1093 lines
33 KiB
C
1093 lines
33 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__0 = 0;
|
|
static real c_b11 = 0.f;
|
|
static real c_b12 = 1.f;
|
|
static integer c__1 = 1;
|
|
static integer c__2 = 2;
|
|
|
|
/* > \brief \b SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with d
|
|
iagonal d and off-diagonal e. Used by sbdsdc. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SLASDA + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasda.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasda.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasda.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, */
|
|
/* DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, */
|
|
/* PERM, GIVNUM, C, S, WORK, IWORK, INFO ) */
|
|
|
|
/* INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE */
|
|
/* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */
|
|
/* $ K( * ), PERM( LDGCOL, * ) */
|
|
/* REAL C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), */
|
|
/* $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), */
|
|
/* $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), */
|
|
/* $ Z( LDU, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > Using a divide and conquer approach, SLASDA computes the singular */
|
|
/* > value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */
|
|
/* > B with diagonal D and offdiagonal E, where M = N + SQRE. The */
|
|
/* > algorithm computes the singular values in the SVD B = U * S * VT. */
|
|
/* > The orthogonal matrices U and VT are optionally computed in */
|
|
/* > compact form. */
|
|
/* > */
|
|
/* > A related subroutine, SLASD0, computes the singular values and */
|
|
/* > the singular vectors in explicit form. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] ICOMPQ */
|
|
/* > \verbatim */
|
|
/* > ICOMPQ is INTEGER */
|
|
/* > Specifies whether singular vectors are to be computed */
|
|
/* > in compact form, as follows */
|
|
/* > = 0: Compute singular values only. */
|
|
/* > = 1: Compute singular vectors of upper bidiagonal */
|
|
/* > matrix in compact form. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SMLSIZ */
|
|
/* > \verbatim */
|
|
/* > SMLSIZ is INTEGER */
|
|
/* > The maximum size of the subproblems at the bottom of the */
|
|
/* > computation tree. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The row dimension of the upper bidiagonal matrix. This is */
|
|
/* > also the dimension of the main diagonal array D. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SQRE */
|
|
/* > \verbatim */
|
|
/* > SQRE is INTEGER */
|
|
/* > Specifies the column dimension of the bidiagonal matrix. */
|
|
/* > = 0: The bidiagonal matrix has column dimension M = N; */
|
|
/* > = 1: The bidiagonal matrix has column dimension M = N + 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] D */
|
|
/* > \verbatim */
|
|
/* > D is REAL array, dimension ( N ) */
|
|
/* > On entry D contains the main diagonal of the bidiagonal */
|
|
/* > matrix. On exit D, if INFO = 0, contains its singular values. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] E */
|
|
/* > \verbatim */
|
|
/* > E is REAL array, dimension ( M-1 ) */
|
|
/* > Contains the subdiagonal entries of the bidiagonal matrix. */
|
|
/* > On exit, E has been destroyed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] U */
|
|
/* > \verbatim */
|
|
/* > U is REAL array, */
|
|
/* > dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */
|
|
/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left */
|
|
/* > singular vector matrices of all subproblems at the bottom */
|
|
/* > level. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU */
|
|
/* > \verbatim */
|
|
/* > LDU is INTEGER, LDU = > N. */
|
|
/* > The leading dimension of arrays U, VT, DIFL, DIFR, POLES, */
|
|
/* > GIVNUM, and Z. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VT */
|
|
/* > \verbatim */
|
|
/* > VT is REAL array, */
|
|
/* > dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */
|
|
/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right */
|
|
/* > singular vector matrices of all subproblems at the bottom */
|
|
/* > level. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER array, dimension ( N ) */
|
|
/* > if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */
|
|
/* > If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */
|
|
/* > secular equation on the computation tree. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DIFL */
|
|
/* > \verbatim */
|
|
/* > DIFL is REAL array, dimension ( LDU, NLVL ), */
|
|
/* > where NLVL = floor(log_2 (N/SMLSIZ))). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DIFR */
|
|
/* > \verbatim */
|
|
/* > DIFR is REAL array, */
|
|
/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and */
|
|
/* > dimension ( N ) if ICOMPQ = 0. */
|
|
/* > If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */
|
|
/* > record distances between singular values on the I-th */
|
|
/* > level and singular values on the (I -1)-th level, and */
|
|
/* > DIFR(1:N, 2 * I ) contains the normalizing factors for */
|
|
/* > the right singular vector matrix. See SLASD8 for details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is REAL array, */
|
|
/* > dimension ( LDU, NLVL ) if ICOMPQ = 1 and */
|
|
/* > dimension ( N ) if ICOMPQ = 0. */
|
|
/* > The first K elements of Z(1, I) contain the components of */
|
|
/* > the deflation-adjusted updating row vector for subproblems */
|
|
/* > on the I-th level. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] POLES */
|
|
/* > \verbatim */
|
|
/* > POLES is REAL array, */
|
|
/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */
|
|
/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */
|
|
/* > POLES(1, 2*I) contain the new and old singular values */
|
|
/* > involved in the secular equations on the I-th level. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] GIVPTR */
|
|
/* > \verbatim */
|
|
/* > GIVPTR is INTEGER array, */
|
|
/* > dimension ( N ) if ICOMPQ = 1, and not referenced if */
|
|
/* > ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */
|
|
/* > the number of Givens rotations performed on the I-th */
|
|
/* > problem on the computation tree. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] GIVCOL */
|
|
/* > \verbatim */
|
|
/* > GIVCOL is INTEGER array, */
|
|
/* > dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */
|
|
/* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
|
|
/* > GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations */
|
|
/* > of Givens rotations performed on the I-th level on the */
|
|
/* > computation tree. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDGCOL */
|
|
/* > \verbatim */
|
|
/* > LDGCOL is INTEGER, LDGCOL = > N. */
|
|
/* > The leading dimension of arrays GIVCOL and PERM. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] PERM */
|
|
/* > \verbatim */
|
|
/* > PERM is INTEGER array, dimension ( LDGCOL, NLVL ) */
|
|
/* > if ICOMPQ = 1, and not referenced */
|
|
/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */
|
|
/* > permutations done on the I-th level of the computation tree. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] GIVNUM */
|
|
/* > \verbatim */
|
|
/* > GIVNUM is REAL array, */
|
|
/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not */
|
|
/* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
|
|
/* > GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */
|
|
/* > values of Givens rotations performed on the I-th level on */
|
|
/* > the computation tree. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] C */
|
|
/* > \verbatim */
|
|
/* > C is REAL array, */
|
|
/* > dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */
|
|
/* > If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */
|
|
/* > C( I ) contains the C-value of a Givens rotation related to */
|
|
/* > the right null space of the I-th subproblem. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is REAL array, dimension ( N ) if */
|
|
/* > ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */
|
|
/* > and the I-th subproblem is not square, on exit, S( I ) */
|
|
/* > contains the S-value of a Givens rotation related to */
|
|
/* > the right null space of the I-th subproblem. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension */
|
|
/* > (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (7*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: if INFO = 1, a singular value did not converge */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup OTHERauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void slasda_(integer *icompq, integer *smlsiz, integer *n,
|
|
integer *sqre, real *d__, real *e, real *u, integer *ldu, real *vt,
|
|
integer *k, real *difl, real *difr, real *z__, real *poles, integer *
|
|
givptr, integer *givcol, integer *ldgcol, integer *perm, real *givnum,
|
|
real *c__, real *s, real *work, integer *iwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1,
|
|
difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset,
|
|
poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset,
|
|
z_dim1, z_offset, i__1, i__2;
|
|
|
|
/* Local variables */
|
|
real beta;
|
|
integer idxq, nlvl, i__, j, m;
|
|
real alpha;
|
|
integer inode, ndiml, ndimr, idxqi, itemp, sqrei, i1;
|
|
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
|
|
integer *), slasd6_(integer *, integer *, integer *, integer *,
|
|
real *, real *, real *, real *, real *, integer *, integer *,
|
|
integer *, integer *, integer *, real *, integer *, real *, real *
|
|
, real *, real *, integer *, real *, real *, real *, integer *,
|
|
integer *);
|
|
integer ic, nwork1, lf, nd, nwork2, ll, nl, vf, nr, vl;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern void slasdq_(
|
|
char *, integer *, integer *, integer *, integer *, integer *,
|
|
real *, real *, real *, integer *, real *, integer *, real *,
|
|
integer *, real *, integer *), slasdt_(integer *, integer
|
|
*, integer *, integer *, integer *, integer *, integer *),
|
|
slaset_(char *, integer *, integer *, real *, real *, real *,
|
|
integer *);
|
|
integer im1, smlszp, ncc, nlf, nrf, vfi, iwk, vli, lvl, nru, ndb1, nlp1,
|
|
lvl2, nrp1;
|
|
|
|
|
|
/* -- LAPACK auxiliary 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..-- */
|
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/* December 2016 */
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/* ===================================================================== */
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/* Test the input parameters. */
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/* Parameter adjustments */
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--d__;
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--e;
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givnum_dim1 = *ldu;
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givnum_offset = 1 + givnum_dim1 * 1;
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givnum -= givnum_offset;
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poles_dim1 = *ldu;
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poles_offset = 1 + poles_dim1 * 1;
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poles -= poles_offset;
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z_dim1 = *ldu;
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z_offset = 1 + z_dim1 * 1;
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z__ -= z_offset;
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difr_dim1 = *ldu;
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difr_offset = 1 + difr_dim1 * 1;
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difr -= difr_offset;
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difl_dim1 = *ldu;
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difl_offset = 1 + difl_dim1 * 1;
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difl -= difl_offset;
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vt_dim1 = *ldu;
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vt_offset = 1 + vt_dim1 * 1;
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vt -= vt_offset;
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u_dim1 = *ldu;
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u_offset = 1 + u_dim1 * 1;
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u -= u_offset;
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--k;
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--givptr;
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perm_dim1 = *ldgcol;
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perm_offset = 1 + perm_dim1 * 1;
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perm -= perm_offset;
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givcol_dim1 = *ldgcol;
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givcol_offset = 1 + givcol_dim1 * 1;
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givcol -= givcol_offset;
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--c__;
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--s;
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--work;
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--iwork;
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/* Function Body */
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*info = 0;
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if (*icompq < 0 || *icompq > 1) {
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*info = -1;
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} else if (*smlsiz < 3) {
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*info = -2;
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} else if (*n < 0) {
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*info = -3;
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} else if (*sqre < 0 || *sqre > 1) {
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*info = -4;
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} else if (*ldu < *n + *sqre) {
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*info = -8;
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} else if (*ldgcol < *n) {
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*info = -17;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SLASDA", &i__1, (ftnlen)6);
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return;
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}
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m = *n + *sqre;
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/* If the input matrix is too small, call SLASDQ to find the SVD. */
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if (*n <= *smlsiz) {
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if (*icompq == 0) {
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slasdq_("U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[
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vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, &
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work[1], info);
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} else {
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slasdq_("U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset]
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, ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1],
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info);
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}
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return;
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}
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/* Book-keeping and set up the computation tree. */
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inode = 1;
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ndiml = inode + *n;
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ndimr = ndiml + *n;
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idxq = ndimr + *n;
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iwk = idxq + *n;
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ncc = 0;
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nru = 0;
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smlszp = *smlsiz + 1;
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vf = 1;
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vl = vf + m;
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nwork1 = vl + m;
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nwork2 = nwork1 + smlszp * smlszp;
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slasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr],
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smlsiz);
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/* for the nodes on bottom level of the tree, solve */
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/* their subproblems by SLASDQ. */
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ndb1 = (nd + 1) / 2;
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i__1 = nd;
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for (i__ = ndb1; i__ <= i__1; ++i__) {
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/* IC : center row of each node */
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/* NL : number of rows of left subproblem */
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/* NR : number of rows of right subproblem */
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/* NLF: starting row of the left subproblem */
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/* NRF: starting row of the right subproblem */
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i1 = i__ - 1;
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ic = iwork[inode + i1];
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nl = iwork[ndiml + i1];
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nlp1 = nl + 1;
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nr = iwork[ndimr + i1];
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nlf = ic - nl;
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nrf = ic + 1;
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idxqi = idxq + nlf - 2;
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vfi = vf + nlf - 1;
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vli = vl + nlf - 1;
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sqrei = 1;
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if (*icompq == 0) {
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slaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
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slasdq_("U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], &
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work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2],
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&nl, &work[nwork2], info);
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itemp = nwork1 + nl * smlszp;
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scopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1);
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scopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1);
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} else {
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slaset_("A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu);
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slaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1],
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ldu);
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slasdq_("U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], &
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vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf +
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u_dim1], ldu, &work[nwork1], info);
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scopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1);
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scopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1)
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;
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}
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if (*info != 0) {
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return;
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}
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i__2 = nl;
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for (j = 1; j <= i__2; ++j) {
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iwork[idxqi + j] = j;
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/* L10: */
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}
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if (i__ == nd && *sqre == 0) {
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sqrei = 0;
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} else {
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sqrei = 1;
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}
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idxqi += nlp1;
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vfi += nlp1;
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vli += nlp1;
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nrp1 = nr + sqrei;
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if (*icompq == 0) {
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slaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
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slasdq_("U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], &
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work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2],
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&nr, &work[nwork2], info);
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itemp = nwork1 + (nrp1 - 1) * smlszp;
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scopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1);
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scopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1);
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} else {
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slaset_("A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu);
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slaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1],
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ldu);
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slasdq_("U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], &
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vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf +
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u_dim1], ldu, &work[nwork1], info);
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scopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1);
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scopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1)
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;
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}
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if (*info != 0) {
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return;
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}
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i__2 = nr;
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for (j = 1; j <= i__2; ++j) {
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iwork[idxqi + j] = j;
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/* L20: */
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}
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/* L30: */
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}
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/* Now conquer each subproblem bottom-up. */
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j = pow_ii(c__2, nlvl);
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for (lvl = nlvl; lvl >= 1; --lvl) {
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lvl2 = (lvl << 1) - 1;
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/* Find the first node LF and last node LL on */
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/* the current level LVL. */
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if (lvl == 1) {
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lf = 1;
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ll = 1;
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} else {
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i__1 = lvl - 1;
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lf = pow_ii(c__2, i__1);
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ll = (lf << 1) - 1;
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}
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i__1 = ll;
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for (i__ = lf; i__ <= i__1; ++i__) {
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im1 = i__ - 1;
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ic = iwork[inode + im1];
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nl = iwork[ndiml + im1];
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nr = iwork[ndimr + im1];
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nlf = ic - nl;
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nrf = ic + 1;
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if (i__ == ll) {
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sqrei = *sqre;
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} else {
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sqrei = 1;
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}
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vfi = vf + nlf - 1;
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vli = vl + nlf - 1;
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idxqi = idxq + nlf - 1;
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alpha = d__[ic];
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beta = e[ic];
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if (*icompq == 0) {
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slasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
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work[vli], &alpha, &beta, &iwork[idxqi], &perm[
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perm_offset], &givptr[1], &givcol[givcol_offset],
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ldgcol, &givnum[givnum_offset], ldu, &poles[
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poles_offset], &difl[difl_offset], &difr[difr_offset],
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&z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1],
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&iwork[iwk], info);
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} else {
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--j;
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slasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
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work[vli], &alpha, &beta, &iwork[idxqi], &perm[nlf +
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lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 *
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givcol_dim1], ldgcol, &givnum[nlf + lvl2 *
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givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], &
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difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 *
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difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[j],
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&s[j], &work[nwork1], &iwork[iwk], info);
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}
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if (*info != 0) {
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return;
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}
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/* L40: */
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}
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/* L50: */
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}
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return;
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/* End of SLASDA */
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} /* slasda_ */
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