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OpenBLAS/lapack-netlib/SRC/zgejsv.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]/Cd(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 doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c_n1 = -1;
static integer c__1 = 1;
static integer c__0 = 0;
static doublereal c_b141 = 1.;
static logical c_false = FALSE_;
/* > \brief \b ZGEJSV */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download ZGEJSV + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgejsv.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgejsv.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgejsv.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE ZGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP, */
/* M, N, A, LDA, SVA, U, LDU, V, LDV, */
/* CWORK, LWORK, RWORK, LRWORK, IWORK, INFO ) */
/* IMPLICIT NONE */
/* INTEGER INFO, LDA, LDU, LDV, LWORK, M, N */
/* COMPLEX*16 A( LDA, * ), U( LDU, * ), V( LDV, * ), CWORK( LWORK ) */
/* DOUBLE PRECISION SVA( N ), RWORK( LRWORK ) */
/* INTEGER IWORK( * ) */
/* CHARACTER*1 JOBA, JOBP, JOBR, JOBT, JOBU, JOBV */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZGEJSV computes the singular value decomposition (SVD) of a complex M-by-N */
/* > matrix [A], where M >= N. The SVD of [A] is written as */
/* > */
/* > [A] = [U] * [SIGMA] * [V]^*, */
/* > */
/* > where [SIGMA] is an N-by-N (M-by-N) matrix which is zero except for its N */
/* > diagonal elements, [U] is an M-by-N (or M-by-M) unitary matrix, and */
/* > [V] is an N-by-N unitary 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. The matrices [U] and [V] */
/* > are computed and stored in the arrays U and V, respectively. The diagonal */
/* > of [SIGMA] is computed and stored in the array SVA. */
/* > \endverbatim */
/* > */
/* > Arguments: */
/* > ========== */
/* > */
/* > \param[in] JOBA */
/* > \verbatim */
/* > JOBA is CHARACTER*1 */
/* > Specifies the level of accuracy: */
/* > = 'C': This option works well (high relative accuracy) if A = B * D, */
/* > with well-conditioned B and arbitrary diagonal matrix D. */
/* > The accuracy cannot be spoiled by COLUMN scaling. The */
/* > accuracy of the computed output depends on the condition of */
/* > B, and the procedure aims at the best theoretical accuracy. */
/* > The relative error max_{i=1:N}|d sigma_i| / sigma_i is */
/* > bounded by f(M,N)*epsilon* cond(B), independent of D. */
/* > The input matrix is preprocessed with the QRF with column */
/* > pivoting. This initial preprocessing and preconditioning by */
/* > a rank revealing QR factorization is common for all values of */
/* > JOBA. Additional actions are specified as follows: */
/* > = 'E': Computation as with 'C' with an additional estimate of the */
/* > condition number of B. It provides a realistic error bound. */
/* > = 'F': If A = D1 * C * D2 with ill-conditioned diagonal scalings */
/* > D1, D2, and well-conditioned matrix C, this option gives */
/* > higher accuracy than the 'C' option. If the structure of the */
/* > input matrix is not known, and relative accuracy is */
/* > desirable, then this option is advisable. The input matrix A */
/* > is preprocessed with QR factorization with FULL (row and */
/* > column) pivoting. */
/* > = 'G': Computation as with 'F' with an additional estimate of the */
/* > condition number of B, where A=B*D. If A has heavily weighted */
/* > rows, then using this condition number gives too pessimistic */
/* > error bound. */
/* > = 'A': Small singular values are not well determined by the data */
/* > and are considered as noisy; the matrix is treated as */
/* > numerically rank deficient. The error in the computed */
/* > singular values is bounded by f(m,n)*epsilon*||A||. */
/* > The computed SVD A = U * S * V^* restores A up to */
/* > f(m,n)*epsilon*||A||. */
/* > This gives the procedure the licence to discard (set to zero) */
/* > all singular values below N*epsilon*||A||. */
/* > = 'R': Similar as in 'A'. Rank revealing property of the initial */
/* > QR factorization is used do reveal (using triangular factor) */
/* > a gap sigma_{r+1} < epsilon * sigma_r in which case the */
/* > numerical RANK is declared to be r. The SVD is computed with */
/* > absolute error bounds, but more accurately than with 'A'. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBU */
/* > \verbatim */
/* > JOBU is CHARACTER*1 */
/* > Specifies whether to compute the columns of U: */
/* > = 'U': N columns of U are returned in the array U. */
/* > = 'F': full set of M left sing. vectors is returned in the array U. */
/* > = 'W': U may be used as workspace of length M*N. See the description */
/* > of U. */
/* > = 'N': U is not computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBV */
/* > \verbatim */
/* > JOBV is CHARACTER*1 */
/* > Specifies whether to compute the matrix V: */
/* > = 'V': N columns of V are returned in the array V; Jacobi rotations */
/* > are not explicitly accumulated. */
/* > = 'J': N columns of V are returned in the array V, but they are */
/* > computed as the product of Jacobi rotations, if JOBT = 'N'. */
/* > = 'W': V may be used as workspace of length N*N. See the description */
/* > of V. */
/* > = 'N': V is not computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBR */
/* > \verbatim */
/* > JOBR is CHARACTER*1 */
/* > Specifies the RANGE for the singular values. Issues the licence to */
/* > set to zero small positive singular values if they are outside */
/* > specified range. If A .NE. 0 is scaled so that the largest singular */
/* > value of c*A is around SQRT(BIG), BIG=DLAMCH('O'), then JOBR issues */
/* > the licence to kill columns of A whose norm in c*A is less than */
/* > SQRT(SFMIN) (for JOBR = 'R'), or less than SMALL=SFMIN/EPSLN, */
/* > where SFMIN=DLAMCH('S'), EPSLN=DLAMCH('E'). */
/* > = 'N': Do not kill small columns of c*A. This option assumes that */
/* > BLAS and QR factorizations and triangular solvers are */
/* > implemented to work in that range. If the condition of A */
/* > is greater than BIG, use ZGESVJ. */
/* > = 'R': RESTRICTED range for sigma(c*A) is [SQRT(SFMIN), SQRT(BIG)] */
/* > (roughly, as described above). This option is recommended. */
/* > =========================== */
/* > For computing the singular values in the FULL range [SFMIN,BIG] */
/* > use ZGESVJ. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBT */
/* > \verbatim */
/* > JOBT is CHARACTER*1 */
/* > If the matrix is square then the procedure may determine to use */
/* > transposed A if A^* seems to be better with respect to convergence. */
/* > If the matrix is not square, JOBT is ignored. */
/* > The decision is based on two values of entropy over the adjoint */
/* > orbit of A^* * A. See the descriptions of WORK(6) and WORK(7). */
/* > = 'T': transpose if entropy test indicates possibly faster */
/* > convergence of Jacobi process if A^* is taken as input. If A is */
/* > replaced with A^*, then the row pivoting is included automatically. */
/* > = 'N': do not speculate. */
/* > The option 'T' can be used to compute only the singular values, or */
/* > the full SVD (U, SIGMA and V). For only one set of singular vectors */
/* > (U or V), the caller should provide both U and V, as one of the */
/* > matrices is used as workspace if the matrix A is transposed. */
/* > The implementer can easily remove this constraint and make the */
/* > code more complicated. See the descriptions of U and V. */
/* > In general, this option is considered experimental, and 'N'; should */
/* > be preferred. This is subject to changes in the future. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBP */
/* > \verbatim */
/* > JOBP is CHARACTER*1 */
/* > Issues the licence to introduce structured perturbations to drown */
/* > denormalized numbers. This licence should be active if the */
/* > denormals are poorly implemented, causing slow computation, */
/* > especially in cases of fast convergence (!). For details see [1,2]. */
/* > For the sake of simplicity, this perturbations are included only */
/* > when the full SVD or only the singular values are requested. The */
/* > implementer/user can easily add the perturbation for the cases of */
/* > computing one set of singular vectors. */
/* > = 'P': introduce perturbation */
/* > = 'N': do not perturb */
/* > \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 COMPLEX*16 array, dimension (LDA,N) */
/* > On entry, the M-by-N matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] SVA */
/* > \verbatim */
/* > SVA is DOUBLE PRECISION array, dimension (N) */
/* > On exit, */
/* > - For WORK(1)/WORK(2) = ONE: The singular values of A. During the */
/* > computation SVA contains Euclidean column norms of the */
/* > iterated matrices in the array A. */
/* > - For WORK(1) .NE. WORK(2): The singular values of A are */
/* > (WORK(1)/WORK(2)) * SVA(1:N). This factored form is used if */
/* > sigma_max(A) overflows or if small singular values have been */
/* > saved from underflow by scaling the input matrix A. */
/* > - If JOBR='R' then some of the singular values may be returned */
/* > as exact zeros obtained by "set to zero" because they are */
/* > below the numerical rank threshold or are denormalized numbers. */
/* > \endverbatim */
/* > */
/* > \param[out] U */
/* > \verbatim */
/* > U is COMPLEX*16 array, dimension ( LDU, N ) */
/* > If JOBU = 'U', then U contains on exit the M-by-N matrix of */
/* > the left singular vectors. */
/* > If JOBU = 'F', then U contains on exit the M-by-M matrix of */
/* > the left singular vectors, including an ONB */
/* > of the orthogonal complement of the Range(A). */
/* > If JOBU = 'W' .AND. (JOBV = 'V' .AND. JOBT = 'T' .AND. M = N), */
/* > then U is used as workspace if the procedure */
/* > replaces A with A^*. In that case, [V] is computed */
/* > in U as left singular vectors of A^* and then */
/* > copied back to the V array. This 'W' option is just */
/* > a reminder to the caller that in this case U is */
/* > reserved as workspace of length N*N. */
/* > If JOBU = 'N' U is not referenced, unless JOBT='T'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDU */
/* > \verbatim */
/* > LDU is INTEGER */
/* > The leading dimension of the array U, LDU >= 1. */
/* > IF JOBU = 'U' or 'F' or 'W', then LDU >= M. */
/* > \endverbatim */
/* > */
/* > \param[out] V */
/* > \verbatim */
/* > V is COMPLEX*16 array, dimension ( LDV, N ) */
/* > If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of */
/* > the right singular vectors; */
/* > If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N), */
/* > then V is used as workspace if the pprocedure */
/* > replaces A with A^*. In that case, [U] is computed */
/* > in V as right singular vectors of A^* and then */
/* > copied back to the U array. This 'W' option is just */
/* > a reminder to the caller that in this case V is */
/* > reserved as workspace of length N*N. */
/* > If JOBV = 'N' V is not referenced, unless JOBT='T'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDV */
/* > \verbatim */
/* > LDV is INTEGER */
/* > The leading dimension of the array V, LDV >= 1. */
/* > If JOBV = 'V' or 'J' or 'W', then LDV >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] CWORK */
/* > \verbatim */
/* > CWORK is COMPLEX*16 array, dimension (MAX(2,LWORK)) */
/* > If the call to ZGEJSV is a workspace query (indicated by LWORK=-1 or */
/* > LRWORK=-1), then on exit CWORK(1) contains the required length of */
/* > CWORK for the job parameters used in the call. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > Length of CWORK to confirm proper allocation of workspace. */
/* > LWORK depends on the job: */
/* > */
/* > 1. If only SIGMA is needed ( JOBU = 'N', JOBV = 'N' ) and */
/* > 1.1 .. no scaled condition estimate required (JOBA.NE.'E'.AND.JOBA.NE.'G'): */
/* > LWORK >= 2*N+1. This is the minimal requirement. */
/* > ->> For optimal performance (blocked code) the optimal value */
/* > is LWORK >= N + (N+1)*NB. Here NB is the optimal */
/* > block size for ZGEQP3 and ZGEQRF. */
/* > In general, optimal LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(ZGEQP3),N+LWORK(ZGEQRF), LWORK(ZGESVJ)). */
/* > 1.2. .. an estimate of the scaled condition number of A is */
/* > required (JOBA='E', or 'G'). In this case, LWORK the minimal */
/* > requirement is LWORK >= N*N + 2*N. */
/* > ->> For optimal performance (blocked code) the optimal value */
/* > is LWORK >= f2cmax(N+(N+1)*NB, N*N+2*N)=N**2+2*N. */
/* > In general, the optimal length LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(ZGEQP3),N+LWORK(ZGEQRF), LWORK(ZGESVJ), */
/* > N*N+LWORK(ZPOCON)). */
/* > 2. If SIGMA and the right singular vectors are needed (JOBV = 'V'), */
/* > (JOBU = 'N') */
/* > 2.1 .. no scaled condition estimate requested (JOBE = 'N'): */
/* > -> the minimal requirement is LWORK >= 3*N. */
/* > -> For optimal performance, */
/* > LWORK >= f2cmax(N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB, */
/* > where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQ, */
/* > ZUNMLQ. In general, the optimal length LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(ZGEQP3), N+LWORK(ZGESVJ), */
/* > N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)). */
/* > 2.2 .. an estimate of the scaled condition number of A is */
/* > required (JOBA='E', or 'G'). */
/* > -> the minimal requirement is LWORK >= 3*N. */
/* > -> For optimal performance, */
/* > LWORK >= f2cmax(N+(N+1)*NB, 2*N,2*N+N*NB)=2*N+N*NB, */
/* > where NB is the optimal block size for ZGEQP3, ZGEQRF, ZGELQ, */
/* > ZUNMLQ. In general, the optimal length LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(ZGEQP3), LWORK(ZPOCON), N+LWORK(ZGESVJ), */
/* > N+LWORK(ZGELQF), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMLQ)). */
/* > 3. If SIGMA and the left singular vectors are needed */
/* > 3.1 .. no scaled condition estimate requested (JOBE = 'N'): */
/* > -> the minimal requirement is LWORK >= 3*N. */
/* > -> For optimal performance: */
/* > if JOBU = 'U' :: LWORK >= f2cmax(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB, */
/* > where NB is the optimal block size for ZGEQP3, ZGEQRF, ZUNMQR. */
/* > In general, the optimal length LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(ZGEQP3), 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMQR)). */
/* > 3.2 .. an estimate of the scaled condition number of A is */
/* > required (JOBA='E', or 'G'). */
/* > -> the minimal requirement is LWORK >= 3*N. */
/* > -> For optimal performance: */
/* > if JOBU = 'U' :: LWORK >= f2cmax(3*N, N+(N+1)*NB, 2*N+N*NB)=2*N+N*NB, */
/* > where NB is the optimal block size for ZGEQP3, ZGEQRF, ZUNMQR. */
/* > In general, the optimal length LWORK is computed as */
/* > LWORK >= f2cmax(N+LWORK(ZGEQP3),N+LWORK(ZPOCON), */
/* > 2*N+LWORK(ZGEQRF), N+LWORK(ZUNMQR)). */
/* > 4. If the full SVD is needed: (JOBU = 'U' or JOBU = 'F') and */
/* > 4.1. if JOBV = 'V' */
/* > the minimal requirement is LWORK >= 5*N+2*N*N. */
/* > 4.2. if JOBV = 'J' the minimal requirement is */
/* > LWORK >= 4*N+N*N. */
/* > In both cases, the allocated CWORK can accommodate blocked runs */
/* > of ZGEQP3, ZGEQRF, ZGELQF, SUNMQR, ZUNMLQ. */
/* > */
/* > If the call to ZGEJSV is a workspace query (indicated by LWORK=-1 or */
/* > LRWORK=-1), then on exit CWORK(1) contains the optimal and CWORK(2) contains the */
/* > minimal length of CWORK for the job parameters used in the call. */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* > RWORK is DOUBLE PRECISION array, dimension (MAX(7,LWORK)) */
/* > On exit, */
/* > RWORK(1) = Determines the scaling factor SCALE = RWORK(2) / RWORK(1) */
/* > such that SCALE*SVA(1:N) are the computed singular values */
/* > of A. (See the description of SVA().) */
/* > RWORK(2) = See the description of RWORK(1). */
/* > RWORK(3) = SCONDA is an estimate for the condition number of */
/* > column equilibrated A. (If JOBA = 'E' or 'G') */
/* > SCONDA is an estimate of SQRT(||(R^* * R)^(-1)||_1). */
/* > It is computed using SPOCON. It holds */
/* > N^(-1/4) * SCONDA <= ||R^(-1)||_2 <= N^(1/4) * SCONDA */
/* > where R is the triangular factor from the QRF of A. */
/* > However, if R is truncated and the numerical rank is */
/* > determined to be strictly smaller than N, SCONDA is */
/* > returned as -1, thus indicating that the smallest */
/* > singular values might be lost. */
/* > */
/* > If full SVD is needed, the following two condition numbers are */
/* > useful for the analysis of the algorithm. They are provied for */
/* > a developer/implementer who is familiar with the details of */
/* > the method. */
/* > */
/* > RWORK(4) = an estimate of the scaled condition number of the */
/* > triangular factor in the first QR factorization. */
/* > RWORK(5) = an estimate of the scaled condition number of the */
/* > triangular factor in the second QR factorization. */
/* > The following two parameters are computed if JOBT = 'T'. */
/* > They are provided for a developer/implementer who is familiar */
/* > with the details of the method. */
/* > RWORK(6) = the entropy of A^* * A :: this is the Shannon entropy */
/* > of diag(A^* * A) / Trace(A^* * A) taken as point in the */
/* > probability simplex. */
/* > RWORK(7) = the entropy of A * A^*. (See the description of RWORK(6).) */
/* > If the call to ZGEJSV is a workspace query (indicated by LWORK=-1 or */
/* > LRWORK=-1), then on exit RWORK(1) contains the required length of */
/* > RWORK for the job parameters used in the call. */
/* > \endverbatim */
/* > */
/* > \param[in] LRWORK */
/* > \verbatim */
/* > LRWORK is INTEGER */
/* > Length of RWORK to confirm proper allocation of workspace. */
/* > LRWORK depends on the job: */
/* > */
/* > 1. If only the singular values are requested i.e. if */
/* > LSAME(JOBU,'N') .AND. LSAME(JOBV,'N') */
/* > then: */
/* > 1.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'), */
/* > then: LRWORK = f2cmax( 7, 2 * M ). */
/* > 1.2. Otherwise, LRWORK = f2cmax( 7, N ). */
/* > 2. If singular values with the right singular vectors are requested */
/* > i.e. if */
/* > (LSAME(JOBV,'V').OR.LSAME(JOBV,'J')) .AND. */
/* > .NOT.(LSAME(JOBU,'U').OR.LSAME(JOBU,'F')) */
/* > then: */
/* > 2.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'), */
/* > then LRWORK = f2cmax( 7, 2 * M ). */
/* > 2.2. Otherwise, LRWORK = f2cmax( 7, N ). */
/* > 3. If singular values with the left singular vectors are requested, i.e. if */
/* > (LSAME(JOBU,'U').OR.LSAME(JOBU,'F')) .AND. */
/* > .NOT.(LSAME(JOBV,'V').OR.LSAME(JOBV,'J')) */
/* > then: */
/* > 3.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'), */
/* > then LRWORK = f2cmax( 7, 2 * M ). */
/* > 3.2. Otherwise, LRWORK = f2cmax( 7, N ). */
/* > 4. If singular values with both the left and the right singular vectors */
/* > are requested, i.e. if */
/* > (LSAME(JOBU,'U').OR.LSAME(JOBU,'F')) .AND. */
/* > (LSAME(JOBV,'V').OR.LSAME(JOBV,'J')) */
/* > then: */
/* > 4.1. If LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G'), */
/* > then LRWORK = f2cmax( 7, 2 * M ). */
/* > 4.2. Otherwise, LRWORK = f2cmax( 7, N ). */
/* > */
/* > If, on entry, LRWORK = -1 or LWORK=-1, a workspace query is assumed and */
/* > the length of RWORK is returned in RWORK(1). */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, of dimension at least 4, that further depends */
/* > on the job: */
/* > */
/* > 1. If only the singular values are requested then: */
/* > If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') ) */
/* > then the length of IWORK is N+M; otherwise the length of IWORK is N. */
/* > 2. If the singular values and the right singular vectors are requested then: */
/* > If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') ) */
/* > then the length of IWORK is N+M; otherwise the length of IWORK is N. */
/* > 3. If the singular values and the left singular vectors are requested then: */
/* > If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') ) */
/* > then the length of IWORK is N+M; otherwise the length of IWORK is N. */
/* > 4. If the singular values with both the left and the right singular vectors */
/* > are requested, then: */
/* > 4.1. If LSAME(JOBV,'J') the length of IWORK is determined as follows: */
/* > If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') ) */
/* > then the length of IWORK is N+M; otherwise the length of IWORK is N. */
/* > 4.2. If LSAME(JOBV,'V') the length of IWORK is determined as follows: */
/* > If ( LSAME(JOBT,'T') .OR. LSAME(JOBA,'F') .OR. LSAME(JOBA,'G') ) */
/* > then the length of IWORK is 2*N+M; otherwise the length of IWORK is 2*N. */
/* > */
/* > On exit, */
/* > IWORK(1) = the numerical rank determined after the initial */
/* > QR factorization with pivoting. See the descriptions */
/* > of JOBA and JOBR. */
/* > IWORK(2) = the number of the computed nonzero singular values */
/* > IWORK(3) = if nonzero, a warning message: */
/* > If IWORK(3) = 1 then some of the column norms of A */
/* > were denormalized floats. The requested high accuracy */
/* > is not warranted by the data. */
/* > IWORK(4) = 1 or -1. If IWORK(4) = 1, then the procedure used A^* to */
/* > do the job as specified by the JOB parameters. */
/* > If the call to ZGEJSV is a workspace query (indicated by LWORK = -1 or */
/* > LRWORK = -1), then on exit IWORK(1) contains the required length of */
/* > IWORK for the job parameters used in the call. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > < 0: if INFO = -i, then the i-th argument had an illegal value. */
/* > = 0: successful exit; */
/* > > 0: ZGEJSV did not converge in the maximal allowed number */
/* > of sweeps. The computed values may be inaccurate. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2016 */
/* > \ingroup complex16GEsing */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > ZGEJSV implements a preconditioned Jacobi SVD algorithm. It uses ZGEQP3, */
/* > ZGEQRF, and ZGELQF as preprocessors and preconditioners. Optionally, an */
/* > additional row pivoting can be used as a preprocessor, which in some */
/* > cases results in much higher accuracy. An example is matrix A with the */
/* > structure A = D1 * C * D2, where D1, D2 are arbitrarily ill-conditioned */
/* > diagonal matrices and C is well-conditioned matrix. In that case, complete */
/* > pivoting in the first QR factorizations provides accuracy dependent on the */
/* > condition number of C, and independent of D1, D2. Such higher accuracy is */
/* > not completely understood theoretically, but it works well in practice. */
/* > Further, if A can be written as A = B*D, with well-conditioned B and some */
/* > diagonal D, then the high accuracy is guaranteed, both theoretically and */
/* > in software, independent of D. For more details see [1], [2]. */
/* > The computational range for the singular values can be the full range */
/* > ( UNDERFLOW,OVERFLOW ), provided that the machine arithmetic and the BLAS */
/* > & LAPACK routines called by ZGEJSV are implemented to work in that range. */
/* > If that is not the case, then the restriction for safe computation with */
/* > the singular values in the range of normalized IEEE numbers is that the */
/* > spectral condition number kappa(A)=sigma_max(A)/sigma_min(A) does not */
/* > overflow. This code (ZGEJSV) is best used in this restricted range, */
/* > meaning that singular values of magnitude below ||A||_2 / DLAMCH('O') are */
/* > returned as zeros. See JOBR for details on this. */
/* > Further, this implementation is somewhat slower than the one described */
/* > in [1,2] due to replacement of some non-LAPACK components, and because */
/* > the choice of some tuning parameters in the iterative part (ZGESVJ) is */
/* > left to the implementer on a particular machine. */
/* > The rank revealing QR factorization (in this code: ZGEQP3) should be */
/* > implemented as in [3]. We have a new version of ZGEQP3 under development */
/* > that is more robust than the current one in LAPACK, with a cleaner cut in */
/* > rank deficient cases. It will be available in the SIGMA library [4]. */
/* > If M is much larger than N, it is obvious that the initial QRF with */
/* > column pivoting can be preprocessed by the QRF without pivoting. That */
/* > well known trick is not used in ZGEJSV because in some cases heavy row */
/* > weighting can be treated with complete pivoting. The overhead in cases */
/* > M much larger than N is then only due to pivoting, but the benefits in */
/* > terms of accuracy have prevailed. The implementer/user can incorporate */
/* > this extra QRF step easily. The implementer can also improve data movement */
/* > (matrix transpose, matrix copy, matrix transposed copy) - this */
/* > implementation of ZGEJSV uses only the simplest, naive data movement. */
/* > \endverbatim */
/* > \par Contributor: */
/* ================== */
/* > */
/* > Zlatko Drmac, Department of Mathematics, Faculty of Science, */
/* > University of Zagreb (Zagreb, Croatia); drmac@math.hr */
/* > \par References: */
/* ================ */
/* > */
/* > \verbatim */
/* > */
/* > [1] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I. */
/* > SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342. */
/* > LAPACK Working note 169. */
/* > [2] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm II. */
/* > SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1343-1362. */
/* > LAPACK Working note 170. */
/* > [3] Z. Drmac and Z. Bujanovic: On the failure of rank-revealing QR */
/* > factorization software - a case study. */
/* > ACM Trans. Math. Softw. Vol. 35, No 2 (2008), pp. 1-28. */
/* > LAPACK Working note 176. */
/* > [4] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV, */
/* > QSVD, (H,K)-SVD computations. */
/* > Department of Mathematics, University of Zagreb, 2008, 2016. */
/* > \endverbatim */
/* > \par Bugs, examples and comments: */
/* ================================= */
/* > */
/* > Please report all bugs and send interesting examples and/or comments to */
/* > drmac@math.hr. Thank you. */
/* > */
/* ===================================================================== */
/* Subroutine */ void zgejsv_(char *joba, char *jobu, char *jobv, char *jobr,
char *jobt, char *jobp, integer *m, integer *n, doublecomplex *a,
integer *lda, doublereal *sva, doublecomplex *u, integer *ldu,
doublecomplex *v, integer *ldv, doublecomplex *cwork, integer *lwork,
doublereal *rwork, integer *lrwork, integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, u_dim1, u_offset, v_dim1, v_offset, i__1, i__2,
i__3, i__4, i__5, i__6, i__7, i__8, i__9, i__10, i__11;
doublereal d__1, d__2, d__3;
doublecomplex z__1;
/* Local variables */
integer lwrk_zgesvj__;
logical defr;
doublereal aapp, aaqq;
integer lwrk_zunmlq__, lwrk_zunmqr__;
logical kill;
integer ierr, lwrk_zgeqp3n__;
doublereal temp1;
integer lwunmqrm, lwqp3, p, q;
logical jracc;
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
integer *);
integer lwrk_zgesvju__, lwrk_zgesvjv__;
extern logical lsame_(char *, char *);
integer lwrk_zunmqrm__;
doublecomplex ctemp;
doublereal entra, small;
integer iwoff;
doublereal sfmin;
logical lsvec;
doublereal epsln;
logical rsvec;
integer lwcon, lwlqf, lwqrf, n1;
extern /* Subroutine */ void zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
logical l2aber;
extern /* Subroutine */ void ztrsm_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *);
doublereal condr1, condr2, uscal1, uscal2;
logical l2kill, l2rank, l2tran, l2pert;
extern /* Subroutine */ void zgeqp3_(integer *, integer *, doublecomplex *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *
, doublereal *, integer *);
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
integer lrwqp3;
extern doublereal dlamch_(char *);
integer nr;
extern /* Subroutine */ void dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *);
extern integer idamax_(integer *, doublereal *, integer *);
doublereal scalem, sconda;
logical goscal;
doublereal aatmin, aatmax;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
logical noscal;
extern /* Subroutine */ void zdscal_(integer *, doublereal *,
doublecomplex *, integer *), zlacgv_(integer *, doublecomplex *,
integer *), dlassq_(integer *, doublereal *, integer *,
doublereal *, doublereal *);
extern integer izamax_(integer *, doublecomplex *, integer *);
extern /* Subroutine */ void zgelqf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
), zlascl_(char *, integer *, integer *, doublereal *, doublereal
*, integer *, integer *, doublecomplex *, integer *, integer *);
doublereal entrat;
logical almort;
doublecomplex cdummy[1];
extern /* Subroutine */ void zgeqrf_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
);
doublereal maxprj;
extern /* Subroutine */ void zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *);
logical errest;
integer lrwcon;
extern /* Subroutine */ void zlapmr_(logical *, integer *, integer *,
doublecomplex *, integer *, integer *);
logical transp;
integer minwrk, lwsvdj;
extern /* Subroutine */ void zpocon_(char *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublecomplex *,
doublereal *, integer *), zgesvj_(char *, char *, char *,
integer *, integer *, doublecomplex *, integer *, doublereal *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *, integer *);
doublereal rdummy[1];
extern /* Subroutine */ void zlassq_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *);
logical lquery;
extern /* Subroutine */ int zlaswp_(integer *, doublecomplex *, integer *,
integer *, integer *, integer *, integer *);
logical rowpiv;
integer optwrk;
extern /* Subroutine */ void zungqr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *), zunmlq_(char *, char *, integer *, integer
*, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *), zunmqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
doublereal big, cond_ok__, xsc;
integer lwrk_zgeqp3__;
doublereal big1;
integer warning, numrank, miniwrk, minrwrk, lrwsvdj, lwunmlq, lwsvdjv,
lwunmqr, lwrk_zgelqf__, lwrk_zgeqrf__;
/* -- LAPACK computational routine (version 3.7.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* June 2017 */
/* =========================================================================== */
/* Test the input arguments */
/* Parameter adjustments */
--sva;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
--cwork;
--rwork;
--iwork;
/* Function Body */
lsvec = lsame_(jobu, "U") || lsame_(jobu, "F");
jracc = lsame_(jobv, "J");
rsvec = lsame_(jobv, "V") || jracc;
rowpiv = lsame_(joba, "F") || lsame_(joba, "G");
l2rank = lsame_(joba, "R");
l2aber = lsame_(joba, "A");
errest = lsame_(joba, "E") || lsame_(joba, "G");
l2tran = lsame_(jobt, "T") && *m == *n;
l2kill = lsame_(jobr, "R");
defr = lsame_(jobr, "N");
l2pert = lsame_(jobp, "P");
lquery = *lwork == -1 || *lrwork == -1;
if (! (rowpiv || l2rank || l2aber || errest || lsame_(joba, "C"))) {
*info = -1;
} else if (! (lsvec || lsame_(jobu, "N") || lsame_(
jobu, "W") && rsvec && l2tran)) {
*info = -2;
} else if (! (rsvec || lsame_(jobv, "N") || lsame_(
jobv, "W") && lsvec && l2tran)) {
*info = -3;
} else if (! (l2kill || defr)) {
*info = -4;
} else if (! (lsame_(jobt, "T") || lsame_(jobt,
"N"))) {
*info = -5;
} else if (! (l2pert || lsame_(jobp, "N"))) {
*info = -6;
} else if (*m < 0) {
*info = -7;
} else if (*n < 0 || *n > *m) {
*info = -8;
} else if (*lda < *m) {
*info = -10;
} else if (lsvec && *ldu < *m) {
*info = -13;
} else if (rsvec && *ldv < *n) {
*info = -15;
} else {
/* #:) */
*info = 0;
}
if (*info == 0) {
/* [[The expressions for computing the minimal and the optimal */
/* values of LCWORK, LRWORK are written with a lot of redundancy and */
/* can be simplified. However, this verbose form is useful for */
/* maintenance and modifications of the code.]] */
/* ZGEQRF of an N x N matrix, ZGELQF of an N x N matrix, */
/* ZUNMLQ for computing N x N matrix, ZUNMQR for computing N x N */
/* matrix, ZUNMQR for computing M x N matrix, respectively. */
lwqp3 = *n + 1;
lwqrf = f2cmax(1,*n);
lwlqf = f2cmax(1,*n);
lwunmlq = f2cmax(1,*n);
lwunmqr = f2cmax(1,*n);
lwunmqrm = f2cmax(1,*m);
lwcon = *n << 1;
/* without and with explicit accumulation of Jacobi rotations */
/* Computing MAX */
i__1 = *n << 1;
lwsvdj = f2cmax(i__1,1);
/* Computing MAX */
i__1 = *n << 1;
lwsvdjv = f2cmax(i__1,1);
lrwqp3 = *n << 1;
lrwcon = *n;
lrwsvdj = *n;
if (lquery) {
zgeqp3_(m, n, &a[a_offset], lda, &iwork[1], cdummy, cdummy, &c_n1,
rdummy, &ierr);
lwrk_zgeqp3__ = (integer) cdummy[0].r;
zgeqrf_(n, n, &a[a_offset], lda, cdummy, cdummy, &c_n1, &ierr);
lwrk_zgeqrf__ = (integer) cdummy[0].r;
zgelqf_(n, n, &a[a_offset], lda, cdummy, cdummy, &c_n1, &ierr);
lwrk_zgelqf__ = (integer) cdummy[0].r;
}
minwrk = 2;
optwrk = 2;
miniwrk = *n;
if (! (lsvec || rsvec)) {
/* only the singular values are requested */
if (errest) {
/* Computing MAX */
/* Computing 2nd power */
i__3 = *n;
i__1 = *n + lwqp3, i__2 = i__3 * i__3 + lwcon, i__1 = f2cmax(
i__1,i__2), i__2 = *n + lwqrf, i__1 = f2cmax(i__1,i__2);
minwrk = f2cmax(i__1,lwsvdj);
} else {
/* Computing MAX */
i__1 = *n + lwqp3, i__2 = *n + lwqrf, i__1 = f2cmax(i__1,i__2);
minwrk = f2cmax(i__1,lwsvdj);
}
if (lquery) {
zgesvj_("L", "N", "N", n, n, &a[a_offset], lda, &sva[1], n, &
v[v_offset], ldv, cdummy, &c_n1, rdummy, &c_n1, &ierr);
lwrk_zgesvj__ = (integer) cdummy[0].r;
if (errest) {
/* Computing MAX */
/* Computing 2nd power */
i__3 = *n;
i__1 = *n + lwrk_zgeqp3__, i__2 = i__3 * i__3 + lwcon,
i__1 = f2cmax(i__1,i__2), i__2 = *n + lwrk_zgeqrf__,
i__1 = f2cmax(i__1,i__2);
optwrk = f2cmax(i__1,lwrk_zgesvj__);
} else {
/* Computing MAX */
i__1 = *n + lwrk_zgeqp3__, i__2 = *n + lwrk_zgeqrf__,
i__1 = f2cmax(i__1,i__2);
optwrk = f2cmax(i__1,lwrk_zgesvj__);
}
}
if (l2tran || rowpiv) {
if (errest) {
/* Computing MAX */
i__1 = 7, i__2 = *m << 1, i__1 = f2cmax(i__1,i__2), i__1 =
f2cmax(i__1,lrwqp3), i__1 = f2cmax(i__1,lrwcon);
minrwrk = f2cmax(i__1,lrwsvdj);
} else {
/* Computing MAX */
i__1 = 7, i__2 = *m << 1, i__1 = f2cmax(i__1,i__2), i__1 =
f2cmax(i__1,lrwqp3);
minrwrk = f2cmax(i__1,lrwsvdj);
}
} else {
if (errest) {
/* Computing MAX */
i__1 = f2cmax(7,lrwqp3), i__1 = f2cmax(i__1,lrwcon);
minrwrk = f2cmax(i__1,lrwsvdj);
} else {
/* Computing MAX */
i__1 = f2cmax(7,lrwqp3);
minrwrk = f2cmax(i__1,lrwsvdj);
}
}
if (rowpiv || l2tran) {
miniwrk += *m;
}
} else if (rsvec && ! lsvec) {
/* singular values and the right singular vectors are requested */
if (errest) {
/* Computing MAX */
i__1 = *n + lwqp3, i__1 = f2cmax(i__1,lwcon), i__1 = f2cmax(i__1,
lwsvdj), i__2 = *n + lwlqf, i__1 = f2cmax(i__1,i__2),
i__2 = (*n << 1) + lwqrf, i__1 = f2cmax(i__1,i__2), i__2
= *n + lwsvdj, i__1 = f2cmax(i__1,i__2), i__2 = *n +
lwunmlq;
minwrk = f2cmax(i__1,i__2);
} else {
/* Computing MAX */
i__1 = *n + lwqp3, i__1 = f2cmax(i__1,lwsvdj), i__2 = *n + lwlqf,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) + lwqrf,
i__1 = f2cmax(i__1,i__2), i__2 = *n + lwsvdj, i__1 = f2cmax(
i__1,i__2), i__2 = *n + lwunmlq;
minwrk = f2cmax(i__1,i__2);
}
if (lquery) {
zgesvj_("L", "U", "N", n, n, &u[u_offset], ldu, &sva[1], n, &
a[a_offset], lda, cdummy, &c_n1, rdummy, &c_n1, &ierr);
lwrk_zgesvj__ = (integer) cdummy[0].r;
zunmlq_("L", "C", n, n, n, &a[a_offset], lda, cdummy, &v[
v_offset], ldv, cdummy, &c_n1, &ierr);
lwrk_zunmlq__ = (integer) cdummy[0].r;
if (errest) {
/* Computing MAX */
i__1 = *n + lwrk_zgeqp3__, i__1 = f2cmax(i__1,lwcon), i__1 =
f2cmax(i__1,lwrk_zgesvj__), i__2 = *n +
lwrk_zgelqf__, i__1 = f2cmax(i__1,i__2), i__2 = (*n
<< 1) + lwrk_zgeqrf__, i__1 = f2cmax(i__1,i__2),
i__2 = *n + lwrk_zgesvj__, i__1 = f2cmax(i__1,i__2),
i__2 = *n + lwrk_zunmlq__;
optwrk = f2cmax(i__1,i__2);
} else {
/* Computing MAX */
i__1 = *n + lwrk_zgeqp3__, i__1 = f2cmax(i__1,lwrk_zgesvj__),
i__2 = *n + lwrk_zgelqf__, i__1 = f2cmax(i__1,i__2),
i__2 = (*n << 1) + lwrk_zgeqrf__, i__1 = f2cmax(
i__1,i__2), i__2 = *n + lwrk_zgesvj__, i__1 = f2cmax(
i__1,i__2), i__2 = *n + lwrk_zunmlq__;
optwrk = f2cmax(i__1,i__2);
}
}
if (l2tran || rowpiv) {
if (errest) {
/* Computing MAX */
i__1 = 7, i__2 = *m << 1, i__1 = f2cmax(i__1,i__2), i__1 =
f2cmax(i__1,lrwqp3), i__1 = f2cmax(i__1,lrwsvdj);
minrwrk = f2cmax(i__1,lrwcon);
} else {
/* Computing MAX */
i__1 = 7, i__2 = *m << 1, i__1 = f2cmax(i__1,i__2), i__1 =
f2cmax(i__1,lrwqp3);
minrwrk = f2cmax(i__1,lrwsvdj);
}
} else {
if (errest) {
/* Computing MAX */
i__1 = f2cmax(7,lrwqp3), i__1 = f2cmax(i__1,lrwsvdj);
minrwrk = f2cmax(i__1,lrwcon);
} else {
/* Computing MAX */
i__1 = f2cmax(7,lrwqp3);
minrwrk = f2cmax(i__1,lrwsvdj);
}
}
if (rowpiv || l2tran) {
miniwrk += *m;
}
} else if (lsvec && ! rsvec) {
/* singular values and the left singular vectors are requested */
if (errest) {
/* Computing MAX */
i__1 = f2cmax(lwqp3,lwcon), i__2 = *n + lwqrf, i__1 = f2cmax(i__1,
i__2), i__1 = f2cmax(i__1,lwsvdj);
minwrk = *n + f2cmax(i__1,lwunmqrm);
} else {
/* Computing MAX */
i__1 = lwqp3, i__2 = *n + lwqrf, i__1 = f2cmax(i__1,i__2), i__1 =
f2cmax(i__1,lwsvdj);
minwrk = *n + f2cmax(i__1,lwunmqrm);
}
if (lquery) {
zgesvj_("L", "U", "N", n, n, &u[u_offset], ldu, &sva[1], n, &
a[a_offset], lda, cdummy, &c_n1, rdummy, &c_n1, &ierr);
lwrk_zgesvj__ = (integer) cdummy[0].r;
zunmqr_("L", "N", m, n, n, &a[a_offset], lda, cdummy, &u[
u_offset], ldu, cdummy, &c_n1, &ierr);
lwrk_zunmqrm__ = (integer) cdummy[0].r;
if (errest) {
/* Computing MAX */
i__1 = f2cmax(lwrk_zgeqp3__,lwcon), i__2 = *n +
lwrk_zgeqrf__, i__1 = f2cmax(i__1,i__2), i__1 = f2cmax(
i__1,lwrk_zgesvj__);
optwrk = *n + f2cmax(i__1,lwrk_zunmqrm__);
} else {
/* Computing MAX */
i__1 = lwrk_zgeqp3__, i__2 = *n + lwrk_zgeqrf__, i__1 =
f2cmax(i__1,i__2), i__1 = f2cmax(i__1,lwrk_zgesvj__);
optwrk = *n + f2cmax(i__1,lwrk_zunmqrm__);
}
}
if (l2tran || rowpiv) {
if (errest) {
/* Computing MAX */
i__1 = 7, i__2 = *m << 1, i__1 = f2cmax(i__1,i__2), i__1 =
f2cmax(i__1,lrwqp3), i__1 = f2cmax(i__1,lrwsvdj);
minrwrk = f2cmax(i__1,lrwcon);
} else {
/* Computing MAX */
i__1 = 7, i__2 = *m << 1, i__1 = f2cmax(i__1,i__2), i__1 =
f2cmax(i__1,lrwqp3);
minrwrk = f2cmax(i__1,lrwsvdj);
}
} else {
if (errest) {
/* Computing MAX */
i__1 = f2cmax(7,lrwqp3), i__1 = f2cmax(i__1,lrwsvdj);
minrwrk = f2cmax(i__1,lrwcon);
} else {
/* Computing MAX */
i__1 = f2cmax(7,lrwqp3);
minrwrk = f2cmax(i__1,lrwsvdj);
}
}
if (rowpiv || l2tran) {
miniwrk += *m;
}
} else {
/* full SVD is requested */
if (! jracc) {
if (errest) {
/* Computing MAX */
/* Computing 2nd power */
i__3 = *n;
/* Computing 2nd power */
i__4 = *n;
/* Computing 2nd power */
i__5 = *n;
/* Computing 2nd power */
i__6 = *n;
/* Computing 2nd power */
i__7 = *n;
/* Computing 2nd power */
i__8 = *n;
/* Computing 2nd power */
i__9 = *n;
/* Computing 2nd power */
i__10 = *n;
/* Computing 2nd power */
i__11 = *n;
i__1 = *n + lwqp3, i__2 = *n + lwcon, i__1 = f2cmax(i__1,
i__2), i__2 = (*n << 1) + i__3 * i__3 + lwcon,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) + lwqrf,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) + lwqp3,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) + i__4 *
i__4 + *n + lwlqf, i__1 = f2cmax(i__1,i__2), i__2 = (
*n << 1) + i__5 * i__5 + *n + i__6 * i__6 + lwcon,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) + i__7 *
i__7 + *n + lwsvdj, i__1 = f2cmax(i__1,i__2), i__2 =
(*n << 1) + i__8 * i__8 + *n + lwsvdjv, i__1 =
f2cmax(i__1,i__2), i__2 = (*n << 1) + i__9 * i__9 + *
n + lwunmqr, i__1 = f2cmax(i__1,i__2), i__2 = (*n <<
1) + i__10 * i__10 + *n + lwunmlq, i__1 = f2cmax(
i__1,i__2), i__2 = *n + i__11 * i__11 + lwsvdj,
i__1 = f2cmax(i__1,i__2), i__2 = *n + lwunmqrm;
minwrk = f2cmax(i__1,i__2);
} else {
/* Computing MAX */
/* Computing 2nd power */
i__3 = *n;
/* Computing 2nd power */
i__4 = *n;
/* Computing 2nd power */
i__5 = *n;
/* Computing 2nd power */
i__6 = *n;
/* Computing 2nd power */
i__7 = *n;
/* Computing 2nd power */
i__8 = *n;
/* Computing 2nd power */
i__9 = *n;
/* Computing 2nd power */
i__10 = *n;
/* Computing 2nd power */
i__11 = *n;
i__1 = *n + lwqp3, i__2 = (*n << 1) + i__3 * i__3 + lwcon,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) + lwqrf,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) + lwqp3,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) + i__4 *
i__4 + *n + lwlqf, i__1 = f2cmax(i__1,i__2), i__2 = (
*n << 1) + i__5 * i__5 + *n + i__6 * i__6 + lwcon,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) + i__7 *
i__7 + *n + lwsvdj, i__1 = f2cmax(i__1,i__2), i__2 =
(*n << 1) + i__8 * i__8 + *n + lwsvdjv, i__1 =
f2cmax(i__1,i__2), i__2 = (*n << 1) + i__9 * i__9 + *
n + lwunmqr, i__1 = f2cmax(i__1,i__2), i__2 = (*n <<
1) + i__10 * i__10 + *n + lwunmlq, i__1 = f2cmax(
i__1,i__2), i__2 = *n + i__11 * i__11 + lwsvdj,
i__1 = f2cmax(i__1,i__2), i__2 = *n + lwunmqrm;
minwrk = f2cmax(i__1,i__2);
}
miniwrk += *n;
if (rowpiv || l2tran) {
miniwrk += *m;
}
} else {
if (errest) {
/* Computing MAX */
/* Computing 2nd power */
i__3 = *n;
/* Computing 2nd power */
i__4 = *n;
i__1 = *n + lwqp3, i__2 = *n + lwcon, i__1 = f2cmax(i__1,
i__2), i__2 = (*n << 1) + lwqrf, i__1 = f2cmax(i__1,
i__2), i__2 = (*n << 1) + i__3 * i__3 + lwsvdjv,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) + i__4 *
i__4 + *n + lwunmqr, i__1 = f2cmax(i__1,i__2), i__2 =
*n + lwunmqrm;
minwrk = f2cmax(i__1,i__2);
} else {
/* Computing MAX */
/* Computing 2nd power */
i__3 = *n;
/* Computing 2nd power */
i__4 = *n;
i__1 = *n + lwqp3, i__2 = (*n << 1) + lwqrf, i__1 = f2cmax(
i__1,i__2), i__2 = (*n << 1) + i__3 * i__3 +
lwsvdjv, i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1)
+ i__4 * i__4 + *n + lwunmqr, i__1 = f2cmax(i__1,
i__2), i__2 = *n + lwunmqrm;
minwrk = f2cmax(i__1,i__2);
}
if (rowpiv || l2tran) {
miniwrk += *m;
}
}
if (lquery) {
zunmqr_("L", "N", m, n, n, &a[a_offset], lda, cdummy, &u[
u_offset], ldu, cdummy, &c_n1, &ierr);
lwrk_zunmqrm__ = (integer) cdummy[0].r;
zunmqr_("L", "N", n, n, n, &a[a_offset], lda, cdummy, &u[
u_offset], ldu, cdummy, &c_n1, &ierr);
lwrk_zunmqr__ = (integer) cdummy[0].r;
if (! jracc) {
zgeqp3_(n, n, &a[a_offset], lda, &iwork[1], cdummy,
cdummy, &c_n1, rdummy, &ierr);
lwrk_zgeqp3n__ = (integer) cdummy[0].r;
zgesvj_("L", "U", "N", n, n, &u[u_offset], ldu, &sva[1],
n, &v[v_offset], ldv, cdummy, &c_n1, rdummy, &
c_n1, &ierr);
lwrk_zgesvj__ = (integer) cdummy[0].r;
zgesvj_("U", "U", "N", n, n, &u[u_offset], ldu, &sva[1],
n, &v[v_offset], ldv, cdummy, &c_n1, rdummy, &
c_n1, &ierr);
lwrk_zgesvju__ = (integer) cdummy[0].r;
zgesvj_("L", "U", "V", n, n, &u[u_offset], ldu, &sva[1],
n, &v[v_offset], ldv, cdummy, &c_n1, rdummy, &
c_n1, &ierr);
lwrk_zgesvjv__ = (integer) cdummy[0].r;
zunmlq_("L", "C", n, n, n, &a[a_offset], lda, cdummy, &v[
v_offset], ldv, cdummy, &c_n1, &ierr);
lwrk_zunmlq__ = (integer) cdummy[0].r;
if (errest) {
/* Computing MAX */
/* Computing 2nd power */
i__3 = *n;
/* Computing 2nd power */
i__4 = *n;
/* Computing 2nd power */
i__5 = *n;
/* Computing 2nd power */
i__6 = *n;
/* Computing 2nd power */
i__7 = *n;
/* Computing 2nd power */
i__8 = *n;
/* Computing 2nd power */
i__9 = *n;
/* Computing 2nd power */
i__10 = *n;
/* Computing 2nd power */
i__11 = *n;
i__1 = *n + lwrk_zgeqp3__, i__2 = *n + lwcon, i__1 =
f2cmax(i__1,i__2), i__2 = (*n << 1) + i__3 *
i__3 + lwcon, i__1 = f2cmax(i__1,i__2), i__2 = (*
n << 1) + lwrk_zgeqrf__, i__1 = f2cmax(i__1,i__2)
, i__2 = (*n << 1) + lwrk_zgeqp3n__, i__1 =
f2cmax(i__1,i__2), i__2 = (*n << 1) + i__4 *
i__4 + *n + lwrk_zgelqf__, i__1 = f2cmax(i__1,
i__2), i__2 = (*n << 1) + i__5 * i__5 + *n +
i__6 * i__6 + lwcon, i__1 = f2cmax(i__1,i__2),
i__2 = (*n << 1) + i__7 * i__7 + *n +
lwrk_zgesvj__, i__1 = f2cmax(i__1,i__2), i__2 = (
*n << 1) + i__8 * i__8 + *n + lwrk_zgesvjv__,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) +
i__9 * i__9 + *n + lwrk_zunmqr__, i__1 = f2cmax(
i__1,i__2), i__2 = (*n << 1) + i__10 * i__10
+ *n + lwrk_zunmlq__, i__1 = f2cmax(i__1,i__2),
i__2 = *n + i__11 * i__11 + lwrk_zgesvju__,
i__1 = f2cmax(i__1,i__2), i__2 = *n +
lwrk_zunmqrm__;
optwrk = f2cmax(i__1,i__2);
} else {
/* Computing MAX */
/* Computing 2nd power */
i__3 = *n;
/* Computing 2nd power */
i__4 = *n;
/* Computing 2nd power */
i__5 = *n;
/* Computing 2nd power */
i__6 = *n;
/* Computing 2nd power */
i__7 = *n;
/* Computing 2nd power */
i__8 = *n;
/* Computing 2nd power */
i__9 = *n;
/* Computing 2nd power */
i__10 = *n;
/* Computing 2nd power */
i__11 = *n;
i__1 = *n + lwrk_zgeqp3__, i__2 = (*n << 1) + i__3 *
i__3 + lwcon, i__1 = f2cmax(i__1,i__2), i__2 = (*
n << 1) + lwrk_zgeqrf__, i__1 = f2cmax(i__1,i__2)
, i__2 = (*n << 1) + lwrk_zgeqp3n__, i__1 =
f2cmax(i__1,i__2), i__2 = (*n << 1) + i__4 *
i__4 + *n + lwrk_zgelqf__, i__1 = f2cmax(i__1,
i__2), i__2 = (*n << 1) + i__5 * i__5 + *n +
i__6 * i__6 + lwcon, i__1 = f2cmax(i__1,i__2),
i__2 = (*n << 1) + i__7 * i__7 + *n +
lwrk_zgesvj__, i__1 = f2cmax(i__1,i__2), i__2 = (
*n << 1) + i__8 * i__8 + *n + lwrk_zgesvjv__,
i__1 = f2cmax(i__1,i__2), i__2 = (*n << 1) +
i__9 * i__9 + *n + lwrk_zunmqr__, i__1 = f2cmax(
i__1,i__2), i__2 = (*n << 1) + i__10 * i__10
+ *n + lwrk_zunmlq__, i__1 = f2cmax(i__1,i__2),
i__2 = *n + i__11 * i__11 + lwrk_zgesvju__,
i__1 = f2cmax(i__1,i__2), i__2 = *n +
lwrk_zunmqrm__;
optwrk = f2cmax(i__1,i__2);
}
} else {
zgesvj_("L", "U", "V", n, n, &u[u_offset], ldu, &sva[1],
n, &v[v_offset], ldv, cdummy, &c_n1, rdummy, &
c_n1, &ierr);
lwrk_zgesvjv__ = (integer) cdummy[0].r;
zunmqr_("L", "N", n, n, n, cdummy, n, cdummy, &v[v_offset]
, ldv, cdummy, &c_n1, &ierr)
;
lwrk_zunmqr__ = (integer) cdummy[0].r;
zunmqr_("L", "N", m, n, n, &a[a_offset], lda, cdummy, &u[
u_offset], ldu, cdummy, &c_n1, &ierr);
lwrk_zunmqrm__ = (integer) cdummy[0].r;
if (errest) {
/* Computing MAX */
/* Computing 2nd power */
i__3 = *n;
/* Computing 2nd power */
i__4 = *n;
/* Computing 2nd power */
i__5 = *n;
i__1 = *n + lwrk_zgeqp3__, i__2 = *n + lwcon, i__1 =
f2cmax(i__1,i__2), i__2 = (*n << 1) +
lwrk_zgeqrf__, i__1 = f2cmax(i__1,i__2), i__2 = (
*n << 1) + i__3 * i__3, i__1 = f2cmax(i__1,i__2),
i__2 = (*n << 1) + i__4 * i__4 +
lwrk_zgesvjv__, i__1 = f2cmax(i__1,i__2), i__2 =
(*n << 1) + i__5 * i__5 + *n + lwrk_zunmqr__,
i__1 = f2cmax(i__1,i__2), i__2 = *n +
lwrk_zunmqrm__;
optwrk = f2cmax(i__1,i__2);
} else {
/* Computing MAX */
/* Computing 2nd power */
i__3 = *n;
/* Computing 2nd power */
i__4 = *n;
/* Computing 2nd power */
i__5 = *n;
i__1 = *n + lwrk_zgeqp3__, i__2 = (*n << 1) +
lwrk_zgeqrf__, i__1 = f2cmax(i__1,i__2), i__2 = (
*n << 1) + i__3 * i__3, i__1 = f2cmax(i__1,i__2),
i__2 = (*n << 1) + i__4 * i__4 +
lwrk_zgesvjv__, i__1 = f2cmax(i__1,i__2), i__2 =
(*n << 1) + i__5 * i__5 + *n + lwrk_zunmqr__,
i__1 = f2cmax(i__1,i__2), i__2 = *n +
lwrk_zunmqrm__;
optwrk = f2cmax(i__1,i__2);
}
}
}
if (l2tran || rowpiv) {
/* Computing MAX */
i__1 = 7, i__2 = *m << 1, i__1 = f2cmax(i__1,i__2), i__1 = f2cmax(
i__1,lrwqp3), i__1 = f2cmax(i__1,lrwsvdj);
minrwrk = f2cmax(i__1,lrwcon);
} else {
/* Computing MAX */
i__1 = f2cmax(7,lrwqp3), i__1 = f2cmax(i__1,lrwsvdj);
minrwrk = f2cmax(i__1,lrwcon);
}
}
minwrk = f2cmax(2,minwrk);
optwrk = f2cmax(minwrk,optwrk);
if (*lwork < minwrk && ! lquery) {
*info = -17;
}
if (*lrwork < minrwrk && ! lquery) {
*info = -19;
}
}
if (*info != 0) {
/* #:( */
i__1 = -(*info);
xerbla_("ZGEJSV", &i__1, (ftnlen)6);
return;
} else if (lquery) {
cwork[1].r = (doublereal) optwrk, cwork[1].i = 0.;
cwork[2].r = (doublereal) minwrk, cwork[2].i = 0.;
rwork[1] = (doublereal) minrwrk;
iwork[1] = f2cmax(4,miniwrk);
return;
}
/* Quick return for void matrix (Y3K safe) */
/* #:) */
if (*m == 0 || *n == 0) {
iwork[1] = 0;
iwork[2] = 0;
iwork[3] = 0;
iwork[4] = 0;
rwork[1] = 0.;
rwork[2] = 0.;
rwork[3] = 0.;
rwork[4] = 0.;
rwork[5] = 0.;
rwork[6] = 0.;
rwork[7] = 0.;
return;
}
/* Determine whether the matrix U should be M x N or M x M */
if (lsvec) {
n1 = *n;
if (lsame_(jobu, "F")) {
n1 = *m;
}
}
/* Set numerical parameters */
/* ! NOTE: Make sure DLAMCH() does not fail on the target architecture. */
epsln = dlamch_("Epsilon");
sfmin = dlamch_("SafeMinimum");
small = sfmin / epsln;
big = dlamch_("O");
/* BIG = ONE / SFMIN */
/* Initialize SVA(1:N) = diag( ||A e_i||_2 )_1^N */
/* (!) If necessary, scale SVA() to protect the largest norm from */
/* overflow. It is possible that this scaling pushes the smallest */
/* column norm left from the underflow threshold (extreme case). */
scalem = 1. / sqrt((doublereal) (*m) * (doublereal) (*n));
noscal = TRUE_;
goscal = TRUE_;
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
aapp = 0.;
aaqq = 1.;
zlassq_(m, &a[p * a_dim1 + 1], &c__1, &aapp, &aaqq);
if (aapp > big) {
*info = -9;
i__2 = -(*info);
xerbla_("ZGEJSV", &i__2, (ftnlen)6);
return;
}
aaqq = sqrt(aaqq);
if (aapp < big / aaqq && noscal) {
sva[p] = aapp * aaqq;
} else {
noscal = FALSE_;
sva[p] = aapp * (aaqq * scalem);
if (goscal) {
goscal = FALSE_;
i__2 = p - 1;
dscal_(&i__2, &scalem, &sva[1], &c__1);
}
}
/* L1874: */
}
if (noscal) {
scalem = 1.;
}
aapp = 0.;
aaqq = big;
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
/* Computing MAX */
d__1 = aapp, d__2 = sva[p];
aapp = f2cmax(d__1,d__2);
if (sva[p] != 0.) {
/* Computing MIN */
d__1 = aaqq, d__2 = sva[p];
aaqq = f2cmin(d__1,d__2);
}
/* L4781: */
}
/* Quick return for zero M x N matrix */
/* #:) */
if (aapp == 0.) {
if (lsvec) {
zlaset_("G", m, &n1, &c_b1, &c_b2, &u[u_offset], ldu);
}
if (rsvec) {
zlaset_("G", n, n, &c_b1, &c_b2, &v[v_offset], ldv);
}
rwork[1] = 1.;
rwork[2] = 1.;
if (errest) {
rwork[3] = 1.;
}
if (lsvec && rsvec) {
rwork[4] = 1.;
rwork[5] = 1.;
}
if (l2tran) {
rwork[6] = 0.;
rwork[7] = 0.;
}
iwork[1] = 0;
iwork[2] = 0;
iwork[3] = 0;
iwork[4] = -1;
return;
}
/* Issue warning if denormalized column norms detected. Override the */
/* high relative accuracy request. Issue licence to kill nonzero columns */
/* (set them to zero) whose norm is less than sigma_max / BIG (roughly). */
/* #:( */
warning = 0;
if (aaqq <= sfmin) {
l2rank = TRUE_;
l2kill = TRUE_;
warning = 1;
}
/* Quick return for one-column matrix */
/* #:) */
if (*n == 1) {
if (lsvec) {
zlascl_("G", &c__0, &c__0, &sva[1], &scalem, m, &c__1, &a[a_dim1
+ 1], lda, &ierr);
zlacpy_("A", m, &c__1, &a[a_offset], lda, &u[u_offset], ldu);
/* computing all M left singular vectors of the M x 1 matrix */
if (n1 != *n) {
i__1 = *lwork - *n;
zgeqrf_(m, n, &u[u_offset], ldu, &cwork[1], &cwork[*n + 1], &
i__1, &ierr);
i__1 = *lwork - *n;
zungqr_(m, &n1, &c__1, &u[u_offset], ldu, &cwork[1], &cwork[*
n + 1], &i__1, &ierr);
zcopy_(m, &a[a_dim1 + 1], &c__1, &u[u_dim1 + 1], &c__1);
}
}
if (rsvec) {
i__1 = v_dim1 + 1;
v[i__1].r = 1., v[i__1].i = 0.;
}
if (sva[1] < big * scalem) {
sva[1] /= scalem;
scalem = 1.;
}
rwork[1] = 1. / scalem;
rwork[2] = 1.;
if (sva[1] != 0.) {
iwork[1] = 1;
if (sva[1] / scalem >= sfmin) {
iwork[2] = 1;
} else {
iwork[2] = 0;
}
} else {
iwork[1] = 0;
iwork[2] = 0;
}
iwork[3] = 0;
iwork[4] = -1;
if (errest) {
rwork[3] = 1.;
}
if (lsvec && rsvec) {
rwork[4] = 1.;
rwork[5] = 1.;
}
if (l2tran) {
rwork[6] = 0.;
rwork[7] = 0.;
}
return;
}
transp = FALSE_;
aatmax = -1.;
aatmin = big;
if (rowpiv || l2tran) {
/* Compute the row norms, needed to determine row pivoting sequence */
/* (in the case of heavily row weighted A, row pivoting is strongly */
/* advised) and to collect information needed to compare the */
/* structures of A * A^* and A^* * A (in the case L2TRAN.EQ..TRUE.). */
if (l2tran) {
i__1 = *m;
for (p = 1; p <= i__1; ++p) {
xsc = 0.;
temp1 = 1.;
zlassq_(n, &a[p + a_dim1], lda, &xsc, &temp1);
/* ZLASSQ gets both the ell_2 and the ell_infinity norm */
/* in one pass through the vector */
rwork[*m + p] = xsc * scalem;
rwork[p] = xsc * (scalem * sqrt(temp1));
/* Computing MAX */
d__1 = aatmax, d__2 = rwork[p];
aatmax = f2cmax(d__1,d__2);
if (rwork[p] != 0.) {
/* Computing MIN */
d__1 = aatmin, d__2 = rwork[p];
aatmin = f2cmin(d__1,d__2);
}
/* L1950: */
}
} else {
i__1 = *m;
for (p = 1; p <= i__1; ++p) {
rwork[*m + p] = scalem * z_abs(&a[p + izamax_(n, &a[p +
a_dim1], lda) * a_dim1]);
/* Computing MAX */
d__1 = aatmax, d__2 = rwork[*m + p];
aatmax = f2cmax(d__1,d__2);
/* Computing MIN */
d__1 = aatmin, d__2 = rwork[*m + p];
aatmin = f2cmin(d__1,d__2);
/* L1904: */
}
}
}
/* For square matrix A try to determine whether A^* would be better */
/* input for the preconditioned Jacobi SVD, with faster convergence. */
/* The decision is based on an O(N) function of the vector of column */
/* and row norms of A, based on the Shannon entropy. This should give */
/* the right choice in most cases when the difference actually matters. */
/* It may fail and pick the slower converging side. */
entra = 0.;
entrat = 0.;
if (l2tran) {
xsc = 0.;
temp1 = 1.;
dlassq_(n, &sva[1], &c__1, &xsc, &temp1);
temp1 = 1. / temp1;
entra = 0.;
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
/* Computing 2nd power */
d__1 = sva[p] / xsc;
big1 = d__1 * d__1 * temp1;
if (big1 != 0.) {
entra += big1 * log(big1);
}
/* L1113: */
}
entra = -entra / log((doublereal) (*n));
/* Now, SVA().^2/Trace(A^* * A) is a point in the probability simplex. */
/* It is derived from the diagonal of A^* * A. Do the same with the */
/* diagonal of A * A^*, compute the entropy of the corresponding */
/* probability distribution. Note that A * A^* and A^* * A have the */
/* same trace. */
entrat = 0.;
i__1 = *m;
for (p = 1; p <= i__1; ++p) {
/* Computing 2nd power */
d__1 = rwork[p] / xsc;
big1 = d__1 * d__1 * temp1;
if (big1 != 0.) {
entrat += big1 * log(big1);
}
/* L1114: */
}
entrat = -entrat / log((doublereal) (*m));
/* Analyze the entropies and decide A or A^*. Smaller entropy */
/* usually means better input for the algorithm. */
transp = entrat < entra;
/* If A^* is better than A, take the adjoint of A. This is allowed */
/* only for square matrices, M=N. */
if (transp) {
/* In an optimal implementation, this trivial transpose */
/* should be replaced with faster transpose. */
i__1 = *n - 1;
for (p = 1; p <= i__1; ++p) {
i__2 = p + p * a_dim1;
d_cnjg(&z__1, &a[p + p * a_dim1]);
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
i__2 = *n;
for (q = p + 1; q <= i__2; ++q) {
d_cnjg(&z__1, &a[q + p * a_dim1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = q + p * a_dim1;
d_cnjg(&z__1, &a[p + q * a_dim1]);
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
i__3 = p + q * a_dim1;
a[i__3].r = ctemp.r, a[i__3].i = ctemp.i;
/* L1116: */
}
/* L1115: */
}
i__1 = *n + *n * a_dim1;
d_cnjg(&z__1, &a[*n + *n * a_dim1]);
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
rwork[*m + p] = sva[p];
sva[p] = rwork[p];
/* previously computed row 2-norms are now column 2-norms */
/* of the transposed matrix */
/* L1117: */
}
temp1 = aapp;
aapp = aatmax;
aatmax = temp1;
temp1 = aaqq;
aaqq = aatmin;
aatmin = temp1;
kill = lsvec;
lsvec = rsvec;
rsvec = kill;
if (lsvec) {
n1 = *n;
}
rowpiv = TRUE_;
}
}
/* END IF L2TRAN */
/* Scale the matrix so that its maximal singular value remains less */
/* than SQRT(BIG) -- the matrix is scaled so that its maximal column */
/* has Euclidean norm equal to SQRT(BIG/N). The only reason to keep */
/* SQRT(BIG) instead of BIG is the fact that ZGEJSV uses LAPACK and */
/* BLAS routines that, in some implementations, are not capable of */
/* working in the full interval [SFMIN,BIG] and that they may provoke */
/* overflows in the intermediate results. If the singular values spread */
/* from SFMIN to BIG, then ZGESVJ will compute them. So, in that case, */
/* one should use ZGESVJ instead of ZGEJSV. */
/* >> change in the April 2016 update: allow bigger range, i.e. the */
/* largest column is allowed up to BIG/N and ZGESVJ will do the rest. */
big1 = sqrt(big);
temp1 = sqrt(big / (doublereal) (*n));
/* TEMP1 = BIG/DBLE(N) */
dlascl_("G", &c__0, &c__0, &aapp, &temp1, n, &c__1, &sva[1], n, &ierr);
if (aaqq > aapp * sfmin) {
aaqq = aaqq / aapp * temp1;
} else {
aaqq = aaqq * temp1 / aapp;
}
temp1 *= scalem;
zlascl_("G", &c__0, &c__0, &aapp, &temp1, m, n, &a[a_offset], lda, &ierr);
/* To undo scaling at the end of this procedure, multiply the */
/* computed singular values with USCAL2 / USCAL1. */
uscal1 = temp1;
uscal2 = aapp;
if (l2kill) {
/* L2KILL enforces computation of nonzero singular values in */
/* the restricted range of condition number of the initial A, */
/* sigma_max(A) / sigma_min(A) approx. SQRT(BIG)/SQRT(SFMIN). */
xsc = sqrt(sfmin);
} else {
xsc = small;
/* Now, if the condition number of A is too big, */
/* sigma_max(A) / sigma_min(A) .GT. SQRT(BIG/N) * EPSLN / SFMIN, */
/* as a precaution measure, the full SVD is computed using ZGESVJ */
/* with accumulated Jacobi rotations. This provides numerically */
/* more robust computation, at the cost of slightly increased run */
/* time. Depending on the concrete implementation of BLAS and LAPACK */
/* (i.e. how they behave in presence of extreme ill-conditioning) the */
/* implementor may decide to remove this switch. */
if (aaqq < sqrt(sfmin) && lsvec && rsvec) {
jracc = TRUE_;
}
}
if (aaqq < xsc) {
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
if (sva[p] < xsc) {
zlaset_("A", m, &c__1, &c_b1, &c_b1, &a[p * a_dim1 + 1], lda);
sva[p] = 0.;
}
/* L700: */
}
}
/* Preconditioning using QR factorization with pivoting */
if (rowpiv) {
/* Optional row permutation (Bjoerck row pivoting): */
/* A result by Cox and Higham shows that the Bjoerck's */
/* row pivoting combined with standard column pivoting */
/* has similar effect as Powell-Reid complete pivoting. */
/* The ell-infinity norms of A are made nonincreasing. */
if (lsvec && rsvec && ! jracc) {
iwoff = *n << 1;
} else {
iwoff = *n;
}
i__1 = *m - 1;
for (p = 1; p <= i__1; ++p) {
i__2 = *m - p + 1;
q = idamax_(&i__2, &rwork[*m + p], &c__1) + p - 1;
iwork[iwoff + p] = q;
if (p != q) {
temp1 = rwork[*m + p];
rwork[*m + p] = rwork[*m + q];
rwork[*m + q] = temp1;
}
/* L1952: */
}
i__1 = *m - 1;
zlaswp_(n, &a[a_offset], lda, &c__1, &i__1, &iwork[iwoff + 1], &c__1);
}
/* End of the preparation phase (scaling, optional sorting and */
/* transposing, optional flushing of small columns). */
/* Preconditioning */
/* If the full SVD is needed, the right singular vectors are computed */
/* from a matrix equation, and for that we need theoretical analysis */
/* of the Businger-Golub pivoting. So we use ZGEQP3 as the first RR QRF. */
/* In all other cases the first RR QRF can be chosen by other criteria */
/* (eg speed by replacing global with restricted window pivoting, such */
/* as in xGEQPX from TOMS # 782). Good results will be obtained using */
/* xGEQPX with properly (!) chosen numerical parameters. */
/* Any improvement of ZGEQP3 improves overal performance of ZGEJSV. */
/* A * P1 = Q1 * [ R1^* 0]^*: */
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
iwork[p] = 0;
/* L1963: */
}
i__1 = *lwork - *n;
zgeqp3_(m, n, &a[a_offset], lda, &iwork[1], &cwork[1], &cwork[*n + 1], &
i__1, &rwork[1], &ierr);
/* The upper triangular matrix R1 from the first QRF is inspected for */
/* rank deficiency and possibilities for deflation, or possible */
/* ill-conditioning. Depending on the user specified flag L2RANK, */
/* the procedure explores possibilities to reduce the numerical */
/* rank by inspecting the computed upper triangular factor. If */
/* L2RANK or L2ABER are up, then ZGEJSV will compute the SVD of */
/* A + dA, where ||dA|| <= f(M,N)*EPSLN. */
nr = 1;
if (l2aber) {
/* Standard absolute error bound suffices. All sigma_i with */
/* sigma_i < N*EPSLN*||A|| are flushed to zero. This is an */
/* aggressive enforcement of lower numerical rank by introducing a */
/* backward error of the order of N*EPSLN*||A||. */
temp1 = sqrt((doublereal) (*n)) * epsln;
i__1 = *n;
for (p = 2; p <= i__1; ++p) {
if (z_abs(&a[p + p * a_dim1]) >= temp1 * z_abs(&a[a_dim1 + 1])) {
++nr;
} else {
goto L3002;
}
/* L3001: */
}
L3002:
;
} else if (l2rank) {
/* Sudden drop on the diagonal of R1 is used as the criterion for */
/* close-to-rank-deficient. */
temp1 = sqrt(sfmin);
i__1 = *n;
for (p = 2; p <= i__1; ++p) {
if (z_abs(&a[p + p * a_dim1]) < epsln * z_abs(&a[p - 1 + (p - 1) *
a_dim1]) || z_abs(&a[p + p * a_dim1]) < small || l2kill
&& z_abs(&a[p + p * a_dim1]) < temp1) {
goto L3402;
}
++nr;
/* L3401: */
}
L3402:
;
} else {
/* The goal is high relative accuracy. However, if the matrix */
/* has high scaled condition number the relative accuracy is in */
/* general not feasible. Later on, a condition number estimator */
/* will be deployed to estimate the scaled condition number. */
/* Here we just remove the underflowed part of the triangular */
/* factor. This prevents the situation in which the code is */
/* working hard to get the accuracy not warranted by the data. */
temp1 = sqrt(sfmin);
i__1 = *n;
for (p = 2; p <= i__1; ++p) {
if (z_abs(&a[p + p * a_dim1]) < small || l2kill && z_abs(&a[p + p
* a_dim1]) < temp1) {
goto L3302;
}
++nr;
/* L3301: */
}
L3302:
;
}
almort = FALSE_;
if (nr == *n) {
maxprj = 1.;
i__1 = *n;
for (p = 2; p <= i__1; ++p) {
temp1 = z_abs(&a[p + p * a_dim1]) / sva[iwork[p]];
maxprj = f2cmin(maxprj,temp1);
/* L3051: */
}
/* Computing 2nd power */
d__1 = maxprj;
if (d__1 * d__1 >= 1. - (doublereal) (*n) * epsln) {
almort = TRUE_;
}
}
sconda = -1.;
condr1 = -1.;
condr2 = -1.;
if (errest) {
if (*n == nr) {
if (rsvec) {
zlacpy_("U", n, n, &a[a_offset], lda, &v[v_offset], ldv);
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
temp1 = sva[iwork[p]];
d__1 = 1. / temp1;
zdscal_(&p, &d__1, &v[p * v_dim1 + 1], &c__1);
/* L3053: */
}
if (lsvec) {
zpocon_("U", n, &v[v_offset], ldv, &c_b141, &temp1, &
cwork[*n + 1], &rwork[1], &ierr);
} else {
zpocon_("U", n, &v[v_offset], ldv, &c_b141, &temp1, &
cwork[1], &rwork[1], &ierr);
}
} else if (lsvec) {
zlacpy_("U", n, n, &a[a_offset], lda, &u[u_offset], ldu);
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
temp1 = sva[iwork[p]];
d__1 = 1. / temp1;
zdscal_(&p, &d__1, &u[p * u_dim1 + 1], &c__1);
/* L3054: */
}
zpocon_("U", n, &u[u_offset], ldu, &c_b141, &temp1, &cwork[*n
+ 1], &rwork[1], &ierr);
} else {
zlacpy_("U", n, n, &a[a_offset], lda, &cwork[1], n)
;
/* [] CALL ZLACPY( 'U', N, N, A, LDA, CWORK(N+1), N ) */
/* Change: here index shifted by N to the left, CWORK(1:N) */
/* not needed for SIGMA only computation */
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
temp1 = sva[iwork[p]];
/* [] CALL ZDSCAL( p, ONE/TEMP1, CWORK(N+(p-1)*N+1), 1 ) */
d__1 = 1. / temp1;
zdscal_(&p, &d__1, &cwork[(p - 1) * *n + 1], &c__1);
/* L3052: */
}
/* [] CALL ZPOCON( 'U', N, CWORK(N+1), N, ONE, TEMP1, */
/* [] $ CWORK(N+N*N+1), RWORK, IERR ) */
zpocon_("U", n, &cwork[1], n, &c_b141, &temp1, &cwork[*n * *n
+ 1], &rwork[1], &ierr);
}
if (temp1 != 0.) {
sconda = 1. / sqrt(temp1);
} else {
sconda = -1.;
}
/* SCONDA is an estimate of SQRT(||(R^* * R)^(-1)||_1). */
/* N^(-1/4) * SCONDA <= ||R^(-1)||_2 <= N^(1/4) * SCONDA */
} else {
sconda = -1.;
}
}
z_div(&z__1, &a[a_dim1 + 1], &a[nr + nr * a_dim1]);
l2pert = l2pert && z_abs(&z__1) > sqrt(big1);
/* If there is no violent scaling, artificial perturbation is not needed. */
/* Phase 3: */
if (! (rsvec || lsvec)) {
/* Singular Values only */
/* Computing MIN */
i__2 = *n - 1;
i__1 = f2cmin(i__2,nr);
for (p = 1; p <= i__1; ++p) {
i__2 = *n - p;
zcopy_(&i__2, &a[p + (p + 1) * a_dim1], lda, &a[p + 1 + p *
a_dim1], &c__1);
i__2 = *n - p + 1;
zlacgv_(&i__2, &a[p + p * a_dim1], &c__1);
/* L1946: */
}
if (nr == *n) {
i__1 = *n + *n * a_dim1;
d_cnjg(&z__1, &a[*n + *n * a_dim1]);
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
}
/* The following two DO-loops introduce small relative perturbation */
/* into the strict upper triangle of the lower triangular matrix. */
/* Small entries below the main diagonal are also changed. */
/* This modification is useful if the computing environment does not */
/* provide/allow FLUSH TO ZERO underflow, for it prevents many */
/* annoying denormalized numbers in case of strongly scaled matrices. */
/* The perturbation is structured so that it does not introduce any */
/* new perturbation of the singular values, and it does not destroy */
/* the job done by the preconditioner. */
/* The licence for this perturbation is in the variable L2PERT, which */
/* should be .FALSE. if FLUSH TO ZERO underflow is active. */
if (! almort) {
if (l2pert) {
/* XSC = SQRT(SMALL) */
xsc = epsln / (doublereal) (*n);
i__1 = nr;
for (q = 1; q <= i__1; ++q) {
d__1 = xsc * z_abs(&a[q + q * a_dim1]);
z__1.r = d__1, z__1.i = 0.;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = *n;
for (p = 1; p <= i__2; ++p) {
if (p > q && z_abs(&a[p + q * a_dim1]) <= temp1 || p <
q) {
i__3 = p + q * a_dim1;
a[i__3].r = ctemp.r, a[i__3].i = ctemp.i;
}
/* $ A(p,q) = TEMP1 * ( A(p,q) / ABS(A(p,q)) ) */
/* L4949: */
}
/* L4947: */
}
} else {
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
, lda);
}
i__1 = *lwork - *n;
zgeqrf_(n, &nr, &a[a_offset], lda, &cwork[1], &cwork[*n + 1], &
i__1, &ierr);
i__1 = nr - 1;
for (p = 1; p <= i__1; ++p) {
i__2 = nr - p;
zcopy_(&i__2, &a[p + (p + 1) * a_dim1], lda, &a[p + 1 + p *
a_dim1], &c__1);
i__2 = nr - p + 1;
zlacgv_(&i__2, &a[p + p * a_dim1], &c__1);
/* L1948: */
}
}
/* Row-cyclic Jacobi SVD algorithm with column pivoting */
/* to drown denormals */
if (l2pert) {
/* XSC = SQRT(SMALL) */
xsc = epsln / (doublereal) (*n);
i__1 = nr;
for (q = 1; q <= i__1; ++q) {
d__1 = xsc * z_abs(&a[q + q * a_dim1]);
z__1.r = d__1, z__1.i = 0.;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = nr;
for (p = 1; p <= i__2; ++p) {
if (p > q && z_abs(&a[p + q * a_dim1]) <= temp1 || p < q)
{
i__3 = p + q * a_dim1;
a[i__3].r = ctemp.r, a[i__3].i = ctemp.i;
}
/* $ A(p,q) = TEMP1 * ( A(p,q) / ABS(A(p,q)) ) */
/* L1949: */
}
/* L1947: */
}
} else {
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1],
lda);
}
/* triangular matrix (plus perturbation which is ignored in */
/* the part which destroys triangular form (confusing?!)) */
zgesvj_("L", "N", "N", &nr, &nr, &a[a_offset], lda, &sva[1], n, &v[
v_offset], ldv, &cwork[1], lwork, &rwork[1], lrwork, info);
scalem = rwork[1];
numrank = i_dnnt(&rwork[2]);
} else if (rsvec && ! lsvec && ! jracc || jracc && ! lsvec && nr != *n) {
/* -> Singular Values and Right Singular Vectors <- */
if (almort) {
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n - p + 1;
zcopy_(&i__2, &a[p + p * a_dim1], lda, &v[p + p * v_dim1], &
c__1);
i__2 = *n - p + 1;
zlacgv_(&i__2, &v[p + p * v_dim1], &c__1);
/* L1998: */
}
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &v[(v_dim1 << 1) + 1],
ldv);
zgesvj_("L", "U", "N", n, &nr, &v[v_offset], ldv, &sva[1], &nr, &
a[a_offset], lda, &cwork[1], lwork, &rwork[1], lrwork,
info);
scalem = rwork[1];
numrank = i_dnnt(&rwork[2]);
} else {
/* accumulated product of Jacobi rotations, three are perfect ) */
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
i__1 = *lwork - *n;
zgelqf_(&nr, n, &a[a_offset], lda, &cwork[1], &cwork[*n + 1], &
i__1, &ierr);
zlacpy_("L", &nr, &nr, &a[a_offset], lda, &v[v_offset], ldv);
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &v[(v_dim1 << 1) + 1],
ldv);
i__1 = *lwork - (*n << 1);
zgeqrf_(&nr, &nr, &v[v_offset], ldv, &cwork[*n + 1], &cwork[(*n <<
1) + 1], &i__1, &ierr);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = nr - p + 1;
zcopy_(&i__2, &v[p + p * v_dim1], ldv, &v[p + p * v_dim1], &
c__1);
i__2 = nr - p + 1;
zlacgv_(&i__2, &v[p + p * v_dim1], &c__1);
/* L8998: */
}
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &v[(v_dim1 << 1) + 1],
ldv);
i__1 = *lwork - *n;
zgesvj_("L", "U", "N", &nr, &nr, &v[v_offset], ldv, &sva[1], &nr,
&u[u_offset], ldu, &cwork[*n + 1], &i__1, &rwork[1],
lrwork, info);
scalem = rwork[1];
numrank = i_dnnt(&rwork[2]);
if (nr < *n) {
i__1 = *n - nr;
zlaset_("A", &i__1, &nr, &c_b1, &c_b1, &v[nr + 1 + v_dim1],
ldv);
i__1 = *n - nr;
zlaset_("A", &nr, &i__1, &c_b1, &c_b1, &v[(nr + 1) * v_dim1 +
1], ldv);
i__1 = *n - nr;
i__2 = *n - nr;
zlaset_("A", &i__1, &i__2, &c_b1, &c_b2, &v[nr + 1 + (nr + 1)
* v_dim1], ldv);
}
i__1 = *lwork - *n;
zunmlq_("L", "C", n, n, &nr, &a[a_offset], lda, &cwork[1], &v[
v_offset], ldv, &cwork[*n + 1], &i__1, &ierr);
}
/* DO 8991 p = 1, N */
/* CALL ZCOPY( N, V(p,1), LDV, A(IWORK(p),1), LDA ) */
/* 8991 CONTINUE */
/* CALL ZLACPY( 'All', N, N, A, LDA, V, LDV ) */
zlapmr_(&c_false, n, n, &v[v_offset], ldv, &iwork[1]);
if (transp) {
zlacpy_("A", n, n, &v[v_offset], ldv, &u[u_offset], ldu);
}
} else if (jracc && ! lsvec && nr == *n) {
i__1 = *n - 1;
i__2 = *n - 1;
zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
zgesvj_("U", "N", "V", n, n, &a[a_offset], lda, &sva[1], n, &v[
v_offset], ldv, &cwork[1], lwork, &rwork[1], lrwork, info);
scalem = rwork[1];
numrank = i_dnnt(&rwork[2]);
zlapmr_(&c_false, n, n, &v[v_offset], ldv, &iwork[1]);
} else if (lsvec && ! rsvec) {
/* Jacobi rotations in the Jacobi iterations. */
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n - p + 1;
zcopy_(&i__2, &a[p + p * a_dim1], lda, &u[p + p * u_dim1], &c__1);
i__2 = *n - p + 1;
zlacgv_(&i__2, &u[p + p * u_dim1], &c__1);
/* L1965: */
}
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &u[(u_dim1 << 1) + 1], ldu);
i__1 = *lwork - (*n << 1);
zgeqrf_(n, &nr, &u[u_offset], ldu, &cwork[*n + 1], &cwork[(*n << 1) +
1], &i__1, &ierr);
i__1 = nr - 1;
for (p = 1; p <= i__1; ++p) {
i__2 = nr - p;
zcopy_(&i__2, &u[p + (p + 1) * u_dim1], ldu, &u[p + 1 + p *
u_dim1], &c__1);
i__2 = *n - p + 1;
zlacgv_(&i__2, &u[p + p * u_dim1], &c__1);
/* L1967: */
}
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &u[(u_dim1 << 1) + 1], ldu);
i__1 = *lwork - *n;
zgesvj_("L", "U", "N", &nr, &nr, &u[u_offset], ldu, &sva[1], &nr, &a[
a_offset], lda, &cwork[*n + 1], &i__1, &rwork[1], lrwork,
info);
scalem = rwork[1];
numrank = i_dnnt(&rwork[2]);
if (nr < *m) {
i__1 = *m - nr;
zlaset_("A", &i__1, &nr, &c_b1, &c_b1, &u[nr + 1 + u_dim1], ldu);
if (nr < n1) {
i__1 = n1 - nr;
zlaset_("A", &nr, &i__1, &c_b1, &c_b1, &u[(nr + 1) * u_dim1 +
1], ldu);
i__1 = *m - nr;
i__2 = n1 - nr;
zlaset_("A", &i__1, &i__2, &c_b1, &c_b2, &u[nr + 1 + (nr + 1)
* u_dim1], ldu);
}
}
i__1 = *lwork - *n;
zunmqr_("L", "N", m, &n1, n, &a[a_offset], lda, &cwork[1], &u[
u_offset], ldu, &cwork[*n + 1], &i__1, &ierr);
if (rowpiv) {
i__1 = *m - 1;
zlaswp_(&n1, &u[u_offset], ldu, &c__1, &i__1, &iwork[iwoff + 1], &
c_n1);
}
i__1 = n1;
for (p = 1; p <= i__1; ++p) {
xsc = 1. / dznrm2_(m, &u[p * u_dim1 + 1], &c__1);
zdscal_(m, &xsc, &u[p * u_dim1 + 1], &c__1);
/* L1974: */
}
if (transp) {
zlacpy_("A", n, n, &u[u_offset], ldu, &v[v_offset], ldv);
}
} else {
if (! jracc) {
if (! almort) {
/* Second Preconditioning Step (QRF [with pivoting]) */
/* Note that the composition of TRANSPOSE, QRF and TRANSPOSE is */
/* equivalent to an LQF CALL. Since in many libraries the QRF */
/* seems to be better optimized than the LQF, we do explicit */
/* transpose and use the QRF. This is subject to changes in an */
/* optimized implementation of ZGEJSV. */
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n - p + 1;
zcopy_(&i__2, &a[p + p * a_dim1], lda, &v[p + p * v_dim1],
&c__1);
i__2 = *n - p + 1;
zlacgv_(&i__2, &v[p + p * v_dim1], &c__1);
/* L1968: */
}
/* denormals in the second QR factorization, where they are */
/* as good as zeros. This is done to avoid painfully slow */
/* computation with denormals. The relative size of the perturbation */
/* is a parameter that can be changed by the implementer. */
/* This perturbation device will be obsolete on machines with */
/* properly implemented arithmetic. */
/* To switch it off, set L2PERT=.FALSE. To remove it from the */
/* code, remove the action under L2PERT=.TRUE., leave the ELSE part. */
/* The following two loops should be blocked and fused with the */
/* transposed copy above. */
if (l2pert) {
xsc = sqrt(small);
i__1 = nr;
for (q = 1; q <= i__1; ++q) {
d__1 = xsc * z_abs(&v[q + q * v_dim1]);
z__1.r = d__1, z__1.i = 0.;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = *n;
for (p = 1; p <= i__2; ++p) {
if (p > q && z_abs(&v[p + q * v_dim1]) <= temp1 ||
p < q) {
i__3 = p + q * v_dim1;
v[i__3].r = ctemp.r, v[i__3].i = ctemp.i;
}
/* $ V(p,q) = TEMP1 * ( V(p,q) / ABS(V(p,q)) ) */
if (p < q) {
i__3 = p + q * v_dim1;
i__4 = p + q * v_dim1;
z__1.r = -v[i__4].r, z__1.i = -v[i__4].i;
v[i__3].r = z__1.r, v[i__3].i = z__1.i;
}
/* L2968: */
}
/* L2969: */
}
} else {
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &v[(v_dim1 << 1)
+ 1], ldv);
}
/* Estimate the row scaled condition number of R1 */
/* (If R1 is rectangular, N > NR, then the condition number */
/* of the leading NR x NR submatrix is estimated.) */
zlacpy_("L", &nr, &nr, &v[v_offset], ldv, &cwork[(*n << 1) +
1], &nr);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = nr - p + 1;
temp1 = dznrm2_(&i__2, &cwork[(*n << 1) + (p - 1) * nr +
p], &c__1);
i__2 = nr - p + 1;
d__1 = 1. / temp1;
zdscal_(&i__2, &d__1, &cwork[(*n << 1) + (p - 1) * nr + p]
, &c__1);
/* L3950: */
}
zpocon_("L", &nr, &cwork[(*n << 1) + 1], &nr, &c_b141, &temp1,
&cwork[(*n << 1) + nr * nr + 1], &rwork[1], &ierr);
condr1 = 1. / sqrt(temp1);
/* R1 is OK for inverse <=> CONDR1 .LT. DBLE(N) */
/* more conservative <=> CONDR1 .LT. SQRT(DBLE(N)) */
cond_ok__ = sqrt(sqrt((doublereal) nr));
/* [TP] COND_OK is a tuning parameter. */
if (condr1 < cond_ok__) {
/* implementation, this QRF should be implemented as the QRF */
/* of a lower triangular matrix. */
/* R1^* = Q2 * R2 */
i__1 = *lwork - (*n << 1);
zgeqrf_(n, &nr, &v[v_offset], ldv, &cwork[*n + 1], &cwork[
(*n << 1) + 1], &i__1, &ierr);
if (l2pert) {
xsc = sqrt(small) / epsln;
i__1 = nr;
for (p = 2; p <= i__1; ++p) {
i__2 = p - 1;
for (q = 1; q <= i__2; ++q) {
/* Computing MIN */
d__2 = z_abs(&v[p + p * v_dim1]), d__3 =
z_abs(&v[q + q * v_dim1]);
d__1 = xsc * f2cmin(d__2,d__3);
z__1.r = d__1, z__1.i = 0.;
ctemp.r = z__1.r, ctemp.i = z__1.i;
if (z_abs(&v[q + p * v_dim1]) <= temp1) {
i__3 = q + p * v_dim1;
v[i__3].r = ctemp.r, v[i__3].i = ctemp.i;
}
/* $ V(q,p) = TEMP1 * ( V(q,p) / ABS(V(q,p)) ) */
/* L3958: */
}
/* L3959: */
}
}
if (nr != *n) {
zlacpy_("A", n, &nr, &v[v_offset], ldv, &cwork[(*n <<
1) + 1], n);
}
i__1 = nr - 1;
for (p = 1; p <= i__1; ++p) {
i__2 = nr - p;
zcopy_(&i__2, &v[p + (p + 1) * v_dim1], ldv, &v[p + 1
+ p * v_dim1], &c__1);
i__2 = nr - p + 1;
zlacgv_(&i__2, &v[p + p * v_dim1], &c__1);
/* L1969: */
}
i__1 = nr + nr * v_dim1;
d_cnjg(&z__1, &v[nr + nr * v_dim1]);
v[i__1].r = z__1.r, v[i__1].i = z__1.i;
condr2 = condr1;
} else {
/* Note that windowed pivoting would be equally good */
/* numerically, and more run-time efficient. So, in */
/* an optimal implementation, the next call to ZGEQP3 */
/* should be replaced with eg. CALL ZGEQPX (ACM TOMS #782) */
/* with properly (carefully) chosen parameters. */
/* R1^* * P2 = Q2 * R2 */
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
iwork[*n + p] = 0;
/* L3003: */
}
i__1 = *lwork - (*n << 1);
zgeqp3_(n, &nr, &v[v_offset], ldv, &iwork[*n + 1], &cwork[
*n + 1], &cwork[(*n << 1) + 1], &i__1, &rwork[1],
&ierr);
/* * CALL ZGEQRF( N, NR, V, LDV, CWORK(N+1), CWORK(2*N+1), */
/* * $ LWORK-2*N, IERR ) */
if (l2pert) {
xsc = sqrt(small);
i__1 = nr;
for (p = 2; p <= i__1; ++p) {
i__2 = p - 1;
for (q = 1; q <= i__2; ++q) {
/* Computing MIN */
d__2 = z_abs(&v[p + p * v_dim1]), d__3 =
z_abs(&v[q + q * v_dim1]);
d__1 = xsc * f2cmin(d__2,d__3);
z__1.r = d__1, z__1.i = 0.;
ctemp.r = z__1.r, ctemp.i = z__1.i;
if (z_abs(&v[q + p * v_dim1]) <= temp1) {
i__3 = q + p * v_dim1;
v[i__3].r = ctemp.r, v[i__3].i = ctemp.i;
}
/* $ V(q,p) = TEMP1 * ( V(q,p) / ABS(V(q,p)) ) */
/* L3968: */
}
/* L3969: */
}
}
zlacpy_("A", n, &nr, &v[v_offset], ldv, &cwork[(*n << 1)
+ 1], n);
if (l2pert) {
xsc = sqrt(small);
i__1 = nr;
for (p = 2; p <= i__1; ++p) {
i__2 = p - 1;
for (q = 1; q <= i__2; ++q) {
/* Computing MIN */
d__2 = z_abs(&v[p + p * v_dim1]), d__3 =
z_abs(&v[q + q * v_dim1]);
d__1 = xsc * f2cmin(d__2,d__3);
z__1.r = d__1, z__1.i = 0.;
ctemp.r = z__1.r, ctemp.i = z__1.i;
/* V(p,q) = - TEMP1*( V(q,p) / ABS(V(q,p)) ) */
i__3 = p + q * v_dim1;
z__1.r = -ctemp.r, z__1.i = -ctemp.i;
v[i__3].r = z__1.r, v[i__3].i = z__1.i;
/* L8971: */
}
/* L8970: */
}
} else {
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &v[v_dim1 +
2], ldv);
}
/* Now, compute R2 = L3 * Q3, the LQ factorization. */
i__1 = *lwork - (*n << 1) - *n * nr - nr;
zgelqf_(&nr, &nr, &v[v_offset], ldv, &cwork[(*n << 1) + *
n * nr + 1], &cwork[(*n << 1) + *n * nr + nr + 1],
&i__1, &ierr);
zlacpy_("L", &nr, &nr, &v[v_offset], ldv, &cwork[(*n << 1)
+ *n * nr + nr + 1], &nr);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
temp1 = dznrm2_(&p, &cwork[(*n << 1) + *n * nr + nr +
p], &nr);
d__1 = 1. / temp1;
zdscal_(&p, &d__1, &cwork[(*n << 1) + *n * nr + nr +
p], &nr);
/* L4950: */
}
zpocon_("L", &nr, &cwork[(*n << 1) + *n * nr + nr + 1], &
nr, &c_b141, &temp1, &cwork[(*n << 1) + *n * nr +
nr + nr * nr + 1], &rwork[1], &ierr);
condr2 = 1. / sqrt(temp1);
if (condr2 >= cond_ok__) {
/* (this overwrites the copy of R2, as it will not be */
/* needed in this branch, but it does not overwritte the */
/* Huseholder vectors of Q2.). */
zlacpy_("U", &nr, &nr, &v[v_offset], ldv, &cwork[(*n
<< 1) + 1], n);
/* WORK(2*N+N*NR+1:2*N+N*NR+N) */
}
}
if (l2pert) {
xsc = sqrt(small);
i__1 = nr;
for (q = 2; q <= i__1; ++q) {
i__2 = q + q * v_dim1;
z__1.r = xsc * v[i__2].r, z__1.i = xsc * v[i__2].i;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = q - 1;
for (p = 1; p <= i__2; ++p) {
/* V(p,q) = - TEMP1*( V(p,q) / ABS(V(p,q)) ) */
i__3 = p + q * v_dim1;
z__1.r = -ctemp.r, z__1.i = -ctemp.i;
v[i__3].r = z__1.r, v[i__3].i = z__1.i;
/* L4969: */
}
/* L4968: */
}
} else {
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &v[(v_dim1 << 1)
+ 1], ldv);
}
/* Second preconditioning finished; continue with Jacobi SVD */
/* The input matrix is lower trinagular. */
/* Recover the right singular vectors as solution of a well */
/* conditioned triangular matrix equation. */
if (condr1 < cond_ok__) {
i__1 = *lwork - (*n << 1) - *n * nr - nr;
zgesvj_("L", "U", "N", &nr, &nr, &v[v_offset], ldv, &sva[
1], &nr, &u[u_offset], ldu, &cwork[(*n << 1) + *n
* nr + nr + 1], &i__1, &rwork[1], lrwork, info);
scalem = rwork[1];
numrank = i_dnnt(&rwork[2]);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
zcopy_(&nr, &v[p * v_dim1 + 1], &c__1, &u[p * u_dim1
+ 1], &c__1);
zdscal_(&nr, &sva[p], &v[p * v_dim1 + 1], &c__1);
/* L3970: */
}
if (nr == *n) {
/* :)) .. best case, R1 is inverted. The solution of this matrix */
/* equation is Q2*V2 = the product of the Jacobi rotations */
/* used in ZGESVJ, premultiplied with the orthogonal matrix */
/* from the second QR factorization. */
ztrsm_("L", "U", "N", "N", &nr, &nr, &c_b2, &a[
a_offset], lda, &v[v_offset], ldv);
} else {
/* is inverted to get the product of the Jacobi rotations */
/* used in ZGESVJ. The Q-factor from the second QR */
/* factorization is then built in explicitly. */
ztrsm_("L", "U", "C", "N", &nr, &nr, &c_b2, &cwork[(*
n << 1) + 1], n, &v[v_offset], ldv);
if (nr < *n) {
i__1 = *n - nr;
zlaset_("A", &i__1, &nr, &c_b1, &c_b1, &v[nr + 1
+ v_dim1], ldv);
i__1 = *n - nr;
zlaset_("A", &nr, &i__1, &c_b1, &c_b1, &v[(nr + 1)
* v_dim1 + 1], ldv);
i__1 = *n - nr;
i__2 = *n - nr;
zlaset_("A", &i__1, &i__2, &c_b1, &c_b2, &v[nr +
1 + (nr + 1) * v_dim1], ldv);
}
i__1 = *lwork - (*n << 1) - *n * nr - nr;
zunmqr_("L", "N", n, n, &nr, &cwork[(*n << 1) + 1], n,
&cwork[*n + 1], &v[v_offset], ldv, &cwork[(*
n << 1) + *n * nr + nr + 1], &i__1, &ierr);
}
} else if (condr2 < cond_ok__) {
/* The matrix R2 is inverted. The solution of the matrix equation */
/* is Q3^* * V3 = the product of the Jacobi rotations (appplied to */
/* the lower triangular L3 from the LQ factorization of */
/* R2=L3*Q3), pre-multiplied with the transposed Q3. */
i__1 = *lwork - (*n << 1) - *n * nr - nr;
zgesvj_("L", "U", "N", &nr, &nr, &v[v_offset], ldv, &sva[
1], &nr, &u[u_offset], ldu, &cwork[(*n << 1) + *n
* nr + nr + 1], &i__1, &rwork[1], lrwork, info);
scalem = rwork[1];
numrank = i_dnnt(&rwork[2]);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
zcopy_(&nr, &v[p * v_dim1 + 1], &c__1, &u[p * u_dim1
+ 1], &c__1);
zdscal_(&nr, &sva[p], &u[p * u_dim1 + 1], &c__1);
/* L3870: */
}
ztrsm_("L", "U", "N", "N", &nr, &nr, &c_b2, &cwork[(*n <<
1) + 1], n, &u[u_offset], ldu);
i__1 = nr;
for (q = 1; q <= i__1; ++q) {
i__2 = nr;
for (p = 1; p <= i__2; ++p) {
i__3 = (*n << 1) + *n * nr + nr + iwork[*n + p];
i__4 = p + q * u_dim1;
cwork[i__3].r = u[i__4].r, cwork[i__3].i = u[i__4]
.i;
/* L872: */
}
i__2 = nr;
for (p = 1; p <= i__2; ++p) {
i__3 = p + q * u_dim1;
i__4 = (*n << 1) + *n * nr + nr + p;
u[i__3].r = cwork[i__4].r, u[i__3].i = cwork[i__4]
.i;
/* L874: */
}
/* L873: */
}
if (nr < *n) {
i__1 = *n - nr;
zlaset_("A", &i__1, &nr, &c_b1, &c_b1, &v[nr + 1 +
v_dim1], ldv);
i__1 = *n - nr;
zlaset_("A", &nr, &i__1, &c_b1, &c_b1, &v[(nr + 1) *
v_dim1 + 1], ldv);
i__1 = *n - nr;
i__2 = *n - nr;
zlaset_("A", &i__1, &i__2, &c_b1, &c_b2, &v[nr + 1 + (
nr + 1) * v_dim1], ldv);
}
i__1 = *lwork - (*n << 1) - *n * nr - nr;
zunmqr_("L", "N", n, n, &nr, &cwork[(*n << 1) + 1], n, &
cwork[*n + 1], &v[v_offset], ldv, &cwork[(*n << 1)
+ *n * nr + nr + 1], &i__1, &ierr);
} else {
/* Last line of defense. */
/* #:( This is a rather pathological case: no scaled condition */
/* improvement after two pivoted QR factorizations. Other */
/* possibility is that the rank revealing QR factorization */
/* or the condition estimator has failed, or the COND_OK */
/* is set very close to ONE (which is unnecessary). Normally, */
/* this branch should never be executed, but in rare cases of */
/* failure of the RRQR or condition estimator, the last line of */
/* defense ensures that ZGEJSV completes the task. */
/* Compute the full SVD of L3 using ZGESVJ with explicit */
/* accumulation of Jacobi rotations. */
i__1 = *lwork - (*n << 1) - *n * nr - nr;
zgesvj_("L", "U", "V", &nr, &nr, &v[v_offset], ldv, &sva[
1], &nr, &u[u_offset], ldu, &cwork[(*n << 1) + *n
* nr + nr + 1], &i__1, &rwork[1], lrwork, info);
scalem = rwork[1];
numrank = i_dnnt(&rwork[2]);
if (nr < *n) {
i__1 = *n - nr;
zlaset_("A", &i__1, &nr, &c_b1, &c_b1, &v[nr + 1 +
v_dim1], ldv);
i__1 = *n - nr;
zlaset_("A", &nr, &i__1, &c_b1, &c_b1, &v[(nr + 1) *
v_dim1 + 1], ldv);
i__1 = *n - nr;
i__2 = *n - nr;
zlaset_("A", &i__1, &i__2, &c_b1, &c_b2, &v[nr + 1 + (
nr + 1) * v_dim1], ldv);
}
i__1 = *lwork - (*n << 1) - *n * nr - nr;
zunmqr_("L", "N", n, n, &nr, &cwork[(*n << 1) + 1], n, &
cwork[*n + 1], &v[v_offset], ldv, &cwork[(*n << 1)
+ *n * nr + nr + 1], &i__1, &ierr);
i__1 = *lwork - (*n << 1) - *n * nr - nr;
zunmlq_("L", "C", &nr, &nr, &nr, &cwork[(*n << 1) + 1], n,
&cwork[(*n << 1) + *n * nr + 1], &u[u_offset],
ldu, &cwork[(*n << 1) + *n * nr + nr + 1], &i__1,
&ierr);
i__1 = nr;
for (q = 1; q <= i__1; ++q) {
i__2 = nr;
for (p = 1; p <= i__2; ++p) {
i__3 = (*n << 1) + *n * nr + nr + iwork[*n + p];
i__4 = p + q * u_dim1;
cwork[i__3].r = u[i__4].r, cwork[i__3].i = u[i__4]
.i;
/* L772: */
}
i__2 = nr;
for (p = 1; p <= i__2; ++p) {
i__3 = p + q * u_dim1;
i__4 = (*n << 1) + *n * nr + nr + p;
u[i__3].r = cwork[i__4].r, u[i__3].i = cwork[i__4]
.i;
/* L774: */
}
/* L773: */
}
}
/* Permute the rows of V using the (column) permutation from the */
/* first QRF. Also, scale the columns to make them unit in */
/* Euclidean norm. This applies to all cases. */
temp1 = sqrt((doublereal) (*n)) * epsln;
i__1 = *n;
for (q = 1; q <= i__1; ++q) {
i__2 = *n;
for (p = 1; p <= i__2; ++p) {
i__3 = (*n << 1) + *n * nr + nr + iwork[p];
i__4 = p + q * v_dim1;
cwork[i__3].r = v[i__4].r, cwork[i__3].i = v[i__4].i;
/* L972: */
}
i__2 = *n;
for (p = 1; p <= i__2; ++p) {
i__3 = p + q * v_dim1;
i__4 = (*n << 1) + *n * nr + nr + p;
v[i__3].r = cwork[i__4].r, v[i__3].i = cwork[i__4].i;
/* L973: */
}
xsc = 1. / dznrm2_(n, &v[q * v_dim1 + 1], &c__1);
if (xsc < 1. - temp1 || xsc > temp1 + 1.) {
zdscal_(n, &xsc, &v[q * v_dim1 + 1], &c__1);
}
/* L1972: */
}
/* At this moment, V contains the right singular vectors of A. */
/* Next, assemble the left singular vector matrix U (M x N). */
if (nr < *m) {
i__1 = *m - nr;
zlaset_("A", &i__1, &nr, &c_b1, &c_b1, &u[nr + 1 + u_dim1]
, ldu);
if (nr < n1) {
i__1 = n1 - nr;
zlaset_("A", &nr, &i__1, &c_b1, &c_b1, &u[(nr + 1) *
u_dim1 + 1], ldu);
i__1 = *m - nr;
i__2 = n1 - nr;
zlaset_("A", &i__1, &i__2, &c_b1, &c_b2, &u[nr + 1 + (
nr + 1) * u_dim1], ldu);
}
}
/* The Q matrix from the first QRF is built into the left singular */
/* matrix U. This applies to all cases. */
i__1 = *lwork - *n;
zunmqr_("L", "N", m, &n1, n, &a[a_offset], lda, &cwork[1], &u[
u_offset], ldu, &cwork[*n + 1], &i__1, &ierr);
/* The columns of U are normalized. The cost is O(M*N) flops. */
temp1 = sqrt((doublereal) (*m)) * epsln;
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
xsc = 1. / dznrm2_(m, &u[p * u_dim1 + 1], &c__1);
if (xsc < 1. - temp1 || xsc > temp1 + 1.) {
zdscal_(m, &xsc, &u[p * u_dim1 + 1], &c__1);
}
/* L1973: */
}
/* If the initial QRF is computed with row pivoting, the left */
/* singular vectors must be adjusted. */
if (rowpiv) {
i__1 = *m - 1;
zlaswp_(&n1, &u[u_offset], ldu, &c__1, &i__1, &iwork[
iwoff + 1], &c_n1);
}
} else {
/* the second QRF is not needed */
zlacpy_("U", n, n, &a[a_offset], lda, &cwork[*n + 1], n);
if (l2pert) {
xsc = sqrt(small);
i__1 = *n;
for (p = 2; p <= i__1; ++p) {
i__2 = *n + (p - 1) * *n + p;
z__1.r = xsc * cwork[i__2].r, z__1.i = xsc * cwork[
i__2].i;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = p - 1;
for (q = 1; q <= i__2; ++q) {
/* CWORK(N+(q-1)*N+p)=-TEMP1 * ( CWORK(N+(p-1)*N+q) / */
/* $ ABS(CWORK(N+(p-1)*N+q)) ) */
i__3 = *n + (q - 1) * *n + p;
z__1.r = -ctemp.r, z__1.i = -ctemp.i;
cwork[i__3].r = z__1.r, cwork[i__3].i = z__1.i;
/* L5971: */
}
/* L5970: */
}
} else {
i__1 = *n - 1;
i__2 = *n - 1;
zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &cwork[*n + 2],
n);
}
i__1 = *lwork - *n - *n * *n;
zgesvj_("U", "U", "N", n, n, &cwork[*n + 1], n, &sva[1], n, &
u[u_offset], ldu, &cwork[*n + *n * *n + 1], &i__1, &
rwork[1], lrwork, info);
scalem = rwork[1];
numrank = i_dnnt(&rwork[2]);
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
zcopy_(n, &cwork[*n + (p - 1) * *n + 1], &c__1, &u[p *
u_dim1 + 1], &c__1);
zdscal_(n, &sva[p], &cwork[*n + (p - 1) * *n + 1], &c__1);
/* L6970: */
}
ztrsm_("L", "U", "N", "N", n, n, &c_b2, &a[a_offset], lda, &
cwork[*n + 1], n);
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
zcopy_(n, &cwork[*n + p], n, &v[iwork[p] + v_dim1], ldv);
/* L6972: */
}
temp1 = sqrt((doublereal) (*n)) * epsln;
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
xsc = 1. / dznrm2_(n, &v[p * v_dim1 + 1], &c__1);
if (xsc < 1. - temp1 || xsc > temp1 + 1.) {
zdscal_(n, &xsc, &v[p * v_dim1 + 1], &c__1);
}
/* L6971: */
}
/* Assemble the left singular vector matrix U (M x N). */
if (*n < *m) {
i__1 = *m - *n;
zlaset_("A", &i__1, n, &c_b1, &c_b1, &u[*n + 1 + u_dim1],
ldu);
if (*n < n1) {
i__1 = n1 - *n;
zlaset_("A", n, &i__1, &c_b1, &c_b1, &u[(*n + 1) *
u_dim1 + 1], ldu);
i__1 = *m - *n;
i__2 = n1 - *n;
zlaset_("A", &i__1, &i__2, &c_b1, &c_b2, &u[*n + 1 + (
*n + 1) * u_dim1], ldu);
}
}
i__1 = *lwork - *n;
zunmqr_("L", "N", m, &n1, n, &a[a_offset], lda, &cwork[1], &u[
u_offset], ldu, &cwork[*n + 1], &i__1, &ierr);
temp1 = sqrt((doublereal) (*m)) * epsln;
i__1 = n1;
for (p = 1; p <= i__1; ++p) {
xsc = 1. / dznrm2_(m, &u[p * u_dim1 + 1], &c__1);
if (xsc < 1. - temp1 || xsc > temp1 + 1.) {
zdscal_(m, &xsc, &u[p * u_dim1 + 1], &c__1);
}
/* L6973: */
}
if (rowpiv) {
i__1 = *m - 1;
zlaswp_(&n1, &u[u_offset], ldu, &c__1, &i__1, &iwork[
iwoff + 1], &c_n1);
}
}
/* end of the >> almost orthogonal case << in the full SVD */
} else {
/* This branch deploys a preconditioned Jacobi SVD with explicitly */
/* accumulated rotations. It is included as optional, mainly for */
/* experimental purposes. It does perform well, and can also be used. */
/* In this implementation, this branch will be automatically activated */
/* if the condition number sigma_max(A) / sigma_min(A) is predicted */
/* to be greater than the overflow threshold. This is because the */
/* a posteriori computation of the singular vectors assumes robust */
/* implementation of BLAS and some LAPACK procedures, capable of working */
/* in presence of extreme values, e.g. when the singular values spread from */
/* the underflow to the overflow threshold. */
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = *n - p + 1;
zcopy_(&i__2, &a[p + p * a_dim1], lda, &v[p + p * v_dim1], &
c__1);
i__2 = *n - p + 1;
zlacgv_(&i__2, &v[p + p * v_dim1], &c__1);
/* L7968: */
}
if (l2pert) {
xsc = sqrt(small / epsln);
i__1 = nr;
for (q = 1; q <= i__1; ++q) {
d__1 = xsc * z_abs(&v[q + q * v_dim1]);
z__1.r = d__1, z__1.i = 0.;
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__2 = *n;
for (p = 1; p <= i__2; ++p) {
if (p > q && z_abs(&v[p + q * v_dim1]) <= temp1 || p <
q) {
i__3 = p + q * v_dim1;
v[i__3].r = ctemp.r, v[i__3].i = ctemp.i;
}
/* $ V(p,q) = TEMP1 * ( V(p,q) / ABS(V(p,q)) ) */
if (p < q) {
i__3 = p + q * v_dim1;
i__4 = p + q * v_dim1;
z__1.r = -v[i__4].r, z__1.i = -v[i__4].i;
v[i__3].r = z__1.r, v[i__3].i = z__1.i;
}
/* L5968: */
}
/* L5969: */
}
} else {
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &v[(v_dim1 << 1) + 1]
, ldv);
}
i__1 = *lwork - (*n << 1);
zgeqrf_(n, &nr, &v[v_offset], ldv, &cwork[*n + 1], &cwork[(*n <<
1) + 1], &i__1, &ierr);
zlacpy_("L", n, &nr, &v[v_offset], ldv, &cwork[(*n << 1) + 1], n);
i__1 = nr;
for (p = 1; p <= i__1; ++p) {
i__2 = nr - p + 1;
zcopy_(&i__2, &v[p + p * v_dim1], ldv, &u[p + p * u_dim1], &
c__1);
i__2 = nr - p + 1;
zlacgv_(&i__2, &u[p + p * u_dim1], &c__1);
/* L7969: */
}
if (l2pert) {
xsc = sqrt(small / epsln);
i__1 = nr;
for (q = 2; q <= i__1; ++q) {
i__2 = q - 1;
for (p = 1; p <= i__2; ++p) {
/* Computing MIN */
d__2 = z_abs(&u[p + p * u_dim1]), d__3 = z_abs(&u[q +
q * u_dim1]);
d__1 = xsc * f2cmin(d__2,d__3);
z__1.r = d__1, z__1.i = 0.;
ctemp.r = z__1.r, ctemp.i = z__1.i;
/* U(p,q) = - TEMP1 * ( U(q,p) / ABS(U(q,p)) ) */
i__3 = p + q * u_dim1;
z__1.r = -ctemp.r, z__1.i = -ctemp.i;
u[i__3].r = z__1.r, u[i__3].i = z__1.i;
/* L9971: */
}
/* L9970: */
}
} else {
i__1 = nr - 1;
i__2 = nr - 1;
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &u[(u_dim1 << 1) + 1]
, ldu);
}
i__1 = *lwork - (*n << 1) - *n * nr;
zgesvj_("L", "U", "V", &nr, &nr, &u[u_offset], ldu, &sva[1], n, &
v[v_offset], ldv, &cwork[(*n << 1) + *n * nr + 1], &i__1,
&rwork[1], lrwork, info);
scalem = rwork[1];
numrank = i_dnnt(&rwork[2]);
if (nr < *n) {
i__1 = *n - nr;
zlaset_("A", &i__1, &nr, &c_b1, &c_b1, &v[nr + 1 + v_dim1],
ldv);
i__1 = *n - nr;
zlaset_("A", &nr, &i__1, &c_b1, &c_b1, &v[(nr + 1) * v_dim1 +
1], ldv);
i__1 = *n - nr;
i__2 = *n - nr;
zlaset_("A", &i__1, &i__2, &c_b1, &c_b2, &v[nr + 1 + (nr + 1)
* v_dim1], ldv);
}
i__1 = *lwork - (*n << 1) - *n * nr - nr;
zunmqr_("L", "N", n, n, &nr, &cwork[(*n << 1) + 1], n, &cwork[*n
+ 1], &v[v_offset], ldv, &cwork[(*n << 1) + *n * nr + nr
+ 1], &i__1, &ierr);
/* Permute the rows of V using the (column) permutation from the */
/* first QRF. Also, scale the columns to make them unit in */
/* Euclidean norm. This applies to all cases. */
temp1 = sqrt((doublereal) (*n)) * epsln;
i__1 = *n;
for (q = 1; q <= i__1; ++q) {
i__2 = *n;
for (p = 1; p <= i__2; ++p) {
i__3 = (*n << 1) + *n * nr + nr + iwork[p];
i__4 = p + q * v_dim1;
cwork[i__3].r = v[i__4].r, cwork[i__3].i = v[i__4].i;
/* L8972: */
}
i__2 = *n;
for (p = 1; p <= i__2; ++p) {
i__3 = p + q * v_dim1;
i__4 = (*n << 1) + *n * nr + nr + p;
v[i__3].r = cwork[i__4].r, v[i__3].i = cwork[i__4].i;
/* L8973: */
}
xsc = 1. / dznrm2_(n, &v[q * v_dim1 + 1], &c__1);
if (xsc < 1. - temp1 || xsc > temp1 + 1.) {
zdscal_(n, &xsc, &v[q * v_dim1 + 1], &c__1);
}
/* L7972: */
}
/* At this moment, V contains the right singular vectors of A. */
/* Next, assemble the left singular vector matrix U (M x N). */
if (nr < *m) {
i__1 = *m - nr;
zlaset_("A", &i__1, &nr, &c_b1, &c_b1, &u[nr + 1 + u_dim1],
ldu);
if (nr < n1) {
i__1 = n1 - nr;
zlaset_("A", &nr, &i__1, &c_b1, &c_b1, &u[(nr + 1) *
u_dim1 + 1], ldu);
i__1 = *m - nr;
i__2 = n1 - nr;
zlaset_("A", &i__1, &i__2, &c_b1, &c_b2, &u[nr + 1 + (nr
+ 1) * u_dim1], ldu);
}
}
i__1 = *lwork - *n;
zunmqr_("L", "N", m, &n1, n, &a[a_offset], lda, &cwork[1], &u[
u_offset], ldu, &cwork[*n + 1], &i__1, &ierr);
if (rowpiv) {
i__1 = *m - 1;
zlaswp_(&n1, &u[u_offset], ldu, &c__1, &i__1, &iwork[iwoff +
1], &c_n1);
}
}
if (transp) {
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
zswap_(n, &u[p * u_dim1 + 1], &c__1, &v[p * v_dim1 + 1], &
c__1);
/* L6974: */
}
}
}
/* end of the full SVD */
/* Undo scaling, if necessary (and possible) */
if (uscal2 <= big / sva[1] * uscal1) {
dlascl_("G", &c__0, &c__0, &uscal1, &uscal2, &nr, &c__1, &sva[1], n, &
ierr);
uscal1 = 1.;
uscal2 = 1.;
}
if (nr < *n) {
i__1 = *n;
for (p = nr + 1; p <= i__1; ++p) {
sva[p] = 0.;
/* L3004: */
}
}
rwork[1] = uscal2 * scalem;
rwork[2] = uscal1;
if (errest) {
rwork[3] = sconda;
}
if (lsvec && rsvec) {
rwork[4] = condr1;
rwork[5] = condr2;
}
if (l2tran) {
rwork[6] = entra;
rwork[7] = entrat;
}
iwork[1] = nr;
iwork[2] = numrank;
iwork[3] = warning;
if (transp) {
iwork[4] = 1;
} else {
iwork[4] = -1;
}
return;
} /* zgejsv_ */
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