2038 lines
67 KiB
C
2038 lines
67 KiB
C
#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_n1 = -1;
|
|
static integer c__0 = 0;
|
|
static real c_b63 = 0.f;
|
|
static integer c__1 = 1;
|
|
static real c_b84 = 1.f;
|
|
|
|
/* > \brief \b SGESDD */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SGESDD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgesdd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgesdd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgesdd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, */
|
|
/* WORK, LWORK, IWORK, INFO ) */
|
|
|
|
/* CHARACTER JOBZ */
|
|
/* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
|
|
/* INTEGER IWORK( * ) */
|
|
/* REAL A( LDA, * ), S( * ), U( LDU, * ), */
|
|
/* $ VT( LDVT, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SGESDD computes the singular value decomposition (SVD) of a real */
|
|
/* > M-by-N matrix A, optionally computing the left and right singular */
|
|
/* > vectors. If singular vectors are desired, it uses a */
|
|
/* > divide-and-conquer algorithm. */
|
|
/* > */
|
|
/* > The SVD is written */
|
|
/* > */
|
|
/* > A = U * SIGMA * transpose(V) */
|
|
/* > */
|
|
/* > where SIGMA is an M-by-N matrix which is zero except for its */
|
|
/* > f2cmin(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */
|
|
/* > V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */
|
|
/* > are the singular values of A; they are real and non-negative, and */
|
|
/* > are returned in descending order. The first f2cmin(m,n) columns of */
|
|
/* > U and V are the left and right singular vectors of A. */
|
|
/* > */
|
|
/* > Note that the routine returns VT = V**T, not V. */
|
|
/* > */
|
|
/* > The divide and conquer algorithm makes very mild assumptions about */
|
|
/* > floating point arithmetic. It will work on machines with a guard */
|
|
/* > digit in add/subtract, or on those binary machines without guard */
|
|
/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
|
|
/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */
|
|
/* > without guard digits, but we know of none. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBZ */
|
|
/* > \verbatim */
|
|
/* > JOBZ is CHARACTER*1 */
|
|
/* > Specifies options for computing all or part of the matrix U: */
|
|
/* > = 'A': all M columns of U and all N rows of V**T are */
|
|
/* > returned in the arrays U and VT; */
|
|
/* > = 'S': the first f2cmin(M,N) columns of U and the first */
|
|
/* > f2cmin(M,N) rows of V**T are returned in the arrays U */
|
|
/* > and VT; */
|
|
/* > = 'O': If M >= N, the first N columns of U are overwritten */
|
|
/* > on the array A and all rows of V**T are returned in */
|
|
/* > the array VT; */
|
|
/* > otherwise, all columns of U are returned in the */
|
|
/* > array U and the first M rows of V**T are overwritten */
|
|
/* > in the array A; */
|
|
/* > = 'N': no columns of U or rows of V**T are computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the input matrix A. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the input matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is REAL array, dimension (LDA,N) */
|
|
/* > On entry, the M-by-N matrix A. */
|
|
/* > On exit, */
|
|
/* > if JOBZ = 'O', A is overwritten with the first N columns */
|
|
/* > of U (the left singular vectors, stored */
|
|
/* > columnwise) if M >= N; */
|
|
/* > A is overwritten with the first M rows */
|
|
/* > of V**T (the right singular vectors, stored */
|
|
/* > rowwise) otherwise. */
|
|
/* > if JOBZ .ne. 'O', the contents of A are destroyed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is REAL array, dimension (f2cmin(M,N)) */
|
|
/* > The singular values of A, sorted so that S(i) >= S(i+1). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] U */
|
|
/* > \verbatim */
|
|
/* > U is REAL array, dimension (LDU,UCOL) */
|
|
/* > UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */
|
|
/* > UCOL = f2cmin(M,N) if JOBZ = 'S'. */
|
|
/* > If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */
|
|
/* > orthogonal matrix U; */
|
|
/* > if JOBZ = 'S', U contains the first f2cmin(M,N) columns of U */
|
|
/* > (the left singular vectors, stored columnwise); */
|
|
/* > if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU */
|
|
/* > \verbatim */
|
|
/* > LDU is INTEGER */
|
|
/* > The leading dimension of the array U. LDU >= 1; if */
|
|
/* > JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VT */
|
|
/* > \verbatim */
|
|
/* > VT is REAL array, dimension (LDVT,N) */
|
|
/* > If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */
|
|
/* > N-by-N orthogonal matrix V**T; */
|
|
/* > if JOBZ = 'S', VT contains the first f2cmin(M,N) rows of */
|
|
/* > V**T (the right singular vectors, stored rowwise); */
|
|
/* > if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVT */
|
|
/* > \verbatim */
|
|
/* > LDVT is INTEGER */
|
|
/* > The leading dimension of the array VT. LDVT >= 1; */
|
|
/* > if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */
|
|
/* > if JOBZ = 'S', LDVT >= f2cmin(M,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK; */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= 1. */
|
|
/* > If LWORK = -1, a workspace query is assumed. The optimal */
|
|
/* > size for the WORK array is calculated and stored in WORK(1), */
|
|
/* > and no other work except argument checking is performed. */
|
|
/* > */
|
|
/* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
|
|
/* > If JOBZ = 'N', LWORK >= 3*mn + f2cmax( mx, 7*mn ). */
|
|
/* > If JOBZ = 'O', LWORK >= 3*mn + f2cmax( mx, 5*mn*mn + 4*mn ). */
|
|
/* > If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn. */
|
|
/* > If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx. */
|
|
/* > These are not tight minimums in all cases; see comments inside code. */
|
|
/* > For good performance, LWORK should generally be larger; */
|
|
/* > a query is recommended. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (8*f2cmin(M,N)) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: SBDSDC did not converge, updating process failed. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup realGEsing */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void sgesdd_(char *jobz, integer *m, integer *n, real *a,
|
|
integer *lda, real *s, real *u, integer *ldu, real *vt, integer *ldvt,
|
|
real *work, integer *lwork, integer *iwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
|
|
i__2, i__3;
|
|
|
|
/* Local variables */
|
|
integer lwork_sgelqf_mn__, lwork_sgeqrf_mn__, iscl, lwork_sorglq_mn__,
|
|
lwork_sorglq_nn__;
|
|
real anrm;
|
|
integer idum[1], ierr, itau, lwork_sorgqr_mm__, lwork_sorgqr_mn__,
|
|
lwork_sormbr_qln_mm__, lwork_sormbr_qln_mn__,
|
|
lwork_sormbr_qln_nn__, lwork_sormbr_prt_mm__,
|
|
lwork_sormbr_prt_mn__, lwork_sormbr_prt_nn__, i__;
|
|
extern logical lsame_(char *, char *);
|
|
integer chunk;
|
|
extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *,
|
|
integer *, real *, real *, integer *, real *, integer *, real *,
|
|
real *, integer *);
|
|
integer minmn, wrkbl, itaup, itauq, mnthr;
|
|
logical wntqa;
|
|
integer nwork;
|
|
logical wntqn, wntqo, wntqs;
|
|
integer ie, il, ir, bdspac, iu, lwork_sorgbr_p_mm__;
|
|
extern /* Subroutine */ void sbdsdc_(char *, char *, integer *, real *,
|
|
real *, real *, integer *, real *, integer *, real *, integer *,
|
|
real *, integer *, integer *);
|
|
integer lwork_sorgbr_q_nn__;
|
|
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);
|
|
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 *);
|
|
extern logical sisnan_(real *);
|
|
extern /* Subroutine */ void sorgbr_(char *, integer *, integer *, integer
|
|
*, real *, integer *, real *, real *, integer *, integer *);
|
|
integer ldwrkl;
|
|
extern /* Subroutine */ void 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 *);
|
|
integer ldwkvt;
|
|
real smlnum;
|
|
logical wntqas;
|
|
extern /* Subroutine */ void sorgqr_(integer *, integer *, integer *, real
|
|
*, integer *, real *, real *, integer *, integer *);
|
|
logical lquery;
|
|
integer blk;
|
|
real dum[1], eps;
|
|
integer ivt, lwork_sgebrd_mm__, lwork_sgebrd_mn__, lwork_sgebrd_nn__;
|
|
|
|
|
|
/* -- LAPACK driver routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input arguments */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--s;
|
|
u_dim1 = *ldu;
|
|
u_offset = 1 + u_dim1 * 1;
|
|
u -= u_offset;
|
|
vt_dim1 = *ldvt;
|
|
vt_offset = 1 + vt_dim1 * 1;
|
|
vt -= vt_offset;
|
|
--work;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
minmn = f2cmin(*m,*n);
|
|
wntqa = lsame_(jobz, "A");
|
|
wntqs = lsame_(jobz, "S");
|
|
wntqas = wntqa || wntqs;
|
|
wntqo = lsame_(jobz, "O");
|
|
wntqn = lsame_(jobz, "N");
|
|
lquery = *lwork == -1;
|
|
|
|
if (! (wntqa || wntqs || wntqo || wntqn)) {
|
|
*info = -1;
|
|
} else if (*m < 0) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -5;
|
|
} else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < *
|
|
m) {
|
|
*info = -8;
|
|
} else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn ||
|
|
wntqo && *m >= *n && *ldvt < *n) {
|
|
*info = -10;
|
|
}
|
|
|
|
/* Compute workspace */
|
|
/* Note: Comments in the code beginning "Workspace:" describe the */
|
|
/* minimal amount of workspace allocated at that point in the code, */
|
|
/* as well as the preferred amount for good performance. */
|
|
/* NB refers to the optimal block size for the immediately */
|
|
/* following subroutine, as returned by ILAENV. */
|
|
|
|
if (*info == 0) {
|
|
minwrk = 1;
|
|
maxwrk = 1;
|
|
bdspac = 0;
|
|
mnthr = (integer) (minmn * 11.f / 6.f);
|
|
if (*m >= *n && minmn > 0) {
|
|
|
|
/* Compute space needed for SBDSDC */
|
|
|
|
if (wntqn) {
|
|
/* sbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6) */
|
|
/* keep 7*N for backwards compatibility. */
|
|
bdspac = *n * 7;
|
|
} else {
|
|
bdspac = *n * 3 * *n + (*n << 2);
|
|
}
|
|
|
|
/* Compute space preferred for each routine */
|
|
sgebrd_(m, n, dum, m, dum, dum, dum, dum, dum, &c_n1, &ierr);
|
|
lwork_sgebrd_mn__ = (integer) dum[0];
|
|
|
|
sgebrd_(n, n, dum, n, dum, dum, dum, dum, dum, &c_n1, &ierr);
|
|
lwork_sgebrd_nn__ = (integer) dum[0];
|
|
|
|
sgeqrf_(m, n, dum, m, dum, dum, &c_n1, &ierr);
|
|
lwork_sgeqrf_mn__ = (integer) dum[0];
|
|
|
|
sorgbr_("Q", n, n, n, dum, n, dum, dum, &c_n1, &ierr);
|
|
lwork_sorgbr_q_nn__ = (integer) dum[0];
|
|
|
|
sorgqr_(m, m, n, dum, m, dum, dum, &c_n1, &ierr);
|
|
lwork_sorgqr_mm__ = (integer) dum[0];
|
|
|
|
sorgqr_(m, n, n, dum, m, dum, dum, &c_n1, &ierr);
|
|
lwork_sorgqr_mn__ = (integer) dum[0];
|
|
|
|
sormbr_("P", "R", "T", n, n, n, dum, n, dum, dum, n, dum, &c_n1, &
|
|
ierr);
|
|
lwork_sormbr_prt_nn__ = (integer) dum[0];
|
|
|
|
sormbr_("Q", "L", "N", n, n, n, dum, n, dum, dum, n, dum, &c_n1, &
|
|
ierr);
|
|
lwork_sormbr_qln_nn__ = (integer) dum[0];
|
|
|
|
sormbr_("Q", "L", "N", m, n, n, dum, m, dum, dum, m, dum, &c_n1, &
|
|
ierr);
|
|
lwork_sormbr_qln_mn__ = (integer) dum[0];
|
|
|
|
sormbr_("Q", "L", "N", m, m, n, dum, m, dum, dum, m, dum, &c_n1, &
|
|
ierr);
|
|
lwork_sormbr_qln_mm__ = (integer) dum[0];
|
|
|
|
if (*m >= mnthr) {
|
|
if (wntqn) {
|
|
|
|
/* Path 1 (M >> N, JOBZ='N') */
|
|
|
|
wrkbl = *n + lwork_sgeqrf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = bdspac + *n;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
minwrk = bdspac + *n;
|
|
} else if (wntqo) {
|
|
|
|
/* Path 2 (M >> N, JOBZ='O') */
|
|
|
|
wrkbl = *n + lwork_sgeqrf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n + lwork_sorgqr_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = wrkbl + (*n << 1) * *n;
|
|
minwrk = bdspac + (*n << 1) * *n + *n * 3;
|
|
} else if (wntqs) {
|
|
|
|
/* Path 3 (M >> N, JOBZ='S') */
|
|
|
|
wrkbl = *n + lwork_sgeqrf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n + lwork_sorgqr_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = wrkbl + *n * *n;
|
|
minwrk = bdspac + *n * *n + *n * 3;
|
|
} else if (wntqa) {
|
|
|
|
/* Path 4 (M >> N, JOBZ='A') */
|
|
|
|
wrkbl = *n + lwork_sgeqrf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n + lwork_sorgqr_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sgebrd_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = wrkbl + *n * *n;
|
|
/* Computing MAX */
|
|
i__1 = *n * 3 + bdspac, i__2 = *n + *m;
|
|
minwrk = *n * *n + f2cmax(i__1,i__2);
|
|
}
|
|
} else {
|
|
|
|
/* Path 5 (M >= N, but not much larger) */
|
|
|
|
wrkbl = *n * 3 + lwork_sgebrd_mn__;
|
|
if (wntqn) {
|
|
/* Path 5n (M >= N, jobz='N') */
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
minwrk = *n * 3 + f2cmax(*m,bdspac);
|
|
} else if (wntqo) {
|
|
/* Path 5o (M >= N, jobz='O') */
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = wrkbl + *m * *n;
|
|
/* Computing MAX */
|
|
i__1 = *m, i__2 = *n * *n + bdspac;
|
|
minwrk = *n * 3 + f2cmax(i__1,i__2);
|
|
} else if (wntqs) {
|
|
/* Path 5s (M >= N, jobz='S') */
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
minwrk = *n * 3 + f2cmax(*m,bdspac);
|
|
} else if (wntqa) {
|
|
/* Path 5a (M >= N, jobz='A') */
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_qln_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + lwork_sormbr_prt_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
minwrk = *n * 3 + f2cmax(*m,bdspac);
|
|
}
|
|
}
|
|
} else if (minmn > 0) {
|
|
|
|
/* Compute space needed for SBDSDC */
|
|
|
|
if (wntqn) {
|
|
/* sbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6) */
|
|
/* keep 7*N for backwards compatibility. */
|
|
bdspac = *m * 7;
|
|
} else {
|
|
bdspac = *m * 3 * *m + (*m << 2);
|
|
}
|
|
|
|
/* Compute space preferred for each routine */
|
|
sgebrd_(m, n, dum, m, dum, dum, dum, dum, dum, &c_n1, &ierr);
|
|
lwork_sgebrd_mn__ = (integer) dum[0];
|
|
|
|
sgebrd_(m, m, &a[a_offset], m, &s[1], dum, dum, dum, dum, &c_n1, &
|
|
ierr);
|
|
lwork_sgebrd_mm__ = (integer) dum[0];
|
|
|
|
sgelqf_(m, n, &a[a_offset], m, dum, dum, &c_n1, &ierr);
|
|
lwork_sgelqf_mn__ = (integer) dum[0];
|
|
|
|
sorglq_(n, n, m, dum, n, dum, dum, &c_n1, &ierr);
|
|
lwork_sorglq_nn__ = (integer) dum[0];
|
|
|
|
sorglq_(m, n, m, &a[a_offset], m, dum, dum, &c_n1, &ierr);
|
|
lwork_sorglq_mn__ = (integer) dum[0];
|
|
|
|
sorgbr_("P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr);
|
|
lwork_sorgbr_p_mm__ = (integer) dum[0];
|
|
|
|
sormbr_("P", "R", "T", m, m, m, dum, m, dum, dum, m, dum, &c_n1, &
|
|
ierr);
|
|
lwork_sormbr_prt_mm__ = (integer) dum[0];
|
|
|
|
sormbr_("P", "R", "T", m, n, m, dum, m, dum, dum, m, dum, &c_n1, &
|
|
ierr);
|
|
lwork_sormbr_prt_mn__ = (integer) dum[0];
|
|
|
|
sormbr_("P", "R", "T", n, n, m, dum, n, dum, dum, n, dum, &c_n1, &
|
|
ierr);
|
|
lwork_sormbr_prt_nn__ = (integer) dum[0];
|
|
|
|
sormbr_("Q", "L", "N", m, m, m, dum, m, dum, dum, m, dum, &c_n1, &
|
|
ierr);
|
|
lwork_sormbr_qln_mm__ = (integer) dum[0];
|
|
|
|
if (*n >= mnthr) {
|
|
if (wntqn) {
|
|
|
|
/* Path 1t (N >> M, JOBZ='N') */
|
|
|
|
wrkbl = *m + lwork_sgelqf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = bdspac + *m;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
minwrk = bdspac + *m;
|
|
} else if (wntqo) {
|
|
|
|
/* Path 2t (N >> M, JOBZ='O') */
|
|
|
|
wrkbl = *m + lwork_sgelqf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m + lwork_sorglq_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = wrkbl + (*m << 1) * *m;
|
|
minwrk = bdspac + (*m << 1) * *m + *m * 3;
|
|
} else if (wntqs) {
|
|
|
|
/* Path 3t (N >> M, JOBZ='S') */
|
|
|
|
wrkbl = *m + lwork_sgelqf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m + lwork_sorglq_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = wrkbl + *m * *m;
|
|
minwrk = bdspac + *m * *m + *m * 3;
|
|
} else if (wntqa) {
|
|
|
|
/* Path 4t (N >> M, JOBZ='A') */
|
|
|
|
wrkbl = *m + lwork_sgelqf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m + lwork_sorglq_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sgebrd_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = wrkbl + *m * *m;
|
|
/* Computing MAX */
|
|
i__1 = *m * 3 + bdspac, i__2 = *m + *n;
|
|
minwrk = *m * *m + f2cmax(i__1,i__2);
|
|
}
|
|
} else {
|
|
|
|
/* Path 5t (N > M, but not much larger) */
|
|
|
|
wrkbl = *m * 3 + lwork_sgebrd_mn__;
|
|
if (wntqn) {
|
|
/* Path 5tn (N > M, jobz='N') */
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
minwrk = *m * 3 + f2cmax(*n,bdspac);
|
|
} else if (wntqo) {
|
|
/* Path 5to (N > M, jobz='O') */
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = wrkbl + *m * *n;
|
|
/* Computing MAX */
|
|
i__1 = *n, i__2 = *m * *m + bdspac;
|
|
minwrk = *m * 3 + f2cmax(i__1,i__2);
|
|
} else if (wntqs) {
|
|
/* Path 5ts (N > M, jobz='S') */
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
minwrk = *m * 3 + f2cmax(*n,bdspac);
|
|
} else if (wntqa) {
|
|
/* Path 5ta (N > M, jobz='A') */
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_qln_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + lwork_sormbr_prt_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
minwrk = *m * 3 + f2cmax(*n,bdspac);
|
|
}
|
|
}
|
|
}
|
|
maxwrk = f2cmax(maxwrk,minwrk);
|
|
work[1] = (real) maxwrk;
|
|
|
|
if (*lwork < minwrk && ! lquery) {
|
|
*info = -12;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SGESDD", &i__1, (ftnlen)6);
|
|
return;
|
|
} 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);
|
|
if (sisnan_(&anrm)) {
|
|
*info = -4;
|
|
return;
|
|
}
|
|
iscl = 0;
|
|
if (anrm > 0.f && anrm < smlnum) {
|
|
iscl = 1;
|
|
slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
|
|
ierr);
|
|
} else if (anrm > bignum) {
|
|
iscl = 1;
|
|
slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
|
|
ierr);
|
|
}
|
|
|
|
if (*m >= *n) {
|
|
|
|
/* A has at least as many rows as columns. If A has sufficiently */
|
|
/* more rows than columns, first reduce using the QR */
|
|
/* decomposition (if sufficient workspace available) */
|
|
|
|
if (*m >= mnthr) {
|
|
|
|
if (wntqn) {
|
|
|
|
/* Path 1 (M >> N, JOBZ='N') */
|
|
/* No singular vectors to be computed */
|
|
|
|
itau = 1;
|
|
nwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* Workspace: need N [tau] + N [work] */
|
|
/* Workspace: prefer N [tau] + N*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__1, &ierr);
|
|
|
|
/* Zero out below R */
|
|
|
|
i__1 = *n - 1;
|
|
i__2 = *n - 1;
|
|
slaset_("L", &i__1, &i__2, &c_b63, &c_b63, &a[a_dim1 + 2],
|
|
lda);
|
|
ie = 1;
|
|
itauq = ie + *n;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* Workspace: need 3*N [e, tauq, taup] + N [work] */
|
|
/* Workspace: prefer 3*N [e, tauq, taup] + 2*N*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
|
|
nwork = ie + *n;
|
|
|
|
/* Perform bidiagonal SVD, computing singular values only */
|
|
/* Workspace: need N [e] + BDSPAC */
|
|
|
|
sbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1,
|
|
dum, idum, &work[nwork], &iwork[1], info);
|
|
|
|
} else if (wntqo) {
|
|
|
|
/* Path 2 (M >> N, JOBZ = 'O') */
|
|
/* N left singular vectors to be overwritten on A and */
|
|
/* N right singular vectors to be computed in VT */
|
|
|
|
ir = 1;
|
|
|
|
/* WORK(IR) is LDWRKR by N */
|
|
|
|
if (*lwork >= *lda * *n + *n * *n + *n * 3 + bdspac) {
|
|
ldwrkr = *lda;
|
|
} else {
|
|
ldwrkr = (*lwork - *n * *n - *n * 3 - bdspac) / *n;
|
|
}
|
|
itau = ir + ldwrkr * *n;
|
|
nwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* Workspace: need N*N [R] + N [tau] + N [work] */
|
|
/* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__1, &ierr);
|
|
|
|
/* Copy R to WORK(IR), zeroing out below it */
|
|
|
|
slacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
|
|
i__1 = *n - 1;
|
|
i__2 = *n - 1;
|
|
slaset_("L", &i__1, &i__2, &c_b63, &c_b63, &work[ir + 1], &
|
|
ldwrkr);
|
|
|
|
/* Generate Q in A */
|
|
/* Workspace: need N*N [R] + N [tau] + N [work] */
|
|
/* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
|
|
&i__1, &ierr);
|
|
ie = itau;
|
|
itauq = ie + *n;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IR) */
|
|
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work] */
|
|
/* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + 2*N*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
|
|
|
|
/* WORK(IU) is N by N */
|
|
|
|
iu = nwork;
|
|
nwork = iu + *n * *n;
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in WORK(IU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in VT */
|
|
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] + BDSPAC */
|
|
|
|
sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[
|
|
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
|
|
info);
|
|
|
|
/* Overwrite WORK(IU) by left singular vectors of R */
|
|
/* and VT by right singular vectors of R */
|
|
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] + N [work] */
|
|
/* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
|
|
itauq], &work[iu], n, &work[nwork], &i__1, &ierr);
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
|
|
/* Multiply Q in A by left singular vectors of R in */
|
|
/* WORK(IU), storing result in WORK(IR) and copying to A */
|
|
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] */
|
|
/* Workspace: prefer M*N [R] + 3*N [e, tauq, taup] + N*N [U] */
|
|
|
|
i__1 = *m;
|
|
i__2 = ldwrkr;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *m - i__ + 1;
|
|
chunk = f2cmin(i__3,ldwrkr);
|
|
sgemm_("N", "N", &chunk, n, n, &c_b84, &a[i__ + a_dim1],
|
|
lda, &work[iu], n, &c_b63, &work[ir], &ldwrkr);
|
|
slacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
|
|
a_dim1], lda);
|
|
/* L10: */
|
|
}
|
|
|
|
} else if (wntqs) {
|
|
|
|
/* Path 3 (M >> N, JOBZ='S') */
|
|
/* N left singular vectors to be computed in U and */
|
|
/* N right singular vectors to be computed in VT */
|
|
|
|
ir = 1;
|
|
|
|
/* WORK(IR) is N by N */
|
|
|
|
ldwrkr = *n;
|
|
itau = ir + ldwrkr * *n;
|
|
nwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* Workspace: need N*N [R] + N [tau] + N [work] */
|
|
/* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Copy R to WORK(IR), zeroing out below it */
|
|
|
|
slacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
|
|
i__2 = *n - 1;
|
|
i__1 = *n - 1;
|
|
slaset_("L", &i__2, &i__1, &c_b63, &c_b63, &work[ir + 1], &
|
|
ldwrkr);
|
|
|
|
/* Generate Q in A */
|
|
/* Workspace: need N*N [R] + N [tau] + N [work] */
|
|
/* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
|
|
&i__2, &ierr);
|
|
ie = itau;
|
|
itauq = ie + *n;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IR) */
|
|
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work] */
|
|
/* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + 2*N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagoal matrix in U and computing right singular */
|
|
/* vectors of bidiagonal matrix in VT */
|
|
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + BDSPAC */
|
|
|
|
sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
|
|
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
|
|
info);
|
|
|
|
/* Overwrite U by left singular vectors of R and VT */
|
|
/* by right singular vectors of R */
|
|
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work] */
|
|
/* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Multiply Q in A by left singular vectors of R in */
|
|
/* WORK(IR), storing result in U */
|
|
/* Workspace: need N*N [R] */
|
|
|
|
slacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
|
|
sgemm_("N", "N", m, n, n, &c_b84, &a[a_offset], lda, &work[ir]
|
|
, &ldwrkr, &c_b63, &u[u_offset], ldu);
|
|
|
|
} else if (wntqa) {
|
|
|
|
/* Path 4 (M >> N, JOBZ='A') */
|
|
/* M left singular vectors to be computed in U and */
|
|
/* N right singular vectors to be computed in VT */
|
|
|
|
iu = 1;
|
|
|
|
/* WORK(IU) is N by N */
|
|
|
|
ldwrku = *n;
|
|
itau = iu + ldwrku * *n;
|
|
nwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* Workspace: need N*N [U] + N [tau] + N [work] */
|
|
/* Workspace: prefer N*N [U] + N [tau] + N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__2, &ierr);
|
|
slacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
|
|
|
|
/* Generate Q in U */
|
|
/* Workspace: need N*N [U] + N [tau] + M [work] */
|
|
/* Workspace: prefer N*N [U] + N [tau] + M*NB [work] */
|
|
i__2 = *lwork - nwork + 1;
|
|
sorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork],
|
|
&i__2, &ierr);
|
|
|
|
/* Produce R in A, zeroing out other entries */
|
|
|
|
i__2 = *n - 1;
|
|
i__1 = *n - 1;
|
|
slaset_("L", &i__2, &i__1, &c_b63, &c_b63, &a[a_dim1 + 2],
|
|
lda);
|
|
ie = itau;
|
|
itauq = ie + *n;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* Workspace: need N*N [U] + 3*N [e, tauq, taup] + N [work] */
|
|
/* Workspace: prefer N*N [U] + 3*N [e, tauq, taup] + 2*N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in WORK(IU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in VT */
|
|
/* Workspace: need N*N [U] + 3*N [e, tauq, taup] + BDSPAC */
|
|
|
|
sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[
|
|
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
|
|
info);
|
|
|
|
/* Overwrite WORK(IU) by left singular vectors of R and VT */
|
|
/* by right singular vectors of R */
|
|
/* Workspace: need N*N [U] + 3*N [e, tauq, taup] + N [work] */
|
|
/* Workspace: prefer N*N [U] + 3*N [e, tauq, taup] + N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[
|
|
itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
|
|
ierr);
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Multiply Q in U by left singular vectors of R in */
|
|
/* WORK(IU), storing result in A */
|
|
/* Workspace: need N*N [U] */
|
|
|
|
sgemm_("N", "N", m, n, n, &c_b84, &u[u_offset], ldu, &work[iu]
|
|
, &ldwrku, &c_b63, &a[a_offset], lda);
|
|
|
|
/* Copy left singular vectors of A from A to U */
|
|
|
|
slacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* M .LT. MNTHR */
|
|
|
|
/* Path 5 (M >= N, but not much larger) */
|
|
/* Reduce to bidiagonal form without QR decomposition */
|
|
|
|
ie = 1;
|
|
itauq = ie + *n;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize A */
|
|
/* Workspace: need 3*N [e, tauq, taup] + M [work] */
|
|
/* Workspace: prefer 3*N [e, tauq, taup] + (M+N)*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
|
|
work[itaup], &work[nwork], &i__2, &ierr);
|
|
if (wntqn) {
|
|
|
|
/* Path 5n (M >= N, JOBZ='N') */
|
|
/* Perform bidiagonal SVD, only computing singular values */
|
|
/* Workspace: need 3*N [e, tauq, taup] + BDSPAC */
|
|
|
|
sbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1,
|
|
dum, idum, &work[nwork], &iwork[1], info);
|
|
} else if (wntqo) {
|
|
/* Path 5o (M >= N, JOBZ='O') */
|
|
iu = nwork;
|
|
if (*lwork >= *m * *n + *n * 3 + bdspac) {
|
|
|
|
/* WORK( IU ) is M by N */
|
|
|
|
ldwrku = *m;
|
|
nwork = iu + ldwrku * *n;
|
|
slaset_("F", m, n, &c_b63, &c_b63, &work[iu], &ldwrku);
|
|
/* IR is unused; silence compile warnings */
|
|
ir = -1;
|
|
} else {
|
|
|
|
/* WORK( IU ) is N by N */
|
|
|
|
ldwrku = *n;
|
|
nwork = iu + ldwrku * *n;
|
|
|
|
/* WORK(IR) is LDWRKR by N */
|
|
|
|
ir = nwork;
|
|
ldwrkr = (*lwork - *n * *n - *n * 3) / *n;
|
|
}
|
|
nwork = iu + ldwrku * *n;
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in WORK(IU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in VT */
|
|
/* Workspace: need 3*N [e, tauq, taup] + N*N [U] + BDSPAC */
|
|
|
|
sbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], &ldwrku, &
|
|
vt[vt_offset], ldvt, dum, idum, &work[nwork], &iwork[
|
|
1], info);
|
|
|
|
/* Overwrite VT by right singular vectors of A */
|
|
/* Workspace: need 3*N [e, tauq, taup] + N*N [U] + N [work] */
|
|
/* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
|
|
ierr);
|
|
|
|
if (*lwork >= *m * *n + *n * 3 + bdspac) {
|
|
|
|
/* Path 5o-fast */
|
|
/* Overwrite WORK(IU) by left singular vectors of A */
|
|
/* Workspace: need 3*N [e, tauq, taup] + M*N [U] + N [work] */
|
|
/* Workspace: prefer 3*N [e, tauq, taup] + M*N [U] + N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
|
|
itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Copy left singular vectors of A from WORK(IU) to A */
|
|
|
|
slacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda);
|
|
} else {
|
|
|
|
/* Path 5o-slow */
|
|
/* Generate Q in A */
|
|
/* Workspace: need 3*N [e, tauq, taup] + N*N [U] + N [work] */
|
|
/* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sorgbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
|
|
work[nwork], &i__2, &ierr);
|
|
|
|
/* Multiply Q in A by left singular vectors of */
|
|
/* bidiagonal matrix in WORK(IU), storing result in */
|
|
/* WORK(IR) and copying to A */
|
|
/* Workspace: need 3*N [e, tauq, taup] + N*N [U] + NB*N [R] */
|
|
/* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + M*N [R] */
|
|
|
|
i__2 = *m;
|
|
i__1 = ldwrkr;
|
|
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
|
|
i__1) {
|
|
/* Computing MIN */
|
|
i__3 = *m - i__ + 1;
|
|
chunk = f2cmin(i__3,ldwrkr);
|
|
sgemm_("N", "N", &chunk, n, n, &c_b84, &a[i__ +
|
|
a_dim1], lda, &work[iu], &ldwrku, &c_b63, &
|
|
work[ir], &ldwrkr);
|
|
slacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
|
|
a_dim1], lda);
|
|
/* L20: */
|
|
}
|
|
}
|
|
|
|
} else if (wntqs) {
|
|
|
|
/* Path 5s (M >= N, JOBZ='S') */
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in U and computing right singular */
|
|
/* vectors of bidiagonal matrix in VT */
|
|
/* Workspace: need 3*N [e, tauq, taup] + BDSPAC */
|
|
|
|
slaset_("F", m, n, &c_b63, &c_b63, &u[u_offset], ldu);
|
|
sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
|
|
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
|
|
info);
|
|
|
|
/* Overwrite U by left singular vectors of A and VT */
|
|
/* by right singular vectors of A */
|
|
/* Workspace: need 3*N [e, tauq, taup] + N [work] */
|
|
/* Workspace: prefer 3*N [e, tauq, taup] + N*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
} else if (wntqa) {
|
|
|
|
/* Path 5a (M >= N, JOBZ='A') */
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in U and computing right singular */
|
|
/* vectors of bidiagonal matrix in VT */
|
|
/* Workspace: need 3*N [e, tauq, taup] + BDSPAC */
|
|
|
|
slaset_("F", m, m, &c_b63, &c_b63, &u[u_offset], ldu);
|
|
sbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
|
|
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
|
|
info);
|
|
|
|
/* Set the right corner of U to identity matrix */
|
|
|
|
if (*m > *n) {
|
|
i__1 = *m - *n;
|
|
i__2 = *m - *n;
|
|
slaset_("F", &i__1, &i__2, &c_b63, &c_b84, &u[*n + 1 + (*
|
|
n + 1) * u_dim1], ldu);
|
|
}
|
|
|
|
/* Overwrite U by left singular vectors of A and VT */
|
|
/* by right singular vectors of A */
|
|
/* Workspace: need 3*N [e, tauq, taup] + M [work] */
|
|
/* Workspace: prefer 3*N [e, tauq, taup] + M*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* A has more columns than rows. If A has sufficiently more */
|
|
/* columns than rows, first reduce using the LQ decomposition (if */
|
|
/* sufficient workspace available) */
|
|
|
|
if (*n >= mnthr) {
|
|
|
|
if (wntqn) {
|
|
|
|
/* Path 1t (N >> M, JOBZ='N') */
|
|
/* No singular vectors to be computed */
|
|
|
|
itau = 1;
|
|
nwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* Workspace: need M [tau] + M [work] */
|
|
/* Workspace: prefer M [tau] + M*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__1, &ierr);
|
|
|
|
/* Zero out above L */
|
|
|
|
i__1 = *m - 1;
|
|
i__2 = *m - 1;
|
|
slaset_("U", &i__1, &i__2, &c_b63, &c_b63, &a[(a_dim1 << 1) +
|
|
1], lda);
|
|
ie = 1;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in A */
|
|
/* Workspace: need 3*M [e, tauq, taup] + M [work] */
|
|
/* Workspace: prefer 3*M [e, tauq, taup] + 2*M*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
|
|
nwork = ie + *m;
|
|
|
|
/* Perform bidiagonal SVD, computing singular values only */
|
|
/* Workspace: need M [e] + BDSPAC */
|
|
|
|
sbdsdc_("U", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1,
|
|
dum, idum, &work[nwork], &iwork[1], info);
|
|
|
|
} else if (wntqo) {
|
|
|
|
/* Path 2t (N >> M, JOBZ='O') */
|
|
/* M right singular vectors to be overwritten on A and */
|
|
/* M left singular vectors to be computed in U */
|
|
|
|
ivt = 1;
|
|
|
|
/* WORK(IVT) is M by M */
|
|
/* WORK(IL) is M by M; it is later resized to M by chunk for gemm */
|
|
|
|
il = ivt + *m * *m;
|
|
if (*lwork >= *m * *n + *m * *m + *m * 3 + bdspac) {
|
|
ldwrkl = *m;
|
|
chunk = *n;
|
|
} else {
|
|
ldwrkl = *m;
|
|
chunk = (*lwork - *m * *m) / *m;
|
|
}
|
|
itau = il + ldwrkl * *m;
|
|
nwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* Workspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
|
|
/* Workspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__1, &ierr);
|
|
|
|
/* Copy L to WORK(IL), zeroing about above it */
|
|
|
|
slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
|
|
i__1 = *m - 1;
|
|
i__2 = *m - 1;
|
|
slaset_("U", &i__1, &i__2, &c_b63, &c_b63, &work[il + ldwrkl],
|
|
&ldwrkl);
|
|
|
|
/* Generate Q in A */
|
|
/* Workspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
|
|
/* Workspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
|
|
&i__1, &ierr);
|
|
ie = itau;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IL) */
|
|
/* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M [work] */
|
|
/* Workspace: prefer M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + 2*M*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in U, and computing right singular */
|
|
/* vectors of bidiagonal matrix in WORK(IVT) */
|
|
/* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + BDSPAC */
|
|
|
|
sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
|
|
work[ivt], m, dum, idum, &work[nwork], &iwork[1],
|
|
info);
|
|
|
|
/* Overwrite U by left singular vectors of L and WORK(IVT) */
|
|
/* by right singular vectors of L */
|
|
/* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M [work] */
|
|
/* Workspace: prefer M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[
|
|
itaup], &work[ivt], m, &work[nwork], &i__1, &ierr);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IVT) by Q */
|
|
/* in A, storing result in WORK(IL) and copying to A */
|
|
/* Workspace: need M*M [VT] + M*M [L] */
|
|
/* Workspace: prefer M*M [VT] + M*N [L] */
|
|
/* At this point, L is resized as M by chunk. */
|
|
|
|
i__1 = *n;
|
|
i__2 = chunk;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *n - i__ + 1;
|
|
blk = f2cmin(i__3,chunk);
|
|
sgemm_("N", "N", m, &blk, m, &c_b84, &work[ivt], m, &a[
|
|
i__ * a_dim1 + 1], lda, &c_b63, &work[il], &
|
|
ldwrkl);
|
|
slacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1
|
|
+ 1], lda);
|
|
/* L30: */
|
|
}
|
|
|
|
} else if (wntqs) {
|
|
|
|
/* Path 3t (N >> M, JOBZ='S') */
|
|
/* M right singular vectors to be computed in VT and */
|
|
/* M left singular vectors to be computed in U */
|
|
|
|
il = 1;
|
|
|
|
/* WORK(IL) is M by M */
|
|
|
|
ldwrkl = *m;
|
|
itau = il + ldwrkl * *m;
|
|
nwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* Workspace: need M*M [L] + M [tau] + M [work] */
|
|
/* Workspace: prefer M*M [L] + M [tau] + M*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Copy L to WORK(IL), zeroing out above it */
|
|
|
|
slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
|
|
i__2 = *m - 1;
|
|
i__1 = *m - 1;
|
|
slaset_("U", &i__2, &i__1, &c_b63, &c_b63, &work[il + ldwrkl],
|
|
&ldwrkl);
|
|
|
|
/* Generate Q in A */
|
|
/* Workspace: need M*M [L] + M [tau] + M [work] */
|
|
/* Workspace: prefer M*M [L] + M [tau] + M*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
|
|
&i__2, &ierr);
|
|
ie = itau;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IU). */
|
|
/* Workspace: need M*M [L] + 3*M [e, tauq, taup] + M [work] */
|
|
/* Workspace: prefer M*M [L] + 3*M [e, tauq, taup] + 2*M*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in U and computing right singular */
|
|
/* vectors of bidiagonal matrix in VT */
|
|
/* Workspace: need M*M [L] + 3*M [e, tauq, taup] + BDSPAC */
|
|
|
|
sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
|
|
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
|
|
info);
|
|
|
|
/* Overwrite U by left singular vectors of L and VT */
|
|
/* by right singular vectors of L */
|
|
/* Workspace: need M*M [L] + 3*M [e, tauq, taup] + M [work] */
|
|
/* Workspace: prefer M*M [L] + 3*M [e, tauq, taup] + M*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IL) by */
|
|
/* Q in A, storing result in VT */
|
|
/* Workspace: need M*M [L] */
|
|
|
|
slacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl);
|
|
sgemm_("N", "N", m, n, m, &c_b84, &work[il], &ldwrkl, &a[
|
|
a_offset], lda, &c_b63, &vt[vt_offset], ldvt);
|
|
|
|
} else if (wntqa) {
|
|
|
|
/* Path 4t (N >> M, JOBZ='A') */
|
|
/* N right singular vectors to be computed in VT and */
|
|
/* M left singular vectors to be computed in U */
|
|
|
|
ivt = 1;
|
|
|
|
/* WORK(IVT) is M by M */
|
|
|
|
ldwkvt = *m;
|
|
itau = ivt + ldwkvt * *m;
|
|
nwork = itau + *m;
|
|
|
|
/* Compute A=L*Q, copying result to VT */
|
|
/* Workspace: need M*M [VT] + M [tau] + M [work] */
|
|
/* Workspace: prefer M*M [VT] + M [tau] + M*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__2, &ierr);
|
|
slacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
|
|
/* Generate Q in VT */
|
|
/* Workspace: need M*M [VT] + M [tau] + N [work] */
|
|
/* Workspace: prefer M*M [VT] + M [tau] + N*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[
|
|
nwork], &i__2, &ierr);
|
|
|
|
/* Produce L in A, zeroing out other entries */
|
|
|
|
i__2 = *m - 1;
|
|
i__1 = *m - 1;
|
|
slaset_("U", &i__2, &i__1, &c_b63, &c_b63, &a[(a_dim1 << 1) +
|
|
1], lda);
|
|
ie = itau;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in A */
|
|
/* Workspace: need M*M [VT] + 3*M [e, tauq, taup] + M [work] */
|
|
/* Workspace: prefer M*M [VT] + 3*M [e, tauq, taup] + 2*M*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in U and computing right singular */
|
|
/* vectors of bidiagonal matrix in WORK(IVT) */
|
|
/* Workspace: need M*M [VT] + 3*M [e, tauq, taup] + BDSPAC */
|
|
|
|
sbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
|
|
work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1]
|
|
, info);
|
|
|
|
/* Overwrite U by left singular vectors of L and WORK(IVT) */
|
|
/* by right singular vectors of L */
|
|
/* Workspace: need M*M [VT] + 3*M [e, tauq, taup]+ M [work] */
|
|
/* Workspace: prefer M*M [VT] + 3*M [e, tauq, taup]+ M*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", m, m, m, &a[a_offset], lda, &work[
|
|
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IVT) by */
|
|
/* Q in VT, storing result in A */
|
|
/* Workspace: need M*M [VT] */
|
|
|
|
sgemm_("N", "N", m, n, m, &c_b84, &work[ivt], &ldwkvt, &vt[
|
|
vt_offset], ldvt, &c_b63, &a[a_offset], lda);
|
|
|
|
/* Copy right singular vectors of A from A to VT */
|
|
|
|
slacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* N .LT. MNTHR */
|
|
|
|
/* Path 5t (N > M, but not much larger) */
|
|
/* Reduce to bidiagonal form without LQ decomposition */
|
|
|
|
ie = 1;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize A */
|
|
/* Workspace: need 3*M [e, tauq, taup] + N [work] */
|
|
/* Workspace: prefer 3*M [e, tauq, taup] + (M+N)*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
|
|
work[itaup], &work[nwork], &i__2, &ierr);
|
|
if (wntqn) {
|
|
|
|
/* Path 5tn (N > M, JOBZ='N') */
|
|
/* Perform bidiagonal SVD, only computing singular values */
|
|
/* Workspace: need 3*M [e, tauq, taup] + BDSPAC */
|
|
|
|
sbdsdc_("L", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1,
|
|
dum, idum, &work[nwork], &iwork[1], info);
|
|
} else if (wntqo) {
|
|
/* Path 5to (N > M, JOBZ='O') */
|
|
ldwkvt = *m;
|
|
ivt = nwork;
|
|
if (*lwork >= *m * *n + *m * 3 + bdspac) {
|
|
|
|
/* WORK( IVT ) is M by N */
|
|
|
|
slaset_("F", m, n, &c_b63, &c_b63, &work[ivt], &ldwkvt);
|
|
nwork = ivt + ldwkvt * *n;
|
|
/* IL is unused; silence compile warnings */
|
|
il = -1;
|
|
} else {
|
|
|
|
/* WORK( IVT ) is M by M */
|
|
|
|
nwork = ivt + ldwkvt * *m;
|
|
il = nwork;
|
|
|
|
/* WORK(IL) is M by CHUNK */
|
|
|
|
chunk = (*lwork - *m * *m - *m * 3) / *m;
|
|
}
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in U and computing right singular */
|
|
/* vectors of bidiagonal matrix in WORK(IVT) */
|
|
/* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + BDSPAC */
|
|
|
|
sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
|
|
work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1]
|
|
, info);
|
|
|
|
/* Overwrite U by left singular vectors of A */
|
|
/* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M [work] */
|
|
/* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
|
|
|
|
if (*lwork >= *m * *n + *m * 3 + bdspac) {
|
|
|
|
/* Path 5to-fast */
|
|
/* Overwrite WORK(IVT) by left singular vectors of A */
|
|
/* Workspace: need 3*M [e, tauq, taup] + M*N [VT] + M [work] */
|
|
/* Workspace: prefer 3*M [e, tauq, taup] + M*N [VT] + M*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[
|
|
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2,
|
|
&ierr);
|
|
|
|
/* Copy right singular vectors of A from WORK(IVT) to A */
|
|
|
|
slacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda);
|
|
} else {
|
|
|
|
/* Path 5to-slow */
|
|
/* Generate P**T in A */
|
|
/* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M [work] */
|
|
/* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*NB [work] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
sorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
|
|
work[nwork], &i__2, &ierr);
|
|
|
|
/* Multiply Q in A by right singular vectors of */
|
|
/* bidiagonal matrix in WORK(IVT), storing result in */
|
|
/* WORK(IL) and copying to A */
|
|
/* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M*NB [L] */
|
|
/* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*N [L] */
|
|
|
|
i__2 = *n;
|
|
i__1 = chunk;
|
|
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
|
|
i__1) {
|
|
/* Computing MIN */
|
|
i__3 = *n - i__ + 1;
|
|
blk = f2cmin(i__3,chunk);
|
|
sgemm_("N", "N", m, &blk, m, &c_b84, &work[ivt], &
|
|
ldwkvt, &a[i__ * a_dim1 + 1], lda, &c_b63, &
|
|
work[il], m);
|
|
slacpy_("F", m, &blk, &work[il], m, &a[i__ * a_dim1 +
|
|
1], lda);
|
|
/* L40: */
|
|
}
|
|
}
|
|
} else if (wntqs) {
|
|
|
|
/* Path 5ts (N > M, JOBZ='S') */
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in U and computing right singular */
|
|
/* vectors of bidiagonal matrix in VT */
|
|
/* Workspace: need 3*M [e, tauq, taup] + BDSPAC */
|
|
|
|
slaset_("F", m, n, &c_b63, &c_b63, &vt[vt_offset], ldvt);
|
|
sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
|
|
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
|
|
info);
|
|
|
|
/* Overwrite U by left singular vectors of A and VT */
|
|
/* by right singular vectors of A */
|
|
/* Workspace: need 3*M [e, tauq, taup] + M [work] */
|
|
/* Workspace: prefer 3*M [e, tauq, taup] + M*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
} else if (wntqa) {
|
|
|
|
/* Path 5ta (N > M, JOBZ='A') */
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in U and computing right singular */
|
|
/* vectors of bidiagonal matrix in VT */
|
|
/* Workspace: need 3*M [e, tauq, taup] + BDSPAC */
|
|
|
|
slaset_("F", n, n, &c_b63, &c_b63, &vt[vt_offset], ldvt);
|
|
sbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
|
|
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
|
|
info);
|
|
|
|
/* Set the right corner of VT to identity matrix */
|
|
|
|
if (*n > *m) {
|
|
i__1 = *n - *m;
|
|
i__2 = *n - *m;
|
|
slaset_("F", &i__1, &i__2, &c_b63, &c_b84, &vt[*m + 1 + (*
|
|
m + 1) * vt_dim1], ldvt);
|
|
}
|
|
|
|
/* Overwrite U by left singular vectors of A and VT */
|
|
/* by right singular vectors of A */
|
|
/* Workspace: need 3*M [e, tauq, taup] + N [work] */
|
|
/* Workspace: prefer 3*M [e, tauq, taup] + N*NB [work] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
|
|
i__1 = *lwork - nwork + 1;
|
|
sormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
/* Undo scaling if necessary */
|
|
|
|
if (iscl == 1) {
|
|
if (anrm > bignum) {
|
|
slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, &ierr);
|
|
}
|
|
if (anrm < smlnum) {
|
|
slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, &ierr);
|
|
}
|
|
}
|
|
|
|
/* Return optimal workspace in WORK(1) */
|
|
|
|
work[1] = (real) maxwrk;
|
|
|
|
return;
|
|
|
|
/* End of SGESDD */
|
|
|
|
} /* sgesdd_ */
|
|
|