1467 lines
44 KiB
C
1467 lines
44 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__6 = 6;
|
|
static integer c__0 = 0;
|
|
static integer c__2 = 2;
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
static doublereal c_b109 = 0.;
|
|
|
|
/* > \brief <b> DGESVDX computes the singular value decomposition (SVD) for GE matrices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DGESVDX + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgesvdx
|
|
.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgesvdx
|
|
.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesvdx
|
|
.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DGESVDX( JOBU, JOBVT, RANGE, M, N, A, LDA, VL, VU, */
|
|
/* $ IL, IU, NS, S, U, LDU, VT, LDVT, WORK, */
|
|
/* $ LWORK, IWORK, INFO ) */
|
|
|
|
|
|
/* CHARACTER JOBU, JOBVT, RANGE */
|
|
/* INTEGER IL, INFO, IU, LDA, LDU, LDVT, LWORK, M, N, NS */
|
|
/* DOUBLE PRECISION VL, VU */
|
|
/* INTEGER IWORK( * ) */
|
|
/* DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), */
|
|
/* $ VT( LDVT, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DGESVDX computes the singular value decomposition (SVD) of a real */
|
|
/* > M-by-N matrix A, optionally computing the left and/or right singular */
|
|
/* > vectors. The SVD is written */
|
|
/* > */
|
|
/* > A = U * SIGMA * transpose(V) */
|
|
/* > */
|
|
/* > where SIGMA is an M-by-N matrix which is zero except for its */
|
|
/* > f2cmin(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */
|
|
/* > V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */
|
|
/* > are the singular values of A; they are real and non-negative, and */
|
|
/* > are returned in descending order. The first f2cmin(m,n) columns of */
|
|
/* > U and V are the left and right singular vectors of A. */
|
|
/* > */
|
|
/* > DGESVDX uses an eigenvalue problem for obtaining the SVD, which */
|
|
/* > allows for the computation of a subset of singular values and */
|
|
/* > vectors. See DBDSVDX for details. */
|
|
/* > */
|
|
/* > Note that the routine returns V**T, not V. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBU */
|
|
/* > \verbatim */
|
|
/* > JOBU is CHARACTER*1 */
|
|
/* > Specifies options for computing all or part of the matrix U: */
|
|
/* > = 'V': the first f2cmin(m,n) columns of U (the left singular */
|
|
/* > vectors) or as specified by RANGE are returned in */
|
|
/* > the array U; */
|
|
/* > = 'N': no columns of U (no left singular vectors) are */
|
|
/* > computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBVT */
|
|
/* > \verbatim */
|
|
/* > JOBVT is CHARACTER*1 */
|
|
/* > Specifies options for computing all or part of the matrix */
|
|
/* > V**T: */
|
|
/* > = 'V': the first f2cmin(m,n) rows of V**T (the right singular */
|
|
/* > vectors) or as specified by RANGE are returned in */
|
|
/* > the array VT; */
|
|
/* > = 'N': no rows of V**T (no right singular vectors) are */
|
|
/* > computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RANGE */
|
|
/* > \verbatim */
|
|
/* > RANGE is CHARACTER*1 */
|
|
/* > = 'A': all singular values will be found. */
|
|
/* > = 'V': all singular values in the half-open interval (VL,VU] */
|
|
/* > will be found. */
|
|
/* > = 'I': the IL-th through IU-th singular values will be found. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the input matrix A. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the input matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
|
|
/* > On entry, the M-by-N matrix A. */
|
|
/* > On exit, the contents of A are destroyed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VL */
|
|
/* > \verbatim */
|
|
/* > VL is DOUBLE PRECISION */
|
|
/* > If RANGE='V', the lower bound of the interval to */
|
|
/* > be searched for singular values. VU > VL. */
|
|
/* > Not referenced if RANGE = 'A' or 'I'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VU */
|
|
/* > \verbatim */
|
|
/* > VU is DOUBLE PRECISION */
|
|
/* > If RANGE='V', the upper bound of the interval to */
|
|
/* > be searched for singular values. VU > VL. */
|
|
/* > Not referenced if RANGE = 'A' or 'I'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IL */
|
|
/* > \verbatim */
|
|
/* > IL is INTEGER */
|
|
/* > If RANGE='I', the index of the */
|
|
/* > smallest singular value to be returned. */
|
|
/* > 1 <= IL <= IU <= f2cmin(M,N), if f2cmin(M,N) > 0. */
|
|
/* > Not referenced if RANGE = 'A' or 'V'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IU */
|
|
/* > \verbatim */
|
|
/* > IU is INTEGER */
|
|
/* > If RANGE='I', the index of the */
|
|
/* > largest singular value to be returned. */
|
|
/* > 1 <= IL <= IU <= f2cmin(M,N), if f2cmin(M,N) > 0. */
|
|
/* > Not referenced if RANGE = 'A' or 'V'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] NS */
|
|
/* > \verbatim */
|
|
/* > NS is INTEGER */
|
|
/* > The total number of singular values found, */
|
|
/* > 0 <= NS <= f2cmin(M,N). */
|
|
/* > If RANGE = 'A', NS = f2cmin(M,N); if RANGE = 'I', NS = IU-IL+1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is DOUBLE PRECISION array, dimension (f2cmin(M,N)) */
|
|
/* > The singular values of A, sorted so that S(i) >= S(i+1). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] U */
|
|
/* > \verbatim */
|
|
/* > U is DOUBLE PRECISION array, dimension (LDU,UCOL) */
|
|
/* > If JOBU = 'V', U contains columns of U (the left singular */
|
|
/* > vectors, stored columnwise) as specified by RANGE; if */
|
|
/* > JOBU = 'N', U is not referenced. */
|
|
/* > Note: The user must ensure that UCOL >= NS; if RANGE = 'V', */
|
|
/* > the exact value of NS is not known in advance and an upper */
|
|
/* > bound must be used. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU */
|
|
/* > \verbatim */
|
|
/* > LDU is INTEGER */
|
|
/* > The leading dimension of the array U. LDU >= 1; if */
|
|
/* > JOBU = 'V', LDU >= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VT */
|
|
/* > \verbatim */
|
|
/* > VT is DOUBLE PRECISION array, dimension (LDVT,N) */
|
|
/* > If JOBVT = 'V', VT contains the rows of V**T (the right singular */
|
|
/* > vectors, stored rowwise) as specified by RANGE; if JOBVT = 'N', */
|
|
/* > VT is not referenced. */
|
|
/* > Note: The user must ensure that LDVT >= NS; if RANGE = 'V', */
|
|
/* > the exact value of NS is not known in advance and an upper */
|
|
/* > bound must be used. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVT */
|
|
/* > \verbatim */
|
|
/* > LDVT is INTEGER */
|
|
/* > The leading dimension of the array VT. LDVT >= 1; if */
|
|
/* > JOBVT = 'V', LDVT >= NS (see above). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION 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. */
|
|
/* > LWORK >= MAX(1,MIN(M,N)*(MIN(M,N)+4)) for the paths (see */
|
|
/* > comments inside the code): */
|
|
/* > - PATH 1 (M much larger than N) */
|
|
/* > - PATH 1t (N much larger than M) */
|
|
/* > LWORK >= MAX(1,MIN(M,N)*2+MAX(M,N)) for the other paths. */
|
|
/* > For good performance, LWORK should generally be larger. */
|
|
/* > */
|
|
/* > 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] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (12*MIN(M,N)) */
|
|
/* > If INFO = 0, the first NS elements of IWORK are zero. If INFO > 0, */
|
|
/* > then IWORK contains the indices of the eigenvectors that failed */
|
|
/* > to converge in DBDSVDX/DSTEVX. */
|
|
/* > \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 = i, then i eigenvectors failed to converge */
|
|
/* > in DBDSVDX/DSTEVX. */
|
|
/* > if INFO = N*2 + 1, an internal error occurred in */
|
|
/* > DBDSVDX */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup doubleGEsing */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dgesvdx_(char *jobu, char *jobvt, char *range, integer *
|
|
m, integer *n, doublereal *a, integer *lda, doublereal *vl,
|
|
doublereal *vu, integer *il, integer *iu, integer *ns, doublereal *s,
|
|
doublereal *u, integer *ldu, doublereal *vt, integer *ldvt,
|
|
doublereal *work, integer *lwork, integer *iwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
address a__1[2];
|
|
integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2],
|
|
i__2, i__3;
|
|
char ch__1[2];
|
|
|
|
/* Local variables */
|
|
integer iscl;
|
|
logical alls, inds;
|
|
integer ilqf;
|
|
doublereal anrm;
|
|
integer ierr, iqrf, itau;
|
|
char jobz[1];
|
|
logical vals;
|
|
integer i__, j;
|
|
extern logical lsame_(char *, char *);
|
|
integer iltgk, itemp, minmn;
|
|
extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *);
|
|
integer itaup, itauq, iutgk, itgkz, mnthr;
|
|
logical wantu;
|
|
integer id, ie;
|
|
extern /* Subroutine */ void dgebrd_(integer *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, integer *, integer *);
|
|
extern doublereal dlamch_(char *), dlange_(char *, integer *,
|
|
integer *, doublereal *, integer *, doublereal *);
|
|
extern /* Subroutine */ void dgelqf_(integer *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, integer *, integer *),
|
|
dlascl_(char *, integer *, integer *, doublereal *, doublereal *,
|
|
integer *, integer *, doublereal *, integer *, integer *),
|
|
dgeqrf_(integer *, integer *, doublereal *, integer *,
|
|
doublereal *, doublereal *, integer *, integer *), dlacpy_(char *,
|
|
integer *, integer *, doublereal *, integer *, doublereal *,
|
|
integer *), dlaset_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, doublereal *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
doublereal bignum, abstol;
|
|
extern /* Subroutine */ void dormbr_(char *, char *, char *, integer *,
|
|
integer *, integer *, doublereal *, integer *, doublereal *,
|
|
doublereal *, integer *, doublereal *, integer *, integer *);
|
|
char rngtgk[1];
|
|
extern /* Subroutine */ void dormlq_(char *, char *, integer *, integer *,
|
|
integer *, doublereal *, integer *, doublereal *, doublereal *,
|
|
integer *, doublereal *, integer *, integer *),
|
|
dormqr_(char *, char *, integer *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, integer *, integer *);
|
|
integer minwrk, maxwrk;
|
|
doublereal smlnum;
|
|
logical lquery, wantvt;
|
|
doublereal dum[1], eps;
|
|
extern /* Subroutine */ void dbdsvdx_(char *, char *, char *, integer *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
|
|
integer *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, integer *, integer *);
|
|
|
|
|
|
/* -- LAPACK driver routine (version 3.8.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input arguments. */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--s;
|
|
u_dim1 = *ldu;
|
|
u_offset = 1 + u_dim1 * 1;
|
|
u -= u_offset;
|
|
vt_dim1 = *ldvt;
|
|
vt_offset = 1 + vt_dim1 * 1;
|
|
vt -= vt_offset;
|
|
--work;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*ns = 0;
|
|
*info = 0;
|
|
abstol = dlamch_("S") * 2;
|
|
lquery = *lwork == -1;
|
|
minmn = f2cmin(*m,*n);
|
|
wantu = lsame_(jobu, "V");
|
|
wantvt = lsame_(jobvt, "V");
|
|
if (wantu || wantvt) {
|
|
*(unsigned char *)jobz = 'V';
|
|
} else {
|
|
*(unsigned char *)jobz = 'N';
|
|
}
|
|
alls = lsame_(range, "A");
|
|
vals = lsame_(range, "V");
|
|
inds = lsame_(range, "I");
|
|
|
|
*info = 0;
|
|
if (! lsame_(jobu, "V") && ! lsame_(jobu, "N")) {
|
|
*info = -1;
|
|
} else if (! lsame_(jobvt, "V") && ! lsame_(jobvt,
|
|
"N")) {
|
|
*info = -2;
|
|
} else if (! (alls || vals || inds)) {
|
|
*info = -3;
|
|
} else if (*m < 0) {
|
|
*info = -4;
|
|
} else if (*n < 0) {
|
|
*info = -5;
|
|
} else if (*m > *lda) {
|
|
*info = -7;
|
|
} else if (minmn > 0) {
|
|
if (vals) {
|
|
if (*vl < 0.) {
|
|
*info = -8;
|
|
} else if (*vu <= *vl) {
|
|
*info = -9;
|
|
}
|
|
} else if (inds) {
|
|
if (*il < 1 || *il > f2cmax(1,minmn)) {
|
|
*info = -10;
|
|
} else if (*iu < f2cmin(minmn,*il) || *iu > minmn) {
|
|
*info = -11;
|
|
}
|
|
}
|
|
if (*info == 0) {
|
|
if (wantu && *ldu < *m) {
|
|
*info = -15;
|
|
} else if (wantvt) {
|
|
if (inds) {
|
|
if (*ldvt < *iu - *il + 1) {
|
|
*info = -17;
|
|
}
|
|
} else if (*ldvt < minmn) {
|
|
*info = -17;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Compute workspace */
|
|
/* (Note: Comments in the code beginning "Workspace:" describe the */
|
|
/* minimal amount of workspace needed at that point in the code, */
|
|
/* as well as the preferred amount for good performance. */
|
|
/* NB refers to the optimal block size for the immediately */
|
|
/* following subroutine, as returned by ILAENV.) */
|
|
|
|
if (*info == 0) {
|
|
minwrk = 1;
|
|
maxwrk = 1;
|
|
if (minmn > 0) {
|
|
if (*m >= *n) {
|
|
/* Writing concatenation */
|
|
i__1[0] = 1, a__1[0] = jobu;
|
|
i__1[1] = 1, a__1[1] = jobvt;
|
|
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
|
|
mnthr = ilaenv_(&c__6, "DGESVD", ch__1, m, n, &c__0, &c__0, (
|
|
ftnlen)6, (ftnlen)2);
|
|
if (*m >= mnthr) {
|
|
|
|
/* Path 1 (M much larger than N) */
|
|
|
|
maxwrk = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m, n, &
|
|
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = *n * (*n + 5) + (*n << 1) * ilaenv_(
|
|
&c__1, "DGEBRD", " ", n, n, &c_n1, &c_n1, (ftnlen)
|
|
6, (ftnlen)1);
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
if (wantu) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = *n * (*n * 3 + 6) + *n *
|
|
ilaenv_(&c__1, "DORMQR", " ", n, n, &c_n1, &
|
|
c_n1, (ftnlen)6, (ftnlen)1);
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
if (wantvt) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = *n * (*n * 3 + 6) + *n *
|
|
ilaenv_(&c__1, "DORMLQ", " ", n, n, &c_n1, &
|
|
c_n1, (ftnlen)6, (ftnlen)1);
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
minwrk = *n * (*n * 3 + 20);
|
|
} else {
|
|
|
|
/* Path 2 (M at least N, but not much larger) */
|
|
|
|
maxwrk = (*n << 2) + (*m + *n) * ilaenv_(&c__1, "DGEBRD",
|
|
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
|
|
if (wantu) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = *n * ((*n << 1) + 5) + *n *
|
|
ilaenv_(&c__1, "DORMQR", " ", n, n, &c_n1, &
|
|
c_n1, (ftnlen)6, (ftnlen)1);
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
if (wantvt) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = *n * ((*n << 1) + 5) + *n *
|
|
ilaenv_(&c__1, "DORMLQ", " ", n, n, &c_n1, &
|
|
c_n1, (ftnlen)6, (ftnlen)1);
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
/* Computing MAX */
|
|
i__2 = *n * ((*n << 1) + 19), i__3 = (*n << 2) + *m;
|
|
minwrk = f2cmax(i__2,i__3);
|
|
}
|
|
} else {
|
|
/* Writing concatenation */
|
|
i__1[0] = 1, a__1[0] = jobu;
|
|
i__1[1] = 1, a__1[1] = jobvt;
|
|
s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2);
|
|
mnthr = ilaenv_(&c__6, "DGESVD", ch__1, m, n, &c__0, &c__0, (
|
|
ftnlen)6, (ftnlen)2);
|
|
if (*n >= mnthr) {
|
|
|
|
/* Path 1t (N much larger than M) */
|
|
|
|
maxwrk = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &
|
|
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = *m * (*m + 5) + (*m << 1) * ilaenv_(
|
|
&c__1, "DGEBRD", " ", m, m, &c_n1, &c_n1, (ftnlen)
|
|
6, (ftnlen)1);
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
if (wantu) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = *m * (*m * 3 + 6) + *m *
|
|
ilaenv_(&c__1, "DORMQR", " ", m, m, &c_n1, &
|
|
c_n1, (ftnlen)6, (ftnlen)1);
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
if (wantvt) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = *m * (*m * 3 + 6) + *m *
|
|
ilaenv_(&c__1, "DORMLQ", " ", m, m, &c_n1, &
|
|
c_n1, (ftnlen)6, (ftnlen)1);
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
minwrk = *m * (*m * 3 + 20);
|
|
} else {
|
|
|
|
/* Path 2t (N at least M, but not much larger) */
|
|
|
|
maxwrk = (*m << 2) + (*m + *n) * ilaenv_(&c__1, "DGEBRD",
|
|
" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
|
|
if (wantu) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = *m * ((*m << 1) + 5) + *m *
|
|
ilaenv_(&c__1, "DORMQR", " ", m, m, &c_n1, &
|
|
c_n1, (ftnlen)6, (ftnlen)1);
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
if (wantvt) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = *m * ((*m << 1) + 5) + *m *
|
|
ilaenv_(&c__1, "DORMLQ", " ", m, m, &c_n1, &
|
|
c_n1, (ftnlen)6, (ftnlen)1);
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
/* Computing MAX */
|
|
i__2 = *m * ((*m << 1) + 19), i__3 = (*m << 2) + *n;
|
|
minwrk = f2cmax(i__2,i__3);
|
|
}
|
|
}
|
|
}
|
|
maxwrk = f2cmax(maxwrk,minwrk);
|
|
work[1] = (doublereal) maxwrk;
|
|
|
|
if (*lwork < minwrk && ! lquery) {
|
|
*info = -19;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__2 = -(*info);
|
|
xerbla_("DGESVDX", &i__2, (ftnlen)7);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*m == 0 || *n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Set singular values indices accord to RANGE. */
|
|
|
|
if (alls) {
|
|
*(unsigned char *)rngtgk = 'I';
|
|
iltgk = 1;
|
|
iutgk = f2cmin(*m,*n);
|
|
} else if (inds) {
|
|
*(unsigned char *)rngtgk = 'I';
|
|
iltgk = *il;
|
|
iutgk = *iu;
|
|
} else {
|
|
*(unsigned char *)rngtgk = 'V';
|
|
iltgk = 0;
|
|
iutgk = 0;
|
|
}
|
|
|
|
/* Get machine constants */
|
|
|
|
eps = dlamch_("P");
|
|
smlnum = sqrt(dlamch_("S")) / eps;
|
|
bignum = 1. / smlnum;
|
|
|
|
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
|
|
|
|
anrm = dlange_("M", m, n, &a[a_offset], lda, dum);
|
|
iscl = 0;
|
|
if (anrm > 0. && anrm < smlnum) {
|
|
iscl = 1;
|
|
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
|
|
info);
|
|
} else if (anrm > bignum) {
|
|
iscl = 1;
|
|
dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
|
|
info);
|
|
}
|
|
|
|
if (*m >= *n) {
|
|
|
|
/* A has at least as many rows as columns. If A has sufficiently */
|
|
/* more rows than columns, first reduce A using the QR */
|
|
/* decomposition. */
|
|
|
|
if (*m >= mnthr) {
|
|
|
|
/* Path 1 (M much larger than N): */
|
|
/* A = Q * R = Q * ( QB * B * PB**T ) */
|
|
/* = Q * ( QB * ( UB * S * VB**T ) * PB**T ) */
|
|
/* U = Q * QB * UB; V**T = VB**T * PB**T */
|
|
|
|
/* Compute A=Q*R */
|
|
/* (Workspace: need 2*N, prefer N+N*NB) */
|
|
|
|
itau = 1;
|
|
itemp = itau + *n;
|
|
i__2 = *lwork - itemp + 1;
|
|
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[itemp], &i__2,
|
|
info);
|
|
|
|
/* Copy R into WORK and bidiagonalize it: */
|
|
/* (Workspace: need N*N+5*N, prefer N*N+4*N+2*N*NB) */
|
|
|
|
iqrf = itemp;
|
|
id = iqrf + *n * *n;
|
|
ie = id + *n;
|
|
itauq = ie + *n;
|
|
itaup = itauq + *n;
|
|
itemp = itaup + *n;
|
|
dlacpy_("U", n, n, &a[a_offset], lda, &work[iqrf], n);
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
dlaset_("L", &i__2, &i__3, &c_b109, &c_b109, &work[iqrf + 1], n);
|
|
i__2 = *lwork - itemp + 1;
|
|
dgebrd_(n, n, &work[iqrf], n, &work[id], &work[ie], &work[itauq],
|
|
&work[itaup], &work[itemp], &i__2, info);
|
|
|
|
/* Solve eigenvalue problem TGK*Z=Z*S. */
|
|
/* (Workspace: need 14*N + 2*N*(N+1)) */
|
|
|
|
itgkz = itemp;
|
|
itemp = itgkz + *n * ((*n << 1) + 1);
|
|
i__2 = *n << 1;
|
|
dbdsvdx_("U", jobz, rngtgk, n, &work[id], &work[ie], vl, vu, &
|
|
iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[
|
|
itemp], &iwork[1], info);
|
|
|
|
/* If needed, compute left singular vectors. */
|
|
|
|
if (wantu) {
|
|
j = itgkz;
|
|
i__2 = *ns;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
dcopy_(n, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1);
|
|
j += *n << 1;
|
|
}
|
|
i__2 = *m - *n;
|
|
dlaset_("A", &i__2, ns, &c_b109, &c_b109, &u[*n + 1 + u_dim1],
|
|
ldu);
|
|
|
|
/* Call DORMBR to compute QB*UB. */
|
|
/* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */
|
|
|
|
i__2 = *lwork - itemp + 1;
|
|
dormbr_("Q", "L", "N", n, ns, n, &work[iqrf], n, &work[itauq],
|
|
&u[u_offset], ldu, &work[itemp], &i__2, info);
|
|
|
|
/* Call DORMQR to compute Q*(QB*UB). */
|
|
/* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */
|
|
|
|
i__2 = *lwork - itemp + 1;
|
|
dormqr_("L", "N", m, ns, n, &a[a_offset], lda, &work[itau], &
|
|
u[u_offset], ldu, &work[itemp], &i__2, info);
|
|
}
|
|
|
|
/* If needed, compute right singular vectors. */
|
|
|
|
if (wantvt) {
|
|
j = itgkz + *n;
|
|
i__2 = *ns;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
dcopy_(n, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt);
|
|
j += *n << 1;
|
|
}
|
|
|
|
/* Call DORMBR to compute VB**T * PB**T */
|
|
/* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */
|
|
|
|
i__2 = *lwork - itemp + 1;
|
|
dormbr_("P", "R", "T", ns, n, n, &work[iqrf], n, &work[itaup],
|
|
&vt[vt_offset], ldvt, &work[itemp], &i__2, info);
|
|
}
|
|
} else {
|
|
|
|
/* Path 2 (M at least N, but not much larger) */
|
|
/* Reduce A to bidiagonal form without QR decomposition */
|
|
/* A = QB * B * PB**T = QB * ( UB * S * VB**T ) * PB**T */
|
|
/* U = QB * UB; V**T = VB**T * PB**T */
|
|
|
|
/* Bidiagonalize A */
|
|
/* (Workspace: need 4*N+M, prefer 4*N+(M+N)*NB) */
|
|
|
|
id = 1;
|
|
ie = id + *n;
|
|
itauq = ie + *n;
|
|
itaup = itauq + *n;
|
|
itemp = itaup + *n;
|
|
i__2 = *lwork - itemp + 1;
|
|
dgebrd_(m, n, &a[a_offset], lda, &work[id], &work[ie], &work[
|
|
itauq], &work[itaup], &work[itemp], &i__2, info);
|
|
|
|
/* Solve eigenvalue problem TGK*Z=Z*S. */
|
|
/* (Workspace: need 14*N + 2*N*(N+1)) */
|
|
|
|
itgkz = itemp;
|
|
itemp = itgkz + *n * ((*n << 1) + 1);
|
|
i__2 = *n << 1;
|
|
dbdsvdx_("U", jobz, rngtgk, n, &work[id], &work[ie], vl, vu, &
|
|
iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[
|
|
itemp], &iwork[1], info);
|
|
|
|
/* If needed, compute left singular vectors. */
|
|
|
|
if (wantu) {
|
|
j = itgkz;
|
|
i__2 = *ns;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
dcopy_(n, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1);
|
|
j += *n << 1;
|
|
}
|
|
i__2 = *m - *n;
|
|
dlaset_("A", &i__2, ns, &c_b109, &c_b109, &u[*n + 1 + u_dim1],
|
|
ldu);
|
|
|
|
/* Call DORMBR to compute QB*UB. */
|
|
/* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */
|
|
|
|
i__2 = *lwork - itemp + 1;
|
|
dormbr_("Q", "L", "N", m, ns, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[itemp], &i__2, &ierr);
|
|
}
|
|
|
|
/* If needed, compute right singular vectors. */
|
|
|
|
if (wantvt) {
|
|
j = itgkz + *n;
|
|
i__2 = *ns;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
dcopy_(n, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt);
|
|
j += *n << 1;
|
|
}
|
|
|
|
/* Call DORMBR to compute VB**T * PB**T */
|
|
/* (Workspace in WORK( ITEMP ): need N, prefer N*NB) */
|
|
|
|
i__2 = *lwork - itemp + 1;
|
|
dormbr_("P", "R", "T", ns, n, n, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[itemp], &i__2, &
|
|
ierr);
|
|
}
|
|
}
|
|
} else {
|
|
|
|
/* A has more columns than rows. If A has sufficiently more */
|
|
/* columns than rows, first reduce A using the LQ decomposition. */
|
|
|
|
if (*n >= mnthr) {
|
|
|
|
/* Path 1t (N much larger than M): */
|
|
/* A = L * Q = ( QB * B * PB**T ) * Q */
|
|
/* = ( QB * ( UB * S * VB**T ) * PB**T ) * Q */
|
|
/* U = QB * UB ; V**T = VB**T * PB**T * Q */
|
|
|
|
/* Compute A=L*Q */
|
|
/* (Workspace: need 2*M, prefer M+M*NB) */
|
|
|
|
itau = 1;
|
|
itemp = itau + *m;
|
|
i__2 = *lwork - itemp + 1;
|
|
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[itemp], &i__2,
|
|
info);
|
|
/* Copy L into WORK and bidiagonalize it: */
|
|
/* (Workspace in WORK( ITEMP ): need M*M+5*N, prefer M*M+4*M+2*M*NB) */
|
|
|
|
ilqf = itemp;
|
|
id = ilqf + *m * *m;
|
|
ie = id + *m;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
itemp = itaup + *m;
|
|
dlacpy_("L", m, m, &a[a_offset], lda, &work[ilqf], m);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
dlaset_("U", &i__2, &i__3, &c_b109, &c_b109, &work[ilqf + *m], m);
|
|
i__2 = *lwork - itemp + 1;
|
|
dgebrd_(m, m, &work[ilqf], m, &work[id], &work[ie], &work[itauq],
|
|
&work[itaup], &work[itemp], &i__2, info);
|
|
|
|
/* Solve eigenvalue problem TGK*Z=Z*S. */
|
|
/* (Workspace: need 2*M*M+14*M) */
|
|
|
|
itgkz = itemp;
|
|
itemp = itgkz + *m * ((*m << 1) + 1);
|
|
i__2 = *m << 1;
|
|
dbdsvdx_("U", jobz, rngtgk, m, &work[id], &work[ie], vl, vu, &
|
|
iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[
|
|
itemp], &iwork[1], info);
|
|
|
|
/* If needed, compute left singular vectors. */
|
|
|
|
if (wantu) {
|
|
j = itgkz;
|
|
i__2 = *ns;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
dcopy_(m, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1);
|
|
j += *m << 1;
|
|
}
|
|
|
|
/* Call DORMBR to compute QB*UB. */
|
|
/* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */
|
|
|
|
i__2 = *lwork - itemp + 1;
|
|
dormbr_("Q", "L", "N", m, ns, m, &work[ilqf], m, &work[itauq],
|
|
&u[u_offset], ldu, &work[itemp], &i__2, info);
|
|
}
|
|
|
|
/* If needed, compute right singular vectors. */
|
|
|
|
if (wantvt) {
|
|
j = itgkz + *m;
|
|
i__2 = *ns;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
dcopy_(m, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt);
|
|
j += *m << 1;
|
|
}
|
|
i__2 = *n - *m;
|
|
dlaset_("A", ns, &i__2, &c_b109, &c_b109, &vt[(*m + 1) *
|
|
vt_dim1 + 1], ldvt);
|
|
|
|
/* Call DORMBR to compute (VB**T)*(PB**T) */
|
|
/* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */
|
|
|
|
i__2 = *lwork - itemp + 1;
|
|
dormbr_("P", "R", "T", ns, m, m, &work[ilqf], m, &work[itaup],
|
|
&vt[vt_offset], ldvt, &work[itemp], &i__2, info);
|
|
|
|
/* Call DORMLQ to compute ((VB**T)*(PB**T))*Q. */
|
|
/* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */
|
|
|
|
i__2 = *lwork - itemp + 1;
|
|
dormlq_("R", "N", ns, n, m, &a[a_offset], lda, &work[itau], &
|
|
vt[vt_offset], ldvt, &work[itemp], &i__2, info);
|
|
}
|
|
} else {
|
|
|
|
/* Path 2t (N greater than M, but not much larger) */
|
|
/* Reduce to bidiagonal form without LQ decomposition */
|
|
/* A = QB * B * PB**T = QB * ( UB * S * VB**T ) * PB**T */
|
|
/* U = QB * UB; V**T = VB**T * PB**T */
|
|
|
|
/* Bidiagonalize A */
|
|
/* (Workspace: need 4*M+N, prefer 4*M+(M+N)*NB) */
|
|
|
|
id = 1;
|
|
ie = id + *m;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
itemp = itaup + *m;
|
|
i__2 = *lwork - itemp + 1;
|
|
dgebrd_(m, n, &a[a_offset], lda, &work[id], &work[ie], &work[
|
|
itauq], &work[itaup], &work[itemp], &i__2, info);
|
|
|
|
/* Solve eigenvalue problem TGK*Z=Z*S. */
|
|
/* (Workspace: need 2*M*M+14*M) */
|
|
|
|
itgkz = itemp;
|
|
itemp = itgkz + *m * ((*m << 1) + 1);
|
|
i__2 = *m << 1;
|
|
dbdsvdx_("L", jobz, rngtgk, m, &work[id], &work[ie], vl, vu, &
|
|
iltgk, &iutgk, ns, &s[1], &work[itgkz], &i__2, &work[
|
|
itemp], &iwork[1], info);
|
|
|
|
/* If needed, compute left singular vectors. */
|
|
|
|
if (wantu) {
|
|
j = itgkz;
|
|
i__2 = *ns;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
dcopy_(m, &work[j], &c__1, &u[i__ * u_dim1 + 1], &c__1);
|
|
j += *m << 1;
|
|
}
|
|
|
|
/* Call DORMBR to compute QB*UB. */
|
|
/* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */
|
|
|
|
i__2 = *lwork - itemp + 1;
|
|
dormbr_("Q", "L", "N", m, ns, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[itemp], &i__2, info);
|
|
}
|
|
|
|
/* If needed, compute right singular vectors. */
|
|
|
|
if (wantvt) {
|
|
j = itgkz + *m;
|
|
i__2 = *ns;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
dcopy_(m, &work[j], &c__1, &vt[i__ + vt_dim1], ldvt);
|
|
j += *m << 1;
|
|
}
|
|
i__2 = *n - *m;
|
|
dlaset_("A", ns, &i__2, &c_b109, &c_b109, &vt[(*m + 1) *
|
|
vt_dim1 + 1], ldvt);
|
|
|
|
/* Call DORMBR to compute VB**T * PB**T */
|
|
/* (Workspace in WORK( ITEMP ): need M, prefer M*NB) */
|
|
|
|
i__2 = *lwork - itemp + 1;
|
|
dormbr_("P", "R", "T", ns, n, m, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[itemp], &i__2,
|
|
info);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Undo scaling if necessary */
|
|
|
|
if (iscl == 1) {
|
|
if (anrm > bignum) {
|
|
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, info);
|
|
}
|
|
if (anrm < smlnum) {
|
|
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, info);
|
|
}
|
|
}
|
|
|
|
/* Return optimal workspace in WORK(1) */
|
|
|
|
work[1] = (doublereal) maxwrk;
|
|
|
|
return;
|
|
|
|
/* End of DGESVDX */
|
|
|
|
} /* dgesvdx_ */
|
|
|