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OpenBLAS/lapack-netlib/SRC/dgesdd.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__0 = 0;
static doublereal c_b63 = 0.;
static integer c__1 = 1;
static doublereal c_b84 = 1.;
/* > \brief \b DGESDD */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DGESDD + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgesdd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgesdd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesdd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, */
/* WORK, LWORK, IWORK, INFO ) */
/* CHARACTER JOBZ */
/* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
/* INTEGER IWORK( * ) */
/* DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), */
/* $ VT( LDVT, * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DGESDD computes the singular value decomposition (SVD) of a real */
/* > M-by-N matrix A, optionally computing the left and right singular */
/* > vectors. If singular vectors are desired, it uses a */
/* > divide-and-conquer algorithm. */
/* > */
/* > The SVD is written */
/* > */
/* > A = U * SIGMA * transpose(V) */
/* > */
/* > where SIGMA is an M-by-N matrix which is zero except for its */
/* > f2cmin(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */
/* > V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */
/* > are the singular values of A; they are real and non-negative, and */
/* > are returned in descending order. The first f2cmin(m,n) columns of */
/* > U and V are the left and right singular vectors of A. */
/* > */
/* > Note that the routine returns VT = V**T, not V. */
/* > */
/* > The divide and conquer algorithm makes very mild assumptions about */
/* > floating point arithmetic. It will work on machines with a guard */
/* > digit in add/subtract, or on those binary machines without guard */
/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/* > without guard digits, but we know of none. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOBZ */
/* > \verbatim */
/* > JOBZ is CHARACTER*1 */
/* > Specifies options for computing all or part of the matrix U: */
/* > = 'A': all M columns of U and all N rows of V**T are */
/* > returned in the arrays U and VT; */
/* > = 'S': the first f2cmin(M,N) columns of U and the first */
/* > f2cmin(M,N) rows of V**T are returned in the arrays U */
/* > and VT; */
/* > = 'O': If M >= N, the first N columns of U are overwritten */
/* > on the array A and all rows of V**T are returned in */
/* > the array VT; */
/* > otherwise, all columns of U are returned in the */
/* > array U and the first M rows of V**T are overwritten */
/* > in the array A; */
/* > = 'N': no columns of U or rows of V**T are computed. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The number of rows of the input matrix A. M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of columns of the input matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
/* > On entry, the M-by-N matrix A. */
/* > On exit, */
/* > if JOBZ = 'O', A is overwritten with the first N columns */
/* > of U (the left singular vectors, stored */
/* > columnwise) if M >= N; */
/* > A is overwritten with the first M rows */
/* > of V**T (the right singular vectors, stored */
/* > rowwise) otherwise. */
/* > if JOBZ .ne. 'O', the contents of A are destroyed. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] S */
/* > \verbatim */
/* > S is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDU,UCOL) */
/* > UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */
/* > UCOL = f2cmin(M,N) if JOBZ = 'S'. */
/* > If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */
/* > orthogonal matrix U; */
/* > if JOBZ = 'S', U contains the first f2cmin(M,N) columns of U */
/* > (the left singular vectors, stored columnwise); */
/* > if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* > LDU is INTEGER */
/* > The leading dimension of the array U. LDU >= 1; if */
/* > JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */
/* > \endverbatim */
/* > */
/* > \param[out] VT */
/* > \verbatim */
/* > VT is DOUBLE PRECISION array, dimension (LDVT,N) */
/* > If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */
/* > N-by-N orthogonal matrix V**T; */
/* > if JOBZ = 'S', VT contains the first f2cmin(M,N) rows of */
/* > V**T (the right singular vectors, stored rowwise); */
/* > if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVT */
/* > \verbatim */
/* > LDVT is INTEGER */
/* > The leading dimension of the array VT. LDVT >= 1; */
/* > if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */
/* > if JOBZ = 'S', LDVT >= f2cmin(M,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK; */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. LWORK >= 1. */
/* > If LWORK = -1, a workspace query is assumed. The optimal */
/* > size for the WORK array is calculated and stored in WORK(1), */
/* > and no other work except argument checking is performed. */
/* > */
/* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
/* > If JOBZ = 'N', LWORK >= 3*mn + f2cmax( mx, 7*mn ). */
/* > If JOBZ = 'O', LWORK >= 3*mn + f2cmax( mx, 5*mn*mn + 4*mn ). */
/* > If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn. */
/* > If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx. */
/* > These are not tight minimums in all cases; see comments inside code. */
/* > For good performance, LWORK should generally be larger; */
/* > a query is recommended. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (8*f2cmin(M,N)) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > > 0: DBDSDC did not converge, updating process failed. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2016 */
/* > \ingroup doubleGEsing */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
/* > California at Berkeley, USA */
/* > */
/* ===================================================================== */
/* Subroutine */ void dgesdd_(char *jobz, integer *m, integer *n, doublereal *
a, integer *lda, doublereal *s, doublereal *u, integer *ldu,
doublereal *vt, integer *ldvt, doublereal *work, integer *lwork,
integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
i__2, i__3;
/* Local variables */
integer lwork_dorglq_mn__, lwork_dorglq_nn__, lwork_dorgqr_mm__,
lwork_dorgqr_mn__, iscl;
doublereal anrm;
integer idum[1], ierr, itau, lwork_dormbr_qln_mm__, lwork_dormbr_qln_mn__,
lwork_dormbr_qln_nn__, lwork_dormbr_prt_mm__,
lwork_dormbr_prt_mn__, lwork_dormbr_prt_nn__, i__;
extern /* Subroutine */ void dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
extern logical lsame_(char *, char *);
integer chunk, minmn, wrkbl, itaup, itauq, mnthr;
logical wntqa;
integer nwork;
logical wntqn, wntqo, wntqs;
integer ie, lwork_dorgbr_p_mm__;
extern /* Subroutine */ void dbdsdc_(char *, char *, integer *, doublereal
*, doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *);
integer il, lwork_dorgbr_q_nn__;
extern /* Subroutine */ void dgebrd_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
integer ir, bdspac;
extern doublereal dlange_(char *, integer *, integer *, doublereal *,
integer *, doublereal *);
integer iu;
extern /* Subroutine */ void dgelqf_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *),
dlascl_(char *, integer *, integer *, doublereal *, doublereal *,
integer *, integer *, doublereal *, integer *, integer *),
dgeqrf_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *), dlacpy_(char *,
integer *, integer *, doublereal *, integer *, doublereal *,
integer *), dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *);
extern int xerbla_(char *, integer *, ftnlen);
extern void dorgbr_(char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, integer *);
extern logical disnan_(doublereal *);
doublereal bignum;
extern /* Subroutine */ void dormbr_(char *, char *, char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *), dorglq_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dorgqr_(integer *, integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *);
integer ldwrkl, ldwrkr, minwrk, ldwrku, maxwrk, ldwkvt;
doublereal smlnum;
logical wntqas, lquery;
integer blk;
doublereal dum[1], eps;
integer ivt, lwork_dgebrd_mm__, lwork_dgebrd_mn__, lwork_dgebrd_nn__,
lwork_dgelqf_mn__, lwork_dgeqrf_mn__;
/* -- LAPACK driver routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2016 */
/* ===================================================================== */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--s;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1 * 1;
vt -= vt_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
minmn = f2cmin(*m,*n);
wntqa = lsame_(jobz, "A");
wntqs = lsame_(jobz, "S");
wntqas = wntqa || wntqs;
wntqo = lsame_(jobz, "O");
wntqn = lsame_(jobz, "N");
lquery = *lwork == -1;
if (! (wntqa || wntqs || wntqo || wntqn)) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < f2cmax(1,*m)) {
*info = -5;
} else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < *
m) {
*info = -8;
} else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn ||
wntqo && *m >= *n && *ldvt < *n) {
*info = -10;
}
/* Compute workspace */
/* Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace allocated at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
if (*info == 0) {
minwrk = 1;
maxwrk = 1;
bdspac = 0;
mnthr = (integer) (minmn * 11. / 6.);
if (*m >= *n && minmn > 0) {
/* Compute space needed for DBDSDC */
if (wntqn) {
/* dbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6) */
/* keep 7*N for backwards compatibility. */
bdspac = *n * 7;
} else {
bdspac = *n * 3 * *n + (*n << 2);
}
/* Compute space preferred for each routine */
dgebrd_(m, n, dum, m, dum, dum, dum, dum, dum, &c_n1, &ierr);
lwork_dgebrd_mn__ = (integer) dum[0];
dgebrd_(n, n, dum, n, dum, dum, dum, dum, dum, &c_n1, &ierr);
lwork_dgebrd_nn__ = (integer) dum[0];
dgeqrf_(m, n, dum, m, dum, dum, &c_n1, &ierr);
lwork_dgeqrf_mn__ = (integer) dum[0];
dorgbr_("Q", n, n, n, dum, n, dum, dum, &c_n1, &ierr);
lwork_dorgbr_q_nn__ = (integer) dum[0];
dorgqr_(m, m, n, dum, m, dum, dum, &c_n1, &ierr);
lwork_dorgqr_mm__ = (integer) dum[0];
dorgqr_(m, n, n, dum, m, dum, dum, &c_n1, &ierr);
lwork_dorgqr_mn__ = (integer) dum[0];
dormbr_("P", "R", "T", n, n, n, dum, n, dum, dum, n, dum, &c_n1, &
ierr);
lwork_dormbr_prt_nn__ = (integer) dum[0];
dormbr_("Q", "L", "N", n, n, n, dum, n, dum, dum, n, dum, &c_n1, &
ierr);
lwork_dormbr_qln_nn__ = (integer) dum[0];
dormbr_("Q", "L", "N", m, n, n, dum, m, dum, dum, m, dum, &c_n1, &
ierr);
lwork_dormbr_qln_mn__ = (integer) dum[0];
dormbr_("Q", "L", "N", m, m, n, dum, m, dum, dum, m, dum, &c_n1, &
ierr);
lwork_dormbr_qln_mm__ = (integer) dum[0];
if (*m >= mnthr) {
if (wntqn) {
/* Path 1 (M >> N, JOBZ='N') */
wrkbl = *n + lwork_dgeqrf_mn__;
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dgebrd_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *n;
maxwrk = f2cmax(i__1,i__2);
minwrk = bdspac + *n;
} else if (wntqo) {
/* Path 2 (M >> N, JOBZ='O') */
wrkbl = *n + lwork_dgeqrf_mn__;
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + lwork_dorgqr_mn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dgebrd_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_qln_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_prt_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
wrkbl = f2cmax(i__1,i__2);
maxwrk = wrkbl + (*n << 1) * *n;
minwrk = bdspac + (*n << 1) * *n + *n * 3;
} else if (wntqs) {
/* Path 3 (M >> N, JOBZ='S') */
wrkbl = *n + lwork_dgeqrf_mn__;
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + lwork_dorgqr_mn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dgebrd_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_qln_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_prt_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
wrkbl = f2cmax(i__1,i__2);
maxwrk = wrkbl + *n * *n;
minwrk = bdspac + *n * *n + *n * 3;
} else if (wntqa) {
/* Path 4 (M >> N, JOBZ='A') */
wrkbl = *n + lwork_dgeqrf_mn__;
/* Computing MAX */
i__1 = wrkbl, i__2 = *n + lwork_dorgqr_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dgebrd_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_qln_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_prt_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
wrkbl = f2cmax(i__1,i__2);
maxwrk = wrkbl + *n * *n;
/* Computing MAX */
i__1 = *n * 3 + bdspac, i__2 = *n + *m;
minwrk = *n * *n + f2cmax(i__1,i__2);
}
} else {
/* Path 5 (M >= N, but not much larger) */
wrkbl = *n * 3 + lwork_dgebrd_mn__;
if (wntqn) {
/* Path 5n (M >= N, jobz='N') */
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
maxwrk = f2cmax(i__1,i__2);
minwrk = *n * 3 + f2cmax(*m,bdspac);
} else if (wntqo) {
/* Path 5o (M >= N, jobz='O') */
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_prt_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_qln_mn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
wrkbl = f2cmax(i__1,i__2);
maxwrk = wrkbl + *m * *n;
/* Computing MAX */
i__1 = *m, i__2 = *n * *n + bdspac;
minwrk = *n * 3 + f2cmax(i__1,i__2);
} else if (wntqs) {
/* Path 5s (M >= N, jobz='S') */
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_qln_mn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_prt_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
maxwrk = f2cmax(i__1,i__2);
minwrk = *n * 3 + f2cmax(*m,bdspac);
} else if (wntqa) {
/* Path 5a (M >= N, jobz='A') */
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_qln_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + lwork_dormbr_prt_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *n * 3 + bdspac;
maxwrk = f2cmax(i__1,i__2);
minwrk = *n * 3 + f2cmax(*m,bdspac);
}
}
} else if (minmn > 0) {
/* Compute space needed for DBDSDC */
if (wntqn) {
/* dbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6) */
/* keep 7*N for backwards compatibility. */
bdspac = *m * 7;
} else {
bdspac = *m * 3 * *m + (*m << 2);
}
/* Compute space preferred for each routine */
dgebrd_(m, n, dum, m, dum, dum, dum, dum, dum, &c_n1, &ierr);
lwork_dgebrd_mn__ = (integer) dum[0];
dgebrd_(m, m, &a[a_offset], m, &s[1], dum, dum, dum, dum, &c_n1, &
ierr);
lwork_dgebrd_mm__ = (integer) dum[0];
dgelqf_(m, n, &a[a_offset], m, dum, dum, &c_n1, &ierr);
lwork_dgelqf_mn__ = (integer) dum[0];
dorglq_(n, n, m, dum, n, dum, dum, &c_n1, &ierr);
lwork_dorglq_nn__ = (integer) dum[0];
dorglq_(m, n, m, &a[a_offset], m, dum, dum, &c_n1, &ierr);
lwork_dorglq_mn__ = (integer) dum[0];
dorgbr_("P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr);
lwork_dorgbr_p_mm__ = (integer) dum[0];
dormbr_("P", "R", "T", m, m, m, dum, m, dum, dum, m, dum, &c_n1, &
ierr);
lwork_dormbr_prt_mm__ = (integer) dum[0];
dormbr_("P", "R", "T", m, n, m, dum, m, dum, dum, m, dum, &c_n1, &
ierr);
lwork_dormbr_prt_mn__ = (integer) dum[0];
dormbr_("P", "R", "T", n, n, m, dum, n, dum, dum, n, dum, &c_n1, &
ierr);
lwork_dormbr_prt_nn__ = (integer) dum[0];
dormbr_("Q", "L", "N", m, m, m, dum, m, dum, dum, m, dum, &c_n1, &
ierr);
lwork_dormbr_qln_mm__ = (integer) dum[0];
if (*n >= mnthr) {
if (wntqn) {
/* Path 1t (N >> M, JOBZ='N') */
wrkbl = *m + lwork_dgelqf_mn__;
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dgebrd_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = bdspac + *m;
maxwrk = f2cmax(i__1,i__2);
minwrk = bdspac + *m;
} else if (wntqo) {
/* Path 2t (N >> M, JOBZ='O') */
wrkbl = *m + lwork_dgelqf_mn__;
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + lwork_dorglq_mn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dgebrd_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_qln_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_prt_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
wrkbl = f2cmax(i__1,i__2);
maxwrk = wrkbl + (*m << 1) * *m;
minwrk = bdspac + (*m << 1) * *m + *m * 3;
} else if (wntqs) {
/* Path 3t (N >> M, JOBZ='S') */
wrkbl = *m + lwork_dgelqf_mn__;
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + lwork_dorglq_mn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dgebrd_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_qln_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_prt_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
wrkbl = f2cmax(i__1,i__2);
maxwrk = wrkbl + *m * *m;
minwrk = bdspac + *m * *m + *m * 3;
} else if (wntqa) {
/* Path 4t (N >> M, JOBZ='A') */
wrkbl = *m + lwork_dgelqf_mn__;
/* Computing MAX */
i__1 = wrkbl, i__2 = *m + lwork_dorglq_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dgebrd_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_qln_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_prt_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
wrkbl = f2cmax(i__1,i__2);
maxwrk = wrkbl + *m * *m;
/* Computing MAX */
i__1 = *m * 3 + bdspac, i__2 = *m + *n;
minwrk = *m * *m + f2cmax(i__1,i__2);
}
} else {
/* Path 5t (N > M, but not much larger) */
wrkbl = *m * 3 + lwork_dgebrd_mn__;
if (wntqn) {
/* Path 5tn (N > M, jobz='N') */
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
maxwrk = f2cmax(i__1,i__2);
minwrk = *m * 3 + f2cmax(*n,bdspac);
} else if (wntqo) {
/* Path 5to (N > M, jobz='O') */
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_qln_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_prt_mn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
wrkbl = f2cmax(i__1,i__2);
maxwrk = wrkbl + *m * *n;
/* Computing MAX */
i__1 = *n, i__2 = *m * *m + bdspac;
minwrk = *m * 3 + f2cmax(i__1,i__2);
} else if (wntqs) {
/* Path 5ts (N > M, jobz='S') */
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_qln_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_prt_mn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
maxwrk = f2cmax(i__1,i__2);
minwrk = *m * 3 + f2cmax(*n,bdspac);
} else if (wntqa) {
/* Path 5ta (N > M, jobz='A') */
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_qln_mm__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + lwork_dormbr_prt_nn__;
wrkbl = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = wrkbl, i__2 = *m * 3 + bdspac;
maxwrk = f2cmax(i__1,i__2);
minwrk = *m * 3 + f2cmax(*n,bdspac);
}
}
}
maxwrk = f2cmax(maxwrk,minwrk);
work[1] = (doublereal) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGESDD", &i__1, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
return;
}
/* Get machine constants */
eps = dlamch_("P");
smlnum = sqrt(dlamch_("S")) / eps;
bignum = 1. / smlnum;
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
anrm = dlange_("M", m, n, &a[a_offset], lda, dum);
if (disnan_(&anrm)) {
*info = -4;
return;
}
iscl = 0;
if (anrm > 0. && anrm < smlnum) {
iscl = 1;
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
ierr);
} else if (anrm > bignum) {
iscl = 1;
dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
ierr);
}
if (*m >= *n) {
/* A has at least as many rows as columns. If A has sufficiently */
/* more rows than columns, first reduce using the QR */
/* decomposition (if sufficient workspace available) */
if (*m >= mnthr) {
if (wntqn) {
/* Path 1 (M >> N, JOBZ='N') */
/* No singular vectors to be computed */
itau = 1;
nwork = itau + *n;
/* Compute A=Q*R */
/* Workspace: need N [tau] + N [work] */
/* Workspace: prefer N [tau] + N*NB [work] */
i__1 = *lwork - nwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Zero out below R */
i__1 = *n - 1;
i__2 = *n - 1;
dlaset_("L", &i__1, &i__2, &c_b63, &c_b63, &a[a_dim1 + 2],
lda);
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize R in A */
/* Workspace: need 3*N [e, tauq, taup] + N [work] */
/* Workspace: prefer 3*N [e, tauq, taup] + 2*N*NB [work] */
i__1 = *lwork - nwork + 1;
dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
nwork = ie + *n;
/* Perform bidiagonal SVD, computing singular values only */
/* Workspace: need N [e] + BDSPAC */
dbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1,
dum, idum, &work[nwork], &iwork[1], info);
} else if (wntqo) {
/* Path 2 (M >> N, JOBZ = 'O') */
/* N left singular vectors to be overwritten on A and */
/* N right singular vectors to be computed in VT */
ir = 1;
/* WORK(IR) is LDWRKR by N */
if (*lwork >= *lda * *n + *n * *n + *n * 3 + bdspac) {
ldwrkr = *lda;
} else {
ldwrkr = (*lwork - *n * *n - *n * 3 - bdspac) / *n;
}
itau = ir + ldwrkr * *n;
nwork = itau + *n;
/* Compute A=Q*R */
/* Workspace: need N*N [R] + N [tau] + N [work] */
/* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */
i__1 = *lwork - nwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Copy R to WORK(IR), zeroing out below it */
dlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
i__1 = *n - 1;
i__2 = *n - 1;
dlaset_("L", &i__1, &i__2, &c_b63, &c_b63, &work[ir + 1], &
ldwrkr);
/* Generate Q in A */
/* Workspace: need N*N [R] + N [tau] + N [work] */
/* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */
i__1 = *lwork - nwork + 1;
dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
&i__1, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize R in WORK(IR) */
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work] */
/* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + 2*N*NB [work] */
i__1 = *lwork - nwork + 1;
dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
/* WORK(IU) is N by N */
iu = nwork;
nwork = iu + *n * *n;
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in WORK(IU) and computing right */
/* singular vectors of bidiagonal matrix in VT */
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] + BDSPAC */
dbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite WORK(IU) by left singular vectors of R */
/* and VT by right singular vectors of R */
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] + N [work] */
/* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
itauq], &work[iu], n, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IU), storing result in WORK(IR) and copying to A */
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N*N [U] */
/* Workspace: prefer M*N [R] + 3*N [e, tauq, taup] + N*N [U] */
i__1 = *m;
i__2 = ldwrkr;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = *m - i__ + 1;
chunk = f2cmin(i__3,ldwrkr);
dgemm_("N", "N", &chunk, n, n, &c_b84, &a[i__ + a_dim1],
lda, &work[iu], n, &c_b63, &work[ir], &ldwrkr);
dlacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
a_dim1], lda);
/* L10: */
}
} else if (wntqs) {
/* Path 3 (M >> N, JOBZ='S') */
/* N left singular vectors to be computed in U and */
/* N right singular vectors to be computed in VT */
ir = 1;
/* WORK(IR) is N by N */
ldwrkr = *n;
itau = ir + ldwrkr * *n;
nwork = itau + *n;
/* Compute A=Q*R */
/* Workspace: need N*N [R] + N [tau] + N [work] */
/* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */
i__2 = *lwork - nwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
/* Copy R to WORK(IR), zeroing out below it */
dlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
i__2 = *n - 1;
i__1 = *n - 1;
dlaset_("L", &i__2, &i__1, &c_b63, &c_b63, &work[ir + 1], &
ldwrkr);
/* Generate Q in A */
/* Workspace: need N*N [R] + N [tau] + N [work] */
/* Workspace: prefer N*N [R] + N [tau] + N*NB [work] */
i__2 = *lwork - nwork + 1;
dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
&i__2, &ierr);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize R in WORK(IR) */
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work] */
/* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + 2*N*NB [work] */
i__2 = *lwork - nwork + 1;
dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagoal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + BDSPAC */
dbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite U by left singular vectors of R and VT */
/* by right singular vectors of R */
/* Workspace: need N*N [R] + 3*N [e, tauq, taup] + N [work] */
/* Workspace: prefer N*N [R] + 3*N [e, tauq, taup] + N*NB [work] */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, n, &work[ir], &ldwrkr, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
/* Multiply Q in A by left singular vectors of R in */
/* WORK(IR), storing result in U */
/* Workspace: need N*N [R] */
dlacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
dgemm_("N", "N", m, n, n, &c_b84, &a[a_offset], lda, &work[ir]
, &ldwrkr, &c_b63, &u[u_offset], ldu);
} else if (wntqa) {
/* Path 4 (M >> N, JOBZ='A') */
/* M left singular vectors to be computed in U and */
/* N right singular vectors to be computed in VT */
iu = 1;
/* WORK(IU) is N by N */
ldwrku = *n;
itau = iu + ldwrku * *n;
nwork = itau + *n;
/* Compute A=Q*R, copying result to U */
/* Workspace: need N*N [U] + N [tau] + N [work] */
/* Workspace: prefer N*N [U] + N [tau] + N*NB [work] */
i__2 = *lwork - nwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
dlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
/* Generate Q in U */
/* Workspace: need N*N [U] + N [tau] + M [work] */
/* Workspace: prefer N*N [U] + N [tau] + M*NB [work] */
i__2 = *lwork - nwork + 1;
dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork],
&i__2, &ierr);
/* Produce R in A, zeroing out other entries */
i__2 = *n - 1;
i__1 = *n - 1;
dlaset_("L", &i__2, &i__1, &c_b63, &c_b63, &a[a_dim1 + 2],
lda);
ie = itau;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize R in A */
/* Workspace: need N*N [U] + 3*N [e, tauq, taup] + N [work] */
/* Workspace: prefer N*N [U] + 3*N [e, tauq, taup] + 2*N*NB [work] */
i__2 = *lwork - nwork + 1;
dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in WORK(IU) and computing right */
/* singular vectors of bidiagonal matrix in VT */
/* Workspace: need N*N [U] + 3*N [e, tauq, taup] + BDSPAC */
dbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], n, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite WORK(IU) by left singular vectors of R and VT */
/* by right singular vectors of R */
/* Workspace: need N*N [U] + 3*N [e, tauq, taup] + N [work] */
/* Workspace: prefer N*N [U] + 3*N [e, tauq, taup] + N*NB [work] */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[
itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
ierr);
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
/* Multiply Q in U by left singular vectors of R in */
/* WORK(IU), storing result in A */
/* Workspace: need N*N [U] */
dgemm_("N", "N", m, n, n, &c_b84, &u[u_offset], ldu, &work[iu]
, &ldwrku, &c_b63, &a[a_offset], lda);
/* Copy left singular vectors of A from A to U */
dlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
}
} else {
/* M .LT. MNTHR */
/* Path 5 (M >= N, but not much larger) */
/* Reduce to bidiagonal form without QR decomposition */
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize A */
/* Workspace: need 3*N [e, tauq, taup] + M [work] */
/* Workspace: prefer 3*N [e, tauq, taup] + (M+N)*NB [work] */
i__2 = *lwork - nwork + 1;
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[nwork], &i__2, &ierr);
if (wntqn) {
/* Path 5n (M >= N, JOBZ='N') */
/* Perform bidiagonal SVD, only computing singular values */
/* Workspace: need 3*N [e, tauq, taup] + BDSPAC */
dbdsdc_("U", "N", n, &s[1], &work[ie], dum, &c__1, dum, &c__1,
dum, idum, &work[nwork], &iwork[1], info);
} else if (wntqo) {
/* Path 5o (M >= N, JOBZ='O') */
iu = nwork;
if (*lwork >= *m * *n + *n * 3 + bdspac) {
/* WORK( IU ) is M by N */
ldwrku = *m;
nwork = iu + ldwrku * *n;
dlaset_("F", m, n, &c_b63, &c_b63, &work[iu], &ldwrku);
/* IR is unused; silence compile warnings */
ir = -1;
} else {
/* WORK( IU ) is N by N */
ldwrku = *n;
nwork = iu + ldwrku * *n;
/* WORK(IR) is LDWRKR by N */
ir = nwork;
ldwrkr = (*lwork - *n * *n - *n * 3) / *n;
}
nwork = iu + ldwrku * *n;
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in WORK(IU) and computing right */
/* singular vectors of bidiagonal matrix in VT */
/* Workspace: need 3*N [e, tauq, taup] + N*N [U] + BDSPAC */
dbdsdc_("U", "I", n, &s[1], &work[ie], &work[iu], &ldwrku, &
vt[vt_offset], ldvt, dum, idum, &work[nwork], &iwork[
1], info);
/* Overwrite VT by right singular vectors of A */
/* Workspace: need 3*N [e, tauq, taup] + N*N [U] + N [work] */
/* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
if (*lwork >= *m * *n + *n * 3 + bdspac) {
/* Path 5o-fast */
/* Overwrite WORK(IU) by left singular vectors of A */
/* Workspace: need 3*N [e, tauq, taup] + M*N [U] + N [work] */
/* Workspace: prefer 3*N [e, tauq, taup] + M*N [U] + N*NB [work] */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
ierr);
/* Copy left singular vectors of A from WORK(IU) to A */
dlacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda);
} else {
/* Path 5o-slow */
/* Generate Q in A */
/* Workspace: need 3*N [e, tauq, taup] + N*N [U] + N [work] */
/* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + N*NB [work] */
i__2 = *lwork - nwork + 1;
dorgbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
work[nwork], &i__2, &ierr);
/* Multiply Q in A by left singular vectors of */
/* bidiagonal matrix in WORK(IU), storing result in */
/* WORK(IR) and copying to A */
/* Workspace: need 3*N [e, tauq, taup] + N*N [U] + NB*N [R] */
/* Workspace: prefer 3*N [e, tauq, taup] + N*N [U] + M*N [R] */
i__2 = *m;
i__1 = ldwrkr;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__1) {
/* Computing MIN */
i__3 = *m - i__ + 1;
chunk = f2cmin(i__3,ldwrkr);
dgemm_("N", "N", &chunk, n, n, &c_b84, &a[i__ +
a_dim1], lda, &work[iu], &ldwrku, &c_b63, &
work[ir], &ldwrkr);
dlacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
a_dim1], lda);
/* L20: */
}
}
} else if (wntqs) {
/* Path 5s (M >= N, JOBZ='S') */
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* Workspace: need 3*N [e, tauq, taup] + BDSPAC */
dlaset_("F", m, n, &c_b63, &c_b63, &u[u_offset], ldu);
dbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite U by left singular vectors of A and VT */
/* by right singular vectors of A */
/* Workspace: need 3*N [e, tauq, taup] + N [work] */
/* Workspace: prefer 3*N [e, tauq, taup] + N*NB [work] */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, n, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
} else if (wntqa) {
/* Path 5a (M >= N, JOBZ='A') */
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* Workspace: need 3*N [e, tauq, taup] + BDSPAC */
dlaset_("F", m, m, &c_b63, &c_b63, &u[u_offset], ldu);
dbdsdc_("U", "I", n, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Set the right corner of U to identity matrix */
if (*m > *n) {
i__1 = *m - *n;
i__2 = *m - *n;
dlaset_("F", &i__1, &i__2, &c_b63, &c_b84, &u[*n + 1 + (*
n + 1) * u_dim1], ldu);
}
/* Overwrite U by left singular vectors of A and VT */
/* by right singular vectors of A */
/* Workspace: need 3*N [e, tauq, taup] + M [work] */
/* Workspace: prefer 3*N [e, tauq, taup] + M*NB [work] */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
}
}
} else {
/* A has more columns than rows. If A has sufficiently more */
/* columns than rows, first reduce using the LQ decomposition (if */
/* sufficient workspace available) */
if (*n >= mnthr) {
if (wntqn) {
/* Path 1t (N >> M, JOBZ='N') */
/* No singular vectors to be computed */
itau = 1;
nwork = itau + *m;
/* Compute A=L*Q */
/* Workspace: need M [tau] + M [work] */
/* Workspace: prefer M [tau] + M*NB [work] */
i__1 = *lwork - nwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Zero out above L */
i__1 = *m - 1;
i__2 = *m - 1;
dlaset_("U", &i__1, &i__2, &c_b63, &c_b63, &a[(a_dim1 << 1) +
1], lda);
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize L in A */
/* Workspace: need 3*M [e, tauq, taup] + M [work] */
/* Workspace: prefer 3*M [e, tauq, taup] + 2*M*NB [work] */
i__1 = *lwork - nwork + 1;
dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
nwork = ie + *m;
/* Perform bidiagonal SVD, computing singular values only */
/* Workspace: need M [e] + BDSPAC */
dbdsdc_("U", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1,
dum, idum, &work[nwork], &iwork[1], info);
} else if (wntqo) {
/* Path 2t (N >> M, JOBZ='O') */
/* M right singular vectors to be overwritten on A and */
/* M left singular vectors to be computed in U */
ivt = 1;
/* WORK(IVT) is M by M */
/* WORK(IL) is M by M; it is later resized to M by chunk for gemm */
il = ivt + *m * *m;
if (*lwork >= *m * *n + *m * *m + *m * 3 + bdspac) {
ldwrkl = *m;
chunk = *n;
} else {
ldwrkl = *m;
chunk = (*lwork - *m * *m) / *m;
}
itau = il + ldwrkl * *m;
nwork = itau + *m;
/* Compute A=L*Q */
/* Workspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
/* Workspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
i__1 = *lwork - nwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__1, &ierr);
/* Copy L to WORK(IL), zeroing about above it */
dlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
i__1 = *m - 1;
i__2 = *m - 1;
dlaset_("U", &i__1, &i__2, &c_b63, &c_b63, &work[il + ldwrkl],
&ldwrkl);
/* Generate Q in A */
/* Workspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
/* Workspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
i__1 = *lwork - nwork + 1;
dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
&i__1, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize L in WORK(IL) */
/* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M [work] */
/* Workspace: prefer M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + 2*M*NB [work] */
i__1 = *lwork - nwork + 1;
dgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U, and computing right singular */
/* vectors of bidiagonal matrix in WORK(IVT) */
/* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + BDSPAC */
dbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
work[ivt], m, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite U by left singular vectors of L and WORK(IVT) */
/* by right singular vectors of L */
/* Workspace: need M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M [work] */
/* Workspace: prefer M*M [VT] + M*M [L] + 3*M [e, tauq, taup] + M*NB [work] */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[
itaup], &work[ivt], m, &work[nwork], &i__1, &ierr);
/* Multiply right singular vectors of L in WORK(IVT) by Q */
/* in A, storing result in WORK(IL) and copying to A */
/* Workspace: need M*M [VT] + M*M [L] */
/* Workspace: prefer M*M [VT] + M*N [L] */
/* At this point, L is resized as M by chunk. */
i__1 = *n;
i__2 = chunk;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = *n - i__ + 1;
blk = f2cmin(i__3,chunk);
dgemm_("N", "N", m, &blk, m, &c_b84, &work[ivt], m, &a[
i__ * a_dim1 + 1], lda, &c_b63, &work[il], &
ldwrkl);
dlacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1
+ 1], lda);
/* L30: */
}
} else if (wntqs) {
/* Path 3t (N >> M, JOBZ='S') */
/* M right singular vectors to be computed in VT and */
/* M left singular vectors to be computed in U */
il = 1;
/* WORK(IL) is M by M */
ldwrkl = *m;
itau = il + ldwrkl * *m;
nwork = itau + *m;
/* Compute A=L*Q */
/* Workspace: need M*M [L] + M [tau] + M [work] */
/* Workspace: prefer M*M [L] + M [tau] + M*NB [work] */
i__2 = *lwork - nwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
/* Copy L to WORK(IL), zeroing out above it */
dlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
i__2 = *m - 1;
i__1 = *m - 1;
dlaset_("U", &i__2, &i__1, &c_b63, &c_b63, &work[il + ldwrkl],
&ldwrkl);
/* Generate Q in A */
/* Workspace: need M*M [L] + M [tau] + M [work] */
/* Workspace: prefer M*M [L] + M [tau] + M*NB [work] */
i__2 = *lwork - nwork + 1;
dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
&i__2, &ierr);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize L in WORK(IU). */
/* Workspace: need M*M [L] + 3*M [e, tauq, taup] + M [work] */
/* Workspace: prefer M*M [L] + 3*M [e, tauq, taup] + 2*M*NB [work] */
i__2 = *lwork - nwork + 1;
dgebrd_(m, m, &work[il], &ldwrkl, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* Workspace: need M*M [L] + 3*M [e, tauq, taup] + BDSPAC */
dbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite U by left singular vectors of L and VT */
/* by right singular vectors of L */
/* Workspace: need M*M [L] + 3*M [e, tauq, taup] + M [work] */
/* Workspace: prefer M*M [L] + 3*M [e, tauq, taup] + M*NB [work] */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", m, m, m, &work[il], &ldwrkl, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
ierr);
/* Multiply right singular vectors of L in WORK(IL) by */
/* Q in A, storing result in VT */
/* Workspace: need M*M [L] */
dlacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl);
dgemm_("N", "N", m, n, m, &c_b84, &work[il], &ldwrkl, &a[
a_offset], lda, &c_b63, &vt[vt_offset], ldvt);
} else if (wntqa) {
/* Path 4t (N >> M, JOBZ='A') */
/* N right singular vectors to be computed in VT and */
/* M left singular vectors to be computed in U */
ivt = 1;
/* WORK(IVT) is M by M */
ldwkvt = *m;
itau = ivt + ldwkvt * *m;
nwork = itau + *m;
/* Compute A=L*Q, copying result to VT */
/* Workspace: need M*M [VT] + M [tau] + M [work] */
/* Workspace: prefer M*M [VT] + M [tau] + M*NB [work] */
i__2 = *lwork - nwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
i__2, &ierr);
dlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
/* Generate Q in VT */
/* Workspace: need M*M [VT] + M [tau] + N [work] */
/* Workspace: prefer M*M [VT] + M [tau] + N*NB [work] */
i__2 = *lwork - nwork + 1;
dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[
nwork], &i__2, &ierr);
/* Produce L in A, zeroing out other entries */
i__2 = *m - 1;
i__1 = *m - 1;
dlaset_("U", &i__2, &i__1, &c_b63, &c_b63, &a[(a_dim1 << 1) +
1], lda);
ie = itau;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize L in A */
/* Workspace: need M*M [VT] + 3*M [e, tauq, taup] + M [work] */
/* Workspace: prefer M*M [VT] + 3*M [e, tauq, taup] + 2*M*NB [work] */
i__2 = *lwork - nwork + 1;
dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in WORK(IVT) */
/* Workspace: need M*M [VT] + 3*M [e, tauq, taup] + BDSPAC */
dbdsdc_("U", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1]
, info);
/* Overwrite U by left singular vectors of L and WORK(IVT) */
/* by right singular vectors of L */
/* Workspace: need M*M [VT] + 3*M [e, tauq, taup]+ M [work] */
/* Workspace: prefer M*M [VT] + 3*M [e, tauq, taup]+ M*NB [work] */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", m, m, m, &a[a_offset], lda, &work[
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &
ierr);
/* Multiply right singular vectors of L in WORK(IVT) by */
/* Q in VT, storing result in A */
/* Workspace: need M*M [VT] */
dgemm_("N", "N", m, n, m, &c_b84, &work[ivt], &ldwkvt, &vt[
vt_offset], ldvt, &c_b63, &a[a_offset], lda);
/* Copy right singular vectors of A from A to VT */
dlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
}
} else {
/* N .LT. MNTHR */
/* Path 5t (N > M, but not much larger) */
/* Reduce to bidiagonal form without LQ decomposition */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize A */
/* Workspace: need 3*M [e, tauq, taup] + N [work] */
/* Workspace: prefer 3*M [e, tauq, taup] + (M+N)*NB [work] */
i__2 = *lwork - nwork + 1;
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[nwork], &i__2, &ierr);
if (wntqn) {
/* Path 5tn (N > M, JOBZ='N') */
/* Perform bidiagonal SVD, only computing singular values */
/* Workspace: need 3*M [e, tauq, taup] + BDSPAC */
dbdsdc_("L", "N", m, &s[1], &work[ie], dum, &c__1, dum, &c__1,
dum, idum, &work[nwork], &iwork[1], info);
} else if (wntqo) {
/* Path 5to (N > M, JOBZ='O') */
ldwkvt = *m;
ivt = nwork;
if (*lwork >= *m * *n + *m * 3 + bdspac) {
/* WORK( IVT ) is M by N */
dlaset_("F", m, n, &c_b63, &c_b63, &work[ivt], &ldwkvt);
nwork = ivt + ldwkvt * *n;
/* IL is unused; silence compile warnings */
il = -1;
} else {
/* WORK( IVT ) is M by M */
nwork = ivt + ldwkvt * *m;
il = nwork;
/* WORK(IL) is M by CHUNK */
chunk = (*lwork - *m * *m - *m * 3) / *m;
}
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in WORK(IVT) */
/* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + BDSPAC */
dbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &
work[ivt], &ldwkvt, dum, idum, &work[nwork], &iwork[1]
, info);
/* Overwrite U by left singular vectors of A */
/* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M [work] */
/* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*NB [work] */
i__2 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
if (*lwork >= *m * *n + *m * 3 + bdspac) {
/* Path 5to-fast */
/* Overwrite WORK(IVT) by left singular vectors of A */
/* Workspace: need 3*M [e, tauq, taup] + M*N [VT] + M [work] */
/* Workspace: prefer 3*M [e, tauq, taup] + M*N [VT] + M*NB [work] */
i__2 = *lwork - nwork + 1;
dormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2,
&ierr);
/* Copy right singular vectors of A from WORK(IVT) to A */
dlacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda);
} else {
/* Path 5to-slow */
/* Generate P**T in A */
/* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M [work] */
/* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*NB [work] */
i__2 = *lwork - nwork + 1;
dorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
work[nwork], &i__2, &ierr);
/* Multiply Q in A by right singular vectors of */
/* bidiagonal matrix in WORK(IVT), storing result in */
/* WORK(IL) and copying to A */
/* Workspace: need 3*M [e, tauq, taup] + M*M [VT] + M*NB [L] */
/* Workspace: prefer 3*M [e, tauq, taup] + M*M [VT] + M*N [L] */
i__2 = *n;
i__1 = chunk;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__1) {
/* Computing MIN */
i__3 = *n - i__ + 1;
blk = f2cmin(i__3,chunk);
dgemm_("N", "N", m, &blk, m, &c_b84, &work[ivt], &
ldwkvt, &a[i__ * a_dim1 + 1], lda, &c_b63, &
work[il], m);
dlacpy_("F", m, &blk, &work[il], m, &a[i__ * a_dim1 +
1], lda);
/* L40: */
}
}
} else if (wntqs) {
/* Path 5ts (N > M, JOBZ='S') */
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* Workspace: need 3*M [e, tauq, taup] + BDSPAC */
dlaset_("F", m, n, &c_b63, &c_b63, &vt[vt_offset], ldvt);
dbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Overwrite U by left singular vectors of A and VT */
/* by right singular vectors of A */
/* Workspace: need 3*M [e, tauq, taup] + M [work] */
/* Workspace: prefer 3*M [e, tauq, taup] + M*NB [work] */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", m, n, m, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
} else if (wntqa) {
/* Path 5ta (N > M, JOBZ='A') */
/* Perform bidiagonal SVD, computing left singular vectors */
/* of bidiagonal matrix in U and computing right singular */
/* vectors of bidiagonal matrix in VT */
/* Workspace: need 3*M [e, tauq, taup] + BDSPAC */
dlaset_("F", n, n, &c_b63, &c_b63, &vt[vt_offset], ldvt);
dbdsdc_("L", "I", m, &s[1], &work[ie], &u[u_offset], ldu, &vt[
vt_offset], ldvt, dum, idum, &work[nwork], &iwork[1],
info);
/* Set the right corner of VT to identity matrix */
if (*n > *m) {
i__1 = *n - *m;
i__2 = *n - *m;
dlaset_("F", &i__1, &i__2, &c_b63, &c_b84, &vt[*m + 1 + (*
m + 1) * vt_dim1], ldvt);
}
/* Overwrite U by left singular vectors of A and VT */
/* by right singular vectors of A */
/* Workspace: need 3*M [e, tauq, taup] + N [work] */
/* Workspace: prefer 3*M [e, tauq, taup] + N*NB [work] */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
i__1 = *lwork - nwork + 1;
dormbr_("P", "R", "T", n, n, m, &a[a_offset], lda, &work[
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
ierr);
}
}
}
/* Undo scaling if necessary */
if (iscl == 1) {
if (anrm > bignum) {
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, &ierr);
}
if (anrm < smlnum) {
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, &ierr);
}
}
/* Return optimal workspace in WORK(1) */
work[1] = (doublereal) maxwrk;
return;
/* End of DGESDD */
} /* dgesdd_ */
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