1138 lines
32 KiB
C
1138 lines
32 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries
|
|
to deflate the size of the problem. Used by sbdsdc. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLASD7 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd7.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd7.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd7.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL, */
|
|
/* VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ, */
|
|
/* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, */
|
|
/* C, S, INFO ) */
|
|
|
|
/* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */
|
|
/* $ NR, SQRE */
|
|
/* DOUBLE PRECISION ALPHA, BETA, C, S */
|
|
/* INTEGER GIVCOL( LDGCOL, * ), IDX( * ), IDXP( * ), */
|
|
/* $ IDXQ( * ), PERM( * ) */
|
|
/* DOUBLE PRECISION D( * ), DSIGMA( * ), GIVNUM( LDGNUM, * ), */
|
|
/* $ VF( * ), VFW( * ), VL( * ), VLW( * ), Z( * ), */
|
|
/* $ ZW( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLASD7 merges the two sets of singular values together into a single */
|
|
/* > sorted set. Then it tries to deflate the size of the problem. There */
|
|
/* > are two ways in which deflation can occur: when two or more singular */
|
|
/* > values are close together or if there is a tiny entry in the Z */
|
|
/* > vector. For each such occurrence the order of the related */
|
|
/* > secular equation problem is reduced by one. */
|
|
/* > */
|
|
/* > DLASD7 is called from DLASD6. */
|
|
/* > \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] NL */
|
|
/* > \verbatim */
|
|
/* > NL is INTEGER */
|
|
/* > The row dimension of the upper block. NL >= 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NR */
|
|
/* > \verbatim */
|
|
/* > NR is INTEGER */
|
|
/* > The row dimension of the lower block. NR >= 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SQRE */
|
|
/* > \verbatim */
|
|
/* > SQRE is INTEGER */
|
|
/* > = 0: the lower block is an NR-by-NR square matrix. */
|
|
/* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
|
|
/* > */
|
|
/* > The bidiagonal matrix has */
|
|
/* > N = NL + NR + 1 rows and */
|
|
/* > M = N + SQRE >= N columns. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER */
|
|
/* > Contains the dimension of the non-deflated matrix, this is */
|
|
/* > the order of the related secular equation. 1 <= K <=N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension ( N ) */
|
|
/* > On entry D contains the singular values of the two submatrices */
|
|
/* > to be combined. On exit D contains the trailing (N-K) updated */
|
|
/* > singular values (those which were deflated) sorted into */
|
|
/* > increasing order. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is DOUBLE PRECISION array, dimension ( M ) */
|
|
/* > On exit Z contains the updating row vector in the secular */
|
|
/* > equation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ZW */
|
|
/* > \verbatim */
|
|
/* > ZW is DOUBLE PRECISION array, dimension ( M ) */
|
|
/* > Workspace for Z. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] VF */
|
|
/* > \verbatim */
|
|
/* > VF is DOUBLE PRECISION array, dimension ( M ) */
|
|
/* > On entry, VF(1:NL+1) contains the first components of all */
|
|
/* > right singular vectors of the upper block; and VF(NL+2:M) */
|
|
/* > contains the first components of all right singular vectors */
|
|
/* > of the lower block. On exit, VF contains the first components */
|
|
/* > of all right singular vectors of the bidiagonal matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VFW */
|
|
/* > \verbatim */
|
|
/* > VFW is DOUBLE PRECISION array, dimension ( M ) */
|
|
/* > Workspace for VF. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] VL */
|
|
/* > \verbatim */
|
|
/* > VL is DOUBLE PRECISION array, dimension ( M ) */
|
|
/* > On entry, VL(1:NL+1) contains the last components of all */
|
|
/* > right singular vectors of the upper block; and VL(NL+2:M) */
|
|
/* > contains the last components of all right singular vectors */
|
|
/* > of the lower block. On exit, VL contains the last components */
|
|
/* > of all right singular vectors of the bidiagonal matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VLW */
|
|
/* > \verbatim */
|
|
/* > VLW is DOUBLE PRECISION array, dimension ( M ) */
|
|
/* > Workspace for VL. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ALPHA */
|
|
/* > \verbatim */
|
|
/* > ALPHA is DOUBLE PRECISION */
|
|
/* > Contains the diagonal element associated with the added row. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] BETA */
|
|
/* > \verbatim */
|
|
/* > BETA is DOUBLE PRECISION */
|
|
/* > Contains the off-diagonal element associated with the added */
|
|
/* > row. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DSIGMA */
|
|
/* > \verbatim */
|
|
/* > DSIGMA is DOUBLE PRECISION array, dimension ( N ) */
|
|
/* > Contains a copy of the diagonal elements (K-1 singular values */
|
|
/* > and one zero) in the secular equation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IDX */
|
|
/* > \verbatim */
|
|
/* > IDX is INTEGER array, dimension ( N ) */
|
|
/* > This will contain the permutation used to sort the contents of */
|
|
/* > D into ascending order. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IDXP */
|
|
/* > \verbatim */
|
|
/* > IDXP is INTEGER array, dimension ( N ) */
|
|
/* > This will contain the permutation used to place deflated */
|
|
/* > values of D at the end of the array. On output IDXP(2:K) */
|
|
/* > points to the nondeflated D-values and IDXP(K+1:N) */
|
|
/* > points to the deflated singular values. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IDXQ */
|
|
/* > \verbatim */
|
|
/* > IDXQ is INTEGER array, dimension ( N ) */
|
|
/* > This contains the permutation which separately sorts the two */
|
|
/* > sub-problems in D into ascending order. Note that entries in */
|
|
/* > the first half of this permutation must first be moved one */
|
|
/* > position backward; and entries in the second half */
|
|
/* > must first have NL+1 added to their values. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] PERM */
|
|
/* > \verbatim */
|
|
/* > PERM is INTEGER array, dimension ( N ) */
|
|
/* > The permutations (from deflation and sorting) to be applied */
|
|
/* > to each singular block. Not referenced if ICOMPQ = 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] GIVPTR */
|
|
/* > \verbatim */
|
|
/* > GIVPTR is INTEGER */
|
|
/* > The number of Givens rotations which took place in this */
|
|
/* > subproblem. Not referenced if ICOMPQ = 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] GIVCOL */
|
|
/* > \verbatim */
|
|
/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */
|
|
/* > Each pair of numbers indicates a pair of columns to take place */
|
|
/* > in a Givens rotation. Not referenced if ICOMPQ = 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDGCOL */
|
|
/* > \verbatim */
|
|
/* > LDGCOL is INTEGER */
|
|
/* > The leading dimension of GIVCOL, must be at least N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] GIVNUM */
|
|
/* > \verbatim */
|
|
/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
|
|
/* > Each number indicates the C or S value to be used in the */
|
|
/* > corresponding Givens rotation. Not referenced if ICOMPQ = 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDGNUM */
|
|
/* > \verbatim */
|
|
/* > LDGNUM is INTEGER */
|
|
/* > The leading dimension of GIVNUM, must be at least N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] C */
|
|
/* > \verbatim */
|
|
/* > C is DOUBLE PRECISION */
|
|
/* > C contains garbage if SQRE =0 and the C-value of a Givens */
|
|
/* > rotation related to the right null space if SQRE = 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is DOUBLE PRECISION */
|
|
/* > S contains garbage if SQRE =0 and the S-value of a Givens */
|
|
/* > rotation related to the right null space if SQRE = 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup OTHERauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlasd7_(integer *icompq, integer *nl, integer *nr,
|
|
integer *sqre, integer *k, doublereal *d__, doublereal *z__,
|
|
doublereal *zw, doublereal *vf, doublereal *vfw, doublereal *vl,
|
|
doublereal *vlw, doublereal *alpha, doublereal *beta, doublereal *
|
|
dsigma, integer *idx, integer *idxp, integer *idxq, integer *perm,
|
|
integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum,
|
|
integer *ldgnum, doublereal *c__, doublereal *s, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, i__1;
|
|
doublereal d__1, d__2;
|
|
|
|
/* Local variables */
|
|
integer idxi, idxj;
|
|
extern /* Subroutine */ void drot_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *);
|
|
integer i__, j, m, n, idxjp;
|
|
extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *);
|
|
integer jprev, k2;
|
|
doublereal z1;
|
|
extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
|
|
integer jp;
|
|
extern /* Subroutine */ void dlamrg_(integer *, integer *, doublereal *,
|
|
integer *, integer *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
doublereal hlftol, eps, tau, tol;
|
|
integer nlp1, nlp2;
|
|
|
|
|
|
/* -- 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..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
--d__;
|
|
--z__;
|
|
--zw;
|
|
--vf;
|
|
--vfw;
|
|
--vl;
|
|
--vlw;
|
|
--dsigma;
|
|
--idx;
|
|
--idxp;
|
|
--idxq;
|
|
--perm;
|
|
givcol_dim1 = *ldgcol;
|
|
givcol_offset = 1 + givcol_dim1 * 1;
|
|
givcol -= givcol_offset;
|
|
givnum_dim1 = *ldgnum;
|
|
givnum_offset = 1 + givnum_dim1 * 1;
|
|
givnum -= givnum_offset;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
n = *nl + *nr + 1;
|
|
m = n + *sqre;
|
|
|
|
if (*icompq < 0 || *icompq > 1) {
|
|
*info = -1;
|
|
} else if (*nl < 1) {
|
|
*info = -2;
|
|
} else if (*nr < 1) {
|
|
*info = -3;
|
|
} else if (*sqre < 0 || *sqre > 1) {
|
|
*info = -4;
|
|
} else if (*ldgcol < n) {
|
|
*info = -22;
|
|
} else if (*ldgnum < n) {
|
|
*info = -24;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DLASD7", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
nlp1 = *nl + 1;
|
|
nlp2 = *nl + 2;
|
|
if (*icompq == 1) {
|
|
*givptr = 0;
|
|
}
|
|
|
|
/* Generate the first part of the vector Z and move the singular */
|
|
/* values in the first part of D one position backward. */
|
|
|
|
z1 = *alpha * vl[nlp1];
|
|
vl[nlp1] = 0.;
|
|
tau = vf[nlp1];
|
|
for (i__ = *nl; i__ >= 1; --i__) {
|
|
z__[i__ + 1] = *alpha * vl[i__];
|
|
vl[i__] = 0.;
|
|
vf[i__ + 1] = vf[i__];
|
|
d__[i__ + 1] = d__[i__];
|
|
idxq[i__ + 1] = idxq[i__] + 1;
|
|
/* L10: */
|
|
}
|
|
vf[1] = tau;
|
|
|
|
/* Generate the second part of the vector Z. */
|
|
|
|
i__1 = m;
|
|
for (i__ = nlp2; i__ <= i__1; ++i__) {
|
|
z__[i__] = *beta * vf[i__];
|
|
vf[i__] = 0.;
|
|
/* L20: */
|
|
}
|
|
|
|
/* Sort the singular values into increasing order */
|
|
|
|
i__1 = n;
|
|
for (i__ = nlp2; i__ <= i__1; ++i__) {
|
|
idxq[i__] += nlp1;
|
|
/* L30: */
|
|
}
|
|
|
|
/* DSIGMA, IDXC, IDXC, and ZW are used as storage space. */
|
|
|
|
i__1 = n;
|
|
for (i__ = 2; i__ <= i__1; ++i__) {
|
|
dsigma[i__] = d__[idxq[i__]];
|
|
zw[i__] = z__[idxq[i__]];
|
|
vfw[i__] = vf[idxq[i__]];
|
|
vlw[i__] = vl[idxq[i__]];
|
|
/* L40: */
|
|
}
|
|
|
|
dlamrg_(nl, nr, &dsigma[2], &c__1, &c__1, &idx[2]);
|
|
|
|
i__1 = n;
|
|
for (i__ = 2; i__ <= i__1; ++i__) {
|
|
idxi = idx[i__] + 1;
|
|
d__[i__] = dsigma[idxi];
|
|
z__[i__] = zw[idxi];
|
|
vf[i__] = vfw[idxi];
|
|
vl[i__] = vlw[idxi];
|
|
/* L50: */
|
|
}
|
|
|
|
/* Calculate the allowable deflation tolerance */
|
|
|
|
eps = dlamch_("Epsilon");
|
|
/* Computing MAX */
|
|
d__1 = abs(*alpha), d__2 = abs(*beta);
|
|
tol = f2cmax(d__1,d__2);
|
|
/* Computing MAX */
|
|
d__2 = (d__1 = d__[n], abs(d__1));
|
|
tol = eps * 64. * f2cmax(d__2,tol);
|
|
|
|
/* There are 2 kinds of deflation -- first a value in the z-vector */
|
|
/* is small, second two (or more) singular values are very close */
|
|
/* together (their difference is small). */
|
|
|
|
/* If the value in the z-vector is small, we simply permute the */
|
|
/* array so that the corresponding singular value is moved to the */
|
|
/* end. */
|
|
|
|
/* If two values in the D-vector are close, we perform a two-sided */
|
|
/* rotation designed to make one of the corresponding z-vector */
|
|
/* entries zero, and then permute the array so that the deflated */
|
|
/* singular value is moved to the end. */
|
|
|
|
/* If there are multiple singular values then the problem deflates. */
|
|
/* Here the number of equal singular values are found. As each equal */
|
|
/* singular value is found, an elementary reflector is computed to */
|
|
/* rotate the corresponding singular subspace so that the */
|
|
/* corresponding components of Z are zero in this new basis. */
|
|
|
|
*k = 1;
|
|
k2 = n + 1;
|
|
i__1 = n;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
if ((d__1 = z__[j], abs(d__1)) <= tol) {
|
|
|
|
/* Deflate due to small z component. */
|
|
|
|
--k2;
|
|
idxp[k2] = j;
|
|
if (j == n) {
|
|
goto L100;
|
|
}
|
|
} else {
|
|
jprev = j;
|
|
goto L70;
|
|
}
|
|
/* L60: */
|
|
}
|
|
L70:
|
|
j = jprev;
|
|
L80:
|
|
++j;
|
|
if (j > n) {
|
|
goto L90;
|
|
}
|
|
if ((d__1 = z__[j], abs(d__1)) <= tol) {
|
|
|
|
/* Deflate due to small z component. */
|
|
|
|
--k2;
|
|
idxp[k2] = j;
|
|
} else {
|
|
|
|
/* Check if singular values are close enough to allow deflation. */
|
|
|
|
if ((d__1 = d__[j] - d__[jprev], abs(d__1)) <= tol) {
|
|
|
|
/* Deflation is possible. */
|
|
|
|
*s = z__[jprev];
|
|
*c__ = z__[j];
|
|
|
|
/* Find sqrt(a**2+b**2) without overflow or */
|
|
/* destructive underflow. */
|
|
|
|
tau = dlapy2_(c__, s);
|
|
z__[j] = tau;
|
|
z__[jprev] = 0.;
|
|
*c__ /= tau;
|
|
*s = -(*s) / tau;
|
|
|
|
/* Record the appropriate Givens rotation */
|
|
|
|
if (*icompq == 1) {
|
|
++(*givptr);
|
|
idxjp = idxq[idx[jprev] + 1];
|
|
idxj = idxq[idx[j] + 1];
|
|
if (idxjp <= nlp1) {
|
|
--idxjp;
|
|
}
|
|
if (idxj <= nlp1) {
|
|
--idxj;
|
|
}
|
|
givcol[*givptr + (givcol_dim1 << 1)] = idxjp;
|
|
givcol[*givptr + givcol_dim1] = idxj;
|
|
givnum[*givptr + (givnum_dim1 << 1)] = *c__;
|
|
givnum[*givptr + givnum_dim1] = *s;
|
|
}
|
|
drot_(&c__1, &vf[jprev], &c__1, &vf[j], &c__1, c__, s);
|
|
drot_(&c__1, &vl[jprev], &c__1, &vl[j], &c__1, c__, s);
|
|
--k2;
|
|
idxp[k2] = jprev;
|
|
jprev = j;
|
|
} else {
|
|
++(*k);
|
|
zw[*k] = z__[jprev];
|
|
dsigma[*k] = d__[jprev];
|
|
idxp[*k] = jprev;
|
|
jprev = j;
|
|
}
|
|
}
|
|
goto L80;
|
|
L90:
|
|
|
|
/* Record the last singular value. */
|
|
|
|
++(*k);
|
|
zw[*k] = z__[jprev];
|
|
dsigma[*k] = d__[jprev];
|
|
idxp[*k] = jprev;
|
|
|
|
L100:
|
|
|
|
/* Sort the singular values into DSIGMA. The singular values which */
|
|
/* were not deflated go into the first K slots of DSIGMA, except */
|
|
/* that DSIGMA(1) is treated separately. */
|
|
|
|
i__1 = n;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
jp = idxp[j];
|
|
dsigma[j] = d__[jp];
|
|
vfw[j] = vf[jp];
|
|
vlw[j] = vl[jp];
|
|
/* L110: */
|
|
}
|
|
if (*icompq == 1) {
|
|
i__1 = n;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
jp = idxp[j];
|
|
perm[j] = idxq[idx[jp] + 1];
|
|
if (perm[j] <= nlp1) {
|
|
--perm[j];
|
|
}
|
|
/* L120: */
|
|
}
|
|
}
|
|
|
|
/* The deflated singular values go back into the last N - K slots of */
|
|
/* D. */
|
|
|
|
i__1 = n - *k;
|
|
dcopy_(&i__1, &dsigma[*k + 1], &c__1, &d__[*k + 1], &c__1);
|
|
|
|
/* Determine DSIGMA(1), DSIGMA(2), Z(1), VF(1), VL(1), VF(M), and */
|
|
/* VL(M). */
|
|
|
|
dsigma[1] = 0.;
|
|
hlftol = tol / 2.;
|
|
if (abs(dsigma[2]) <= hlftol) {
|
|
dsigma[2] = hlftol;
|
|
}
|
|
if (m > n) {
|
|
z__[1] = dlapy2_(&z1, &z__[m]);
|
|
if (z__[1] <= tol) {
|
|
*c__ = 1.;
|
|
*s = 0.;
|
|
z__[1] = tol;
|
|
} else {
|
|
*c__ = z1 / z__[1];
|
|
*s = -z__[m] / z__[1];
|
|
}
|
|
drot_(&c__1, &vf[m], &c__1, &vf[1], &c__1, c__, s);
|
|
drot_(&c__1, &vl[m], &c__1, &vl[1], &c__1, c__, s);
|
|
} else {
|
|
if (abs(z1) <= tol) {
|
|
z__[1] = tol;
|
|
} else {
|
|
z__[1] = z1;
|
|
}
|
|
}
|
|
|
|
/* Restore Z, VF, and VL. */
|
|
|
|
i__1 = *k - 1;
|
|
dcopy_(&i__1, &zw[2], &c__1, &z__[2], &c__1);
|
|
i__1 = n - 1;
|
|
dcopy_(&i__1, &vfw[2], &c__1, &vf[2], &c__1);
|
|
i__1 = n - 1;
|
|
dcopy_(&i__1, &vlw[2], &c__1, &vl[2], &c__1);
|
|
|
|
return;
|
|
|
|
/* End of DLASD7 */
|
|
|
|
} /* dlasd7_ */
|
|
|