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OpenBLAS/lapack-netlib/SRC/sgesvdx.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__1 = 1;
static integer c_n1 = -1;
static real c_b109 = 0.f;
/* > \brief <b> SGESVDX 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 SGESVDX + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgesvdx
.f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgesvdx
.f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgesvdx
.f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGESVDX( JOBU, JOBVT, RANGE, M, N, A, LDA, VL, VU, */
/* $ IL, IU, NS, S, U, LDU, VT, LDVT, WORK, */
/* $ LWORK, IWORK, INFO ) */
/* CHARACTER JOBU, JOBVT, RANGE */
/* INTEGER IL, INFO, IU, LDA, LDU, LDVT, LWORK, M, N, NS */
/* REAL VL, VU */
/* INTEGER IWORK( * ) */
/* REAL A( LDA, * ), S( * ), U( LDU, * ), */
/* $ VT( LDVT, * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGESVDX 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. */
/* > */
/* > SGESVDX uses an eigenvalue problem for obtaining the SVD, which */
/* > allows for the computation of a subset of singular values and */
/* > vectors. See SBDSVDX for details. */
/* > */
/* > 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: */
/* > = 'V': the first f2cmin(m,n) columns of U (the left singular */
/* > vectors) or as specified by RANGE are returned in */
/* > the array U; */
/* > = '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: */
/* > = 'V': the first f2cmin(m,n) rows of V**T (the right singular */
/* > vectors) or as specified by RANGE are returned in */
/* > the array VT; */
/* > = 'N': no rows of V**T (no right singular vectors) are */
/* > computed. */
/* > \endverbatim */
/* > */
/* > \param[in] RANGE */
/* > \verbatim */
/* > RANGE is CHARACTER*1 */
/* > = 'A': all singular values will be found. */
/* > = 'V': all singular values in the half-open interval (VL,VU] */
/* > will be found. */
/* > = 'I': the IL-th through IU-th singular values will be found. */
/* > \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, 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[in] VL */
/* > \verbatim */
/* > VL is REAL */
/* > If RANGE='V', the lower bound of the interval to */
/* > be searched for singular values. VU > VL. */
/* > Not referenced if RANGE = 'A' or 'I'. */
/* > \endverbatim */
/* > */
/* > \param[in] VU */
/* > \verbatim */
/* > VU is REAL */
/* > If RANGE='V', the upper bound of the interval to */
/* > be searched for singular values. VU > VL. */
/* > Not referenced if RANGE = 'A' or 'I'. */
/* > \endverbatim */
/* > */
/* > \param[in] IL */
/* > \verbatim */
/* > IL is INTEGER */
/* > If RANGE='I', the index of the */
/* > smallest singular value to be returned. */
/* > 1 <= IL <= IU <= f2cmin(M,N), if f2cmin(M,N) > 0. */
/* > Not referenced if RANGE = 'A' or 'V'. */
/* > \endverbatim */
/* > */
/* > \param[in] IU */
/* > \verbatim */
/* > IU is INTEGER */
/* > If RANGE='I', the index of the */
/* > largest singular value to be returned. */
/* > 1 <= IL <= IU <= f2cmin(M,N), if f2cmin(M,N) > 0. */
/* > Not referenced if RANGE = 'A' or 'V'. */
/* > \endverbatim */
/* > */
/* > \param[out] NS */
/* > \verbatim */
/* > NS is INTEGER */
/* > The total number of singular values found, */
/* > 0 <= NS <= f2cmin(M,N). */
/* > If RANGE = 'A', NS = f2cmin(M,N); if RANGE = 'I', NS = IU-IL+1. */
/* > \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) */
/* > If JOBU = 'V', U contains columns of U (the left singular */
/* > vectors, stored columnwise) as specified by RANGE; if */
/* > JOBU = 'N', U is not referenced. */
/* > Note: The user must ensure that UCOL >= NS; if RANGE = 'V', */
/* > the exact value of NS is not known in advance and an upper */
/* > bound must be used. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* > LDU is INTEGER */
/* > The leading dimension of the array U. LDU >= 1; if */
/* > JOBU = 'V', LDU >= M. */
/* > \endverbatim */
/* > */
/* > \param[out] VT */
/* > \verbatim */
/* > VT is REAL array, dimension (LDVT,N) */
/* > If JOBVT = 'V', VT contains the rows of V**T (the right singular */
/* > vectors, stored rowwise) as specified by RANGE; if JOBVT = 'N', */
/* > VT is not referenced. */
/* > Note: The user must ensure that LDVT >= NS; if RANGE = 'V', */
/* > the exact value of NS is not known in advance and an upper */
/* > bound must be used. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVT */
/* > \verbatim */
/* > LDVT is INTEGER */
/* > The leading dimension of the array VT. LDVT >= 1; if */
/* > JOBVT = 'V', LDVT >= NS (see above). */
/* > \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 >= MAX(1,MIN(M,N)*(MIN(M,N)+4)) for the paths (see */
/* > comments inside the code): */
/* > - PATH 1 (M much larger than N) */
/* > - PATH 1t (N much larger than M) */
/* > LWORK >= MAX(1,MIN(M,N)*2+MAX(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] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (12*MIN(M,N)) */
/* > If INFO = 0, the first NS elements of IWORK are zero. If INFO > 0, */
/* > then IWORK contains the indices of the eigenvectors that failed */
/* > to converge in SBDSVDX/SSTEVX. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > > 0: if INFO = i, then i eigenvectors failed to converge */
/* > in SBDSVDX/SSTEVX. */
/* > if INFO = N*2 + 1, an internal error occurred in */
/* > SBDSVDX */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2016 */
/* > \ingroup realGEsing */
/* ===================================================================== */
/* Subroutine */ void sgesvdx_(char *jobu, char *jobvt, char *range, integer *
m, integer *n, real *a, integer *lda, real *vl, real *vu, integer *il,
integer *iu, integer *ns, real *s, real *u, integer *ldu, real *vt,
integer *ldvt, real *work, integer *lwork, integer *iwork, 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;
char ch__1[2];
/* Local variables */
integer iscl;
logical alls, inds;
integer ilqf;
real anrm;
integer ierr, iqrf, itau;
char jobz[1];
logical vals;
integer i__, j;
extern logical lsame_(char *, char *);
integer iltgk, itemp, minmn, itaup, itauq, iutgk, itgkz, mnthr;
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
integer *);
logical wantu;
integer id, ie;
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 *);
real abstol;
extern /* Subroutine */ void sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *), slacpy_(char *, integer
*, integer *, real *, integer *, real *, integer *);
char rngtgk[1];
extern /* Subroutine */ void slaset_(char *, integer *, integer *, real *,
real *, real *, integer *), sormbr_(char *, char *, char *
, integer *, integer *, integer *, real *, integer *, real *,
real *, integer *, real *, integer *, integer *);
integer minwrk, maxwrk;
real smlnum;
extern /* Subroutine */ void sormlq_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
logical lquery, wantvt;
extern /* Subroutine */ void sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
real dum[1], eps;
extern /* Subroutine */ void sbdsvdx_(char *, char *, char *, integer *,
real *, real *, real *, real *, integer *, integer *, integer *,
real *, real *, integer *, real *, integer *, integer *);
/* -- LAPACK driver routine (version 3.8.0) -- */
/* -- 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 */
*ns = 0;
*info = 0;
abstol = slamch_("S") * 2;
lquery = *lwork == -1;
minmn = f2cmin(*m,*n);
wantu = lsame_(jobu, "V");
wantvt = lsame_(jobvt, "V");
if (wantu || wantvt) {
*(unsigned char *)jobz = 'V';
} else {
*(unsigned char *)jobz = 'N';
}
alls = lsame_(range, "A");
vals = lsame_(range, "V");
inds = lsame_(range, "I");
*info = 0;
if (! lsame_(jobu, "V") && ! lsame_(jobu, "N")) {
*info = -1;
} else if (! lsame_(jobvt, "V") && ! lsame_(jobvt,
"N")) {
*info = -2;
} else if (! (alls || vals || inds)) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*m > *lda) {
*info = -7;
} else if (minmn > 0) {
if (vals) {
if (*vl < 0.f) {
*info = -8;
} else if (*vu <= *vl) {
*info = -9;
}
} else if (inds) {
if (*il < 1 || *il > f2cmax(1,minmn)) {
*info = -10;
} else if (*iu < f2cmin(minmn,*il) || *iu > minmn) {
*info = -11;
}
}
if (*info == 0) {
if (wantu && *ldu < *m) {
*info = -15;
} else if (wantvt) {
if (inds) {
if (*ldvt < *iu - *il + 1) {
*info = -17;
}
} else if (*ldvt < minmn) {
*info = -17;
}
}
}
}
/* 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 (minmn > 0) {
if (*m >= *n) {
/* 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);
if (*m >= mnthr) {
/* Path 1 (M much larger than N) */
maxwrk = *n + *n * ilaenv_(&c__1, "SGEQRF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * (*n + 5) + (*n << 1) * ilaenv_(
&c__1, "SGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)
6, (ftnlen)1);
maxwrk = f2cmax(i__2,i__3);
if (wantu) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * (*n * 3 + 6) + *n *
ilaenv_(&c__1, "SORMQR", " ", n, n, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__2,i__3);
}
if (wantvt) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * (*n * 3 + 6) + *n *
ilaenv_(&c__1, "SORMLQ", " ", n, n, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__2,i__3);
}
minwrk = *n * (*n * 3 + 20);
} else {
/* Path 2 (M at least N, but not much larger) */
maxwrk = (*n << 2) + (*m + *n) * ilaenv_(&c__1, "SGEBRD",
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
if (wantu) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * ((*n << 1) + 5) + *n *
ilaenv_(&c__1, "SORMQR", " ", n, n, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__2,i__3);
}
if (wantvt) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *n * ((*n << 1) + 5) + *n *
ilaenv_(&c__1, "SORMLQ", " ", n, n, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__2,i__3);
}
/* Computing MAX */
i__2 = *n * ((*n << 1) + 19), i__3 = (*n << 2) + *m;
minwrk = f2cmax(i__2,i__3);
}
} else {
/* 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);
if (*n >= mnthr) {
/* Path 1t (N much larger than M) */
maxwrk = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, &
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * (*m + 5) + (*m << 1) * ilaenv_(
&c__1, "SGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)
6, (ftnlen)1);
maxwrk = f2cmax(i__2,i__3);
if (wantu) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * (*m * 3 + 6) + *m *
ilaenv_(&c__1, "SORMQR", " ", m, m, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__2,i__3);
}
if (wantvt) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * (*m * 3 + 6) + *m *
ilaenv_(&c__1, "SORMLQ", " ", m, m, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__2,i__3);
}
minwrk = *m * (*m * 3 + 20);
} else {
/* Path 2t (N at least M, but not much larger) */
maxwrk = (*m << 2) + (*m + *n) * ilaenv_(&c__1, "SGEBRD",
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
if (wantu) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * ((*m << 1) + 5) + *m *
ilaenv_(&c__1, "SORMQR", " ", m, m, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__2,i__3);
}
if (wantvt) {
/* Computing MAX */
i__2 = maxwrk, i__3 = *m * ((*m << 1) + 5) + *m *
ilaenv_(&c__1, "SORMLQ", " ", m, m, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = f2cmax(i__2,i__3);
}
/* Computing MAX */
i__2 = *m * ((*m << 1) + 19), i__3 = (*m << 2) + *n;
minwrk = f2cmax(i__2,i__3);
}
}
}
maxwrk = f2cmax(maxwrk,minwrk);
work[1] = (real) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -19;
}
}
if (*info != 0) {
i__2 = -(*info);
xerbla_("SGESVDX", &i__2, (ftnlen)7);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return;
}
/* Set singular values indices accord to RANGE. */
if (alls) {
*(unsigned char *)rngtgk = 'I';
iltgk = 1;
iutgk = f2cmin(*m,*n);
} else if (inds) {
*(unsigned char *)rngtgk = 'I';
iltgk = *il;
iutgk = *iu;
} else {
*(unsigned char *)rngtgk = 'V';
iltgk = 0;
iutgk = 0;
}
/* Get machine constants */
eps = slamch_("P");
smlnum = sqrt(slamch_("S")) / eps;
bignum = 1.f / smlnum;
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
anrm = slange_("M", m, n, &a[a_offset], lda, dum);
iscl = 0;
if (anrm > 0.f && anrm < smlnum) {
iscl = 1;
slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
info);
} else if (anrm > bignum) {
iscl = 1;
slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
info);
}
if (*m >= *n) {
/* A has at least as many rows as columns. If A has sufficiently */
/* more rows than columns, first reduce A using the QR */
/* decomposition. */
if (*m >= mnthr) {
/* Path 1 (M much larger than N): */
/* A = Q * R = Q * ( QB * B * PB**T ) */
/* = Q * ( QB * ( UB * S * VB**T ) * PB**T ) */
/* U = Q * QB * UB; V**T = VB**T * PB**T */
/* Compute A=Q*R */
/* (Workspace: need 2*N, prefer N+N*NB) */
itau = 1;
itemp = itau + *n;
i__2 = *lwork - itemp + 1;
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[itemp], &i__2,
info);
/* Copy R into WORK and bidiagonalize it: */
/* (Workspace: need N*N+5*N, prefer N*N+4*N+2*N*NB) */
iqrf = itemp;
id = iqrf + *n * *n;
ie = id + *n;
itauq = ie + *n;
itaup = itauq + *n;
itemp = itaup + *n;
slacpy_("U", n, n, &a[a_offset], lda, &work[iqrf], n);
i__2 = *n - 1;
i__3 = *n - 1;
slaset_("L", &i__2, &i__3, &c_b109, &c_b109, &work[iqrf + 1], n);
i__2 = *lwork - itemp + 1;
sgebrd_(n, n, &work[iqrf], n, &work[id], &work[ie], &work[itauq],
&work[itaup], &work[itemp], &i__2, info);
/* Solve eigenvalue problem TGK*Z=Z*S. */
/* (Workspace: need 14*N + 2*N*(N+1)) */
itgkz = itemp;
itemp = itgkz + *n * ((*n << 1) + 1);
i__2 = *n << 1;
sbdsvdx_("U", jobz, rngtgk, n, &work[id], &work[ie], vl, vu, &
iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[
itemp], &iwork[1], info);
/* If needed, compute left singular vectors. */
if (wantu) {
j = itgkz;
i__2 = *ns;
for (i__ = 1; i__ <= i__2; ++i__) {
scopy_(n, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1);
j += *n << 1;
}
i__2 = *m - *n;
slaset_("A", &i__2, ns, &c_b109, &c_b109, &u[*n + 1 + u_dim1],
ldu);
/* Call SORMBR to compute QB*UB. */
/* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */
i__2 = *lwork - itemp + 1;
sormbr_("Q", "L", "N", n, ns, n, &work[iqrf], n, &work[itauq],
&u[u_offset], ldu, &work[itemp], &i__2, info);
/* Call SORMQR to compute Q*(QB*UB). */
/* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */
i__2 = *lwork - itemp + 1;
sormqr_("L", "N", m, ns, n, &a[a_offset], lda, &work[itau], &
u[u_offset], ldu, &work[itemp], &i__2, info);
}
/* If needed, compute right singular vectors. */
if (wantvt) {
j = itgkz + *n;
i__2 = *ns;
for (i__ = 1; i__ <= i__2; ++i__) {
scopy_(n, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt);
j += *n << 1;
}
/* Call SORMBR to compute VB**T * PB**T */
/* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */
i__2 = *lwork - itemp + 1;
sormbr_("P", "R", "T", ns, n, n, &work[iqrf], n, &work[itaup],
&vt[vt_offset], ldvt, &work[itemp], &i__2, info);
}
} else {
/* Path 2 (M at least N, but not much larger) */
/* Reduce A to bidiagonal form without QR decomposition */
/* A = QB * B * PB**T = QB * ( UB * S * VB**T ) * PB**T */
/* U = QB * UB; V**T = VB**T * PB**T */
/* Bidiagonalize A */
/* (Workspace: need 4*N+M, prefer 4*N+(M+N)*NB) */
id = 1;
ie = id + *n;
itauq = ie + *n;
itaup = itauq + *n;
itemp = itaup + *n;
i__2 = *lwork - itemp + 1;
sgebrd_(m, n, &a[a_offset], lda, &work[id], &work[ie], &work[
itauq], &work[itaup], &work[itemp], &i__2, info);
/* Solve eigenvalue problem TGK*Z=Z*S. */
/* (Workspace: need 14*N + 2*N*(N+1)) */
itgkz = itemp;
itemp = itgkz + *n * ((*n << 1) + 1);
i__2 = *n << 1;
sbdsvdx_("U", jobz, rngtgk, n, &work[id], &work[ie], vl, vu, &
iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[
itemp], &iwork[1], info);
/* If needed, compute left singular vectors. */
if (wantu) {
j = itgkz;
i__2 = *ns;
for (i__ = 1; i__ <= i__2; ++i__) {
scopy_(n, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1);
j += *n << 1;
}
i__2 = *m - *n;
slaset_("A", &i__2, ns, &c_b109, &c_b109, &u[*n + 1 + u_dim1],
ldu);
/* Call SORMBR to compute QB*UB. */
/* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */
i__2 = *lwork - itemp + 1;
sormbr_("Q", "L", "N", m, ns, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[itemp], &i__2, &ierr);
}
/* If needed, compute right singular vectors. */
if (wantvt) {
j = itgkz + *n;
i__2 = *ns;
for (i__ = 1; i__ <= i__2; ++i__) {
scopy_(n, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt);
j += *n << 1;
}
/* Call SORMBR to compute VB**T * PB**T */
/* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */
i__2 = *lwork - itemp + 1;
sormbr_("P", "R", "T", ns, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[itemp], &i__2, &
ierr);
}
}
} else {
/* A has more columns than rows. If A has sufficiently more */
/* columns than rows, first reduce A using the LQ decomposition. */
if (*n >= mnthr) {
/* Path 1t (N much larger than M): */
/* A = L * Q = ( QB * B * PB**T ) * Q */
/* = ( QB * ( UB * S * VB**T ) * PB**T ) * Q */
/* U = QB * UB ; V**T = VB**T * PB**T * Q */
/* Compute A=L*Q */
/* (Workspace: need 2*M, prefer M+M*NB) */
itau = 1;
itemp = itau + *m;
i__2 = *lwork - itemp + 1;
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[itemp], &i__2,
info);
/* Copy L into WORK and bidiagonalize it: */
/* (Workspace in WORK( ITEMP ): need M*M+5*N, prefer M*M+4*M+2*M*NB) */
ilqf = itemp;
id = ilqf + *m * *m;
ie = id + *m;
itauq = ie + *m;
itaup = itauq + *m;
itemp = itaup + *m;
slacpy_("L", m, m, &a[a_offset], lda, &work[ilqf], m);
i__2 = *m - 1;
i__3 = *m - 1;
slaset_("U", &i__2, &i__3, &c_b109, &c_b109, &work[ilqf + *m], m);
i__2 = *lwork - itemp + 1;
sgebrd_(m, m, &work[ilqf], m, &work[id], &work[ie], &work[itauq],
&work[itaup], &work[itemp], &i__2, info);
/* Solve eigenvalue problem TGK*Z=Z*S. */
/* (Workspace: need 2*M*M+14*M) */
itgkz = itemp;
itemp = itgkz + *m * ((*m << 1) + 1);
i__2 = *m << 1;
sbdsvdx_("U", jobz, rngtgk, m, &work[id], &work[ie], vl, vu, &
iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[
itemp], &iwork[1], info);
/* If needed, compute left singular vectors. */
if (wantu) {
j = itgkz;
i__2 = *ns;
for (i__ = 1; i__ <= i__2; ++i__) {
scopy_(m, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1);
j += *m << 1;
}
/* Call SORMBR to compute QB*UB. */
/* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */
i__2 = *lwork - itemp + 1;
sormbr_("Q", "L", "N", m, ns, m, &work[ilqf], m, &work[itauq],
&u[u_offset], ldu, &work[itemp], &i__2, info);
}
/* If needed, compute right singular vectors. */
if (wantvt) {
j = itgkz + *m;
i__2 = *ns;
for (i__ = 1; i__ <= i__2; ++i__) {
scopy_(m, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt);
j += *m << 1;
}
i__2 = *n - *m;
slaset_("A", ns, &i__2, &c_b109, &c_b109, &vt[(*m + 1) *
vt_dim1 + 1], ldvt);
/* Call SORMBR to compute (VB**T)*(PB**T) */
/* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */
i__2 = *lwork - itemp + 1;
sormbr_("P", "R", "T", ns, m, m, &work[ilqf], m, &work[itaup],
&vt[vt_offset], ldvt, &work[itemp], &i__2, info);
/* Call SORMLQ to compute ((VB**T)*(PB**T))*Q. */
/* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */
i__2 = *lwork - itemp + 1;
sormlq_("R", "N", ns, n, m, &a[a_offset], lda, &work[itau], &
vt[vt_offset], ldvt, &work[itemp], &i__2, info);
}
} else {
/* Path 2t (N greater than M, but not much larger) */
/* Reduce to bidiagonal form without LQ decomposition */
/* A = QB * B * PB**T = QB * ( UB * S * VB**T ) * PB**T */
/* U = QB * UB; V**T = VB**T * PB**T */
/* Bidiagonalize A */
/* (Workspace: need 4*M+N, prefer 4*M+(M+N)*NB) */
id = 1;
ie = id + *m;
itauq = ie + *m;
itaup = itauq + *m;
itemp = itaup + *m;
i__2 = *lwork - itemp + 1;
sgebrd_(m, n, &a[a_offset], lda, &work[id], &work[ie], &work[
itauq], &work[itaup], &work[itemp], &i__2, info);
/* Solve eigenvalue problem TGK*Z=Z*S. */
/* (Workspace: need 2*M*M+14*M) */
itgkz = itemp;
itemp = itgkz + *m * ((*m << 1) + 1);
i__2 = *m << 1;
sbdsvdx_("L", jobz, rngtgk, m, &work[id], &work[ie], vl, vu, &
iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[
itemp], &iwork[1], info);
/* If needed, compute left singular vectors. */
if (wantu) {
j = itgkz;
i__2 = *ns;
for (i__ = 1; i__ <= i__2; ++i__) {
scopy_(m, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1);
j += *m << 1;
}
/* Call SORMBR to compute QB*UB. */
/* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */
i__2 = *lwork - itemp + 1;
sormbr_("Q", "L", "N", m, ns, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[itemp], &i__2, info);
}
/* If needed, compute right singular vectors. */
if (wantvt) {
j = itgkz + *m;
i__2 = *ns;
for (i__ = 1; i__ <= i__2; ++i__) {
scopy_(m, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt);
j += *m << 1;
}
i__2 = *n - *m;
slaset_("A", ns, &i__2, &c_b109, &c_b109, &vt[(*m + 1) *
vt_dim1 + 1], ldvt);
/* Call SORMBR to compute VB**T * PB**T */
/* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */
i__2 = *lwork - itemp + 1;
sormbr_("P", "R", "T", ns, n, m, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[itemp], &i__2,
info);
}
}
}
/* Undo scaling if necessary */
if (iscl == 1) {
if (anrm > bignum) {
slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
}
if (anrm < smlnum) {
slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
}
}
/* Return optimal workspace in WORK(1) */
work[1] = (real) maxwrk;
return;
/* End of SGESVDX */
} /* sgesvdx_ */
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