1254 lines
36 KiB
C
1254 lines
36 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#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]);}
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#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]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#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++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#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]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle_() continue;
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#define myceiling_(w) {ceil(w)}
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#define myhuge_(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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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_b1 = 0.;
|
|
static doublereal c_b15 = 1.;
|
|
static integer c__1 = 1;
|
|
static doublereal c_b44 = -1.;
|
|
|
|
/* > \brief \b DTGSJA */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DTGSJA + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgsja.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgsja.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgsja.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, */
|
|
/* LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, */
|
|
/* Q, LDQ, WORK, NCALL MYCYCLE, INFO ) */
|
|
|
|
/* CHARACTER JOBQ, JOBU, JOBV */
|
|
/* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, */
|
|
/* $ NCALL MYCYCLE, P */
|
|
/* DOUBLE PRECISION TOLA, TOLB */
|
|
/* DOUBLE PRECISION A( LDA, * ), ALPHA( * ), B( LDB, * ), */
|
|
/* $ BETA( * ), Q( LDQ, * ), U( LDU, * ), */
|
|
/* $ V( LDV, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DTGSJA computes the generalized singular value decomposition (GSVD) */
|
|
/* > of two real upper triangular (or trapezoidal) matrices A and B. */
|
|
/* > */
|
|
/* > On entry, it is assumed that matrices A and B have the following */
|
|
/* > forms, which may be obtained by the preprocessing subroutine DGGSVP */
|
|
/* > from a general M-by-N matrix A and P-by-N matrix B: */
|
|
/* > */
|
|
/* > N-K-L K L */
|
|
/* > A = K ( 0 A12 A13 ) if M-K-L >= 0; */
|
|
/* > L ( 0 0 A23 ) */
|
|
/* > M-K-L ( 0 0 0 ) */
|
|
/* > */
|
|
/* > N-K-L K L */
|
|
/* > A = K ( 0 A12 A13 ) if M-K-L < 0; */
|
|
/* > M-K ( 0 0 A23 ) */
|
|
/* > */
|
|
/* > N-K-L K L */
|
|
/* > B = L ( 0 0 B13 ) */
|
|
/* > P-L ( 0 0 0 ) */
|
|
/* > */
|
|
/* > where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */
|
|
/* > upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */
|
|
/* > otherwise A23 is (M-K)-by-L upper trapezoidal. */
|
|
/* > */
|
|
/* > On exit, */
|
|
/* > */
|
|
/* > U**T *A*Q = D1*( 0 R ), V**T *B*Q = D2*( 0 R ), */
|
|
/* > */
|
|
/* > where U, V and Q are orthogonal matrices. */
|
|
/* > R is a nonsingular upper triangular matrix, and D1 and D2 are */
|
|
/* > ``diagonal'' matrices, which are of the following structures: */
|
|
/* > */
|
|
/* > If M-K-L >= 0, */
|
|
/* > */
|
|
/* > K L */
|
|
/* > D1 = K ( I 0 ) */
|
|
/* > L ( 0 C ) */
|
|
/* > M-K-L ( 0 0 ) */
|
|
/* > */
|
|
/* > K L */
|
|
/* > D2 = L ( 0 S ) */
|
|
/* > P-L ( 0 0 ) */
|
|
/* > */
|
|
/* > N-K-L K L */
|
|
/* > ( 0 R ) = K ( 0 R11 R12 ) K */
|
|
/* > L ( 0 0 R22 ) L */
|
|
/* > */
|
|
/* > where */
|
|
/* > */
|
|
/* > C = diag( ALPHA(K+1), ... , ALPHA(K+L) ), */
|
|
/* > S = diag( BETA(K+1), ... , BETA(K+L) ), */
|
|
/* > C**2 + S**2 = I. */
|
|
/* > */
|
|
/* > R is stored in A(1:K+L,N-K-L+1:N) on exit. */
|
|
/* > */
|
|
/* > If M-K-L < 0, */
|
|
/* > */
|
|
/* > K M-K K+L-M */
|
|
/* > D1 = K ( I 0 0 ) */
|
|
/* > M-K ( 0 C 0 ) */
|
|
/* > */
|
|
/* > K M-K K+L-M */
|
|
/* > D2 = M-K ( 0 S 0 ) */
|
|
/* > K+L-M ( 0 0 I ) */
|
|
/* > P-L ( 0 0 0 ) */
|
|
/* > */
|
|
/* > N-K-L K M-K K+L-M */
|
|
/* > ( 0 R ) = K ( 0 R11 R12 R13 ) */
|
|
/* > M-K ( 0 0 R22 R23 ) */
|
|
/* > K+L-M ( 0 0 0 R33 ) */
|
|
/* > */
|
|
/* > where */
|
|
/* > C = diag( ALPHA(K+1), ... , ALPHA(M) ), */
|
|
/* > S = diag( BETA(K+1), ... , BETA(M) ), */
|
|
/* > C**2 + S**2 = I. */
|
|
/* > */
|
|
/* > R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored */
|
|
/* > ( 0 R22 R23 ) */
|
|
/* > in B(M-K+1:L,N+M-K-L+1:N) on exit. */
|
|
/* > */
|
|
/* > The computation of the orthogonal transformation matrices U, V or Q */
|
|
/* > is optional. These matrices may either be formed explicitly, or they */
|
|
/* > may be postmultiplied into input matrices U1, V1, or Q1. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBU */
|
|
/* > \verbatim */
|
|
/* > JOBU is CHARACTER*1 */
|
|
/* > = 'U': U must contain an orthogonal matrix U1 on entry, and */
|
|
/* > the product U1*U is returned; */
|
|
/* > = 'I': U is initialized to the unit matrix, and the */
|
|
/* > orthogonal matrix U is returned; */
|
|
/* > = 'N': U is not computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBV */
|
|
/* > \verbatim */
|
|
/* > JOBV is CHARACTER*1 */
|
|
/* > = 'V': V must contain an orthogonal matrix V1 on entry, and */
|
|
/* > the product V1*V is returned; */
|
|
/* > = 'I': V is initialized to the unit matrix, and the */
|
|
/* > orthogonal matrix V is returned; */
|
|
/* > = 'N': V is not computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBQ */
|
|
/* > \verbatim */
|
|
/* > JOBQ is CHARACTER*1 */
|
|
/* > = 'Q': Q must contain an orthogonal matrix Q1 on entry, and */
|
|
/* > the product Q1*Q is returned; */
|
|
/* > = 'I': Q is initialized to the unit matrix, and the */
|
|
/* > orthogonal matrix Q is returned; */
|
|
/* > = 'N': Q is not computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix A. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] P */
|
|
/* > \verbatim */
|
|
/* > P is INTEGER */
|
|
/* > The number of rows of the matrix B. P >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrices A and B. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] L */
|
|
/* > \verbatim */
|
|
/* > L is INTEGER */
|
|
/* > */
|
|
/* > K and L specify the subblocks in the input matrices A and B: */
|
|
/* > A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,N-L+1:N) */
|
|
/* > of A and B, whose GSVD is going to be computed by DTGSJA. */
|
|
/* > See Further Details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
|
|
/* > On entry, the M-by-N matrix A. */
|
|
/* > On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular */
|
|
/* > matrix R or part of R. See Purpose for details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is DOUBLE PRECISION array, dimension (LDB,N) */
|
|
/* > On entry, the P-by-N matrix B. */
|
|
/* > On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains */
|
|
/* > a part of R. See Purpose for details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,P). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TOLA */
|
|
/* > \verbatim */
|
|
/* > TOLA is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TOLB */
|
|
/* > \verbatim */
|
|
/* > TOLB is DOUBLE PRECISION */
|
|
/* > */
|
|
/* > TOLA and TOLB are the convergence criteria for the Jacobi- */
|
|
/* > Kogbetliantz iteration procedure. Generally, they are the */
|
|
/* > same as used in the preprocessing step, say */
|
|
/* > TOLA = f2cmax(M,N)*norm(A)*MAZHEPS, */
|
|
/* > TOLB = f2cmax(P,N)*norm(B)*MAZHEPS. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ALPHA */
|
|
/* > \verbatim */
|
|
/* > ALPHA is DOUBLE PRECISION array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BETA */
|
|
/* > \verbatim */
|
|
/* > BETA is DOUBLE PRECISION array, dimension (N) */
|
|
/* > */
|
|
/* > On exit, ALPHA and BETA contain the generalized singular */
|
|
/* > value pairs of A and B; */
|
|
/* > ALPHA(1:K) = 1, */
|
|
/* > BETA(1:K) = 0, */
|
|
/* > and if M-K-L >= 0, */
|
|
/* > ALPHA(K+1:K+L) = diag(C), */
|
|
/* > BETA(K+1:K+L) = diag(S), */
|
|
/* > or if M-K-L < 0, */
|
|
/* > ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0 */
|
|
/* > BETA(K+1:M) = S, BETA(M+1:K+L) = 1. */
|
|
/* > Furthermore, if K+L < N, */
|
|
/* > ALPHA(K+L+1:N) = 0 and */
|
|
/* > BETA(K+L+1:N) = 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] U */
|
|
/* > \verbatim */
|
|
/* > U is DOUBLE PRECISION array, dimension (LDU,M) */
|
|
/* > On entry, if JOBU = 'U', U must contain a matrix U1 (usually */
|
|
/* > the orthogonal matrix returned by DGGSVP). */
|
|
/* > On exit, */
|
|
/* > if JOBU = 'I', U contains the orthogonal matrix U; */
|
|
/* > if JOBU = 'U', U contains the product U1*U. */
|
|
/* > If JOBU = 'N', U is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU */
|
|
/* > \verbatim */
|
|
/* > LDU is INTEGER */
|
|
/* > The leading dimension of the array U. LDU >= f2cmax(1,M) if */
|
|
/* > JOBU = 'U'; LDU >= 1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] V */
|
|
/* > \verbatim */
|
|
/* > V is DOUBLE PRECISION array, dimension (LDV,P) */
|
|
/* > On entry, if JOBV = 'V', V must contain a matrix V1 (usually */
|
|
/* > the orthogonal matrix returned by DGGSVP). */
|
|
/* > On exit, */
|
|
/* > if JOBV = 'I', V contains the orthogonal matrix V; */
|
|
/* > if JOBV = 'V', V contains the product V1*V. */
|
|
/* > If JOBV = 'N', V is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDV */
|
|
/* > \verbatim */
|
|
/* > LDV is INTEGER */
|
|
/* > The leading dimension of the array V. LDV >= f2cmax(1,P) if */
|
|
/* > JOBV = 'V'; LDV >= 1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
|
|
/* > On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually */
|
|
/* > the orthogonal matrix returned by DGGSVP). */
|
|
/* > On exit, */
|
|
/* > if JOBQ = 'I', Q contains the orthogonal matrix Q; */
|
|
/* > if JOBQ = 'Q', Q contains the product Q1*Q. */
|
|
/* > If JOBQ = 'N', Q is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. LDQ >= f2cmax(1,N) if */
|
|
/* > JOBQ = 'Q'; LDQ >= 1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] NCALL MYCYCLE */
|
|
/* > \verbatim */
|
|
/* > NCALL MYCYCLE is INTEGER */
|
|
/* > The number of cycles required for convergence. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > = 1: the procedure does not converge after MAXIT cycles. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > Internal Parameters */
|
|
/* > =================== */
|
|
/* > */
|
|
/* > MAXIT INTEGER */
|
|
/* > MAXIT specifies the total loops that the iterative procedure */
|
|
/* > may take. If after MAXIT cycles, the routine fails to */
|
|
/* > converge, we return INFO = 1. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleOTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce */
|
|
/* > f2cmin(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L */
|
|
/* > matrix B13 to the form: */
|
|
/* > */
|
|
/* > U1**T *A13*Q1 = C1*R1; V1**T *B13*Q1 = S1*R1, */
|
|
/* > */
|
|
/* > where U1, V1 and Q1 are orthogonal matrix, and Z**T is the transpose */
|
|
/* > of Z. C1 and S1 are diagonal matrices satisfying */
|
|
/* > */
|
|
/* > C1**2 + S1**2 = I, */
|
|
/* > */
|
|
/* > and R1 is an L-by-L nonsingular upper triangular matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dtgsja_(char *jobu, char *jobv, char *jobq, integer *m,
|
|
integer *p, integer *n, integer *k, integer *l, doublereal *a,
|
|
integer *lda, doublereal *b, integer *ldb, doublereal *tola,
|
|
doublereal *tolb, doublereal *alpha, doublereal *beta, doublereal *u,
|
|
integer *ldu, doublereal *v, integer *ldv, doublereal *q, integer *
|
|
ldq, doublereal *work, integer *ncallmycycle, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
|
|
u_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4;
|
|
doublereal d__1;
|
|
|
|
/* Local variables */
|
|
extern /* Subroutine */ void drot_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *);
|
|
integer kcallmycycle, i__, j;
|
|
doublereal gamma;
|
|
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
|
|
integer *);
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *);
|
|
doublereal a1;
|
|
logical initq;
|
|
doublereal a2, a3, b1;
|
|
logical initu, initv, wantq, upper;
|
|
doublereal b2, b3;
|
|
logical wantu, wantv;
|
|
doublereal error, ssmin;
|
|
extern /* Subroutine */ void dlags2_(logical *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *), dlapll_(integer *, doublereal *,
|
|
integer *, doublereal *, integer *, doublereal *), dlartg_(
|
|
doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *), dlaset_(char *, integer *, integer *, doublereal *,
|
|
doublereal *, doublereal *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
// extern integer myhuge_(doublereal *);
|
|
doublereal csq, csu, csv, snq, rwk, snu, snv;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
|
|
/* Decode and test the input parameters */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
--alpha;
|
|
--beta;
|
|
u_dim1 = *ldu;
|
|
u_offset = 1 + u_dim1 * 1;
|
|
u -= u_offset;
|
|
v_dim1 = *ldv;
|
|
v_offset = 1 + v_dim1 * 1;
|
|
v -= v_offset;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
initu = lsame_(jobu, "I");
|
|
wantu = initu || lsame_(jobu, "U");
|
|
|
|
initv = lsame_(jobv, "I");
|
|
wantv = initv || lsame_(jobv, "V");
|
|
|
|
initq = lsame_(jobq, "I");
|
|
wantq = initq || lsame_(jobq, "Q");
|
|
|
|
*info = 0;
|
|
if (! (initu || wantu || lsame_(jobu, "N"))) {
|
|
*info = -1;
|
|
} else if (! (initv || wantv || lsame_(jobv, "N")))
|
|
{
|
|
*info = -2;
|
|
} else if (! (initq || wantq || lsame_(jobq, "N")))
|
|
{
|
|
*info = -3;
|
|
} else if (*m < 0) {
|
|
*info = -4;
|
|
} else if (*p < 0) {
|
|
*info = -5;
|
|
} else if (*n < 0) {
|
|
*info = -6;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -10;
|
|
} else if (*ldb < f2cmax(1,*p)) {
|
|
*info = -12;
|
|
} else if (*ldu < 1 || wantu && *ldu < *m) {
|
|
*info = -18;
|
|
} else if (*ldv < 1 || wantv && *ldv < *p) {
|
|
*info = -20;
|
|
} else if (*ldq < 1 || wantq && *ldq < *n) {
|
|
*info = -22;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DTGSJA", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Initialize U, V and Q, if necessary */
|
|
|
|
if (initu) {
|
|
dlaset_("Full", m, m, &c_b1, &c_b15, &u[u_offset], ldu);
|
|
}
|
|
if (initv) {
|
|
dlaset_("Full", p, p, &c_b1, &c_b15, &v[v_offset], ldv);
|
|
}
|
|
if (initq) {
|
|
dlaset_("Full", n, n, &c_b1, &c_b15, &q[q_offset], ldq);
|
|
}
|
|
|
|
/* Loop until convergence */
|
|
|
|
upper = FALSE_;
|
|
for (kcallmycycle = 1; kcallmycycle <= 40; ++kcallmycycle) {
|
|
|
|
upper = ! upper;
|
|
|
|
i__1 = *l - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *l;
|
|
for (j = i__ + 1; j <= i__2; ++j) {
|
|
|
|
a1 = 0.;
|
|
a2 = 0.;
|
|
a3 = 0.;
|
|
if (*k + i__ <= *m) {
|
|
a1 = a[*k + i__ + (*n - *l + i__) * a_dim1];
|
|
}
|
|
if (*k + j <= *m) {
|
|
a3 = a[*k + j + (*n - *l + j) * a_dim1];
|
|
}
|
|
|
|
b1 = b[i__ + (*n - *l + i__) * b_dim1];
|
|
b3 = b[j + (*n - *l + j) * b_dim1];
|
|
|
|
if (upper) {
|
|
if (*k + i__ <= *m) {
|
|
a2 = a[*k + i__ + (*n - *l + j) * a_dim1];
|
|
}
|
|
b2 = b[i__ + (*n - *l + j) * b_dim1];
|
|
} else {
|
|
if (*k + j <= *m) {
|
|
a2 = a[*k + j + (*n - *l + i__) * a_dim1];
|
|
}
|
|
b2 = b[j + (*n - *l + i__) * b_dim1];
|
|
}
|
|
|
|
dlags2_(&upper, &a1, &a2, &a3, &b1, &b2, &b3, &csu, &snu, &
|
|
csv, &snv, &csq, &snq);
|
|
|
|
/* Update (K+I)-th and (K+J)-th rows of matrix A: U**T *A */
|
|
|
|
if (*k + j <= *m) {
|
|
drot_(l, &a[*k + j + (*n - *l + 1) * a_dim1], lda, &a[*k
|
|
+ i__ + (*n - *l + 1) * a_dim1], lda, &csu, &snu);
|
|
}
|
|
|
|
/* Update I-th and J-th rows of matrix B: V**T *B */
|
|
|
|
drot_(l, &b[j + (*n - *l + 1) * b_dim1], ldb, &b[i__ + (*n - *
|
|
l + 1) * b_dim1], ldb, &csv, &snv);
|
|
|
|
/* Update (N-L+I)-th and (N-L+J)-th columns of matrices */
|
|
/* A and B: A*Q and B*Q */
|
|
|
|
/* Computing MIN */
|
|
i__4 = *k + *l;
|
|
i__3 = f2cmin(i__4,*m);
|
|
drot_(&i__3, &a[(*n - *l + j) * a_dim1 + 1], &c__1, &a[(*n - *
|
|
l + i__) * a_dim1 + 1], &c__1, &csq, &snq);
|
|
|
|
drot_(l, &b[(*n - *l + j) * b_dim1 + 1], &c__1, &b[(*n - *l +
|
|
i__) * b_dim1 + 1], &c__1, &csq, &snq);
|
|
|
|
if (upper) {
|
|
if (*k + i__ <= *m) {
|
|
a[*k + i__ + (*n - *l + j) * a_dim1] = 0.;
|
|
}
|
|
b[i__ + (*n - *l + j) * b_dim1] = 0.;
|
|
} else {
|
|
if (*k + j <= *m) {
|
|
a[*k + j + (*n - *l + i__) * a_dim1] = 0.;
|
|
}
|
|
b[j + (*n - *l + i__) * b_dim1] = 0.;
|
|
}
|
|
|
|
/* Update orthogonal matrices U, V, Q, if desired. */
|
|
|
|
if (wantu && *k + j <= *m) {
|
|
drot_(m, &u[(*k + j) * u_dim1 + 1], &c__1, &u[(*k + i__) *
|
|
u_dim1 + 1], &c__1, &csu, &snu);
|
|
}
|
|
|
|
if (wantv) {
|
|
drot_(p, &v[j * v_dim1 + 1], &c__1, &v[i__ * v_dim1 + 1],
|
|
&c__1, &csv, &snv);
|
|
}
|
|
|
|
if (wantq) {
|
|
drot_(n, &q[(*n - *l + j) * q_dim1 + 1], &c__1, &q[(*n - *
|
|
l + i__) * q_dim1 + 1], &c__1, &csq, &snq);
|
|
}
|
|
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
if (! upper) {
|
|
|
|
/* The matrices A13 and B13 were lower triangular at the start */
|
|
/* of the cycle, and are now upper triangular. */
|
|
|
|
/* Convergence test: test the parallelism of the corresponding */
|
|
/* rows of A and B. */
|
|
|
|
error = 0.;
|
|
/* Computing MIN */
|
|
i__2 = *l, i__3 = *m - *k;
|
|
i__1 = f2cmin(i__2,i__3);
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *l - i__ + 1;
|
|
dcopy_(&i__2, &a[*k + i__ + (*n - *l + i__) * a_dim1], lda, &
|
|
work[1], &c__1);
|
|
i__2 = *l - i__ + 1;
|
|
dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &work[*
|
|
l + 1], &c__1);
|
|
i__2 = *l - i__ + 1;
|
|
dlapll_(&i__2, &work[1], &c__1, &work[*l + 1], &c__1, &ssmin);
|
|
error = f2cmax(error,ssmin);
|
|
/* L30: */
|
|
}
|
|
|
|
if (abs(error) <= f2cmin(*tola,*tolb)) {
|
|
goto L50;
|
|
}
|
|
}
|
|
|
|
/* End of cycle loop */
|
|
|
|
/* L40: */
|
|
}
|
|
|
|
/* The algorithm has not converged after MAXIT cycles. */
|
|
|
|
*info = 1;
|
|
goto L100;
|
|
|
|
L50:
|
|
|
|
/* If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged. */
|
|
/* Compute the generalized singular value pairs (ALPHA, BETA), and */
|
|
/* set the triangular matrix R to array A. */
|
|
|
|
i__1 = *k;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
alpha[i__] = 1.;
|
|
beta[i__] = 0.;
|
|
/* L60: */
|
|
}
|
|
|
|
/* Computing MIN */
|
|
i__2 = *l, i__3 = *m - *k;
|
|
i__1 = f2cmin(i__2,i__3);
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
|
|
a1 = a[*k + i__ + (*n - *l + i__) * a_dim1];
|
|
b1 = b[i__ + (*n - *l + i__) * b_dim1];
|
|
gamma = b1 / a1;
|
|
|
|
if (gamma <= (doublereal) myhuge_(&c_b1) && gamma >= -((doublereal)
|
|
myhuge_(&c_b1))) {
|
|
|
|
/* change sign if necessary */
|
|
|
|
if (gamma < 0.) {
|
|
i__2 = *l - i__ + 1;
|
|
dscal_(&i__2, &c_b44, &b[i__ + (*n - *l + i__) * b_dim1], ldb)
|
|
;
|
|
if (wantv) {
|
|
dscal_(p, &c_b44, &v[i__ * v_dim1 + 1], &c__1);
|
|
}
|
|
}
|
|
|
|
d__1 = abs(gamma);
|
|
dlartg_(&d__1, &c_b15, &beta[*k + i__], &alpha[*k + i__], &rwk);
|
|
|
|
if (alpha[*k + i__] >= beta[*k + i__]) {
|
|
i__2 = *l - i__ + 1;
|
|
d__1 = 1. / alpha[*k + i__];
|
|
dscal_(&i__2, &d__1, &a[*k + i__ + (*n - *l + i__) * a_dim1],
|
|
lda);
|
|
} else {
|
|
i__2 = *l - i__ + 1;
|
|
d__1 = 1. / beta[*k + i__];
|
|
dscal_(&i__2, &d__1, &b[i__ + (*n - *l + i__) * b_dim1], ldb);
|
|
i__2 = *l - i__ + 1;
|
|
dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k
|
|
+ i__ + (*n - *l + i__) * a_dim1], lda);
|
|
}
|
|
|
|
} else {
|
|
|
|
alpha[*k + i__] = 0.;
|
|
beta[*k + i__] = 1.;
|
|
i__2 = *l - i__ + 1;
|
|
dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k +
|
|
i__ + (*n - *l + i__) * a_dim1], lda);
|
|
|
|
}
|
|
|
|
/* L70: */
|
|
}
|
|
|
|
/* Post-assignment */
|
|
|
|
i__1 = *k + *l;
|
|
for (i__ = *m + 1; i__ <= i__1; ++i__) {
|
|
alpha[i__] = 0.;
|
|
beta[i__] = 1.;
|
|
/* L80: */
|
|
}
|
|
|
|
if (*k + *l < *n) {
|
|
i__1 = *n;
|
|
for (i__ = *k + *l + 1; i__ <= i__1; ++i__) {
|
|
alpha[i__] = 0.;
|
|
beta[i__] = 0.;
|
|
/* L90: */
|
|
}
|
|
}
|
|
|
|
L100:
|
|
*ncallmycycle = kcallmycycle;
|
|
return;
|
|
|
|
/* End of DTGSJA */
|
|
|
|
} /* dtgsja_ */
|
|
|