1071 lines
31 KiB
C
1071 lines
31 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]/df(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 integer c_n1 = -1;
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief <b> CGGSVD3 computes the singular value decomposition (SVD) for OTHER matrices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CGGSVD3 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cggsvd3
|
|
.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cggsvd3
|
|
.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cggsvd3
|
|
.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CGGSVD3( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B, */
|
|
/* LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, */
|
|
/* LWORK, RWORK, IWORK, INFO ) */
|
|
|
|
/* CHARACTER JOBQ, JOBU, JOBV */
|
|
/* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P, LWORK */
|
|
/* INTEGER IWORK( * ) */
|
|
/* REAL ALPHA( * ), BETA( * ), RWORK( * ) */
|
|
/* COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ), */
|
|
/* $ U( LDU, * ), V( LDV, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CGGSVD3 computes the generalized singular value decomposition (GSVD) */
|
|
/* > of an M-by-N complex matrix A and P-by-N complex matrix B: */
|
|
/* > */
|
|
/* > U**H*A*Q = D1*( 0 R ), V**H*B*Q = D2*( 0 R ) */
|
|
/* > */
|
|
/* > where U, V and Q are unitary matrices. */
|
|
/* > Let K+L = the effective numerical rank of the */
|
|
/* > matrix (A**H,B**H)**H, then R is a (K+L)-by-(K+L) nonsingular upper */
|
|
/* > triangular matrix, D1 and D2 are M-by-(K+L) and P-by-(K+L) "diagonal" */
|
|
/* > matrices and of the following structures, respectively: */
|
|
/* > */
|
|
/* > 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 ) */
|
|
/* > L ( 0 0 R22 ) */
|
|
/* > */
|
|
/* > 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. */
|
|
/* > */
|
|
/* > (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 routine computes C, S, R, and optionally the unitary */
|
|
/* > transformation matrices U, V and Q. */
|
|
/* > */
|
|
/* > In particular, if B is an N-by-N nonsingular matrix, then the GSVD of */
|
|
/* > A and B implicitly gives the SVD of A*inv(B): */
|
|
/* > A*inv(B) = U*(D1*inv(D2))*V**H. */
|
|
/* > If ( A**H,B**H)**H has orthonormal columns, then the GSVD of A and B is also */
|
|
/* > equal to the CS decomposition of A and B. Furthermore, the GSVD can */
|
|
/* > be used to derive the solution of the eigenvalue problem: */
|
|
/* > A**H*A x = lambda* B**H*B x. */
|
|
/* > In some literature, the GSVD of A and B is presented in the form */
|
|
/* > U**H*A*X = ( 0 D1 ), V**H*B*X = ( 0 D2 ) */
|
|
/* > where U and V are orthogonal and X is nonsingular, and D1 and D2 are */
|
|
/* > ``diagonal''. The former GSVD form can be converted to the latter */
|
|
/* > form by taking the nonsingular matrix X as */
|
|
/* > */
|
|
/* > X = Q*( I 0 ) */
|
|
/* > ( 0 inv(R) ) */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBU */
|
|
/* > \verbatim */
|
|
/* > JOBU is CHARACTER*1 */
|
|
/* > = 'U': Unitary matrix U is computed; */
|
|
/* > = 'N': U is not computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBV */
|
|
/* > \verbatim */
|
|
/* > JOBV is CHARACTER*1 */
|
|
/* > = 'V': Unitary matrix V is computed; */
|
|
/* > = 'N': V is not computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBQ */
|
|
/* > \verbatim */
|
|
/* > JOBQ is CHARACTER*1 */
|
|
/* > = 'Q': Unitary matrix Q is computed; */
|
|
/* > = '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] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrices A and B. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] P */
|
|
/* > \verbatim */
|
|
/* > P is INTEGER */
|
|
/* > The number of rows of the matrix B. P >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] L */
|
|
/* > \verbatim */
|
|
/* > L is INTEGER */
|
|
/* > */
|
|
/* > On exit, K and L specify the dimension of the subblocks */
|
|
/* > described in Purpose. */
|
|
/* > K + L = effective numerical rank of (A**H,B**H)**H. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX array, dimension (LDA,N) */
|
|
/* > On entry, the M-by-N matrix A. */
|
|
/* > On exit, A 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 COMPLEX array, dimension (LDB,N) */
|
|
/* > On entry, the P-by-N matrix B. */
|
|
/* > On exit, B contains part of the triangular matrix R if */
|
|
/* > M-K-L < 0. 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[out] ALPHA */
|
|
/* > \verbatim */
|
|
/* > ALPHA is REAL array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BETA */
|
|
/* > \verbatim */
|
|
/* > BETA is REAL 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) = C, */
|
|
/* > BETA(K+1:K+L) = 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 */
|
|
/* > and */
|
|
/* > ALPHA(K+L+1:N) = 0 */
|
|
/* > BETA(K+L+1:N) = 0 */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] U */
|
|
/* > \verbatim */
|
|
/* > U is COMPLEX array, dimension (LDU,M) */
|
|
/* > If JOBU = 'U', U contains the M-by-M unitary matrix 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[out] V */
|
|
/* > \verbatim */
|
|
/* > V is COMPLEX array, dimension (LDV,P) */
|
|
/* > If JOBV = 'V', V contains the P-by-P unitary matrix 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[out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is COMPLEX array, dimension (LDQ,N) */
|
|
/* > If JOBQ = 'Q', Q contains the N-by-N unitary matrix 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 COMPLEX array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is REAL array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (N) */
|
|
/* > On exit, IWORK stores the sorting information. More */
|
|
/* > precisely, the following loop will sort ALPHA */
|
|
/* > for I = K+1, f2cmin(M,K+L) */
|
|
/* > swap ALPHA(I) and ALPHA(IWORK(I)) */
|
|
/* > endfor */
|
|
/* > such that ALPHA(1) >= ALPHA(2) >= ... >= ALPHA(N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: if INFO = 1, the Jacobi-type procedure failed to */
|
|
/* > converge. For further details, see subroutine CTGSJA. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Internal Parameters: */
|
|
/* ========================= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > TOLA REAL */
|
|
/* > TOLB REAL */
|
|
/* > TOLA and TOLB are the thresholds to determine the effective */
|
|
/* > rank of (A**H,B**H)**H. Generally, they are set to */
|
|
/* > TOLA = MAX(M,N)*norm(A)*MACHEPS, */
|
|
/* > TOLB = MAX(P,N)*norm(B)*MACHEPS. */
|
|
/* > The size of TOLA and TOLB may affect the size of backward */
|
|
/* > errors of the decomposition. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \date August 2015 */
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/* > \ingroup complexGEsing */
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/* > \par Contributors: */
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/* ================== */
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/* > */
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/* > Ming Gu and Huan Ren, Computer Science Division, University of */
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/* > California at Berkeley, USA */
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/* > */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > CGGSVD3 replaces the deprecated subroutine CGGSVD. */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ void cggsvd3_(char *jobu, char *jobv, char *jobq, integer *m,
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integer *n, integer *p, integer *k, integer *l, complex *a, integer *
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lda, complex *b, integer *ldb, real *alpha, real *beta, complex *u,
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integer *ldu, complex *v, integer *ldv, complex *q, integer *ldq,
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complex *work, integer *lwork, real *rwork, integer *iwork, integer *
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info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
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u_offset, v_dim1, v_offset, i__1, i__2;
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complex q__1;
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/* Local variables */
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integer ibnd;
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real tola;
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integer isub;
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real tolb, unfl, temp, smax;
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integer ncallmycycle, i__, j;
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extern logical lsame_(char *, char *);
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real anorm, bnorm;
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logical wantq;
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extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
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integer *);
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logical wantu, wantv;
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extern real clange_(char *, integer *, integer *, complex *, integer *,
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real *), slamch_(char *);
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extern /* Subroutine */ void ctgsja_(char *, char *, char *, integer *,
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integer *, integer *, integer *, integer *, complex *, integer *,
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complex *, integer *, real *, real *, real *, real *, complex *,
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integer *, complex *, integer *, complex *, integer *, complex *,
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integer *, integer *);
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extern int xerbla_(char *, integer *, ftnlen);
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integer lwkopt;
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logical lquery;
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extern /* Subroutine */ void cggsvp3_(char *, char *, char *, integer *,
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integer *, integer *, complex *, integer *, complex *, integer *,
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real *, real *, integer *, integer *, complex *, integer *,
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complex *, integer *, complex *, integer *, integer *, real *,
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complex *, complex *, integer *, integer *);
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real ulp;
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/* -- LAPACK driver routine (version 3.7.0) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* August 2015 */
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/* ===================================================================== */
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/* Decode and test the input parameters */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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a -= a_offset;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1 * 1;
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b -= b_offset;
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--alpha;
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--beta;
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u_dim1 = *ldu;
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u_offset = 1 + u_dim1 * 1;
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u -= u_offset;
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v_dim1 = *ldv;
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v_offset = 1 + v_dim1 * 1;
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v -= v_offset;
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q_dim1 = *ldq;
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q_offset = 1 + q_dim1 * 1;
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q -= q_offset;
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--work;
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--rwork;
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--iwork;
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/* Function Body */
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wantu = lsame_(jobu, "U");
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wantv = lsame_(jobv, "V");
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wantq = lsame_(jobq, "Q");
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lquery = *lwork == -1;
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lwkopt = 1;
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/* Test the input arguments */
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*info = 0;
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if (! (wantu || lsame_(jobu, "N"))) {
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*info = -1;
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} else if (! (wantv || lsame_(jobv, "N"))) {
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*info = -2;
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} else if (! (wantq || lsame_(jobq, "N"))) {
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*info = -3;
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} else if (*m < 0) {
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*info = -4;
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} else if (*n < 0) {
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*info = -5;
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} else if (*p < 0) {
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*info = -6;
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} else if (*lda < f2cmax(1,*m)) {
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*info = -10;
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} else if (*ldb < f2cmax(1,*p)) {
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*info = -12;
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} else if (*ldu < 1 || wantu && *ldu < *m) {
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*info = -16;
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} else if (*ldv < 1 || wantv && *ldv < *p) {
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*info = -18;
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} else if (*ldq < 1 || wantq && *ldq < *n) {
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*info = -20;
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} else if (*lwork < 1 && ! lquery) {
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*info = -24;
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}
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/* Compute workspace */
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if (*info == 0) {
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cggsvp3_(jobu, jobv, jobq, m, p, n, &a[a_offset], lda, &b[b_offset],
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ldb, &tola, &tolb, k, l, &u[u_offset], ldu, &v[v_offset], ldv,
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&q[q_offset], ldq, &iwork[1], &rwork[1], &work[1], &work[1],
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&c_n1, info);
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lwkopt = *n + (integer) work[1].r;
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/* Computing MAX */
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i__1 = *n << 1;
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lwkopt = f2cmax(i__1,lwkopt);
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lwkopt = f2cmax(1,lwkopt);
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q__1.r = (real) lwkopt, q__1.i = 0.f;
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work[1].r = q__1.r, work[1].i = q__1.i;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("CGGSVD3", &i__1, (ftnlen)7);
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return;
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}
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if (lquery) {
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return;
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}
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/* Compute the Frobenius norm of matrices A and B */
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anorm = clange_("1", m, n, &a[a_offset], lda, &rwork[1]);
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bnorm = clange_("1", p, n, &b[b_offset], ldb, &rwork[1]);
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/* Get machine precision and set up threshold for determining */
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/* the effective numerical rank of the matrices A and B. */
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ulp = slamch_("Precision");
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unfl = slamch_("Safe Minimum");
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tola = f2cmax(*m,*n) * f2cmax(anorm,unfl) * ulp;
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tolb = f2cmax(*p,*n) * f2cmax(bnorm,unfl) * ulp;
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i__1 = *lwork - *n;
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cggsvp3_(jobu, jobv, jobq, m, p, n, &a[a_offset], lda, &b[b_offset], ldb,
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&tola, &tolb, k, l, &u[u_offset], ldu, &v[v_offset], ldv, &q[
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q_offset], ldq, &iwork[1], &rwork[1], &work[1], &work[*n + 1], &
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i__1, info);
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/* Compute the GSVD of two upper "triangular" matrices */
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ctgsja_(jobu, jobv, jobq, m, p, n, k, l, &a[a_offset], lda, &b[b_offset],
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ldb, &tola, &tolb, &alpha[1], &beta[1], &u[u_offset], ldu, &v[
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v_offset], ldv, &q[q_offset], ldq, &work[1], &ncallmycycle, info);
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/* Sort the singular values and store the pivot indices in IWORK */
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/* Copy ALPHA to RWORK, then sort ALPHA in RWORK */
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scopy_(n, &alpha[1], &c__1, &rwork[1], &c__1);
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/* Computing MIN */
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i__1 = *l, i__2 = *m - *k;
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ibnd = f2cmin(i__1,i__2);
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i__1 = ibnd;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Scan for largest ALPHA(K+I) */
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isub = i__;
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smax = rwork[*k + i__];
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i__2 = ibnd;
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for (j = i__ + 1; j <= i__2; ++j) {
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temp = rwork[*k + j];
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if (temp > smax) {
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isub = j;
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smax = temp;
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}
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/* L10: */
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}
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if (isub != i__) {
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rwork[*k + isub] = rwork[*k + i__];
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rwork[*k + i__] = smax;
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iwork[*k + i__] = *k + isub;
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} else {
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iwork[*k + i__] = *k + i__;
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}
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/* L20: */
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}
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q__1.r = (real) lwkopt, q__1.i = 0.f;
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work[1].r = q__1.r, work[1].i = q__1.i;
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return;
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/* End of CGGSVD3 */
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} /* cggsvd3_ */
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