1079 lines
31 KiB
C
1079 lines
31 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublereal c_b5 = -1.;
|
|
static integer c__1 = 1;
|
|
static doublereal c_b11 = 1.;
|
|
static doublereal c_b13 = 0.;
|
|
static integer c__0 = 0;
|
|
|
|
/* > \brief \b DLALS0 applies back multiplying factors in solving the least squares problem using divide and c
|
|
onquer SVD approach. Used by sgelsd. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLALS0 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlals0.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlals0.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlals0.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, */
|
|
/* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, */
|
|
/* POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO ) */
|
|
|
|
/* INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, */
|
|
/* $ LDGNUM, NL, NR, NRHS, SQRE */
|
|
/* DOUBLE PRECISION C, S */
|
|
/* INTEGER GIVCOL( LDGCOL, * ), PERM( * ) */
|
|
/* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), DIFL( * ), */
|
|
/* $ DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ), */
|
|
/* $ POLES( LDGNUM, * ), WORK( * ), Z( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLALS0 applies back the multiplying factors of either the left or the */
|
|
/* > right singular vector matrix of a diagonal matrix appended by a row */
|
|
/* > to the right hand side matrix B in solving the least squares problem */
|
|
/* > using the divide-and-conquer SVD approach. */
|
|
/* > */
|
|
/* > For the left singular vector matrix, three types of orthogonal */
|
|
/* > matrices are involved: */
|
|
/* > */
|
|
/* > (1L) Givens rotations: the number of such rotations is GIVPTR; the */
|
|
/* > pairs of columns/rows they were applied to are stored in GIVCOL; */
|
|
/* > and the C- and S-values of these rotations are stored in GIVNUM. */
|
|
/* > */
|
|
/* > (2L) Permutation. The (NL+1)-st row of B is to be moved to the first */
|
|
/* > row, and for J=2:N, PERM(J)-th row of B is to be moved to the */
|
|
/* > J-th row. */
|
|
/* > */
|
|
/* > (3L) The left singular vector matrix of the remaining matrix. */
|
|
/* > */
|
|
/* > For the right singular vector matrix, four types of orthogonal */
|
|
/* > matrices are involved: */
|
|
/* > */
|
|
/* > (1R) The right singular vector matrix of the remaining matrix. */
|
|
/* > */
|
|
/* > (2R) If SQRE = 1, one extra Givens rotation to generate the right */
|
|
/* > null space. */
|
|
/* > */
|
|
/* > (3R) The inverse transformation of (2L). */
|
|
/* > */
|
|
/* > (4R) The inverse transformation of (1L). */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] ICOMPQ */
|
|
/* > \verbatim */
|
|
/* > ICOMPQ is INTEGER */
|
|
/* > Specifies whether singular vectors are to be computed in */
|
|
/* > factored form: */
|
|
/* > = 0: Left singular vector matrix. */
|
|
/* > = 1: Right singular vector matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NL */
|
|
/* > \verbatim */
|
|
/* > NL is INTEGER */
|
|
/* > The row dimension of the upper block. NL >= 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NR */
|
|
/* > \verbatim */
|
|
/* > NR is INTEGER */
|
|
/* > The row dimension of the lower block. NR >= 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SQRE */
|
|
/* > \verbatim */
|
|
/* > SQRE is INTEGER */
|
|
/* > = 0: the lower block is an NR-by-NR square matrix. */
|
|
/* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
|
|
/* > */
|
|
/* > The bidiagonal matrix has row dimension N = NL + NR + 1, */
|
|
/* > and column dimension M = N + SQRE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NRHS */
|
|
/* > \verbatim */
|
|
/* > NRHS is INTEGER */
|
|
/* > The number of columns of B and BX. NRHS must be at least 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) */
|
|
/* > On input, B contains the right hand sides of the least */
|
|
/* > squares problem in rows 1 through M. On output, B contains */
|
|
/* > the solution X in rows 1 through N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of B. LDB must be at least */
|
|
/* > f2cmax(1,MAX( M, N ) ). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BX */
|
|
/* > \verbatim */
|
|
/* > BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDBX */
|
|
/* > \verbatim */
|
|
/* > LDBX is INTEGER */
|
|
/* > The leading dimension of BX. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] PERM */
|
|
/* > \verbatim */
|
|
/* > PERM is INTEGER array, dimension ( N ) */
|
|
/* > The permutations (from deflation and sorting) applied */
|
|
/* > to the two blocks. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] GIVPTR */
|
|
/* > \verbatim */
|
|
/* > GIVPTR is INTEGER */
|
|
/* > The number of Givens rotations which took place in this */
|
|
/* > subproblem. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] GIVCOL */
|
|
/* > \verbatim */
|
|
/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */
|
|
/* > Each pair of numbers indicates a pair of rows/columns */
|
|
/* > involved in a Givens rotation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDGCOL */
|
|
/* > \verbatim */
|
|
/* > LDGCOL is INTEGER */
|
|
/* > The leading dimension of GIVCOL, must be at least N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] GIVNUM */
|
|
/* > \verbatim */
|
|
/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
|
|
/* > Each number indicates the C or S value used in the */
|
|
/* > corresponding Givens rotation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDGNUM */
|
|
/* > \verbatim */
|
|
/* > LDGNUM is INTEGER */
|
|
/* > The leading dimension of arrays DIFR, POLES and */
|
|
/* > GIVNUM, must be at least K. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] POLES */
|
|
/* > \verbatim */
|
|
/* > POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
|
|
/* > On entry, POLES(1:K, 1) contains the new singular */
|
|
/* > values obtained from solving the secular equation, and */
|
|
/* > POLES(1:K, 2) is an array containing the poles in the secular */
|
|
/* > equation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] DIFL */
|
|
/* > \verbatim */
|
|
/* > DIFL is DOUBLE PRECISION array, dimension ( K ). */
|
|
/* > On entry, DIFL(I) is the distance between I-th updated */
|
|
/* > (undeflated) singular value and the I-th (undeflated) old */
|
|
/* > singular value. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] DIFR */
|
|
/* > \verbatim */
|
|
/* > DIFR is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). */
|
|
/* > On entry, DIFR(I, 1) contains the distances between I-th */
|
|
/* > updated (undeflated) singular value and the I+1-th */
|
|
/* > (undeflated) old singular value. And DIFR(I, 2) is the */
|
|
/* > normalizing factor for the I-th right singular vector. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] Z */
|
|
/* > \verbatim */
|
|
/* > Z is DOUBLE PRECISION array, dimension ( K ) */
|
|
/* > Contain the components of the deflation-adjusted updating row */
|
|
/* > vector. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER */
|
|
/* > Contains the dimension of the non-deflated matrix, */
|
|
/* > This is the order of the related secular equation. 1 <= K <=N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] C */
|
|
/* > \verbatim */
|
|
/* > C is DOUBLE PRECISION */
|
|
/* > C contains garbage if SQRE =0 and the C-value of a Givens */
|
|
/* > rotation related to the right null space if SQRE = 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] S */
|
|
/* > \verbatim */
|
|
/* > S is DOUBLE PRECISION */
|
|
/* > S contains garbage if SQRE =0 and the S-value of a Givens */
|
|
/* > rotation related to the right null space if SQRE = 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension ( K ) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleOTHERcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA \n */
|
|
/* > Osni Marques, LBNL/NERSC, USA \n */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlals0_(integer *icompq, integer *nl, integer *nr,
|
|
integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal
|
|
*bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol,
|
|
integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal *
|
|
poles, doublereal *difl, doublereal *difr, doublereal *z__, integer *
|
|
k, doublereal *c__, doublereal *s, doublereal *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset,
|
|
difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1,
|
|
poles_offset, i__1, i__2;
|
|
doublereal d__1;
|
|
|
|
/* Local variables */
|
|
doublereal temp;
|
|
extern /* Subroutine */ void drot_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *);
|
|
extern doublereal dnrm2_(integer *, doublereal *, integer *);
|
|
integer i__, j, m, n;
|
|
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
|
|
integer *);
|
|
doublereal diflj, difrj, dsigj;
|
|
extern /* Subroutine */ void dgemv_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, doublereal *, integer *), dcopy_(integer *,
|
|
doublereal *, integer *, doublereal *, integer *);
|
|
extern doublereal dlamc3_(doublereal *, doublereal *);
|
|
doublereal dj;
|
|
extern /* Subroutine */ void dlascl_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, integer *, doublereal *,
|
|
integer *, integer *), dlacpy_(char *, integer *, integer
|
|
*, doublereal *, integer *, doublereal *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
doublereal dsigjp;
|
|
integer nlp1;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
bx_dim1 = *ldbx;
|
|
bx_offset = 1 + bx_dim1 * 1;
|
|
bx -= bx_offset;
|
|
--perm;
|
|
givcol_dim1 = *ldgcol;
|
|
givcol_offset = 1 + givcol_dim1 * 1;
|
|
givcol -= givcol_offset;
|
|
difr_dim1 = *ldgnum;
|
|
difr_offset = 1 + difr_dim1 * 1;
|
|
difr -= difr_offset;
|
|
poles_dim1 = *ldgnum;
|
|
poles_offset = 1 + poles_dim1 * 1;
|
|
poles -= poles_offset;
|
|
givnum_dim1 = *ldgnum;
|
|
givnum_offset = 1 + givnum_dim1 * 1;
|
|
givnum -= givnum_offset;
|
|
--difl;
|
|
--z__;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
n = *nl + *nr + 1;
|
|
|
|
if (*icompq < 0 || *icompq > 1) {
|
|
*info = -1;
|
|
} else if (*nl < 1) {
|
|
*info = -2;
|
|
} else if (*nr < 1) {
|
|
*info = -3;
|
|
} else if (*sqre < 0 || *sqre > 1) {
|
|
*info = -4;
|
|
} else if (*nrhs < 1) {
|
|
*info = -5;
|
|
} else if (*ldb < n) {
|
|
*info = -7;
|
|
} else if (*ldbx < n) {
|
|
*info = -9;
|
|
} else if (*givptr < 0) {
|
|
*info = -11;
|
|
} else if (*ldgcol < n) {
|
|
*info = -13;
|
|
} else if (*ldgnum < n) {
|
|
*info = -15;
|
|
//} else if (*k < 1) {
|
|
} else if (*k < 0) {
|
|
*info = -20;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DLALS0", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
m = n + *sqre;
|
|
nlp1 = *nl + 1;
|
|
|
|
if (*icompq == 0) {
|
|
|
|
/* Apply back orthogonal transformations from the left. */
|
|
|
|
/* Step (1L): apply back the Givens rotations performed. */
|
|
|
|
i__1 = *givptr;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
|
|
b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
|
|
(givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]);
|
|
/* L10: */
|
|
}
|
|
|
|
/* Step (2L): permute rows of B. */
|
|
|
|
dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx);
|
|
i__1 = n;
|
|
for (i__ = 2; i__ <= i__1; ++i__) {
|
|
dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1],
|
|
ldbx);
|
|
/* L20: */
|
|
}
|
|
|
|
/* Step (3L): apply the inverse of the left singular vector */
|
|
/* matrix to BX. */
|
|
|
|
if (*k == 1) {
|
|
dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb);
|
|
if (z__[1] < 0.) {
|
|
dscal_(nrhs, &c_b5, &b[b_offset], ldb);
|
|
}
|
|
} else {
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
diflj = difl[j];
|
|
dj = poles[j + poles_dim1];
|
|
dsigj = -poles[j + (poles_dim1 << 1)];
|
|
if (j < *k) {
|
|
difrj = -difr[j + difr_dim1];
|
|
dsigjp = -poles[j + 1 + (poles_dim1 << 1)];
|
|
}
|
|
if (z__[j] == 0. || poles[j + (poles_dim1 << 1)] == 0.) {
|
|
work[j] = 0.;
|
|
} else {
|
|
work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj /
|
|
(poles[j + (poles_dim1 << 1)] + dj);
|
|
}
|
|
i__2 = j - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] ==
|
|
0.) {
|
|
work[i__] = 0.;
|
|
} else {
|
|
work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
|
|
/ (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &
|
|
dsigj) - diflj) / (poles[i__ + (poles_dim1 <<
|
|
1)] + dj);
|
|
}
|
|
/* L30: */
|
|
}
|
|
i__2 = *k;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] ==
|
|
0.) {
|
|
work[i__] = 0.;
|
|
} else {
|
|
work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__]
|
|
/ (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &
|
|
dsigjp) + difrj) / (poles[i__ + (poles_dim1 <<
|
|
1)] + dj);
|
|
}
|
|
/* L40: */
|
|
}
|
|
work[1] = -1.;
|
|
temp = dnrm2_(k, &work[1], &c__1);
|
|
dgemv_("T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], &
|
|
c__1, &c_b13, &b[j + b_dim1], ldb);
|
|
dlascl_("G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j +
|
|
b_dim1], ldb, info);
|
|
/* L50: */
|
|
}
|
|
}
|
|
|
|
/* Move the deflated rows of BX to B also. */
|
|
|
|
if (*k < f2cmax(m,n)) {
|
|
i__1 = n - *k;
|
|
dlacpy_("A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1
|
|
+ b_dim1], ldb);
|
|
}
|
|
} else {
|
|
|
|
/* Apply back the right orthogonal transformations. */
|
|
|
|
/* Step (1R): apply back the new right singular vector matrix */
|
|
/* to B. */
|
|
|
|
if (*k == 1) {
|
|
dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx);
|
|
} else {
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
dsigj = poles[j + (poles_dim1 << 1)];
|
|
if (z__[j] == 0.) {
|
|
work[j] = 0.;
|
|
} else {
|
|
work[j] = -z__[j] / difl[j] / (dsigj + poles[j +
|
|
poles_dim1]) / difr[j + (difr_dim1 << 1)];
|
|
}
|
|
i__2 = j - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
if (z__[j] == 0.) {
|
|
work[i__] = 0.;
|
|
} else {
|
|
d__1 = -poles[i__ + 1 + (poles_dim1 << 1)];
|
|
work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[
|
|
i__ + difr_dim1]) / (dsigj + poles[i__ +
|
|
poles_dim1]) / difr[i__ + (difr_dim1 << 1)];
|
|
}
|
|
/* L60: */
|
|
}
|
|
i__2 = *k;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
if (z__[j] == 0.) {
|
|
work[i__] = 0.;
|
|
} else {
|
|
d__1 = -poles[i__ + (poles_dim1 << 1)];
|
|
work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[
|
|
i__]) / (dsigj + poles[i__ + poles_dim1]) /
|
|
difr[i__ + (difr_dim1 << 1)];
|
|
}
|
|
/* L70: */
|
|
}
|
|
dgemv_("T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], &
|
|
c__1, &c_b13, &bx[j + bx_dim1], ldbx);
|
|
/* L80: */
|
|
}
|
|
}
|
|
|
|
/* Step (2R): if SQRE = 1, apply back the rotation that is */
|
|
/* related to the right null space of the subproblem. */
|
|
|
|
if (*sqre == 1) {
|
|
dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx);
|
|
drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__,
|
|
s);
|
|
}
|
|
if (*k < f2cmax(m,n)) {
|
|
i__1 = n - *k;
|
|
dlacpy_("A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 +
|
|
bx_dim1], ldbx);
|
|
}
|
|
|
|
/* Step (3R): permute rows of B. */
|
|
|
|
dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb);
|
|
if (*sqre == 1) {
|
|
dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb);
|
|
}
|
|
i__1 = n;
|
|
for (i__ = 2; i__ <= i__1; ++i__) {
|
|
dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1],
|
|
ldb);
|
|
/* L90: */
|
|
}
|
|
|
|
/* Step (4R): apply back the Givens rotations performed. */
|
|
|
|
for (i__ = *givptr; i__ >= 1; --i__) {
|
|
d__1 = -givnum[i__ + givnum_dim1];
|
|
drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, &
|
|
b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ +
|
|
(givnum_dim1 << 1)], &d__1);
|
|
/* L100: */
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of DLALS0 */
|
|
|
|
} /* dlals0_ */
|
|
|