4728 lines
146 KiB
C
4728 lines
146 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 complex c_b1 = {0.f,0.f};
|
|
static complex c_b2 = {1.f,0.f};
|
|
static integer c__6 = 6;
|
|
static integer c__0 = 0;
|
|
static integer c__2 = 2;
|
|
static integer c_n1 = -1;
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief <b> CGESVD 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 CGESVD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgesvd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgesvd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgesvd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, */
|
|
/* WORK, LWORK, RWORK, INFO ) */
|
|
|
|
/* CHARACTER JOBU, JOBVT */
|
|
/* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
|
|
/* REAL RWORK( * ), S( * ) */
|
|
/* COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ), */
|
|
/* $ WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CGESVD computes the singular value decomposition (SVD) of a complex */
|
|
/* > M-by-N matrix A, optionally computing the left and/or right singular */
|
|
/* > vectors. The SVD is written */
|
|
/* > */
|
|
/* > A = U * SIGMA * conjugate-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 unitary matrix, and */
|
|
/* > V is an N-by-N unitary 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. */
|
|
/* > */
|
|
/* > Note that the routine returns V**H, not V. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBU */
|
|
/* > \verbatim */
|
|
/* > JOBU is CHARACTER*1 */
|
|
/* > Specifies options for computing all or part of the matrix U: */
|
|
/* > = 'A': all M columns of U are returned in array U: */
|
|
/* > = 'S': the first f2cmin(m,n) columns of U (the left singular */
|
|
/* > vectors) are returned in the array U; */
|
|
/* > = 'O': the first f2cmin(m,n) columns of U (the left singular */
|
|
/* > vectors) are overwritten on the array A; */
|
|
/* > = '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**H: */
|
|
/* > = 'A': all N rows of V**H are returned in the array VT; */
|
|
/* > = 'S': the first f2cmin(m,n) rows of V**H (the right singular */
|
|
/* > vectors) are returned in the array VT; */
|
|
/* > = 'O': the first f2cmin(m,n) rows of V**H (the right singular */
|
|
/* > vectors) are overwritten on the array A; */
|
|
/* > = 'N': no rows of V**H (no right singular vectors) are */
|
|
/* > computed. */
|
|
/* > */
|
|
/* > JOBVT and JOBU cannot both be 'O'. */
|
|
/* > \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 COMPLEX array, dimension (LDA,N) */
|
|
/* > On entry, the M-by-N matrix A. */
|
|
/* > On exit, */
|
|
/* > if JOBU = 'O', A is overwritten with the first f2cmin(m,n) */
|
|
/* > columns of U (the left singular vectors, */
|
|
/* > stored columnwise); */
|
|
/* > if JOBVT = 'O', A is overwritten with the first f2cmin(m,n) */
|
|
/* > rows of V**H (the right singular vectors, */
|
|
/* > stored rowwise); */
|
|
/* > if JOBU .ne. 'O' and JOBVT .ne. 'O', 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[out] S */
|
|
/* > \verbatim */
|
|
/* > S is REAL 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 COMPLEX array, dimension (LDU,UCOL) */
|
|
/* > (LDU,M) if JOBU = 'A' or (LDU,f2cmin(M,N)) if JOBU = 'S'. */
|
|
/* > If JOBU = 'A', U contains the M-by-M unitary matrix U; */
|
|
/* > if JOBU = 'S', U contains the first f2cmin(m,n) columns of U */
|
|
/* > (the left singular vectors, stored columnwise); */
|
|
/* > if JOBU = 'N' or 'O', U is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU */
|
|
/* > \verbatim */
|
|
/* > LDU is INTEGER */
|
|
/* > The leading dimension of the array U. LDU >= 1; if */
|
|
/* > JOBU = 'S' or 'A', LDU >= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VT */
|
|
/* > \verbatim */
|
|
/* > VT is COMPLEX array, dimension (LDVT,N) */
|
|
/* > If JOBVT = 'A', VT contains the N-by-N unitary matrix */
|
|
/* > V**H; */
|
|
/* > if JOBVT = 'S', VT contains the first f2cmin(m,n) rows of */
|
|
/* > V**H (the right singular vectors, stored rowwise); */
|
|
/* > if JOBVT = 'N' or 'O', VT is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVT */
|
|
/* > \verbatim */
|
|
/* > LDVT is INTEGER */
|
|
/* > The leading dimension of the array VT. LDVT >= 1; if */
|
|
/* > JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= f2cmin(M,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. */
|
|
/* > LWORK >= MAX(1,2*MIN(M,N)+MAX(M,N)). */
|
|
/* > 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] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is REAL array, dimension (5*f2cmin(M,N)) */
|
|
/* > On exit, if INFO > 0, RWORK(1:MIN(M,N)-1) contains the */
|
|
/* > unconverged superdiagonal elements of an upper bidiagonal */
|
|
/* > matrix B whose diagonal is in S (not necessarily sorted). */
|
|
/* > B satisfies A = U * B * VT, so it has the same singular */
|
|
/* > values as A, and singular vectors related by U and VT. */
|
|
/* > \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 CBDSQR did not converge, INFO specifies how many */
|
|
/* > superdiagonals of an intermediate bidiagonal form B */
|
|
/* > did not converge to zero. See the description of RWORK */
|
|
/* > above for details. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date April 2012 */
|
|
|
|
/* > \ingroup complexGEsing */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void cgesvd_(char *jobu, char *jobvt, integer *m, integer *n,
|
|
complex *a, integer *lda, real *s, complex *u, integer *ldu, complex *
|
|
vt, integer *ldvt, complex *work, integer *lwork, real *rwork,
|
|
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, i__4;
|
|
char ch__1[2];
|
|
|
|
/* Local variables */
|
|
complex cdum[1];
|
|
integer iscl;
|
|
real anrm;
|
|
integer ierr, itau, ncvt, nrvt, lwork_cgebrd__, lwork_cgelqf__,
|
|
lwork_cgeqrf__, i__;
|
|
extern /* Subroutine */ void cgemm_(char *, char *, integer *, integer *,
|
|
integer *, complex *, complex *, integer *, complex *, integer *,
|
|
complex *, complex *, integer *);
|
|
extern logical lsame_(char *, char *);
|
|
integer chunk, minmn, wrkbl, itaup, itauq, mnthr, iwork;
|
|
logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs;
|
|
integer ie;
|
|
extern /* Subroutine */ void cgebrd_(integer *, integer *, complex *,
|
|
integer *, real *, real *, complex *, complex *, complex *,
|
|
integer *, integer *);
|
|
extern real clange_(char *, integer *, integer *, complex *, integer *,
|
|
real *);
|
|
integer ir, iu;
|
|
extern /* Subroutine */ void cgelqf_(integer *, integer *, complex *,
|
|
integer *, complex *, complex *, integer *, integer *), clascl_(
|
|
char *, integer *, integer *, real *, real *, integer *, integer *
|
|
, complex *, integer *, integer *), cgeqrf_(integer *,
|
|
integer *, complex *, integer *, complex *, complex *, integer *,
|
|
integer *);
|
|
extern real slamch_(char *);
|
|
extern /* Subroutine */ void clacpy_(char *, integer *, integer *, complex
|
|
*, integer *, complex *, integer *), claset_(char *,
|
|
integer *, integer *, complex *, complex *, complex *, integer *), cbdsqr_(char *, integer *, integer *, integer *, integer
|
|
*, real *, real *, complex *, integer *, complex *, integer *,
|
|
complex *, integer *, real *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
extern void cungbr_(char *, integer *, integer *, integer
|
|
*, complex *, integer *, complex *, complex *, integer *, integer
|
|
*);
|
|
real bignum;
|
|
extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *,
|
|
real *, integer *, integer *, real *, integer *, integer *);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern /* Subroutine */ void cunmbr_(char *, char *, char *, integer *,
|
|
integer *, integer *, complex *, integer *, complex *, complex *,
|
|
integer *, complex *, integer *, integer *), cunglq_(integer *, integer *, integer *, complex *,
|
|
integer *, complex *, complex *, integer *, integer *), cungqr_(
|
|
integer *, integer *, integer *, complex *, integer *, complex *,
|
|
complex *, integer *, integer *);
|
|
integer ldwrkr, minwrk, ldwrku, maxwrk;
|
|
real smlnum;
|
|
integer irwork;
|
|
logical lquery, wntuas, wntvas;
|
|
integer lwork_cungbr_p__, lwork_cungbr_q__, lwork_cunglq_n__,
|
|
lwork_cunglq_m__, lwork_cungqr_m__, lwork_cungqr_n__, blk, ncu;
|
|
real dum[1], eps;
|
|
integer nru;
|
|
|
|
|
|
/* -- LAPACK driver 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..-- */
|
|
/* April 2012 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* 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;
|
|
--rwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
minmn = f2cmin(*m,*n);
|
|
wntua = lsame_(jobu, "A");
|
|
wntus = lsame_(jobu, "S");
|
|
wntuas = wntua || wntus;
|
|
wntuo = lsame_(jobu, "O");
|
|
wntun = lsame_(jobu, "N");
|
|
wntva = lsame_(jobvt, "A");
|
|
wntvs = lsame_(jobvt, "S");
|
|
wntvas = wntva || wntvs;
|
|
wntvo = lsame_(jobvt, "O");
|
|
wntvn = lsame_(jobvt, "N");
|
|
lquery = *lwork == -1;
|
|
|
|
if (! (wntua || wntus || wntuo || wntun)) {
|
|
*info = -1;
|
|
} else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) {
|
|
*info = -2;
|
|
} else if (*m < 0) {
|
|
*info = -3;
|
|
} else if (*n < 0) {
|
|
*info = -4;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -6;
|
|
} else if (*ldu < 1 || wntuas && *ldu < *m) {
|
|
*info = -9;
|
|
} else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) {
|
|
*info = -11;
|
|
}
|
|
|
|
/* 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. */
|
|
/* CWorkspace refers to complex workspace, and RWorkspace to */
|
|
/* real workspace. NB refers to the optimal block size for the */
|
|
/* immediately following subroutine, as returned by ILAENV.) */
|
|
|
|
if (*info == 0) {
|
|
minwrk = 1;
|
|
maxwrk = 1;
|
|
if (*m >= *n && minmn > 0) {
|
|
|
|
/* Space needed for ZBDSQR is BDSPAC = 5*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, "CGESVD", ch__1, m, n, &c__0, &c__0, (
|
|
ftnlen)6, (ftnlen)2);
|
|
/* Compute space needed for CGEQRF */
|
|
cgeqrf_(m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
|
|
lwork_cgeqrf__ = (integer) cdum[0].r;
|
|
/* Compute space needed for CUNGQR */
|
|
cungqr_(m, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
|
|
lwork_cungqr_n__ = (integer) cdum[0].r;
|
|
cungqr_(m, m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
|
|
lwork_cungqr_m__ = (integer) cdum[0].r;
|
|
/* Compute space needed for CGEBRD */
|
|
cgebrd_(n, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_cgebrd__ = (integer) cdum[0].r;
|
|
/* Compute space needed for CUNGBR */
|
|
cungbr_("P", n, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
|
|
lwork_cungbr_p__ = (integer) cdum[0].r;
|
|
cungbr_("Q", n, n, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
|
|
lwork_cungbr_q__ = (integer) cdum[0].r;
|
|
|
|
/* 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, "CGESVD", ch__1, m, n, &c__0, &c__0, (
|
|
ftnlen)6, (ftnlen)2);
|
|
if (*m >= mnthr) {
|
|
if (wntun) {
|
|
|
|
/* Path 1 (M much larger than N, JOBU='N') */
|
|
|
|
maxwrk = *n + lwork_cgeqrf__;
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = (*n << 1) + lwork_cgebrd__;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
if (wntvo || wntvas) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_p__;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
minwrk = *n * 3;
|
|
} else if (wntuo && wntvn) {
|
|
|
|
/* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
|
|
|
|
wrkbl = *n + lwork_cgeqrf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
minwrk = (*n << 1) + *m;
|
|
} else if (wntuo && wntvas) {
|
|
|
|
/* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */
|
|
/* 'A') */
|
|
|
|
wrkbl = *n + lwork_cgeqrf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
minwrk = (*n << 1) + *m;
|
|
} else if (wntus && wntvn) {
|
|
|
|
/* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
|
|
|
|
wrkbl = *n + lwork_cgeqrf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = *n * *n + wrkbl;
|
|
minwrk = (*n << 1) + *m;
|
|
} else if (wntus && wntvo) {
|
|
|
|
/* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
|
|
|
|
wrkbl = *n + lwork_cgeqrf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = (*n << 1) * *n + wrkbl;
|
|
minwrk = (*n << 1) + *m;
|
|
} else if (wntus && wntvas) {
|
|
|
|
/* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or */
|
|
/* 'A') */
|
|
|
|
wrkbl = *n + lwork_cgeqrf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *n + lwork_cungqr_n__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = *n * *n + wrkbl;
|
|
minwrk = (*n << 1) + *m;
|
|
} else if (wntua && wntvn) {
|
|
|
|
/* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
|
|
|
|
wrkbl = *n + lwork_cgeqrf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *n + lwork_cungqr_m__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = *n * *n + wrkbl;
|
|
minwrk = (*n << 1) + *m;
|
|
} else if (wntua && wntvo) {
|
|
|
|
/* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
|
|
|
|
wrkbl = *n + lwork_cgeqrf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *n + lwork_cungqr_m__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = (*n << 1) * *n + wrkbl;
|
|
minwrk = (*n << 1) + *m;
|
|
} else if (wntua && wntvas) {
|
|
|
|
/* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or */
|
|
/* 'A') */
|
|
|
|
wrkbl = *n + lwork_cgeqrf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *n + lwork_cungqr_m__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*n << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = *n * *n + wrkbl;
|
|
minwrk = (*n << 1) + *m;
|
|
}
|
|
} else {
|
|
|
|
/* Path 10 (M at least N, but not much larger) */
|
|
|
|
cgebrd_(m, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum,
|
|
&c_n1, &ierr);
|
|
lwork_cgebrd__ = (integer) cdum[0].r;
|
|
maxwrk = (*n << 1) + lwork_cgebrd__;
|
|
if (wntus || wntuo) {
|
|
cungbr_("Q", m, n, n, &a[a_offset], lda, cdum, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_cungbr_q__ = (integer) cdum[0].r;
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_q__;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
if (wntua) {
|
|
cungbr_("Q", m, m, n, &a[a_offset], lda, cdum, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_cungbr_q__ = (integer) cdum[0].r;
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_q__;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
if (! wntvn) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = (*n << 1) + lwork_cungbr_p__;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
minwrk = (*n << 1) + *m;
|
|
}
|
|
} else if (minmn > 0) {
|
|
|
|
/* Space needed for CBDSQR is BDSPAC = 5*M */
|
|
|
|
/* 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, "CGESVD", ch__1, m, n, &c__0, &c__0, (
|
|
ftnlen)6, (ftnlen)2);
|
|
/* Compute space needed for CGELQF */
|
|
cgelqf_(m, n, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
|
|
lwork_cgelqf__ = (integer) cdum[0].r;
|
|
/* Compute space needed for CUNGLQ */
|
|
cunglq_(n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
|
|
lwork_cunglq_n__ = (integer) cdum[0].r;
|
|
cunglq_(m, n, m, &a[a_offset], lda, cdum, cdum, &c_n1, &ierr);
|
|
lwork_cunglq_m__ = (integer) cdum[0].r;
|
|
/* Compute space needed for CGEBRD */
|
|
cgebrd_(m, m, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_cgebrd__ = (integer) cdum[0].r;
|
|
/* Compute space needed for CUNGBR P */
|
|
cungbr_("P", m, m, m, &a[a_offset], n, cdum, cdum, &c_n1, &ierr);
|
|
lwork_cungbr_p__ = (integer) cdum[0].r;
|
|
/* Compute space needed for CUNGBR Q */
|
|
cungbr_("Q", m, m, m, &a[a_offset], n, cdum, cdum, &c_n1, &ierr);
|
|
lwork_cungbr_q__ = (integer) cdum[0].r;
|
|
if (*n >= mnthr) {
|
|
if (wntvn) {
|
|
|
|
/* Path 1t(N much larger than M, JOBVT='N') */
|
|
|
|
maxwrk = *m + lwork_cgelqf__;
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = (*m << 1) + lwork_cgebrd__;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
if (wntuo || wntuas) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_q__;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
minwrk = *m * 3;
|
|
} else if (wntvo && wntun) {
|
|
|
|
/* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
|
|
|
|
wrkbl = *m + lwork_cgelqf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
minwrk = (*m << 1) + *n;
|
|
} else if (wntvo && wntuas) {
|
|
|
|
/* Path 3t(N much larger than M, JOBU='S' or 'A', */
|
|
/* JOBVT='O') */
|
|
|
|
wrkbl = *m + lwork_cgelqf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
minwrk = (*m << 1) + *n;
|
|
} else if (wntvs && wntun) {
|
|
|
|
/* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
|
|
|
|
wrkbl = *m + lwork_cgelqf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = *m * *m + wrkbl;
|
|
minwrk = (*m << 1) + *n;
|
|
} else if (wntvs && wntuo) {
|
|
|
|
/* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
|
|
|
|
wrkbl = *m + lwork_cgelqf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = (*m << 1) * *m + wrkbl;
|
|
minwrk = (*m << 1) + *n;
|
|
} else if (wntvs && wntuas) {
|
|
|
|
/* Path 6t(N much larger than M, JOBU='S' or 'A', */
|
|
/* JOBVT='S') */
|
|
|
|
wrkbl = *m + lwork_cgelqf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *m + lwork_cunglq_m__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = *m * *m + wrkbl;
|
|
minwrk = (*m << 1) + *n;
|
|
} else if (wntva && wntun) {
|
|
|
|
/* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
|
|
|
|
wrkbl = *m + lwork_cgelqf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *m + lwork_cunglq_n__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = *m * *m + wrkbl;
|
|
minwrk = (*m << 1) + *n;
|
|
} else if (wntva && wntuo) {
|
|
|
|
/* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
|
|
|
|
wrkbl = *m + lwork_cgelqf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *m + lwork_cunglq_n__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = (*m << 1) * *m + wrkbl;
|
|
minwrk = (*m << 1) + *n;
|
|
} else if (wntva && wntuas) {
|
|
|
|
/* Path 9t(N much larger than M, JOBU='S' or 'A', */
|
|
/* JOBVT='A') */
|
|
|
|
wrkbl = *m + lwork_cgelqf__;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *m + lwork_cunglq_n__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cgebrd__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_p__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = (*m << 1) + lwork_cungbr_q__;
|
|
wrkbl = f2cmax(i__2,i__3);
|
|
maxwrk = *m * *m + wrkbl;
|
|
minwrk = (*m << 1) + *n;
|
|
}
|
|
} else {
|
|
|
|
/* Path 10t(N greater than M, but not much larger) */
|
|
|
|
cgebrd_(m, n, &a[a_offset], lda, &s[1], dum, cdum, cdum, cdum,
|
|
&c_n1, &ierr);
|
|
lwork_cgebrd__ = (integer) cdum[0].r;
|
|
maxwrk = (*m << 1) + lwork_cgebrd__;
|
|
if (wntvs || wntvo) {
|
|
/* Compute space needed for CUNGBR P */
|
|
cungbr_("P", m, n, m, &a[a_offset], n, cdum, cdum, &c_n1,
|
|
&ierr);
|
|
lwork_cungbr_p__ = (integer) cdum[0].r;
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_p__;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
if (wntva) {
|
|
cungbr_("P", n, n, m, &a[a_offset], n, cdum, cdum, &c_n1,
|
|
&ierr);
|
|
lwork_cungbr_p__ = (integer) cdum[0].r;
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_p__;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
if (! wntun) {
|
|
/* Computing MAX */
|
|
i__2 = maxwrk, i__3 = (*m << 1) + lwork_cungbr_q__;
|
|
maxwrk = f2cmax(i__2,i__3);
|
|
}
|
|
minwrk = (*m << 1) + *n;
|
|
}
|
|
}
|
|
maxwrk = f2cmax(minwrk,maxwrk);
|
|
work[1].r = (real) maxwrk, work[1].i = 0.f;
|
|
|
|
if (*lwork < minwrk && ! lquery) {
|
|
*info = -13;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__2 = -(*info);
|
|
xerbla_("CGESVD", &i__2, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*m == 0 || *n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Get machine constants */
|
|
|
|
eps = slamch_("P");
|
|
smlnum = sqrt(slamch_("S")) / eps;
|
|
bignum = 1.f / smlnum;
|
|
|
|
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
|
|
|
|
anrm = clange_("M", m, n, &a[a_offset], lda, dum);
|
|
iscl = 0;
|
|
if (anrm > 0.f && anrm < smlnum) {
|
|
iscl = 1;
|
|
clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
|
|
ierr);
|
|
} else if (anrm > bignum) {
|
|
iscl = 1;
|
|
clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &
|
|
ierr);
|
|
}
|
|
|
|
if (*m >= *n) {
|
|
|
|
/* A has at least as many rows as columns. If A has sufficiently */
|
|
/* more rows than columns, first reduce using the QR */
|
|
/* decomposition (if sufficient workspace available) */
|
|
|
|
if (*m >= mnthr) {
|
|
|
|
if (wntun) {
|
|
|
|
/* Path 1 (M much larger than N, JOBU='N') */
|
|
/* No left singular vectors to be computed */
|
|
|
|
itau = 1;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: need 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Zero out below R */
|
|
|
|
if (*n > 1) {
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[a_dim1 + 2],
|
|
lda);
|
|
}
|
|
ie = 1;
|
|
itauq = 1;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
|
|
ncvt = 0;
|
|
if (wntvo || wntvas) {
|
|
|
|
/* If right singular vectors desired, generate P'. */
|
|
/* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &
|
|
work[iwork], &i__2, &ierr);
|
|
ncvt = *n;
|
|
}
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing right */
|
|
/* singular vectors of A in A if desired */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, &ncvt, &c__0, &c__0, &s[1], &rwork[ie], &a[
|
|
a_offset], lda, cdum, &c__1, cdum, &c__1, &rwork[
|
|
irwork], info);
|
|
|
|
/* If right singular vectors desired in VT, copy them there */
|
|
|
|
if (wntvas) {
|
|
clacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
}
|
|
|
|
} else if (wntuo && wntvn) {
|
|
|
|
/* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */
|
|
/* N left singular vectors to be overwritten on A and */
|
|
/* no right singular vectors to be computed */
|
|
|
|
if (*lwork >= *n * *n + *n * 3) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
ir = 1;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *lda * *n;
|
|
if (*lwork >= f2cmax(i__2,i__3) + *lda * *n) {
|
|
|
|
/* WORK(IU) is LDA by N, WORK(IR) is LDA by N */
|
|
|
|
ldwrku = *lda;
|
|
ldwrkr = *lda;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *lda * *n;
|
|
if (*lwork >= f2cmax(i__2,i__3) + *n * *n) {
|
|
|
|
/* WORK(IU) is LDA by N, WORK(IR) is N by N */
|
|
|
|
ldwrku = *lda;
|
|
ldwrkr = *n;
|
|
} else {
|
|
|
|
/* WORK(IU) is LDWRKU by N, WORK(IR) is N by N */
|
|
|
|
ldwrku = (*lwork - *n * *n) / *n;
|
|
ldwrkr = *n;
|
|
}
|
|
}
|
|
itau = ir + ldwrkr * *n;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
|
|
, &i__2, &ierr);
|
|
|
|
/* Copy R to WORK(IR) and zero out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1], &
|
|
ldwrkr);
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IR) */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Generate left vectors bidiagonalizing R */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
|
|
/* (RWorkspace: need 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
|
|
work[iwork], &i__2, &ierr);
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of R in WORK(IR) */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie], cdum,
|
|
&c__1, &work[ir], &ldwrkr, cdum, &c__1, &rwork[
|
|
irwork], info);
|
|
iu = itauq;
|
|
|
|
/* Multiply Q in A by left singular vectors of R in */
|
|
/* WORK(IR), storing result in WORK(IU) and copying to A */
|
|
/* (CWorkspace: need N*N+N, prefer N*N+M*N) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *m;
|
|
i__3 = ldwrku;
|
|
for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
|
|
i__3) {
|
|
/* Computing MIN */
|
|
i__4 = *m - i__ + 1;
|
|
chunk = f2cmin(i__4,ldwrku);
|
|
cgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1]
|
|
, lda, &work[ir], &ldwrkr, &c_b1, &work[iu], &
|
|
ldwrku);
|
|
clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
|
|
a_dim1], lda);
|
|
/* L10: */
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
ie = 1;
|
|
itauq = 1;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize A */
|
|
/* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) */
|
|
/* (RWorkspace: N) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[iwork], &i__3, &ierr);
|
|
|
|
/* Generate left vectors bidiagonalizing A */
|
|
/* (CWorkspace: need 3*N, prefer 2*N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
|
|
work[iwork], &i__3, &ierr);
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in A */
|
|
/* (CWorkspace: need 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie], cdum,
|
|
&c__1, &a[a_offset], lda, cdum, &c__1, &rwork[
|
|
irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntuo && wntvas) {
|
|
|
|
/* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') */
|
|
/* N left singular vectors to be overwritten on A and */
|
|
/* N right singular vectors to be computed in VT */
|
|
|
|
if (*lwork >= *n * *n + *n * 3) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
ir = 1;
|
|
/* Computing MAX */
|
|
i__3 = wrkbl, i__2 = *lda * *n;
|
|
if (*lwork >= f2cmax(i__3,i__2) + *lda * *n) {
|
|
|
|
/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
|
|
|
|
ldwrku = *lda;
|
|
ldwrkr = *lda;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__3 = wrkbl, i__2 = *lda * *n;
|
|
if (*lwork >= f2cmax(i__3,i__2) + *n * *n) {
|
|
|
|
/* WORK(IU) is LDA by N and WORK(IR) is N by N */
|
|
|
|
ldwrku = *lda;
|
|
ldwrkr = *n;
|
|
} else {
|
|
|
|
/* WORK(IU) is LDWRKU by N and WORK(IR) is N by N */
|
|
|
|
ldwrku = (*lwork - *n * *n) / *n;
|
|
ldwrkr = *n;
|
|
}
|
|
}
|
|
itau = ir + ldwrkr * *n;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
|
|
, &i__3, &ierr);
|
|
|
|
/* Copy R to VT, zeroing out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
if (*n > 1) {
|
|
i__3 = *n - 1;
|
|
i__2 = *n - 1;
|
|
claset_("L", &i__3, &i__2, &c_b1, &c_b1, &vt[vt_dim1
|
|
+ 2], ldvt);
|
|
}
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__3, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in VT, copying result to WORK(IR) */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &i__3, &
|
|
ierr);
|
|
clacpy_("L", n, n, &vt[vt_offset], ldvt, &work[ir], &
|
|
ldwrkr);
|
|
|
|
/* Generate left vectors bidiagonalizing R in WORK(IR) */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &
|
|
work[iwork], &i__3, &ierr);
|
|
|
|
/* Generate right vectors bidiagonalizing R in VT */
|
|
/* (CWorkspace: need N*N+3*N-1, prefer N*N+2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
|
|
&work[iwork], &i__3, &ierr);
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of R in WORK(IR) and computing right */
|
|
/* singular vectors of R in VT */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &work[ir], &ldwrkr, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
iu = itauq;
|
|
|
|
/* Multiply Q in A by left singular vectors of R in */
|
|
/* WORK(IR), storing result in WORK(IU) and copying to A */
|
|
/* (CWorkspace: need N*N+N, prefer N*N+M*N) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *m;
|
|
i__2 = ldwrku;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__4 = *m - i__ + 1;
|
|
chunk = f2cmin(i__4,ldwrku);
|
|
cgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1]
|
|
, lda, &work[ir], &ldwrkr, &c_b1, &work[iu], &
|
|
ldwrku);
|
|
clacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
|
|
a_dim1], lda);
|
|
/* L20: */
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
|
|
, &i__2, &ierr);
|
|
|
|
/* Copy R to VT, zeroing out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
if (*n > 1) {
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[vt_dim1
|
|
+ 2], ldvt);
|
|
}
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in VT */
|
|
/* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
|
|
/* (RWorkspace: N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Multiply Q in A by left vectors bidiagonalizing R */
|
|
/* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt, &
|
|
work[itauq], &a[a_offset], lda, &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Generate right vectors bidiagonalizing R in VT */
|
|
/* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup],
|
|
&work[iwork], &i__2, &ierr);
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in A and computing right */
|
|
/* singular vectors of A in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntus) {
|
|
|
|
if (wntvn) {
|
|
|
|
/* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */
|
|
/* N left singular vectors to be computed in U and */
|
|
/* no right singular vectors to be computed */
|
|
|
|
if (*lwork >= *n * *n + *n * 3) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
ir = 1;
|
|
if (*lwork >= wrkbl + *lda * *n) {
|
|
|
|
/* WORK(IR) is LDA by N */
|
|
|
|
ldwrkr = *lda;
|
|
} else {
|
|
|
|
/* WORK(IR) is N by N */
|
|
|
|
ldwrkr = *n;
|
|
}
|
|
itau = ir + ldwrkr * *n;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Copy R to WORK(IR), zeroing out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &
|
|
ldwrkr);
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1]
|
|
, &ldwrkr);
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IR) */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Generate left vectors bidiagonalizing R in WORK(IR) */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
|
|
, &work[iwork], &i__2, &ierr);
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of R in WORK(IR) */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie],
|
|
cdum, &c__1, &work[ir], &ldwrkr, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
/* Multiply Q in A by left singular vectors of R in */
|
|
/* WORK(IR), storing result in U */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
|
|
work[ir], &ldwrkr, &c_b1, &u[u_offset], ldu);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Generate Q in U */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Zero out below R in A */
|
|
|
|
if (*n > 1) {
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
|
|
a_dim1 + 2], lda);
|
|
}
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply Q in U by left vectors bidiagonalizing R */
|
|
/* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
|
|
work[itauq], &u[u_offset], ldu, &work[iwork],
|
|
&i__2, &ierr)
|
|
;
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in U */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie],
|
|
cdum, &c__1, &u[u_offset], ldu, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntvo) {
|
|
|
|
/* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */
|
|
/* N left singular vectors to be computed in U and */
|
|
/* N right singular vectors to be overwritten on A */
|
|
|
|
if (*lwork >= (*n << 1) * *n + *n * 3) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
iu = 1;
|
|
if (*lwork >= wrkbl + (*lda << 1) * *n) {
|
|
|
|
/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
|
|
|
|
ldwrku = *lda;
|
|
ir = iu + ldwrku * *n;
|
|
ldwrkr = *lda;
|
|
} else if (*lwork >= wrkbl + (*lda + *n) * *n) {
|
|
|
|
/* WORK(IU) is LDA by N and WORK(IR) is N by N */
|
|
|
|
ldwrku = *lda;
|
|
ir = iu + ldwrku * *n;
|
|
ldwrkr = *n;
|
|
} else {
|
|
|
|
/* WORK(IU) is N by N and WORK(IR) is N by N */
|
|
|
|
ldwrku = *n;
|
|
ir = iu + ldwrku * *n;
|
|
ldwrkr = *n;
|
|
}
|
|
itau = ir + ldwrkr * *n;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Copy R to WORK(IU), zeroing out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
|
|
ldwrku);
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
|
|
, &ldwrku);
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IU), copying result to */
|
|
/* WORK(IR) */
|
|
/* (CWorkspace: need 2*N*N+3*N, */
|
|
/* prefer 2*N*N+2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
clacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
|
|
ldwrkr);
|
|
|
|
/* Generate left bidiagonalizing vectors in WORK(IU) */
|
|
/* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
|
|
, &work[iwork], &i__2, &ierr);
|
|
|
|
/* Generate right bidiagonalizing vectors in WORK(IR) */
|
|
/* (CWorkspace: need 2*N*N+3*N-1, */
|
|
/* prefer 2*N*N+2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
|
|
, &work[iwork], &i__2, &ierr);
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of R in WORK(IU) and computing */
|
|
/* right singular vectors of R in WORK(IR) */
|
|
/* (CWorkspace: need 2*N*N) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &work[
|
|
ir], &ldwrkr, &work[iu], &ldwrku, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
/* Multiply Q in A by left singular vectors of R in */
|
|
/* WORK(IU), storing result in U */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
|
|
work[iu], &ldwrku, &c_b1, &u[u_offset], ldu);
|
|
|
|
/* Copy right singular vectors of R to A */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
clacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
|
|
lda);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Generate Q in U */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Zero out below R in A */
|
|
|
|
if (*n > 1) {
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
|
|
a_dim1 + 2], lda);
|
|
}
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply Q in U by left vectors bidiagonalizing R */
|
|
/* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
|
|
work[itauq], &u[u_offset], ldu, &work[iwork],
|
|
&i__2, &ierr)
|
|
;
|
|
|
|
/* Generate right vectors bidiagonalizing R in A */
|
|
/* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
|
|
&work[iwork], &i__2, &ierr);
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in U and computing right */
|
|
/* singular vectors of A in A */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &a[
|
|
a_offset], lda, &u[u_offset], ldu, cdum, &
|
|
c__1, &rwork[irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntvas) {
|
|
|
|
/* Path 6 (M much larger than N, JOBU='S', JOBVT='S' */
|
|
/* or 'A') */
|
|
/* N left singular vectors to be computed in U and */
|
|
/* N right singular vectors to be computed in VT */
|
|
|
|
if (*lwork >= *n * *n + *n * 3) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
iu = 1;
|
|
if (*lwork >= wrkbl + *lda * *n) {
|
|
|
|
/* WORK(IU) is LDA by N */
|
|
|
|
ldwrku = *lda;
|
|
} else {
|
|
|
|
/* WORK(IU) is N by N */
|
|
|
|
ldwrku = *n;
|
|
}
|
|
itau = iu + ldwrku * *n;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Copy R to WORK(IU), zeroing out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
|
|
ldwrku);
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
|
|
, &ldwrku);
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, n, n, &a[a_offset], lda, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IU), copying result to VT */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
clacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Generate left bidiagonalizing vectors in WORK(IU) */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
|
|
, &work[iwork], &i__2, &ierr);
|
|
|
|
/* Generate right bidiagonalizing vectors in VT */
|
|
/* (CWorkspace: need N*N+3*N-1, */
|
|
/* prefer N*N+2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
|
|
itaup], &work[iwork], &i__2, &ierr)
|
|
;
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of R in WORK(IU) and computing */
|
|
/* right singular vectors of R in VT */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &work[iu], &ldwrku, cdum, &
|
|
c__1, &rwork[irwork], info);
|
|
|
|
/* Multiply Q in A by left singular vectors of R in */
|
|
/* WORK(IU), storing result in U */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &
|
|
work[iu], &ldwrku, &c_b1, &u[u_offset], ldu);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Generate Q in U */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, n, n, &u[u_offset], ldu, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
|
|
/* Copy R to VT, zeroing out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
if (*n > 1) {
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[
|
|
vt_dim1 + 2], ldvt);
|
|
}
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in VT */
|
|
/* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie],
|
|
&work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply Q in U by left bidiagonalizing vectors */
|
|
/* in VT */
|
|
/* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
|
|
&work[itauq], &u[u_offset], ldu, &work[iwork],
|
|
&i__2, &ierr);
|
|
|
|
/* Generate right bidiagonalizing vectors in VT */
|
|
/* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
|
|
itaup], &work[iwork], &i__2, &ierr)
|
|
;
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in U and computing right */
|
|
/* singular vectors of A in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &u[u_offset], ldu, cdum, &
|
|
c__1, &rwork[irwork], info);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else if (wntua) {
|
|
|
|
if (wntvn) {
|
|
|
|
/* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */
|
|
/* M left singular vectors to be computed in U and */
|
|
/* no right singular vectors to be computed */
|
|
|
|
/* Computing MAX */
|
|
i__2 = *n + *m, i__3 = *n * 3;
|
|
if (*lwork >= *n * *n + f2cmax(i__2,i__3)) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
ir = 1;
|
|
if (*lwork >= wrkbl + *lda * *n) {
|
|
|
|
/* WORK(IR) is LDA by N */
|
|
|
|
ldwrkr = *lda;
|
|
} else {
|
|
|
|
/* WORK(IR) is N by N */
|
|
|
|
ldwrkr = *n;
|
|
}
|
|
itau = ir + ldwrkr * *n;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Copy R to WORK(IR), zeroing out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &work[ir], &
|
|
ldwrkr);
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[ir + 1]
|
|
, &ldwrkr);
|
|
|
|
/* Generate Q in U */
|
|
/* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IR) */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Generate left bidiagonalizing vectors in WORK(IR) */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", n, n, n, &work[ir], &ldwrkr, &work[itauq]
|
|
, &work[iwork], &i__2, &ierr);
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of R in WORK(IR) */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, &c__0, n, &c__0, &s[1], &rwork[ie],
|
|
cdum, &c__1, &work[ir], &ldwrkr, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
/* Multiply Q in U by left singular vectors of R in */
|
|
/* WORK(IR), storing result in A */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &
|
|
work[ir], &ldwrkr, &c_b1, &a[a_offset], lda);
|
|
|
|
/* Copy left singular vectors of A from A to U */
|
|
|
|
clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Generate Q in U */
|
|
/* (CWorkspace: need N+M, prefer N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Zero out below R in A */
|
|
|
|
if (*n > 1) {
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
|
|
a_dim1 + 2], lda);
|
|
}
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply Q in U by left bidiagonalizing vectors */
|
|
/* in A */
|
|
/* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
|
|
work[itauq], &u[u_offset], ldu, &work[iwork],
|
|
&i__2, &ierr)
|
|
;
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in U */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, &c__0, m, &c__0, &s[1], &rwork[ie],
|
|
cdum, &c__1, &u[u_offset], ldu, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntvo) {
|
|
|
|
/* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */
|
|
/* M left singular vectors to be computed in U and */
|
|
/* N right singular vectors to be overwritten on A */
|
|
|
|
/* Computing MAX */
|
|
i__2 = *n + *m, i__3 = *n * 3;
|
|
if (*lwork >= (*n << 1) * *n + f2cmax(i__2,i__3)) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
iu = 1;
|
|
if (*lwork >= wrkbl + (*lda << 1) * *n) {
|
|
|
|
/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */
|
|
|
|
ldwrku = *lda;
|
|
ir = iu + ldwrku * *n;
|
|
ldwrkr = *lda;
|
|
} else if (*lwork >= wrkbl + (*lda + *n) * *n) {
|
|
|
|
/* WORK(IU) is LDA by N and WORK(IR) is N by N */
|
|
|
|
ldwrku = *lda;
|
|
ir = iu + ldwrku * *n;
|
|
ldwrkr = *n;
|
|
} else {
|
|
|
|
/* WORK(IU) is N by N and WORK(IR) is N by N */
|
|
|
|
ldwrku = *n;
|
|
ir = iu + ldwrku * *n;
|
|
ldwrkr = *n;
|
|
}
|
|
itau = ir + ldwrkr * *n;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Generate Q in U */
|
|
/* (CWorkspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
|
|
/* Copy R to WORK(IU), zeroing out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
|
|
ldwrku);
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
|
|
, &ldwrku);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IU), copying result to */
|
|
/* WORK(IR) */
|
|
/* (CWorkspace: need 2*N*N+3*N, */
|
|
/* prefer 2*N*N+2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
clacpy_("U", n, n, &work[iu], &ldwrku, &work[ir], &
|
|
ldwrkr);
|
|
|
|
/* Generate left bidiagonalizing vectors in WORK(IU) */
|
|
/* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
|
|
, &work[iwork], &i__2, &ierr);
|
|
|
|
/* Generate right bidiagonalizing vectors in WORK(IR) */
|
|
/* (CWorkspace: need 2*N*N+3*N-1, */
|
|
/* prefer 2*N*N+2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &work[ir], &ldwrkr, &work[itaup]
|
|
, &work[iwork], &i__2, &ierr);
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of R in WORK(IU) and computing */
|
|
/* right singular vectors of R in WORK(IR) */
|
|
/* (CWorkspace: need 2*N*N) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &work[
|
|
ir], &ldwrkr, &work[iu], &ldwrku, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
/* Multiply Q in U by left singular vectors of R in */
|
|
/* WORK(IU), storing result in A */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &
|
|
work[iu], &ldwrku, &c_b1, &a[a_offset], lda);
|
|
|
|
/* Copy left singular vectors of A from A to U */
|
|
|
|
clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Copy right singular vectors of R from WORK(IR) to A */
|
|
|
|
clacpy_("F", n, n, &work[ir], &ldwrkr, &a[a_offset],
|
|
lda);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Generate Q in U */
|
|
/* (CWorkspace: need N+M, prefer N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Zero out below R in A */
|
|
|
|
if (*n > 1) {
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &a[
|
|
a_dim1 + 2], lda);
|
|
}
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply Q in U by left bidiagonalizing vectors */
|
|
/* in A */
|
|
/* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("Q", "R", "N", m, n, n, &a[a_offset], lda, &
|
|
work[itauq], &u[u_offset], ldu, &work[iwork],
|
|
&i__2, &ierr)
|
|
;
|
|
|
|
/* Generate right bidiagonalizing vectors in A */
|
|
/* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup],
|
|
&work[iwork], &i__2, &ierr);
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in U and computing right */
|
|
/* singular vectors of A in A */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &a[
|
|
a_offset], lda, &u[u_offset], ldu, cdum, &
|
|
c__1, &rwork[irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntvas) {
|
|
|
|
/* Path 9 (M much larger than N, JOBU='A', JOBVT='S' */
|
|
/* or 'A') */
|
|
/* M left singular vectors to be computed in U and */
|
|
/* N right singular vectors to be computed in VT */
|
|
|
|
/* Computing MAX */
|
|
i__2 = *n + *m, i__3 = *n * 3;
|
|
if (*lwork >= *n * *n + f2cmax(i__2,i__3)) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
iu = 1;
|
|
if (*lwork >= wrkbl + *lda * *n) {
|
|
|
|
/* WORK(IU) is LDA by N */
|
|
|
|
ldwrku = *lda;
|
|
} else {
|
|
|
|
/* WORK(IU) is N by N */
|
|
|
|
ldwrku = *n;
|
|
}
|
|
itau = iu + ldwrku * *n;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Generate Q in U */
|
|
/* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
|
|
/* Copy R to WORK(IU), zeroing out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &work[iu], &
|
|
ldwrku);
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &work[iu + 1]
|
|
, &ldwrku);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IU), copying result to VT */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &work[iu], &ldwrku, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
clacpy_("U", n, n, &work[iu], &ldwrku, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Generate left bidiagonalizing vectors in WORK(IU) */
|
|
/* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", n, n, n, &work[iu], &ldwrku, &work[itauq]
|
|
, &work[iwork], &i__2, &ierr);
|
|
|
|
/* Generate right bidiagonalizing vectors in VT */
|
|
/* (CWorkspace: need N*N+3*N-1, */
|
|
/* prefer N*N+2*N+(N-1)*NB) */
|
|
/* (RWorkspace: need 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
|
|
itaup], &work[iwork], &i__2, &ierr)
|
|
;
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of R in WORK(IU) and computing */
|
|
/* right singular vectors of R in VT */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, n, n, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &work[iu], &ldwrku, cdum, &
|
|
c__1, &rwork[irwork], info);
|
|
|
|
/* Multiply Q in U by left singular vectors of R in */
|
|
/* WORK(IU), storing result in A */
|
|
/* (CWorkspace: need N*N) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, n, &c_b2, &u[u_offset], ldu, &
|
|
work[iu], &ldwrku, &c_b1, &a[a_offset], lda);
|
|
|
|
/* Copy left singular vectors of A from A to U */
|
|
|
|
clacpy_("F", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* (CWorkspace: need 2*N, prefer N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Generate Q in U */
|
|
/* (CWorkspace: need N+M, prefer N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
|
|
/* Copy R from A to VT, zeroing out below it */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
if (*n > 1) {
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
claset_("L", &i__2, &i__3, &c_b1, &c_b1, &vt[
|
|
vt_dim1 + 2], ldvt);
|
|
}
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in VT */
|
|
/* (CWorkspace: need 3*N, prefer 2*N+2*N*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &rwork[ie],
|
|
&work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply Q in U by left bidiagonalizing vectors */
|
|
/* in VT */
|
|
/* (CWorkspace: need 2*N+M, prefer 2*N+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("Q", "R", "N", m, n, n, &vt[vt_offset], ldvt,
|
|
&work[itauq], &u[u_offset], ldu, &work[iwork],
|
|
&i__2, &ierr);
|
|
|
|
/* Generate right bidiagonalizing vectors in VT */
|
|
/* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[
|
|
itaup], &work[iwork], &i__2, &ierr)
|
|
;
|
|
irwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in U and computing right */
|
|
/* singular vectors of A in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, n, m, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &u[u_offset], ldu, cdum, &
|
|
c__1, &rwork[irwork], info);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* M .LT. MNTHR */
|
|
|
|
/* Path 10 (M at least N, but not much larger) */
|
|
/* Reduce to bidiagonal form without QR decomposition */
|
|
|
|
ie = 1;
|
|
itauq = 1;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize A */
|
|
/* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) */
|
|
/* (RWorkspace: need N) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
|
|
&work[itaup], &work[iwork], &i__2, &ierr);
|
|
if (wntuas) {
|
|
|
|
/* If left singular vectors desired in U, copy result to U */
|
|
/* and generate left bidiagonalizing vectors in U */
|
|
/* (CWorkspace: need 2*N+NCU, prefer 2*N+NCU*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
clacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
|
|
if (wntus) {
|
|
ncu = *n;
|
|
}
|
|
if (wntua) {
|
|
ncu = *m;
|
|
}
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], &
|
|
work[iwork], &i__2, &ierr);
|
|
}
|
|
if (wntvas) {
|
|
|
|
/* If right singular vectors desired in VT, copy result to */
|
|
/* VT and generate right bidiagonalizing vectors in VT */
|
|
/* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
clacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
|
|
work[iwork], &i__2, &ierr);
|
|
}
|
|
if (wntuo) {
|
|
|
|
/* If left singular vectors desired in A, generate left */
|
|
/* bidiagonalizing vectors in A */
|
|
/* (CWorkspace: need 3*N, prefer 2*N+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
|
|
iwork], &i__2, &ierr);
|
|
}
|
|
if (wntvo) {
|
|
|
|
/* If right singular vectors desired in A, generate right */
|
|
/* bidiagonalizing vectors in A */
|
|
/* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[
|
|
iwork], &i__2, &ierr);
|
|
}
|
|
irwork = ie + *n;
|
|
if (wntuas || wntuo) {
|
|
nru = *m;
|
|
}
|
|
if (wntun) {
|
|
nru = 0;
|
|
}
|
|
if (wntvas || wntvo) {
|
|
ncvt = *n;
|
|
}
|
|
if (wntvn) {
|
|
ncvt = 0;
|
|
}
|
|
if (! wntuo && ! wntvo) {
|
|
|
|
/* Perform bidiagonal QR iteration, if desired, computing */
|
|
/* left singular vectors in U and computing right singular */
|
|
/* vectors in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &u[u_offset], ldu, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
} else if (! wntuo && wntvo) {
|
|
|
|
/* Perform bidiagonal QR iteration, if desired, computing */
|
|
/* left singular vectors in U and computing right singular */
|
|
/* vectors in A */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &a[
|
|
a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
} else {
|
|
|
|
/* Perform bidiagonal QR iteration, if desired, computing */
|
|
/* left singular vectors in A and computing right singular */
|
|
/* vectors in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", n, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* A has more columns than rows. If A has sufficiently more */
|
|
/* columns than rows, first reduce using the LQ decomposition (if */
|
|
/* sufficient workspace available) */
|
|
|
|
if (*n >= mnthr) {
|
|
|
|
if (wntvn) {
|
|
|
|
/* Path 1t(N much larger than M, JOBVT='N') */
|
|
/* No right singular vectors to be computed */
|
|
|
|
itau = 1;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Zero out above L */
|
|
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
|
|
, lda);
|
|
ie = 1;
|
|
itauq = 1;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in A */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
|
|
if (wntuo || wntuas) {
|
|
|
|
/* If left singular vectors desired, generate Q */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq], &
|
|
work[iwork], &i__2, &ierr);
|
|
}
|
|
irwork = ie + *m;
|
|
nru = 0;
|
|
if (wntuo || wntuas) {
|
|
nru = *m;
|
|
}
|
|
|
|
/* Perform bidiagonal QR iteration, computing left singular */
|
|
/* vectors of A in A if desired */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, &c__0, &nru, &c__0, &s[1], &rwork[ie], cdum, &
|
|
c__1, &a[a_offset], lda, cdum, &c__1, &rwork[irwork],
|
|
info);
|
|
|
|
/* If left singular vectors desired in U, copy them there */
|
|
|
|
if (wntuas) {
|
|
clacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
|
|
}
|
|
|
|
} else if (wntvo && wntun) {
|
|
|
|
/* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */
|
|
/* M right singular vectors to be overwritten on A and */
|
|
/* no left singular vectors to be computed */
|
|
|
|
if (*lwork >= *m * *m + *m * 3) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
ir = 1;
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *lda * *n;
|
|
if (*lwork >= f2cmax(i__2,i__3) + *lda * *m) {
|
|
|
|
/* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
|
|
|
|
ldwrku = *lda;
|
|
chunk = *n;
|
|
ldwrkr = *lda;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__2 = wrkbl, i__3 = *lda * *n;
|
|
if (*lwork >= f2cmax(i__2,i__3) + *m * *m) {
|
|
|
|
/* WORK(IU) is LDA by N and WORK(IR) is M by M */
|
|
|
|
ldwrku = *lda;
|
|
chunk = *n;
|
|
ldwrkr = *m;
|
|
} else {
|
|
|
|
/* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
|
|
|
|
ldwrku = *m;
|
|
chunk = (*lwork - *m * *m) / *m;
|
|
ldwrkr = *m;
|
|
}
|
|
}
|
|
itau = ir + ldwrkr * *m;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
|
|
, &i__2, &ierr);
|
|
|
|
/* Copy L to WORK(IR) and zero out above it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
|
|
ldwrkr], &ldwrkr);
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IR) */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Generate right vectors bidiagonalizing L */
|
|
/* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
|
|
work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing right */
|
|
/* singular vectors of L in WORK(IR) */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &work[
|
|
ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &rwork[
|
|
irwork], info);
|
|
iu = itauq;
|
|
|
|
/* Multiply right singular vectors of L in WORK(IR) by Q */
|
|
/* in A, storing result in WORK(IU) and copying to A */
|
|
/* (CWorkspace: need M*M+M, prefer M*M+M*N) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *n;
|
|
i__3 = chunk;
|
|
for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
|
|
i__3) {
|
|
/* Computing MIN */
|
|
i__4 = *n - i__ + 1;
|
|
blk = f2cmin(i__4,chunk);
|
|
cgemm_("N", "N", m, &blk, m, &c_b2, &work[ir], &
|
|
ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b1, &
|
|
work[iu], &ldwrku);
|
|
clacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
|
|
a_dim1 + 1], lda);
|
|
/* L30: */
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
ie = 1;
|
|
itauq = 1;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize A */
|
|
/* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[iwork], &i__3, &ierr);
|
|
|
|
/* Generate right vectors bidiagonalizing A */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
|
|
work[iwork], &i__3, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing right */
|
|
/* singular vectors of A in A */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("L", m, n, &c__0, &c__0, &s[1], &rwork[ie], &a[
|
|
a_offset], lda, cdum, &c__1, cdum, &c__1, &rwork[
|
|
irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntvo && wntuas) {
|
|
|
|
/* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') */
|
|
/* M right singular vectors to be overwritten on A and */
|
|
/* M left singular vectors to be computed in U */
|
|
|
|
if (*lwork >= *m * *m + *m * 3) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
ir = 1;
|
|
/* Computing MAX */
|
|
i__3 = wrkbl, i__2 = *lda * *n;
|
|
if (*lwork >= f2cmax(i__3,i__2) + *lda * *m) {
|
|
|
|
/* WORK(IU) is LDA by N and WORK(IR) is LDA by M */
|
|
|
|
ldwrku = *lda;
|
|
chunk = *n;
|
|
ldwrkr = *lda;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__3 = wrkbl, i__2 = *lda * *n;
|
|
if (*lwork >= f2cmax(i__3,i__2) + *m * *m) {
|
|
|
|
/* WORK(IU) is LDA by N and WORK(IR) is M by M */
|
|
|
|
ldwrku = *lda;
|
|
chunk = *n;
|
|
ldwrkr = *m;
|
|
} else {
|
|
|
|
/* WORK(IU) is M by CHUNK and WORK(IR) is M by M */
|
|
|
|
ldwrku = *m;
|
|
chunk = (*lwork - *m * *m) / *m;
|
|
ldwrkr = *m;
|
|
}
|
|
}
|
|
itau = ir + ldwrkr * *m;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
|
|
, &i__3, &ierr);
|
|
|
|
/* Copy L to U, zeroing about above it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
|
|
i__3 = *m - 1;
|
|
i__2 = *m - 1;
|
|
claset_("U", &i__3, &i__2, &c_b1, &c_b1, &u[(u_dim1 << 1)
|
|
+ 1], ldu);
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__3, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in U, copying result to WORK(IR) */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[iwork], &i__3, &ierr);
|
|
clacpy_("U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr);
|
|
|
|
/* Generate right vectors bidiagonalizing L in WORK(IR) */
|
|
/* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &
|
|
work[iwork], &i__3, &ierr);
|
|
|
|
/* Generate left vectors bidiagonalizing L in U */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
|
|
work[iwork], &i__3, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of L in U, and computing right */
|
|
/* singular vectors of L in WORK(IR) */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[ir],
|
|
&ldwrkr, &u[u_offset], ldu, cdum, &c__1, &rwork[
|
|
irwork], info);
|
|
iu = itauq;
|
|
|
|
/* Multiply right singular vectors of L in WORK(IR) by Q */
|
|
/* in A, storing result in WORK(IU) and copying to A */
|
|
/* (CWorkspace: need M*M+M, prefer M*M+M*N)) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__3 = *n;
|
|
i__2 = chunk;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__4 = *n - i__ + 1;
|
|
blk = f2cmin(i__4,chunk);
|
|
cgemm_("N", "N", m, &blk, m, &c_b2, &work[ir], &
|
|
ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b1, &
|
|
work[iu], &ldwrku);
|
|
clacpy_("F", m, &blk, &work[iu], &ldwrku, &a[i__ *
|
|
a_dim1 + 1], lda);
|
|
/* L40: */
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork]
|
|
, &i__2, &ierr);
|
|
|
|
/* Copy L to U, zeroing out above it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 << 1)
|
|
+ 1], ldu);
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in U */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[iwork], &i__2, &ierr);
|
|
|
|
/* Multiply right vectors bidiagonalizing L by Q in A */
|
|
/* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &work[
|
|
itaup], &a[a_offset], lda, &work[iwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Generate left vectors bidiagonalizing L in U */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq], &
|
|
work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in U and computing right */
|
|
/* singular vectors of A in A */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &a[
|
|
a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntvs) {
|
|
|
|
if (wntun) {
|
|
|
|
/* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */
|
|
/* M right singular vectors to be computed in VT and */
|
|
/* no left singular vectors to be computed */
|
|
|
|
if (*lwork >= *m * *m + *m * 3) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
ir = 1;
|
|
if (*lwork >= wrkbl + *lda * *m) {
|
|
|
|
/* WORK(IR) is LDA by M */
|
|
|
|
ldwrkr = *lda;
|
|
} else {
|
|
|
|
/* WORK(IR) is M by M */
|
|
|
|
ldwrkr = *m;
|
|
}
|
|
itau = ir + ldwrkr * *m;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Copy L to WORK(IR), zeroing out above it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
|
|
ldwrkr);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
|
|
ldwrkr], &ldwrkr);
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IR) */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Generate right vectors bidiagonalizing L in */
|
|
/* WORK(IR) */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
|
|
, &work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing right */
|
|
/* singular vectors of L in WORK(IR) */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &
|
|
work[ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IR) by */
|
|
/* Q in A, storing result in VT */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, m, &c_b2, &work[ir], &ldwrkr, &
|
|
a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Copy result to VT */
|
|
|
|
clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Generate Q in VT */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Zero out above L in A */
|
|
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
|
|
1) + 1], lda);
|
|
|
|
/* Bidiagonalize L in A */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply right vectors bidiagonalizing L by Q in VT */
|
|
/* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
|
|
work[itaup], &vt[vt_offset], ldvt, &work[
|
|
iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing right */
|
|
/* singular vectors of A in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, n, &c__0, &c__0, &s[1], &rwork[ie], &
|
|
vt[vt_offset], ldvt, cdum, &c__1, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntuo) {
|
|
|
|
/* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */
|
|
/* M right singular vectors to be computed in VT and */
|
|
/* M left singular vectors to be overwritten on A */
|
|
|
|
if (*lwork >= (*m << 1) * *m + *m * 3) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
iu = 1;
|
|
if (*lwork >= wrkbl + (*lda << 1) * *m) {
|
|
|
|
/* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
|
|
|
|
ldwrku = *lda;
|
|
ir = iu + ldwrku * *m;
|
|
ldwrkr = *lda;
|
|
} else if (*lwork >= wrkbl + (*lda + *m) * *m) {
|
|
|
|
/* WORK(IU) is LDA by M and WORK(IR) is M by M */
|
|
|
|
ldwrku = *lda;
|
|
ir = iu + ldwrku * *m;
|
|
ldwrkr = *m;
|
|
} else {
|
|
|
|
/* WORK(IU) is M by M and WORK(IR) is M by M */
|
|
|
|
ldwrku = *m;
|
|
ir = iu + ldwrku * *m;
|
|
ldwrkr = *m;
|
|
}
|
|
itau = ir + ldwrkr * *m;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Copy L to WORK(IU), zeroing out below it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
|
|
ldwrku);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
|
|
ldwrku], &ldwrku);
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IU), copying result to */
|
|
/* WORK(IR) */
|
|
/* (CWorkspace: need 2*M*M+3*M, */
|
|
/* prefer 2*M*M+2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
clacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
|
|
ldwrkr);
|
|
|
|
/* Generate right bidiagonalizing vectors in WORK(IU) */
|
|
/* (CWorkspace: need 2*M*M+3*M-1, */
|
|
/* prefer 2*M*M+2*M+(M-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
|
|
, &work[iwork], &i__2, &ierr);
|
|
|
|
/* Generate left bidiagonalizing vectors in WORK(IR) */
|
|
/* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
|
|
, &work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of L in WORK(IR) and computing */
|
|
/* right singular vectors of L in WORK(IU) */
|
|
/* (CWorkspace: need 2*M*M) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
|
|
iu], &ldwrku, &work[ir], &ldwrkr, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IU) by */
|
|
/* Q in A, storing result in VT */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
|
|
a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
|
|
|
|
/* Copy left singular vectors of L to A */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
clacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
|
|
lda);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q, copying result to VT */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Generate Q in VT */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Zero out above L in A */
|
|
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
|
|
1) + 1], lda);
|
|
|
|
/* Bidiagonalize L in A */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply right vectors bidiagonalizing L by Q in VT */
|
|
/* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
|
|
work[itaup], &vt[vt_offset], ldvt, &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Generate left bidiagonalizing vectors of L in A */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
|
|
&work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in A and computing right */
|
|
/* singular vectors of A in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &a[a_offset], lda, cdum, &
|
|
c__1, &rwork[irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntuas) {
|
|
|
|
/* Path 6t(N much larger than M, JOBU='S' or 'A', */
|
|
/* JOBVT='S') */
|
|
/* M right singular vectors to be computed in VT and */
|
|
/* M left singular vectors to be computed in U */
|
|
|
|
if (*lwork >= *m * *m + *m * 3) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
iu = 1;
|
|
if (*lwork >= wrkbl + *lda * *m) {
|
|
|
|
/* WORK(IU) is LDA by N */
|
|
|
|
ldwrku = *lda;
|
|
} else {
|
|
|
|
/* WORK(IU) is LDA by M */
|
|
|
|
ldwrku = *m;
|
|
}
|
|
itau = iu + ldwrku * *m;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Copy L to WORK(IU), zeroing out above it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
|
|
ldwrku);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
|
|
ldwrku], &ldwrku);
|
|
|
|
/* Generate Q in A */
|
|
/* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(m, n, m, &a[a_offset], lda, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IU), copying result to U */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
clacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Generate right bidiagonalizing vectors in WORK(IU) */
|
|
/* (CWorkspace: need M*M+3*M-1, */
|
|
/* prefer M*M+2*M+(M-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
|
|
, &work[iwork], &i__2, &ierr);
|
|
|
|
/* Generate left bidiagonalizing vectors in U */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
|
|
&work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of L in U and computing right */
|
|
/* singular vectors of L in WORK(IU) */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
|
|
iu], &ldwrku, &u[u_offset], ldu, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IU) by */
|
|
/* Q in A, storing result in VT */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
|
|
a[a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q, copying result to VT */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Generate Q in VT */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
|
|
/* Copy L to U, zeroing out above it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 <<
|
|
1) + 1], ldu);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in U */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply right bidiagonalizing vectors in U by Q */
|
|
/* in VT */
|
|
/* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &
|
|
work[itaup], &vt[vt_offset], ldvt, &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Generate left bidiagonalizing vectors in U */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
|
|
&work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in U and computing right */
|
|
/* singular vectors of A in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &u[u_offset], ldu, cdum, &
|
|
c__1, &rwork[irwork], info);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else if (wntva) {
|
|
|
|
if (wntun) {
|
|
|
|
/* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */
|
|
/* N right singular vectors to be computed in VT and */
|
|
/* no left singular vectors to be computed */
|
|
|
|
/* Computing MAX */
|
|
i__2 = *n + *m, i__3 = *m * 3;
|
|
if (*lwork >= *m * *m + f2cmax(i__2,i__3)) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
ir = 1;
|
|
if (*lwork >= wrkbl + *lda * *m) {
|
|
|
|
/* WORK(IR) is LDA by M */
|
|
|
|
ldwrkr = *lda;
|
|
} else {
|
|
|
|
/* WORK(IR) is M by M */
|
|
|
|
ldwrkr = *m;
|
|
}
|
|
itau = ir + ldwrkr * *m;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q, copying result to VT */
|
|
/* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Copy L to WORK(IR), zeroing out above it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &work[ir], &
|
|
ldwrkr);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[ir +
|
|
ldwrkr], &ldwrkr);
|
|
|
|
/* Generate Q in VT */
|
|
/* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IR) */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Generate right bidiagonalizing vectors in WORK(IR) */
|
|
/* (CWorkspace: need M*M+3*M-1, */
|
|
/* prefer M*M+2*M+(M-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", m, m, m, &work[ir], &ldwrkr, &work[itaup]
|
|
, &work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing right */
|
|
/* singular vectors of L in WORK(IR) */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, m, &c__0, &c__0, &s[1], &rwork[ie], &
|
|
work[ir], &ldwrkr, cdum, &c__1, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IR) by */
|
|
/* Q in VT, storing result in A */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, m, &c_b2, &work[ir], &ldwrkr, &
|
|
vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
|
|
|
|
/* Copy right singular vectors of A from A to VT */
|
|
|
|
clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q, copying result to VT */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Generate Q in VT */
|
|
/* (CWorkspace: need M+N, prefer M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Zero out above L in A */
|
|
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
|
|
1) + 1], lda);
|
|
|
|
/* Bidiagonalize L in A */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply right bidiagonalizing vectors in A by Q */
|
|
/* in VT */
|
|
/* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
|
|
work[itaup], &vt[vt_offset], ldvt, &work[
|
|
iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing right */
|
|
/* singular vectors of A in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, n, &c__0, &c__0, &s[1], &rwork[ie], &
|
|
vt[vt_offset], ldvt, cdum, &c__1, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntuo) {
|
|
|
|
/* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */
|
|
/* N right singular vectors to be computed in VT and */
|
|
/* M left singular vectors to be overwritten on A */
|
|
|
|
/* Computing MAX */
|
|
i__2 = *n + *m, i__3 = *m * 3;
|
|
if (*lwork >= (*m << 1) * *m + f2cmax(i__2,i__3)) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
iu = 1;
|
|
if (*lwork >= wrkbl + (*lda << 1) * *m) {
|
|
|
|
/* WORK(IU) is LDA by M and WORK(IR) is LDA by M */
|
|
|
|
ldwrku = *lda;
|
|
ir = iu + ldwrku * *m;
|
|
ldwrkr = *lda;
|
|
} else if (*lwork >= wrkbl + (*lda + *m) * *m) {
|
|
|
|
/* WORK(IU) is LDA by M and WORK(IR) is M by M */
|
|
|
|
ldwrku = *lda;
|
|
ir = iu + ldwrku * *m;
|
|
ldwrkr = *m;
|
|
} else {
|
|
|
|
/* WORK(IU) is M by M and WORK(IR) is M by M */
|
|
|
|
ldwrku = *m;
|
|
ir = iu + ldwrku * *m;
|
|
ldwrkr = *m;
|
|
}
|
|
itau = ir + ldwrkr * *m;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q, copying result to VT */
|
|
/* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Generate Q in VT */
|
|
/* (CWorkspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
|
|
/* Copy L to WORK(IU), zeroing out above it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
|
|
ldwrku);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
|
|
ldwrku], &ldwrku);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IU), copying result to */
|
|
/* WORK(IR) */
|
|
/* (CWorkspace: need 2*M*M+3*M, */
|
|
/* prefer 2*M*M+2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
clacpy_("L", m, m, &work[iu], &ldwrku, &work[ir], &
|
|
ldwrkr);
|
|
|
|
/* Generate right bidiagonalizing vectors in WORK(IU) */
|
|
/* (CWorkspace: need 2*M*M+3*M-1, */
|
|
/* prefer 2*M*M+2*M+(M-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
|
|
, &work[iwork], &i__2, &ierr);
|
|
|
|
/* Generate left bidiagonalizing vectors in WORK(IR) */
|
|
/* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &work[ir], &ldwrkr, &work[itauq]
|
|
, &work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of L in WORK(IR) and computing */
|
|
/* right singular vectors of L in WORK(IU) */
|
|
/* (CWorkspace: need 2*M*M) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
|
|
iu], &ldwrku, &work[ir], &ldwrkr, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IU) by */
|
|
/* Q in VT, storing result in A */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
|
|
vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
|
|
|
|
/* Copy right singular vectors of A from A to VT */
|
|
|
|
clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Copy left singular vectors of A from WORK(IR) to A */
|
|
|
|
clacpy_("F", m, m, &work[ir], &ldwrkr, &a[a_offset],
|
|
lda);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q, copying result to VT */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Generate Q in VT */
|
|
/* (CWorkspace: need M+N, prefer M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Zero out above L in A */
|
|
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &a[(a_dim1 <<
|
|
1) + 1], lda);
|
|
|
|
/* Bidiagonalize L in A */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply right bidiagonalizing vectors in A by Q */
|
|
/* in VT */
|
|
/* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("P", "L", "C", m, n, m, &a[a_offset], lda, &
|
|
work[itaup], &vt[vt_offset], ldvt, &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Generate left bidiagonalizing vectors in A */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &a[a_offset], lda, &work[itauq],
|
|
&work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in A and computing right */
|
|
/* singular vectors of A in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &a[a_offset], lda, cdum, &
|
|
c__1, &rwork[irwork], info);
|
|
|
|
}
|
|
|
|
} else if (wntuas) {
|
|
|
|
/* Path 9t(N much larger than M, JOBU='S' or 'A', */
|
|
/* JOBVT='A') */
|
|
/* N right singular vectors to be computed in VT and */
|
|
/* M left singular vectors to be computed in U */
|
|
|
|
/* Computing MAX */
|
|
i__2 = *n + *m, i__3 = *m * 3;
|
|
if (*lwork >= *m * *m + f2cmax(i__2,i__3)) {
|
|
|
|
/* Sufficient workspace for a fast algorithm */
|
|
|
|
iu = 1;
|
|
if (*lwork >= wrkbl + *lda * *m) {
|
|
|
|
/* WORK(IU) is LDA by M */
|
|
|
|
ldwrku = *lda;
|
|
} else {
|
|
|
|
/* WORK(IU) is M by M */
|
|
|
|
ldwrku = *m;
|
|
}
|
|
itau = iu + ldwrku * *m;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q, copying result to VT */
|
|
/* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Generate Q in VT */
|
|
/* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
|
|
/* Copy L to WORK(IU), zeroing out above it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &work[iu], &
|
|
ldwrku);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &work[iu +
|
|
ldwrku], &ldwrku);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IU), copying result to U */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &work[iu], &ldwrku, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
clacpy_("L", m, m, &work[iu], &ldwrku, &u[u_offset],
|
|
ldu);
|
|
|
|
/* Generate right bidiagonalizing vectors in WORK(IU) */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", m, m, m, &work[iu], &ldwrku, &work[itaup]
|
|
, &work[iwork], &i__2, &ierr);
|
|
|
|
/* Generate left bidiagonalizing vectors in U */
|
|
/* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
|
|
&work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of L in U and computing right */
|
|
/* singular vectors of L in WORK(IU) */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, m, m, &c__0, &s[1], &rwork[ie], &work[
|
|
iu], &ldwrku, &u[u_offset], ldu, cdum, &c__1,
|
|
&rwork[irwork], info);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IU) by */
|
|
/* Q in VT, storing result in A */
|
|
/* (CWorkspace: need M*M) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
cgemm_("N", "N", m, n, m, &c_b2, &work[iu], &ldwrku, &
|
|
vt[vt_offset], ldvt, &c_b1, &a[a_offset], lda);
|
|
|
|
/* Copy right singular vectors of A from A to VT */
|
|
|
|
clacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
} else {
|
|
|
|
/* Insufficient workspace for a fast algorithm */
|
|
|
|
itau = 1;
|
|
iwork = itau + *m;
|
|
|
|
/* Compute A=L*Q, copying result to VT */
|
|
/* (CWorkspace: need 2*M, prefer M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[
|
|
iwork], &i__2, &ierr);
|
|
clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset],
|
|
ldvt);
|
|
|
|
/* Generate Q in VT */
|
|
/* (CWorkspace: need M+N, prefer M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &
|
|
work[iwork], &i__2, &ierr);
|
|
|
|
/* Copy L to U, zeroing out above it */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset],
|
|
ldu);
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
claset_("U", &i__2, &i__3, &c_b1, &c_b1, &u[(u_dim1 <<
|
|
1) + 1], ldu);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in U */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+2*M*NB) */
|
|
/* (RWorkspace: need M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, m, &u[u_offset], ldu, &s[1], &rwork[ie], &
|
|
work[itauq], &work[itaup], &work[iwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Multiply right bidiagonalizing vectors in U by Q */
|
|
/* in VT */
|
|
/* (CWorkspace: need 2*M+N, prefer 2*M+N*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cunmbr_("P", "L", "C", m, n, m, &u[u_offset], ldu, &
|
|
work[itaup], &vt[vt_offset], ldvt, &work[
|
|
iwork], &i__2, &ierr);
|
|
|
|
/* Generate left bidiagonalizing vectors in U */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, m, &u[u_offset], ldu, &work[itauq],
|
|
&work[iwork], &i__2, &ierr);
|
|
irwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, computing left */
|
|
/* singular vectors of A in U and computing right */
|
|
/* singular vectors of A in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("U", m, n, m, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &u[u_offset], ldu, cdum, &
|
|
c__1, &rwork[irwork], info);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* N .LT. MNTHR */
|
|
|
|
/* Path 10t(N greater than M, but not much larger) */
|
|
/* Reduce to bidiagonal form without LQ decomposition */
|
|
|
|
ie = 1;
|
|
itauq = 1;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize A */
|
|
/* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) */
|
|
/* (RWorkspace: M) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
|
|
&work[itaup], &work[iwork], &i__2, &ierr);
|
|
if (wntuas) {
|
|
|
|
/* If left singular vectors desired in U, copy result to U */
|
|
/* and generate left bidiagonalizing vectors in U */
|
|
/* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
clacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
|
|
iwork], &i__2, &ierr);
|
|
}
|
|
if (wntvas) {
|
|
|
|
/* If right singular vectors desired in VT, copy result to */
|
|
/* VT and generate right bidiagonalizing vectors in VT */
|
|
/* (CWorkspace: need 2*M+NRVT, prefer 2*M+NRVT*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
clacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
if (wntva) {
|
|
nrvt = *n;
|
|
}
|
|
if (wntvs) {
|
|
nrvt = *m;
|
|
}
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup],
|
|
&work[iwork], &i__2, &ierr);
|
|
}
|
|
if (wntuo) {
|
|
|
|
/* If left singular vectors desired in A, generate left */
|
|
/* bidiagonalizing vectors in A */
|
|
/* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[
|
|
iwork], &i__2, &ierr);
|
|
}
|
|
if (wntvo) {
|
|
|
|
/* If right singular vectors desired in A, generate right */
|
|
/* bidiagonalizing vectors in A */
|
|
/* (CWorkspace: need 3*M, prefer 2*M+M*NB) */
|
|
/* (RWorkspace: 0) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
cungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
|
|
iwork], &i__2, &ierr);
|
|
}
|
|
irwork = ie + *m;
|
|
if (wntuas || wntuo) {
|
|
nru = *m;
|
|
}
|
|
if (wntun) {
|
|
nru = 0;
|
|
}
|
|
if (wntvas || wntvo) {
|
|
ncvt = *n;
|
|
}
|
|
if (wntvn) {
|
|
ncvt = 0;
|
|
}
|
|
if (! wntuo && ! wntvo) {
|
|
|
|
/* Perform bidiagonal QR iteration, if desired, computing */
|
|
/* left singular vectors in U and computing right singular */
|
|
/* vectors in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &u[u_offset], ldu, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
} else if (! wntuo && wntvo) {
|
|
|
|
/* Perform bidiagonal QR iteration, if desired, computing */
|
|
/* left singular vectors in U and computing right singular */
|
|
/* vectors in A */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &a[
|
|
a_offset], lda, &u[u_offset], ldu, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
} else {
|
|
|
|
/* Perform bidiagonal QR iteration, if desired, computing */
|
|
/* left singular vectors in A and computing right singular */
|
|
/* vectors in VT */
|
|
/* (CWorkspace: 0) */
|
|
/* (RWorkspace: need BDSPAC) */
|
|
|
|
cbdsqr_("L", m, &ncvt, &nru, &c__0, &s[1], &rwork[ie], &vt[
|
|
vt_offset], ldvt, &a[a_offset], lda, cdum, &c__1, &
|
|
rwork[irwork], info);
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
/* Undo scaling if necessary */
|
|
|
|
if (iscl == 1) {
|
|
if (anrm > bignum) {
|
|
slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, &ierr);
|
|
}
|
|
if (*info != 0 && anrm > bignum) {
|
|
i__2 = minmn - 1;
|
|
slascl_("G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &rwork[
|
|
ie], &minmn, &ierr);
|
|
}
|
|
if (anrm < smlnum) {
|
|
slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, &ierr);
|
|
}
|
|
if (*info != 0 && anrm < smlnum) {
|
|
i__2 = minmn - 1;
|
|
slascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &rwork[
|
|
ie], &minmn, &ierr);
|
|
}
|
|
}
|
|
|
|
/* Return optimal workspace in WORK(1) */
|
|
|
|
work[1].r = (real) maxwrk, work[1].i = 0.f;
|
|
|
|
return;
|
|
|
|
/* End of CGESVD */
|
|
|
|
} /* cgesvd_ */
|
|
|