) {
	lvl2 = (lvl << 1) - 1;

/*        Find the first node LF and last node LL on */
/*        the current level LVL. */

	if (lvl == 1) {
	    lf = 1;
	    ll = 1;
	} else {
	    i__1 = lvl - 1;
	    lf = pow_ii(&c__2, &i__1);
	    ll = (lf << 1) - 1;
	}
	i__1 = ll;
	for (i__ = lf; i__ <= i__1; ++i__) {
	    im1 = i__ - 1;
	    ic = iwork[inode + im1];
	    nl = iwork[ndiml + im1];
	    nr = iwork[ndimr + im1];
	    nlf = ic - nl;
	    nrf = ic + 1;
	    if (i__ == ll) {
		sqrei = *sqre;
	    } else {
		sqrei = 1;
	    }
	    vfi = vf + nlf - 1;
	    vli = vl + nlf - 1;
	    idxqi = idxq + nlf - 1;
	    alpha = d__[ic];
	    beta = e[ic];
	    if (*icompq == 0) {
		slasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
			work[vli], &alpha, &beta, &iwork[idxqi], &perm[
			perm_offset], &givptr[1], &givcol[givcol_offset], 
			ldgcol, &givnum[givnum_offset], ldu, &poles[
			poles_offset], &difl[difl_offset], &difr[difr_offset],
			 &z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1],
			 &iwork[iwk], info);
	    } else {
		--j;
		slasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
			work[vli], &alpha, &beta, &iwork[idxqi], &perm[nlf + 
			lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 * 
			givcol_dim1], ldgcol, &givnum[nlf + lvl2 * 
			givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], &
			difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * 
			difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[j], 
			&s[j], &work[nwork1], &iwork[iwk], info);
	    }
	    if (*info != 0) {
		return 0;
	    }
/* L40: */
	}
/* L50: */
    }

    return 0;

/*     End of SLASDA */

} /* slasda_ */