1433 lines
42 KiB
C
1433 lines
42 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 integer c__6 = 6;
|
|
static integer c_n1 = -1;
|
|
static integer c__1 = 1;
|
|
static integer c__0 = 0;
|
|
static real c_b50 = 0.f;
|
|
static real c_b83 = 1.f;
|
|
|
|
/* > \brief <b> SGELSS solves overdetermined or underdetermined systems for GE matrices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SGELSS + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgelss.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgelss.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgelss.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, */
|
|
/* WORK, LWORK, INFO ) */
|
|
|
|
/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */
|
|
/* REAL RCOND */
|
|
/* REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SGELSS computes the minimum norm solution to a real linear least */
|
|
/* > squares problem: */
|
|
/* > */
|
|
/* > Minimize 2-norm(| b - A*x |). */
|
|
/* > */
|
|
/* > using the singular value decomposition (SVD) of A. A is an M-by-N */
|
|
/* > matrix which may be rank-deficient. */
|
|
/* > */
|
|
/* > Several right hand side vectors b and solution vectors x can be */
|
|
/* > handled in a single call; they are stored as the columns of the */
|
|
/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix */
|
|
/* > X. */
|
|
/* > */
|
|
/* > The effective rank of A is determined by treating as zero those */
|
|
/* > singular values which are less than RCOND times the largest singular */
|
|
/* > value. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix A. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NRHS */
|
|
/* > \verbatim */
|
|
/* > NRHS is INTEGER */
|
|
/* > The number of right hand sides, i.e., the number of columns */
|
|
/* > of the matrices B and X. NRHS >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is REAL array, dimension (LDA,N) */
|
|
/* > On entry, the M-by-N matrix A. */
|
|
/* > On exit, the first f2cmin(m,n) rows of A are overwritten with */
|
|
/* > its right singular vectors, stored rowwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is REAL array, dimension (LDB,NRHS) */
|
|
/* > On entry, the M-by-NRHS right hand side matrix B. */
|
|
/* > On exit, B is overwritten by the N-by-NRHS solution */
|
|
/* > matrix X. If m >= n and RANK = n, the residual */
|
|
/* > sum-of-squares for the solution in the i-th column is given */
|
|
/* > by the sum of squares of elements n+1:m in that column. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,f2cmax(M,N)). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is REAL array, dimension (f2cmin(M,N)) */
|
|
/* > The singular values of A in decreasing order. */
|
|
/* > The condition number of A in the 2-norm = S(1)/S(f2cmin(m,n)). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RCOND */
|
|
/* > \verbatim */
|
|
/* > RCOND is REAL */
|
|
/* > RCOND is used to determine the effective rank of A. */
|
|
/* > Singular values S(i) <= RCOND*S(1) are treated as zero. */
|
|
/* > If RCOND < 0, machine precision is used instead. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RANK */
|
|
/* > \verbatim */
|
|
/* > RANK is INTEGER */
|
|
/* > The effective rank of A, i.e., the number of singular values */
|
|
/* > which are greater than RCOND*S(1). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= 1, and also: */
|
|
/* > LWORK >= 3*f2cmin(M,N) + f2cmax( 2*f2cmin(M,N), f2cmax(M,N), NRHS ) */
|
|
/* > For good performance, LWORK should generally be larger. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: the algorithm for computing the SVD failed to converge; */
|
|
/* > if INFO = i, i off-diagonal elements of an intermediate */
|
|
/* > bidiagonal form did not converge to zero. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup realGEsolve */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int sgelss_(integer *m, integer *n, integer *nrhs, real *a,
|
|
integer *lda, real *b, integer *ldb, real *s, real *rcond, integer *
|
|
rank, real *work, integer *lwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
|
|
real r__1;
|
|
|
|
/* Local variables */
|
|
real anrm, bnrm;
|
|
integer itau, lwork_sgebrd__, lwork_sgeqrf__, i__, lwork_sorgbr__,
|
|
lwork_sormbr__, lwork_sormlq__, iascl, ibscl, lwork_sormqr__,
|
|
chunk;
|
|
extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
|
|
integer *, real *, real *, integer *, real *, integer *, real *,
|
|
real *, integer *);
|
|
real sfmin;
|
|
integer minmn, maxmn;
|
|
extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
|
|
real *, integer *, real *, integer *, real *, real *, integer *);
|
|
integer itaup, itauq;
|
|
extern /* Subroutine */ int srscl_(integer *, real *, real *, integer *);
|
|
integer mnthr, iwork;
|
|
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
|
|
integer *);
|
|
integer bl, ie, il;
|
|
extern /* Subroutine */ int slabad_(real *, real *);
|
|
integer mm, bdspac;
|
|
extern /* Subroutine */ int sgebrd_(integer *, integer *, real *, integer
|
|
*, real *, real *, real *, real *, real *, integer *, integer *);
|
|
extern real slamch_(char *), slange_(char *, integer *, integer *,
|
|
real *, integer *, real *);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
real bignum;
|
|
extern /* Subroutine */ int sgelqf_(integer *, integer *, real *, integer
|
|
*, real *, real *, integer *, integer *), slascl_(char *, integer
|
|
*, integer *, real *, real *, integer *, integer *, real *,
|
|
integer *, integer *), sgeqrf_(integer *, integer *, real
|
|
*, integer *, real *, real *, integer *, integer *), slacpy_(char
|
|
*, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *,
|
|
real *, integer *), sbdsqr_(char *, integer *, integer *,
|
|
integer *, integer *, real *, real *, real *, integer *, real *,
|
|
integer *, real *, integer *, real *, integer *), sorgbr_(
|
|
char *, integer *, integer *, integer *, real *, integer *, real *
|
|
, real *, integer *, integer *);
|
|
integer ldwork;
|
|
extern /* Subroutine */ int sormbr_(char *, char *, char *, integer *,
|
|
integer *, integer *, real *, integer *, real *, real *, integer *
|
|
, real *, integer *, integer *);
|
|
integer minwrk, maxwrk;
|
|
real smlnum;
|
|
extern /* Subroutine */ int sormlq_(char *, char *, integer *, integer *,
|
|
integer *, real *, integer *, real *, real *, integer *, real *,
|
|
integer *, integer *);
|
|
logical lquery;
|
|
extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *,
|
|
integer *, real *, integer *, real *, real *, integer *, real *,
|
|
integer *, integer *);
|
|
real dum[1], eps, thr;
|
|
|
|
|
|
/* -- 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..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input arguments */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
--s;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
minmn = f2cmin(*m,*n);
|
|
maxmn = f2cmax(*m,*n);
|
|
lquery = *lwork == -1;
|
|
if (*m < 0) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*nrhs < 0) {
|
|
*info = -3;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -5;
|
|
} else if (*ldb < f2cmax(1,maxmn)) {
|
|
*info = -7;
|
|
}
|
|
|
|
/* Compute workspace */
|
|
/* (Note: Comments in the code beginning "Workspace:" describe the */
|
|
/* minimal amount of workspace needed at that point in the code, */
|
|
/* as well as the preferred amount for good performance. */
|
|
/* NB refers to the optimal block size for the immediately */
|
|
/* following subroutine, as returned by ILAENV.) */
|
|
|
|
if (*info == 0) {
|
|
minwrk = 1;
|
|
maxwrk = 1;
|
|
if (minmn > 0) {
|
|
mm = *m;
|
|
mnthr = ilaenv_(&c__6, "SGELSS", " ", m, n, nrhs, &c_n1, (ftnlen)
|
|
6, (ftnlen)1);
|
|
if (*m >= *n && *m >= mnthr) {
|
|
|
|
/* Path 1a - overdetermined, with many more rows than */
|
|
/* columns */
|
|
|
|
/* Compute space needed for SGEQRF */
|
|
sgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info);
|
|
lwork_sgeqrf__ = dum[0];
|
|
/* Compute space needed for SORMQR */
|
|
sormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, dum, &b[
|
|
b_offset], ldb, dum, &c_n1, info);
|
|
lwork_sormqr__ = dum[0];
|
|
mm = *n;
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *n + lwork_sgeqrf__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *n + lwork_sormqr__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
}
|
|
if (*m >= *n) {
|
|
|
|
/* Path 1 - overdetermined or exactly determined */
|
|
|
|
/* Compute workspace needed for SBDSQR */
|
|
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n * 5;
|
|
bdspac = f2cmax(i__1,i__2);
|
|
/* Compute space needed for SGEBRD */
|
|
sgebrd_(&mm, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum,
|
|
&c_n1, info);
|
|
lwork_sgebrd__ = dum[0];
|
|
/* Compute space needed for SORMBR */
|
|
sormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, dum, &
|
|
b[b_offset], ldb, dum, &c_n1, info);
|
|
lwork_sormbr__ = dum[0];
|
|
/* Compute space needed for SORGBR */
|
|
sorgbr_("P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1,
|
|
info);
|
|
lwork_sorgbr__ = dum[0];
|
|
/* Compute total workspace needed */
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *n * 3 + lwork_sgebrd__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *n * 3 + lwork_sormbr__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *n * 3 + lwork_sorgbr__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
maxwrk = f2cmax(maxwrk,bdspac);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *n * *nrhs;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = f2cmax(i__1,
|
|
i__2);
|
|
minwrk = f2cmax(i__1,bdspac);
|
|
maxwrk = f2cmax(minwrk,maxwrk);
|
|
}
|
|
if (*n > *m) {
|
|
|
|
/* Compute workspace needed for SBDSQR */
|
|
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *m * 5;
|
|
bdspac = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = f2cmax(i__1,
|
|
i__2);
|
|
minwrk = f2cmax(i__1,bdspac);
|
|
if (*n >= mnthr) {
|
|
|
|
/* Path 2a - underdetermined, with many more columns */
|
|
/* than rows */
|
|
|
|
/* Compute space needed for SGEBRD */
|
|
sgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum,
|
|
dum, &c_n1, info);
|
|
lwork_sgebrd__ = dum[0];
|
|
/* Compute space needed for SORMBR */
|
|
sormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, dum,
|
|
&b[b_offset], ldb, dum, &c_n1, info);
|
|
lwork_sormbr__ = dum[0];
|
|
/* Compute space needed for SORGBR */
|
|
sorgbr_("P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1,
|
|
info);
|
|
lwork_sorgbr__ = dum[0];
|
|
/* Compute space needed for SORMLQ */
|
|
sormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, dum, &b[
|
|
b_offset], ldb, dum, &c_n1, info);
|
|
lwork_sormlq__ = dum[0];
|
|
/* Compute total workspace needed */
|
|
maxwrk = *m + *m * ilaenv_(&c__1, "SGELQF", " ", m, n, &
|
|
c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) +
|
|
lwork_sgebrd__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) +
|
|
lwork_sormbr__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) +
|
|
lwork_sorgbr__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + *m + bdspac;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
if (*nrhs > 1) {
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
} else {
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
}
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m + lwork_sormlq__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
} else {
|
|
|
|
/* Path 2 - underdetermined */
|
|
|
|
/* Compute space needed for SGEBRD */
|
|
sgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum,
|
|
dum, &c_n1, info);
|
|
lwork_sgebrd__ = dum[0];
|
|
/* Compute space needed for SORMBR */
|
|
sormbr_("Q", "L", "T", m, nrhs, m, &a[a_offset], lda, dum,
|
|
&b[b_offset], ldb, dum, &c_n1, info);
|
|
lwork_sormbr__ = dum[0];
|
|
/* Compute space needed for SORGBR */
|
|
sorgbr_("P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1,
|
|
info);
|
|
lwork_sorgbr__ = dum[0];
|
|
maxwrk = *m * 3 + lwork_sgebrd__;
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * 3 + lwork_sormbr__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * 3 + lwork_sorgbr__;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
maxwrk = f2cmax(maxwrk,bdspac);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *n * *nrhs;
|
|
maxwrk = f2cmax(i__1,i__2);
|
|
}
|
|
}
|
|
maxwrk = f2cmax(minwrk,maxwrk);
|
|
}
|
|
work[1] = (real) maxwrk;
|
|
|
|
if (*lwork < minwrk && ! lquery) {
|
|
*info = -12;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SGELSS", &i__1, (ftnlen)6);
|
|
return 0;
|
|
} else if (lquery) {
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*m == 0 || *n == 0) {
|
|
*rank = 0;
|
|
return 0;
|
|
}
|
|
|
|
/* Get machine parameters */
|
|
|
|
eps = slamch_("P");
|
|
sfmin = slamch_("S");
|
|
smlnum = sfmin / eps;
|
|
bignum = 1.f / smlnum;
|
|
slabad_(&smlnum, &bignum);
|
|
|
|
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
|
|
|
|
anrm = slange_("M", m, n, &a[a_offset], lda, &work[1]);
|
|
iascl = 0;
|
|
if (anrm > 0.f && anrm < smlnum) {
|
|
|
|
/* Scale matrix norm up to SMLNUM */
|
|
|
|
slascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
|
|
info);
|
|
iascl = 1;
|
|
} else if (anrm > bignum) {
|
|
|
|
/* Scale matrix norm down to BIGNUM */
|
|
|
|
slascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
|
|
info);
|
|
iascl = 2;
|
|
} else if (anrm == 0.f) {
|
|
|
|
/* Matrix all zero. Return zero solution. */
|
|
|
|
i__1 = f2cmax(*m,*n);
|
|
slaset_("F", &i__1, nrhs, &c_b50, &c_b50, &b[b_offset], ldb);
|
|
slaset_("F", &minmn, &c__1, &c_b50, &c_b50, &s[1], &minmn);
|
|
*rank = 0;
|
|
goto L70;
|
|
}
|
|
|
|
/* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */
|
|
|
|
bnrm = slange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
|
|
ibscl = 0;
|
|
if (bnrm > 0.f && bnrm < smlnum) {
|
|
|
|
/* Scale matrix norm up to SMLNUM */
|
|
|
|
slascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
ibscl = 1;
|
|
} else if (bnrm > bignum) {
|
|
|
|
/* Scale matrix norm down to BIGNUM */
|
|
|
|
slascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
ibscl = 2;
|
|
}
|
|
|
|
/* Overdetermined case */
|
|
|
|
if (*m >= *n) {
|
|
|
|
/* Path 1 - overdetermined or exactly determined */
|
|
|
|
mm = *m;
|
|
if (*m >= mnthr) {
|
|
|
|
/* Path 1a - overdetermined, with many more rows than columns */
|
|
|
|
mm = *n;
|
|
itau = 1;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* (Workspace: need 2*N, prefer N+N*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
sgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1,
|
|
info);
|
|
|
|
/* Multiply B by transpose(Q) */
|
|
/* (Workspace: need N+NRHS, prefer N+NRHS*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
sormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
|
|
b_offset], ldb, &work[iwork], &i__1, info);
|
|
|
|
/* Zero out below R */
|
|
|
|
if (*n > 1) {
|
|
i__1 = *n - 1;
|
|
i__2 = *n - 1;
|
|
slaset_("L", &i__1, &i__2, &c_b50, &c_b50, &a[a_dim1 + 2],
|
|
lda);
|
|
}
|
|
}
|
|
|
|
ie = 1;
|
|
itauq = ie + *n;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
sgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
|
|
work[itaup], &work[iwork], &i__1, info);
|
|
|
|
/* Multiply B by transpose of left bidiagonalizing vectors of R */
|
|
/* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
sormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq],
|
|
&b[b_offset], ldb, &work[iwork], &i__1, info);
|
|
|
|
/* Generate right bidiagonalizing vectors of R in A */
|
|
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
sorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &
|
|
i__1, info);
|
|
iwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration */
|
|
/* multiply B by transpose of left singular vectors */
|
|
/* compute right singular vectors in A */
|
|
/* (Workspace: need BDSPAC) */
|
|
|
|
sbdsqr_("U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda,
|
|
dum, &c__1, &b[b_offset], ldb, &work[iwork], info);
|
|
if (*info != 0) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Multiply B by reciprocals of singular values */
|
|
|
|
/* Computing MAX */
|
|
r__1 = *rcond * s[1];
|
|
thr = f2cmax(r__1,sfmin);
|
|
if (*rcond < 0.f) {
|
|
/* Computing MAX */
|
|
r__1 = eps * s[1];
|
|
thr = f2cmax(r__1,sfmin);
|
|
}
|
|
*rank = 0;
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (s[i__] > thr) {
|
|
srscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
|
|
++(*rank);
|
|
} else {
|
|
slaset_("F", &c__1, nrhs, &c_b50, &c_b50, &b[i__ + b_dim1],
|
|
ldb);
|
|
}
|
|
/* L10: */
|
|
}
|
|
|
|
/* Multiply B by right singular vectors */
|
|
/* (Workspace: need N, prefer N*NRHS) */
|
|
|
|
if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
|
|
sgemm_("T", "N", n, nrhs, n, &c_b83, &a[a_offset], lda, &b[
|
|
b_offset], ldb, &c_b50, &work[1], ldb);
|
|
slacpy_("G", n, nrhs, &work[1], ldb, &b[b_offset], ldb)
|
|
;
|
|
} else if (*nrhs > 1) {
|
|
chunk = *lwork / *n;
|
|
i__1 = *nrhs;
|
|
i__2 = chunk;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *nrhs - i__ + 1;
|
|
bl = f2cmin(i__3,chunk);
|
|
sgemm_("T", "N", n, &bl, n, &c_b83, &a[a_offset], lda, &b[i__
|
|
* b_dim1 + 1], ldb, &c_b50, &work[1], n);
|
|
slacpy_("G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb);
|
|
/* L20: */
|
|
}
|
|
} else {
|
|
sgemv_("T", n, n, &c_b83, &a[a_offset], lda, &b[b_offset], &c__1,
|
|
&c_b50, &work[1], &c__1);
|
|
scopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
|
|
}
|
|
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__2 = *m, i__1 = (*m << 1) - 4, i__2 = f2cmax(i__2,i__1), i__2 = f2cmax(
|
|
i__2,*nrhs), i__1 = *n - *m * 3;
|
|
if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + f2cmax(i__2,i__1)) {
|
|
|
|
/* Path 2a - underdetermined, with many more columns than rows */
|
|
/* and sufficient workspace for an efficient algorithm */
|
|
|
|
ldwork = *m;
|
|
/* Computing MAX */
|
|
/* Computing MAX */
|
|
i__3 = *m, i__4 = (*m << 1) - 4, i__3 = f2cmax(i__3,i__4), i__3 =
|
|
f2cmax(i__3,*nrhs), i__4 = *n - *m * 3;
|
|
i__2 = (*m << 2) + *m * *lda + f2cmax(i__3,i__4), i__1 = *m * *lda +
|
|
*m + *m * *nrhs;
|
|
if (*lwork >= f2cmax(i__2,i__1)) {
|
|
ldwork = *lda;
|
|
}
|
|
itau = 1;
|
|
iwork = *m + 1;
|
|
|
|
/* Compute A=L*Q */
|
|
/* (Workspace: need 2*M, prefer M+M*NB) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
sgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2,
|
|
info);
|
|
il = iwork;
|
|
|
|
/* Copy L to WORK(IL), zeroing out above it */
|
|
|
|
slacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
|
|
i__2 = *m - 1;
|
|
i__1 = *m - 1;
|
|
slaset_("U", &i__2, &i__1, &c_b50, &c_b50, &work[il + ldwork], &
|
|
ldwork);
|
|
ie = il + ldwork * *m;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IL) */
|
|
/* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
sgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq],
|
|
&work[itaup], &work[iwork], &i__2, info);
|
|
|
|
/* Multiply B by transpose of left bidiagonalizing vectors of L */
|
|
/* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
sormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[
|
|
itauq], &b[b_offset], ldb, &work[iwork], &i__2, info);
|
|
|
|
/* Generate right bidiagonalizing vectors of R in WORK(IL) */
|
|
/* (Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
sorgbr_("P", m, m, m, &work[il], &ldwork, &work[itaup], &work[
|
|
iwork], &i__2, info);
|
|
iwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, */
|
|
/* computing right singular vectors of L in WORK(IL) and */
|
|
/* multiplying B by transpose of left singular vectors */
|
|
/* (Workspace: need M*M+M+BDSPAC) */
|
|
|
|
sbdsqr_("U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], &
|
|
ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork]
|
|
, info);
|
|
if (*info != 0) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Multiply B by reciprocals of singular values */
|
|
|
|
/* Computing MAX */
|
|
r__1 = *rcond * s[1];
|
|
thr = f2cmax(r__1,sfmin);
|
|
if (*rcond < 0.f) {
|
|
/* Computing MAX */
|
|
r__1 = eps * s[1];
|
|
thr = f2cmax(r__1,sfmin);
|
|
}
|
|
*rank = 0;
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
if (s[i__] > thr) {
|
|
srscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
|
|
++(*rank);
|
|
} else {
|
|
slaset_("F", &c__1, nrhs, &c_b50, &c_b50, &b[i__ + b_dim1]
|
|
, ldb);
|
|
}
|
|
/* L30: */
|
|
}
|
|
iwork = ie;
|
|
|
|
/* Multiply B by right singular vectors of L in WORK(IL) */
|
|
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) */
|
|
|
|
if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) {
|
|
sgemm_("T", "N", m, nrhs, m, &c_b83, &work[il], &ldwork, &b[
|
|
b_offset], ldb, &c_b50, &work[iwork], ldb);
|
|
slacpy_("G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb);
|
|
} else if (*nrhs > 1) {
|
|
chunk = (*lwork - iwork + 1) / *m;
|
|
i__2 = *nrhs;
|
|
i__1 = chunk;
|
|
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
|
|
i__1) {
|
|
/* Computing MIN */
|
|
i__3 = *nrhs - i__ + 1;
|
|
bl = f2cmin(i__3,chunk);
|
|
sgemm_("T", "N", m, &bl, m, &c_b83, &work[il], &ldwork, &
|
|
b[i__ * b_dim1 + 1], ldb, &c_b50, &work[iwork], m);
|
|
slacpy_("G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1]
|
|
, ldb);
|
|
/* L40: */
|
|
}
|
|
} else {
|
|
sgemv_("T", m, m, &c_b83, &work[il], &ldwork, &b[b_dim1 + 1],
|
|
&c__1, &c_b50, &work[iwork], &c__1);
|
|
scopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1);
|
|
}
|
|
|
|
/* Zero out below first M rows of B */
|
|
|
|
i__1 = *n - *m;
|
|
slaset_("F", &i__1, nrhs, &c_b50, &c_b50, &b[*m + 1 + b_dim1],
|
|
ldb);
|
|
iwork = itau + *m;
|
|
|
|
/* Multiply transpose(Q) by B */
|
|
/* (Workspace: need M+NRHS, prefer M+NRHS*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
sormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
|
|
b_offset], ldb, &work[iwork], &i__1, info);
|
|
|
|
} else {
|
|
|
|
/* Path 2 - remaining underdetermined cases */
|
|
|
|
ie = 1;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize A */
|
|
/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
sgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
|
|
work[itaup], &work[iwork], &i__1, info);
|
|
|
|
/* Multiply B by transpose of left bidiagonalizing vectors */
|
|
/* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
sormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq]
|
|
, &b[b_offset], ldb, &work[iwork], &i__1, info);
|
|
|
|
/* Generate right bidiagonalizing vectors in A */
|
|
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
sorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
|
|
iwork], &i__1, info);
|
|
iwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, */
|
|
/* computing right singular vectors of A in A and */
|
|
/* multiplying B by transpose of left singular vectors */
|
|
/* (Workspace: need BDSPAC) */
|
|
|
|
sbdsqr_("L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset],
|
|
lda, dum, &c__1, &b[b_offset], ldb, &work[iwork], info);
|
|
if (*info != 0) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Multiply B by reciprocals of singular values */
|
|
|
|
/* Computing MAX */
|
|
r__1 = *rcond * s[1];
|
|
thr = f2cmax(r__1,sfmin);
|
|
if (*rcond < 0.f) {
|
|
/* Computing MAX */
|
|
r__1 = eps * s[1];
|
|
thr = f2cmax(r__1,sfmin);
|
|
}
|
|
*rank = 0;
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (s[i__] > thr) {
|
|
srscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
|
|
++(*rank);
|
|
} else {
|
|
slaset_("F", &c__1, nrhs, &c_b50, &c_b50, &b[i__ + b_dim1]
|
|
, ldb);
|
|
}
|
|
/* L50: */
|
|
}
|
|
|
|
/* Multiply B by right singular vectors of A */
|
|
/* (Workspace: need N, prefer N*NRHS) */
|
|
|
|
if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
|
|
sgemm_("T", "N", n, nrhs, m, &c_b83, &a[a_offset], lda, &b[
|
|
b_offset], ldb, &c_b50, &work[1], ldb);
|
|
slacpy_("F", n, nrhs, &work[1], ldb, &b[b_offset], ldb);
|
|
} else if (*nrhs > 1) {
|
|
chunk = *lwork / *n;
|
|
i__1 = *nrhs;
|
|
i__2 = chunk;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *nrhs - i__ + 1;
|
|
bl = f2cmin(i__3,chunk);
|
|
sgemm_("T", "N", n, &bl, m, &c_b83, &a[a_offset], lda, &b[
|
|
i__ * b_dim1 + 1], ldb, &c_b50, &work[1], n);
|
|
slacpy_("F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1],
|
|
ldb);
|
|
/* L60: */
|
|
}
|
|
} else {
|
|
sgemv_("T", m, n, &c_b83, &a[a_offset], lda, &b[b_offset], &
|
|
c__1, &c_b50, &work[1], &c__1);
|
|
scopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Undo scaling */
|
|
|
|
if (iascl == 1) {
|
|
slascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
slascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, info);
|
|
} else if (iascl == 2) {
|
|
slascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
slascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, info);
|
|
}
|
|
if (ibscl == 1) {
|
|
slascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
} else if (ibscl == 2) {
|
|
slascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
}
|
|
|
|
L70:
|
|
work[1] = (real) maxwrk;
|
|
return 0;
|
|
|
|
/* End of SGELSS */
|
|
|
|
} /* sgelss_ */
|
|
|