OpenBLAS/lapack-netlib/SRC/sgesdd.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

#if defined(OS_WINDOWS) && defined(__64BIT__)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif

#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(OS_WINDOWS) && defined(__64BIT__)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif

typedef blasint 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_n1 = -1;
static integer c__0 = 0;
static real c_b63 = 0.f;
static integer c__1 = 1;
static real c_b84 = 1.f;

/* > \brief \b SGESDD */

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

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

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

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

/*       SUBROUTINE SGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, */
/*                          WORK, LWORK, IWORK, INFO ) */

/*       CHARACTER          JOBZ */
/*       INTEGER            INFO, LDA, LDU, LDVT, LWORK, M, N */
/*       INTEGER            IWORK( * ) */
/*       REAL   A( LDA, * ), S( * ), U( LDU, * ), */
/*      $                   VT( LDVT, * ), WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGESDD computes the singular value decomposition (SVD) of a real */
/* > M-by-N matrix A, optionally computing the left and right singular */
/* > vectors.  If singular vectors are desired, it uses a */
/* > divide-and-conquer algorithm. */
/* > */
/* > The SVD is written */
/* > */
/* >      A = U * SIGMA * transpose(V) */
/* > */
/* > where SIGMA is an M-by-N matrix which is zero except for its */
/* > f2cmin(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */
/* > V is an N-by-N orthogonal matrix.  The diagonal elements of SIGMA */
/* > are the singular values of A; they are real and non-negative, and */
/* > are returned in descending order.  The first f2cmin(m,n) columns of */
/* > U and V are the left and right singular vectors of A. */
/* > */
/* > Note that the routine returns VT = V**T, not V. */
/* > */
/* > The divide and conquer algorithm makes very mild assumptions about */
/* > floating point arithmetic. It will work on machines with a guard */
/* > digit in add/subtract, or on those binary machines without guard */
/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/* > without guard digits, but we know of none. */
/* > \endverbatim */

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

/* > \param[in] JOBZ */
/* > \verbatim */
/* >          JOBZ is CHARACTER*1 */
/* >          Specifies options for computing all or part of the matrix U: */
/* >          = 'A':  all M columns of U and all N rows of V**T are */
/* >                  returned in the arrays U and VT; */
/* >          = 'S':  the first f2cmin(M,N) columns of U and the first */
/* >                  f2cmin(M,N) rows of V**T are returned in the arrays U */
/* >                  and VT; */
/* >          = 'O':  If M >= N, the first N columns of U are overwritten */
/* >                  on the array A and all rows of V**T are returned in */
/* >                  the array VT; */
/* >                  otherwise, all columns of U are returned in the */
/* >                  array U and the first M rows of V**T are overwritten */
/* >                  in the array A; */
/* >          = 'N':  no columns of U or rows of V**T are computed. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The number of rows of the input matrix A.  M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The number of columns of the input matrix A.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is REAL array, dimension (LDA,N) */
/* >          On entry, the M-by-N matrix A. */
/* >          On exit, */
/* >          if JOBZ = 'O',  A is overwritten with the first N columns */
/* >                          of U (the left singular vectors, stored */
/* >                          columnwise) if M >= N; */
/* >                          A is overwritten with the first M rows */
/* >                          of V**T (the right singular vectors, stored */
/* >                          rowwise) otherwise. */
/* >          if JOBZ .ne. 'O', the contents of A are destroyed. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] S */
/* > \verbatim */
/* >          S is REAL array, dimension (f2cmin(M,N)) */
/* >          The singular values of A, sorted so that S(i) >= S(i+1). */
/* > \endverbatim */
/* > */
/* > \param[out] U */
/* > \verbatim */
/* >          U is REAL array, dimension (LDU,UCOL) */
/* >          UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */
/* >          UCOL = f2cmin(M,N) if JOBZ = 'S'. */
/* >          If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */
/* >          orthogonal matrix U; */
/* >          if JOBZ = 'S', U contains the first f2cmin(M,N) columns of U */
/* >          (the left singular vectors, stored columnwise); */
/* >          if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* >          LDU is INTEGER */
/* >          The leading dimension of the array U.  LDU >= 1; if */
/* >          JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */
/* > \endverbatim */
/* > */
/* > \param[out] VT */
/* > \verbatim */
/* >          VT is REAL array, dimension (LDVT,N) */
/* >          If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */
/* >          N-by-N orthogonal matrix V**T; */
/* >          if JOBZ = 'S', VT contains the first f2cmin(M,N) rows of */
/* >          V**T (the right singular vectors, stored rowwise); */
/* >          if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVT */
/* > \verbatim */
/* >          LDVT is INTEGER */
/* >          The leading dimension of the array VT.  LDVT >= 1; */
/* >          if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */
/* >          if JOBZ = 'S', LDVT >= f2cmin(M,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is REAL 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 >= 1. */
/* >          If LWORK = -1, a workspace query is assumed.  The optimal */
/* >          size for the WORK array is calculated and stored in WORK(1), */
/* >          and no other work except argument checking is performed. */
/* > */
/* >          Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
/* >          If JOBZ = 'N', LWORK >= 3*mn + f2cmax( mx, 7*mn ). */
/* >          If JOBZ = 'O', LWORK >= 3*mn + f2cmax( mx, 5*mn*mn + 4*mn ). */
/* >          If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn. */
/* >          If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx. */
/* >          These are not tight minimums in all cases; see comments inside code. */
/* >          For good performance, LWORK should generally be larger; */
/* >          a query is recommended. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* >          IWORK is INTEGER array, dimension (8*f2cmin(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. */
/* >          > 0:  SBDSDC did not converge, updating process failed. */
/* > \endverbatim */

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

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

/* > \date June 2016 */

/* > \ingroup realGEsing */

/* > \par Contributors: */
/*  ================== */
/* > */
/* >     Ming Gu and Huan Ren, Computer Science Division, University of */
/* >     California at Berkeley, USA */
/* > */
/*  ===================================================================== */
/* Subroutine */ int sgesdd_(char *jobz, integer *m, integer *n, real *a, 
	integer *lda, real *s, real *u, integer *ldu, real *vt, integer *ldvt,
	 real *work, integer *lwork, integer *iwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, 
	    i__2, i__3;

    /* Local variables */
    integer lwork_sgelqf_mn__, lwork_sgeqrf_mn__, iscl, lwork_sorglq_mn__, 
	    lwork_sorglq_nn__;
    real anrm;
    integer idum[1], ierr, itau, lwork_sorgqr_mm__, lwork_sorgqr_mn__, 
	    lwork_sormbr_qln_mm__, lwork_sormbr_qln_mn__, 
	    lwork_sormbr_qln_nn__, lwork_sormbr_prt_mm__, 
	    lwork_sormbr_prt_mn__, lwork_sormbr_prt_nn__, i__;
    extern logical lsame_(char *, char *);
    integer chunk;
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    integer minmn, wrkbl, itaup, itauq, mnthr;
    logical wntqa;
    integer nwork;
    logical wntqn, wntqo, wntqs;
    integer ie, il, ir, bdspac, iu, lwork_sorgbr_p_mm__;
    extern /* Subroutine */ int sbdsdc_(char *, char *, integer *, real *, 
	    real *, real *, integer *, real *, integer *, real *, integer *, 
	    real *, integer *, integer *);
    integer lwork_sorgbr_q_nn__;
    extern /* Subroutine */ int sgebrd_(integer *, integer *, real *, integer 
	    *, real *, real *, real *, real *, real *, integer *, integer *);
    extern real slamch_(char *), slange_(char *, integer *, integer *,
	     real *, integer *, real *);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    real bignum;
    extern /* Subroutine */ int sgelqf_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *), slascl_(char *, integer 
	    *, integer *, real *, real *, integer *, integer *, real *, 
	    integer *, integer *), sgeqrf_(integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *), slacpy_(char 
	    *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, 
	    real *, integer *);
    extern logical sisnan_(real *);
    extern /* Subroutine */ int sorgbr_(char *, integer *, integer *, integer 
	    *, real *, integer *, real *, real *, integer *, integer *);
    integer ldwrkl;
    extern /* Subroutine */ int sormbr_(char *, char *, char *, integer *, 
	    integer *, integer *, real *, integer *, real *, real *, integer *
	    , real *, integer *, integer *);
    integer ldwrkr, minwrk, ldwrku, maxwrk;
    extern /* Subroutine */ int sorglq_(integer *, integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *);
    integer ldwkvt;
    real smlnum;
    logical wntqas;
    extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *);
    logical lquery;
    integer blk;
    real dum[1], eps;
    integer ivt, lwork_sgebrd_mm__, lwork_sgebrd_mn__, lwork_sgebrd_nn__;


/*  -- 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;
    --s;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1 * 1;
    u -= u_offset;
    vt_dim1 = *ldvt;
    vt_offset = 1 + vt_dim1 * 1;
    vt -= vt_offset;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    minmn = f2cmin(*m,*n);
    wntqa = lsame_(jobz, "A");
    wntqs = lsame_(jobz, "S");
    wntqas = wntqa || wntqs;
    wntqo = lsame_(jobz, "O");
    wntqn = lsame_(jobz, "N");
    lquery = *lwork == -1;

    if (! (wntqa || wntqs || wntqo || wntqn)) {
	*info = -1;
    } else if (*m < 0) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*lda < f2cmax(1,*m)) {
	*info = -5;
    } else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < *
	    m) {
	*info = -8;
    } else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn || 
	    wntqo && *m >= *n && *ldvt < *n) {
	*info = -10;
    }

/*     Compute workspace */
/*       Note: Comments in the code beginning "Workspace:" describe the */
/*       minimal amount of workspace allocated at that point in the code, */
/*       as well as the preferred amount for good performance. */
/*       NB refers to the optimal block size for the immediately */
/*       following subroutine, as returned by ILAENV. */

    if (*info == 0) {
	minwrk = 1;
	maxwrk = 1;
	bdspac = 0;
	mnthr = (integer) (minmn * 11.f / 6.f);
	if (*m >= *n && minmn > 0) {

/*           Compute space needed for SBDSDC */

	    if (wntqn) {
/*              sbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6) */
/*              keep 7*N for backwards compatibility. */
		bdspac = *n * 7;
	    } else {
		bdspac = *n * 3 * *n + (*n << 2);
	    }

/*           Compute space preferred for each routine */
	    sgebrd_(m, n, dum, m, dum, dum, dum, dum, dum, &c_n1, &ierr);
	    lwork_sgebrd_mn__ = (integer) dum[0];

	    sgebrd_(n, n, dum, n, dum, dum, dum, dum, dum, &c_n1, &ierr);
	    lwork_sgebrd_nn__ = (integer) dum[0];

	    sgeqrf_(m, n, dum, m, dum, dum, &c_n1, &ierr);
	    lwork_sgeqrf_mn__ = (integer) dum[0];

	    sorgbr_("Q", n, n, n, dum, n, dum, dum, &c_n1, &ierr);
	    lwork_sorgbr_q_nn__ = (integer) dum[0];

	    sorgqr_(m, m, n, dum, m, dum, dum, &c_n1, &ierr);
	    lwork_sorgqr_mm__ = (integer) dum[0];

	    sorgqr_(m, n, n, dum, m, dum, dum, &c_n1, &ierr);
	    lwork_sorgqr_mn__ = (integer) dum[0];

	    sormbr_("P", "R", "T", n, n, n, dum, n, dum, dum, n, dum, &c_n1, &
		    ierr);
	    lwork_sormbr_prt_nn__ = (integer) dum[0];

	    sormbr_("Q", "L", "N", n, n, n, dum, n, dum, dum, n, dum, &c_n1, &
		    ierr);
	    lwork_sormbr_qln_nn__ = (integer) dum[0];

	    sormbr_("Q", "L", "N", m, n, n, dum, m, dum, dum, m, dum, &c_n1, &
		    ierr);
	    lwork_sormbr_qln_mn__ = (integer) dum[0];

	    sormbr_("Q", "L", "N", m, m, n, dum, m, dum, dum, m, dum, &c_n1, &
		    ierr);
	    lwork_sormbr_qln_mm__ = (integer) dum[0];

	    if (*m >= mnthr) {
		if (wntqn) {

/*                 Path 1 (M >> N, JOBZ='N') */

		    wrkbl = *n + lwork_sgeqrf_mn__;
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = bdspac + *n;
		    maxwrk = f2cmax(i__1,i__2);
		    minwrk = bdspac + *n;
		} else if (wntqo) {

/*                 Path 2 (M >> N, JOBZ='O') */

		    wrkbl = *n + lwork_sgeqrf_mn__;
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n + lwork_sorgqr_mn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + bdspac;
		    wrkbl = f2cmax(i__1,i__2);
		    maxwrk = wrkbl + (*n << 1) * *n;
		    minwrk = bdspac + (*n << 1) * *n + *n * 3;
		} else if (wntqs) {

/*                 Path 3 (M >> N, JOBZ='S') */

		    wrkbl = *n + lwork_sgeqrf_mn__;
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n + lwork_sorgqr_mn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + bdspac;
		    wrkbl = f2cmax(i__1,i__2);
		    maxwrk = wrkbl + *n * *n;
		    minwrk = bdspac + *n * *n + *n * 3;
		} else if (wntqa) {

/*                 Path 4 (M >> N, JOBZ='A') */

		    wrkbl = *n + lwork_sgeqrf_mn__;
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n + lwork_sorgqr_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + bdspac;
		    wrkbl = f2cmax(i__1,i__2);
		    maxwrk = wrkbl + *n * *n;
/* Computing MAX */
		    i__1 = *n * 3 + bdspac, i__2 = *n + *m;
		    minwrk = *n * *n + f2cmax(i__1,i__2);
		}
	    } else {

/*              Path 5 (M >= N, but not much larger) */

		wrkbl = *n * 3 + lwork_sgebrd_mn__;
		if (wntqn) {
/*                 Path 5n (M >= N, jobz='N') */
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + bdspac;
		    maxwrk = f2cmax(i__1,i__2);
		    minwrk = *n * 3 + f2cmax(*m,bdspac);
		} else if (wntqo) {
/*                 Path 5o (M >= N, jobz='O') */
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_mn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + bdspac;
		    wrkbl = f2cmax(i__1,i__2);
		    maxwrk = wrkbl + *m * *n;
/* Computing MAX */
		    i__1 = *m, i__2 = *n * *n + bdspac;
		    minwrk = *n * 3 + f2cmax(i__1,i__2);
		} else if (wntqs) {
/*                 Path 5s (M >= N, jobz='S') */
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_mn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + bdspac;
		    maxwrk = f2cmax(i__1,i__2);
		    minwrk = *n * 3 + f2cmax(*m,bdspac);
		} else if (wntqa) {
/*                 Path 5a (M >= N, jobz='A') */
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *n * 3 + bdspac;
		    maxwrk = f2cmax(i__1,i__2);
		    minwrk = *n * 3 + f2cmax(*m,bdspac);
		}
	    }
	} else if (minmn > 0) {

/*           Compute space needed for SBDSDC */

	    if (wntqn) {
/*              sbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6) */
/*              keep 7*N for backwards compatibility. */
		bdspac = *m * 7;
	    } else {
		bdspac = *m * 3 * *m + (*m << 2);
	    }

/*           Compute space preferred for each routine */
	    sgebrd_(m, n, dum, m, dum, dum, dum, dum, dum, &c_n1, &ierr);
	    lwork_sgebrd_mn__ = (integer) dum[0];

	    sgebrd_(m, m, &a[a_offset], m, &s[1], dum, dum, dum, dum, &c_n1, &
		    ierr);
	    lwork_sgebrd_mm__ = (integer) dum[0];

	    sgelqf_(m, n, &a[a_offset], m, dum, dum, &c_n1, &ierr);
	    lwork_sgelqf_mn__ = (integer) dum[0];

	    sorglq_(n, n, m, dum, n, dum, dum, &c_n1, &ierr);
	    lwork_sorglq_nn__ = (integer) dum[0];

	    sorglq_(m, n, m, &a[a_offset], m, dum, dum, &c_n1, &ierr);
	    lwork_sorglq_mn__ = (integer) dum[0];

	    sorgbr_("P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr);
	    lwork_sorgbr_p_mm__ = (integer) dum[0];

	    sormbr_("P", "R", "T", m, m, m, dum, m, dum, dum, m, dum, &c_n1, &
		    ierr);
	    lwork_sormbr_prt_mm__ = (integer) dum[0];

	    sormbr_("P", "R", "T", m, n, m, dum, m, dum, dum, m, dum, &c_n1, &
		    ierr);
	    lwork_sormbr_prt_mn__ = (integer) dum[0];

	    sormbr_("P", "R", "T", n, n, m, dum, n, dum, dum, n, dum, &c_n1, &
		    ierr);
	    lwork_sormbr_prt_nn__ = (integer) dum[0];

	    sormbr_("Q", "L", "N", m, m, m, dum, m, dum, dum, m, dum, &c_n1, &
		    ierr);
	    lwork_sormbr_qln_mm__ = (integer) dum[0];

	    if (*n >= mnthr) {
		if (wntqn) {

/*                 Path 1t (N >> M, JOBZ='N') */

		    wrkbl = *m + lwork_sgelqf_mn__;
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = bdspac + *m;
		    maxwrk = f2cmax(i__1,i__2);
		    minwrk = bdspac + *m;
		} else if (wntqo) {

/*                 Path 2t (N >> M, JOBZ='O') */

		    wrkbl = *m + lwork_sgelqf_mn__;
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m + lwork_sorglq_mn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + bdspac;
		    wrkbl = f2cmax(i__1,i__2);
		    maxwrk = wrkbl + (*m << 1) * *m;
		    minwrk = bdspac + (*m << 1) * *m + *m * 3;
		} else if (wntqs) {

/*                 Path 3t (N >> M, JOBZ='S') */

		    wrkbl = *m + lwork_sgelqf_mn__;
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m + lwork_sorglq_mn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + bdspac;
		    wrkbl = f2cmax(i__1,i__2);
		    maxwrk = wrkbl + *m * *m;
		    minwrk = bdspac + *m * *m + *m * 3;
		} else if (wntqa) {

/*                 Path 4t (N >> M, JOBZ='A') */

		    wrkbl = *m + lwork_sgelqf_mn__;
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m + lwork_sorglq_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + bdspac;
		    wrkbl = f2cmax(i__1,i__2);
		    maxwrk = wrkbl + *m * *m;
/* Computing MAX */
		    i__1 = *m * 3 + bdspac, i__2 = *m + *n;
		    minwrk = *m * *m + f2cmax(i__1,i__2);
		}
	    } else {

/*              Path 5t (N > M, but not much larger) */

		wrkbl = *m * 3 + lwork_sgebrd_mn__;
		if (wntqn) {
/*                 Path 5tn (N > M, jobz='N') */
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + bdspac;
		    maxwrk = f2cmax(i__1,i__2);
		    minwrk = *m * 3 + f2cmax(*n,bdspac);
		} else if (wntqo) {
/*                 Path 5to (N > M, jobz='O') */
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + bdspac;
		    wrkbl = f2cmax(i__1,i__2);
		    maxwrk = wrkbl + *m * *n;
/* Computing MAX */
		    i__1 = *n, i__2 = *m * *m + bdspac;
		    minwrk = *m * 3 + f2cmax(i__1,i__2);
		} else if (wntqs) {
/*                 Path 5ts (N > M, jobz='S') */
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + bdspac;
		    maxwrk = f2cmax(i__1,i__2);
		    minwrk = *m * 3 + f2cmax(*n,bdspac);
		} else if (wntqa) {
/*                 Path 5ta (N > M, jobz='A') */
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_nn__;
		    wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
		    i__1 = wrkbl, i__2 = *m * 3 + bdspac;
		    maxwrk = f2cmax(i__1,i__2);
		    minwrk = *m * 3 + f2cmax(*n,bdspac);
		}
	    }
	}
	maxwrk = f2cmax(maxwrk,minwrk);
	work[1] = (real) maxwrk;

	if (*lwork < minwrk && ! lquery) {
	    *info = -12;
	}
    }

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

/*     Quick return if possible */

    if (*m == 0 || *n == 0) {
	return 0;
    }

/*     Get machine constants */

    eps = slamch_("P");
    smlnum = sqrt(slamch_("S")) / eps;
    bignum = 1.f / smlnum;

/*     Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */

    anrm = slange_("M", m, n, &a[a_offset], lda, dum);
    if (sisnan_(&anrm)) {
	*info = -4;
	return 0;
    }
    iscl = 0;
    if (anrm > 0.f && anrm < smlnum) {
	iscl = 1;
	slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
		ierr);
    } else if (anrm > bignum) {
	iscl = 1;
	slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
		ierr);
    }

    if (*m >= *n) {

/*        A has at least as many rows as columns. If A has sufficiently */
/*        more rows than columns, first reduce using the QR */
/*        decomposition (if sufficient workspace available) */

	if (*m >= mnthr) {

	    if (wntqn) {

/*              Path 1 (M >> N, JOBZ='N') */
/*              No singular vectors to be computed */

		itau = 1;
		nwork = itau + *n;

/*              Compute A=Q*R */
/*              Workspace: need   N [tau] + N    [work] */
/*              Workspace: prefer N [tau] + N*NB [work] */

		i__1 = *lwork - nwork + 1;
		sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
			i__1, &ierr);

/*              Zero out below R */

		i__1 = *n - 1;
		i__2 = *n - 1;
		slaset_("L", &i__1, &i__2, &c_b63, &c_b63, &a[a_dim1 + 2], 
			lda);
		ie = 1;
		itauq = ie + *n;
		itaup = itauq + *n;
		nwork = itaup + *n;

/*              Bidiagonalize R in A */
/*              Workspace: need   3*N [e, tauq, taup] + N      [work] */
/*              Workspace: prefer 3*N [e, tauq, taup] + 2*N*NB [work] */

		i__1 = *lwork - nwork + 1;
		sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
			itauq], &work[itaup], &work[nwork], &i__1, &ierr);
		nwork = ie + *n;

/*              Perform bidiagonal SVD, computing singular values only */
/*              Workspace: need   N [e] + BDSPAC */

		sbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1,
			 dum, idum, &work[nwork], &iwork[1], info);

	    } else if (wntqo) {

/*              Path 2 (M >> N, JOBZ = 'O') */
/*              N left singular vectors to be overwritten on A and */
/*              N right singular vectors to be computed in VT */

		ir = 1;

/*              WORK(IR) is LDWRKR by N */

		if (*lwork >= *lda * *n + *n * *n + *n * 3 + bdspac) {
		    ldwrkr = *lda;
		} else {
		    ldwrkr = (*lwork - *n * *n - *n * 3 - bdspac) / *n;
		}
		itau = ir + ldwrkr * *n;
		nwork = itau + *n;

/*              Compute A=Q*R */
/*              Workspace: need   N*N [R] + N [tau] + N    [work] */
/*              Workspace: prefer N*N [R] + N [tau] + N*NB [work] */

		i__1 = *lwork - nwork + 1;
		sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
			i__1, &ierr);

/*              Copy R to WORK(IR), zeroing out below it */

		slacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
		i__1 = *n - 1;
		i__2 = *n - 1;
		slaset_("L", &i__1, &i__2, &c_b63, &c_b63, &work[ir + 1], &
			ldwrkr);

/*              Generate Q in A */
/*              Workspace: need   N*N [R] + N [tau] + N    [work] */
/*              Workspace: prefer N*N [R] + N [tau] + N*NB [work] */

		i__1 = *lwork - nwork + 1;
		sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
			 &i__1, &ierr);
		ie = itau;
		itauq = ie + *n;
		itaup = itauq + *n;
		nwork = itaup + *n;

/*              Bidiagonalize R in WORK(IR) */
/*              Workspace: need   N*N [R] + 3*N [e, tauq, taup] + N      [work] */
/*              Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + 2*N*NB [work] */

		i__1 = *lwork - nwork + 1;
		sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
			itauq], &work[itaup], &work[nwork], &i__1, &ierr);

/*              WORK(IU) is N by N */

		iu = nwork;
		nwork = iu + *n * *n;

/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in WORK(IU) and computing right */
/*              singular vectors of bidiagonal matrix in VT */
/*              Workspace: need   N*N [R] + 3*N [e, tauq, taup] + N*N [U] + BDSPAC */

		sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[
			vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], 
			info);

/*              Overwrite WORK(IU) by left singular vectors of R */
/*              and VT by right singular vectors of R */
/*              Workspace: need   N*N [R] + 3*N [e, tauq, taup] + N*N [U] + N    [work] */
/*              Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */

		i__1 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
			itauq], &work[iu], n, &work[nwork], &i__1, &ierr);
		i__1 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[
			itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
			ierr);

/*              Multiply Q in A by left singular vectors of R in */
/*              WORK(IU), storing result in WORK(IR) and copying to A */
/*              Workspace: need   N*N [R] + 3*N [e, tauq, taup] + N*N [U] */
/*              Workspace: prefer M*N [R] + 3*N [e, tauq, taup] + N*N [U] */

		i__1 = *m;
		i__2 = ldwrkr;
		for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += 
			i__2) {
/* Computing MIN */
		    i__3 = *m - i__ + 1;
		    chunk = f2cmin(i__3,ldwrkr);
		    sgemm_("N", "N", &chunk, n, n, &c_b84, &a[i__ + a_dim1], 
			    lda, &work[iu], n, &c_b63, &work[ir], &ldwrkr);
		    slacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ + 
			    a_dim1], lda);
/* L10: */
		}

	    } else if (wntqs) {

/*              Path 3 (M >> N, JOBZ='S') */
/*              N left singular vectors to be computed in U and */
/*              N right singular vectors to be computed in VT */

		ir = 1;

/*              WORK(IR) is N by N */

		ldwrkr = *n;
		itau = ir + ldwrkr * *n;
		nwork = itau + *n;

/*              Compute A=Q*R */
/*              Workspace: need   N*N [R] + N [tau] + N    [work] */
/*              Workspace: prefer N*N [R] + N [tau] + N*NB [work] */

		i__2 = *lwork - nwork + 1;
		sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
			i__2, &ierr);

/*              Copy R to WORK(IR), zeroing out below it */

		slacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
		i__2 = *n - 1;
		i__1 = *n - 1;
		slaset_("L", &i__2, &i__1, &c_b63, &c_b63, &work[ir + 1], &
			ldwrkr);

/*              Generate Q in A */
/*              Workspace: need   N*N [R] + N [tau] + N    [work] */
/*              Workspace: prefer N*N [R] + N [tau] + N*NB [work] */

		i__2 = *lwork - nwork + 1;
		sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
			 &i__2, &ierr);
		ie = itau;
		itauq = ie + *n;
		itaup = itauq + *n;
		nwork = itaup + *n;

/*              Bidiagonalize R in WORK(IR) */
/*              Workspace: need   N*N [R] + 3*N [e, tauq, taup] + N      [work] */
/*              Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + 2*N*NB [work] */

		i__2 = *lwork - nwork + 1;
		sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
			itauq], &work[itaup], &work[nwork], &i__2, &ierr);

/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagoal matrix in U and computing right singular */
/*              vectors of bidiagonal matrix in VT */
/*              Workspace: need   N*N [R] + 3*N [e, tauq, taup] + BDSPAC */

		sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
			vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], 
			info);

/*              Overwrite U by left singular vectors of R and VT */
/*              by right singular vectors of R */
/*              Workspace: need   N*N [R] + 3*N [e, tauq, taup] + N    [work] */
/*              Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + N*NB [work] */

		i__2 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
			itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);

		i__2 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[
			itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
			ierr);

/*              Multiply Q in A by left singular vectors of R in */
/*              WORK(IR), storing result in U */
/*              Workspace: need   N*N [R] */

		slacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
		sgemm_("N", "N", m, n, n, &c_b84, &a[a_offset], lda, &work[ir]
			, &ldwrkr, &c_b63, &u[u_offset], ldu);

	    } else if (wntqa) {

/*              Path 4 (M >> N, JOBZ='A') */
/*              M left singular vectors to be computed in U and */
/*              N right singular vectors to be computed in VT */

		iu = 1;

/*              WORK(IU) is N by N */

		ldwrku = *n;
		itau = iu + ldwrku * *n;
		nwork = itau + *n;

/*              Compute A=Q*R, copying result to U */
/*              Workspace: need   N*N [U] + N [tau] + N    [work] */
/*              Workspace: prefer N*N [U] + N [tau] + N*NB [work] */

		i__2 = *lwork - nwork + 1;
		sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
			i__2, &ierr);
		slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);

/*              Generate Q in U */
/*              Workspace: need   N*N [U] + N [tau] + M    [work] */
/*              Workspace: prefer N*N [U] + N [tau] + M*NB [work] */
		i__2 = *lwork - nwork + 1;
		sorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork],
			 &i__2, &ierr);

/*              Produce R in A, zeroing out other entries */

		i__2 = *n - 1;
		i__1 = *n - 1;
		slaset_("L", &i__2, &i__1, &c_b63, &c_b63, &a[a_dim1 + 2], 
			lda);
		ie = itau;
		itauq = ie + *n;
		itaup = itauq + *n;
		nwork = itaup + *n;

/*              Bidiagonalize R in A */
/*              Workspace: need   N*N [U] + 3*N [e, tauq, taup] + N      [work] */
/*              Workspace: prefer N*N [U] + 3*N [e, tauq, taup] + 2*N*NB [work] */

		i__2 = *lwork - nwork + 1;
		sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
			itauq], &work[itaup], &work[nwork], &i__2, &ierr);

/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in WORK(IU) and computing right */
/*              singular vectors of bidiagonal matrix in VT */
/*              Workspace: need   N*N [U] + 3*N [e, tauq, taup] + BDSPAC */

		sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[
			vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], 
			info);

/*              Overwrite WORK(IU) by left singular vectors of R and VT */
/*              by right singular vectors of R */
/*              Workspace: need   N*N [U] + 3*N [e, tauq, taup] + N    [work] */
/*              Workspace: prefer N*N [U] + 3*N [e, tauq, taup] + N*NB [work] */

		i__2 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[
			itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
			ierr);
		i__2 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
			itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
			ierr);

/*              Multiply Q in U by left singular vectors of R in */
/*              WORK(IU), storing result in A */
/*              Workspace: need   N*N [U] */

		sgemm_("N", "N", m, n, n, &c_b84, &u[u_offset], ldu, &work[iu]
			, &ldwrku, &c_b63, &a[a_offset], lda);

/*              Copy left singular vectors of A from A to U */

		slacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);

	    }

	} else {

/*           M .LT. MNTHR */

/*           Path 5 (M >= N, but not much larger) */
/*           Reduce to bidiagonal form without QR decomposition */

	    ie = 1;
	    itauq = ie + *n;
	    itaup = itauq + *n;
	    nwork = itaup + *n;

/*           Bidiagonalize A */
/*           Workspace: need   3*N [e, tauq, taup] + M        [work] */
/*           Workspace: prefer 3*N [e, tauq, taup] + (M+N)*NB [work] */

	    i__2 = *lwork - nwork + 1;
	    sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
		    work[itaup], &work[nwork], &i__2, &ierr);
	    if (wntqn) {

/*              Path 5n (M >= N, JOBZ='N') */
/*              Perform bidiagonal SVD, only computing singular values */
/*              Workspace: need   3*N [e, tauq, taup] + BDSPAC */

		sbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1,
			 dum, idum, &work[nwork], &iwork[1], info);
	    } else if (wntqo) {
/*              Path 5o (M >= N, JOBZ='O') */
		iu = nwork;
		if (*lwork >= *m * *n + *n * 3 + bdspac) {

/*                 WORK( IU ) is M by N */

		    ldwrku = *m;
		    nwork = iu + ldwrku * *n;
		    slaset_("F", m, n, &c_b63, &c_b63, &work[iu], &ldwrku);
/*                 IR is unused; silence compile warnings */
		    ir = -1;
		} else {

/*                 WORK( IU ) is N by N */

		    ldwrku = *n;
		    nwork = iu + ldwrku * *n;

/*                 WORK(IR) is LDWRKR by N */

		    ir = nwork;
		    ldwrkr = (*lwork - *n * *n - *n * 3) / *n;
		}
		nwork = iu + ldwrku * *n;

/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in WORK(IU) and computing right */
/*              singular vectors of bidiagonal matrix in VT */
/*              Workspace: need   3*N [e, tauq, taup] + N*N [U] + BDSPAC */

		sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], &ldwrku, &
			vt[vt_offset], ldvt, dum, idum, &work[nwork], &iwork[
			1], info);

/*              Overwrite VT by right singular vectors of A */
/*              Workspace: need   3*N [e, tauq, taup] + N*N [U] + N    [work] */
/*              Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */

		i__2 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
			itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
			ierr);

		if (*lwork >= *m * *n + *n * 3 + bdspac) {

/*                 Path 5o-fast */
/*                 Overwrite WORK(IU) by left singular vectors of A */
/*                 Workspace: need   3*N [e, tauq, taup] + M*N [U] + N    [work] */
/*                 Workspace: prefer 3*N [e, tauq, taup] + M*N [U] + N*NB [work] */

		    i__2 = *lwork - nwork + 1;
		    sormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
			    itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
			    ierr);

/*                 Copy left singular vectors of A from WORK(IU) to A */

		    slacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda);
		} else {

/*                 Path 5o-slow */
/*                 Generate Q in A */
/*                 Workspace: need   3*N [e, tauq, taup] + N*N [U] + N    [work] */
/*                 Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */

		    i__2 = *lwork - nwork + 1;
		    sorgbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
			    work[nwork], &i__2, &ierr);

/*                 Multiply Q in A by left singular vectors of */
/*                 bidiagonal matrix in WORK(IU), storing result in */
/*                 WORK(IR) and copying to A */
/*                 Workspace: need   3*N [e, tauq, taup] + N*N [U] + NB*N [R] */
/*                 Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + M*N  [R] */

		    i__2 = *m;
		    i__1 = ldwrkr;
		    for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
			     i__1) {
/* Computing MIN */
			i__3 = *m - i__ + 1;
			chunk = f2cmin(i__3,ldwrkr);
			sgemm_("N", "N", &chunk, n, n, &c_b84, &a[i__ + 
				a_dim1], lda, &work[iu], &ldwrku, &c_b63, &
				work[ir], &ldwrkr);
			slacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ + 
				a_dim1], lda);
/* L20: */
		    }
		}

	    } else if (wntqs) {

/*              Path 5s (M >= N, JOBZ='S') */
/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in U and computing right singular */
/*              vectors of bidiagonal matrix in VT */
/*              Workspace: need   3*N [e, tauq, taup] + BDSPAC */

		slaset_("F", m, n, &c_b63, &c_b63, &u[u_offset], ldu);
		sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
			vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], 
			info);

/*              Overwrite U by left singular vectors of A and VT */
/*              by right singular vectors of A */
/*              Workspace: need   3*N [e, tauq, taup] + N    [work] */
/*              Workspace: prefer 3*N [e, tauq, taup] + N*NB [work] */

		i__1 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
			itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
		i__1 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
			itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
			ierr);
	    } else if (wntqa) {

/*              Path 5a (M >= N, JOBZ='A') */
/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in U and computing right singular */
/*              vectors of bidiagonal matrix in VT */
/*              Workspace: need   3*N [e, tauq, taup] + BDSPAC */

		slaset_("F", m, m, &c_b63, &c_b63, &u[u_offset], ldu);
		sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
			vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], 
			info);

/*              Set the right corner of U to identity matrix */

		if (*m > *n) {
		    i__1 = *m - *n;
		    i__2 = *m - *n;
		    slaset_("F", &i__1, &i__2, &c_b63, &c_b84, &u[*n + 1 + (*
			    n + 1) * u_dim1], ldu);
		}

/*              Overwrite U by left singular vectors of A and VT */
/*              by right singular vectors of A */
/*              Workspace: need   3*N [e, tauq, taup] + M    [work] */
/*              Workspace: prefer 3*N [e, tauq, taup] + M*NB [work] */

		i__1 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
			itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
		i__1 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[
			itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
			ierr);
	    }

	}

    } else {

/*        A has more columns than rows. If A has sufficiently more */
/*        columns than rows, first reduce using the LQ decomposition (if */
/*        sufficient workspace available) */

	if (*n >= mnthr) {

	    if (wntqn) {

/*              Path 1t (N >> M, JOBZ='N') */
/*              No singular vectors to be computed */

		itau = 1;
		nwork = itau + *m;

/*              Compute A=L*Q */
/*              Workspace: need   M [tau] + M [work] */
/*              Workspace: prefer M [tau] + M*NB [work] */

		i__1 = *lwork - nwork + 1;
		sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
			i__1, &ierr);

/*              Zero out above L */

		i__1 = *m - 1;
		i__2 = *m - 1;
		slaset_("U", &i__1, &i__2, &c_b63, &c_b63, &a[(a_dim1 << 1) + 
			1], lda);
		ie = 1;
		itauq = ie + *m;
		itaup = itauq + *m;
		nwork = itaup + *m;

/*              Bidiagonalize L in A */
/*              Workspace: need   3*M [e, tauq, taup] + M      [work] */
/*              Workspace: prefer 3*M [e, tauq, taup] + 2*M*NB [work] */

		i__1 = *lwork - nwork + 1;
		sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
			itauq], &work[itaup], &work[nwork], &i__1, &ierr);
		nwork = ie + *m;

/*              Perform bidiagonal SVD, computing singular values only */
/*              Workspace: need   M [e] + BDSPAC */

		sbdsdc_("U", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1,
			 dum, idum, &work[nwork], &iwork[1], info);

	    } else if (wntqo) {

/*              Path 2t (N >> M, JOBZ='O') */
/*              M right singular vectors to be overwritten on A and */
/*              M left singular vectors to be computed in U */

		ivt = 1;

/*              WORK(IVT) is M by M */
/*              WORK(IL)  is M by M; it is later resized to M by chunk for gemm */

		il = ivt + *m * *m;
		if (*lwork >= *m * *n + *m * *m + *m * 3 + bdspac) {
		    ldwrkl = *m;
		    chunk = *n;
		} else {
		    ldwrkl = *m;
		    chunk = (*lwork - *m * *m) / *m;
		}
		itau = il + ldwrkl * *m;
		nwork = itau + *m;

/*              Compute A=L*Q */
/*              Workspace: need   M*M [VT] + M*M [L] + M [tau] + M    [work] */
/*              Workspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */

		i__1 = *lwork - nwork + 1;
		sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
			i__1, &ierr);

/*              Copy L to WORK(IL), zeroing about above it */

		slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
		i__1 = *m - 1;
		i__2 = *m - 1;
		slaset_("U", &i__1, &i__2, &c_b63, &c_b63, &work[il + ldwrkl],
			 &ldwrkl);

/*              Generate Q in A */
/*              Workspace: need   M*M [VT] + M*M [L] + M [tau] + M    [work] */
/*              Workspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */

		i__1 = *lwork - nwork + 1;
		sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
			 &i__1, &ierr);
		ie = itau;
		itauq = ie + *m;
		itaup = itauq + *m;
		nwork = itaup + *m;

/*              Bidiagonalize L in WORK(IL) */
/*              Workspace: need   M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M      [work] */
/*              Workspace: prefer M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + 2*M*NB [work] */

		i__1 = *lwork - nwork + 1;
		sgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[
			itauq], &work[itaup], &work[nwork], &i__1, &ierr);

/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in U, and computing right singular */
/*              vectors of bidiagonal matrix in WORK(IVT) */
/*              Workspace: need   M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + BDSPAC */

		sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
			work[ivt], m, dum, idum, &work[nwork], &iwork[1], 
			info);

/*              Overwrite U by left singular vectors of L and WORK(IVT) */
/*              by right singular vectors of L */
/*              Workspace: need   M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M    [work] */
/*              Workspace: prefer M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M*NB [work] */

		i__1 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
			itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
		i__1 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[
			itaup], &work[ivt], m, &work[nwork], &i__1, &ierr);

/*              Multiply right singular vectors of L in WORK(IVT) by Q */
/*              in A, storing result in WORK(IL) and copying to A */
/*              Workspace: need   M*M [VT] + M*M [L] */
/*              Workspace: prefer M*M [VT] + M*N [L] */
/*              At this point, L is resized as M by chunk. */

		i__1 = *n;
		i__2 = chunk;
		for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += 
			i__2) {
/* Computing MIN */
		    i__3 = *n - i__ + 1;
		    blk = f2cmin(i__3,chunk);
		    sgemm_("N", "N", m, &blk, m, &c_b84, &work[ivt], m, &a[
			    i__ * a_dim1 + 1], lda, &c_b63, &work[il], &
			    ldwrkl);
		    slacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1 
			    + 1], lda);
/* L30: */
		}

	    } else if (wntqs) {

/*              Path 3t (N >> M, JOBZ='S') */
/*              M right singular vectors to be computed in VT and */
/*              M left singular vectors to be computed in U */

		il = 1;

/*              WORK(IL) is M by M */

		ldwrkl = *m;
		itau = il + ldwrkl * *m;
		nwork = itau + *m;

/*              Compute A=L*Q */
/*              Workspace: need   M*M [L] + M [tau] + M    [work] */
/*              Workspace: prefer M*M [L] + M [tau] + M*NB [work] */

		i__2 = *lwork - nwork + 1;
		sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
			i__2, &ierr);

/*              Copy L to WORK(IL), zeroing out above it */

		slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
		i__2 = *m - 1;
		i__1 = *m - 1;
		slaset_("U", &i__2, &i__1, &c_b63, &c_b63, &work[il + ldwrkl],
			 &ldwrkl);

/*              Generate Q in A */
/*              Workspace: need   M*M [L] + M [tau] + M    [work] */
/*              Workspace: prefer M*M [L] + M [tau] + M*NB [work] */

		i__2 = *lwork - nwork + 1;
		sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
			 &i__2, &ierr);
		ie = itau;
		itauq = ie + *m;
		itaup = itauq + *m;
		nwork = itaup + *m;

/*              Bidiagonalize L in WORK(IU). */
/*              Workspace: need   M*M [L] + 3*M [e, tauq, taup] + M      [work] */
/*              Workspace: prefer M*M [L] + 3*M [e, tauq, taup] + 2*M*NB [work] */

		i__2 = *lwork - nwork + 1;
		sgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[
			itauq], &work[itaup], &work[nwork], &i__2, &ierr);

/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in U and computing right singular */
/*              vectors of bidiagonal matrix in VT */
/*              Workspace: need   M*M [L] + 3*M [e, tauq, taup] + BDSPAC */

		sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
			vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], 
			info);

/*              Overwrite U by left singular vectors of L and VT */
/*              by right singular vectors of L */
/*              Workspace: need   M*M [L] + 3*M [e, tauq, taup] + M    [work] */
/*              Workspace: prefer M*M [L] + 3*M [e, tauq, taup] + M*NB [work] */

		i__2 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
			itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
		i__2 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[
			itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
			ierr);

/*              Multiply right singular vectors of L in WORK(IL) by */
/*              Q in A, storing result in VT */
/*              Workspace: need   M*M [L] */

		slacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl);
		sgemm_("N", "N", m, n, m, &c_b84, &work[il], &ldwrkl, &a[
			a_offset], lda, &c_b63, &vt[vt_offset], ldvt);

	    } else if (wntqa) {

/*              Path 4t (N >> M, JOBZ='A') */
/*              N right singular vectors to be computed in VT and */
/*              M left singular vectors to be computed in U */

		ivt = 1;

/*              WORK(IVT) is M by M */

		ldwkvt = *m;
		itau = ivt + ldwkvt * *m;
		nwork = itau + *m;

/*              Compute A=L*Q, copying result to VT */
/*              Workspace: need   M*M [VT] + M [tau] + M    [work] */
/*              Workspace: prefer M*M [VT] + M [tau] + M*NB [work] */

		i__2 = *lwork - nwork + 1;
		sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
			i__2, &ierr);
		slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);

/*              Generate Q in VT */
/*              Workspace: need   M*M [VT] + M [tau] + N    [work] */
/*              Workspace: prefer M*M [VT] + M [tau] + N*NB [work] */

		i__2 = *lwork - nwork + 1;
		sorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[
			nwork], &i__2, &ierr);

/*              Produce L in A, zeroing out other entries */

		i__2 = *m - 1;
		i__1 = *m - 1;
		slaset_("U", &i__2, &i__1, &c_b63, &c_b63, &a[(a_dim1 << 1) + 
			1], lda);
		ie = itau;
		itauq = ie + *m;
		itaup = itauq + *m;
		nwork = itaup + *m;

/*              Bidiagonalize L in A */
/*              Workspace: need   M*M [VT] + 3*M [e, tauq, taup] + M      [work] */
/*              Workspace: prefer M*M [VT] + 3*M [e, tauq, taup] + 2*M*NB [work] */

		i__2 = *lwork - nwork + 1;
		sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
			itauq], &work[itaup], &work[nwork], &i__2, &ierr);

/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in U and computing right singular */
/*              vectors of bidiagonal matrix in WORK(IVT) */
/*              Workspace: need   M*M [VT] + 3*M [e, tauq, taup] + BDSPAC */

		sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
			work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1]
			, info);

/*              Overwrite U by left singular vectors of L and WORK(IVT) */
/*              by right singular vectors of L */
/*              Workspace: need   M*M [VT] + 3*M [e, tauq, taup]+ M    [work] */
/*              Workspace: prefer M*M [VT] + 3*M [e, tauq, taup]+ M*NB [work] */

		i__2 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[
			itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
		i__2 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", m, m, m, &a[a_offset], lda, &work[
			itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &
			ierr);

/*              Multiply right singular vectors of L in WORK(IVT) by */
/*              Q in VT, storing result in A */
/*              Workspace: need   M*M [VT] */

		sgemm_("N", "N", m, n, m, &c_b84, &work[ivt], &ldwkvt, &vt[
			vt_offset], ldvt, &c_b63, &a[a_offset], lda);

/*              Copy right singular vectors of A from A to VT */

		slacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);

	    }

	} else {

/*           N .LT. MNTHR */

/*           Path 5t (N > M, but not much larger) */
/*           Reduce to bidiagonal form without LQ decomposition */

	    ie = 1;
	    itauq = ie + *m;
	    itaup = itauq + *m;
	    nwork = itaup + *m;

/*           Bidiagonalize A */
/*           Workspace: need   3*M [e, tauq, taup] + N        [work] */
/*           Workspace: prefer 3*M [e, tauq, taup] + (M+N)*NB [work] */

	    i__2 = *lwork - nwork + 1;
	    sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
		    work[itaup], &work[nwork], &i__2, &ierr);
	    if (wntqn) {

/*              Path 5tn (N > M, JOBZ='N') */
/*              Perform bidiagonal SVD, only computing singular values */
/*              Workspace: need   3*M [e, tauq, taup] + BDSPAC */

		sbdsdc_("L", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1,
			 dum, idum, &work[nwork], &iwork[1], info);
	    } else if (wntqo) {
/*              Path 5to (N > M, JOBZ='O') */
		ldwkvt = *m;
		ivt = nwork;
		if (*lwork >= *m * *n + *m * 3 + bdspac) {

/*                 WORK( IVT ) is M by N */

		    slaset_("F", m, n, &c_b63, &c_b63, &work[ivt], &ldwkvt);
		    nwork = ivt + ldwkvt * *n;
/*                 IL is unused; silence compile warnings */
		    il = -1;
		} else {

/*                 WORK( IVT ) is M by M */

		    nwork = ivt + ldwkvt * *m;
		    il = nwork;

/*                 WORK(IL) is M by CHUNK */

		    chunk = (*lwork - *m * *m - *m * 3) / *m;
		}

/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in U and computing right singular */
/*              vectors of bidiagonal matrix in WORK(IVT) */
/*              Workspace: need   3*M [e, tauq, taup] + M*M [VT] + BDSPAC */

		sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
			work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1]
			, info);

/*              Overwrite U by left singular vectors of A */
/*              Workspace: need   3*M [e, tauq, taup] + M*M [VT] + M    [work] */
/*              Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*NB [work] */

		i__2 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
			itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);

		if (*lwork >= *m * *n + *m * 3 + bdspac) {

/*                 Path 5to-fast */
/*                 Overwrite WORK(IVT) by left singular vectors of A */
/*                 Workspace: need   3*M [e, tauq, taup] + M*N [VT] + M    [work] */
/*                 Workspace: prefer 3*M [e, tauq, taup] + M*N [VT] + M*NB [work] */

		    i__2 = *lwork - nwork + 1;
		    sormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[
			    itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, 
			    &ierr);

/*                 Copy right singular vectors of A from WORK(IVT) to A */

		    slacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda);
		} else {

/*                 Path 5to-slow */
/*                 Generate P**T in A */
/*                 Workspace: need   3*M [e, tauq, taup] + M*M [VT] + M    [work] */
/*                 Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*NB [work] */

		    i__2 = *lwork - nwork + 1;
		    sorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
			    work[nwork], &i__2, &ierr);

/*                 Multiply Q in A by right singular vectors of */
/*                 bidiagonal matrix in WORK(IVT), storing result in */
/*                 WORK(IL) and copying to A */
/*                 Workspace: need   3*M [e, tauq, taup] + M*M [VT] + M*NB [L] */
/*                 Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*N  [L] */

		    i__2 = *n;
		    i__1 = chunk;
		    for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
			     i__1) {
/* Computing MIN */
			i__3 = *n - i__ + 1;
			blk = f2cmin(i__3,chunk);
			sgemm_("N", "N", m, &blk, m, &c_b84, &work[ivt], &
				ldwkvt, &a[i__ * a_dim1 + 1], lda, &c_b63, &
				work[il], m);
			slacpy_("F", m, &blk, &work[il], m, &a[i__ * a_dim1 + 
				1], lda);
/* L40: */
		    }
		}
	    } else if (wntqs) {

/*              Path 5ts (N > M, JOBZ='S') */
/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in U and computing right singular */
/*              vectors of bidiagonal matrix in VT */
/*              Workspace: need   3*M [e, tauq, taup] + BDSPAC */

		slaset_("F", m, n, &c_b63, &c_b63, &vt[vt_offset], ldvt);
		sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
			vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], 
			info);

/*              Overwrite U by left singular vectors of A and VT */
/*              by right singular vectors of A */
/*              Workspace: need   3*M [e, tauq, taup] + M    [work] */
/*              Workspace: prefer 3*M [e, tauq, taup] + M*NB [work] */

		i__1 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
			itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
		i__1 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[
			itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
			ierr);
	    } else if (wntqa) {

/*              Path 5ta (N > M, JOBZ='A') */
/*              Perform bidiagonal SVD, computing left singular vectors */
/*              of bidiagonal matrix in U and computing right singular */
/*              vectors of bidiagonal matrix in VT */
/*              Workspace: need   3*M [e, tauq, taup] + BDSPAC */

		slaset_("F", n, n, &c_b63, &c_b63, &vt[vt_offset], ldvt);
		sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
			vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1], 
			info);

/*              Set the right corner of VT to identity matrix */

		if (*n > *m) {
		    i__1 = *n - *m;
		    i__2 = *n - *m;
		    slaset_("F", &i__1, &i__2, &c_b63, &c_b84, &vt[*m + 1 + (*
			    m + 1) * vt_dim1], ldvt);
		}

/*              Overwrite U by left singular vectors of A and VT */
/*              by right singular vectors of A */
/*              Workspace: need   3*M [e, tauq, taup] + N    [work] */
/*              Workspace: prefer 3*M [e, tauq, taup] + N*NB [work] */

		i__1 = *lwork - nwork + 1;
		sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
			itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
		i__1 = *lwork - nwork + 1;
		sormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[
			itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
			ierr);
	    }

	}

    }

/*     Undo scaling if necessary */

    if (iscl == 1) {
	if (anrm > bignum) {
	    slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
		    minmn, &ierr);
	}
	if (anrm < smlnum) {
	    slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
		    minmn, &ierr);
	}
    }

/*     Return optimal workspace in WORK(1) */

    work[1] = (real) maxwrk;

    return 0;

/*     End of SGESDD */

} /* sgesdd_ */