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OpenBLAS/lapack-netlib/SRC/dgesvj.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 int logical;
typedef short int shortlogical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
/* procedure parameter types for -A and -C++ */
#define F2C_proc_par_types 1
#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 doublereal c_b17 = 0.;
static doublereal c_b18 = 1.;
static integer c__1 = 1;
static integer c__0 = 0;
static integer c__2 = 2;
/* > \brief \b DGESVJ */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DGESVJ + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgesvj.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgesvj.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesvj.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, */
/* LDV, WORK, LWORK, INFO ) */
/* INTEGER INFO, LDA, LDV, LWORK, M, MV, N */
/* CHARACTER*1 JOBA, JOBU, JOBV */
/* DOUBLE PRECISION A( LDA, * ), SVA( N ), V( LDV, * ), */
/* $ WORK( LWORK ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DGESVJ computes the singular value decomposition (SVD) of a real */
/* > M-by-N matrix A, where M >= N. The SVD of A is written as */
/* > [++] [xx] [x0] [xx] */
/* > A = U * SIGMA * V^t, [++] = [xx] * [ox] * [xx] */
/* > [++] [xx] */
/* > where SIGMA is an N-by-N diagonal matrix, U is an M-by-N orthonormal */
/* > matrix, and V is an N-by-N orthogonal matrix. The diagonal elements */
/* > of SIGMA are the singular values of A. The columns of U and V are the */
/* > left and the right singular vectors of A, respectively. */
/* > DGESVJ can sometimes compute tiny singular values and their singular vectors much */
/* > more accurately than other SVD routines, see below under Further Details. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOBA */
/* > \verbatim */
/* > JOBA is CHARACTER*1 */
/* > Specifies the structure of A. */
/* > = 'L': The input matrix A is lower triangular; */
/* > = 'U': The input matrix A is upper triangular; */
/* > = 'G': The input matrix A is general M-by-N matrix, M >= N. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBU */
/* > \verbatim */
/* > JOBU is CHARACTER*1 */
/* > Specifies whether to compute the left singular vectors */
/* > (columns of U): */
/* > = 'U': The left singular vectors corresponding to the nonzero */
/* > singular values are computed and returned in the leading */
/* > columns of A. See more details in the description of A. */
/* > The default numerical orthogonality threshold is set to */
/* > approximately TOL=CTOL*EPS, CTOL=DSQRT(M), EPS=DLAMCH('E'). */
/* > = 'C': Analogous to JOBU='U', except that user can control the */
/* > level of numerical orthogonality of the computed left */
/* > singular vectors. TOL can be set to TOL = CTOL*EPS, where */
/* > CTOL is given on input in the array WORK. */
/* > No CTOL smaller than ONE is allowed. CTOL greater */
/* > than 1 / EPS is meaningless. The option 'C' */
/* > can be used if M*EPS is satisfactory orthogonality */
/* > of the computed left singular vectors, so CTOL=M could */
/* > save few sweeps of Jacobi rotations. */
/* > See the descriptions of A and WORK(1). */
/* > = 'N': The matrix U is not computed. However, see the */
/* > description of A. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBV */
/* > \verbatim */
/* > JOBV is CHARACTER*1 */
/* > Specifies whether to compute the right singular vectors, that */
/* > is, the matrix V: */
/* > = 'V': the matrix V is computed and returned in the array V */
/* > = 'A': the Jacobi rotations are applied to the MV-by-N */
/* > array V. In other words, the right singular vector */
/* > matrix V is not computed explicitly, instead it is */
/* > applied to an MV-by-N matrix initially stored in the */
/* > first MV rows of V. */
/* > = 'N': the matrix V is not computed and the array V is not */
/* > referenced */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The number of rows of the input matrix A. 1/DLAMCH('E') > 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 DOUBLE PRECISION array, dimension (LDA,N) */
/* > On entry, the M-by-N matrix A. */
/* > On exit : */
/* > If JOBU = 'U' .OR. JOBU = 'C' : */
/* > If INFO = 0 : */
/* > RANKA orthonormal columns of U are returned in the */
/* > leading RANKA columns of the array A. Here RANKA <= N */
/* > is the number of computed singular values of A that are */
/* > above the underflow threshold DLAMCH('S'). The singular */
/* > vectors corresponding to underflowed or zero singular */
/* > values are not computed. The value of RANKA is returned */
/* > in the array WORK as RANKA=NINT(WORK(2)). Also see the */
/* > descriptions of SVA and WORK. The computed columns of U */
/* > are mutually numerically orthogonal up to approximately */
/* > TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU = 'C'), */
/* > see the description of JOBU. */
/* > If INFO > 0 : */
/* > the procedure DGESVJ did not converge in the given number */
/* > of iterations (sweeps). In that case, the computed */
/* > columns of U may not be orthogonal up to TOL. The output */
/* > U (stored in A), SIGMA (given by the computed singular */
/* > values in SVA(1:N)) and V is still a decomposition of the */
/* > input matrix A in the sense that the residual */
/* > ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small. */
/* > */
/* > If JOBU = 'N' : */
/* > If INFO = 0 : */
/* > Note that the left singular vectors are 'for free' in the */
/* > one-sided Jacobi SVD algorithm. However, if only the */
/* > singular values are needed, the level of numerical */
/* > orthogonality of U is not an issue and iterations are */
/* > stopped when the columns of the iterated matrix are */
/* > numerically orthogonal up to approximately M*EPS. Thus, */
/* > on exit, A contains the columns of U scaled with the */
/* > corresponding singular values. */
/* > If INFO > 0 : */
/* > the procedure DGESVJ did not converge in the given number */
/* > of iterations (sweeps). */
/* > \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 : */
/* > If INFO = 0 : */
/* > depending on the value SCALE = WORK(1), we have: */
/* > If SCALE = ONE : */
/* > SVA(1:N) contains the computed singular values of A. */
/* > During the computation SVA contains the Euclidean column */
/* > norms of the iterated matrices in the array A. */
/* > If SCALE .NE. ONE : */
/* > The singular values of A are SCALE*SVA(1:N), and this */
/* > factored representation is due to the fact that some of the */
/* > singular values of A might underflow or overflow. */
/* > If INFO > 0 : */
/* > the procedure DGESVJ did not converge in the given number of */
/* > iterations (sweeps) and SCALE*SVA(1:N) may not be accurate. */
/* > \endverbatim */
/* > */
/* > \param[in] MV */
/* > \verbatim */
/* > MV is INTEGER */
/* > If JOBV = 'A', then the product of Jacobi rotations in DGESVJ */
/* > is applied to the first MV rows of V. See the description of JOBV. */
/* > \endverbatim */
/* > */
/* > \param[in,out] V */
/* > \verbatim */
/* > V is DOUBLE PRECISION array, dimension (LDV,N) */
/* > If JOBV = 'V', then V contains on exit the N-by-N matrix of */
/* > the right singular vectors; */
/* > If JOBV = 'A', then V contains the product of the computed right */
/* > singular vector matrix and the initial matrix in */
/* > the array V. */
/* > If JOBV = 'N', then V is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDV */
/* > \verbatim */
/* > LDV is INTEGER */
/* > The leading dimension of the array V, LDV >= 1. */
/* > If JOBV = 'V', then LDV >= f2cmax(1,N). */
/* > If JOBV = 'A', then LDV >= f2cmax(1,MV) . */
/* > \endverbatim */
/* > */
/* > \param[in,out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension (LWORK) */
/* > On entry : */
/* > If JOBU = 'C' : */
/* > WORK(1) = CTOL, where CTOL defines the threshold for convergence. */
/* > The process stops if all columns of A are mutually */
/* > orthogonal up to CTOL*EPS, EPS=DLAMCH('E'). */
/* > It is required that CTOL >= ONE, i.e. it is not */
/* > allowed to force the routine to obtain orthogonality */
/* > below EPS. */
/* > On exit : */
/* > WORK(1) = SCALE is the scaling factor such that SCALE*SVA(1:N) */
/* > are the computed singular values of A. */
/* > (See description of SVA().) */
/* > WORK(2) = NINT(WORK(2)) is the number of the computed nonzero */
/* > singular values. */
/* > WORK(3) = NINT(WORK(3)) is the number of the computed singular */
/* > values that are larger than the underflow threshold. */
/* > WORK(4) = NINT(WORK(4)) is the number of sweeps of Jacobi */
/* > rotations needed for numerical convergence. */
/* > WORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep. */
/* > This is useful information in cases when DGESVJ did */
/* > not converge, as it can be used to estimate whether */
/* > the output is still useful and for post festum analysis. */
/* > WORK(6) = the largest absolute value over all sines of the */
/* > Jacobi rotation angles in the last sweep. It can be */
/* > useful for a post festum analysis. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > length of WORK, WORK >= MAX(6,M+N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, then the i-th argument had an illegal value */
/* > > 0: DGESVJ did not converge in the maximal allowed number (30) */
/* > of sweeps. The output may still be useful. See the */
/* > description of WORK. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date June 2017 */
/* > \ingroup doubleGEcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > The orthogonal N-by-N matrix V is obtained as a product of Jacobi plane */
/* > rotations. The rotations are implemented as fast scaled rotations of */
/* > Anda and Park [1]. In the case of underflow of the Jacobi angle, a */
/* > modified Jacobi transformation of Drmac [4] is used. Pivot strategy uses */
/* > column interchanges of de Rijk [2]. The relative accuracy of the computed */
/* > singular values and the accuracy of the computed singular vectors (in */
/* > angle metric) is as guaranteed by the theory of Demmel and Veselic [3]. */
/* > The condition number that determines the accuracy in the full rank case */
/* > is essentially min_{D=diag} kappa(A*D), where kappa(.) is the */
/* > spectral condition number. The best performance of this Jacobi SVD */
/* > procedure is achieved if used in an accelerated version of Drmac and */
/* > Veselic [5,6], and it is the kernel routine in the SIGMA library [7]. */
/* > Some tunning parameters (marked with [TP]) are available for the */
/* > implementer. */
/* > The computational range for the nonzero singular values is the machine */
/* > number interval ( UNDERFLOW , OVERFLOW ). In extreme cases, even */
/* > denormalized singular values can be computed with the corresponding */
/* > gradual loss of accurate digits. */
/* > \endverbatim */
/* > \par Contributors: */
/* ================== */
/* > */
/* > \verbatim */
/* > */
/* > ============ */
/* > */
/* > Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) */
/* > \endverbatim */
/* > \par References: */
/* ================ */
/* > */
/* > \verbatim */
/* > */
/* > [1] A. A. Anda and H. Park: Fast plane rotations with dynamic scaling. */
/* > SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174. */
/* > [2] P. P. M. De Rijk: A one-sided Jacobi algorithm for computing the */
/* > singular value decomposition on a vector computer. */
/* > SIAM J. Sci. Stat. Comp., Vol. 10 (1998), pp. 359-371. */
/* > [3] J. Demmel and K. Veselic: Jacobi method is more accurate than QR. */
/* > [4] Z. Drmac: Implementation of Jacobi rotations for accurate singular */
/* > value computation in floating point arithmetic. */
/* > SIAM J. Sci. Comp., Vol. 18 (1997), pp. 1200-1222. */
/* > [5] 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. */
/* > [6] 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. */
/* > [7] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV, */
/* > QSVD, (H,K)-SVD computations. */
/* > Department of Mathematics, University of Zagreb, 2008. */
/* > \endverbatim */
/* > \par Bugs, examples and comments: */
/* ================================= */
/* > */
/* > \verbatim */
/* > =========================== */
/* > Please report all bugs and send interesting test examples and comments to */
/* > drmac@math.hr. Thank you. */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void dgesvj_(char *joba, char *jobu, char *jobv, integer *m,
integer *n, doublereal *a, integer *lda, doublereal *sva, integer *mv,
doublereal *v, integer *ldv, doublereal *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2;
/* Local variables */
doublereal aapp, aapq, aaqq;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
doublereal ctol;
integer ierr;
doublereal bigtheta;
integer pskipped;
doublereal aapp0;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
doublereal temp1;
integer i__, p, q;
doublereal t;
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
integer *);
doublereal large, apoaq, aqoap;
extern logical lsame_(char *, char *);
doublereal theta, small, sfmin;
logical lsvec;
extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
doublereal fastr[5];
extern /* Subroutine */ void dswap_(integer *, doublereal *, integer *,
doublereal *, integer *);
doublereal epsln;
logical applv, rsvec;
extern /* Subroutine */ void daxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
logical uctol;
extern /* Subroutine */ void drotm_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *);
logical lower, upper, rotok;
integer n2, n4;
extern /* Subroutine */ void dgsvj0_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *), dgsvj1_(
char *, integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
integer *, integer *);
doublereal rootsfmin;
integer n34;
doublereal cs;
extern doublereal dlamch_(char *);
doublereal sn;
extern /* Subroutine */ void dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ void dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *);
extern int xerbla_(char *, integer *, ftnlen);
integer ijblsk, swband, blskip;
doublereal mxaapq;
extern /* Subroutine */ void dlassq_(integer *, doublereal *, integer *,
doublereal *, doublereal *);
doublereal thsign, mxsinj;
integer ir1, emptsw, notrot, iswrot, jbc;
doublereal big;
integer kbl, lkahead, igl, ibr, jgl, nbl;
doublereal skl;
logical goscale;
doublereal tol;
integer mvl;
logical noscale;
doublereal rootbig, rooteps;
integer rowskip;
doublereal roottol;
/* -- 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 */
/* ===================================================================== */
/* from BLAS */
/* from LAPACK */
/* from BLAS */
/* from LAPACK */
/* Test the input arguments */
/* Parameter adjustments */
--sva;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
--work;
/* Function Body */
lsvec = lsame_(jobu, "U");
uctol = lsame_(jobu, "C");
rsvec = lsame_(jobv, "V");
applv = lsame_(jobv, "A");
upper = lsame_(joba, "U");
lower = lsame_(joba, "L");
if (! (upper || lower || lsame_(joba, "G"))) {
*info = -1;
} else if (! (lsvec || uctol || lsame_(jobu, "N")))
{
*info = -2;
} else if (! (rsvec || applv || lsame_(jobv, "N")))
{
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*n < 0 || *n > *m) {
*info = -5;
} else if (*lda < *m) {
*info = -7;
} else if (*mv < 0) {
*info = -9;
} else if (rsvec && *ldv < *n || applv && *ldv < *mv) {
*info = -11;
} else if (uctol && work[1] <= 1.) {
*info = -12;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = *m + *n;
if (*lwork < f2cmax(i__1,6)) {
*info = -13;
} else {
*info = 0;
}
}
/* #:( */
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGESVJ", &i__1, (ftnlen)6);
return;
}
/* #:) Quick return for void matrix */
if (*m == 0 || *n == 0) {
return;
}
/* Set numerical parameters */
/* The stopping criterion for Jacobi rotations is */
/* max_{i<>j}|A(:,i)^T * A(:,j)|/(||A(:,i)||*||A(:,j)||) < CTOL*EPS */
/* where EPS is the round-off and CTOL is defined as follows: */
if (uctol) {
/* ... user controlled */
ctol = work[1];
} else {
/* ... default */
if (lsvec || rsvec || applv) {
ctol = sqrt((doublereal) (*m));
} else {
ctol = (doublereal) (*m);
}
}
/* ... and the machine dependent parameters are */
/* [!] (Make sure that DLAMCH() works properly on the target machine.) */
epsln = dlamch_("Epsilon");
rooteps = sqrt(epsln);
sfmin = dlamch_("SafeMinimum");
rootsfmin = sqrt(sfmin);
small = sfmin / epsln;
big = dlamch_("Overflow");
/* BIG = ONE / SFMIN */
rootbig = 1. / rootsfmin;
large = big / sqrt((doublereal) (*m * *n));
bigtheta = 1. / rooteps;
tol = ctol * epsln;
roottol = sqrt(tol);
if ((doublereal) (*m) * epsln >= 1.) {
*info = -4;
i__1 = -(*info);
xerbla_("DGESVJ", &i__1, (ftnlen)6);
return;
}
/* Initialize the right singular vector matrix. */
if (rsvec) {
mvl = *n;
dlaset_("A", &mvl, n, &c_b17, &c_b18, &v[v_offset], ldv);
} else if (applv) {
mvl = *mv;
}
rsvec = rsvec || applv;
/* Initialize SVA( 1:N ) = ( ||A e_i||_2, i = 1:N ) */
/* (!) If necessary, scale A to protect the largest singular value */
/* from overflow. It is possible that saving the largest singular */
/* value destroys the information about the small ones. */
/* This initial scaling is almost minimal in the sense that the */
/* goal is to make sure that no column norm overflows, and that */
/* DSQRT(N)*max_i SVA(i) does not overflow. If INFinite entries */
/* in A are detected, the procedure returns with INFO=-6. */
skl = 1. / sqrt((doublereal) (*m) * (doublereal) (*n));
noscale = TRUE_;
goscale = TRUE_;
if (lower) {
/* the input matrix is M-by-N lower triangular (trapezoidal) */
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
aapp = 0.;
aaqq = 1.;
i__2 = *m - p + 1;
dlassq_(&i__2, &a[p + p * a_dim1], &c__1, &aapp, &aaqq);
if (aapp > big) {
*info = -6;
i__2 = -(*info);
xerbla_("DGESVJ", &i__2, (ftnlen)6);
return;
}
aaqq = sqrt(aaqq);
if (aapp < big / aaqq && noscale) {
sva[p] = aapp * aaqq;
} else {
noscale = FALSE_;
sva[p] = aapp * (aaqq * skl);
if (goscale) {
goscale = FALSE_;
i__2 = p - 1;
for (q = 1; q <= i__2; ++q) {
sva[q] *= skl;
/* L1873: */
}
}
}
/* L1874: */
}
} else if (upper) {
/* the input matrix is M-by-N upper triangular (trapezoidal) */
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
aapp = 0.;
aaqq = 1.;
dlassq_(&p, &a[p * a_dim1 + 1], &c__1, &aapp, &aaqq);
if (aapp > big) {
*info = -6;
i__2 = -(*info);
xerbla_("DGESVJ", &i__2, (ftnlen)6);
return;
}
aaqq = sqrt(aaqq);
if (aapp < big / aaqq && noscale) {
sva[p] = aapp * aaqq;
} else {
noscale = FALSE_;
sva[p] = aapp * (aaqq * skl);
if (goscale) {
goscale = FALSE_;
i__2 = p - 1;
for (q = 1; q <= i__2; ++q) {
sva[q] *= skl;
/* L2873: */
}
}
}
/* L2874: */
}
} else {
/* the input matrix is M-by-N general dense */
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
aapp = 0.;
aaqq = 1.;
dlassq_(m, &a[p * a_dim1 + 1], &c__1, &aapp, &aaqq);
if (aapp > big) {
*info = -6;
i__2 = -(*info);
xerbla_("DGESVJ", &i__2, (ftnlen)6);
return;
}
aaqq = sqrt(aaqq);
if (aapp < big / aaqq && noscale) {
sva[p] = aapp * aaqq;
} else {
noscale = FALSE_;
sva[p] = aapp * (aaqq * skl);
if (goscale) {
goscale = FALSE_;
i__2 = p - 1;
for (q = 1; q <= i__2; ++q) {
sva[q] *= skl;
/* L3873: */
}
}
}
/* L3874: */
}
}
if (noscale) {
skl = 1.;
}
/* Move the smaller part of the spectrum from the underflow threshold */
/* (!) Start by determining the position of the nonzero entries of the */
/* array SVA() relative to ( SFMIN, BIG ). */
aapp = 0.;
aaqq = big;
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
if (sva[p] != 0.) {
/* Computing MIN */
d__1 = aaqq, d__2 = sva[p];
aaqq = f2cmin(d__1,d__2);
}
/* Computing MAX */
d__1 = aapp, d__2 = sva[p];
aapp = f2cmax(d__1,d__2);
/* L4781: */
}
/* #:) Quick return for zero matrix */
if (aapp == 0.) {
if (lsvec) {
dlaset_("G", m, n, &c_b17, &c_b18, &a[a_offset], lda);
}
work[1] = 1.;
work[2] = 0.;
work[3] = 0.;
work[4] = 0.;
work[5] = 0.;
work[6] = 0.;
return;
}
/* #:) Quick return for one-column matrix */
if (*n == 1) {
if (lsvec) {
dlascl_("G", &c__0, &c__0, &sva[1], &skl, m, &c__1, &a[a_dim1 + 1]
, lda, &ierr);
}
work[1] = 1. / skl;
if (sva[1] >= sfmin) {
work[2] = 1.;
} else {
work[2] = 0.;
}
work[3] = 0.;
work[4] = 0.;
work[5] = 0.;
work[6] = 0.;
return;
}
/* Protect small singular values from underflow, and try to */
/* avoid underflows/overflows in computing Jacobi rotations. */
sn = sqrt(sfmin / epsln);
temp1 = sqrt(big / (doublereal) (*n));
if (aapp <= sn || aaqq >= temp1 || sn <= aaqq && aapp <= temp1) {
/* Computing MIN */
d__1 = big, d__2 = temp1 / aapp;
temp1 = f2cmin(d__1,d__2);
/* AAQQ = AAQQ*TEMP1 */
/* AAPP = AAPP*TEMP1 */
} else if (aaqq <= sn && aapp <= temp1) {
/* Computing MIN */
d__1 = sn / aaqq, d__2 = big / (aapp * sqrt((doublereal) (*n)));
temp1 = f2cmin(d__1,d__2);
/* AAQQ = AAQQ*TEMP1 */
/* AAPP = AAPP*TEMP1 */
} else if (aaqq >= sn && aapp >= temp1) {
/* Computing MAX */
d__1 = sn / aaqq, d__2 = temp1 / aapp;
temp1 = f2cmax(d__1,d__2);
/* AAQQ = AAQQ*TEMP1 */
/* AAPP = AAPP*TEMP1 */
} else if (aaqq <= sn && aapp >= temp1) {
/* Computing MIN */
d__1 = sn / aaqq, d__2 = big / (sqrt((doublereal) (*n)) * aapp);
temp1 = f2cmin(d__1,d__2);
/* AAQQ = AAQQ*TEMP1 */
/* AAPP = AAPP*TEMP1 */
} else {
temp1 = 1.;
}
/* Scale, if necessary */
if (temp1 != 1.) {
dlascl_("G", &c__0, &c__0, &c_b18, &temp1, n, &c__1, &sva[1], n, &
ierr);
}
skl = temp1 * skl;
if (skl != 1.) {
dlascl_(joba, &c__0, &c__0, &c_b18, &skl, m, n, &a[a_offset], lda, &
ierr);
skl = 1. / skl;
}
/* Row-cyclic Jacobi SVD algorithm with column pivoting */
emptsw = *n * (*n - 1) / 2;
notrot = 0;
fastr[0] = 0.;
/* A is represented in factored form A = A * diag(WORK), where diag(WORK) */
/* is initialized to identity. WORK is updated during fast scaled */
/* rotations. */
i__1 = *n;
for (q = 1; q <= i__1; ++q) {
work[q] = 1.;
/* L1868: */
}
swband = 3;
/* [TP] SWBAND is a tuning parameter [TP]. It is meaningful and effective */
/* if DGESVJ is used as a computational routine in the preconditioned */
/* Jacobi SVD algorithm DGESVJ. For sweeps i=1:SWBAND the procedure */
/* works on pivots inside a band-like region around the diagonal. */
/* The boundaries are determined dynamically, based on the number of */
/* pivots above a threshold. */
kbl = f2cmin(8,*n);
/* [TP] KBL is a tuning parameter that defines the tile size in the */
/* tiling of the p-q loops of pivot pairs. In general, an optimal */
/* value of KBL depends on the matrix dimensions and on the */
/* parameters of the computer's memory. */
nbl = *n / kbl;
if (nbl * kbl != *n) {
++nbl;
}
/* Computing 2nd power */
i__1 = kbl;
blskip = i__1 * i__1;
/* [TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. */
rowskip = f2cmin(5,kbl);
/* [TP] ROWSKIP is a tuning parameter. */
lkahead = 1;
/* [TP] LKAHEAD is a tuning parameter. */
/* Quasi block transformations, using the lower (upper) triangular */
/* structure of the input matrix. The quasi-block-cycling usually */
/* invokes cubic convergence. Big part of this cycle is done inside */
/* canonical subspaces of dimensions less than M. */
/* Computing MAX */
i__1 = 64, i__2 = kbl << 2;
if ((lower || upper) && *n > f2cmax(i__1,i__2)) {
/* [TP] The number of partition levels and the actual partition are */
/* tuning parameters. */
n4 = *n / 4;
n2 = *n / 2;
n34 = n4 * 3;
if (applv) {
q = 0;
} else {
q = 1;
}
if (lower) {
/* This works very well on lower triangular matrices, in particular */
/* in the framework of the preconditioned Jacobi SVD (xGEJSV). */
/* The idea is simple: */
/* [+ 0 0 0] Note that Jacobi transformations of [0 0] */
/* [+ + 0 0] [0 0] */
/* [+ + x 0] actually work on [x 0] [x 0] */
/* [+ + x x] [x x]. [x x] */
i__1 = *m - n34;
i__2 = *n - n34;
i__3 = *lwork - *n;
dgsvj0_(jobv, &i__1, &i__2, &a[n34 + 1 + (n34 + 1) * a_dim1], lda,
&work[n34 + 1], &sva[n34 + 1], &mvl, &v[n34 * q + 1 + (
n34 + 1) * v_dim1], ldv, &epsln, &sfmin, &tol, &c__2, &
work[*n + 1], &i__3, &ierr);
i__1 = *m - n2;
i__2 = n34 - n2;
i__3 = *lwork - *n;
dgsvj0_(jobv, &i__1, &i__2, &a[n2 + 1 + (n2 + 1) * a_dim1], lda, &
work[n2 + 1], &sva[n2 + 1], &mvl, &v[n2 * q + 1 + (n2 + 1)
* v_dim1], ldv, &epsln, &sfmin, &tol, &c__2, &work[*n +
1], &i__3, &ierr);
i__1 = *m - n2;
i__2 = *n - n2;
i__3 = *lwork - *n;
dgsvj1_(jobv, &i__1, &i__2, &n4, &a[n2 + 1 + (n2 + 1) * a_dim1],
lda, &work[n2 + 1], &sva[n2 + 1], &mvl, &v[n2 * q + 1 + (
n2 + 1) * v_dim1], ldv, &epsln, &sfmin, &tol, &c__1, &
work[*n + 1], &i__3, &ierr);
i__1 = *m - n4;
i__2 = n2 - n4;
i__3 = *lwork - *n;
dgsvj0_(jobv, &i__1, &i__2, &a[n4 + 1 + (n4 + 1) * a_dim1], lda, &
work[n4 + 1], &sva[n4 + 1], &mvl, &v[n4 * q + 1 + (n4 + 1)
* v_dim1], ldv, &epsln, &sfmin, &tol, &c__1, &work[*n +
1], &i__3, &ierr);
i__1 = *lwork - *n;
dgsvj0_(jobv, m, &n4, &a[a_offset], lda, &work[1], &sva[1], &mvl,
&v[v_offset], ldv, &epsln, &sfmin, &tol, &c__1, &work[*n
+ 1], &i__1, &ierr);
i__1 = *lwork - *n;
dgsvj1_(jobv, m, &n2, &n4, &a[a_offset], lda, &work[1], &sva[1], &
mvl, &v[v_offset], ldv, &epsln, &sfmin, &tol, &c__1, &
work[*n + 1], &i__1, &ierr);
} else if (upper) {
i__1 = *lwork - *n;
dgsvj0_(jobv, &n4, &n4, &a[a_offset], lda, &work[1], &sva[1], &
mvl, &v[v_offset], ldv, &epsln, &sfmin, &tol, &c__2, &
work[*n + 1], &i__1, &ierr);
i__1 = *lwork - *n;
dgsvj0_(jobv, &n2, &n4, &a[(n4 + 1) * a_dim1 + 1], lda, &work[n4
+ 1], &sva[n4 + 1], &mvl, &v[n4 * q + 1 + (n4 + 1) *
v_dim1], ldv, &epsln, &sfmin, &tol, &c__1, &work[*n + 1],
&i__1, &ierr);
i__1 = *lwork - *n;
dgsvj1_(jobv, &n2, &n2, &n4, &a[a_offset], lda, &work[1], &sva[1],
&mvl, &v[v_offset], ldv, &epsln, &sfmin, &tol, &c__1, &
work[*n + 1], &i__1, &ierr);
i__1 = n2 + n4;
i__2 = *lwork - *n;
dgsvj0_(jobv, &i__1, &n4, &a[(n2 + 1) * a_dim1 + 1], lda, &work[
n2 + 1], &sva[n2 + 1], &mvl, &v[n2 * q + 1 + (n2 + 1) *
v_dim1], ldv, &epsln, &sfmin, &tol, &c__1, &work[*n + 1],
&i__2, &ierr);
}
}
for (i__ = 1; i__ <= 30; ++i__) {
mxaapq = 0.;
mxsinj = 0.;
iswrot = 0;
notrot = 0;
pskipped = 0;
/* Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs */
/* 1 <= p < q <= N. This is the first step toward a blocked implementation */
/* of the rotations. New implementation, based on block transformations, */
/* is under development. */
i__1 = nbl;
for (ibr = 1; ibr <= i__1; ++ibr) {
igl = (ibr - 1) * kbl + 1;
/* Computing MIN */
i__3 = lkahead, i__4 = nbl - ibr;
i__2 = f2cmin(i__3,i__4);
for (ir1 = 0; ir1 <= i__2; ++ir1) {
igl += ir1 * kbl;
/* Computing MIN */
i__4 = igl + kbl - 1, i__5 = *n - 1;
i__3 = f2cmin(i__4,i__5);
for (p = igl; p <= i__3; ++p) {
i__4 = *n - p + 1;
q = idamax_(&i__4, &sva[p], &c__1) + p - 1;
if (p != q) {
dswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 +
1], &c__1);
if (rsvec) {
dswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
v_dim1 + 1], &c__1);
}
temp1 = sva[p];
sva[p] = sva[q];
sva[q] = temp1;
temp1 = work[p];
work[p] = work[q];
work[q] = temp1;
}
if (ir1 == 0) {
/* Column norms are periodically updated by explicit */
/* norm computation. */
/* Caveat: */
/* Unfortunately, some BLAS implementations compute DNRM2(M,A(1,p),1) */
/* as DSQRT(DDOT(M,A(1,p),1,A(1,p),1)), which may cause the result to */
/* overflow for ||A(:,p)||_2 > DSQRT(overflow_threshold), and to */
/* underflow for ||A(:,p)||_2 < DSQRT(underflow_threshold). */
/* Hence, DNRM2 cannot be trusted, not even in the case when */
/* the true norm is far from the under(over)flow boundaries. */
/* If properly implemented DNRM2 is available, the IF-THEN-ELSE */
/* below should read "AAPP = DNRM2( M, A(1,p), 1 ) * WORK(p)". */
if (sva[p] < rootbig && sva[p] > rootsfmin) {
sva[p] = dnrm2_(m, &a[p * a_dim1 + 1], &c__1) *
work[p];
} else {
temp1 = 0.;
aapp = 1.;
dlassq_(m, &a[p * a_dim1 + 1], &c__1, &temp1, &
aapp);
sva[p] = temp1 * sqrt(aapp) * work[p];
}
aapp = sva[p];
} else {
aapp = sva[p];
}
if (aapp > 0.) {
pskipped = 0;
/* Computing MIN */
i__5 = igl + kbl - 1;
i__4 = f2cmin(i__5,*n);
for (q = p + 1; q <= i__4; ++q) {
aaqq = sva[q];
if (aaqq > 0.) {
aapp0 = aapp;
if (aaqq >= 1.) {
rotok = small * aapp <= aaqq;
if (aapp < big / aaqq) {
aapq = ddot_(m, &a[p * a_dim1 + 1], &
c__1, &a[q * a_dim1 + 1], &
c__1) * work[p] * work[q] /
aaqq / aapp;
} else {
dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
work[*n + 1], &c__1);
dlascl_("G", &c__0, &c__0, &aapp, &
work[p], m, &c__1, &work[*n +
1], lda, &ierr);
aapq = ddot_(m, &work[*n + 1], &c__1,
&a[q * a_dim1 + 1], &c__1) *
work[q] / aaqq;
}
} else {
rotok = aapp <= aaqq / small;
if (aapp > small / aaqq) {
aapq = ddot_(m, &a[p * a_dim1 + 1], &
c__1, &a[q * a_dim1 + 1], &
c__1) * work[p] * work[q] /
aaqq / aapp;
} else {
dcopy_(m, &a[q * a_dim1 + 1], &c__1, &
work[*n + 1], &c__1);
dlascl_("G", &c__0, &c__0, &aaqq, &
work[q], m, &c__1, &work[*n +
1], lda, &ierr);
aapq = ddot_(m, &work[*n + 1], &c__1,
&a[p * a_dim1 + 1], &c__1) *
work[p] / aapp;
}
}
/* Computing MAX */
d__1 = mxaapq, d__2 = abs(aapq);
mxaapq = f2cmax(d__1,d__2);
/* TO rotate or NOT to rotate, THAT is the question ... */
if (abs(aapq) > tol) {
/* [RTD] ROTATED = ROTATED + ONE */
if (ir1 == 0) {
notrot = 0;
pskipped = 0;
++iswrot;
}
if (rotok) {
aqoap = aaqq / aapp;
apoaq = aapp / aaqq;
theta = (d__1 = aqoap - apoaq, abs(
d__1)) * -.5 / aapq;
if (abs(theta) > bigtheta) {
t = .5 / theta;
fastr[2] = t * work[p] / work[q];
fastr[3] = -t * work[q] / work[p];
drotm_(m, &a[p * a_dim1 + 1], &
c__1, &a[q * a_dim1 + 1],
&c__1, fastr);
if (rsvec) {
drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
v_dim1 + 1], &c__1, fastr);
}
/* Computing MAX */
d__1 = 0., d__2 = t * apoaq *
aapq + 1.;
sva[q] = aaqq * sqrt((f2cmax(d__1,
d__2)));
/* Computing MAX */
d__1 = 0., d__2 = 1. - t * aqoap *
aapq;
aapp *= sqrt((f2cmax(d__1,d__2)));
/* Computing MAX */
d__1 = mxsinj, d__2 = abs(t);
mxsinj = f2cmax(d__1,d__2);
} else {
thsign = -d_sign(&c_b18, &aapq);
t = 1. / (theta + thsign * sqrt(
theta * theta + 1.));
cs = sqrt(1. / (t * t + 1.));
sn = t * cs;
/* Computing MAX */
d__1 = mxsinj, d__2 = abs(sn);
mxsinj = f2cmax(d__1,d__2);
/* Computing MAX */
d__1 = 0., d__2 = t * apoaq *
aapq + 1.;
sva[q] = aaqq * sqrt((f2cmax(d__1,
d__2)));
/* Computing MAX */
d__1 = 0., d__2 = 1. - t * aqoap *
aapq;
aapp *= sqrt((f2cmax(d__1,d__2)));
apoaq = work[p] / work[q];
aqoap = work[q] / work[p];
if (work[p] >= 1.) {
if (work[q] >= 1.) {
fastr[2] = t * apoaq;
fastr[3] = -t * aqoap;
work[p] *= cs;
work[q] *= cs;
drotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q *
a_dim1 + 1], &c__1, fastr);
if (rsvec) {
drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[
q * v_dim1 + 1], &c__1, fastr);
}
} else {
d__1 = -t * aqoap;
daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
p * a_dim1 + 1], &c__1);
d__1 = cs * sn * apoaq;
daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
q * a_dim1 + 1], &c__1);
work[p] *= cs;
work[q] /= cs;
if (rsvec) {
d__1 = -t * aqoap;
daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
c__1, &v[p * v_dim1 + 1], &c__1);
d__1 = cs * sn * apoaq;
daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
c__1, &v[q * v_dim1 + 1], &c__1);
}
}
} else {
if (work[q] >= 1.) {
d__1 = t * apoaq;
daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
q * a_dim1 + 1], &c__1);
d__1 = -cs * sn * aqoap;
daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
p * a_dim1 + 1], &c__1);
work[p] /= cs;
work[q] *= cs;
if (rsvec) {
d__1 = t * apoaq;
daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
c__1, &v[q * v_dim1 + 1], &c__1);
d__1 = -cs * sn * aqoap;
daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
c__1, &v[p * v_dim1 + 1], &c__1);
}
} else {
if (work[p] >= work[q]) {
d__1 = -t * aqoap;
daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1,
&a[p * a_dim1 + 1], &c__1);
d__1 = cs * sn * apoaq;
daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1,
&a[q * a_dim1 + 1], &c__1);
work[p] *= cs;
work[q] /= cs;
if (rsvec) {
d__1 = -t * aqoap;
daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1],
&c__1, &v[p * v_dim1 + 1], &
c__1);
d__1 = cs * sn * apoaq;
daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1],
&c__1, &v[q * v_dim1 + 1], &
c__1);
}
} else {
d__1 = t * apoaq;
daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1,
&a[q * a_dim1 + 1], &c__1);
d__1 = -cs * sn * aqoap;
daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1,
&a[p * a_dim1 + 1], &c__1);
work[p] /= cs;
work[q] *= cs;
if (rsvec) {
d__1 = t * apoaq;
daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1],
&c__1, &v[q * v_dim1 + 1], &
c__1);
d__1 = -cs * sn * aqoap;
daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1],
&c__1, &v[p * v_dim1 + 1], &
c__1);
}
}
}
}
}
} else {
dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
work[*n + 1], &c__1);
dlascl_("G", &c__0, &c__0, &aapp, &
c_b18, m, &c__1, &work[*n + 1]
, lda, &ierr);
dlascl_("G", &c__0, &c__0, &aaqq, &
c_b18, m, &c__1, &a[q *
a_dim1 + 1], lda, &ierr);
temp1 = -aapq * work[p] / work[q];
daxpy_(m, &temp1, &work[*n + 1], &
c__1, &a[q * a_dim1 + 1], &
c__1);
dlascl_("G", &c__0, &c__0, &c_b18, &
aaqq, m, &c__1, &a[q * a_dim1
+ 1], lda, &ierr);
/* Computing MAX */
d__1 = 0., d__2 = 1. - aapq * aapq;
sva[q] = aaqq * sqrt((f2cmax(d__1,d__2)))
;
mxsinj = f2cmax(mxsinj,sfmin);
}
/* END IF ROTOK THEN ... ELSE */
/* In the case of cancellation in updating SVA(q), SVA(p) */
/* recompute SVA(q), SVA(p). */
/* Computing 2nd power */
d__1 = sva[q] / aaqq;
if (d__1 * d__1 <= rooteps) {
if (aaqq < rootbig && aaqq >
rootsfmin) {
sva[q] = dnrm2_(m, &a[q * a_dim1
+ 1], &c__1) * work[q];
} else {
t = 0.;
aaqq = 1.;
dlassq_(m, &a[q * a_dim1 + 1], &
c__1, &t, &aaqq);
sva[q] = t * sqrt(aaqq) * work[q];
}
}
if (aapp / aapp0 <= rooteps) {
if (aapp < rootbig && aapp >
rootsfmin) {
aapp = dnrm2_(m, &a[p * a_dim1 +
1], &c__1) * work[p];
} else {
t = 0.;
aapp = 1.;
dlassq_(m, &a[p * a_dim1 + 1], &
c__1, &t, &aapp);
aapp = t * sqrt(aapp) * work[p];
}
sva[p] = aapp;
}
} else {
/* A(:,p) and A(:,q) already numerically orthogonal */
if (ir1 == 0) {
++notrot;
}
/* [RTD] SKIPPED = SKIPPED + 1 */
++pskipped;
}
} else {
/* A(:,q) is zero column */
if (ir1 == 0) {
++notrot;
}
++pskipped;
}
if (i__ <= swband && pskipped > rowskip) {
if (ir1 == 0) {
aapp = -aapp;
}
notrot = 0;
goto L2103;
}
/* L2002: */
}
/* END q-LOOP */
L2103:
/* bailed out of q-loop */
sva[p] = aapp;
} else {
sva[p] = aapp;
if (ir1 == 0 && aapp == 0.) {
/* Computing MIN */
i__4 = igl + kbl - 1;
notrot = notrot + f2cmin(i__4,*n) - p;
}
}
/* L2001: */
}
/* end of the p-loop */
/* end of doing the block ( ibr, ibr ) */
/* L1002: */
}
/* end of ir1-loop */
/* ... go to the off diagonal blocks */
igl = (ibr - 1) * kbl + 1;
i__2 = nbl;
for (jbc = ibr + 1; jbc <= i__2; ++jbc) {
jgl = (jbc - 1) * kbl + 1;
/* doing the block at ( ibr, jbc ) */
ijblsk = 0;
/* Computing MIN */
i__4 = igl + kbl - 1;
i__3 = f2cmin(i__4,*n);
for (p = igl; p <= i__3; ++p) {
aapp = sva[p];
if (aapp > 0.) {
pskipped = 0;
/* Computing MIN */
i__5 = jgl + kbl - 1;
i__4 = f2cmin(i__5,*n);
for (q = jgl; q <= i__4; ++q) {
aaqq = sva[q];
if (aaqq > 0.) {
aapp0 = aapp;
/* Safe Gram matrix computation */
if (aaqq >= 1.) {
if (aapp >= aaqq) {
rotok = small * aapp <= aaqq;
} else {
rotok = small * aaqq <= aapp;
}
if (aapp < big / aaqq) {
aapq = ddot_(m, &a[p * a_dim1 + 1], &
c__1, &a[q * a_dim1 + 1], &
c__1) * work[p] * work[q] /
aaqq / aapp;
} else {
dcopy_(m, &a[p * a_dim1 + 1], &c__1, &
work[*n + 1], &c__1);
dlascl_("G", &c__0, &c__0, &aapp, &
work[p], m, &c__1, &work[*n +
1], lda, &ierr);
aapq = ddot_(m, &work[*n + 1], &c__1,
&a[q * a_dim1 + 1], &c__1) *
work[q] / aaqq;
}
} else {
if (aapp >= aaqq) {
rotok = aapp <= aaqq / small;
} else {
rotok = aaqq <= aapp / small;
}
if (aapp > small / aaqq) {
aapq = ddot_(m, &a[p * a_dim1 + 1], &
c__1, &a[q * a_dim1 + 1], &
c__1) * work[p] * work[q] /
aaqq / aapp;
} else {
dcopy_(m, &a[q * a_dim1 + 1], &c__1, &
work[*n + 1], &c__1);
dlascl_("G", &c__0, &c__0, &aaqq, &
work[q], m, &c__1, &work[*n +
1], lda, &ierr);
aapq = ddot_(m, &work[*n + 1], &c__1,
&a[p * a_dim1 + 1], &c__1) *
work[p] / aapp;
}
}
/* Computing MAX */
d__1 = mxaapq, d__2 = abs(aapq);
mxaapq = f2cmax(d__1,d__2);
/* TO rotate or NOT to rotate, THAT is the question ... */
if (abs(aapq) > tol) {
notrot = 0;
/* [RTD] ROTATED = ROTATED + 1 */
pskipped = 0;
++iswrot;
if (rotok) {
aqoap = aaqq / aapp;
apoaq = aapp / aaqq;
theta = (d__1 = aqoap - apoaq, abs(
d__1)) * -.5 / aapq;
if (aaqq > aapp0) {
theta = -theta;
}
if (abs(theta) > bigtheta) {
t = .5 / theta;
fastr[2] = t * work[p] / work[q];
fastr[3] = -t * work[q] / work[p];
drotm_(m, &a[p * a_dim1 + 1], &
c__1, &a[q * a_dim1 + 1],
&c__1, fastr);
if (rsvec) {
drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q *
v_dim1 + 1], &c__1, fastr);
}
/* Computing MAX */
d__1 = 0., d__2 = t * apoaq *
aapq + 1.;
sva[q] = aaqq * sqrt((f2cmax(d__1,
d__2)));
/* Computing MAX */
d__1 = 0., d__2 = 1. - t * aqoap *
aapq;
aapp *= sqrt((f2cmax(d__1,d__2)));
/* Computing MAX */
d__1 = mxsinj, d__2 = abs(t);
mxsinj = f2cmax(d__1,d__2);
} else {
thsign = -d_sign(&c_b18, &aapq);
if (aaqq > aapp0) {
thsign = -thsign;
}
t = 1. / (theta + thsign * sqrt(
theta * theta + 1.));
cs = sqrt(1. / (t * t + 1.));
sn = t * cs;
/* Computing MAX */
d__1 = mxsinj, d__2 = abs(sn);
mxsinj = f2cmax(d__1,d__2);
/* Computing MAX */
d__1 = 0., d__2 = t * apoaq *
aapq + 1.;
sva[q] = aaqq * sqrt((f2cmax(d__1,
d__2)));
/* Computing MAX */
d__1 = 0., d__2 = 1. - t * aqoap *
aapq;
aapp *= sqrt((f2cmax(d__1,d__2)));
apoaq = work[p] / work[q];
aqoap = work[q] / work[p];
if (work[p] >= 1.) {
if (work[q] >= 1.) {
fastr[2] = t * apoaq;
fastr[3] = -t * aqoap;
work[p] *= cs;
work[q] *= cs;
drotm_(m, &a[p * a_dim1 + 1], &c__1, &a[q *
a_dim1 + 1], &c__1, fastr);
if (rsvec) {
drotm_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[
q * v_dim1 + 1], &c__1, fastr);
}
} else {
d__1 = -t * aqoap;
daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
p * a_dim1 + 1], &c__1);
d__1 = cs * sn * apoaq;
daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
q * a_dim1 + 1], &c__1);
if (rsvec) {
d__1 = -t * aqoap;
daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
c__1, &v[p * v_dim1 + 1], &c__1);
d__1 = cs * sn * apoaq;
daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
c__1, &v[q * v_dim1 + 1], &c__1);
}
work[p] *= cs;
work[q] /= cs;
}
} else {
if (work[q] >= 1.) {
d__1 = t * apoaq;
daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1, &a[
q * a_dim1 + 1], &c__1);
d__1 = -cs * sn * aqoap;
daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1, &a[
p * a_dim1 + 1], &c__1);
if (rsvec) {
d__1 = t * apoaq;
daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1], &
c__1, &v[q * v_dim1 + 1], &c__1);
d__1 = -cs * sn * aqoap;
daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1], &
c__1, &v[p * v_dim1 + 1], &c__1);
}
work[p] /= cs;
work[q] *= cs;
} else {
if (work[p] >= work[q]) {
d__1 = -t * aqoap;
daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1,
&a[p * a_dim1 + 1], &c__1);
d__1 = cs * sn * apoaq;
daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1,
&a[q * a_dim1 + 1], &c__1);
work[p] *= cs;
work[q] /= cs;
if (rsvec) {
d__1 = -t * aqoap;
daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1],
&c__1, &v[p * v_dim1 + 1], &
c__1);
d__1 = cs * sn * apoaq;
daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1],
&c__1, &v[q * v_dim1 + 1], &
c__1);
}
} else {
d__1 = t * apoaq;
daxpy_(m, &d__1, &a[p * a_dim1 + 1], &c__1,
&a[q * a_dim1 + 1], &c__1);
d__1 = -cs * sn * aqoap;
daxpy_(m, &d__1, &a[q * a_dim1 + 1], &c__1,
&a[p * a_dim1 + 1], &c__1);
work[p] /= cs;
work[q] *= cs;
if (rsvec) {
d__1 = t * apoaq;
daxpy_(&mvl, &d__1, &v[p * v_dim1 + 1],
&c__1, &v[q * v_dim1 + 1], &
c__1);
d__1 = -cs * sn * aqoap;
daxpy_(&mvl, &d__1, &v[q * v_dim1 + 1],
&c__1, &v[p * v_dim1 + 1], &
c__1);
}
}
}
}
}
} else {
if (aapp > aaqq) {
dcopy_(m, &a[p * a_dim1 + 1], &
c__1, &work[*n + 1], &
c__1);
dlascl_("G", &c__0, &c__0, &aapp,
&c_b18, m, &c__1, &work[*
n + 1], lda, &ierr);
dlascl_("G", &c__0, &c__0, &aaqq,
&c_b18, m, &c__1, &a[q *
a_dim1 + 1], lda, &ierr);
temp1 = -aapq * work[p] / work[q];
daxpy_(m, &temp1, &work[*n + 1], &
c__1, &a[q * a_dim1 + 1],
&c__1);
dlascl_("G", &c__0, &c__0, &c_b18,
&aaqq, m, &c__1, &a[q *
a_dim1 + 1], lda, &ierr);
/* Computing MAX */
d__1 = 0., d__2 = 1. - aapq *
aapq;
sva[q] = aaqq * sqrt((f2cmax(d__1,
d__2)));
mxsinj = f2cmax(mxsinj,sfmin);
} else {
dcopy_(m, &a[q * a_dim1 + 1], &
c__1, &work[*n + 1], &
c__1);
dlascl_("G", &c__0, &c__0, &aaqq,
&c_b18, m, &c__1, &work[*
n + 1], lda, &ierr);
dlascl_("G", &c__0, &c__0, &aapp,
&c_b18, m, &c__1, &a[p *
a_dim1 + 1], lda, &ierr);
temp1 = -aapq * work[q] / work[p];
daxpy_(m, &temp1, &work[*n + 1], &
c__1, &a[p * a_dim1 + 1],
&c__1);
dlascl_("G", &c__0, &c__0, &c_b18,
&aapp, m, &c__1, &a[p *
a_dim1 + 1], lda, &ierr);
/* Computing MAX */
d__1 = 0., d__2 = 1. - aapq *
aapq;
sva[p] = aapp * sqrt((f2cmax(d__1,
d__2)));
mxsinj = f2cmax(mxsinj,sfmin);
}
}
/* END IF ROTOK THEN ... ELSE */
/* In the case of cancellation in updating SVA(q) */
/* Computing 2nd power */
d__1 = sva[q] / aaqq;
if (d__1 * d__1 <= rooteps) {
if (aaqq < rootbig && aaqq >
rootsfmin) {
sva[q] = dnrm2_(m, &a[q * a_dim1
+ 1], &c__1) * work[q];
} else {
t = 0.;
aaqq = 1.;
dlassq_(m, &a[q * a_dim1 + 1], &
c__1, &t, &aaqq);
sva[q] = t * sqrt(aaqq) * work[q];
}
}
/* Computing 2nd power */
d__1 = aapp / aapp0;
if (d__1 * d__1 <= rooteps) {
if (aapp < rootbig && aapp >
rootsfmin) {
aapp = dnrm2_(m, &a[p * a_dim1 +
1], &c__1) * work[p];
} else {
t = 0.;
aapp = 1.;
dlassq_(m, &a[p * a_dim1 + 1], &
c__1, &t, &aapp);
aapp = t * sqrt(aapp) * work[p];
}
sva[p] = aapp;
}
/* end of OK rotation */
} else {
++notrot;
/* [RTD] SKIPPED = SKIPPED + 1 */
++pskipped;
++ijblsk;
}
} else {
++notrot;
++pskipped;
++ijblsk;
}
if (i__ <= swband && ijblsk >= blskip) {
sva[p] = aapp;
notrot = 0;
goto L2011;
}
if (i__ <= swband && pskipped > rowskip) {
aapp = -aapp;
notrot = 0;
goto L2203;
}
/* L2200: */
}
/* end of the q-loop */
L2203:
sva[p] = aapp;
} else {
if (aapp == 0.) {
/* Computing MIN */
i__4 = jgl + kbl - 1;
notrot = notrot + f2cmin(i__4,*n) - jgl + 1;
}
if (aapp < 0.) {
notrot = 0;
}
}
/* L2100: */
}
/* end of the p-loop */
/* L2010: */
}
/* end of the jbc-loop */
L2011:
/* 2011 bailed out of the jbc-loop */
/* Computing MIN */
i__3 = igl + kbl - 1;
i__2 = f2cmin(i__3,*n);
for (p = igl; p <= i__2; ++p) {
sva[p] = (d__1 = sva[p], abs(d__1));
/* L2012: */
}
/* ** */
/* L2000: */
}
/* 2000 :: end of the ibr-loop */
if (sva[*n] < rootbig && sva[*n] > rootsfmin) {
sva[*n] = dnrm2_(m, &a[*n * a_dim1 + 1], &c__1) * work[*n];
} else {
t = 0.;
aapp = 1.;
dlassq_(m, &a[*n * a_dim1 + 1], &c__1, &t, &aapp);
sva[*n] = t * sqrt(aapp) * work[*n];
}
/* Additional steering devices */
if (i__ < swband && (mxaapq <= roottol || iswrot <= *n)) {
swband = i__;
}
if (i__ > swband + 1 && mxaapq < sqrt((doublereal) (*n)) * tol && (
doublereal) (*n) * mxaapq * mxsinj < tol) {
goto L1994;
}
if (notrot >= emptsw) {
goto L1994;
}
/* L1993: */
}
/* end i=1:NSWEEP loop */
/* #:( Reaching this point means that the procedure has not converged. */
*info = 29;
goto L1995;
L1994:
/* #:) Reaching this point means numerical convergence after the i-th */
/* sweep. */
*info = 0;
/* #:) INFO = 0 confirms successful iterations. */
L1995:
/* Sort the singular values and find how many are above */
/* the underflow threshold. */
n2 = 0;
n4 = 0;
i__1 = *n - 1;
for (p = 1; p <= i__1; ++p) {
i__2 = *n - p + 1;
q = idamax_(&i__2, &sva[p], &c__1) + p - 1;
if (p != q) {
temp1 = sva[p];
sva[p] = sva[q];
sva[q] = temp1;
temp1 = work[p];
work[p] = work[q];
work[q] = temp1;
dswap_(m, &a[p * a_dim1 + 1], &c__1, &a[q * a_dim1 + 1], &c__1);
if (rsvec) {
dswap_(&mvl, &v[p * v_dim1 + 1], &c__1, &v[q * v_dim1 + 1], &
c__1);
}
}
if (sva[p] != 0.) {
++n4;
if (sva[p] * skl > sfmin) {
++n2;
}
}
/* L5991: */
}
if (sva[*n] != 0.) {
++n4;
if (sva[*n] * skl > sfmin) {
++n2;
}
}
/* Normalize the left singular vectors. */
if (lsvec || uctol) {
i__1 = n2;
for (p = 1; p <= i__1; ++p) {
d__1 = work[p] / sva[p];
dscal_(m, &d__1, &a[p * a_dim1 + 1], &c__1);
/* L1998: */
}
}
/* Scale the product of Jacobi rotations (assemble the fast rotations). */
if (rsvec) {
if (applv) {
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
dscal_(&mvl, &work[p], &v[p * v_dim1 + 1], &c__1);
/* L2398: */
}
} else {
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
temp1 = 1. / dnrm2_(&mvl, &v[p * v_dim1 + 1], &c__1);
dscal_(&mvl, &temp1, &v[p * v_dim1 + 1], &c__1);
/* L2399: */
}
}
}
/* Undo scaling, if necessary (and possible). */
if (skl > 1. && sva[1] < big / skl || skl < 1. && sva[f2cmax(n2,1)] > sfmin /
skl) {
i__1 = *n;
for (p = 1; p <= i__1; ++p) {
sva[p] = skl * sva[p];
/* L2400: */
}
skl = 1.;
}
work[1] = skl;
/* The singular values of A are SKL*SVA(1:N). If SKL.NE.ONE */
/* then some of the singular values may overflow or underflow and */
/* the spectrum is given in this factored representation. */
work[2] = (doublereal) n4;
/* N4 is the number of computed nonzero singular values of A. */
work[3] = (doublereal) n2;
/* N2 is the number of singular values of A greater than SFMIN. */
/* If N2<N, SVA(N2:N) contains ZEROS and/or denormalized numbers */
/* that may carry some information. */
work[4] = (doublereal) i__;
/* i is the index of the last sweep before declaring convergence. */
work[5] = mxaapq;
/* MXAAPQ is the largest absolute value of scaled pivots in the */
/* last sweep */
work[6] = mxsinj;
/* MXSINJ is the largest absolute value of the sines of Jacobi angles */
/* in the last sweep */
return;
} /* dgesvj_ */
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