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OpenBLAS/lapack-netlib/SRC/sgesvdq.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 pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
/* procedure parameter types for -A and -C++ */
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif
static float spow_ui(float x, integer n) {
float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static double dpow_ui(double x, integer n) {
double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
complex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
for(u = n; ; ) {
if(u & 01) pow.r *= x.r, pow.i *= x.i;
if(u >>= 1) x.r *= x.r, x.i *= x.i;
else break;
}
}
_Fcomplex p={pow.r, pow.i};
return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
_Complex float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
_Dcomplex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
for(u = n; ; ) {
if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
else break;
}
}
_Dcomplex p = {pow._Val[0], pow._Val[1]};
return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
_Complex double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
integer pow; unsigned long int u;
if (n <= 0) {
if (n == 0 || x == 1) pow = 1;
else if (x != -1) pow = x == 0 ? 1/x : 0;
else n = -n;
}
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
u = n;
for(pow = 1; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
double m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
float m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i]) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i]) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static integer c_n1 = -1;
static integer c__1 = 1;
static real c_b72 = 0.f;
static real c_b76 = 1.f;
static integer c__0 = 0;
static logical c_false = FALSE_;
/* > \brief <b> SGESVDQ computes the singular value decomposition (SVD) with a QR-Preconditioned QR SVD Method
for GE matrices</b> */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGESVDQ + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgesvdq
.f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgesvdq
.f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgesvdq
.f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGESVDQ( JOBA, JOBP, JOBR, JOBU, JOBV, M, N, A, LDA, */
/* S, U, LDU, V, LDV, NUMRANK, IWORK, LIWORK, */
/* WORK, LWORK, RWORK, LRWORK, INFO ) */
/* IMPLICIT NONE */
/* CHARACTER JOBA, JOBP, JOBR, JOBU, JOBV */
/* INTEGER M, N, LDA, LDU, LDV, NUMRANK, LIWORK, LWORK, LRWORK, */
/* INFO */
/* REAL A( LDA, * ), U( LDU, * ), V( LDV, * ), WORK( * ) */
/* REAL S( * ), RWORK( * ) */
/* INTEGER IWORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGESVDQ computes the singular value decomposition (SVD) of a real */
/* > M-by-N matrix A, where M >= N. The SVD of A is written as */
/* > [++] [xx] [x0] [xx] */
/* > A = U * SIGMA * V^*, [++] = [xx] * [ox] * [xx] */
/* > [++] [xx] */
/* > where SIGMA is an N-by-N diagonal matrix, U is an M-by-N orthonormal */
/* > matrix, and V is an N-by-N orthogonal matrix. The diagonal elements */
/* > of SIGMA are the singular values of A. The columns of U and V are the */
/* > left and the right singular vectors of A, respectively. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOBA */
/* > \verbatim */
/* > JOBA is CHARACTER*1 */
/* > Specifies the level of accuracy in the computed SVD */
/* > = 'A' The requested accuracy corresponds to having the backward */
/* > error bounded by || delta A ||_F <= f(m,n) * EPS * || A ||_F, */
/* > where EPS = SLAMCH('Epsilon'). This authorises CGESVDQ to */
/* > truncate the computed triangular factor in a rank revealing */
/* > QR factorization whenever the truncated part is below the */
/* > threshold of the order of EPS * ||A||_F. This is aggressive */
/* > truncation level. */
/* > = 'M' Similarly as with 'A', but the truncation is more gentle: it */
/* > is allowed only when there is a drop on the diagonal of the */
/* > triangular factor in the QR factorization. This is medium */
/* > truncation level. */
/* > = 'H' High accuracy requested. No numerical rank determination based */
/* > on the rank revealing QR factorization is attempted. */
/* > = 'E' Same as 'H', and in addition the condition number of column */
/* > scaled A is estimated and returned in RWORK(1). */
/* > N^(-1/4)*RWORK(1) <= ||pinv(A_scaled)||_2 <= N^(1/4)*RWORK(1) */
/* > \endverbatim */
/* > */
/* > \param[in] JOBP */
/* > \verbatim */
/* > JOBP is CHARACTER*1 */
/* > = 'P' The rows of A are ordered in decreasing order with respect to */
/* > ||A(i,:)||_\infty. This enhances numerical accuracy at the cost */
/* > of extra data movement. Recommended for numerical robustness. */
/* > = 'N' No row pivoting. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBR */
/* > \verbatim */
/* > JOBR is CHARACTER*1 */
/* > = 'T' After the initial pivoted QR factorization, SGESVD is applied to */
/* > the transposed R**T of the computed triangular factor R. This involves */
/* > some extra data movement (matrix transpositions). Useful for */
/* > experiments, research and development. */
/* > = 'N' The triangular factor R is given as input to SGESVD. This may be */
/* > preferred as it involves less data movement. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBU */
/* > \verbatim */
/* > JOBU is CHARACTER*1 */
/* > = 'A' All M left singular vectors are computed and returned in the */
/* > matrix U. See the description of U. */
/* > = 'S' or 'U' N = f2cmin(M,N) left singular vectors are computed and returned */
/* > in the matrix U. See the description of U. */
/* > = 'R' Numerical rank NUMRANK is determined and only NUMRANK left singular */
/* > vectors are computed and returned in the matrix U. */
/* > = 'F' The N left singular vectors are returned in factored form as the */
/* > product of the Q factor from the initial QR factorization and the */
/* > N left singular vectors of (R**T , 0)**T. If row pivoting is used, */
/* > then the necessary information on the row pivoting is stored in */
/* > IWORK(N+1:N+M-1). */
/* > = 'N' The left singular vectors are not computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBV */
/* > \verbatim */
/* > JOBV is CHARACTER*1 */
/* > = 'A', 'V' All N right singular vectors are computed and returned in */
/* > the matrix V. */
/* > = 'R' Numerical rank NUMRANK is determined and only NUMRANK right singular */
/* > vectors are computed and returned in the matrix V. This option is */
/* > allowed only if JOBU = 'R' or JOBU = 'N'; otherwise it is illegal. */
/* > = 'N' The right singular vectors are not 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. M >= N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is REAL array of dimensions LDA x N */
/* > On entry, the input matrix A. */
/* > On exit, if JOBU .NE. 'N' or JOBV .NE. 'N', the lower triangle of A contains */
/* > the Householder vectors as stored by SGEQP3. If JOBU = 'F', these Householder */
/* > vectors together with WORK(1:N) can be used to restore the Q factors from */
/* > the initial pivoted QR factorization of A. See the description of U. */
/* > \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 of dimension N. */
/* > The singular values of A, ordered so that S(i) >= S(i+1). */
/* > \endverbatim */
/* > */
/* > \param[out] U */
/* > \verbatim */
/* > U is REAL array, dimension */
/* > LDU x M if JOBU = 'A'; see the description of LDU. In this case, */
/* > on exit, U contains the M left singular vectors. */
/* > LDU x N if JOBU = 'S', 'U', 'R' ; see the description of LDU. In this */
/* > case, U contains the leading N or the leading NUMRANK left singular vectors. */
/* > LDU x N if JOBU = 'F' ; see the description of LDU. In this case U */
/* > contains N x N orthogonal matrix that can be used to form the left */
/* > singular vectors. */
/* > If JOBU = 'N', U is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* > LDU is INTEGER. */
/* > The leading dimension of the array U. */
/* > If JOBU = 'A', 'S', 'U', 'R', LDU >= f2cmax(1,M). */
/* > If JOBU = 'F', LDU >= f2cmax(1,N). */
/* > Otherwise, LDU >= 1. */
/* > \endverbatim */
/* > */
/* > \param[out] V */
/* > \verbatim */
/* > V is REAL array, dimension */
/* > LDV x N if JOBV = 'A', 'V', 'R' or if JOBA = 'E' . */
/* > If JOBV = 'A', or 'V', V contains the N-by-N orthogonal matrix V**T; */
/* > If JOBV = 'R', V contains the first NUMRANK rows of V**T (the right */
/* > singular vectors, stored rowwise, of the NUMRANK largest singular values). */
/* > If JOBV = 'N' and JOBA = 'E', V is used as a workspace. */
/* > If JOBV = 'N', and JOBA.NE.'E', V is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDV */
/* > \verbatim */
/* > LDV is INTEGER */
/* > The leading dimension of the array V. */
/* > If JOBV = 'A', 'V', 'R', or JOBA = 'E', LDV >= f2cmax(1,N). */
/* > Otherwise, LDV >= 1. */
/* > \endverbatim */
/* > */
/* > \param[out] NUMRANK */
/* > \verbatim */
/* > NUMRANK is INTEGER */
/* > NUMRANK is the numerical rank first determined after the rank */
/* > revealing QR factorization, following the strategy specified by the */
/* > value of JOBA. If JOBV = 'R' and JOBU = 'R', only NUMRANK */
/* > leading singular values and vectors are then requested in the call */
/* > of SGESVD. The final value of NUMRANK might be further reduced if */
/* > some singular values are computed as zeros. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (f2cmax(1, LIWORK)). */
/* > On exit, IWORK(1:N) contains column pivoting permutation of the */
/* > rank revealing QR factorization. */
/* > If JOBP = 'P', IWORK(N+1:N+M-1) contains the indices of the sequence */
/* > of row swaps used in row pivoting. These can be used to restore the */
/* > left singular vectors in the case JOBU = 'F'. */
/* > */
/* > If LIWORK, LWORK, or LRWORK = -1, then on exit, if INFO = 0, */
/* > LIWORK(1) returns the minimal LIWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LIWORK */
/* > \verbatim */
/* > LIWORK is INTEGER */
/* > The dimension of the array IWORK. */
/* > LIWORK >= N + M - 1, if JOBP = 'P' and JOBA .NE. 'E'; */
/* > LIWORK >= N if JOBP = 'N' and JOBA .NE. 'E'; */
/* > LIWORK >= N + M - 1 + N, if JOBP = 'P' and JOBA = 'E'; */
/* > LIWORK >= N + N if JOBP = 'N' and JOBA = 'E'. */
/* > If LIWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates and returns the optimal and minimal sizes */
/* > for the WORK, IWORK, and RWORK arrays, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (f2cmax(2, LWORK)), used as a workspace. */
/* > On exit, if, on entry, LWORK.NE.-1, WORK(1:N) contains parameters */
/* > needed to recover the Q factor from the QR factorization computed by */
/* > SGEQP3. */
/* > */
/* > If LIWORK, LWORK, or LRWORK = -1, then on exit, if INFO = 0, */
/* > WORK(1) returns the optimal LWORK, and */
/* > WORK(2) returns the minimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in,out] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. It is determined as follows: */
/* > Let LWQP3 = 3*N+1, LWCON = 3*N, and let */
/* > LWORQ = { MAX( N, 1 ), if JOBU = 'R', 'S', or 'U' */
/* > { MAX( M, 1 ), if JOBU = 'A' */
/* > LWSVD = MAX( 5*N, 1 ) */
/* > LWLQF = MAX( N/2, 1 ), LWSVD2 = MAX( 5*(N/2), 1 ), LWORLQ = MAX( N, 1 ), */
/* > LWQRF = MAX( N/2, 1 ), LWORQ2 = MAX( N, 1 ) */
/* > Then the minimal value of LWORK is: */
/* > = MAX( N + LWQP3, LWSVD ) if only the singular values are needed; */
/* > = MAX( N + LWQP3, LWCON, LWSVD ) if only the singular values are needed, */
/* > and a scaled condition estimate requested; */
/* > */
/* > = N + MAX( LWQP3, LWSVD, LWORQ ) if the singular values and the left */
/* > singular vectors are requested; */
/* > = N + MAX( LWQP3, LWCON, LWSVD, LWORQ ) if the singular values and the left */
/* > singular vectors are requested, and also */
/* > a scaled condition estimate requested; */
/* > */
/* > = N + MAX( LWQP3, LWSVD ) if the singular values and the right */
/* > singular vectors are requested; */
/* > = N + MAX( LWQP3, LWCON, LWSVD ) if the singular values and the right */
/* > singular vectors are requested, and also */
/* > a scaled condition etimate requested; */
/* > */
/* > = N + MAX( LWQP3, LWSVD, LWORQ ) if the full SVD is requested with JOBV = 'R'; */
/* > independent of JOBR; */
/* > = N + MAX( LWQP3, LWCON, LWSVD, LWORQ ) if the full SVD is requested, */
/* > JOBV = 'R' and, also a scaled condition */
/* > estimate requested; independent of JOBR; */
/* > = MAX( N + MAX( LWQP3, LWSVD, LWORQ ), */
/* > N + MAX( LWQP3, N/2+LWLQF, N/2+LWSVD2, N/2+LWORLQ, LWORQ) ) if the */
/* > full SVD is requested with JOBV = 'A' or 'V', and */
/* > JOBR ='N' */
/* > = MAX( N + MAX( LWQP3, LWCON, LWSVD, LWORQ ), */
/* > N + MAX( LWQP3, LWCON, N/2+LWLQF, N/2+LWSVD2, N/2+LWORLQ, LWORQ ) ) */
/* > if the full SVD is requested with JOBV = 'A' or 'V', and */
/* > JOBR ='N', and also a scaled condition number estimate */
/* > requested. */
/* > = MAX( N + MAX( LWQP3, LWSVD, LWORQ ), */
/* > N + MAX( LWQP3, N/2+LWQRF, N/2+LWSVD2, N/2+LWORQ2, LWORQ ) ) if the */
/* > full SVD is requested with JOBV = 'A', 'V', and JOBR ='T' */
/* > = MAX( N + MAX( LWQP3, LWCON, LWSVD, LWORQ ), */
/* > N + MAX( LWQP3, LWCON, N/2+LWQRF, N/2+LWSVD2, N/2+LWORQ2, LWORQ ) ) */
/* > if the full SVD is requested with JOBV = 'A' or 'V', and */
/* > JOBR ='T', and also a scaled condition number estimate */
/* > requested. */
/* > Finally, LWORK must be at least two: LWORK = MAX( 2, LWORK ). */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates and returns the optimal and minimal sizes */
/* > for the WORK, IWORK, and RWORK arrays, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* > RWORK is REAL array, dimension (f2cmax(1, LRWORK)). */
/* > On exit, */
/* > 1. If JOBA = 'E', RWORK(1) contains an estimate of the condition */
/* > number of column scaled A. If A = C * D where D is diagonal and C */
/* > has unit columns in the Euclidean norm, then, assuming full column rank, */
/* > N^(-1/4) * RWORK(1) <= ||pinv(C)||_2 <= N^(1/4) * RWORK(1). */
/* > Otherwise, RWORK(1) = -1. */
/* > 2. RWORK(2) contains the number of singular values computed as */
/* > exact zeros in SGESVD applied to the upper triangular or trapeziodal */
/* > R (from the initial QR factorization). In case of early exit (no call to */
/* > SGESVD, such as in the case of zero matrix) RWORK(2) = -1. */
/* > */
/* > If LIWORK, LWORK, or LRWORK = -1, then on exit, if INFO = 0, */
/* > RWORK(1) returns the minimal LRWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LRWORK */
/* > \verbatim */
/* > LRWORK is INTEGER. */
/* > The dimension of the array RWORK. */
/* > If JOBP ='P', then LRWORK >= MAX(2, M). */
/* > Otherwise, LRWORK >= 2 */
/* > If LRWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates and returns the optimal and minimal sizes */
/* > for the WORK, IWORK, and RWORK arrays, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > > 0: if SBDSQR did not converge, INFO specifies how many superdiagonals */
/* > of an intermediate bidiagonal form B (computed in SGESVD) did not */
/* > converge to zero. */
/* > \endverbatim */
/* > \par Further Details: */
/* ======================== */
/* > */
/* > \verbatim */
/* > */
/* > 1. The data movement (matrix transpose) is coded using simple nested */
/* > DO-loops because BLAS and LAPACK do not provide corresponding subroutines. */
/* > Those DO-loops are easily identified in this source code - by the CONTINUE */
/* > statements labeled with 11**. In an optimized version of this code, the */
/* > nested DO loops should be replaced with calls to an optimized subroutine. */
/* > 2. This code scales A by 1/SQRT(M) if the largest ABS(A(i,j)) could cause */
/* > column norm overflow. This is the minial precaution and it is left to the */
/* > SVD routine (CGESVD) to do its own preemptive scaling if potential over- */
/* > or underflows are detected. To avoid repeated scanning of the array A, */
/* > an optimal implementation would do all necessary scaling before calling */
/* > CGESVD and the scaling in CGESVD can be switched off. */
/* > 3. Other comments related to code optimization are given in comments in the */
/* > code, enlosed in [[double brackets]]. */
/* > \endverbatim */
/* > \par Bugs, examples and comments */
/* =========================== */
/* > \verbatim */
/* > Please report all bugs and send interesting examples and/or comments to */
/* > drmac@math.hr. Thank you. */
/* > \endverbatim */
/* > \par References */
/* =============== */
/* > \verbatim */
/* > [1] Zlatko Drmac, Algorithm 977: A QR-Preconditioned QR SVD Method for */
/* > Computing the SVD with High Accuracy. ACM Trans. Math. Softw. */
/* > 44(1): 11:1-11:30 (2017) */
/* > */
/* > SIGMA library, xGESVDQ section updated February 2016. */
/* > Developed and coded by Zlatko Drmac, Department of Mathematics */
/* > University of Zagreb, Croatia, drmac@math.hr */
/* > \endverbatim */
/* > \par Contributors: */
/* ================== */
/* > */
/* > \verbatim */
/* > Developed and coded by Zlatko Drmac, Department of Mathematics */
/* > University of Zagreb, Croatia, drmac@math.hr */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date November 2018 */
/* > \ingroup realGEsing */
/* ===================================================================== */
/* Subroutine */ void sgesvdq_(char *joba, char *jobp, char *jobr, char *jobu,
char *jobv, integer *m, integer *n, real *a, integer *lda, real *s,
real *u, integer *ldu, real *v, integer *ldv, integer *numrank,
integer *iwork, integer *liwork, real *work, integer *lwork, real *
rwork, integer *lrwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, u_dim1, u_offset, v_dim1, v_offset, i__1, i__2;
real r__1, r__2, r__3;
/* Local variables */
integer lwrk_sormlq__, lwrk_sormqr__, ierr, lwrk_sgesvd2__;
real rtmp;
integer lwrk_sormqr2__, optratio;
logical lsvc0;
extern real snrm2_(integer *, real *, integer *);
logical accla;
integer lwqp3;
logical acclh, acclm;
integer p, q;
logical conda;
extern logical lsame_(char *, char *);
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
integer iwoff;
logical lsvec;
real sfmin, epsln;
integer lwcon;
logical rsvec;
integer lwlqf, lwqrf, n1, lwsvd;
logical dntwu, dntwv, wntua;
integer lworq;
logical wntuf, wntva, wntur, wntus, wntvr;
extern /* Subroutine */ void sgeqp3_(integer *, integer *, real *, integer
*, integer *, real *, real *, integer *, integer *);
integer lwsvd2, lworq2, nr;
real sconda;
extern real slamch_(char *), slange_(char *, integer *, integer *,
real *, integer *, real *);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern void sgelqf_(
integer *, integer *, real *, integer *, real *, real *, integer *
, integer *), slascl_(char *, integer *, integer *, real *, real *
, integer *, integer *, real *, integer *, integer *);
extern integer isamax_(integer *, real *, integer *);
extern /* Subroutine */ void sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *), sgesvd_(char *, char *,
integer *, integer *, real *, integer *, real *, real *, integer *
, real *, integer *, real *, integer *, integer *)
, slacpy_(char *, integer *, integer *, real *, integer *, real *,
integer *), slaset_(char *, integer *, integer *, real *,
real *, real *, integer *), slapmt_(logical *, integer *,
integer *, real *, integer *, integer *), spocon_(char *,
integer *, real *, integer *, real *, real *, real *, integer *,
integer *);
integer minwrk;
logical rtrans;
extern /* Subroutine */ int slaswp_(integer *, real *, integer *, integer
*, integer *, integer *, integer *);
real rdummy[1];
extern /* Subroutine */ void sormlq_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
logical lquery;
integer lwunlq;
extern /* Subroutine */ void sormqr_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, real *, integer *, real *,
integer *, integer *);
integer optwrk;
logical rowprm;
real big;
integer minwrk2;
logical ascaled;
integer optwrk2, lwrk_sgeqp3__, iminwrk, rminwrk, lwrk_sgelqf__,
lwrk_sgeqrf__, lwrk_sgesvd__;
/* ===================================================================== */
/* 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;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
--iwork;
--work;
--rwork;
/* Function Body */
wntus = lsame_(jobu, "S") || lsame_(jobu, "U");
wntur = lsame_(jobu, "R");
wntua = lsame_(jobu, "A");
wntuf = lsame_(jobu, "F");
lsvc0 = wntus || wntur || wntua;
lsvec = lsvc0 || wntuf;
dntwu = lsame_(jobu, "N");
wntvr = lsame_(jobv, "R");
wntva = lsame_(jobv, "A") || lsame_(jobv, "V");
rsvec = wntvr || wntva;
dntwv = lsame_(jobv, "N");
accla = lsame_(joba, "A");
acclm = lsame_(joba, "M");
conda = lsame_(joba, "E");
acclh = lsame_(joba, "H") || conda;
rowprm = lsame_(jobp, "P");
rtrans = lsame_(jobr, "T");
if (rowprm) {
if (conda) {
/* Computing MAX */
i__1 = 1, i__2 = *n + *m - 1 + *n;
iminwrk = f2cmax(i__1,i__2);
} else {
/* Computing MAX */
i__1 = 1, i__2 = *n + *m - 1;
iminwrk = f2cmax(i__1,i__2);
}
rminwrk = f2cmax(2,*m);
} else {
if (conda) {
/* Computing MAX */
i__1 = 1, i__2 = *n + *n;
iminwrk = f2cmax(i__1,i__2);
} else {
iminwrk = f2cmax(1,*n);
}
rminwrk = 2;
}
lquery = *liwork == -1 || *lwork == -1 || *lrwork == -1;
*info = 0;
if (! (accla || acclm || acclh)) {
*info = -1;
} else if (! (rowprm || lsame_(jobp, "N"))) {
*info = -2;
} else if (! (rtrans || lsame_(jobr, "N"))) {
*info = -3;
} else if (! (lsvec || dntwu)) {
*info = -4;
} else if (wntur && wntva) {
*info = -5;
} else if (! (rsvec || dntwv)) {
*info = -5;
} else if (*m < 0) {
*info = -6;
} else if (*n < 0 || *n > *m) {
*info = -7;
} else if (*lda < f2cmax(1,*m)) {
*info = -9;
} else if (*ldu < 1 || lsvc0 && *ldu < *m || wntuf && *ldu < *n) {
*info = -12;
} else if (*ldv < 1 || rsvec && *ldv < *n || conda && *ldv < *n) {
*info = -14;
} else if (*liwork < iminwrk && ! lquery) {
*info = -17;
}
if (*info == 0) {
/* [[The expressions for computing the minimal and the optimal */
/* values of LWORK are written with a lot of redundancy and */
/* can be simplified. However, this detailed form is easier for */
/* maintenance and modifications of the code.]] */
lwqp3 = *n * 3 + 1;
if (wntus || wntur) {
lworq = f2cmax(*n,1);
} else if (wntua) {
lworq = f2cmax(*m,1);
}
lwcon = *n * 3;
/* Computing MAX */
i__1 = *n * 5;
lwsvd = f2cmax(i__1,1);
if (lquery) {
sgeqp3_(m, n, &a[a_offset], lda, &iwork[1], rdummy, rdummy, &c_n1,
&ierr);
lwrk_sgeqp3__ = (integer) rdummy[0];
if (wntus || wntur) {
sormqr_("L", "N", m, n, n, &a[a_offset], lda, rdummy, &u[
u_offset], ldu, rdummy, &c_n1, &ierr);
lwrk_sormqr__ = (integer) rdummy[0];
} else if (wntua) {
sormqr_("L", "N", m, m, n, &a[a_offset], lda, rdummy, &u[
u_offset], ldu, rdummy, &c_n1, &ierr);
lwrk_sormqr__ = (integer) rdummy[0];
} else {
lwrk_sormqr__ = 0;
}
}
minwrk = 2;
optwrk = 2;
if (! (lsvec || rsvec)) {
/* only the singular values are requested */
if (conda) {
/* Computing MAX */
i__1 = *n + lwqp3, i__1 = f2cmax(i__1,lwcon);
minwrk = f2cmax(i__1,lwsvd);
} else {
/* Computing MAX */
i__1 = *n + lwqp3;
minwrk = f2cmax(i__1,lwsvd);
}
if (lquery) {
sgesvd_("N", "N", n, n, &a[a_offset], lda, &s[1], &u[u_offset]
, ldu, &v[v_offset], ldv, rdummy, &c_n1, &ierr);
lwrk_sgesvd__ = (integer) rdummy[0];
if (conda) {
/* Computing MAX */
i__1 = *n + lwrk_sgeqp3__, i__2 = *n + lwcon, i__1 = f2cmax(
i__1,i__2);
optwrk = f2cmax(i__1,lwrk_sgesvd__);
} else {
/* Computing MAX */
i__1 = *n + lwrk_sgeqp3__;
optwrk = f2cmax(i__1,lwrk_sgesvd__);
}
}
} else if (lsvec && ! rsvec) {
/* singular values and the left singular vectors are requested */
if (conda) {
/* Computing MAX */
i__1 = f2cmax(lwqp3,lwcon), i__1 = f2cmax(i__1,lwsvd);
minwrk = *n + f2cmax(i__1,lworq);
} else {
/* Computing MAX */
i__1 = f2cmax(lwqp3,lwsvd);
minwrk = *n + f2cmax(i__1,lworq);
}
if (lquery) {
if (rtrans) {
sgesvd_("N", "O", n, n, &a[a_offset], lda, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, rdummy, &c_n1,
&ierr);
} else {
sgesvd_("O", "N", n, n, &a[a_offset], lda, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, rdummy, &c_n1,
&ierr);
}
lwrk_sgesvd__ = (integer) rdummy[0];
if (conda) {
/* Computing MAX */
i__1 = f2cmax(lwrk_sgeqp3__,lwcon), i__1 = f2cmax(i__1,
lwrk_sgesvd__);
optwrk = *n + f2cmax(i__1,lwrk_sormqr__);
} else {
/* Computing MAX */
i__1 = f2cmax(lwrk_sgeqp3__,lwrk_sgesvd__);
optwrk = *n + f2cmax(i__1,lwrk_sormqr__);
}
}
} else if (rsvec && ! lsvec) {
/* singular values and the right singular vectors are requested */
if (conda) {
/* Computing MAX */
i__1 = f2cmax(lwqp3,lwcon);
minwrk = *n + f2cmax(i__1,lwsvd);
} else {
minwrk = *n + f2cmax(lwqp3,lwsvd);
}
if (lquery) {
if (rtrans) {
sgesvd_("O", "N", n, n, &a[a_offset], lda, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, rdummy, &c_n1,
&ierr);
} else {
sgesvd_("N", "O", n, n, &a[a_offset], lda, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, rdummy, &c_n1,
&ierr);
}
lwrk_sgesvd__ = (integer) rdummy[0];
if (conda) {
/* Computing MAX */
i__1 = f2cmax(lwrk_sgeqp3__,lwcon);
optwrk = *n + f2cmax(i__1,lwrk_sgesvd__);
} else {
optwrk = *n + f2cmax(lwrk_sgeqp3__,lwrk_sgesvd__);
}
}
} else {
/* full SVD is requested */
if (rtrans) {
/* Computing MAX */
i__1 = f2cmax(lwqp3,lwsvd);
minwrk = f2cmax(i__1,lworq);
if (conda) {
minwrk = f2cmax(minwrk,lwcon);
}
minwrk += *n;
if (wntva) {
/* Computing MAX */
i__1 = *n / 2;
lwqrf = f2cmax(i__1,1);
/* Computing MAX */
i__1 = *n / 2 * 5;
lwsvd2 = f2cmax(i__1,1);
lworq2 = f2cmax(*n,1);
/* Computing MAX */
i__1 = lwqp3, i__2 = *n / 2 + lwqrf, i__1 = f2cmax(i__1,i__2)
, i__2 = *n / 2 + lwsvd2, i__1 = f2cmax(i__1,i__2),
i__2 = *n / 2 + lworq2, i__1 = f2cmax(i__1,i__2);
minwrk2 = f2cmax(i__1,lworq);
if (conda) {
minwrk2 = f2cmax(minwrk2,lwcon);
}
minwrk2 = *n + minwrk2;
minwrk = f2cmax(minwrk,minwrk2);
}
} else {
/* Computing MAX */
i__1 = f2cmax(lwqp3,lwsvd);
minwrk = f2cmax(i__1,lworq);
if (conda) {
minwrk = f2cmax(minwrk,lwcon);
}
minwrk += *n;
if (wntva) {
/* Computing MAX */
i__1 = *n / 2;
lwlqf = f2cmax(i__1,1);
/* Computing MAX */
i__1 = *n / 2 * 5;
lwsvd2 = f2cmax(i__1,1);
lwunlq = f2cmax(*n,1);
/* Computing MAX */
i__1 = lwqp3, i__2 = *n / 2 + lwlqf, i__1 = f2cmax(i__1,i__2)
, i__2 = *n / 2 + lwsvd2, i__1 = f2cmax(i__1,i__2),
i__2 = *n / 2 + lwunlq, i__1 = f2cmax(i__1,i__2);
minwrk2 = f2cmax(i__1,lworq);
if (conda) {
minwrk2 = f2cmax(minwrk2,lwcon);
}
minwrk2 = *n + minwrk2;
minwrk = f2cmax(minwrk,minwrk2);
}
}
if (lquery) {
if (rtrans) {
sgesvd_("O", "A", n, n, &a[a_offset], lda, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, rdummy, &c_n1,
&ierr);
lwrk_sgesvd__ = (integer) rdummy[0];
/* Computing MAX */
i__1 = f2cmax(lwrk_sgeqp3__,lwrk_sgesvd__);
optwrk = f2cmax(i__1,lwrk_sormqr__);
if (conda) {
optwrk = f2cmax(optwrk,lwcon);
}
optwrk = *n + optwrk;
if (wntva) {
i__1 = *n / 2;
sgeqrf_(n, &i__1, &u[u_offset], ldu, rdummy, rdummy, &
c_n1, &ierr);
lwrk_sgeqrf__ = (integer) rdummy[0];
i__1 = *n / 2;
i__2 = *n / 2;
sgesvd_("S", "O", &i__1, &i__2, &v[v_offset], ldv, &s[
1], &u[u_offset], ldu, &v[v_offset], ldv,
rdummy, &c_n1, &ierr);
lwrk_sgesvd2__ = (integer) rdummy[0];
i__1 = *n / 2;
sormqr_("R", "C", n, n, &i__1, &u[u_offset], ldu,
rdummy, &v[v_offset], ldv, rdummy, &c_n1, &
ierr);
lwrk_sormqr2__ = (integer) rdummy[0];
/* Computing MAX */
i__1 = lwrk_sgeqp3__, i__2 = *n / 2 + lwrk_sgeqrf__,
i__1 = f2cmax(i__1,i__2), i__2 = *n / 2 +
lwrk_sgesvd2__, i__1 = f2cmax(i__1,i__2), i__2 =
*n / 2 + lwrk_sormqr2__;
optwrk2 = f2cmax(i__1,i__2);
if (conda) {
optwrk2 = f2cmax(optwrk2,lwcon);
}
optwrk2 = *n + optwrk2;
optwrk = f2cmax(optwrk,optwrk2);
}
} else {
sgesvd_("S", "O", n, n, &a[a_offset], lda, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, rdummy, &c_n1,
&ierr);
lwrk_sgesvd__ = (integer) rdummy[0];
/* Computing MAX */
i__1 = f2cmax(lwrk_sgeqp3__,lwrk_sgesvd__);
optwrk = f2cmax(i__1,lwrk_sormqr__);
if (conda) {
optwrk = f2cmax(optwrk,lwcon);
}
optwrk = *n + optwrk;
if (wntva) {
i__1 = *n / 2;
sgelqf_(&i__1, n, &u[u_offset], ldu, rdummy, rdummy, &
c_n1, &ierr);
lwrk_sgelqf__ = (integer) rdummy[0];
i__1 = *n / 2;
i__2 = *n / 2;
sgesvd_("S", "O", &i__1, &i__2, &v[v_offset], ldv, &s[
1], &u[u_offset], ldu, &v[v_offset], ldv,
rdummy, &c_n1, &ierr);
lwrk_sgesvd2__ = (integer) rdummy[0];
i__1 = *n / 2;
sormlq_("R", "N", n, n, &i__1, &u[u_offset], ldu,
rdummy, &v[v_offset], ldv, rdummy, &c_n1, &
ierr);
lwrk_sormlq__ = (integer) rdummy[0];
/* Computing MAX */
i__1 = lwrk_sgeqp3__, i__2 = *n / 2 + lwrk_sgelqf__,
i__1 = f2cmax(i__1,i__2), i__2 = *n / 2 +
lwrk_sgesvd2__, i__1 = f2cmax(i__1,i__2), i__2 =
*n / 2 + lwrk_sormlq__;
optwrk2 = f2cmax(i__1,i__2);
if (conda) {
optwrk2 = f2cmax(optwrk2,lwcon);
}
optwrk2 = *n + optwrk2;
optwrk = f2cmax(optwrk,optwrk2);
}
}
}
}
minwrk = f2cmax(2,minwrk);
optwrk = f2cmax(2,optwrk);
if (*lwork < minwrk && ! lquery) {
*info = -19;
}
}
if (*info == 0 && *lrwork < rminwrk && ! lquery) {
*info = -21;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGESVDQ", &i__1, (ftnlen)7);
return;
} else if (lquery) {
/* Return optimal workspace */
iwork[1] = iminwrk;
work[1] = (real) optwrk;
work[2] = (real) minwrk;
rwork[1] = (real) rminwrk;
return;
}
/* Quick return if the matrix is void. */
if (*m == 0 || *n == 0) {
return;
}
big = slamch_("O");
ascaled = FALSE_;
iwoff = 1;
if (rowprm) {
iwoff = *m;
/* ell-infinity norm - this enhances numerical robustness in */
/* the case of differently scaled rows. */
i__1 = *m;
for (p = 1; p <= i__1; ++p) {
/* RWORK(p) = ABS( A(p,ICAMAX(N,A(p,1),LDA)) ) */
/* [[SLANGE will return NaN if an entry of the p-th row is Nan]] */
rwork[p] = slange_("M", &c__1, n, &a[p + a_dim1], lda, rdummy);
if (rwork[p] != rwork[p] || rwork[p] * 0.f != 0.f) {
*info = -8;
i__2 = -(*info);
xerbla_("SGESVDQ", &i__2, (ftnlen)7);
return;
}
/* L1904: */
}
i__1 = *m - 1;
for (p = 1; p <= i__1; ++p) {
i__2 = *m - p + 1;
q = isamax_(&i__2, &rwork[p], &c__1) + p - 1;
iwork[*n + p] = q;
if (p != q) {
rtmp = rwork[p];
rwork[p] = rwork[q];
rwork[q] = rtmp;
}
/* L1952: */
}
if (rwork[1] == 0.f) {
/* Quick return: A is the M x N zero matrix. */
*numrank = 0;
slaset_("G", n, &c__1, &c_b72, &c_b72, &s[1], n);
if (wntus) {
slaset_("G", m, n, &c_b72, &c_b76, &u[u_offset], ldu);
}
if (wntua) {
slaset_("G", m, m, &c_b72, &c_b76, &u[u_offset], ldu);
}
if (wntva) {
slaset_("G", n, n, &c_b72, &c_b76, &v[v_offset], ldv);
}
if (wntuf) {
slaset_("G", n, &c__1, &c_b72, &c_b72, &work[1], n)
;
slaset_("G", m, n, &c_b72, &c_b76, &u[u_offset], ldu);
}
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
iwork[p] = p;
/* L5001: */
}
if (rowprm) {
i__1 = *n + *m - 1;
for (p = *n + 1; p <= i__1; ++p) {
iwork[p] = p - *n;
/* L5002: */
}
}
if (conda) {
rwork[1] = -1.f;
}
rwork[2] = -1.f;
return;
}
if (rwork[1] > big / sqrt((real) (*m))) {
/* matrix by 1/sqrt(M) if too large entry detected */
r__1 = sqrt((real) (*m));
slascl_("G", &c__0, &c__0, &r__1, &c_b76, m, n, &a[a_offset], lda,
&ierr);
ascaled = TRUE_;
}
i__1 = *m - 1;
slaswp_(n, &a[a_offset], lda, &c__1, &i__1, &iwork[*n + 1], &c__1);
}
/* norms overflows during the QR factorization. The SVD procedure should */
/* have its own scaling to save the singular values from overflows and */
/* underflows. That depends on the SVD procedure. */
if (! rowprm) {
rtmp = slange_("M", m, n, &a[a_offset], lda, rdummy);
if (rtmp != rtmp || rtmp * 0.f != 0.f) {
*info = -8;
i__1 = -(*info);
xerbla_("SGESVDQ", &i__1, (ftnlen)7);
return;
}
if (rtmp > big / sqrt((real) (*m))) {
/* matrix by 1/sqrt(M) if too large entry detected */
r__1 = sqrt((real) (*m));
slascl_("G", &c__0, &c__0, &r__1, &c_b76, m, n, &a[a_offset], lda,
&ierr);
ascaled = TRUE_;
}
}
/* A * P = Q * [ R ] */
/* [ 0 ] */
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
iwork[p] = 0;
/* L1963: */
}
i__1 = *lwork - *n;
sgeqp3_(m, n, &a[a_offset], lda, &iwork[1], &work[1], &work[*n + 1], &
i__1, &ierr);
/* If the user requested accuracy level allows truncation in the */
/* computed upper triangular factor, the matrix R is examined and, */
/* if possible, replaced with its leading upper trapezoidal part. */
epsln = slamch_("E");
sfmin = slamch_("S");
/* SMALL = SFMIN / EPSLN */
nr = *n;
if (accla) {
/* Standard absolute error bound suffices. All sigma_i with */
/* sigma_i < N*EPS*||A||_F are flushed to zero. This is an */
/* aggressive enforcement of lower numerical rank by introducing a */
/* backward error of the order of N*EPS*||A||_F. */
nr = 1;
rtmp = sqrt((real) (*n)) * epsln;
i__1 = *n;
for (p = 2; p <= i__1; ++p) {
if ((r__2 = a[p + p * a_dim1], abs(r__2)) < rtmp * (r__1 = a[
a_dim1 + 1], abs(r__1))) {
goto L3002;
}
++nr;
/* L3001: */
}
L3002:
;
} else if (acclm) {
/* Sudden drop on the diagonal of R is used as the criterion for being */
/* close-to-rank-deficient. The threshold is set to EPSLN=SLAMCH('E'). */
/* [[This can be made more flexible by replacing this hard-coded value */
/* with a user specified threshold.]] Also, the values that underflow */
/* will be truncated. */
nr = 1;
i__1 = *n;
for (p = 2; p <= i__1; ++p) {
if ((r__2 = a[p + p * a_dim1], abs(r__2)) < epsln * (r__1 = a[p -
1 + (p - 1) * a_dim1], abs(r__1)) || (r__3 = a[p + p *
a_dim1], abs(r__3)) < sfmin) {
goto L3402;
}
++nr;
/* L3401: */
}
L3402:
;
} else {
/* obvious case of zero pivots. */
/* R(i,i)=0 => R(i:N,i:N)=0. */
nr = 1;
i__1 = *n;
for (p = 2; p <= i__1; ++p) {
if ((r__1 = a[p + p * a_dim1], abs(r__1)) == 0.f) {
goto L3502;
}
++nr;
/* L3501: */
}
L3502:
if (conda) {
/* Estimate the scaled condition number of A. Use the fact that it is */
/* the same as the scaled condition number of R. */
slacpy_("U", n, n, &a[a_offset], lda, &v[v_offset], ldv);
/* Only the leading NR x NR submatrix of the triangular factor */
/* is considered. Only if NR=N will this give a reliable error */
/* bound. However, even for NR < N, this can be used on an */
/* expert level and obtain useful information in the sense of */
/* perturbation theory. */
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
rtmp = snrm2_(&p, &v[p * v_dim1 + 1], &c__1);
r__1 = 1.f / rtmp;
sscal_(&p, &r__1, &v[p * v_dim1 + 1], &c__1);
/* L3053: */
}
if (! (lsvec || rsvec)) {
spocon_("U", &nr, &v[v_offset], ldv, &c_b76, &rtmp, &work[1],
&iwork[*n + iwoff], &ierr);
} else {
spocon_("U", &nr, &v[v_offset], ldv, &c_b76, &rtmp, &work[*n
+ 1], &iwork[*n + iwoff], &ierr);
}
sconda = 1.f / sqrt(rtmp);
/* For NR=N, SCONDA is an estimate of SQRT(||(R^* * R)^(-1)||_1), */
/* N^(-1/4) * SCONDA <= ||R^(-1)||_2 <= N^(1/4) * SCONDA */
/* See the reference [1] for more details. */
}
}
if (wntur) {
n1 = nr;
} else if (wntus || wntuf) {
n1 = *n;
} else if (wntua) {
n1 = *m;
}
if (! (rsvec || lsvec)) {
/* ....................................................................... */
/* ....................................................................... */
if (rtrans) {
/* the upper triangle of [A] to zero. */
i__1 = f2cmin(*n,nr);
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = p + 1; q <= i__2; ++q) {
a[q + p * a_dim1] = a[p + q * a_dim1];
if (q <= nr) {
a[p + q * a_dim1] = 0.f;
}
/* L1147: */
}
/* L1146: */
}
sgesvd_("N", "N", n, &nr, &a[a_offset], lda, &s[1], &u[u_offset],
ldu, &v[v_offset], ldv, &work[1], lwork, info);
} else {
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("L", &i__1, &i__2, &c_b72, &c_b72, &a[a_dim1 + 2],
lda);
}
sgesvd_("N", "N", &nr, n, &a[a_offset], lda, &s[1], &u[u_offset],
ldu, &v[v_offset], ldv, &work[1], lwork, info);
}
} else if (lsvec && ! rsvec) {
/* ....................................................................... */
/* ......................................................................."""""""" */
if (rtrans) {
/* vectors of R */
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = p; q <= i__2; ++q) {
u[q + p * u_dim1] = a[p + q * a_dim1];
/* L1193: */
}
/* L1192: */
}
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("U", &i__1, &i__2, &c_b72, &c_b72, &u[(u_dim1 << 1) +
1], ldu);
}
/* vectors overwrite [U](1:NR,1:NR) as transposed. These */
/* will be pre-multiplied by Q to build the left singular vectors of A. */
i__1 = *lwork - *n;
sgesvd_("N", "O", n, &nr, &u[u_offset], ldu, &s[1], &u[u_offset],
ldu, &u[u_offset], ldu, &work[*n + 1], &i__1, info);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = nr;
for (q = p + 1; q <= i__2; ++q) {
rtmp = u[q + p * u_dim1];
u[q + p * u_dim1] = u[p + q * u_dim1];
u[p + q * u_dim1] = rtmp;
/* L1120: */
}
/* L1119: */
}
} else {
slacpy_("U", &nr, n, &a[a_offset], lda, &u[u_offset], ldu);
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("L", &i__1, &i__2, &c_b72, &c_b72, &u[u_dim1 + 2],
ldu);
}
/* vectors overwrite [U](1:NR,1:NR) */
i__1 = *lwork - *n;
sgesvd_("O", "N", &nr, n, &u[u_offset], ldu, &s[1], &u[u_offset],
ldu, &v[v_offset], ldv, &work[*n + 1], &i__1, info);
/* R. These will be pre-multiplied by Q to build the left singular */
/* vectors of A. */
}
/* (M x NR) or (M x N) or (M x M). */
if (nr < *m && ! wntuf) {
i__1 = *m - nr;
slaset_("A", &i__1, &nr, &c_b72, &c_b72, &u[nr + 1 + u_dim1], ldu);
if (nr < n1) {
i__1 = n1 - nr;
slaset_("A", &nr, &i__1, &c_b72, &c_b72, &u[(nr + 1) * u_dim1
+ 1], ldu);
i__1 = *m - nr;
i__2 = n1 - nr;
slaset_("A", &i__1, &i__2, &c_b72, &c_b76, &u[nr + 1 + (nr +
1) * u_dim1], ldu);
}
}
/* The Q matrix from the first QRF is built into the left singular */
/* vectors matrix U. */
if (! wntuf) {
i__1 = *lwork - *n;
sormqr_("L", "N", m, &n1, n, &a[a_offset], lda, &work[1], &u[
u_offset], ldu, &work[*n + 1], &i__1, &ierr);
}
if (rowprm && ! wntuf) {
i__1 = *m - 1;
slaswp_(&n1, &u[u_offset], ldu, &c__1, &i__1, &iwork[*n + 1], &
c_n1);
}
} else if (rsvec && ! lsvec) {
/* ....................................................................... */
/* ....................................................................... */
if (rtrans) {
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = p; q <= i__2; ++q) {
v[q + p * v_dim1] = a[p + q * a_dim1];
/* L1166: */
}
/* L1165: */
}
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("U", &i__1, &i__2, &c_b72, &c_b72, &v[(v_dim1 << 1) +
1], ldv);
}
/* vectors not computed */
if (wntvr || nr == *n) {
i__1 = *lwork - *n;
sgesvd_("O", "N", n, &nr, &v[v_offset], ldv, &s[1], &u[
u_offset], ldu, &u[u_offset], ldu, &work[*n + 1], &
i__1, info);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = nr;
for (q = p + 1; q <= i__2; ++q) {
rtmp = v[q + p * v_dim1];
v[q + p * v_dim1] = v[p + q * v_dim1];
v[p + q * v_dim1] = rtmp;
/* L1122: */
}
/* L1121: */
}
if (nr < *n) {
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = nr + 1; q <= i__2; ++q) {
v[p + q * v_dim1] = v[q + p * v_dim1];
/* L1104: */
}
/* L1103: */
}
}
slapmt_(&c_false, &nr, n, &v[v_offset], ldv, &iwork[1]);
} else {
/* [!] This is simple implementation that augments [V](1:N,1:NR) */
/* by padding a zero block. In the case NR << N, a more efficient */
/* way is to first use the QR factorization. For more details */
/* how to implement this, see the " FULL SVD " branch. */
i__1 = *n - nr;
slaset_("G", n, &i__1, &c_b72, &c_b72, &v[(nr + 1) * v_dim1 +
1], ldv);
i__1 = *lwork - *n;
sgesvd_("O", "N", n, n, &v[v_offset], ldv, &s[1], &u[u_offset]
, ldu, &u[u_offset], ldu, &work[*n + 1], &i__1, info);
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = p + 1; q <= i__2; ++q) {
rtmp = v[q + p * v_dim1];
v[q + p * v_dim1] = v[p + q * v_dim1];
v[p + q * v_dim1] = rtmp;
/* L1124: */
}
/* L1123: */
}
slapmt_(&c_false, n, n, &v[v_offset], ldv, &iwork[1]);
}
} else {
slacpy_("U", &nr, n, &a[a_offset], lda, &v[v_offset], ldv);
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("L", &i__1, &i__2, &c_b72, &c_b72, &v[v_dim1 + 2],
ldv);
}
/* vectors stored in U(1:NR,1:NR) */
if (wntvr || nr == *n) {
i__1 = *lwork - *n;
sgesvd_("N", "O", &nr, n, &v[v_offset], ldv, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, &work[*n + 1], &
i__1, info);
slapmt_(&c_false, &nr, n, &v[v_offset], ldv, &iwork[1]);
} else {
/* [!] This is simple implementation that augments [V](1:NR,1:N) */
/* by padding a zero block. In the case NR << N, a more efficient */
/* way is to first use the LQ factorization. For more details */
/* how to implement this, see the " FULL SVD " branch. */
i__1 = *n - nr;
slaset_("G", &i__1, n, &c_b72, &c_b72, &v[nr + 1 + v_dim1],
ldv);
i__1 = *lwork - *n;
sgesvd_("N", "O", n, n, &v[v_offset], ldv, &s[1], &u[u_offset]
, ldu, &v[v_offset], ldv, &work[*n + 1], &i__1, info);
slapmt_(&c_false, n, n, &v[v_offset], ldv, &iwork[1]);
}
/* vectors of A. */
}
} else {
/* ....................................................................... */
/* ....................................................................... */
if (rtrans) {
if (wntvr || nr == *n) {
/* vectors of R**T */
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = p; q <= i__2; ++q) {
v[q + p * v_dim1] = a[p + q * a_dim1];
/* L1169: */
}
/* L1168: */
}
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("U", &i__1, &i__2, &c_b72, &c_b72, &v[(v_dim1 <<
1) + 1], ldv);
}
/* singular vectors of R**T stored in [U](1:NR,1:NR) as transposed */
i__1 = *lwork - *n;
sgesvd_("O", "A", n, &nr, &v[v_offset], ldv, &s[1], &v[
v_offset], ldv, &u[u_offset], ldu, &work[*n + 1], &
i__1, info);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = nr;
for (q = p + 1; q <= i__2; ++q) {
rtmp = v[q + p * v_dim1];
v[q + p * v_dim1] = v[p + q * v_dim1];
v[p + q * v_dim1] = rtmp;
/* L1116: */
}
/* L1115: */
}
if (nr < *n) {
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = nr + 1; q <= i__2; ++q) {
v[p + q * v_dim1] = v[q + p * v_dim1];
/* L1102: */
}
/* L1101: */
}
}
slapmt_(&c_false, &nr, n, &v[v_offset], ldv, &iwork[1]);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = nr;
for (q = p + 1; q <= i__2; ++q) {
rtmp = u[q + p * u_dim1];
u[q + p * u_dim1] = u[p + q * u_dim1];
u[p + q * u_dim1] = rtmp;
/* L1118: */
}
/* L1117: */
}
if (nr < *m && ! wntuf) {
i__1 = *m - nr;
slaset_("A", &i__1, &nr, &c_b72, &c_b72, &u[nr + 1 +
u_dim1], ldu);
if (nr < n1) {
i__1 = n1 - nr;
slaset_("A", &nr, &i__1, &c_b72, &c_b72, &u[(nr + 1) *
u_dim1 + 1], ldu);
i__1 = *m - nr;
i__2 = n1 - nr;
slaset_("A", &i__1, &i__2, &c_b72, &c_b76, &u[nr + 1
+ (nr + 1) * u_dim1], ldu);
}
}
} else {
/* vectors of R**T */
/* [[The optimal ratio N/NR for using QRF instead of padding */
/* with zeros. Here hard coded to 2; it must be at least */
/* two due to work space constraints.]] */
/* OPTRATIO = ILAENV(6, 'SGESVD', 'S' // 'O', NR,N,0,0) */
/* OPTRATIO = MAX( OPTRATIO, 2 ) */
optratio = 2;
if (optratio * nr > *n) {
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = p; q <= i__2; ++q) {
v[q + p * v_dim1] = a[p + q * a_dim1];
/* L1199: */
}
/* L1198: */
}
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("U", &i__1, &i__2, &c_b72, &c_b72, &v[(v_dim1
<< 1) + 1], ldv);
}
i__1 = *n - nr;
slaset_("A", n, &i__1, &c_b72, &c_b72, &v[(nr + 1) *
v_dim1 + 1], ldv);
i__1 = *lwork - *n;
sgesvd_("O", "A", n, n, &v[v_offset], ldv, &s[1], &v[
v_offset], ldv, &u[u_offset], ldu, &work[*n + 1],
&i__1, info);
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = p + 1; q <= i__2; ++q) {
rtmp = v[q + p * v_dim1];
v[q + p * v_dim1] = v[p + q * v_dim1];
v[p + q * v_dim1] = rtmp;
/* L1114: */
}
/* L1113: */
}
slapmt_(&c_false, n, n, &v[v_offset], ldv, &iwork[1]);
/* (M x N1), i.e. (M x N) or (M x M). */
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = p + 1; q <= i__2; ++q) {
rtmp = u[q + p * u_dim1];
u[q + p * u_dim1] = u[p + q * u_dim1];
u[p + q * u_dim1] = rtmp;
/* L1112: */
}
/* L1111: */
}
if (*n < *m && ! wntuf) {
i__1 = *m - *n;
slaset_("A", &i__1, n, &c_b72, &c_b72, &u[*n + 1 +
u_dim1], ldu);
if (*n < n1) {
i__1 = n1 - *n;
slaset_("A", n, &i__1, &c_b72, &c_b72, &u[(*n + 1)
* u_dim1 + 1], ldu);
i__1 = *m - *n;
i__2 = n1 - *n;
slaset_("A", &i__1, &i__2, &c_b72, &c_b76, &u[*n
+ 1 + (*n + 1) * u_dim1], ldu);
}
}
} else {
/* singular vectors of R */
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = p; q <= i__2; ++q) {
u[q + (nr + p) * u_dim1] = a[p + q * a_dim1];
/* L1197: */
}
/* L1196: */
}
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("U", &i__1, &i__2, &c_b72, &c_b72, &u[(nr + 2)
* u_dim1 + 1], ldu);
}
i__1 = *lwork - *n - nr;
sgeqrf_(n, &nr, &u[(nr + 1) * u_dim1 + 1], ldu, &work[*n
+ 1], &work[*n + nr + 1], &i__1, &ierr);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n;
for (q = 1; q <= i__2; ++q) {
v[q + p * v_dim1] = u[p + (nr + q) * u_dim1];
/* L1144: */
}
/* L1143: */
}
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("U", &i__1, &i__2, &c_b72, &c_b72, &v[(v_dim1 <<
1) + 1], ldv);
i__1 = *lwork - *n - nr;
sgesvd_("S", "O", &nr, &nr, &v[v_offset], ldv, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, &work[*n + nr
+ 1], &i__1, info);
i__1 = *n - nr;
slaset_("A", &i__1, &nr, &c_b72, &c_b72, &v[nr + 1 +
v_dim1], ldv);
i__1 = *n - nr;
slaset_("A", &nr, &i__1, &c_b72, &c_b72, &v[(nr + 1) *
v_dim1 + 1], ldv);
i__1 = *n - nr;
i__2 = *n - nr;
slaset_("A", &i__1, &i__2, &c_b72, &c_b76, &v[nr + 1 + (
nr + 1) * v_dim1], ldv);
i__1 = *lwork - *n - nr;
sormqr_("R", "C", n, n, &nr, &u[(nr + 1) * u_dim1 + 1],
ldu, &work[*n + 1], &v[v_offset], ldv, &work[*n +
nr + 1], &i__1, &ierr);
slapmt_(&c_false, n, n, &v[v_offset], ldv, &iwork[1]);
/* (M x NR) or (M x N) or (M x M). */
if (nr < *m && ! wntuf) {
i__1 = *m - nr;
slaset_("A", &i__1, &nr, &c_b72, &c_b72, &u[nr + 1 +
u_dim1], ldu);
if (nr < n1) {
i__1 = n1 - nr;
slaset_("A", &nr, &i__1, &c_b72, &c_b72, &u[(nr +
1) * u_dim1 + 1], ldu);
i__1 = *m - nr;
i__2 = n1 - nr;
slaset_("A", &i__1, &i__2, &c_b72, &c_b76, &u[nr
+ 1 + (nr + 1) * u_dim1], ldu);
}
}
}
}
} else {
if (wntvr || nr == *n) {
slacpy_("U", &nr, n, &a[a_offset], lda, &v[v_offset], ldv);
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("L", &i__1, &i__2, &c_b72, &c_b72, &v[v_dim1 + 2],
ldv);
}
/* singular vectors of R stored in [U](1:NR,1:NR) */
i__1 = *lwork - *n;
sgesvd_("S", "O", &nr, n, &v[v_offset], ldv, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, &work[*n + 1], &
i__1, info);
slapmt_(&c_false, &nr, n, &v[v_offset], ldv, &iwork[1]);
/* (M x NR) or (M x N) or (M x M). */
if (nr < *m && ! wntuf) {
i__1 = *m - nr;
slaset_("A", &i__1, &nr, &c_b72, &c_b72, &u[nr + 1 +
u_dim1], ldu);
if (nr < n1) {
i__1 = n1 - nr;
slaset_("A", &nr, &i__1, &c_b72, &c_b72, &u[(nr + 1) *
u_dim1 + 1], ldu);
i__1 = *m - nr;
i__2 = n1 - nr;
slaset_("A", &i__1, &i__2, &c_b72, &c_b76, &u[nr + 1
+ (nr + 1) * u_dim1], ldu);
}
}
} else {
/* is then N1 (N or M) */
/* [[The optimal ratio N/NR for using LQ instead of padding */
/* with zeros. Here hard coded to 2; it must be at least */
/* two due to work space constraints.]] */
/* OPTRATIO = ILAENV(6, 'SGESVD', 'S' // 'O', NR,N,0,0) */
/* OPTRATIO = MAX( OPTRATIO, 2 ) */
optratio = 2;
if (optratio * nr > *n) {
slacpy_("U", &nr, n, &a[a_offset], lda, &v[v_offset], ldv);
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("L", &i__1, &i__2, &c_b72, &c_b72, &v[v_dim1
+ 2], ldv);
}
/* singular vectors of R stored in [U](1:NR,1:NR) */
i__1 = *n - nr;
slaset_("A", &i__1, n, &c_b72, &c_b72, &v[nr + 1 + v_dim1]
, ldv);
i__1 = *lwork - *n;
sgesvd_("S", "O", n, n, &v[v_offset], ldv, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, &work[*n + 1],
&i__1, info);
slapmt_(&c_false, n, n, &v[v_offset], ldv, &iwork[1]);
/* singular vectors of A. The leading N left singular vectors */
/* are in [U](1:N,1:N) */
/* (M x N1), i.e. (M x N) or (M x M). */
if (*n < *m && ! wntuf) {
i__1 = *m - *n;
slaset_("A", &i__1, n, &c_b72, &c_b72, &u[*n + 1 +
u_dim1], ldu);
if (*n < n1) {
i__1 = n1 - *n;
slaset_("A", n, &i__1, &c_b72, &c_b72, &u[(*n + 1)
* u_dim1 + 1], ldu);
i__1 = *m - *n;
i__2 = n1 - *n;
slaset_("A", &i__1, &i__2, &c_b72, &c_b76, &u[*n
+ 1 + (*n + 1) * u_dim1], ldu);
}
}
} else {
slacpy_("U", &nr, n, &a[a_offset], lda, &u[nr + 1 +
u_dim1], ldu);
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("L", &i__1, &i__2, &c_b72, &c_b72, &u[nr + 2
+ u_dim1], ldu);
}
i__1 = *lwork - *n - nr;
sgelqf_(&nr, n, &u[nr + 1 + u_dim1], ldu, &work[*n + 1], &
work[*n + nr + 1], &i__1, &ierr);
slacpy_("L", &nr, &nr, &u[nr + 1 + u_dim1], ldu, &v[
v_offset], ldv);
if (nr > 1) {
i__1 = nr - 1;
i__2 = nr - 1;
slaset_("U", &i__1, &i__2, &c_b72, &c_b72, &v[(v_dim1
<< 1) + 1], ldv);
}
i__1 = *lwork - *n - nr;
sgesvd_("S", "O", &nr, &nr, &v[v_offset], ldv, &s[1], &u[
u_offset], ldu, &v[v_offset], ldv, &work[*n + nr
+ 1], &i__1, info);
i__1 = *n - nr;
slaset_("A", &i__1, &nr, &c_b72, &c_b72, &v[nr + 1 +
v_dim1], ldv);
i__1 = *n - nr;
slaset_("A", &nr, &i__1, &c_b72, &c_b72, &v[(nr + 1) *
v_dim1 + 1], ldv);
i__1 = *n - nr;
i__2 = *n - nr;
slaset_("A", &i__1, &i__2, &c_b72, &c_b76, &v[nr + 1 + (
nr + 1) * v_dim1], ldv);
i__1 = *lwork - *n - nr;
sormlq_("R", "N", n, n, &nr, &u[nr + 1 + u_dim1], ldu, &
work[*n + 1], &v[v_offset], ldv, &work[*n + nr +
1], &i__1, &ierr);
slapmt_(&c_false, n, n, &v[v_offset], ldv, &iwork[1]);
/* (M x NR) or (M x N) or (M x M). */
if (nr < *m && ! wntuf) {
i__1 = *m - nr;
slaset_("A", &i__1, &nr, &c_b72, &c_b72, &u[nr + 1 +
u_dim1], ldu);
if (nr < n1) {
i__1 = n1 - nr;
slaset_("A", &nr, &i__1, &c_b72, &c_b72, &u[(nr +
1) * u_dim1 + 1], ldu);
i__1 = *m - nr;
i__2 = n1 - nr;
slaset_("A", &i__1, &i__2, &c_b72, &c_b76, &u[nr
+ 1 + (nr + 1) * u_dim1], ldu);
}
}
}
}
}
/* The Q matrix from the first QRF is built into the left singular */
/* vectors matrix U. */
if (! wntuf) {
i__1 = *lwork - *n;
sormqr_("L", "N", m, &n1, n, &a[a_offset], lda, &work[1], &u[
u_offset], ldu, &work[*n + 1], &i__1, &ierr);
}
if (rowprm && ! wntuf) {
i__1 = *m - 1;
slaswp_(&n1, &u[u_offset], ldu, &c__1, &i__1, &iwork[*n + 1], &
c_n1);
}
/* ... end of the "full SVD" branch */
}
/* Check whether some singular values are returned as zeros, e.g. */
/* due to underflow, and update the numerical rank. */
p = nr;
for (q = p; q >= 1; --q) {
if (s[q] > 0.f) {
goto L4002;
}
--nr;
/* L4001: */
}
L4002:
/* singular values are set to zero. */
if (nr < *n) {
i__1 = *n - nr;
slaset_("G", &i__1, &c__1, &c_b72, &c_b72, &s[nr + 1], n);
}
/* values. */
if (ascaled) {
r__1 = sqrt((real) (*m));
slascl_("G", &c__0, &c__0, &c_b76, &r__1, &nr, &c__1, &s[1], n, &ierr);
}
if (conda) {
rwork[1] = sconda;
}
rwork[2] = (real) (p - nr);
/* exact zeros in SGESVD() applied to the (possibly truncated) */
/* full row rank triangular (trapezoidal) factor of A. */
*numrank = nr;
return;
/* End of SGESVDQ */
} /* sgesvdq_ */
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