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OpenBLAS/lapack-netlib/SRC/sgesvd.c

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#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(_WIN64)
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(_WIN64)
#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;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
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;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef blasint logical;
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)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#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) = conjf(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) (cimagf(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 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);}
#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)}
/* -- 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__6 = 6;
static integer c__0 = 0;
static integer c__2 = 2;
static integer c_n1 = -1;
static real c_b57 = 0.f;
static integer c__1 = 1;
static real c_b79 = 1.f;
/* > \brief <b> SGESVD computes the singular value decomposition (SVD) for GE matrices</b> */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGESVD + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgesvd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgesvd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgesvd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, */
/* WORK, LWORK, INFO ) */
/* CHARACTER JOBU, JOBVT */
/* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
/* REAL A( LDA, * ), S( * ), U( LDU, * ), */
/* $ VT( LDVT, * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGESVD computes the singular value decomposition (SVD) of a real */
/* > M-by-N matrix A, optionally computing the left and/or right singular */
/* > vectors. 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 V**T, not V. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOBU */
/* > \verbatim */
/* > JOBU is CHARACTER*1 */
/* > Specifies options for computing all or part of the matrix U: */
/* > = 'A': all M columns of U are returned in array U: */
/* > = 'S': the first f2cmin(m,n) columns of U (the left singular */
/* > vectors) are returned in the array U; */
/* > = 'O': the first f2cmin(m,n) columns of U (the left singular */
/* > vectors) are overwritten on the array A; */
/* > = 'N': no columns of U (no left singular vectors) are */
/* > computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVT */
/* > \verbatim */
/* > JOBVT is CHARACTER*1 */
/* > Specifies options for computing all or part of the matrix */
/* > V**T: */
/* > = 'A': all N rows of V**T are returned in the array VT; */
/* > = 'S': the first f2cmin(m,n) rows of V**T (the right singular */
/* > vectors) are returned in the array VT; */
/* > = 'O': the first f2cmin(m,n) rows of V**T (the right singular */
/* > vectors) are overwritten on the array A; */
/* > = 'N': no rows of V**T (no right singular vectors) are */
/* > computed. */
/* > */
/* > JOBVT and JOBU cannot both be 'O'. */
/* > \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 JOBU = 'O', A is overwritten with the first f2cmin(m,n) */
/* > columns of U (the left singular vectors, */
/* > stored columnwise); */
/* > if JOBVT = 'O', A is overwritten with the first f2cmin(m,n) */
/* > rows of V**T (the right singular vectors, */
/* > stored rowwise); */
/* > if JOBU .ne. 'O' and JOBVT .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) */
/* > (LDU,M) if JOBU = 'A' or (LDU,f2cmin(M,N)) if JOBU = 'S'. */
/* > If JOBU = 'A', U contains the M-by-M orthogonal matrix U; */
/* > if JOBU = 'S', U contains the first f2cmin(m,n) columns of U */
/* > (the left singular vectors, stored columnwise); */
/* > if JOBU = 'N' or 'O', U is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* > LDU is INTEGER */
/* > The leading dimension of the array U. LDU >= 1; if */
/* > JOBU = 'S' or 'A', LDU >= M. */
/* > \endverbatim */
/* > */
/* > \param[out] VT */
/* > \verbatim */
/* > VT is REAL array, dimension (LDVT,N) */
/* > If JOBVT = 'A', VT contains the N-by-N orthogonal matrix */
/* > V**T; */
/* > if JOBVT = 'S', VT contains the first f2cmin(m,n) rows of */
/* > V**T (the right singular vectors, stored rowwise); */
/* > if JOBVT = 'N' or 'O', VT is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVT */
/* > \verbatim */
/* > LDVT is INTEGER */
/* > The leading dimension of the array VT. LDVT >= 1; if */
/* > JOBVT = 'A', LDVT >= N; if JOBVT = '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; */
/* > if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged */
/* > superdiagonal elements of an upper bidiagonal matrix B */
/* > whose diagonal is in S (not necessarily sorted). B */
/* > satisfies A = U * B * VT, so it has the same singular values */
/* > as A, and singular vectors related by U and VT. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. */
/* > LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code): */
/* > - PATH 1 (M much larger than N, JOBU='N') */
/* > - PATH 1t (N much larger than M, JOBVT='N') */
/* > LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)) for the other paths */
/* > For good performance, LWORK should generally be larger. */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal size of the WORK array, returns */
/* > this value as the first entry of the WORK array, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > > 0: if SBDSQR did not converge, INFO specifies how many */
/* > superdiagonals of an intermediate bidiagonal form B */
/* > did not converge to zero. See the description of WORK */
/* > above for details. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date April 2012 */
/* > \ingroup realGEsing */
/* ===================================================================== */
/* Subroutine */ void sgesvd_(char *jobu, char *jobvt, integer *m, integer *n,
real *a, integer *lda, real *s, real *u, integer *ldu, real *vt,
integer *ldvt, real *work, integer *lwork, integer *info)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2],
i__2, i__3, i__4;
char ch__1[2];
/* Local variables */
integer iscl;
real anrm;
integer ierr, itau, ncvt, nrvt, lwork_sgebrd__, lwork_sgelqf__,
lwork_sgeqrf__, i__;
extern logical lsame_(char *, char *);
integer chunk;
extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *);
integer minmn, wrkbl, itaup, itauq, mnthr, iwork;
logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs;
integer ie, ir, bdspac, iu;
extern /* Subroutine */ void 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);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
real bignum;
extern /* Subroutine */ void 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 *), sbdsqr_(char *, integer *, integer *,
integer *, integer *, real *, real *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *), sorgbr_(
char *, integer *, integer *, integer *, real *, integer *, real *
, real *, integer *, integer *), sormbr_(char *, char *,
char *, integer *, integer *, integer *, real *, integer *, real *
, real *, integer *, real *, integer *, integer *);
integer ldwrkr, minwrk, ldwrku, maxwrk;
extern /* Subroutine */ void sorglq_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *);
real smlnum;
extern /* Subroutine */ void sorgqr_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *);
logical lquery, wntuas, wntvas;
integer blk, lwork_sorgbr_p__, lwork_sorgbr_q__, lwork_sorglq_m__,
lwork_sorglq_n__, ncu, lwork_sorgqr_n__, lwork_sorgqr_m__;
real eps, dum[1];
integer nru;
/* -- 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..-- */
/* April 2012 */
/* ===================================================================== */
/* 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;
/* Function Body */
*info = 0;
minmn = f2cmin(*m,*n);
wntua = lsame_(jobu, "A");
wntus = lsame_(jobu, "S");
wntuas = wntua || wntus;
wntuo = lsame_(jobu, "O");
wntun = lsame_(jobu, "N");
wntva = lsame_(jobvt, "A");
wntvs = lsame_(jobvt, "S");
wntvas = wntva || wntvs;
wntvo = lsame_(jobvt, "O");
wntvn = lsame_(jobvt, "N");
lquery = *lwork == -1;
if (! (wntua || wntus || wntuo || wntun)) {
*info = -1;
} else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*lda < f2cmax(1,*m)) {
*info = -6;
} else if (*ldu < 1 || wntuas && *ldu < *m) {
*info = -9;
} else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) {
*info = -11;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV.) */
if (*info == 0) {
minwrk = 1;
maxwrk = 1;
if (*m >= *n && minmn > 0) {
/* Compute space needed for SBDSQR */
/* Writing concatenation */
i__1[0] = 1, a__1[0] = jobu;
i__1[1] = 1, a__1[1] = jobvt;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
mnthr = ilaenv_(&c__6, "SGESVD", ch__1, m, n, &c__0, &c__0, (
ftnlen)6, (ftnlen)2);
bdspac = *n * 5;
/* Compute space needed for SGEQRF */
sgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_sgeqrf__ = (integer) dum[0];
/* Compute space needed for SORGQR */
sorgqr_(m, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_sorgqr_n__ = (integer) dum[0];
sorgqr_(m, m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_sorgqr_m__ = (integer) dum[0];
/* Compute space needed for SGEBRD */
sgebrd_(n, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1,
&ierr);
lwork_sgebrd__ = (integer) dum[0];
/* Compute space needed for SORGBR P */
sorgbr_("P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_sorgbr_p__ = (integer) dum[0];
/* Compute space needed for SORGBR Q */
sorgbr_("Q", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_sorgbr_q__ = (integer) dum[0];
if (*m >= mnthr) {
if (wntun) {
/* Path 1 (M much larger than N, JOBU='N') */
maxwrk = *n + lwork_sgeqrf__;
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * 3 + lwork_sgebrd__;
maxwrk = f2cmax(i__2,i__3);
if (wntvo || wntvas) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * 3 + lwork_sorgbr_p__;
maxwrk = f2cmax(i__2,i__3);
}
maxwrk = f2cmax(maxwrk,bdspac);
/* Computing MAX */
i__2 = *n << 2;
minwrk = f2cmax(i__2,bdspac);
} else if (wntuo && wntvn) {
/* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
wrkbl = *n + lwork_sgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_sorgqr_n__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
/* Computing MAX */
i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n;
maxwrk = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = f2cmax(i__2,bdspac);
} else if (wntuo && wntvas) {
/* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */
/* 'A') */
wrkbl = *n + lwork_sgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_sorgqr_n__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
/* Computing MAX */
i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n;
maxwrk = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = f2cmax(i__2,bdspac);
} else if (wntus && wntvn) {
/* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
wrkbl = *n + lwork_sgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_sorgqr_n__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = *n * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = f2cmax(i__2,bdspac);
} else if (wntus && wntvo) {
/* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
wrkbl = *n + lwork_sgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_sorgqr_n__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = (*n << 1) * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = f2cmax(i__2,bdspac);
} else if (wntus && wntvas) {
/* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or */
/* 'A') */
wrkbl = *n + lwork_sgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_sorgqr_n__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = *n * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = f2cmax(i__2,bdspac);
} else if (wntua && wntvn) {
/* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
wrkbl = *n + lwork_sgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_sorgqr_m__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = *n * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = f2cmax(i__2,bdspac);
} else if (wntua && wntvo) {
/* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
wrkbl = *n + lwork_sgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_sorgqr_m__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = (*n << 1) * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = f2cmax(i__2,bdspac);
} else if (wntua && wntvas) {
/* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or */
/* 'A') */
wrkbl = *n + lwork_sgeqrf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *n + lwork_sorgqr_m__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *n * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = *n * *n + wrkbl;
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = f2cmax(i__2,bdspac);
}
} else {
/* Path 10 (M at least N, but not much larger) */
sgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &
c_n1, &ierr);
lwork_sgebrd__ = (integer) dum[0];
maxwrk = *n * 3 + lwork_sgebrd__;
if (wntus || wntuo) {
sorgbr_("Q", m, n, n, &a[a_offset], lda, dum, dum, &c_n1,
&ierr);
lwork_sorgbr_q__ = (integer) dum[0];
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * 3 + lwork_sorgbr_q__;
maxwrk = f2cmax(i__2,i__3);
}
if (wntua) {
sorgbr_("Q", m, m, n, &a[a_offset], lda, dum, dum, &c_n1,
&ierr);
lwork_sorgbr_q__ = (integer) dum[0];
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * 3 + lwork_sorgbr_q__;
maxwrk = f2cmax(i__2,i__3);
}
if (! wntvn) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * 3 + lwork_sorgbr_p__;
maxwrk = f2cmax(i__2,i__3);
}
maxwrk = f2cmax(maxwrk,bdspac);
/* Computing MAX */
i__2 = *n * 3 + *m;
minwrk = f2cmax(i__2,bdspac);
}
} else if (minmn > 0) {
/* Compute space needed for SBDSQR */
/* Writing concatenation */
i__1[0] = 1, a__1[0] = jobu;
i__1[1] = 1, a__1[1] = jobvt;
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
mnthr = ilaenv_(&c__6, "SGESVD", ch__1, m, n, &c__0, &c__0, (
ftnlen)6, (ftnlen)2);
bdspac = *m * 5;
/* Compute space needed for SGELQF */
sgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_sgelqf__ = (integer) dum[0];
/* Compute space needed for SORGLQ */
sorglq_(n, n, m, dum, n, dum, dum, &c_n1, &ierr);
lwork_sorglq_n__ = (integer) dum[0];
sorglq_(m, n, m, &a[a_offset], lda, dum, dum, &c_n1, &ierr);
lwork_sorglq_m__ = (integer) dum[0];
/* Compute space needed for SGEBRD */
sgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1,
&ierr);
lwork_sgebrd__ = (integer) dum[0];
/* Compute space needed for SORGBR P */
sorgbr_("P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr);
lwork_sorgbr_p__ = (integer) dum[0];
/* Compute space needed for SORGBR Q */
sorgbr_("Q", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr);
lwork_sorgbr_q__ = (integer) dum[0];
if (*n >= mnthr) {
if (wntvn) {
/* Path 1t(N much larger than M, JOBVT='N') */
maxwrk = *m + lwork_sgelqf__;
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * 3 + lwork_sgebrd__;
maxwrk = f2cmax(i__2,i__3);
if (wntuo || wntuas) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * 3 + lwork_sorgbr_q__;
maxwrk = f2cmax(i__2,i__3);
}
maxwrk = f2cmax(maxwrk,bdspac);
/* Computing MAX */
i__2 = *m << 2;
minwrk = f2cmax(i__2,bdspac);
} else if (wntvo && wntun) {
/* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
wrkbl = *m + lwork_sgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_sorglq_m__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
/* Computing MAX */
i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m;
maxwrk = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = f2cmax(i__2,bdspac);
} else if (wntvo && wntuas) {
/* Path 3t(N much larger than M, JOBU='S' or 'A', */
/* JOBVT='O') */
wrkbl = *m + lwork_sgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_sorglq_m__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
/* Computing MAX */
i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m;
maxwrk = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = f2cmax(i__2,bdspac);
} else if (wntvs && wntun) {
/* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
wrkbl = *m + lwork_sgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_sorglq_m__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = *m * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = f2cmax(i__2,bdspac);
} else if (wntvs && wntuo) {
/* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
wrkbl = *m + lwork_sgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_sorglq_m__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = (*m << 1) * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = f2cmax(i__2,bdspac);
maxwrk = f2cmax(maxwrk,minwrk);
} else if (wntvs && wntuas) {
/* Path 6t(N much larger than M, JOBU='S' or 'A', */
/* JOBVT='S') */
wrkbl = *m + lwork_sgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_sorglq_m__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = *m * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = f2cmax(i__2,bdspac);
} else if (wntva && wntun) {
/* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
wrkbl = *m + lwork_sgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_sorglq_n__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = *m * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = f2cmax(i__2,bdspac);
} else if (wntva && wntuo) {
/* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
wrkbl = *m + lwork_sgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_sorglq_n__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = (*m << 1) * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = f2cmax(i__2,bdspac);
} else if (wntva && wntuas) {
/* Path 9t(N much larger than M, JOBU='S' or 'A', */
/* JOBVT='A') */
wrkbl = *m + lwork_sgelqf__;
/* Computing MAX */
i__2 = wrkbl, i__3 = *m + lwork_sorglq_n__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sgebrd__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_p__;
wrkbl = f2cmax(i__2,i__3);
/* Computing MAX */
i__2 = wrkbl, i__3 = *m * 3 + lwork_sorgbr_q__;
wrkbl = f2cmax(i__2,i__3);
wrkbl = f2cmax(wrkbl,bdspac);
maxwrk = *m * *m + wrkbl;
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = f2cmax(i__2,bdspac);
}
} else {
/* Path 10t(N greater than M, but not much larger) */
sgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &
c_n1, &ierr);
lwork_sgebrd__ = (integer) dum[0];
maxwrk = *m * 3 + lwork_sgebrd__;
if (wntvs || wntvo) {
/* Compute space needed for SORGBR P */
sorgbr_("P", m, n, m, &a[a_offset], n, dum, dum, &c_n1, &
ierr);
lwork_sorgbr_p__ = (integer) dum[0];
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * 3 + lwork_sorgbr_p__;
maxwrk = f2cmax(i__2,i__3);
}
if (wntva) {
sorgbr_("P", n, n, m, &a[a_offset], n, dum, dum, &c_n1, &
ierr);
lwork_sorgbr_p__ = (integer) dum[0];
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * 3 + lwork_sorgbr_p__;
maxwrk = f2cmax(i__2,i__3);
}
if (! wntun) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * 3 + lwork_sorgbr_q__;
maxwrk = f2cmax(i__2,i__3);
}
maxwrk = f2cmax(maxwrk,bdspac);
/* Computing MAX */
i__2 = *m * 3 + *n;
minwrk = f2cmax(i__2,bdspac);
}
}
maxwrk = f2cmax(maxwrk,minwrk);
work[1] = (real) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -13;
}
}
if (*info != 0) {
i__2 = -(*info);
xerbla_("SGESVD", &i__2, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return;
}
/* 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);
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 (wntun) {
/* Path 1 (M much larger than N, JOBU='N') */
/* No left singular vectors to be computed */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
i__2, &ierr);
/* Zero out below R */
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2],
lda);
}
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in A */
/* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
ncvt = 0;
if (wntvo || wntvas) {
/* If right singular vectors desired, generate P'. */
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &
work[iwork], &i__2, &ierr);
ncvt = *n;
}
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of A in A if desired */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, &ncvt, &c__0, &c__0, &s[1], &work[ie], &a[
a_offset], lda, dum, &c__1, dum, &c__1, &work[iwork],
info);
/* If right singular vectors desired in VT, copy them there */
if (wntvas) {
slacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
}
} else if (wntuo && wntvn) {
/* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
/* N left singular vectors to be overwritten on A and */
/* no right singular vectors to be computed */
/* Computing MAX */
i__2 = *n << 2;
if (*lwork >= *n * *n + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
/* Computing MAX */
i__2 = wrkbl, i__3 = *lda * *n + *n;
if (*lwork >= f2cmax(i__2,i__3) + *lda * *n) {
/* WORK(IU) is LDA by N, WORK(IR) is LDA by N */
ldwrku = *lda;
ldwrkr = *lda;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__2 = wrkbl, i__3 = *lda * *n + *n;
if (*lwork >= f2cmax(i__2,i__3) + *n * *n) {
/* WORK(IU) is LDA by N, WORK(IR) is N by N */
ldwrku = *lda;
ldwrkr = *n;
} else {
/* WORK(IU) is LDWRKU by N, WORK(IR) is N by N */
ldwrku = (*lwork - *n * *n - *n) / *n;
ldwrkr = *n;
}
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__2, &ierr);
/* Copy R to WORK(IR) and zero out below it */
slacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + 1],
&ldwrkr);
/* Generate Q in A */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IR) */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
/* Generate left vectors bidiagonalizing R */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
work[iwork], &i__2, &ierr);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IR) */
/* (Workspace: need N*N+BDSPAC) */
sbdsqr_("U", n, &c__0, n, &c__0, &s[1], &work[ie], dum, &
c__1, &work[ir], &ldwrkr, dum, &c__1, &work[iwork]
, info);
iu = ie + *n;
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IR), storing result in WORK(IU) and copying to A */
/* (Workspace: need N*N+2*N, prefer N*N+M*N+N) */
i__2 = *m;
i__3 = ldwrku;
for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__3) {
/* Computing MIN */
i__4 = *m - i__ + 1;
chunk = f2cmin(i__4,ldwrku);
sgemm_("N", "N", &chunk, n, n, &c_b79, &a[i__ +
a_dim1], lda, &work[ir], &ldwrkr, &c_b57, &
work[iu], &ldwrku);
slacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
a_dim1], lda);
/* L10: */
}
} else {
/* Insufficient workspace for a fast algorithm */
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize A */
/* (Workspace: need 3*N+M, prefer 3*N+(M+N)*NB) */
i__3 = *lwork - iwork + 1;
sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__3, &ierr);
/* Generate left vectors bidiagonalizing A */
/* (Workspace: need 4*N, prefer 3*N+N*NB) */
i__3 = *lwork - iwork + 1;
sorgbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
work[iwork], &i__3, &ierr);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in A */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, &c__0, m, &c__0, &s[1], &work[ie], dum, &
c__1, &a[a_offset], lda, dum, &c__1, &work[iwork],
info);
}
} else if (wntuo && wntvas) {
/* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') */
/* N left singular vectors to be overwritten on A and */
/* N right singular vectors to be computed in VT */
/* Computing MAX */
i__3 = *n << 2;
if (*lwork >= *n * *n + f2cmax(i__3,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
/* Computing MAX */
i__3 = wrkbl, i__2 = *lda * *n + *n;
if (*lwork >= f2cmax(i__3,i__2) + *lda * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
ldwrku = *lda;
ldwrkr = *lda;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__3 = wrkbl, i__2 = *lda * *n + *n;
if (*lwork >= f2cmax(i__3,i__2) + *n * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is N by N */
ldwrku = *lda;
ldwrkr = *n;
} else {
/* WORK(IU) is LDWRKU by N and WORK(IR) is N by N */
ldwrku = (*lwork - *n * *n - *n) / *n;
ldwrkr = *n;
}
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__3 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__3, &ierr);
/* Copy R to VT, zeroing out below it */
slacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
if (*n > 1) {
i__3 = *n - 1;
i__2 = *n - 1;
slaset_("L", &i__3, &i__2, &c_b57, &c_b57, &vt[
vt_dim1 + 2], ldvt);
}
/* Generate Q in A */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__3 = *lwork - iwork + 1;
sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__3, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in VT, copying result to WORK(IR) */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
i__3 = *lwork - iwork + 1;
sgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &i__3, &
ierr);
slacpy_("L", n, n, &vt[vt_offset], ldvt, &work[ir], &
ldwrkr);
/* Generate left vectors bidiagonalizing R in WORK(IR) */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
i__3 = *lwork - iwork + 1;
sorgbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
work[iwork], &i__3, &ierr);
/* Generate right vectors bidiagonalizing R in VT */
/* (Workspace: need N*N+4*N-1, prefer N*N+3*N+(N-1)*NB) */
i__3 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
&work[iwork], &i__3, &ierr);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IR) and computing right */
/* singular vectors of R in VT */
/* (Workspace: need N*N+BDSPAC) */
sbdsqr_("U", n, n, n, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &work[ir], &ldwrkr, dum, &c__1,
&work[iwork], info);
iu = ie + *n;
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IR), storing result in WORK(IU) and copying to A */
/* (Workspace: need N*N+2*N, prefer N*N+M*N+N) */
i__3 = *m;
i__2 = ldwrku;
for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
i__2) {
/* Computing MIN */
i__4 = *m - i__ + 1;
chunk = f2cmin(i__4,ldwrku);
sgemm_("N", "N", &chunk, n, n, &c_b79, &a[i__ +
a_dim1], lda, &work[ir], &ldwrkr, &c_b57, &
work[iu], &ldwrku);
slacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
a_dim1], lda);
/* L20: */
}
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__2, &ierr);
/* Copy R to VT, zeroing out below it */
slacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &vt[
vt_dim1 + 2], ldvt);
}
/* Generate Q in A */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in VT */
/* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &i__2, &
ierr);
/* Multiply Q in A by left vectors bidiagonalizing R */
/* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt, &
work[itauq], &a[a_offset], lda, &work[iwork], &
i__2, &ierr);
/* Generate right vectors bidiagonalizing R in VT */
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
&work[iwork], &i__2, &ierr);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in A and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, &
work[iwork], info);
}
} else if (wntus) {
if (wntvn) {
/* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
/* N left singular vectors to be computed in U and */
/* no right singular vectors to be computed */
/* Computing MAX */
i__2 = *n << 2;
if (*lwork >= *n * *n + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
if (*lwork >= wrkbl + *lda * *n) {
/* WORK(IR) is LDA by N */
ldwrkr = *lda;
} else {
/* WORK(IR) is N by N */
ldwrkr = *n;
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &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__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &work[ir +
1], &ldwrkr);
/* Generate Q in A */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IR) */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Generate left vectors bidiagonalizing R in WORK(IR) */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
, &work[iwork], &i__2, &ierr);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IR) */
/* (Workspace: need N*N+BDSPAC) */
sbdsqr_("U", n, &c__0, n, &c__0, &s[1], &work[ie],
dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, &
work[iwork], info);
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IR), storing result in U */
/* (Workspace: need N*N) */
sgemm_("N", "N", m, n, n, &c_b79, &a[a_offset], lda, &
work[ir], &ldwrkr, &c_b57, &u[u_offset], ldu);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
ldu);
/* Generate Q in U */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Zero out below R in A */
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &a[
a_dim1 + 2], lda);
}
/* Bidiagonalize R in A */
/* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left vectors bidiagonalizing R */
/* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr)
;
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, &c__0, m, &c__0, &s[1], &work[ie],
dum, &c__1, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info);
}
} else if (wntvo) {
/* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
/* N left singular vectors to be computed in U and */
/* N right singular vectors to be overwritten on A */
/* Computing MAX */
i__2 = *n << 2;
if (*lwork >= (*n << 1) * *n + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + (*lda << 1) * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
ldwrku = *lda;
ir = iu + ldwrku * *n;
ldwrkr = *lda;
} else if (*lwork >= wrkbl + (*lda + *n) * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is N by N */
ldwrku = *lda;
ir = iu + ldwrku * *n;
ldwrkr = *n;
} else {
/* WORK(IU) is N by N and WORK(IR) is N by N */
ldwrku = *n;
ir = iu + ldwrku * *n;
ldwrkr = *n;
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy R to WORK(IU), zeroing out below it */
slacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
ldwrku);
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
1], &ldwrku);
/* Generate Q in A */
/* (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IU), copying result to */
/* WORK(IR) */
/* (Workspace: need 2*N*N+4*N, */
/* prefer 2*N*N+3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
slacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
ldwrkr);
/* Generate left bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need 2*N*N+4*N, prefer 2*N*N+3*N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
, &work[iwork], &i__2, &ierr);
/* Generate right bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need 2*N*N+4*N-1, */
/* prefer 2*N*N+3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
, &work[iwork], &i__2, &ierr);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IU) and computing */
/* right singular vectors of R in WORK(IR) */
/* (Workspace: need 2*N*N+BDSPAC) */
sbdsqr_("U", n, n, n, &c__0, &s[1], &work[ie], &work[
ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1,
&work[iwork], info);
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IU), storing result in U */
/* (Workspace: need N*N) */
sgemm_("N", "N", m, n, n, &c_b79, &a[a_offset], lda, &
work[iu], &ldwrku, &c_b57, &u[u_offset], ldu);
/* Copy right singular vectors of R to A */
/* (Workspace: need N*N) */
slacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
lda);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
ldu);
/* Generate Q in U */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Zero out below R in A */
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &a[
a_dim1 + 2], lda);
}
/* Bidiagonalize R in A */
/* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left vectors bidiagonalizing R */
/* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr)
;
/* Generate right vectors bidiagonalizing R in A */
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
&work[iwork], &i__2, &ierr);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in A */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, n, m, &c__0, &s[1], &work[ie], &a[
a_offset], lda, &u[u_offset], ldu, dum, &c__1,
&work[iwork], info);
}
} else if (wntvas) {
/* Path 6 (M much larger than N, JOBU='S', JOBVT='S' */
/* or 'A') */
/* N left singular vectors to be computed in U and */
/* N right singular vectors to be computed in VT */
/* Computing MAX */
i__2 = *n << 2;
if (*lwork >= *n * *n + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + *lda * *n) {
/* WORK(IU) is LDA by N */
ldwrku = *lda;
} else {
/* WORK(IU) is N by N */
ldwrku = *n;
}
itau = iu + ldwrku * *n;
iwork = itau + *n;
/* Compute A=Q*R */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy R to WORK(IU), zeroing out below it */
slacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
ldwrku);
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
1], &ldwrku);
/* Generate Q in A */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IU), copying result to VT */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
slacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
ldvt);
/* Generate left bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
, &work[iwork], &i__2, &ierr);
/* Generate right bidiagonalizing vectors in VT */
/* (Workspace: need N*N+4*N-1, */
/* prefer N*N+3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
itaup], &work[iwork], &i__2, &ierr)
;
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IU) and computing */
/* right singular vectors of R in VT */
/* (Workspace: need N*N+BDSPAC) */
sbdsqr_("U", n, n, n, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &work[iu], &ldwrku, dum, &
c__1, &work[iwork], info);
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IU), storing result in U */
/* (Workspace: need N*N) */
sgemm_("N", "N", m, n, n, &c_b79, &a[a_offset], lda, &
work[iu], &ldwrku, &c_b57, &u[u_offset], ldu);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
ldu);
/* Generate Q in U */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy R to VT, zeroing out below it */
slacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &vt[
vt_dim1 + 2], ldvt);
}
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in VT */
/* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie],
&work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left bidiagonalizing vectors */
/* in VT */
/* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
&work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr);
/* Generate right bidiagonalizing vectors in VT */
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
itaup], &work[iwork], &i__2, &ierr)
;
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &
c__1, &work[iwork], info);
}
}
} else if (wntua) {
if (wntvn) {
/* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
/* M left singular vectors to be computed in U and */
/* no right singular vectors to be computed */
/* Computing MAX */
i__2 = *n + *m, i__3 = *n << 2, i__2 = f2cmax(i__2,i__3);
if (*lwork >= *n * *n + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
if (*lwork >= wrkbl + *lda * *n) {
/* WORK(IR) is LDA by N */
ldwrkr = *lda;
} else {
/* WORK(IR) is N by N */
ldwrkr = *n;
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
ldu);
/* 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__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &work[ir +
1], &ldwrkr);
/* Generate Q in U */
/* (Workspace: need N*N+N+M, prefer N*N+N+M*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IR) */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Generate left bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
, &work[iwork], &i__2, &ierr);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IR) */
/* (Workspace: need N*N+BDSPAC) */
sbdsqr_("U", n, &c__0, n, &c__0, &s[1], &work[ie],
dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, &
work[iwork], info);
/* Multiply Q in U by left singular vectors of R in */
/* WORK(IR), storing result in A */
/* (Workspace: need N*N) */
sgemm_("N", "N", m, n, n, &c_b79, &u[u_offset], ldu, &
work[ir], &ldwrkr, &c_b57, &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 {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
ldu);
/* Generate Q in U */
/* (Workspace: need N+M, prefer N+M*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Zero out below R in A */
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &a[
a_dim1 + 2], lda);
}
/* Bidiagonalize R in A */
/* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left bidiagonalizing vectors */
/* in A */
/* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr)
;
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, &c__0, m, &c__0, &s[1], &work[ie],
dum, &c__1, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info);
}
} else if (wntvo) {
/* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
/* M left singular vectors to be computed in U and */
/* N right singular vectors to be overwritten on A */
/* Computing MAX */
i__2 = *n + *m, i__3 = *n << 2, i__2 = f2cmax(i__2,i__3);
if (*lwork >= (*n << 1) * *n + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + (*lda << 1) * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
ldwrku = *lda;
ir = iu + ldwrku * *n;
ldwrkr = *lda;
} else if (*lwork >= wrkbl + (*lda + *n) * *n) {
/* WORK(IU) is LDA by N and WORK(IR) is N by N */
ldwrku = *lda;
ir = iu + ldwrku * *n;
ldwrkr = *n;
} else {
/* WORK(IU) is N by N and WORK(IR) is N by N */
ldwrku = *n;
ir = iu + ldwrku * *n;
ldwrkr = *n;
}
itau = ir + ldwrkr * *n;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
ldu);
/* Generate Q in U */
/* (Workspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy R to WORK(IU), zeroing out below it */
slacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
ldwrku);
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
1], &ldwrku);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IU), copying result to */
/* WORK(IR) */
/* (Workspace: need 2*N*N+4*N, */
/* prefer 2*N*N+3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
slacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
ldwrkr);
/* Generate left bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need 2*N*N+4*N, prefer 2*N*N+3*N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
, &work[iwork], &i__2, &ierr);
/* Generate right bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need 2*N*N+4*N-1, */
/* prefer 2*N*N+3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
, &work[iwork], &i__2, &ierr);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IU) and computing */
/* right singular vectors of R in WORK(IR) */
/* (Workspace: need 2*N*N+BDSPAC) */
sbdsqr_("U", n, n, n, &c__0, &s[1], &work[ie], &work[
ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1,
&work[iwork], info);
/* Multiply Q in U by left singular vectors of R in */
/* WORK(IU), storing result in A */
/* (Workspace: need N*N) */
sgemm_("N", "N", m, n, n, &c_b79, &u[u_offset], ldu, &
work[iu], &ldwrku, &c_b57, &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);
/* Copy right singular vectors of R from WORK(IR) to A */
slacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
lda);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
ldu);
/* Generate Q in U */
/* (Workspace: need N+M, prefer N+M*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Zero out below R in A */
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &a[
a_dim1 + 2], lda);
}
/* Bidiagonalize R in A */
/* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left bidiagonalizing vectors */
/* in A */
/* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr)
;
/* Generate right bidiagonalizing vectors in A */
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
&work[iwork], &i__2, &ierr);
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in A */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, n, m, &c__0, &s[1], &work[ie], &a[
a_offset], lda, &u[u_offset], ldu, dum, &c__1,
&work[iwork], info);
}
} else if (wntvas) {
/* Path 9 (M much larger than N, JOBU='A', JOBVT='S' */
/* or 'A') */
/* M left singular vectors to be computed in U and */
/* N right singular vectors to be computed in VT */
/* Computing MAX */
i__2 = *n + *m, i__3 = *n << 2, i__2 = f2cmax(i__2,i__3);
if (*lwork >= *n * *n + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + *lda * *n) {
/* WORK(IU) is LDA by N */
ldwrku = *lda;
} else {
/* WORK(IU) is N by N */
ldwrku = *n;
}
itau = iu + ldwrku * *n;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need N*N+2*N, prefer N*N+N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
ldu);
/* Generate Q in U */
/* (Workspace: need N*N+N+M, prefer N*N+N+M*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy R to WORK(IU), zeroing out below it */
slacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
ldwrku);
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
1], &ldwrku);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in WORK(IU), copying result to VT */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
slacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
ldvt);
/* Generate left bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need N*N+4*N, prefer N*N+3*N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
, &work[iwork], &i__2, &ierr);
/* Generate right bidiagonalizing vectors in VT */
/* (Workspace: need N*N+4*N-1, */
/* prefer N*N+3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
itaup], &work[iwork], &i__2, &ierr)
;
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of R in WORK(IU) and computing */
/* right singular vectors of R in VT */
/* (Workspace: need N*N+BDSPAC) */
sbdsqr_("U", n, n, n, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &work[iu], &ldwrku, dum, &
c__1, &work[iwork], info);
/* Multiply Q in U by left singular vectors of R in */
/* WORK(IU), storing result in A */
/* (Workspace: need N*N) */
sgemm_("N", "N", m, n, n, &c_b79, &u[u_offset], ldu, &
work[iu], &ldwrku, &c_b57, &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 {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* (Workspace: need 2*N, prefer N+N*NB) */
i__2 = *lwork - iwork + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
ldu);
/* Generate Q in U */
/* (Workspace: need N+M, prefer N+M*NB) */
i__2 = *lwork - iwork + 1;
sorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy R from A to VT, zeroing out below it */
slacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
if (*n > 1) {
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b57, &c_b57, &vt[
vt_dim1 + 2], ldvt);
}
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in VT */
/* (Workspace: need 4*N, prefer 3*N+2*N*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie],
&work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply Q in U by left bidiagonalizing vectors */
/* in VT */
/* (Workspace: need 3*N+M, prefer 3*N+M*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
&work[itauq], &u[u_offset], ldu, &work[iwork],
&i__2, &ierr);
/* Generate right bidiagonalizing vectors in VT */
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
itaup], &work[iwork], &i__2, &ierr)
;
iwork = ie + *n;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &
c__1, &work[iwork], info);
}
}
}
} else {
/* M .LT. MNTHR */
/* Path 10 (M at least N, but not much larger) */
/* Reduce to bidiagonal form without QR decomposition */
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize A */
/* (Workspace: need 3*N+M, prefer 3*N+(M+N)*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[iwork], &i__2, &ierr);
if (wntuas) {
/* If left singular vectors desired in U, copy result to U */
/* and generate left bidiagonalizing vectors in U */
/* (Workspace: need 3*N+NCU, prefer 3*N+NCU*NB) */
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
if (wntus) {
ncu = *n;
}
if (wntua) {
ncu = *m;
}
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], &
work[iwork], &i__2, &ierr);
}
if (wntvas) {
/* If right singular vectors desired in VT, copy result to */
/* VT and generate right bidiagonalizing vectors in VT */
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
slacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
work[iwork], &i__2, &ierr);
}
if (wntuo) {
/* If left singular vectors desired in A, generate left */
/* bidiagonalizing vectors in A */
/* (Workspace: need 4*N, prefer 3*N+N*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
iwork], &i__2, &ierr);
}
if (wntvo) {
/* If right singular vectors desired in A, generate right */
/* bidiagonalizing vectors in A */
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[
iwork], &i__2, &ierr);
}
iwork = ie + *n;
if (wntuas || wntuo) {
nru = *m;
}
if (wntun) {
nru = 0;
}
if (wntvas || wntvo) {
ncvt = *n;
}
if (wntvn) {
ncvt = 0;
}
if (! wntuo && ! wntvo) {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in U and computing right singular */
/* vectors in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info);
} else if (! wntuo && wntvo) {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in U and computing right singular */
/* vectors in A */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[
a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[
iwork], info);
} else {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in A and computing right singular */
/* vectors in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, &
work[iwork], info);
}
}
} 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 (wntvn) {
/* Path 1t(N much larger than M, JOBVT='N') */
/* No right singular vectors to be computed */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
i__2, &ierr);
/* Zero out above L */
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) +
1], lda);
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
if (wntuo || wntuas) {
/* If left singular vectors desired, generate Q */
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq], &
work[iwork], &i__2, &ierr);
}
iwork = ie + *m;
nru = 0;
if (wntuo || wntuas) {
nru = *m;
}
/* Perform bidiagonal QR iteration, computing left singular */
/* vectors of A in A if desired */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", m, &c__0, &nru, &c__0, &s[1], &work[ie], dum, &
c__1, &a[a_offset], lda, dum, &c__1, &work[iwork],
info);
/* If left singular vectors desired in U, copy them there */
if (wntuas) {
slacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
}
} else if (wntvo && wntun) {
/* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
/* M right singular vectors to be overwritten on A and */
/* no left singular vectors to be computed */
/* Computing MAX */
i__2 = *m << 2;
if (*lwork >= *m * *m + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
/* Computing MAX */
i__2 = wrkbl, i__3 = *lda * *n + *m;
if (*lwork >= f2cmax(i__2,i__3) + *lda * *m) {
/* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
ldwrku = *lda;
chunk = *n;
ldwrkr = *lda;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__2 = wrkbl, i__3 = *lda * *n + *m;
if (*lwork >= f2cmax(i__2,i__3) + *m * *m) {
/* WORK(IU) is LDA by N and WORK(IR) is M by M */
ldwrku = *lda;
chunk = *n;
ldwrkr = *m;
} else {
/* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
ldwrku = *m;
chunk = (*lwork - *m * *m - *m) / *m;
ldwrkr = *m;
}
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__2, &ierr);
/* Copy L to WORK(IR) and zero out above it */
slacpy_("L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &work[ir +
ldwrkr], &ldwrkr);
/* Generate Q in A */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IR) */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
/* Generate right vectors bidiagonalizing L */
/* (Workspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of L in WORK(IR) */
/* (Workspace: need M*M+BDSPAC) */
sbdsqr_("U", m, m, &c__0, &c__0, &s[1], &work[ie], &work[
ir], &ldwrkr, dum, &c__1, dum, &c__1, &work[iwork]
, info);
iu = ie + *m;
/* Multiply right singular vectors of L in WORK(IR) by Q */
/* in A, storing result in WORK(IU) and copying to A */
/* (Workspace: need M*M+2*M, prefer M*M+M*N+M) */
i__2 = *n;
i__3 = chunk;
for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__3) {
/* Computing MIN */
i__4 = *n - i__ + 1;
blk = f2cmin(i__4,chunk);
sgemm_("N", "N", m, &blk, m, &c_b79, &work[ir], &
ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, &
work[iu], &ldwrku);
slacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
a_dim1 + 1], lda);
/* L30: */
}
} else {
/* Insufficient workspace for a fast algorithm */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize A */
/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
i__3 = *lwork - iwork + 1;
sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__3, &ierr);
/* Generate right vectors bidiagonalizing A */
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
i__3 = *lwork - iwork + 1;
sorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
work[iwork], &i__3, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of A in A */
/* (Workspace: need BDSPAC) */
sbdsqr_("L", m, n, &c__0, &c__0, &s[1], &work[ie], &a[
a_offset], lda, dum, &c__1, dum, &c__1, &work[
iwork], info);
}
} else if (wntvo && wntuas) {
/* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') */
/* M right singular vectors to be overwritten on A and */
/* M left singular vectors to be computed in U */
/* Computing MAX */
i__3 = *m << 2;
if (*lwork >= *m * *m + f2cmax(i__3,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
/* Computing MAX */
i__3 = wrkbl, i__2 = *lda * *n + *m;
if (*lwork >= f2cmax(i__3,i__2) + *lda * *m) {
/* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
ldwrku = *lda;
chunk = *n;
ldwrkr = *lda;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__3 = wrkbl, i__2 = *lda * *n + *m;
if (*lwork >= f2cmax(i__3,i__2) + *m * *m) {
/* WORK(IU) is LDA by N and WORK(IR) is M by M */
ldwrku = *lda;
chunk = *n;
ldwrkr = *m;
} else {
/* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
ldwrku = *m;
chunk = (*lwork - *m * *m - *m) / *m;
ldwrkr = *m;
}
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__3 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__3, &ierr);
/* Copy L to U, zeroing about above it */
slacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
i__3 = *m - 1;
i__2 = *m - 1;
slaset_("U", &i__3, &i__2, &c_b57, &c_b57, &u[(u_dim1 <<
1) + 1], ldu);
/* Generate Q in A */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__3 = *lwork - iwork + 1;
sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
iwork], &i__3, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in U, copying result to WORK(IR) */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
i__3 = *lwork - iwork + 1;
sgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__3, &ierr);
slacpy_("U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr);
/* Generate right vectors bidiagonalizing L in WORK(IR) */
/* (Workspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB) */
i__3 = *lwork - iwork + 1;
sorgbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
work[iwork], &i__3, &ierr);
/* Generate left vectors bidiagonalizing L in U */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB) */
i__3 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
work[iwork], &i__3, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of L in U, and computing right */
/* singular vectors of L in WORK(IR) */
/* (Workspace: need M*M+BDSPAC) */
sbdsqr_("U", m, m, m, &c__0, &s[1], &work[ie], &work[ir],
&ldwrkr, &u[u_offset], ldu, dum, &c__1, &work[
iwork], info);
iu = ie + *m;
/* Multiply right singular vectors of L in WORK(IR) by Q */
/* in A, storing result in WORK(IU) and copying to A */
/* (Workspace: need M*M+2*M, prefer M*M+M*N+M)) */
i__3 = *n;
i__2 = chunk;
for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
i__2) {
/* Computing MIN */
i__4 = *n - i__ + 1;
blk = f2cmin(i__4,chunk);
sgemm_("N", "N", m, &blk, m, &c_b79, &work[ir], &
ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, &
work[iu], &ldwrku);
slacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
a_dim1 + 1], lda);
/* L40: */
}
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
, &i__2, &ierr);
/* Copy L to U, zeroing out above it */
slacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 <<
1) + 1], ldu);
/* Generate Q in A */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in U */
/* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
/* Multiply right vectors bidiagonalizing L by Q in A */
/* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("P", "L", "T", m, n, m, &u[u_offset], ldu, &work[
itaup], &a[a_offset], lda, &work[iwork], &i__2, &
ierr);
/* Generate left vectors bidiagonalizing L in U */
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in A */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", m, n, m, &c__0, &s[1], &work[ie], &a[
a_offset], lda, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info);
}
} else if (wntvs) {
if (wntun) {
/* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
/* M right singular vectors to be computed in VT and */
/* no left singular vectors to be computed */
/* Computing MAX */
i__2 = *m << 2;
if (*lwork >= *m * *m + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
if (*lwork >= wrkbl + *lda * *m) {
/* WORK(IR) is LDA by M */
ldwrkr = *lda;
} else {
/* WORK(IR) is M by M */
ldwrkr = *m;
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy L to WORK(IR), zeroing out above it */
slacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
ldwrkr);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &work[ir +
ldwrkr], &ldwrkr);
/* Generate Q in A */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IR) */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Generate right vectors bidiagonalizing L in */
/* WORK(IR) */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
, &work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of L in WORK(IR) */
/* (Workspace: need M*M+BDSPAC) */
sbdsqr_("U", m, m, &c__0, &c__0, &s[1], &work[ie], &
work[ir], &ldwrkr, dum, &c__1, dum, &c__1, &
work[iwork], info);
/* Multiply right singular vectors of L in WORK(IR) by */
/* Q in A, storing result in VT */
/* (Workspace: need M*M) */
sgemm_("N", "N", m, n, m, &c_b79, &work[ir], &ldwrkr,
&a[a_offset], lda, &c_b57, &vt[vt_offset],
ldvt);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy result to VT */
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
/* Generate Q in VT */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Zero out above L in A */
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1
<< 1) + 1], lda);
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right vectors bidiagonalizing L by Q in VT */
/* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("P", "L", "T", m, n, m, &a[a_offset], lda, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", m, n, &c__0, &c__0, &s[1], &work[ie], &
vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, &
work[iwork], info);
}
} else if (wntuo) {
/* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
/* M right singular vectors to be computed in VT and */
/* M left singular vectors to be overwritten on A */
/* Computing MAX */
i__2 = *m << 2;
if (*lwork >= (*m << 1) * *m + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + (*lda << 1) * *m) {
/* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
ldwrku = *lda;
ir = iu + ldwrku * *m;
ldwrkr = *lda;
} else if (*lwork >= wrkbl + (*lda + *m) * *m) {
/* WORK(IU) is LDA by M and WORK(IR) is M by M */
ldwrku = *lda;
ir = iu + ldwrku * *m;
ldwrkr = *m;
} else {
/* WORK(IU) is M by M and WORK(IR) is M by M */
ldwrku = *m;
ir = iu + ldwrku * *m;
ldwrkr = *m;
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy L to WORK(IU), zeroing out below it */
slacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
ldwrku);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
ldwrku], &ldwrku);
/* Generate Q in A */
/* (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IU), copying result to */
/* WORK(IR) */
/* (Workspace: need 2*M*M+4*M, */
/* prefer 2*M*M+3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
slacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
ldwrkr);
/* Generate right bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need 2*M*M+4*M-1, */
/* prefer 2*M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
, &work[iwork], &i__2, &ierr);
/* Generate left bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need 2*M*M+4*M, prefer 2*M*M+3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
, &work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of L in WORK(IR) and computing */
/* right singular vectors of L in WORK(IU) */
/* (Workspace: need 2*M*M+BDSPAC) */
sbdsqr_("U", m, m, m, &c__0, &s[1], &work[ie], &work[
iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1,
&work[iwork], info);
/* Multiply right singular vectors of L in WORK(IU) by */
/* Q in A, storing result in VT */
/* (Workspace: need M*M) */
sgemm_("N", "N", m, n, m, &c_b79, &work[iu], &ldwrku,
&a[a_offset], lda, &c_b57, &vt[vt_offset],
ldvt);
/* Copy left singular vectors of L to A */
/* (Workspace: need M*M) */
slacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
lda);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
/* Generate Q in VT */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Zero out above L in A */
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1
<< 1) + 1], lda);
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right vectors bidiagonalizing L by Q in VT */
/* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("P", "L", "T", m, n, m, &a[a_offset], lda, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr);
/* Generate left bidiagonalizing vectors of L in A */
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
&work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, compute left */
/* singular vectors of A in A and compute right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", m, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &a[a_offset], lda, dum, &
c__1, &work[iwork], info);
}
} else if (wntuas) {
/* Path 6t(N much larger than M, JOBU='S' or 'A', */
/* JOBVT='S') */
/* M right singular vectors to be computed in VT and */
/* M left singular vectors to be computed in U */
/* Computing MAX */
i__2 = *m << 2;
if (*lwork >= *m * *m + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + *lda * *m) {
/* WORK(IU) is LDA by N */
ldwrku = *lda;
} else {
/* WORK(IU) is LDA by M */
ldwrku = *m;
}
itau = iu + ldwrku * *m;
iwork = itau + *m;
/* Compute A=L*Q */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
/* Copy L to WORK(IU), zeroing out above it */
slacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
ldwrku);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
ldwrku], &ldwrku);
/* Generate Q in A */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IU), copying result to U */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
slacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
ldu);
/* Generate right bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need M*M+4*M-1, */
/* prefer M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
, &work[iwork], &i__2, &ierr);
/* Generate left bidiagonalizing vectors in U */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
&work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of L in U and computing right */
/* singular vectors of L in WORK(IU) */
/* (Workspace: need M*M+BDSPAC) */
sbdsqr_("U", m, m, m, &c__0, &s[1], &work[ie], &work[
iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info);
/* Multiply right singular vectors of L in WORK(IU) by */
/* Q in A, storing result in VT */
/* (Workspace: need M*M) */
sgemm_("N", "N", m, n, m, &c_b79, &work[iu], &ldwrku,
&a[a_offset], lda, &c_b57, &vt[vt_offset],
ldvt);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
/* Generate Q in VT */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy L to U, zeroing out above it */
slacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
ldu);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1
<< 1) + 1], ldu);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in U */
/* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right bidiagonalizing vectors in U by Q */
/* in VT */
/* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("P", "L", "T", m, n, m, &u[u_offset], ldu, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr);
/* Generate left bidiagonalizing vectors in U */
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
&work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", m, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &
c__1, &work[iwork], info);
}
}
} else if (wntva) {
if (wntun) {
/* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
/* N right singular vectors to be computed in VT and */
/* no left singular vectors to be computed */
/* Computing MAX */
i__2 = *n + *m, i__3 = *m << 2, i__2 = f2cmax(i__2,i__3);
if (*lwork >= *m * *m + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
ir = 1;
if (*lwork >= wrkbl + *lda * *m) {
/* WORK(IR) is LDA by M */
ldwrkr = *lda;
} else {
/* WORK(IR) is M by M */
ldwrkr = *m;
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
/* Copy L to WORK(IR), zeroing out above it */
slacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
ldwrkr);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &work[ir +
ldwrkr], &ldwrkr);
/* Generate Q in VT */
/* (Workspace: need M*M+M+N, prefer M*M+M+N*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IR) */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Generate right bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need M*M+4*M-1, */
/* prefer M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
, &work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of L in WORK(IR) */
/* (Workspace: need M*M+BDSPAC) */
sbdsqr_("U", m, m, &c__0, &c__0, &s[1], &work[ie], &
work[ir], &ldwrkr, dum, &c__1, dum, &c__1, &
work[iwork], info);
/* Multiply right singular vectors of L in WORK(IR) by */
/* Q in VT, storing result in A */
/* (Workspace: need M*M) */
sgemm_("N", "N", m, n, m, &c_b79, &work[ir], &ldwrkr,
&vt[vt_offset], ldvt, &c_b57, &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 {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
/* Generate Q in VT */
/* (Workspace: need M+N, prefer M+N*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Zero out above L in A */
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1
<< 1) + 1], lda);
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right bidiagonalizing vectors in A by Q */
/* in VT */
/* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("P", "L", "T", m, n, m, &a[a_offset], lda, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", m, n, &c__0, &c__0, &s[1], &work[ie], &
vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, &
work[iwork], info);
}
} else if (wntuo) {
/* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
/* N right singular vectors to be computed in VT and */
/* M left singular vectors to be overwritten on A */
/* Computing MAX */
i__2 = *n + *m, i__3 = *m << 2, i__2 = f2cmax(i__2,i__3);
if (*lwork >= (*m << 1) * *m + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + (*lda << 1) * *m) {
/* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
ldwrku = *lda;
ir = iu + ldwrku * *m;
ldwrkr = *lda;
} else if (*lwork >= wrkbl + (*lda + *m) * *m) {
/* WORK(IU) is LDA by M and WORK(IR) is M by M */
ldwrku = *lda;
ir = iu + ldwrku * *m;
ldwrkr = *m;
} else {
/* WORK(IU) is M by M and WORK(IR) is M by M */
ldwrku = *m;
ir = iu + ldwrku * *m;
ldwrkr = *m;
}
itau = ir + ldwrkr * *m;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
/* Generate Q in VT */
/* (Workspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy L to WORK(IU), zeroing out above it */
slacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
ldwrku);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
ldwrku], &ldwrku);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IU), copying result to */
/* WORK(IR) */
/* (Workspace: need 2*M*M+4*M, */
/* prefer 2*M*M+3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
slacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
ldwrkr);
/* Generate right bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need 2*M*M+4*M-1, */
/* prefer 2*M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
, &work[iwork], &i__2, &ierr);
/* Generate left bidiagonalizing vectors in WORK(IR) */
/* (Workspace: need 2*M*M+4*M, prefer 2*M*M+3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
, &work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of L in WORK(IR) and computing */
/* right singular vectors of L in WORK(IU) */
/* (Workspace: need 2*M*M+BDSPAC) */
sbdsqr_("U", m, m, m, &c__0, &s[1], &work[ie], &work[
iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1,
&work[iwork], info);
/* Multiply right singular vectors of L in WORK(IU) by */
/* Q in VT, storing result in A */
/* (Workspace: need M*M) */
sgemm_("N", "N", m, n, m, &c_b79, &work[iu], &ldwrku,
&vt[vt_offset], ldvt, &c_b57, &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);
/* Copy left singular vectors of A from WORK(IR) to A */
slacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
lda);
} else {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
/* Generate Q in VT */
/* (Workspace: need M+N, prefer M+N*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Zero out above L in A */
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1
<< 1) + 1], lda);
/* Bidiagonalize L in A */
/* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right bidiagonalizing vectors in A by Q */
/* in VT */
/* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("P", "L", "T", m, n, m, &a[a_offset], lda, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr);
/* Generate left bidiagonalizing vectors in A */
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
&work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in A and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", m, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &a[a_offset], lda, dum, &
c__1, &work[iwork], info);
}
} else if (wntuas) {
/* Path 9t(N much larger than M, JOBU='S' or 'A', */
/* JOBVT='A') */
/* N right singular vectors to be computed in VT and */
/* M left singular vectors to be computed in U */
/* Computing MAX */
i__2 = *n + *m, i__3 = *m << 2, i__2 = f2cmax(i__2,i__3);
if (*lwork >= *m * *m + f2cmax(i__2,bdspac)) {
/* Sufficient workspace for a fast algorithm */
iu = 1;
if (*lwork >= wrkbl + *lda * *m) {
/* WORK(IU) is LDA by M */
ldwrku = *lda;
} else {
/* WORK(IU) is M by M */
ldwrku = *m;
}
itau = iu + ldwrku * *m;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
/* Generate Q in VT */
/* (Workspace: need M*M+M+N, prefer M*M+M+N*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy L to WORK(IU), zeroing out above it */
slacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
ldwrku);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &work[iu +
ldwrku], &ldwrku);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IU), copying result to U */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
slacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
ldu);
/* Generate right bidiagonalizing vectors in WORK(IU) */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
, &work[iwork], &i__2, &ierr);
/* Generate left bidiagonalizing vectors in U */
/* (Workspace: need M*M+4*M, prefer M*M+3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
&work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of L in U and computing right */
/* singular vectors of L in WORK(IU) */
/* (Workspace: need M*M+BDSPAC) */
sbdsqr_("U", m, m, m, &c__0, &s[1], &work[ie], &work[
iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info);
/* Multiply right singular vectors of L in WORK(IU) by */
/* Q in VT, storing result in A */
/* (Workspace: need M*M) */
sgemm_("N", "N", m, n, m, &c_b79, &work[iu], &ldwrku,
&vt[vt_offset], ldvt, &c_b57, &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 {
/* Insufficient workspace for a fast algorithm */
itau = 1;
iwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* (Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
iwork], &i__2, &ierr);
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
ldvt);
/* Generate Q in VT */
/* (Workspace: need M+N, prefer M+N*NB) */
i__2 = *lwork - iwork + 1;
sorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
work[iwork], &i__2, &ierr);
/* Copy L to U, zeroing out above it */
slacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
ldu);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1
<< 1) + 1], ldu);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in U */
/* (Workspace: need 4*M, prefer 3*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &
work[itauq], &work[itaup], &work[iwork], &
i__2, &ierr);
/* Multiply right bidiagonalizing vectors in U by Q */
/* in VT */
/* (Workspace: need 3*M+N, prefer 3*M+N*NB) */
i__2 = *lwork - iwork + 1;
sormbr_("P", "L", "T", m, n, m, &u[u_offset], ldu, &
work[itaup], &vt[vt_offset], ldvt, &work[
iwork], &i__2, &ierr);
/* Generate left bidiagonalizing vectors in U */
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
&work[iwork], &i__2, &ierr);
iwork = ie + *m;
/* Perform bidiagonal QR iteration, computing left */
/* singular vectors of A in U and computing right */
/* singular vectors of A in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("U", m, n, m, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &
c__1, &work[iwork], info);
}
}
}
} else {
/* N .LT. MNTHR */
/* Path 10t(N greater than M, but not much larger) */
/* Reduce to bidiagonal form without LQ decomposition */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize A */
/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
i__2 = *lwork - iwork + 1;
sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[iwork], &i__2, &ierr);
if (wntuas) {
/* If left singular vectors desired in U, copy result to U */
/* and generate left bidiagonalizing vectors in U */
/* (Workspace: need 4*M-1, prefer 3*M+(M-1)*NB) */
slacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
iwork], &i__2, &ierr);
}
if (wntvas) {
/* If right singular vectors desired in VT, copy result to */
/* VT and generate right bidiagonalizing vectors in VT */
/* (Workspace: need 3*M+NRVT, prefer 3*M+NRVT*NB) */
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
if (wntva) {
nrvt = *n;
}
if (wntvs) {
nrvt = *m;
}
i__2 = *lwork - iwork + 1;
sorgbr_("P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup],
&work[iwork], &i__2, &ierr);
}
if (wntuo) {
/* If left singular vectors desired in A, generate left */
/* bidiagonalizing vectors in A */
/* (Workspace: need 4*M-1, prefer 3*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[
iwork], &i__2, &ierr);
}
if (wntvo) {
/* If right singular vectors desired in A, generate right */
/* bidiagonalizing vectors in A */
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
i__2 = *lwork - iwork + 1;
sorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
iwork], &i__2, &ierr);
}
iwork = ie + *m;
if (wntuas || wntuo) {
nru = *m;
}
if (wntun) {
nru = 0;
}
if (wntvas || wntvo) {
ncvt = *n;
}
if (wntvn) {
ncvt = 0;
}
if (! wntuo && ! wntvo) {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in U and computing right singular */
/* vectors in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, &
work[iwork], info);
} else if (! wntuo && wntvo) {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in U and computing right singular */
/* vectors in A */
/* (Workspace: need BDSPAC) */
sbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[
a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[
iwork], info);
} else {
/* Perform bidiagonal QR iteration, if desired, computing */
/* left singular vectors in A and computing right singular */
/* vectors in VT */
/* (Workspace: need BDSPAC) */
sbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[
vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, &
work[iwork], info);
}
}
}
/* If SBDSQR failed to converge, copy unconverged superdiagonals */
/* to WORK( 2:MINMN ) */
if (*info != 0) {
if (ie > 2) {
i__2 = minmn - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__ + 1] = work[i__ + ie - 1];
/* L50: */
}
}
if (ie < 2) {
for (i__ = minmn - 1; i__ >= 1; --i__) {
work[i__ + 1] = work[i__ + ie - 1];
/* L60: */
}
}
}
/* 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 (*info != 0 && anrm > bignum) {
i__2 = minmn - 1;
slascl_("G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &work[2],
&minmn, &ierr);
}
if (anrm < smlnum) {
slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, &ierr);
}
if (*info != 0 && anrm < smlnum) {
i__2 = minmn - 1;
slascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &work[2],
&minmn, &ierr);
}
}
/* Return optimal workspace in WORK(1) */
work[1] = (real) maxwrk;
return;
/* End of SGESVD */
} /* sgesvd_ */
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