1095 lines
32 KiB
C
1095 lines
32 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__9 = 9;
|
|
static integer c__0 = 0;
|
|
static doublereal c_b15 = 1.;
|
|
static integer c__1 = 1;
|
|
static doublereal c_b29 = 0.;
|
|
|
|
/* > \brief \b DBDSDC */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DBDSDC + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dbdsdc.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dbdsdc.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dbdsdc.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, */
|
|
/* WORK, IWORK, INFO ) */
|
|
|
|
/* CHARACTER COMPQ, UPLO */
|
|
/* INTEGER INFO, LDU, LDVT, N */
|
|
/* INTEGER IQ( * ), IWORK( * ) */
|
|
/* DOUBLE PRECISION D( * ), E( * ), Q( * ), U( LDU, * ), */
|
|
/* $ VT( LDVT, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DBDSDC computes the singular value decomposition (SVD) of a real */
|
|
/* > N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT, */
|
|
/* > using a divide and conquer method, where S is a diagonal matrix */
|
|
/* > with non-negative diagonal elements (the singular values of B), and */
|
|
/* > U and VT are orthogonal matrices of left and right singular vectors, */
|
|
/* > respectively. DBDSDC can be used to compute all singular values, */
|
|
/* > and optionally, singular vectors or singular vectors in compact form. */
|
|
/* > */
|
|
/* > This code makes very mild assumptions about floating point */
|
|
/* > arithmetic. It will work on machines with a guard digit in */
|
|
/* > add/subtract, or on those binary machines without guard digits */
|
|
/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
|
|
/* > It could conceivably fail on hexadecimal or decimal machines */
|
|
/* > without guard digits, but we know of none. See DLASD3 for details. */
|
|
/* > */
|
|
/* > The code currently calls DLASDQ if singular values only are desired. */
|
|
/* > However, it can be slightly modified to compute singular values */
|
|
/* > using the divide and conquer method. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > = 'U': B is upper bidiagonal. */
|
|
/* > = 'L': B is lower bidiagonal. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] COMPQ */
|
|
/* > \verbatim */
|
|
/* > COMPQ is CHARACTER*1 */
|
|
/* > Specifies whether singular vectors are to be computed */
|
|
/* > as follows: */
|
|
/* > = 'N': Compute singular values only; */
|
|
/* > = 'P': Compute singular values and compute singular */
|
|
/* > vectors in compact form; */
|
|
/* > = 'I': Compute singular values and singular vectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix B. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On entry, the n diagonal elements of the bidiagonal matrix B. */
|
|
/* > On exit, if INFO=0, the singular values of B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > On entry, the elements of E contain the offdiagonal */
|
|
/* > elements of the bidiagonal matrix whose SVD is desired. */
|
|
/* > On exit, E has been destroyed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] U */
|
|
/* > \verbatim */
|
|
/* > U is DOUBLE PRECISION array, dimension (LDU,N) */
|
|
/* > If COMPQ = 'I', then: */
|
|
/* > On exit, if INFO = 0, U contains the left singular vectors */
|
|
/* > of the bidiagonal matrix. */
|
|
/* > For other values of COMPQ, U is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU */
|
|
/* > \verbatim */
|
|
/* > LDU is INTEGER */
|
|
/* > The leading dimension of the array U. LDU >= 1. */
|
|
/* > If singular vectors are desired, then LDU >= f2cmax( 1, N ). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VT */
|
|
/* > \verbatim */
|
|
/* > VT is DOUBLE PRECISION array, dimension (LDVT,N) */
|
|
/* > If COMPQ = 'I', then: */
|
|
/* > On exit, if INFO = 0, VT**T contains the right singular */
|
|
/* > vectors of the bidiagonal matrix. */
|
|
/* > For other values of COMPQ, VT is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVT */
|
|
/* > \verbatim */
|
|
/* > LDVT is INTEGER */
|
|
/* > The leading dimension of the array VT. LDVT >= 1. */
|
|
/* > If singular vectors are desired, then LDVT >= f2cmax( 1, N ). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is DOUBLE PRECISION array, dimension (LDQ) */
|
|
/* > If COMPQ = 'P', then: */
|
|
/* > On exit, if INFO = 0, Q and IQ contain the left */
|
|
/* > and right singular vectors in a compact form, */
|
|
/* > requiring O(N log N) space instead of 2*N**2. */
|
|
/* > In particular, Q contains all the DOUBLE PRECISION data in */
|
|
/* > LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1)))) */
|
|
/* > words of memory, where SMLSIZ is returned by ILAENV and */
|
|
/* > is equal to the maximum size of the subproblems at the */
|
|
/* > bottom of the computation tree (usually about 25). */
|
|
/* > For other values of COMPQ, Q is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IQ */
|
|
/* > \verbatim */
|
|
/* > IQ is INTEGER array, dimension (LDIQ) */
|
|
/* > If COMPQ = 'P', then: */
|
|
/* > On exit, if INFO = 0, Q and IQ contain the left */
|
|
/* > and right singular vectors in a compact form, */
|
|
/* > requiring O(N log N) space instead of 2*N**2. */
|
|
/* > In particular, IQ contains all INTEGER data in */
|
|
/* > LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1)))) */
|
|
/* > words of memory, where SMLSIZ is returned by ILAENV and */
|
|
/* > is equal to the maximum size of the subproblems at the */
|
|
/* > bottom of the computation tree (usually about 25). */
|
|
/* > For other values of COMPQ, IQ is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
|
|
/* > If COMPQ = 'N' then LWORK >= (4 * N). */
|
|
/* > If COMPQ = 'P' then LWORK >= (6 * N). */
|
|
/* > If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (8*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: The algorithm failed to compute a singular value. */
|
|
/* > The update process of divide and conquer failed. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup auxOTHERcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dbdsdc_(char *uplo, char *compq, integer *n, doublereal *
|
|
d__, doublereal *e, doublereal *u, integer *ldu, doublereal *vt,
|
|
integer *ldvt, doublereal *q, integer *iq, doublereal *work, integer *
|
|
iwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2;
|
|
doublereal d__1;
|
|
|
|
/* Local variables */
|
|
integer difl, difr, ierr, perm, mlvl, sqre, i__, j, k;
|
|
doublereal p, r__;
|
|
integer z__;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void dlasr_(char *, char *, char *, integer *,
|
|
integer *, doublereal *, doublereal *, doublereal *, integer *), dcopy_(integer *, doublereal *, integer *
|
|
, doublereal *, integer *), dswap_(integer *, doublereal *,
|
|
integer *, doublereal *, integer *);
|
|
integer poles, iuplo, nsize, start;
|
|
extern /* Subroutine */ void dlasd0_(integer *, integer *, doublereal *,
|
|
doublereal *, doublereal *, integer *, doublereal *, integer *,
|
|
integer *, integer *, doublereal *, integer *);
|
|
integer ic, ii, kk;
|
|
doublereal cs;
|
|
extern doublereal dlamch_(char *);
|
|
extern /* Subroutine */ void dlasda_(integer *, integer *, integer *,
|
|
integer *, doublereal *, doublereal *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, integer *, integer *, integer *, integer *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
|
|
integer *);
|
|
integer is, iu;
|
|
doublereal sn;
|
|
extern /* Subroutine */ void dlascl_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, integer *, doublereal *,
|
|
integer *, integer *), dlasdq_(char *, integer *, integer
|
|
*, integer *, integer *, integer *, doublereal *, doublereal *,
|
|
doublereal *, integer *, doublereal *, integer *, doublereal *,
|
|
integer *, doublereal *, integer *), dlaset_(char *,
|
|
integer *, integer *, doublereal *, doublereal *, doublereal *,
|
|
integer *), dlartg_(doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
integer givcol;
|
|
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
|
|
integer icompq;
|
|
doublereal orgnrm;
|
|
integer givnum, givptr, nm1, qstart, smlsiz, wstart, smlszp;
|
|
doublereal eps;
|
|
integer ivt;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
/* Changed dimension statement in comment describing E from (N) to */
|
|
/* (N-1). Sven, 17 Feb 05. */
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
--d__;
|
|
--e;
|
|
u_dim1 = *ldu;
|
|
u_offset = 1 + u_dim1 * 1;
|
|
u -= u_offset;
|
|
vt_dim1 = *ldvt;
|
|
vt_offset = 1 + vt_dim1 * 1;
|
|
vt -= vt_offset;
|
|
--q;
|
|
--iq;
|
|
--work;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
iuplo = 0;
|
|
if (lsame_(uplo, "U")) {
|
|
iuplo = 1;
|
|
}
|
|
if (lsame_(uplo, "L")) {
|
|
iuplo = 2;
|
|
}
|
|
if (lsame_(compq, "N")) {
|
|
icompq = 0;
|
|
} else if (lsame_(compq, "P")) {
|
|
icompq = 1;
|
|
} else if (lsame_(compq, "I")) {
|
|
icompq = 2;
|
|
} else {
|
|
icompq = -1;
|
|
}
|
|
if (iuplo == 0) {
|
|
*info = -1;
|
|
} else if (icompq < 0) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*ldu < 1 || icompq == 2 && *ldu < *n) {
|
|
*info = -7;
|
|
} else if (*ldvt < 1 || icompq == 2 && *ldvt < *n) {
|
|
*info = -9;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DBDSDC", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
smlsiz = ilaenv_(&c__9, "DBDSDC", " ", &c__0, &c__0, &c__0, &c__0, (
|
|
ftnlen)6, (ftnlen)1);
|
|
if (*n == 1) {
|
|
if (icompq == 1) {
|
|
q[1] = d_sign(&c_b15, &d__[1]);
|
|
q[smlsiz * *n + 1] = 1.;
|
|
} else if (icompq == 2) {
|
|
u[u_dim1 + 1] = d_sign(&c_b15, &d__[1]);
|
|
vt[vt_dim1 + 1] = 1.;
|
|
}
|
|
d__[1] = abs(d__[1]);
|
|
return;
|
|
}
|
|
nm1 = *n - 1;
|
|
|
|
/* If matrix lower bidiagonal, rotate to be upper bidiagonal */
|
|
/* by applying Givens rotations on the left */
|
|
|
|
wstart = 1;
|
|
qstart = 3;
|
|
if (icompq == 1) {
|
|
dcopy_(n, &d__[1], &c__1, &q[1], &c__1);
|
|
i__1 = *n - 1;
|
|
dcopy_(&i__1, &e[1], &c__1, &q[*n + 1], &c__1);
|
|
}
|
|
if (iuplo == 2) {
|
|
qstart = 5;
|
|
if (icompq == 2) {
|
|
wstart = (*n << 1) - 1;
|
|
}
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
|
|
d__[i__] = r__;
|
|
e[i__] = sn * d__[i__ + 1];
|
|
d__[i__ + 1] = cs * d__[i__ + 1];
|
|
if (icompq == 1) {
|
|
q[i__ + (*n << 1)] = cs;
|
|
q[i__ + *n * 3] = sn;
|
|
} else if (icompq == 2) {
|
|
work[i__] = cs;
|
|
work[nm1 + i__] = -sn;
|
|
}
|
|
/* L10: */
|
|
}
|
|
}
|
|
|
|
/* If ICOMPQ = 0, use DLASDQ to compute the singular values. */
|
|
|
|
if (icompq == 0) {
|
|
/* Ignore WSTART, instead using WORK( 1 ), since the two vectors */
|
|
/* for CS and -SN above are added only if ICOMPQ == 2, */
|
|
/* and adding them exceeds documented WORK size of 4*n. */
|
|
dlasdq_("U", &c__0, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[
|
|
vt_offset], ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[
|
|
1], info);
|
|
goto L40;
|
|
}
|
|
|
|
/* If N is smaller than the minimum divide size SMLSIZ, then solve */
|
|
/* the problem with another solver. */
|
|
|
|
if (*n <= smlsiz) {
|
|
if (icompq == 2) {
|
|
dlaset_("A", n, n, &c_b29, &c_b15, &u[u_offset], ldu);
|
|
dlaset_("A", n, n, &c_b29, &c_b15, &vt[vt_offset], ldvt);
|
|
dlasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &vt[vt_offset]
|
|
, ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[
|
|
wstart], info);
|
|
} else if (icompq == 1) {
|
|
iu = 1;
|
|
ivt = iu + *n;
|
|
dlaset_("A", n, n, &c_b29, &c_b15, &q[iu + (qstart - 1) * *n], n);
|
|
dlaset_("A", n, n, &c_b29, &c_b15, &q[ivt + (qstart - 1) * *n], n);
|
|
dlasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &q[ivt + (
|
|
qstart - 1) * *n], n, &q[iu + (qstart - 1) * *n], n, &q[
|
|
iu + (qstart - 1) * *n], n, &work[wstart], info);
|
|
}
|
|
goto L40;
|
|
}
|
|
|
|
if (icompq == 2) {
|
|
dlaset_("A", n, n, &c_b29, &c_b15, &u[u_offset], ldu);
|
|
dlaset_("A", n, n, &c_b29, &c_b15, &vt[vt_offset], ldvt);
|
|
}
|
|
|
|
/* Scale. */
|
|
|
|
orgnrm = dlanst_("M", n, &d__[1], &e[1]);
|
|
if (orgnrm == 0.) {
|
|
return;
|
|
}
|
|
dlascl_("G", &c__0, &c__0, &orgnrm, &c_b15, n, &c__1, &d__[1], n, &ierr);
|
|
dlascl_("G", &c__0, &c__0, &orgnrm, &c_b15, &nm1, &c__1, &e[1], &nm1, &
|
|
ierr);
|
|
|
|
eps = dlamch_("Epsilon") * .9;
|
|
|
|
mlvl = (integer) (log((doublereal) (*n) / (doublereal) (smlsiz + 1)) /
|
|
log(2.)) + 1;
|
|
smlszp = smlsiz + 1;
|
|
|
|
if (icompq == 1) {
|
|
iu = 1;
|
|
ivt = smlsiz + 1;
|
|
difl = ivt + smlszp;
|
|
difr = difl + mlvl;
|
|
z__ = difr + (mlvl << 1);
|
|
ic = z__ + mlvl;
|
|
is = ic + 1;
|
|
poles = is + 1;
|
|
givnum = poles + (mlvl << 1);
|
|
|
|
k = 1;
|
|
givptr = 2;
|
|
perm = 3;
|
|
givcol = perm + mlvl;
|
|
}
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if ((d__1 = d__[i__], abs(d__1)) < eps) {
|
|
d__[i__] = d_sign(&eps, &d__[i__]);
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
start = 1;
|
|
sqre = 0;
|
|
|
|
i__1 = nm1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if ((d__1 = e[i__], abs(d__1)) < eps || i__ == nm1) {
|
|
|
|
/* Subproblem found. First determine its size and then */
|
|
/* apply divide and conquer on it. */
|
|
|
|
if (i__ < nm1) {
|
|
|
|
/* A subproblem with E(I) small for I < NM1. */
|
|
|
|
nsize = i__ - start + 1;
|
|
} else if ((d__1 = e[i__], abs(d__1)) >= eps) {
|
|
|
|
/* A subproblem with E(NM1) not too small but I = NM1. */
|
|
|
|
nsize = *n - start + 1;
|
|
} else {
|
|
|
|
/* A subproblem with E(NM1) small. This implies an */
|
|
/* 1-by-1 subproblem at D(N). Solve this 1-by-1 problem */
|
|
/* first. */
|
|
|
|
nsize = i__ - start + 1;
|
|
if (icompq == 2) {
|
|
u[*n + *n * u_dim1] = d_sign(&c_b15, &d__[*n]);
|
|
vt[*n + *n * vt_dim1] = 1.;
|
|
} else if (icompq == 1) {
|
|
q[*n + (qstart - 1) * *n] = d_sign(&c_b15, &d__[*n]);
|
|
q[*n + (smlsiz + qstart - 1) * *n] = 1.;
|
|
}
|
|
d__[*n] = (d__1 = d__[*n], abs(d__1));
|
|
}
|
|
if (icompq == 2) {
|
|
dlasd0_(&nsize, &sqre, &d__[start], &e[start], &u[start +
|
|
start * u_dim1], ldu, &vt[start + start * vt_dim1],
|
|
ldvt, &smlsiz, &iwork[1], &work[wstart], info);
|
|
} else {
|
|
dlasda_(&icompq, &smlsiz, &nsize, &sqre, &d__[start], &e[
|
|
start], &q[start + (iu + qstart - 2) * *n], n, &q[
|
|
start + (ivt + qstart - 2) * *n], &iq[start + k * *n],
|
|
&q[start + (difl + qstart - 2) * *n], &q[start + (
|
|
difr + qstart - 2) * *n], &q[start + (z__ + qstart -
|
|
2) * *n], &q[start + (poles + qstart - 2) * *n], &iq[
|
|
start + givptr * *n], &iq[start + givcol * *n], n, &
|
|
iq[start + perm * *n], &q[start + (givnum + qstart -
|
|
2) * *n], &q[start + (ic + qstart - 2) * *n], &q[
|
|
start + (is + qstart - 2) * *n], &work[wstart], &
|
|
iwork[1], info);
|
|
}
|
|
if (*info != 0) {
|
|
return;
|
|
}
|
|
start = i__ + 1;
|
|
}
|
|
/* L30: */
|
|
}
|
|
|
|
/* Unscale */
|
|
|
|
dlascl_("G", &c__0, &c__0, &c_b15, &orgnrm, n, &c__1, &d__[1], n, &ierr);
|
|
L40:
|
|
|
|
/* Use Selection Sort to minimize swaps of singular vectors */
|
|
|
|
i__1 = *n;
|
|
for (ii = 2; ii <= i__1; ++ii) {
|
|
i__ = ii - 1;
|
|
kk = i__;
|
|
p = d__[i__];
|
|
i__2 = *n;
|
|
for (j = ii; j <= i__2; ++j) {
|
|
if (d__[j] > p) {
|
|
kk = j;
|
|
p = d__[j];
|
|
}
|
|
/* L50: */
|
|
}
|
|
if (kk != i__) {
|
|
d__[kk] = d__[i__];
|
|
d__[i__] = p;
|
|
if (icompq == 1) {
|
|
iq[i__] = kk;
|
|
} else if (icompq == 2) {
|
|
dswap_(n, &u[i__ * u_dim1 + 1], &c__1, &u[kk * u_dim1 + 1], &
|
|
c__1);
|
|
dswap_(n, &vt[i__ + vt_dim1], ldvt, &vt[kk + vt_dim1], ldvt);
|
|
}
|
|
} else if (icompq == 1) {
|
|
iq[i__] = i__;
|
|
}
|
|
/* L60: */
|
|
}
|
|
|
|
/* If ICOMPQ = 1, use IQ(N,1) as the indicator for UPLO */
|
|
|
|
if (icompq == 1) {
|
|
if (iuplo == 1) {
|
|
iq[*n] = 1;
|
|
} else {
|
|
iq[*n] = 0;
|
|
}
|
|
}
|
|
|
|
/* If B is lower bidiagonal, update U by those Givens rotations */
|
|
/* which rotated B to be upper bidiagonal */
|
|
|
|
if (iuplo == 2 && icompq == 2) {
|
|
dlasr_("L", "V", "B", n, n, &work[1], &work[*n], &u[u_offset], ldu);
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of DBDSDC */
|
|
|
|
} /* dbdsdc_ */
|
|
|