930 lines
25 KiB
C
930 lines
25 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 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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#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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/* -- translated by f2c (version 20000121).
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You must link the resulting object file with the libraries:
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-lf2c -lm (in that order)
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*/
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/* Table of constant values */
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static integer c_n1 = -1;
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static real c_b14 = 0.f;
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static real c_b24 = 1.f;
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/* > \brief \b SGGSVP3 */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download SGGSVP3 + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sggsvp3
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.f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sggsvp3
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.f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sggsvp3
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.f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE SGGSVP3( JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, */
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/* TOLA, TOLB, K, L, U, LDU, V, LDV, Q, LDQ, */
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/* IWORK, TAU, WORK, LWORK, INFO ) */
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/* CHARACTER JOBQ, JOBU, JOBV */
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/* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P, LWORK */
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/* REAL TOLA, TOLB */
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/* INTEGER IWORK( * ) */
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/* REAL A( LDA, * ), B( LDB, * ), Q( LDQ, * ), */
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/* $ TAU( * ), U( LDU, * ), V( LDV, * ), WORK( * ) */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > SGGSVP3 computes orthogonal matrices U, V and Q such that */
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/* > */
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/* > N-K-L K L */
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/* > U**T*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0; */
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/* > L ( 0 0 A23 ) */
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/* > M-K-L ( 0 0 0 ) */
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/* > */
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/* > N-K-L K L */
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/* > = K ( 0 A12 A13 ) if M-K-L < 0; */
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/* > M-K ( 0 0 A23 ) */
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/* > */
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/* > N-K-L K L */
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/* > V**T*B*Q = L ( 0 0 B13 ) */
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/* > P-L ( 0 0 0 ) */
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/* > */
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/* > where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */
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/* > upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */
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/* > otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective */
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/* > numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T. */
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/* > */
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/* > This decomposition is the preprocessing step for computing the */
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/* > Generalized Singular Value Decomposition (GSVD), see subroutine */
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/* > SGGSVD3. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] JOBU */
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/* > \verbatim */
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/* > JOBU is CHARACTER*1 */
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/* > = 'U': Orthogonal matrix U is computed; */
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/* > = 'N': U is not computed. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] JOBV */
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/* > \verbatim */
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/* > JOBV is CHARACTER*1 */
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/* > = 'V': Orthogonal matrix V is computed; */
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/* > = 'N': V is not computed. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] JOBQ */
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/* > \verbatim */
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/* > JOBQ is CHARACTER*1 */
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/* > = 'Q': Orthogonal matrix Q is computed; */
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/* > = 'N': Q is not computed. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] M */
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/* > \verbatim */
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/* > M is INTEGER */
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/* > The number of rows of the matrix A. M >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] P */
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/* > \verbatim */
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/* > P is INTEGER */
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/* > The number of rows of the matrix B. P >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The number of columns of the matrices A and B. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] A */
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/* > \verbatim */
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/* > A is REAL array, dimension (LDA,N) */
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/* > On entry, the M-by-N matrix A. */
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/* > On exit, A contains the triangular (or trapezoidal) matrix */
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/* > described in the Purpose section. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] B */
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/* > \verbatim */
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/* > B is REAL array, dimension (LDB,N) */
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/* > On entry, the P-by-N matrix B. */
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/* > On exit, B contains the triangular matrix described in */
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/* > the Purpose section. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDB */
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/* > \verbatim */
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/* > LDB is INTEGER */
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/* > The leading dimension of the array B. LDB >= f2cmax(1,P). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] TOLA */
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/* > \verbatim */
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/* > TOLA is REAL */
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/* > \endverbatim */
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/* > */
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/* > \param[in] TOLB */
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/* > \verbatim */
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/* > TOLB is REAL */
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/* > */
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/* > TOLA and TOLB are the thresholds to determine the effective */
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/* > numerical rank of matrix B and a subblock of A. Generally, */
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/* > they are set to */
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/* > TOLA = MAX(M,N)*norm(A)*MACHEPS, */
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/* > TOLB = MAX(P,N)*norm(B)*MACHEPS. */
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/* > The size of TOLA and TOLB may affect the size of backward */
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/* > errors of the decomposition. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] K */
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/* > \verbatim */
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/* > K is INTEGER */
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/* > \endverbatim */
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/* > */
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/* > \param[out] L */
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/* > \verbatim */
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/* > L is INTEGER */
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/* > */
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/* > On exit, K and L specify the dimension of the subblocks */
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/* > described in Purpose section. */
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/* > K + L = effective numerical rank of (A**T,B**T)**T. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] U */
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/* > \verbatim */
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/* > U is REAL array, dimension (LDU,M) */
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/* > If JOBU = 'U', U contains the orthogonal matrix U. */
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/* > If JOBU = 'N', U is not referenced. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDU */
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/* > \verbatim */
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/* > LDU is INTEGER */
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|
/* > The leading dimension of the array U. LDU >= f2cmax(1,M) if */
|
|
/* > JOBU = 'U'; LDU >= 1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] V */
|
|
/* > \verbatim */
|
|
/* > V is REAL array, dimension (LDV,P) */
|
|
/* > If JOBV = 'V', V contains the orthogonal 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 REAL array, dimension (LDQ,N) */
|
|
/* > If JOBQ = 'Q', Q contains the orthogonal 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] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] TAU */
|
|
/* > \verbatim */
|
|
/* > TAU is REAL array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL 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] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date August 2015 */
|
|
|
|
/* > \ingroup realOTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The subroutine uses LAPACK subroutine SGEQP3 for the QR factorization */
|
|
/* > with column pivoting to detect the effective numerical rank of the */
|
|
/* > a matrix. It may be replaced by a better rank determination strategy. */
|
|
/* > */
|
|
/* > SGGSVP3 replaces the deprecated subroutine SGGSVP. */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void sggsvp3_(char *jobu, char *jobv, char *jobq, integer *m,
|
|
integer *p, integer *n, real *a, integer *lda, real *b, integer *ldb,
|
|
real *tola, real *tolb, integer *k, integer *l, real *u, integer *ldu,
|
|
real *v, integer *ldv, real *q, integer *ldq, integer *iwork, real *
|
|
tau, real *work, integer *lwork, 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;
|
|
real r__1;
|
|
|
|
/* Local variables */
|
|
integer i__, j;
|
|
extern logical lsame_(char *, char *);
|
|
logical wantq, wantu, wantv;
|
|
extern /* Subroutine */ void sgeqp3_(integer *, integer *, real *, integer
|
|
*, integer *, real *, real *, integer *, integer *), sgeqr2_(
|
|
integer *, integer *, real *, integer *, real *, real *, integer *
|
|
), sgerq2_(integer *, integer *, real *, integer *, real *, real *
|
|
, integer *), sorg2r_(integer *, integer *, integer *, real *,
|
|
integer *, real *, real *, integer *), sorm2r_(char *, char *,
|
|
integer *, integer *, integer *, real *, integer *, real *, real *
|
|
, integer *, real *, integer *), sormr2_(char *,
|
|
char *, integer *, integer *, integer *, real *, integer *, real *
|
|
, real *, integer *, real *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
extern void slacpy_(char *, integer *, integer *,
|
|
real *, integer *, real *, integer *), slaset_(char *,
|
|
integer *, integer *, real *, real *, real *, integer *),
|
|
slapmt_(logical *, integer *, integer *, real *, integer *,
|
|
integer *);
|
|
logical forwrd;
|
|
integer lwkopt;
|
|
logical lquery;
|
|
|
|
|
|
/* -- 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..-- */
|
|
/* August 2015 */
|
|
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* 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;
|
|
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;
|
|
--iwork;
|
|
--tau;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
wantu = lsame_(jobu, "U");
|
|
wantv = lsame_(jobv, "V");
|
|
wantq = lsame_(jobq, "Q");
|
|
forwrd = TRUE_;
|
|
lquery = *lwork == -1;
|
|
lwkopt = 1;
|
|
|
|
/* Test the input arguments */
|
|
|
|
*info = 0;
|
|
if (! (wantu || lsame_(jobu, "N"))) {
|
|
*info = -1;
|
|
} else if (! (wantv || lsame_(jobv, "N"))) {
|
|
*info = -2;
|
|
} else if (! (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 = -8;
|
|
} else if (*ldb < f2cmax(1,*p)) {
|
|
*info = -10;
|
|
} else if (*ldu < 1 || wantu && *ldu < *m) {
|
|
*info = -16;
|
|
} else if (*ldv < 1 || wantv && *ldv < *p) {
|
|
*info = -18;
|
|
} else if (*ldq < 1 || wantq && *ldq < *n) {
|
|
*info = -20;
|
|
} else if (*lwork < 1 && ! lquery) {
|
|
*info = -24;
|
|
}
|
|
|
|
/* Compute workspace */
|
|
|
|
if (*info == 0) {
|
|
sgeqp3_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], &c_n1,
|
|
info);
|
|
lwkopt = (integer) work[1];
|
|
if (wantv) {
|
|
lwkopt = f2cmax(lwkopt,*p);
|
|
}
|
|
/* Computing MAX */
|
|
i__1 = lwkopt, i__2 = f2cmin(*n,*p);
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
lwkopt = f2cmax(lwkopt,*m);
|
|
if (wantq) {
|
|
lwkopt = f2cmax(lwkopt,*n);
|
|
}
|
|
sgeqp3_(m, n, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], &c_n1,
|
|
info);
|
|
/* Computing MAX */
|
|
i__1 = lwkopt, i__2 = (integer) work[1];
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
lwkopt = f2cmax(1,lwkopt);
|
|
work[1] = (real) lwkopt;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SGGSVP3", &i__1, (ftnlen)7);
|
|
return;
|
|
}
|
|
if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* QR with column pivoting of B: B*P = V*( S11 S12 ) */
|
|
/* ( 0 0 ) */
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
iwork[i__] = 0;
|
|
/* L10: */
|
|
}
|
|
sgeqp3_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], lwork,
|
|
info);
|
|
|
|
/* Update A := A*P */
|
|
|
|
slapmt_(&forwrd, m, n, &a[a_offset], lda, &iwork[1]);
|
|
|
|
/* Determine the effective rank of matrix B. */
|
|
|
|
*l = 0;
|
|
i__1 = f2cmin(*p,*n);
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if ((r__1 = b[i__ + i__ * b_dim1], abs(r__1)) > *tolb) {
|
|
++(*l);
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
if (wantv) {
|
|
|
|
/* Copy the details of V, and form V. */
|
|
|
|
slaset_("Full", p, p, &c_b14, &c_b14, &v[v_offset], ldv);
|
|
if (*p > 1) {
|
|
i__1 = *p - 1;
|
|
slacpy_("Lower", &i__1, n, &b[b_dim1 + 2], ldb, &v[v_dim1 + 2],
|
|
ldv);
|
|
}
|
|
i__1 = f2cmin(*p,*n);
|
|
sorg2r_(p, p, &i__1, &v[v_offset], ldv, &tau[1], &work[1], info);
|
|
}
|
|
|
|
/* Clean up B */
|
|
|
|
i__1 = *l - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *l;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
b[i__ + j * b_dim1] = 0.f;
|
|
/* L30: */
|
|
}
|
|
/* L40: */
|
|
}
|
|
if (*p > *l) {
|
|
i__1 = *p - *l;
|
|
slaset_("Full", &i__1, n, &c_b14, &c_b14, &b[*l + 1 + b_dim1], ldb);
|
|
}
|
|
|
|
if (wantq) {
|
|
|
|
/* Set Q = I and Update Q := Q*P */
|
|
|
|
slaset_("Full", n, n, &c_b14, &c_b24, &q[q_offset], ldq);
|
|
slapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
|
|
}
|
|
|
|
if (*p >= *l && *n != *l) {
|
|
|
|
/* RQ factorization of (S11 S12): ( S11 S12 ) = ( 0 S12 )*Z */
|
|
|
|
sgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);
|
|
|
|
/* Update A := A*Z**T */
|
|
|
|
sormr2_("Right", "Transpose", m, n, l, &b[b_offset], ldb, &tau[1], &a[
|
|
a_offset], lda, &work[1], info);
|
|
|
|
if (wantq) {
|
|
|
|
/* Update Q := Q*Z**T */
|
|
|
|
sormr2_("Right", "Transpose", n, n, l, &b[b_offset], ldb, &tau[1],
|
|
&q[q_offset], ldq, &work[1], info);
|
|
}
|
|
|
|
/* Clean up B */
|
|
|
|
i__1 = *n - *l;
|
|
slaset_("Full", l, &i__1, &c_b14, &c_b14, &b[b_offset], ldb);
|
|
i__1 = *n;
|
|
for (j = *n - *l + 1; j <= i__1; ++j) {
|
|
i__2 = *l;
|
|
for (i__ = j - *n + *l + 1; i__ <= i__2; ++i__) {
|
|
b[i__ + j * b_dim1] = 0.f;
|
|
/* L50: */
|
|
}
|
|
/* L60: */
|
|
}
|
|
|
|
}
|
|
|
|
/* Let N-L L */
|
|
/* A = ( A11 A12 ) M, */
|
|
|
|
/* then the following does the complete QR decomposition of A11: */
|
|
|
|
/* A11 = U*( 0 T12 )*P1**T */
|
|
/* ( 0 0 ) */
|
|
|
|
i__1 = *n - *l;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
iwork[i__] = 0;
|
|
/* L70: */
|
|
}
|
|
i__1 = *n - *l;
|
|
sgeqp3_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], lwork,
|
|
info);
|
|
|
|
/* Determine the effective rank of A11 */
|
|
|
|
*k = 0;
|
|
/* Computing MIN */
|
|
i__2 = *m, i__3 = *n - *l;
|
|
i__1 = f2cmin(i__2,i__3);
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if ((r__1 = a[i__ + i__ * a_dim1], abs(r__1)) > *tola) {
|
|
++(*k);
|
|
}
|
|
/* L80: */
|
|
}
|
|
|
|
/* Update A12 := U**T*A12, where A12 = A( 1:M, N-L+1:N ) */
|
|
|
|
/* Computing MIN */
|
|
i__2 = *m, i__3 = *n - *l;
|
|
i__1 = f2cmin(i__2,i__3);
|
|
sorm2r_("Left", "Transpose", m, l, &i__1, &a[a_offset], lda, &tau[1], &a[(
|
|
*n - *l + 1) * a_dim1 + 1], lda, &work[1], info);
|
|
|
|
if (wantu) {
|
|
|
|
/* Copy the details of U, and form U */
|
|
|
|
slaset_("Full", m, m, &c_b14, &c_b14, &u[u_offset], ldu);
|
|
if (*m > 1) {
|
|
i__1 = *m - 1;
|
|
i__2 = *n - *l;
|
|
slacpy_("Lower", &i__1, &i__2, &a[a_dim1 + 2], lda, &u[u_dim1 + 2]
|
|
, ldu);
|
|
}
|
|
/* Computing MIN */
|
|
i__2 = *m, i__3 = *n - *l;
|
|
i__1 = f2cmin(i__2,i__3);
|
|
sorg2r_(m, m, &i__1, &u[u_offset], ldu, &tau[1], &work[1], info);
|
|
}
|
|
|
|
if (wantq) {
|
|
|
|
/* Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1 */
|
|
|
|
i__1 = *n - *l;
|
|
slapmt_(&forwrd, n, &i__1, &q[q_offset], ldq, &iwork[1]);
|
|
}
|
|
|
|
/* Clean up A: set the strictly lower triangular part of */
|
|
/* A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0. */
|
|
|
|
i__1 = *k - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *k;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
a[i__ + j * a_dim1] = 0.f;
|
|
/* L90: */
|
|
}
|
|
/* L100: */
|
|
}
|
|
if (*m > *k) {
|
|
i__1 = *m - *k;
|
|
i__2 = *n - *l;
|
|
slaset_("Full", &i__1, &i__2, &c_b14, &c_b14, &a[*k + 1 + a_dim1],
|
|
lda);
|
|
}
|
|
|
|
if (*n - *l > *k) {
|
|
|
|
/* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
|
|
|
|
i__1 = *n - *l;
|
|
sgerq2_(k, &i__1, &a[a_offset], lda, &tau[1], &work[1], info);
|
|
|
|
if (wantq) {
|
|
|
|
/* Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**T */
|
|
|
|
i__1 = *n - *l;
|
|
sormr2_("Right", "Transpose", n, &i__1, k, &a[a_offset], lda, &
|
|
tau[1], &q[q_offset], ldq, &work[1], info);
|
|
}
|
|
|
|
/* Clean up A */
|
|
|
|
i__1 = *n - *l - *k;
|
|
slaset_("Full", k, &i__1, &c_b14, &c_b14, &a[a_offset], lda);
|
|
i__1 = *n - *l;
|
|
for (j = *n - *l - *k + 1; j <= i__1; ++j) {
|
|
i__2 = *k;
|
|
for (i__ = j - *n + *l + *k + 1; i__ <= i__2; ++i__) {
|
|
a[i__ + j * a_dim1] = 0.f;
|
|
/* L110: */
|
|
}
|
|
/* L120: */
|
|
}
|
|
|
|
}
|
|
|
|
if (*m > *k) {
|
|
|
|
/* QR factorization of A( K+1:M,N-L+1:N ) */
|
|
|
|
i__1 = *m - *k;
|
|
sgeqr2_(&i__1, l, &a[*k + 1 + (*n - *l + 1) * a_dim1], lda, &tau[1], &
|
|
work[1], info);
|
|
|
|
if (wantu) {
|
|
|
|
/* Update U(:,K+1:M) := U(:,K+1:M)*U1 */
|
|
|
|
i__1 = *m - *k;
|
|
/* Computing MIN */
|
|
i__3 = *m - *k;
|
|
i__2 = f2cmin(i__3,*l);
|
|
sorm2r_("Right", "No transpose", m, &i__1, &i__2, &a[*k + 1 + (*n
|
|
- *l + 1) * a_dim1], lda, &tau[1], &u[(*k + 1) * u_dim1 +
|
|
1], ldu, &work[1], info);
|
|
}
|
|
|
|
/* Clean up */
|
|
|
|
i__1 = *n;
|
|
for (j = *n - *l + 1; j <= i__1; ++j) {
|
|
i__2 = *m;
|
|
for (i__ = j - *n + *k + *l + 1; i__ <= i__2; ++i__) {
|
|
a[i__ + j * a_dim1] = 0.f;
|
|
/* L130: */
|
|
}
|
|
/* L140: */
|
|
}
|
|
|
|
}
|
|
|
|
work[1] = (real) lwkopt;
|
|
return;
|
|
|
|
/* End of SGGSVP3 */
|
|
|
|
} /* sggsvp3_ */
|
|
|