2978 lines
102 KiB
C
2978 lines
102 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 int logical;
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typedef short int shortlogical;
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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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#define F2C_proc_par_types 1
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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 {
|
|
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 doublecomplex c_b1 = {0.,0.};
|
|
static doublecomplex c_b2 = {1.,0.};
|
|
static integer c_n1 = -1;
|
|
static integer c__0 = 0;
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZGESDD */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZGESDD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgesdd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgesdd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgesdd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, */
|
|
/* WORK, LWORK, RWORK, IWORK, INFO ) */
|
|
|
|
/* CHARACTER JOBZ */
|
|
/* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */
|
|
/* INTEGER IWORK( * ) */
|
|
/* DOUBLE PRECISION RWORK( * ), S( * ) */
|
|
/* COMPLEX*16 A( LDA, * ), U( LDU, * ), VT( LDVT, * ), */
|
|
/* $ WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZGESDD computes the singular value decomposition (SVD) of a complex */
|
|
/* > M-by-N matrix A, optionally computing the left and/or right singular */
|
|
/* > vectors, by using divide-and-conquer method. 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 VT = V**H, not V. */
|
|
/* > */
|
|
/* > The divide and conquer algorithm makes very mild assumptions about */
|
|
/* > floating point arithmetic. It will work on machines with a guard */
|
|
/* > digit in add/subtract, or on those binary machines without guard */
|
|
/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
|
|
/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */
|
|
/* > without guard digits, but we know of none. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBZ */
|
|
/* > \verbatim */
|
|
/* > JOBZ is CHARACTER*1 */
|
|
/* > Specifies options for computing all or part of the matrix U: */
|
|
/* > = 'A': all M columns of U and all N rows of V**H are */
|
|
/* > returned in the arrays U and VT; */
|
|
/* > = 'S': the first f2cmin(M,N) columns of U and the first */
|
|
/* > f2cmin(M,N) rows of V**H are returned in the arrays U */
|
|
/* > and VT; */
|
|
/* > = 'O': If M >= N, the first N columns of U are overwritten */
|
|
/* > in the array A and all rows of V**H are returned in */
|
|
/* > the array VT; */
|
|
/* > otherwise, all columns of U are returned in the */
|
|
/* > array U and the first M rows of V**H are overwritten */
|
|
/* > in the array A; */
|
|
/* > = 'N': no columns of U or rows of V**H are computed. */
|
|
/* > \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*16 array, dimension (LDA,N) */
|
|
/* > On entry, the M-by-N matrix A. */
|
|
/* > On exit, */
|
|
/* > if JOBZ = 'O', A is overwritten with the first N columns */
|
|
/* > of U (the left singular vectors, stored */
|
|
/* > columnwise) if M >= N; */
|
|
/* > A is overwritten with the first M rows */
|
|
/* > of V**H (the right singular vectors, stored */
|
|
/* > rowwise) otherwise. */
|
|
/* > if JOBZ .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 DOUBLE PRECISION array, dimension (f2cmin(M,N)) */
|
|
/* > The singular values of A, sorted so that S(i) >= S(i+1). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] U */
|
|
/* > \verbatim */
|
|
/* > U is COMPLEX*16 array, dimension (LDU,UCOL) */
|
|
/* > UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */
|
|
/* > UCOL = f2cmin(M,N) if JOBZ = 'S'. */
|
|
/* > If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */
|
|
/* > unitary matrix U; */
|
|
/* > if JOBZ = 'S', U contains the first f2cmin(M,N) columns of U */
|
|
/* > (the left singular vectors, stored columnwise); */
|
|
/* > if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU */
|
|
/* > \verbatim */
|
|
/* > LDU is INTEGER */
|
|
/* > The leading dimension of the array U. LDU >= 1; */
|
|
/* > if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VT */
|
|
/* > \verbatim */
|
|
/* > VT is COMPLEX*16 array, dimension (LDVT,N) */
|
|
/* > If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */
|
|
/* > N-by-N unitary matrix V**H; */
|
|
/* > if JOBZ = 'S', VT contains the first f2cmin(M,N) rows of */
|
|
/* > V**H (the right singular vectors, stored rowwise); */
|
|
/* > if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVT */
|
|
/* > \verbatim */
|
|
/* > LDVT is INTEGER */
|
|
/* > The leading dimension of the array VT. LDVT >= 1; */
|
|
/* > if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */
|
|
/* > if JOBZ = 'S', LDVT >= f2cmin(M,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 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 >= 1. */
|
|
/* > If LWORK = -1, a workspace query is assumed. The optimal */
|
|
/* > size for the WORK array is calculated and stored in WORK(1), */
|
|
/* > and no other work except argument checking is performed. */
|
|
/* > */
|
|
/* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
|
|
/* > If JOBZ = 'N', LWORK >= 2*mn + mx. */
|
|
/* > If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx. */
|
|
/* > If JOBZ = 'S', LWORK >= mn*mn + 3*mn. */
|
|
/* > If JOBZ = 'A', LWORK >= mn*mn + 2*mn + mx. */
|
|
/* > These are not tight minimums in all cases; see comments inside code. */
|
|
/* > For good performance, LWORK should generally be larger; */
|
|
/* > a query is recommended. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */
|
|
/* > Let mx = f2cmax(M,N) and mn = f2cmin(M,N). */
|
|
/* > If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn); */
|
|
/* > else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn; */
|
|
/* > else LRWORK >= f2cmax( 5*mn*mn + 5*mn, */
|
|
/* > 2*mx*mn + 2*mn*mn + mn ). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (8*f2cmin(M,N)) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: The updating process of DBDSDC did not converge. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup complex16GEsing */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zgesdd_(char *jobz, integer *m, integer *n,
|
|
doublecomplex *a, integer *lda, doublereal *s, doublecomplex *u,
|
|
integer *ldu, doublecomplex *vt, integer *ldvt, doublecomplex *work,
|
|
integer *lwork, doublereal *rwork, integer *iwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
|
|
i__2, i__3;
|
|
|
|
/* Local variables */
|
|
integer lwork_zgebrd_mm__, lwork_zgebrd_mn__, lwork_zgebrd_nn__,
|
|
lwork_zgelqf_mn__, lwork_zgeqrf_mn__;
|
|
doublecomplex cdum[1];
|
|
integer iscl;
|
|
doublereal anrm;
|
|
integer idum[1], ierr, itau, lwork_zunglq_mn__, lwork_zunglq_nn__,
|
|
lwork_zungqr_mm__, lwork_zungqr_mn__, irvt, lwork_zunmbr_prc_mm__,
|
|
lwork_zunmbr_prc_mn__, lwork_zunmbr_prc_nn__,
|
|
lwork_zunmbr_qln_mm__, lwork_zunmbr_qln_mn__,
|
|
lwork_zunmbr_qln_nn__, i__;
|
|
extern logical lsame_(char *, char *);
|
|
integer chunk, minmn;
|
|
extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *);
|
|
integer wrkbl, itaup, itauq;
|
|
logical wntqa;
|
|
integer nwork;
|
|
logical wntqn, wntqo, wntqs;
|
|
extern /* Subroutine */ void zlacp2_(char *, integer *, integer *,
|
|
doublereal *, integer *, doublecomplex *, integer *);
|
|
integer mnthr1, mnthr2, ie;
|
|
extern /* Subroutine */ void dbdsdc_(char *, char *, integer *, doublereal
|
|
*, doublereal *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, integer *, integer *);
|
|
integer il;
|
|
extern doublereal dlamch_(char *);
|
|
integer ir, iu;
|
|
extern /* Subroutine */ void dlascl_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, integer *, doublereal *,
|
|
integer *, integer *);
|
|
integer lwork_zungbr_p_mn__, lwork_zungbr_p_nn__, lwork_zungbr_q_mn__,
|
|
lwork_zungbr_q_mm__;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
doublereal bignum;
|
|
extern /* Subroutine */ void zgebrd_(integer *, integer *, doublecomplex *,
|
|
integer *, doublereal *, doublereal *, doublecomplex *,
|
|
doublecomplex *, doublecomplex *, integer *, integer *);
|
|
extern logical disnan_(doublereal *);
|
|
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
|
|
integer *, doublereal *);
|
|
extern /* Subroutine */ void zgelqf_(integer *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *, integer *
|
|
), zlacrm_(integer *, integer *, doublecomplex *, integer *,
|
|
doublereal *, integer *, doublecomplex *, integer *, doublereal *)
|
|
, zlarcm_(integer *, integer *, doublereal *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublereal *), zlascl_(char *, integer *, integer *, doublereal *,
|
|
doublereal *, integer *, integer *, doublecomplex *, integer *,
|
|
integer *), zgeqrf_(integer *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *, integer *
|
|
);
|
|
integer ldwrkl;
|
|
extern /* Subroutine */ void zlacpy_(char *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *),
|
|
zlaset_(char *, integer *, integer *, doublecomplex *,
|
|
doublecomplex *, doublecomplex *, integer *);
|
|
integer ldwrkr, minwrk, ldwrku, maxwrk;
|
|
extern /* Subroutine */ void zungbr_(char *, integer *, integer *, integer
|
|
*, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *, integer *);
|
|
integer ldwkvt;
|
|
doublereal smlnum;
|
|
logical wntqas;
|
|
extern /* Subroutine */ void zunmbr_(char *, char *, char *, integer *,
|
|
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *, integer *
|
|
), zunglq_(integer *, integer *, integer *
|
|
, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *, integer *);
|
|
logical lquery;
|
|
integer nrwork;
|
|
extern /* Subroutine */ void zungqr_(integer *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *, integer *);
|
|
integer blk;
|
|
doublereal dum[1], eps;
|
|
integer iru, ivt;
|
|
|
|
|
|
/* -- 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..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input arguments */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--s;
|
|
u_dim1 = *ldu;
|
|
u_offset = 1 + u_dim1 * 1;
|
|
u -= u_offset;
|
|
vt_dim1 = *ldvt;
|
|
vt_offset = 1 + vt_dim1 * 1;
|
|
vt -= vt_offset;
|
|
--work;
|
|
--rwork;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
minmn = f2cmin(*m,*n);
|
|
mnthr1 = (integer) (minmn * 17. / 9.);
|
|
mnthr2 = (integer) (minmn * 5. / 3.);
|
|
wntqa = lsame_(jobz, "A");
|
|
wntqs = lsame_(jobz, "S");
|
|
wntqas = wntqa || wntqs;
|
|
wntqo = lsame_(jobz, "O");
|
|
wntqn = lsame_(jobz, "N");
|
|
lquery = *lwork == -1;
|
|
minwrk = 1;
|
|
maxwrk = 1;
|
|
|
|
if (! (wntqa || wntqs || wntqo || wntqn)) {
|
|
*info = -1;
|
|
} else if (*m < 0) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -5;
|
|
} else if (*ldu < 1 || wntqas && *ldu < *m || wntqo && *m < *n && *ldu < *
|
|
m) {
|
|
*info = -8;
|
|
} else if (*ldvt < 1 || wntqa && *ldvt < *n || wntqs && *ldvt < minmn ||
|
|
wntqo && *m >= *n && *ldvt < *n) {
|
|
*info = -10;
|
|
}
|
|
|
|
/* Compute workspace */
|
|
/* Note: Comments in the code beginning "Workspace:" describe the */
|
|
/* minimal amount of workspace allocated 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) {
|
|
|
|
/* There is no complex work space needed for bidiagonal SVD */
|
|
/* The real work space needed for bidiagonal SVD (dbdsdc) is */
|
|
/* BDSPAC = 3*N*N + 4*N for singular values and vectors; */
|
|
/* BDSPAC = 4*N for singular values only; */
|
|
/* not including e, RU, and RVT matrices. */
|
|
|
|
/* Compute space preferred for each routine */
|
|
zgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zgebrd_mn__ = (integer) cdum[0].r;
|
|
|
|
zgebrd_(n, n, cdum, n, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zgebrd_nn__ = (integer) cdum[0].r;
|
|
|
|
zgeqrf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zgeqrf_mn__ = (integer) cdum[0].r;
|
|
|
|
zungbr_("P", n, n, n, cdum, n, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zungbr_p_nn__ = (integer) cdum[0].r;
|
|
|
|
zungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zungbr_q_mm__ = (integer) cdum[0].r;
|
|
|
|
zungbr_("Q", m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zungbr_q_mn__ = (integer) cdum[0].r;
|
|
|
|
zungqr_(m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zungqr_mm__ = (integer) cdum[0].r;
|
|
|
|
zungqr_(m, n, n, cdum, m, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zungqr_mn__ = (integer) cdum[0].r;
|
|
|
|
zunmbr_("P", "R", "C", n, n, n, cdum, n, cdum, cdum, n, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_zunmbr_prc_nn__ = (integer) cdum[0].r;
|
|
|
|
zunmbr_("Q", "L", "N", m, m, n, cdum, m, cdum, cdum, m, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_zunmbr_qln_mm__ = (integer) cdum[0].r;
|
|
|
|
zunmbr_("Q", "L", "N", m, n, n, cdum, m, cdum, cdum, m, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_zunmbr_qln_mn__ = (integer) cdum[0].r;
|
|
|
|
zunmbr_("Q", "L", "N", n, n, n, cdum, n, cdum, cdum, n, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_zunmbr_qln_nn__ = (integer) cdum[0].r;
|
|
|
|
if (*m >= mnthr1) {
|
|
if (wntqn) {
|
|
|
|
/* Path 1 (M >> N, JOBZ='N') */
|
|
|
|
maxwrk = *n + lwork_zgeqrf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zgebrd_nn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
minwrk = *n * 3;
|
|
} else if (wntqo) {
|
|
|
|
/* Path 2 (M >> N, JOBZ='O') */
|
|
|
|
wrkbl = *n + lwork_zgeqrf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n + lwork_zungqr_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*n << 1) + lwork_zgebrd_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_qln_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = *m * *n + *n * *n + wrkbl;
|
|
minwrk = (*n << 1) * *n + *n * 3;
|
|
} else if (wntqs) {
|
|
|
|
/* Path 3 (M >> N, JOBZ='S') */
|
|
|
|
wrkbl = *n + lwork_zgeqrf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n + lwork_zungqr_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*n << 1) + lwork_zgebrd_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_qln_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = *n * *n + wrkbl;
|
|
minwrk = *n * *n + *n * 3;
|
|
} else if (wntqa) {
|
|
|
|
/* Path 4 (M >> N, JOBZ='A') */
|
|
|
|
wrkbl = *n + lwork_zgeqrf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *n + lwork_zungqr_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*n << 1) + lwork_zgebrd_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_qln_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = *n * *n + wrkbl;
|
|
/* Computing MAX */
|
|
i__1 = *n * 3, i__2 = *n + *m;
|
|
minwrk = *n * *n + f2cmax(i__1,i__2);
|
|
}
|
|
} else if (*m >= mnthr2) {
|
|
|
|
/* Path 5 (M >> N, but not as much as MNTHR1) */
|
|
|
|
maxwrk = (*n << 1) + lwork_zgebrd_mn__;
|
|
minwrk = (*n << 1) + *m;
|
|
if (wntqo) {
|
|
/* Path 5o (M >> N, JOBZ='O') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_p_nn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_q_mn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
maxwrk += *m * *n;
|
|
minwrk += *n * *n;
|
|
} else if (wntqs) {
|
|
/* Path 5s (M >> N, JOBZ='S') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_p_nn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_q_mn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
} else if (wntqa) {
|
|
/* Path 5a (M >> N, JOBZ='A') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_p_nn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zungbr_q_mm__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
}
|
|
} else {
|
|
|
|
/* Path 6 (M >= N, but not much larger) */
|
|
|
|
maxwrk = (*n << 1) + lwork_zgebrd_mn__;
|
|
minwrk = (*n << 1) + *m;
|
|
if (wntqo) {
|
|
/* Path 6o (M >= N, JOBZ='O') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_qln_mn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
maxwrk += *m * *n;
|
|
minwrk += *n * *n;
|
|
} else if (wntqs) {
|
|
/* Path 6s (M >= N, JOBZ='S') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_qln_mn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
} else if (wntqa) {
|
|
/* Path 6a (M >= N, JOBZ='A') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_qln_mm__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*n << 1) + lwork_zunmbr_prc_nn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
}
|
|
}
|
|
} else if (minmn > 0) {
|
|
|
|
/* There is no complex work space needed for bidiagonal SVD */
|
|
/* The real work space needed for bidiagonal SVD (dbdsdc) is */
|
|
/* BDSPAC = 3*M*M + 4*M for singular values and vectors; */
|
|
/* BDSPAC = 4*M for singular values only; */
|
|
/* not including e, RU, and RVT matrices. */
|
|
|
|
/* Compute space preferred for each routine */
|
|
zgebrd_(m, n, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zgebrd_mn__ = (integer) cdum[0].r;
|
|
|
|
zgebrd_(m, m, cdum, m, dum, dum, cdum, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zgebrd_mm__ = (integer) cdum[0].r;
|
|
|
|
zgelqf_(m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zgelqf_mn__ = (integer) cdum[0].r;
|
|
|
|
zungbr_("P", m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zungbr_p_mn__ = (integer) cdum[0].r;
|
|
|
|
zungbr_("P", n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zungbr_p_nn__ = (integer) cdum[0].r;
|
|
|
|
zungbr_("Q", m, m, n, cdum, m, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zungbr_q_mm__ = (integer) cdum[0].r;
|
|
|
|
zunglq_(m, n, m, cdum, m, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zunglq_mn__ = (integer) cdum[0].r;
|
|
|
|
zunglq_(n, n, m, cdum, n, cdum, cdum, &c_n1, &ierr);
|
|
lwork_zunglq_nn__ = (integer) cdum[0].r;
|
|
|
|
zunmbr_("P", "R", "C", m, m, m, cdum, m, cdum, cdum, m, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_zunmbr_prc_mm__ = (integer) cdum[0].r;
|
|
|
|
zunmbr_("P", "R", "C", m, n, m, cdum, m, cdum, cdum, m, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_zunmbr_prc_mn__ = (integer) cdum[0].r;
|
|
|
|
zunmbr_("P", "R", "C", n, n, m, cdum, n, cdum, cdum, n, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_zunmbr_prc_nn__ = (integer) cdum[0].r;
|
|
|
|
zunmbr_("Q", "L", "N", m, m, m, cdum, m, cdum, cdum, m, cdum, &
|
|
c_n1, &ierr);
|
|
lwork_zunmbr_qln_mm__ = (integer) cdum[0].r;
|
|
|
|
if (*n >= mnthr1) {
|
|
if (wntqn) {
|
|
|
|
/* Path 1t (N >> M, JOBZ='N') */
|
|
|
|
maxwrk = *m + lwork_zgelqf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zgebrd_mm__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
minwrk = *m * 3;
|
|
} else if (wntqo) {
|
|
|
|
/* Path 2t (N >> M, JOBZ='O') */
|
|
|
|
wrkbl = *m + lwork_zgelqf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m + lwork_zunglq_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*m << 1) + lwork_zgebrd_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_prc_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = *m * *n + *m * *m + wrkbl;
|
|
minwrk = (*m << 1) * *m + *m * 3;
|
|
} else if (wntqs) {
|
|
|
|
/* Path 3t (N >> M, JOBZ='S') */
|
|
|
|
wrkbl = *m + lwork_zgelqf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m + lwork_zunglq_mn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*m << 1) + lwork_zgebrd_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_prc_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = *m * *m + wrkbl;
|
|
minwrk = *m * *m + *m * 3;
|
|
} else if (wntqa) {
|
|
|
|
/* Path 4t (N >> M, JOBZ='A') */
|
|
|
|
wrkbl = *m + lwork_zgelqf_mn__;
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = *m + lwork_zunglq_nn__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*m << 1) + lwork_zgebrd_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = wrkbl, i__2 = (*m << 1) + lwork_zunmbr_prc_mm__;
|
|
wrkbl = f2cmax(i__1,i__2);
|
|
maxwrk = *m * *m + wrkbl;
|
|
/* Computing MAX */
|
|
i__1 = *m * 3, i__2 = *m + *n;
|
|
minwrk = *m * *m + f2cmax(i__1,i__2);
|
|
}
|
|
} else if (*n >= mnthr2) {
|
|
|
|
/* Path 5t (N >> M, but not as much as MNTHR1) */
|
|
|
|
maxwrk = (*m << 1) + lwork_zgebrd_mn__;
|
|
minwrk = (*m << 1) + *n;
|
|
if (wntqo) {
|
|
/* Path 5to (N >> M, JOBZ='O') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_q_mm__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_p_mn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
maxwrk += *m * *n;
|
|
minwrk += *m * *m;
|
|
} else if (wntqs) {
|
|
/* Path 5ts (N >> M, JOBZ='S') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_q_mm__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_p_mn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
} else if (wntqa) {
|
|
/* Path 5ta (N >> M, JOBZ='A') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_q_mm__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zungbr_p_nn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
}
|
|
} else {
|
|
|
|
/* Path 6t (N > M, but not much larger) */
|
|
|
|
maxwrk = (*m << 1) + lwork_zgebrd_mn__;
|
|
minwrk = (*m << 1) + *n;
|
|
if (wntqo) {
|
|
/* Path 6to (N > M, JOBZ='O') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_prc_mn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
maxwrk += *m * *n;
|
|
minwrk += *m * *m;
|
|
} else if (wntqs) {
|
|
/* Path 6ts (N > M, JOBZ='S') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_prc_mn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
} else if (wntqa) {
|
|
/* Path 6ta (N > M, JOBZ='A') */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_qln_mm__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = (*m << 1) + lwork_zunmbr_prc_nn__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
}
|
|
}
|
|
}
|
|
maxwrk = f2cmax(maxwrk,minwrk);
|
|
}
|
|
if (*info == 0) {
|
|
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
|
|
if (*lwork < minwrk && ! lquery) {
|
|
*info = -12;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZGESDD", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*m == 0 || *n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Get machine constants */
|
|
|
|
eps = dlamch_("P");
|
|
smlnum = sqrt(dlamch_("S")) / eps;
|
|
bignum = 1. / smlnum;
|
|
|
|
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
|
|
|
|
anrm = zlange_("M", m, n, &a[a_offset], lda, dum);
|
|
if (disnan_(&anrm)) {
|
|
*info = -4;
|
|
return;
|
|
}
|
|
iscl = 0;
|
|
if (anrm > 0. && anrm < smlnum) {
|
|
iscl = 1;
|
|
zlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &
|
|
ierr);
|
|
} else if (anrm > bignum) {
|
|
iscl = 1;
|
|
zlascl_("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 >= mnthr1) {
|
|
|
|
if (wntqn) {
|
|
|
|
/* Path 1 (M >> N, JOBZ='N') */
|
|
/* No singular vectors to be computed */
|
|
|
|
itau = 1;
|
|
nwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* CWorkspace: need N [tau] + N [work] */
|
|
/* CWorkspace: prefer N [tau] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__1, &ierr);
|
|
|
|
/* Zero out below R */
|
|
|
|
i__1 = *n - 1;
|
|
i__2 = *n - 1;
|
|
zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
|
|
ie = 1;
|
|
itauq = 1;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + 2*N*NB [work] */
|
|
/* RWorkspace: need N [e] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
|
|
nrwork = ie + *n;
|
|
|
|
/* Perform bidiagonal SVD, compute singular values only */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + BDSPAC */
|
|
|
|
dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
|
|
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
|
|
|
|
} else if (wntqo) {
|
|
|
|
/* Path 2 (M >> N, JOBZ='O') */
|
|
/* N left singular vectors to be overwritten on A and */
|
|
/* N right singular vectors to be computed in VT */
|
|
|
|
iu = 1;
|
|
|
|
/* WORK(IU) is N by N */
|
|
|
|
ldwrku = *n;
|
|
ir = iu + ldwrku * *n;
|
|
if (*lwork >= *m * *n + *n * *n + *n * 3) {
|
|
|
|
/* WORK(IR) is M by N */
|
|
|
|
ldwrkr = *m;
|
|
} else {
|
|
ldwrkr = (*lwork - *n * *n - *n * 3) / *n;
|
|
}
|
|
itau = ir + ldwrkr * *n;
|
|
nwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */
|
|
/* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__1, &ierr);
|
|
|
|
/* Copy R to WORK( IR ), zeroing out below it */
|
|
|
|
zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
|
|
i__1 = *n - 1;
|
|
i__2 = *n - 1;
|
|
zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &work[ir + 1], &
|
|
ldwrkr);
|
|
|
|
/* Generate Q in A */
|
|
/* CWorkspace: need N*N [U] + N*N [R] + N [tau] + N [work] */
|
|
/* CWorkspace: prefer N*N [U] + N*N [R] + N [tau] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
|
|
&i__1, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IR) */
|
|
/* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */
|
|
/* RWorkspace: need N [e] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of R in WORK(IRU) and computing right singular vectors */
|
|
/* of R in WORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
|
|
|
|
iru = ie + *n;
|
|
irvt = iru + *n * *n;
|
|
nrwork = irvt + *n * *n;
|
|
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
|
|
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
|
|
/* Overwrite WORK(IU) by the left singular vectors of R */
|
|
/* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
|
|
itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
|
|
ierr);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix VT */
|
|
/* Overwrite VT by the right singular vectors of R */
|
|
/* CWorkspace: need N*N [U] + N*N [R] + 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer N*N [U] + N*N [R] + 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
|
|
/* Multiply Q in A by left singular vectors of R in */
|
|
/* WORK(IU), storing result in WORK(IR) and copying to A */
|
|
/* CWorkspace: need N*N [U] + N*N [R] */
|
|
/* CWorkspace: prefer N*N [U] + M*N [R] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__1 = *m;
|
|
i__2 = ldwrkr;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *m - i__ + 1;
|
|
chunk = f2cmin(i__3,ldwrkr);
|
|
zgemm_("N", "N", &chunk, n, n, &c_b2, &a[i__ + a_dim1],
|
|
lda, &work[iu], &ldwrku, &c_b1, &work[ir], &
|
|
ldwrkr);
|
|
zlacpy_("F", &chunk, n, &work[ir], &ldwrkr, &a[i__ +
|
|
a_dim1], lda);
|
|
/* L10: */
|
|
}
|
|
|
|
} else if (wntqs) {
|
|
|
|
/* Path 3 (M >> N, JOBZ='S') */
|
|
/* N left singular vectors to be computed in U and */
|
|
/* N right singular vectors to be computed in VT */
|
|
|
|
ir = 1;
|
|
|
|
/* WORK(IR) is N by N */
|
|
|
|
ldwrkr = *n;
|
|
itau = ir + ldwrkr * *n;
|
|
nwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* CWorkspace: need N*N [R] + N [tau] + N [work] */
|
|
/* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Copy R to WORK(IR), zeroing out below it */
|
|
|
|
zlacpy_("U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr);
|
|
i__2 = *n - 1;
|
|
i__1 = *n - 1;
|
|
zlaset_("L", &i__2, &i__1, &c_b1, &c_b1, &work[ir + 1], &
|
|
ldwrkr);
|
|
|
|
/* Generate Q in A */
|
|
/* CWorkspace: need N*N [R] + N [tau] + N [work] */
|
|
/* CWorkspace: prefer N*N [R] + N [tau] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zungqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[nwork],
|
|
&i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in WORK(IR) */
|
|
/* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + 2*N*NB [work] */
|
|
/* RWorkspace: need N [e] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
|
|
|
|
iru = ie + *n;
|
|
irvt = iru + *n * *n;
|
|
nrwork = irvt + *n * *n;
|
|
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
|
|
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix U */
|
|
/* Overwrite U by left singular vectors of R */
|
|
/* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", n, n, n, &work[ir], &ldwrkr, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix VT */
|
|
/* Overwrite VT by right singular vectors of R */
|
|
/* CWorkspace: need N*N [R] + 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer N*N [R] + 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", n, n, n, &work[ir], &ldwrkr, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Multiply Q in A by left singular vectors of R in */
|
|
/* WORK(IR), storing result in U */
|
|
/* CWorkspace: need N*N [R] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("F", n, n, &u[u_offset], ldu, &work[ir], &ldwrkr);
|
|
zgemm_("N", "N", m, n, n, &c_b2, &a[a_offset], lda, &work[ir],
|
|
&ldwrkr, &c_b1, &u[u_offset], ldu);
|
|
|
|
} else if (wntqa) {
|
|
|
|
/* Path 4 (M >> N, JOBZ='A') */
|
|
/* M left singular vectors to be computed in U and */
|
|
/* N right singular vectors to be computed in VT */
|
|
|
|
iu = 1;
|
|
|
|
/* WORK(IU) is N by N */
|
|
|
|
ldwrku = *n;
|
|
itau = iu + ldwrku * *n;
|
|
nwork = itau + *n;
|
|
|
|
/* Compute A=Q*R, copying result to U */
|
|
/* CWorkspace: need N*N [U] + N [tau] + N [work] */
|
|
/* CWorkspace: prefer N*N [U] + N [tau] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__2, &ierr);
|
|
zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
|
|
|
|
/* Generate Q in U */
|
|
/* CWorkspace: need N*N [U] + N [tau] + M [work] */
|
|
/* CWorkspace: prefer N*N [U] + N [tau] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zungqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[nwork],
|
|
&i__2, &ierr);
|
|
|
|
/* Produce R in A, zeroing out below it */
|
|
|
|
i__2 = *n - 1;
|
|
i__1 = *n - 1;
|
|
zlaset_("L", &i__2, &i__1, &c_b1, &c_b1, &a[a_dim1 + 2], lda);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + 2*N*NB [work] */
|
|
/* RWorkspace: need N [e] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zgebrd_(n, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
|
|
iru = ie + *n;
|
|
irvt = iru + *n * *n;
|
|
nrwork = irvt + *n * *n;
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
|
|
|
|
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
|
|
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
|
|
/* Overwrite WORK(IU) by left singular vectors of R */
|
|
/* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", n, n, n, &a[a_offset], lda, &work[
|
|
itauq], &work[iu], &ldwrku, &work[nwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix VT */
|
|
/* Overwrite VT by right singular vectors of R */
|
|
/* CWorkspace: need N*N [U] + 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer N*N [U] + 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Multiply Q in U by left singular vectors of R in */
|
|
/* WORK(IU), storing result in A */
|
|
/* CWorkspace: need N*N [U] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zgemm_("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 */
|
|
|
|
zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
|
|
|
|
}
|
|
|
|
} else if (*m >= mnthr2) {
|
|
|
|
/* MNTHR2 <= M < MNTHR1 */
|
|
|
|
/* Path 5 (M >> N, but not as much as MNTHR1) */
|
|
/* Reduce to bidiagonal form without QR decomposition, use */
|
|
/* ZUNGBR and matrix multiplication to compute singular vectors */
|
|
|
|
ie = 1;
|
|
nrwork = ie + *n;
|
|
itauq = 1;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */
|
|
/* RWorkspace: need N [e] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
|
|
&work[itaup], &work[nwork], &i__2, &ierr);
|
|
if (wntqn) {
|
|
|
|
/* Path 5n (M >> N, JOBZ='N') */
|
|
/* Compute singular values only */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + BDSPAC */
|
|
|
|
dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
|
|
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
|
|
} else if (wntqo) {
|
|
iu = nwork;
|
|
iru = nrwork;
|
|
irvt = iru + *n * *n;
|
|
nrwork = irvt + *n * *n;
|
|
|
|
/* Path 5o (M >> N, JOBZ='O') */
|
|
/* Copy A to VT, generate P**H */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
i__2 = *lwork - nwork + 1;
|
|
zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
|
|
work[nwork], &i__2, &ierr);
|
|
|
|
/* Generate Q in A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[
|
|
nwork], &i__2, &ierr);
|
|
|
|
if (*lwork >= *m * *n + *n * 3) {
|
|
|
|
/* WORK( IU ) is M by N */
|
|
|
|
ldwrku = *m;
|
|
} else {
|
|
|
|
/* WORK(IU) is LDWRKU by N */
|
|
|
|
ldwrku = (*lwork - *n * 3) / *n;
|
|
}
|
|
nwork = iu + ldwrku * *n;
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
|
|
|
|
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
|
|
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Multiply real matrix RWORK(IRVT) by P**H in VT, */
|
|
/* storing the result in WORK(IU), copying to VT */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
|
|
|
|
zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &work[iu]
|
|
, &ldwrku, &rwork[nrwork]);
|
|
zlacpy_("F", n, n, &work[iu], &ldwrku, &vt[vt_offset], ldvt);
|
|
|
|
/* Multiply Q in A by real matrix RWORK(IRU), storing the */
|
|
/* result in WORK(IU), copying to A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */
|
|
/* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */
|
|
/* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
|
|
|
|
nrwork = irvt;
|
|
i__2 = *m;
|
|
i__1 = ldwrku;
|
|
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
|
|
i__1) {
|
|
/* Computing MIN */
|
|
i__3 = *m - i__ + 1;
|
|
chunk = f2cmin(i__3,ldwrku);
|
|
zlacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru], n,
|
|
&work[iu], &ldwrku, &rwork[nrwork]);
|
|
zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
|
|
a_dim1], lda);
|
|
/* L20: */
|
|
}
|
|
|
|
} else if (wntqs) {
|
|
|
|
/* Path 5s (M >> N, JOBZ='S') */
|
|
/* Copy A to VT, generate P**H */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
i__1 = *lwork - nwork + 1;
|
|
zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
|
|
work[nwork], &i__1, &ierr);
|
|
|
|
/* Copy A to U, generate Q */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
|
|
i__1 = *lwork - nwork + 1;
|
|
zungbr_("Q", m, n, n, &u[u_offset], ldu, &work[itauq], &work[
|
|
nwork], &i__1, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
|
|
|
|
iru = nrwork;
|
|
irvt = iru + *n * *n;
|
|
nrwork = irvt + *n * *n;
|
|
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
|
|
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Multiply real matrix RWORK(IRVT) by P**H in VT, */
|
|
/* storing the result in A, copying to VT */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
|
|
|
|
zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
|
|
a_offset], lda, &rwork[nrwork]);
|
|
zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
|
|
/* Multiply Q in U by real matrix RWORK(IRU), storing the */
|
|
/* result in A, copying to U */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
|
|
|
|
nrwork = irvt;
|
|
zlacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
|
|
lda, &rwork[nrwork]);
|
|
zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
|
|
} else {
|
|
|
|
/* Path 5a (M >> N, JOBZ='A') */
|
|
/* Copy A to VT, generate P**H */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
i__1 = *lwork - nwork + 1;
|
|
zungbr_("P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &
|
|
work[nwork], &i__1, &ierr);
|
|
|
|
/* Copy A to U, generate Q */
|
|
/* CWorkspace: need 2*N [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("L", m, n, &a[a_offset], lda, &u[u_offset], ldu);
|
|
i__1 = *lwork - nwork + 1;
|
|
zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
|
|
nwork], &i__1, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
|
|
|
|
iru = nrwork;
|
|
irvt = iru + *n * *n;
|
|
nrwork = irvt + *n * *n;
|
|
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
|
|
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Multiply real matrix RWORK(IRVT) by P**H in VT, */
|
|
/* storing the result in A, copying to VT */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + 2*N*N [rwork] */
|
|
|
|
zlarcm_(n, n, &rwork[irvt], n, &vt[vt_offset], ldvt, &a[
|
|
a_offset], lda, &rwork[nrwork]);
|
|
zlacpy_("F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
|
|
/* Multiply Q in U by real matrix RWORK(IRU), storing the */
|
|
/* result in A, copying to U */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
|
|
|
|
nrwork = irvt;
|
|
zlacrm_(m, n, &u[u_offset], ldu, &rwork[iru], n, &a[a_offset],
|
|
lda, &rwork[nrwork]);
|
|
zlacpy_("F", m, n, &a[a_offset], lda, &u[u_offset], ldu);
|
|
}
|
|
|
|
} else {
|
|
|
|
/* M .LT. MNTHR2 */
|
|
|
|
/* Path 6 (M >= N, but not much larger) */
|
|
/* Reduce to bidiagonal form without QR decomposition */
|
|
/* Use ZUNMBR to compute singular vectors */
|
|
|
|
ie = 1;
|
|
nrwork = ie + *n;
|
|
itauq = 1;
|
|
itaup = itauq + *n;
|
|
nwork = itaup + *n;
|
|
|
|
/* Bidiagonalize A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + (M+N)*NB [work] */
|
|
/* RWorkspace: need N [e] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
|
|
&work[itaup], &work[nwork], &i__1, &ierr);
|
|
if (wntqn) {
|
|
|
|
/* Path 6n (M >= N, JOBZ='N') */
|
|
/* Compute singular values only */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + BDSPAC */
|
|
|
|
dbdsdc_("U", "N", n, &s[1], &rwork[ie], dum, &c__1, dum, &
|
|
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
|
|
} else if (wntqo) {
|
|
iu = nwork;
|
|
iru = nrwork;
|
|
irvt = iru + *n * *n;
|
|
nrwork = irvt + *n * *n;
|
|
if (*lwork >= *m * *n + *n * 3) {
|
|
|
|
/* WORK( IU ) is M by N */
|
|
|
|
ldwrku = *m;
|
|
} else {
|
|
|
|
/* WORK( IU ) is LDWRKU by N */
|
|
|
|
ldwrku = (*lwork - *n * 3) / *n;
|
|
}
|
|
nwork = iu + ldwrku * *n;
|
|
|
|
/* Path 6o (M >= N, JOBZ='O') */
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
|
|
|
|
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
|
|
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix VT */
|
|
/* Overwrite VT by right singular vectors of A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
|
|
|
|
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
|
|
if (*lwork >= *m * *n + *n * 3) {
|
|
|
|
/* Path 6o-fast */
|
|
/* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
|
|
/* Overwrite WORK(IU) by left singular vectors of A, copying */
|
|
/* to A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + M*N [U] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] + N*NB [work] */
|
|
/* RWorkspace: need N [e] + N*N [RU] */
|
|
|
|
zlaset_("F", m, n, &c_b1, &c_b1, &work[iu], &ldwrku);
|
|
zlacp2_("F", n, n, &rwork[iru], n, &work[iu], &ldwrku);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
|
|
itauq], &work[iu], &ldwrku, &work[nwork], &i__1, &
|
|
ierr);
|
|
zlacpy_("F", m, n, &work[iu], &ldwrku, &a[a_offset], lda);
|
|
} else {
|
|
|
|
/* Path 6o-slow */
|
|
/* Generate Q in A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N*N [U] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + N*N [U] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zungbr_("Q", m, n, n, &a[a_offset], lda, &work[itauq], &
|
|
work[nwork], &i__1, &ierr);
|
|
|
|
/* Multiply Q in A by real matrix RWORK(IRU), storing the */
|
|
/* result in WORK(IU), copying to A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N*N [U] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + M*N [U] */
|
|
/* RWorkspace: need N [e] + N*N [RU] + 2*N*N [rwork] */
|
|
/* RWorkspace: prefer N [e] + N*N [RU] + 2*M*N [rwork] < N + 5*N*N since M < 2*N here */
|
|
|
|
nrwork = irvt;
|
|
i__1 = *m;
|
|
i__2 = ldwrku;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *m - i__ + 1;
|
|
chunk = f2cmin(i__3,ldwrku);
|
|
zlacrm_(&chunk, n, &a[i__ + a_dim1], lda, &rwork[iru],
|
|
n, &work[iu], &ldwrku, &rwork[nrwork]);
|
|
zlacpy_("F", &chunk, n, &work[iu], &ldwrku, &a[i__ +
|
|
a_dim1], lda);
|
|
/* L30: */
|
|
}
|
|
}
|
|
|
|
} else if (wntqs) {
|
|
|
|
/* Path 6s (M >= N, JOBZ='S') */
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
|
|
|
|
iru = nrwork;
|
|
irvt = iru + *n * *n;
|
|
nrwork = irvt + *n * *n;
|
|
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
|
|
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix U */
|
|
/* Overwrite U by left singular vectors of A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
|
|
|
|
zlaset_("F", m, n, &c_b1, &c_b1, &u[u_offset], ldu)
|
|
;
|
|
zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", m, n, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix VT */
|
|
/* Overwrite VT by right singular vectors of A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
|
|
|
|
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
|
|
ierr);
|
|
} else {
|
|
|
|
/* Path 6a (M >= N, JOBZ='A') */
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] + BDSPAC */
|
|
|
|
iru = nrwork;
|
|
irvt = iru + *n * *n;
|
|
nrwork = irvt + *n * *n;
|
|
dbdsdc_("U", "I", n, &s[1], &rwork[ie], &rwork[iru], n, &
|
|
rwork[irvt], n, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Set the right corner of U to identity matrix */
|
|
|
|
zlaset_("F", m, m, &c_b1, &c_b1, &u[u_offset], ldu)
|
|
;
|
|
if (*m > *n) {
|
|
i__2 = *m - *n;
|
|
i__1 = *m - *n;
|
|
zlaset_("F", &i__2, &i__1, &c_b1, &c_b2, &u[*n + 1 + (*n
|
|
+ 1) * u_dim1], ldu);
|
|
}
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix U */
|
|
/* Overwrite U by left singular vectors of A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
|
|
|
|
zlacp2_("F", n, n, &rwork[iru], n, &u[u_offset], ldu);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix VT */
|
|
/* Overwrite VT by right singular vectors of A */
|
|
/* CWorkspace: need 2*N [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*N [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need N [e] + N*N [RU] + N*N [RVT] */
|
|
|
|
zlacp2_("F", n, n, &rwork[irvt], n, &vt[vt_offset], ldvt);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", n, n, n, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__2, &
|
|
ierr);
|
|
}
|
|
|
|
}
|
|
|
|
} 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 >= mnthr1) {
|
|
|
|
if (wntqn) {
|
|
|
|
/* Path 1t (N >> M, JOBZ='N') */
|
|
/* No singular vectors to be computed */
|
|
|
|
itau = 1;
|
|
nwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* CWorkspace: need M [tau] + M [work] */
|
|
/* CWorkspace: prefer M [tau] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Zero out above L */
|
|
|
|
i__2 = *m - 1;
|
|
i__1 = *m - 1;
|
|
zlaset_("U", &i__2, &i__1, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
|
|
, lda);
|
|
ie = 1;
|
|
itauq = 1;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + 2*M*NB [work] */
|
|
/* RWorkspace: need M [e] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
|
|
nrwork = ie + *m;
|
|
|
|
/* Perform bidiagonal SVD, compute singular values only */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + BDSPAC */
|
|
|
|
dbdsdc_("U", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
|
|
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
|
|
|
|
} else if (wntqo) {
|
|
|
|
/* Path 2t (N >> M, JOBZ='O') */
|
|
/* M right singular vectors to be overwritten on A and */
|
|
/* M left singular vectors to be computed in U */
|
|
|
|
ivt = 1;
|
|
ldwkvt = *m;
|
|
|
|
/* WORK(IVT) is M by M */
|
|
|
|
il = ivt + ldwkvt * *m;
|
|
if (*lwork >= *m * *n + *m * *m + *m * 3) {
|
|
|
|
/* WORK(IL) M by N */
|
|
|
|
ldwrkl = *m;
|
|
chunk = *n;
|
|
} else {
|
|
|
|
/* WORK(IL) is M by CHUNK */
|
|
|
|
ldwrkl = *m;
|
|
chunk = (*lwork - *m * *m - *m * 3) / *m;
|
|
}
|
|
itau = il + ldwrkl * chunk;
|
|
nwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
|
|
/* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__2, &ierr);
|
|
|
|
/* Copy L to WORK(IL), zeroing about above it */
|
|
|
|
zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
|
|
i__2 = *m - 1;
|
|
i__1 = *m - 1;
|
|
zlaset_("U", &i__2, &i__1, &c_b1, &c_b1, &work[il + ldwrkl], &
|
|
ldwrkl);
|
|
|
|
/* Generate Q in A */
|
|
/* CWorkspace: need M*M [VT] + M*M [L] + M [tau] + M [work] */
|
|
/* CWorkspace: prefer M*M [VT] + M*M [L] + M [tau] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
|
|
&i__2, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IL) */
|
|
/* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */
|
|
/* RWorkspace: need M [e] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__2, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
|
|
|
|
iru = ie + *m;
|
|
irvt = iru + *m * *m;
|
|
nrwork = irvt + *m * *m;
|
|
dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
|
|
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix WORK(IU) */
|
|
/* Overwrite WORK(IU) by the left singular vectors of L */
|
|
/* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
|
|
/* Overwrite WORK(IVT) by the right singular vectors of L */
|
|
/* CWorkspace: need M*M [VT] + M*M [L] + 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer M*M [VT] + M*M [L] + 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
|
|
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2, &
|
|
ierr);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IL) by Q */
|
|
/* in A, storing result in WORK(IL) and copying to A */
|
|
/* CWorkspace: need M*M [VT] + M*M [L] */
|
|
/* CWorkspace: prefer M*M [VT] + M*N [L] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__2 = *n;
|
|
i__1 = chunk;
|
|
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
|
|
i__1) {
|
|
/* Computing MIN */
|
|
i__3 = *n - i__ + 1;
|
|
blk = f2cmin(i__3,chunk);
|
|
zgemm_("N", "N", m, &blk, m, &c_b2, &work[ivt], m, &a[i__
|
|
* a_dim1 + 1], lda, &c_b1, &work[il], &ldwrkl);
|
|
zlacpy_("F", m, &blk, &work[il], &ldwrkl, &a[i__ * a_dim1
|
|
+ 1], lda);
|
|
/* L40: */
|
|
}
|
|
|
|
} else if (wntqs) {
|
|
|
|
/* Path 3t (N >> M, JOBZ='S') */
|
|
/* M right singular vectors to be computed in VT and */
|
|
/* M left singular vectors to be computed in U */
|
|
|
|
il = 1;
|
|
|
|
/* WORK(IL) is M by M */
|
|
|
|
ldwrkl = *m;
|
|
itau = il + ldwrkl * *m;
|
|
nwork = itau + *m;
|
|
|
|
/* Compute A=L*Q */
|
|
/* CWorkspace: need M*M [L] + M [tau] + M [work] */
|
|
/* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__1, &ierr);
|
|
|
|
/* Copy L to WORK(IL), zeroing out above it */
|
|
|
|
zlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwrkl);
|
|
i__1 = *m - 1;
|
|
i__2 = *m - 1;
|
|
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &work[il + ldwrkl], &
|
|
ldwrkl);
|
|
|
|
/* Generate Q in A */
|
|
/* CWorkspace: need M*M [L] + M [tau] + M [work] */
|
|
/* CWorkspace: prefer M*M [L] + M [tau] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zunglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[nwork],
|
|
&i__1, &ierr);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IL) */
|
|
/* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + 2*M*NB [work] */
|
|
/* RWorkspace: need M [e] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zgebrd_(m, m, &work[il], &ldwrkl, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
|
|
|
|
iru = ie + *m;
|
|
irvt = iru + *m * *m;
|
|
nrwork = irvt + *m * *m;
|
|
dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
|
|
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix U */
|
|
/* Overwrite U by left singular vectors of L */
|
|
/* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", m, m, m, &work[il], &ldwrkl, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix VT */
|
|
/* Overwrite VT by left singular vectors of L */
|
|
/* CWorkspace: need M*M [L] + 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer M*M [L] + 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", m, m, m, &work[il], &ldwrkl, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
|
|
/* Copy VT to WORK(IL), multiply right singular vectors of L */
|
|
/* in WORK(IL) by Q in A, storing result in VT */
|
|
/* CWorkspace: need M*M [L] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("F", m, m, &vt[vt_offset], ldvt, &work[il], &ldwrkl);
|
|
zgemm_("N", "N", m, n, m, &c_b2, &work[il], &ldwrkl, &a[
|
|
a_offset], lda, &c_b1, &vt[vt_offset], ldvt);
|
|
|
|
} else if (wntqa) {
|
|
|
|
/* Path 4t (N >> M, JOBZ='A') */
|
|
/* N right singular vectors to be computed in VT and */
|
|
/* M left singular vectors to be computed in U */
|
|
|
|
ivt = 1;
|
|
|
|
/* WORK(IVT) is M by M */
|
|
|
|
ldwkvt = *m;
|
|
itau = ivt + ldwkvt * *m;
|
|
nwork = itau + *m;
|
|
|
|
/* Compute A=L*Q, copying result to VT */
|
|
/* CWorkspace: need M*M [VT] + M [tau] + M [work] */
|
|
/* CWorkspace: prefer M*M [VT] + M [tau] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &
|
|
i__1, &ierr);
|
|
zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
|
|
/* Generate Q in VT */
|
|
/* CWorkspace: need M*M [VT] + M [tau] + N [work] */
|
|
/* CWorkspace: prefer M*M [VT] + M [tau] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zunglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[
|
|
nwork], &i__1, &ierr);
|
|
|
|
/* Produce L in A, zeroing out above it */
|
|
|
|
i__1 = *m - 1;
|
|
i__2 = *m - 1;
|
|
zlaset_("U", &i__1, &i__2, &c_b1, &c_b1, &a[(a_dim1 << 1) + 1]
|
|
, lda);
|
|
ie = 1;
|
|
itauq = itau;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in A */
|
|
/* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + 2*M*NB [work] */
|
|
/* RWorkspace: need M [e] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zgebrd_(m, m, &a[a_offset], lda, &s[1], &rwork[ie], &work[
|
|
itauq], &work[itaup], &work[nwork], &i__1, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RU] + M*M [RVT] + BDSPAC */
|
|
|
|
iru = ie + *m;
|
|
irvt = iru + *m * *m;
|
|
nrwork = irvt + *m * *m;
|
|
dbdsdc_("U", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
|
|
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix U */
|
|
/* Overwrite U by left singular vectors of L */
|
|
/* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", m, m, m, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
|
|
/* Overwrite WORK(IVT) by right singular vectors of L */
|
|
/* CWorkspace: need M*M [VT] + 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer M*M [VT] + 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", m, m, m, &a[a_offset], lda, &work[
|
|
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
|
|
/* Multiply right singular vectors of L in WORK(IVT) by */
|
|
/* Q in VT, storing result in A */
|
|
/* CWorkspace: need M*M [VT] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zgemm_("N", "N", m, n, m, &c_b2, &work[ivt], &ldwkvt, &vt[
|
|
vt_offset], ldvt, &c_b1, &a[a_offset], lda);
|
|
|
|
/* Copy right singular vectors of A from A to VT */
|
|
|
|
zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
|
|
}
|
|
|
|
} else if (*n >= mnthr2) {
|
|
|
|
/* MNTHR2 <= N < MNTHR1 */
|
|
|
|
/* Path 5t (N >> M, but not as much as MNTHR1) */
|
|
/* Reduce to bidiagonal form without QR decomposition, use */
|
|
/* ZUNGBR and matrix multiplication to compute singular vectors */
|
|
|
|
ie = 1;
|
|
nrwork = ie + *m;
|
|
itauq = 1;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */
|
|
/* RWorkspace: need M [e] */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
|
|
&work[itaup], &work[nwork], &i__1, &ierr);
|
|
|
|
if (wntqn) {
|
|
|
|
/* Path 5tn (N >> M, JOBZ='N') */
|
|
/* Compute singular values only */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + BDSPAC */
|
|
|
|
dbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
|
|
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
|
|
} else if (wntqo) {
|
|
irvt = nrwork;
|
|
iru = irvt + *m * *m;
|
|
nrwork = iru + *m * *m;
|
|
ivt = nwork;
|
|
|
|
/* Path 5to (N >> M, JOBZ='O') */
|
|
/* Copy A to U, generate Q */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
|
|
i__1 = *lwork - nwork + 1;
|
|
zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
|
|
nwork], &i__1, &ierr);
|
|
|
|
/* Generate P**H in A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__1 = *lwork - nwork + 1;
|
|
zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
|
|
nwork], &i__1, &ierr);
|
|
|
|
ldwkvt = *m;
|
|
if (*lwork >= *m * *n + *m * 3) {
|
|
|
|
/* WORK( IVT ) is M by N */
|
|
|
|
nwork = ivt + ldwkvt * *n;
|
|
chunk = *n;
|
|
} else {
|
|
|
|
/* WORK( IVT ) is M by CHUNK */
|
|
|
|
chunk = (*lwork - *m * 3) / *m;
|
|
nwork = ivt + ldwkvt * chunk;
|
|
}
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
|
|
|
|
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
|
|
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Multiply Q in U by real matrix RWORK(IRVT) */
|
|
/* storing the result in WORK(IVT), copying to U */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
|
|
|
|
zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &work[ivt], &
|
|
ldwkvt, &rwork[nrwork]);
|
|
zlacpy_("F", m, m, &work[ivt], &ldwkvt, &u[u_offset], ldu);
|
|
|
|
/* Multiply RWORK(IRVT) by P**H in A, storing the */
|
|
/* result in WORK(IVT), copying to A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */
|
|
/* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
|
|
|
|
nrwork = iru;
|
|
i__1 = *n;
|
|
i__2 = chunk;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *n - i__ + 1;
|
|
blk = f2cmin(i__3,chunk);
|
|
zlarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1],
|
|
lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
|
|
zlacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
|
|
a_dim1 + 1], lda);
|
|
/* L50: */
|
|
}
|
|
} else if (wntqs) {
|
|
|
|
/* Path 5ts (N >> M, JOBZ='S') */
|
|
/* Copy A to U, generate Q */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
|
|
i__2 = *lwork - nwork + 1;
|
|
zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
|
|
nwork], &i__2, &ierr);
|
|
|
|
/* Copy A to VT, generate P**H */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
i__2 = *lwork - nwork + 1;
|
|
zungbr_("P", m, n, m, &vt[vt_offset], ldvt, &work[itaup], &
|
|
work[nwork], &i__2, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
|
|
|
|
irvt = nrwork;
|
|
iru = irvt + *m * *m;
|
|
nrwork = iru + *m * *m;
|
|
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
|
|
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Multiply Q in U by real matrix RWORK(IRU), storing the */
|
|
/* result in A, copying to U */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
|
|
|
|
zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
|
|
lda, &rwork[nrwork]);
|
|
zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
|
|
|
|
/* Multiply real matrix RWORK(IRVT) by P**H in VT, */
|
|
/* storing the result in A, copying to VT */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
|
|
|
|
nrwork = iru;
|
|
zlarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
|
|
a_offset], lda, &rwork[nrwork]);
|
|
zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
} else {
|
|
|
|
/* Path 5ta (N >> M, JOBZ='A') */
|
|
/* Copy A to U, generate Q */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("L", m, m, &a[a_offset], lda, &u[u_offset], ldu);
|
|
i__2 = *lwork - nwork + 1;
|
|
zungbr_("Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[
|
|
nwork], &i__2, &ierr);
|
|
|
|
/* Copy A to VT, generate P**H */
|
|
/* CWorkspace: need 2*M [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
zlacpy_("U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
i__2 = *lwork - nwork + 1;
|
|
zungbr_("P", n, n, m, &vt[vt_offset], ldvt, &work[itaup], &
|
|
work[nwork], &i__2, &ierr);
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
|
|
|
|
irvt = nrwork;
|
|
iru = irvt + *m * *m;
|
|
nrwork = iru + *m * *m;
|
|
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
|
|
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Multiply Q in U by real matrix RWORK(IRU), storing the */
|
|
/* result in A, copying to U */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + 2*M*M [rwork] */
|
|
|
|
zlacrm_(m, m, &u[u_offset], ldu, &rwork[iru], m, &a[a_offset],
|
|
lda, &rwork[nrwork]);
|
|
zlacpy_("F", m, m, &a[a_offset], lda, &u[u_offset], ldu);
|
|
|
|
/* Multiply real matrix RWORK(IRVT) by P**H in VT, */
|
|
/* storing the result in A, copying to VT */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
|
|
|
|
nrwork = iru;
|
|
zlarcm_(m, n, &rwork[irvt], m, &vt[vt_offset], ldvt, &a[
|
|
a_offset], lda, &rwork[nrwork]);
|
|
zlacpy_("F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt);
|
|
}
|
|
|
|
} else {
|
|
|
|
/* N .LT. MNTHR2 */
|
|
|
|
/* Path 6t (N > M, but not much larger) */
|
|
/* Reduce to bidiagonal form without LQ decomposition */
|
|
/* Use ZUNMBR to compute singular vectors */
|
|
|
|
ie = 1;
|
|
nrwork = ie + *m;
|
|
itauq = 1;
|
|
itaup = itauq + *m;
|
|
nwork = itaup + *m;
|
|
|
|
/* Bidiagonalize A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + (M+N)*NB [work] */
|
|
/* RWorkspace: need M [e] */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zgebrd_(m, n, &a[a_offset], lda, &s[1], &rwork[ie], &work[itauq],
|
|
&work[itaup], &work[nwork], &i__2, &ierr);
|
|
if (wntqn) {
|
|
|
|
/* Path 6tn (N > M, JOBZ='N') */
|
|
/* Compute singular values only */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + BDSPAC */
|
|
|
|
dbdsdc_("L", "N", m, &s[1], &rwork[ie], dum, &c__1, dum, &
|
|
c__1, dum, idum, &rwork[nrwork], &iwork[1], info);
|
|
} else if (wntqo) {
|
|
/* Path 6to (N > M, JOBZ='O') */
|
|
ldwkvt = *m;
|
|
ivt = nwork;
|
|
if (*lwork >= *m * *n + *m * 3) {
|
|
|
|
/* WORK( IVT ) is M by N */
|
|
|
|
zlaset_("F", m, n, &c_b1, &c_b1, &work[ivt], &ldwkvt);
|
|
nwork = ivt + ldwkvt * *n;
|
|
} else {
|
|
|
|
/* WORK( IVT ) is M by CHUNK */
|
|
|
|
chunk = (*lwork - *m * 3) / *m;
|
|
nwork = ivt + ldwkvt * chunk;
|
|
}
|
|
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
|
|
|
|
irvt = nrwork;
|
|
iru = irvt + *m * *m;
|
|
nrwork = iru + *m * *m;
|
|
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
|
|
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix U */
|
|
/* Overwrite U by left singular vectors of A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
|
|
|
|
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__2, &ierr);
|
|
|
|
if (*lwork >= *m * *n + *m * 3) {
|
|
|
|
/* Path 6to-fast */
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix WORK(IVT) */
|
|
/* Overwrite WORK(IVT) by right singular vectors of A, */
|
|
/* copying to A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M*N [VT] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] + M*NB [work] */
|
|
/* RWorkspace: need M [e] + M*M [RVT] */
|
|
|
|
zlacp2_("F", m, m, &rwork[irvt], m, &work[ivt], &ldwkvt);
|
|
i__2 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
|
|
itaup], &work[ivt], &ldwkvt, &work[nwork], &i__2,
|
|
&ierr);
|
|
zlacpy_("F", m, n, &work[ivt], &ldwkvt, &a[a_offset], lda);
|
|
} else {
|
|
|
|
/* Path 6to-slow */
|
|
/* Generate P**H in A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M*M [VT] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*M [VT] + M*NB [work] */
|
|
/* RWorkspace: need 0 */
|
|
|
|
i__2 = *lwork - nwork + 1;
|
|
zungbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &
|
|
work[nwork], &i__2, &ierr);
|
|
|
|
/* Multiply Q in A by real matrix RWORK(IRU), storing the */
|
|
/* result in WORK(IU), copying to A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M*M [VT] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*N [VT] */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + 2*M*M [rwork] */
|
|
/* RWorkspace: prefer M [e] + M*M [RVT] + 2*M*N [rwork] < M + 5*M*M since N < 2*M here */
|
|
|
|
nrwork = iru;
|
|
i__2 = *n;
|
|
i__1 = chunk;
|
|
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
|
|
i__1) {
|
|
/* Computing MIN */
|
|
i__3 = *n - i__ + 1;
|
|
blk = f2cmin(i__3,chunk);
|
|
zlarcm_(m, &blk, &rwork[irvt], m, &a[i__ * a_dim1 + 1]
|
|
, lda, &work[ivt], &ldwkvt, &rwork[nrwork]);
|
|
zlacpy_("F", m, &blk, &work[ivt], &ldwkvt, &a[i__ *
|
|
a_dim1 + 1], lda);
|
|
/* L60: */
|
|
}
|
|
}
|
|
} else if (wntqs) {
|
|
|
|
/* Path 6ts (N > M, JOBZ='S') */
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
|
|
|
|
irvt = nrwork;
|
|
iru = irvt + *m * *m;
|
|
nrwork = iru + *m * *m;
|
|
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
|
|
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix U */
|
|
/* Overwrite U by left singular vectors of A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
|
|
|
|
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix VT */
|
|
/* Overwrite VT by right singular vectors of A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need M [e] + M*M [RVT] */
|
|
|
|
zlaset_("F", m, n, &c_b1, &c_b1, &vt[vt_offset], ldvt);
|
|
zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", m, n, m, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
} else {
|
|
|
|
/* Path 6ta (N > M, JOBZ='A') */
|
|
/* Perform bidiagonal SVD, computing left singular vectors */
|
|
/* of bidiagonal matrix in RWORK(IRU) and computing right */
|
|
/* singular vectors of bidiagonal matrix in RWORK(IRVT) */
|
|
/* CWorkspace: need 0 */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] + BDSPAC */
|
|
|
|
irvt = nrwork;
|
|
iru = irvt + *m * *m;
|
|
nrwork = iru + *m * *m;
|
|
|
|
dbdsdc_("L", "I", m, &s[1], &rwork[ie], &rwork[iru], m, &
|
|
rwork[irvt], m, dum, idum, &rwork[nrwork], &iwork[1],
|
|
info);
|
|
|
|
/* Copy real matrix RWORK(IRU) to complex matrix U */
|
|
/* Overwrite U by left singular vectors of A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + M [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + M*NB [work] */
|
|
/* RWorkspace: need M [e] + M*M [RVT] + M*M [RU] */
|
|
|
|
zlacp2_("F", m, m, &rwork[iru], m, &u[u_offset], ldu);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("Q", "L", "N", m, m, n, &a[a_offset], lda, &work[
|
|
itauq], &u[u_offset], ldu, &work[nwork], &i__1, &ierr);
|
|
|
|
/* Set all of VT to identity matrix */
|
|
|
|
zlaset_("F", n, n, &c_b1, &c_b2, &vt[vt_offset], ldvt);
|
|
|
|
/* Copy real matrix RWORK(IRVT) to complex matrix VT */
|
|
/* Overwrite VT by right singular vectors of A */
|
|
/* CWorkspace: need 2*M [tauq, taup] + N [work] */
|
|
/* CWorkspace: prefer 2*M [tauq, taup] + N*NB [work] */
|
|
/* RWorkspace: need M [e] + M*M [RVT] */
|
|
|
|
zlacp2_("F", m, m, &rwork[irvt], m, &vt[vt_offset], ldvt);
|
|
i__1 = *lwork - nwork + 1;
|
|
zunmbr_("P", "R", "C", n, n, m, &a[a_offset], lda, &work[
|
|
itaup], &vt[vt_offset], ldvt, &work[nwork], &i__1, &
|
|
ierr);
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
/* Undo scaling if necessary */
|
|
|
|
if (iscl == 1) {
|
|
if (anrm > bignum) {
|
|
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, &ierr);
|
|
}
|
|
if (*info != 0 && anrm > bignum) {
|
|
i__1 = minmn - 1;
|
|
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &i__1, &c__1, &rwork[
|
|
ie], &minmn, &ierr);
|
|
}
|
|
if (anrm < smlnum) {
|
|
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, &ierr);
|
|
}
|
|
if (*info != 0 && anrm < smlnum) {
|
|
i__1 = minmn - 1;
|
|
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &i__1, &c__1, &rwork[
|
|
ie], &minmn, &ierr);
|
|
}
|
|
}
|
|
|
|
/* Return optimal workspace in WORK(1) */
|
|
|
|
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
|
|
|
|
return;
|
|
|
|
/* End of ZGESDD */
|
|
|
|
} /* zgesdd_ */
|
|
|