963 lines
27 KiB
C
963 lines
27 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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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__1 = 1;
|
|
|
|
/* > \brief \b DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by
|
|
sbdsdc. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLASDQ + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasdq.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasdq.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasdq.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, */
|
|
/* U, LDU, C, LDC, WORK, INFO ) */
|
|
|
|
/* CHARACTER UPLO */
|
|
/* INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE */
|
|
/* DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), */
|
|
/* $ VT( LDVT, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLASDQ computes the singular value decomposition (SVD) of a real */
|
|
/* > (upper or lower) bidiagonal matrix with diagonal D and offdiagonal */
|
|
/* > E, accumulating the transformations if desired. Letting B denote */
|
|
/* > the input bidiagonal matrix, the algorithm computes orthogonal */
|
|
/* > matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose */
|
|
/* > of P). The singular values S are overwritten on D. */
|
|
/* > */
|
|
/* > The input matrix U is changed to U * Q if desired. */
|
|
/* > The input matrix VT is changed to P**T * VT if desired. */
|
|
/* > The input matrix C is changed to Q**T * C if desired. */
|
|
/* > */
|
|
/* > See "Computing Small Singular Values of Bidiagonal Matrices With */
|
|
/* > Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */
|
|
/* > LAPACK Working Note #3, for a detailed description of the algorithm. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > On entry, UPLO specifies whether the input bidiagonal matrix */
|
|
/* > is upper or lower bidiagonal, and whether it is square are */
|
|
/* > not. */
|
|
/* > UPLO = 'U' or 'u' B is upper bidiagonal. */
|
|
/* > UPLO = 'L' or 'l' B is lower bidiagonal. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SQRE */
|
|
/* > \verbatim */
|
|
/* > SQRE is INTEGER */
|
|
/* > = 0: then the input matrix is N-by-N. */
|
|
/* > = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and */
|
|
/* > (N+1)-by-N if UPLU = 'L'. */
|
|
/* > */
|
|
/* > The bidiagonal matrix has */
|
|
/* > N = NL + NR + 1 rows and */
|
|
/* > M = N + SQRE >= N columns. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > On entry, N specifies the number of rows and columns */
|
|
/* > in the matrix. N must be at least 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NCVT */
|
|
/* > \verbatim */
|
|
/* > NCVT is INTEGER */
|
|
/* > On entry, NCVT specifies the number of columns of */
|
|
/* > the matrix VT. NCVT must be at least 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NRU */
|
|
/* > \verbatim */
|
|
/* > NRU is INTEGER */
|
|
/* > On entry, NRU specifies the number of rows of */
|
|
/* > the matrix U. NRU must be at least 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NCC */
|
|
/* > \verbatim */
|
|
/* > NCC is INTEGER */
|
|
/* > On entry, NCC specifies the number of columns of */
|
|
/* > the matrix C. NCC must be at least 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On entry, D contains the diagonal entries of the */
|
|
/* > bidiagonal matrix whose SVD is desired. On normal exit, */
|
|
/* > D contains the singular values in ascending order. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array. */
|
|
/* > dimension is (N-1) if SQRE = 0 and N if SQRE = 1. */
|
|
/* > On entry, the entries of E contain the offdiagonal entries */
|
|
/* > of the bidiagonal matrix whose SVD is desired. On normal */
|
|
/* > exit, E will contain 0. If the algorithm does not converge, */
|
|
/* > D and E will contain the diagonal and superdiagonal entries */
|
|
/* > of a bidiagonal matrix orthogonally equivalent to the one */
|
|
/* > given as input. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] VT */
|
|
/* > \verbatim */
|
|
/* > VT is DOUBLE PRECISION array, dimension (LDVT, NCVT) */
|
|
/* > On entry, contains a matrix which on exit has been */
|
|
/* > premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 */
|
|
/* > and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVT */
|
|
/* > \verbatim */
|
|
/* > LDVT is INTEGER */
|
|
/* > On entry, LDVT specifies the leading dimension of VT as */
|
|
/* > declared in the calling (sub) program. LDVT must be at */
|
|
/* > least 1. If NCVT is nonzero LDVT must also be at least N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] U */
|
|
/* > \verbatim */
|
|
/* > U is DOUBLE PRECISION array, dimension (LDU, N) */
|
|
/* > On entry, contains a matrix which on exit has been */
|
|
/* > postmultiplied by Q, dimension NRU-by-N if SQRE = 0 */
|
|
/* > and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU */
|
|
/* > \verbatim */
|
|
/* > LDU is INTEGER */
|
|
/* > On entry, LDU specifies the leading dimension of U as */
|
|
/* > declared in the calling (sub) program. LDU must be at */
|
|
/* > least f2cmax( 1, NRU ) . */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] C */
|
|
/* > \verbatim */
|
|
/* > C is DOUBLE PRECISION array, dimension (LDC, NCC) */
|
|
/* > On entry, contains an N-by-NCC matrix which on exit */
|
|
/* > has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 */
|
|
/* > and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDC */
|
|
/* > \verbatim */
|
|
/* > LDC is INTEGER */
|
|
/* > On entry, LDC specifies the leading dimension of C as */
|
|
/* > declared in the calling (sub) program. LDC must be at */
|
|
/* > least 1. If NCC is nonzero, LDC must also be at least N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (4*N) */
|
|
/* > Workspace. Only referenced if one of NCVT, NRU, or NCC is */
|
|
/* > nonzero, and if N is at least 2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > On exit, a value of 0 indicates a successful exit. */
|
|
/* > If INFO < 0, argument number -INFO is illegal. */
|
|
/* > If INFO > 0, the algorithm did not converge, and INFO */
|
|
/* > specifies how many superdiagonals did not converge. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup OTHERauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlasdq_(char *uplo, integer *sqre, integer *n, integer *
|
|
ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e,
|
|
doublereal *vt, integer *ldvt, doublereal *u, integer *ldu,
|
|
doublereal *c__, integer *ldc, doublereal *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
|
|
i__2;
|
|
|
|
/* Local variables */
|
|
integer isub;
|
|
doublereal smin;
|
|
integer sqre1, i__, j;
|
|
doublereal r__;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void dlasr_(char *, char *, char *, integer *,
|
|
integer *, doublereal *, doublereal *, doublereal *, integer *), dswap_(integer *, doublereal *, integer *
|
|
, doublereal *, integer *);
|
|
integer iuplo;
|
|
doublereal cs, sn;
|
|
extern /* Subroutine */ void dlartg_(doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
extern void dbdsqr_(char *, integer *, integer *, integer
|
|
*, integer *, doublereal *, doublereal *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, integer *, doublereal *,
|
|
integer *);
|
|
logical rotate;
|
|
integer np1;
|
|
|
|
|
|
/* -- 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..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
--d__;
|
|
--e;
|
|
vt_dim1 = *ldvt;
|
|
vt_offset = 1 + vt_dim1 * 1;
|
|
vt -= vt_offset;
|
|
u_dim1 = *ldu;
|
|
u_offset = 1 + u_dim1 * 1;
|
|
u -= u_offset;
|
|
c_dim1 = *ldc;
|
|
c_offset = 1 + c_dim1 * 1;
|
|
c__ -= c_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
iuplo = 0;
|
|
if (lsame_(uplo, "U")) {
|
|
iuplo = 1;
|
|
}
|
|
if (lsame_(uplo, "L")) {
|
|
iuplo = 2;
|
|
}
|
|
if (iuplo == 0) {
|
|
*info = -1;
|
|
} else if (*sqre < 0 || *sqre > 1) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*ncvt < 0) {
|
|
*info = -4;
|
|
} else if (*nru < 0) {
|
|
*info = -5;
|
|
} else if (*ncc < 0) {
|
|
*info = -6;
|
|
} else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < f2cmax(1,*n)) {
|
|
*info = -10;
|
|
} else if (*ldu < f2cmax(1,*nru)) {
|
|
*info = -12;
|
|
} else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < f2cmax(1,*n)) {
|
|
*info = -14;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DLASDQ", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* ROTATE is true if any singular vectors desired, false otherwise */
|
|
|
|
rotate = *ncvt > 0 || *nru > 0 || *ncc > 0;
|
|
np1 = *n + 1;
|
|
sqre1 = *sqre;
|
|
|
|
/* If matrix non-square upper bidiagonal, rotate to be lower */
|
|
/* bidiagonal. The rotations are on the right. */
|
|
|
|
if (iuplo == 1 && sqre1 == 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 (rotate) {
|
|
work[i__] = cs;
|
|
work[*n + i__] = sn;
|
|
}
|
|
/* L10: */
|
|
}
|
|
dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__);
|
|
d__[*n] = r__;
|
|
e[*n] = 0.;
|
|
if (rotate) {
|
|
work[*n] = cs;
|
|
work[*n + *n] = sn;
|
|
}
|
|
iuplo = 2;
|
|
sqre1 = 0;
|
|
|
|
/* Update singular vectors if desired. */
|
|
|
|
if (*ncvt > 0) {
|
|
dlasr_("L", "V", "F", &np1, ncvt, &work[1], &work[np1], &vt[
|
|
vt_offset], ldvt);
|
|
}
|
|
}
|
|
|
|
/* If matrix lower bidiagonal, rotate to be upper bidiagonal */
|
|
/* by applying Givens rotations on the left. */
|
|
|
|
if (iuplo == 2) {
|
|
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 (rotate) {
|
|
work[i__] = cs;
|
|
work[*n + i__] = sn;
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
/* If matrix (N+1)-by-N lower bidiagonal, one additional */
|
|
/* rotation is needed. */
|
|
|
|
if (sqre1 == 1) {
|
|
dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__);
|
|
d__[*n] = r__;
|
|
if (rotate) {
|
|
work[*n] = cs;
|
|
work[*n + *n] = sn;
|
|
}
|
|
}
|
|
|
|
/* Update singular vectors if desired. */
|
|
|
|
if (*nru > 0) {
|
|
if (sqre1 == 0) {
|
|
dlasr_("R", "V", "F", nru, n, &work[1], &work[np1], &u[
|
|
u_offset], ldu);
|
|
} else {
|
|
dlasr_("R", "V", "F", nru, &np1, &work[1], &work[np1], &u[
|
|
u_offset], ldu);
|
|
}
|
|
}
|
|
if (*ncc > 0) {
|
|
if (sqre1 == 0) {
|
|
dlasr_("L", "V", "F", n, ncc, &work[1], &work[np1], &c__[
|
|
c_offset], ldc);
|
|
} else {
|
|
dlasr_("L", "V", "F", &np1, ncc, &work[1], &work[np1], &c__[
|
|
c_offset], ldc);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Call DBDSQR to compute the SVD of the reduced real */
|
|
/* N-by-N upper bidiagonal matrix. */
|
|
|
|
dbdsqr_("U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[
|
|
u_offset], ldu, &c__[c_offset], ldc, &work[1], info);
|
|
|
|
/* Sort the singular values into ascending order (insertion sort on */
|
|
/* singular values, but only one transposition per singular vector) */
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
|
|
/* Scan for smallest D(I). */
|
|
|
|
isub = i__;
|
|
smin = d__[i__];
|
|
i__2 = *n;
|
|
for (j = i__ + 1; j <= i__2; ++j) {
|
|
if (d__[j] < smin) {
|
|
isub = j;
|
|
smin = d__[j];
|
|
}
|
|
/* L30: */
|
|
}
|
|
if (isub != i__) {
|
|
|
|
/* Swap singular values and vectors. */
|
|
|
|
d__[isub] = d__[i__];
|
|
d__[i__] = smin;
|
|
if (*ncvt > 0) {
|
|
dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1],
|
|
ldvt);
|
|
}
|
|
if (*nru > 0) {
|
|
dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1]
|
|
, &c__1);
|
|
}
|
|
if (*ncc > 0) {
|
|
dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc)
|
|
;
|
|
}
|
|
}
|
|
/* L40: */
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of DLASDQ */
|
|
|
|
} /* dlasdq_ */
|
|
|