1805 lines
54 KiB
C
1805 lines
54 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 doublecomplex c_b1 = {-1.,0.};
|
|
static doublereal c_b11 = -.125;
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZBBCSD */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZBBCSD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zbbcsd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zbbcsd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zbbcsd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, */
|
|
/* THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, */
|
|
/* V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, */
|
|
/* B22D, B22E, RWORK, LRWORK, INFO ) */
|
|
|
|
/* CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS */
|
|
/* INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LRWORK, M, P, Q */
|
|
/* DOUBLE PRECISION B11D( * ), B11E( * ), B12D( * ), B12E( * ), */
|
|
/* $ B21D( * ), B21E( * ), B22D( * ), B22E( * ), */
|
|
/* $ PHI( * ), THETA( * ), RWORK( * ) */
|
|
/* COMPLEX*16 U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ), */
|
|
/* $ V2T( LDV2T, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZBBCSD computes the CS decomposition of a unitary matrix in */
|
|
/* > bidiagonal-block form, */
|
|
/* > */
|
|
/* > */
|
|
/* > [ B11 | B12 0 0 ] */
|
|
/* > [ 0 | 0 -I 0 ] */
|
|
/* > X = [----------------] */
|
|
/* > [ B21 | B22 0 0 ] */
|
|
/* > [ 0 | 0 0 I ] */
|
|
/* > */
|
|
/* > [ C | -S 0 0 ] */
|
|
/* > [ U1 | ] [ 0 | 0 -I 0 ] [ V1 | ]**H */
|
|
/* > = [---------] [---------------] [---------] . */
|
|
/* > [ | U2 ] [ S | C 0 0 ] [ | V2 ] */
|
|
/* > [ 0 | 0 0 I ] */
|
|
/* > */
|
|
/* > X is M-by-M, its top-left block is P-by-Q, and Q must be no larger */
|
|
/* > than P, M-P, or M-Q. (If Q is not the smallest index, then X must be */
|
|
/* > transposed and/or permuted. This can be done in constant time using */
|
|
/* > the TRANS and SIGNS options. See ZUNCSD for details.) */
|
|
/* > */
|
|
/* > The bidiagonal matrices B11, B12, B21, and B22 are represented */
|
|
/* > implicitly by angles THETA(1:Q) and PHI(1:Q-1). */
|
|
/* > */
|
|
/* > The unitary matrices U1, U2, V1T, and V2T are input/output. */
|
|
/* > The input matrices are pre- or post-multiplied by the appropriate */
|
|
/* > singular vector matrices. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBU1 */
|
|
/* > \verbatim */
|
|
/* > JOBU1 is CHARACTER */
|
|
/* > = 'Y': U1 is updated; */
|
|
/* > otherwise: U1 is not updated. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBU2 */
|
|
/* > \verbatim */
|
|
/* > JOBU2 is CHARACTER */
|
|
/* > = 'Y': U2 is updated; */
|
|
/* > otherwise: U2 is not updated. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBV1T */
|
|
/* > \verbatim */
|
|
/* > JOBV1T is CHARACTER */
|
|
/* > = 'Y': V1T is updated; */
|
|
/* > otherwise: V1T is not updated. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBV2T */
|
|
/* > \verbatim */
|
|
/* > JOBV2T is CHARACTER */
|
|
/* > = 'Y': V2T is updated; */
|
|
/* > otherwise: V2T is not updated. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TRANS */
|
|
/* > \verbatim */
|
|
/* > TRANS is CHARACTER */
|
|
/* > = 'T': X, U1, U2, V1T, and V2T are stored in row-major */
|
|
/* > order; */
|
|
/* > otherwise: X, U1, U2, V1T, and V2T are stored in column- */
|
|
/* > major order. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows and columns in X, the unitary matrix in */
|
|
/* > bidiagonal-block form. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] P */
|
|
/* > \verbatim */
|
|
/* > P is INTEGER */
|
|
/* > The number of rows in the top-left block of X. 0 <= P <= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] Q */
|
|
/* > \verbatim */
|
|
/* > Q is INTEGER */
|
|
/* > The number of columns in the top-left block of X. */
|
|
/* > 0 <= Q <= MIN(P,M-P,M-Q). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] THETA */
|
|
/* > \verbatim */
|
|
/* > THETA is DOUBLE PRECISION array, dimension (Q) */
|
|
/* > On entry, the angles THETA(1),...,THETA(Q) that, along with */
|
|
/* > PHI(1), ...,PHI(Q-1), define the matrix in bidiagonal-block */
|
|
/* > form. On exit, the angles whose cosines and sines define the */
|
|
/* > diagonal blocks in the CS decomposition. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] PHI */
|
|
/* > \verbatim */
|
|
/* > PHI is DOUBLE PRECISION array, dimension (Q-1) */
|
|
/* > The angles PHI(1),...,PHI(Q-1) that, along with THETA(1),..., */
|
|
/* > THETA(Q), define the matrix in bidiagonal-block form. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] U1 */
|
|
/* > \verbatim */
|
|
/* > U1 is COMPLEX*16 array, dimension (LDU1,P) */
|
|
/* > On entry, a P-by-P matrix. On exit, U1 is postmultiplied */
|
|
/* > by the left singular vector matrix common to [ B11 ; 0 ] and */
|
|
/* > [ B12 0 0 ; 0 -I 0 0 ]. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU1 */
|
|
/* > \verbatim */
|
|
/* > LDU1 is INTEGER */
|
|
/* > The leading dimension of the array U1, LDU1 >= MAX(1,P). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] U2 */
|
|
/* > \verbatim */
|
|
/* > U2 is COMPLEX*16 array, dimension (LDU2,M-P) */
|
|
/* > On entry, an (M-P)-by-(M-P) matrix. On exit, U2 is */
|
|
/* > postmultiplied by the left singular vector matrix common to */
|
|
/* > [ B21 ; 0 ] and [ B22 0 0 ; 0 0 I ]. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU2 */
|
|
/* > \verbatim */
|
|
/* > LDU2 is INTEGER */
|
|
/* > The leading dimension of the array U2, LDU2 >= MAX(1,M-P). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] V1T */
|
|
/* > \verbatim */
|
|
/* > V1T is COMPLEX*16 array, dimension (LDV1T,Q) */
|
|
/* > On entry, a Q-by-Q matrix. On exit, V1T is premultiplied */
|
|
/* > by the conjugate transpose of the right singular vector */
|
|
/* > matrix common to [ B11 ; 0 ] and [ B21 ; 0 ]. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDV1T */
|
|
/* > \verbatim */
|
|
/* > LDV1T is INTEGER */
|
|
/* > The leading dimension of the array V1T, LDV1T >= MAX(1,Q). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] V2T */
|
|
/* > \verbatim */
|
|
/* > V2T is COMPLEX*16 array, dimension (LDV2T,M-Q) */
|
|
/* > On entry, an (M-Q)-by-(M-Q) matrix. On exit, V2T is */
|
|
/* > premultiplied by the conjugate transpose of the right */
|
|
/* > singular vector matrix common to [ B12 0 0 ; 0 -I 0 ] and */
|
|
/* > [ B22 0 0 ; 0 0 I ]. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDV2T */
|
|
/* > \verbatim */
|
|
/* > LDV2T is INTEGER */
|
|
/* > The leading dimension of the array V2T, LDV2T >= MAX(1,M-Q). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] B11D */
|
|
/* > \verbatim */
|
|
/* > B11D is DOUBLE PRECISION array, dimension (Q) */
|
|
/* > When ZBBCSD converges, B11D contains the cosines of THETA(1), */
|
|
/* > ..., THETA(Q). If ZBBCSD fails to converge, then B11D */
|
|
/* > contains the diagonal of the partially reduced top-left */
|
|
/* > block. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] B11E */
|
|
/* > \verbatim */
|
|
/* > B11E is DOUBLE PRECISION array, dimension (Q-1) */
|
|
/* > When ZBBCSD converges, B11E contains zeros. If ZBBCSD fails */
|
|
/* > to converge, then B11E contains the superdiagonal of the */
|
|
/* > partially reduced top-left block. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] B12D */
|
|
/* > \verbatim */
|
|
/* > B12D is DOUBLE PRECISION array, dimension (Q) */
|
|
/* > When ZBBCSD converges, B12D contains the negative sines of */
|
|
/* > THETA(1), ..., THETA(Q). If ZBBCSD fails to converge, then */
|
|
/* > B12D contains the diagonal of the partially reduced top-right */
|
|
/* > block. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] B12E */
|
|
/* > \verbatim */
|
|
/* > B12E is DOUBLE PRECISION array, dimension (Q-1) */
|
|
/* > When ZBBCSD converges, B12E contains zeros. If ZBBCSD fails */
|
|
/* > to converge, then B12E contains the subdiagonal of the */
|
|
/* > partially reduced top-right block. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] B21D */
|
|
/* > \verbatim */
|
|
/* > B21D is DOUBLE PRECISION array, dimension (Q) */
|
|
/* > When ZBBCSD converges, B21D contains the negative sines of */
|
|
/* > THETA(1), ..., THETA(Q). If ZBBCSD fails to converge, then */
|
|
/* > B21D contains the diagonal of the partially reduced bottom-left */
|
|
/* > block. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] B21E */
|
|
/* > \verbatim */
|
|
/* > B21E is DOUBLE PRECISION array, dimension (Q-1) */
|
|
/* > When ZBBCSD converges, B21E contains zeros. If ZBBCSD fails */
|
|
/* > to converge, then B21E contains the subdiagonal of the */
|
|
/* > partially reduced bottom-left block. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] B22D */
|
|
/* > \verbatim */
|
|
/* > B22D is DOUBLE PRECISION array, dimension (Q) */
|
|
/* > When ZBBCSD converges, B22D contains the negative sines of */
|
|
/* > THETA(1), ..., THETA(Q). If ZBBCSD fails to converge, then */
|
|
/* > B22D contains the diagonal of the partially reduced bottom-right */
|
|
/* > block. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] B22E */
|
|
/* > \verbatim */
|
|
/* > B22E is DOUBLE PRECISION array, dimension (Q-1) */
|
|
/* > When ZBBCSD converges, B22E contains zeros. If ZBBCSD fails */
|
|
/* > to converge, then B22E contains the subdiagonal of the */
|
|
/* > partially reduced bottom-right block. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */
|
|
/* > On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LRWORK */
|
|
/* > \verbatim */
|
|
/* > LRWORK is INTEGER */
|
|
/* > The dimension of the array RWORK. LRWORK >= MAX(1,8*Q). */
|
|
/* > */
|
|
/* > If LRWORK = -1, then a workspace query is assumed; the */
|
|
/* > routine only calculates the optimal size of the RWORK array, */
|
|
/* > returns this value as the first entry of the work array, and */
|
|
/* > no error message related to LRWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: if ZBBCSD did not converge, INFO specifies the number */
|
|
/* > of nonzero entries in PHI, and B11D, B11E, etc., */
|
|
/* > contain the partially reduced matrix. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Internal Parameters: */
|
|
/* ========================= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > TOLMUL DOUBLE PRECISION, default = MAX(10,MIN(100,EPS**(-1/8))) */
|
|
/* > TOLMUL controls the convergence criterion of the QR loop. */
|
|
/* > Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they */
|
|
/* > are within TOLMUL*EPS of either bound. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. */
|
|
/* > Algorithms, 50(1):33-65, 2009. */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \date June 2016 */
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/* > \ingroup complex16OTHERcomputational */
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/* ===================================================================== */
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/* Subroutine */ void zbbcsd_(char *jobu1, char *jobu2, char *jobv1t, char *
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jobv2t, char *trans, integer *m, integer *p, integer *q, doublereal *
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theta, doublereal *phi, doublecomplex *u1, integer *ldu1,
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doublecomplex *u2, integer *ldu2, doublecomplex *v1t, integer *ldv1t,
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doublecomplex *v2t, integer *ldv2t, doublereal *b11d, doublereal *
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b11e, doublereal *b12d, doublereal *b12e, doublereal *b21d,
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doublereal *b21e, doublereal *b22d, doublereal *b22e, doublereal *
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rwork, integer *lrwork, integer *info)
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{
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/* System generated locals */
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integer u1_dim1, u1_offset, u2_dim1, u2_offset, v1t_dim1, v1t_offset,
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v2t_dim1, v2t_offset, i__1, i__2;
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doublereal d__1, d__2, d__3, d__4;
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/* Local variables */
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integer imin, mini, imax, iter;
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doublereal unfl, temp;
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logical colmajor;
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doublereal thetamin, thetamax;
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logical restart11, restart12, restart21, restart22;
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extern /* Subroutine */ void dlas2_(doublereal *, doublereal *, doublereal
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*, doublereal *, doublereal *);
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integer iu1cs, iu2cs, iu1sn, iu2sn, i__, j;
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doublereal r__;
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extern logical lsame_(char *, char *);
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extern /* Subroutine */ void zscal_(integer *, doublecomplex *,
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doublecomplex *, integer *);
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integer maxit;
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doublereal dummy;
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extern /* Subroutine */ void zlasr_(char *, char *, char *, integer *,
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integer *, doublereal *, doublereal *, doublecomplex *, integer *), zswap_(integer *, doublecomplex *,
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integer *, doublecomplex *, integer *);
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doublereal x1, x2, y1, y2;
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integer lrworkmin, iv1tcs, iv2tcs;
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logical wantu1, wantu2;
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integer lrworkopt, iv1tsn, iv2tsn;
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extern doublereal dlamch_(char *);
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doublereal mu, nu, sigma11, sigma21;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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doublereal thresh, tolmul;
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extern /* Subroutine */ void mecago_();
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logical lquery;
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doublereal b11bulge;
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logical wantv1t, wantv2t;
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doublereal b12bulge, b21bulge, b22bulge, eps, tol;
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extern /* Subroutine */ void dlartgp_(doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *), dlartgs_(doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *);
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/* -- LAPACK computational routine (version 3.7.1) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* June 2016 */
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/* =================================================================== */
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/* Test input arguments */
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/* Parameter adjustments */
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--theta;
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--phi;
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u1_dim1 = *ldu1;
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u1_offset = 1 + u1_dim1 * 1;
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u1 -= u1_offset;
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u2_dim1 = *ldu2;
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u2_offset = 1 + u2_dim1 * 1;
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u2 -= u2_offset;
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v1t_dim1 = *ldv1t;
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v1t_offset = 1 + v1t_dim1 * 1;
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v1t -= v1t_offset;
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v2t_dim1 = *ldv2t;
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v2t_offset = 1 + v2t_dim1 * 1;
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v2t -= v2t_offset;
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--b11d;
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--b11e;
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--b12d;
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--b12e;
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--b21d;
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--b21e;
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--b22d;
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--b22e;
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--rwork;
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/* Function Body */
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*info = 0;
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lquery = *lrwork == -1;
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wantu1 = lsame_(jobu1, "Y");
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wantu2 = lsame_(jobu2, "Y");
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wantv1t = lsame_(jobv1t, "Y");
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wantv2t = lsame_(jobv2t, "Y");
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colmajor = ! lsame_(trans, "T");
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if (*m < 0) {
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*info = -6;
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} else if (*p < 0 || *p > *m) {
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*info = -7;
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} else if (*q < 0 || *q > *m) {
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*info = -8;
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} else if (*q > *p || *q > *m - *p || *q > *m - *q) {
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*info = -8;
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} else if (wantu1 && *ldu1 < *p) {
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*info = -12;
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} else if (wantu2 && *ldu2 < *m - *p) {
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*info = -14;
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} else if (wantv1t && *ldv1t < *q) {
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*info = -16;
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} else if (wantv2t && *ldv2t < *m - *q) {
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*info = -18;
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}
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/* Quick return if Q = 0 */
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if (*info == 0 && *q == 0) {
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lrworkmin = 1;
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rwork[1] = (doublereal) lrworkmin;
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return;
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}
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/* Compute workspace */
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if (*info == 0) {
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iu1cs = 1;
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iu1sn = iu1cs + *q;
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iu2cs = iu1sn + *q;
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iu2sn = iu2cs + *q;
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iv1tcs = iu2sn + *q;
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iv1tsn = iv1tcs + *q;
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iv2tcs = iv1tsn + *q;
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iv2tsn = iv2tcs + *q;
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lrworkopt = iv2tsn + *q - 1;
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lrworkmin = lrworkopt;
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rwork[1] = (doublereal) lrworkopt;
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if (*lrwork < lrworkmin && ! lquery) {
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*info = -28;
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}
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("ZBBCSD", &i__1, (ftnlen)6);
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return;
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} else if (lquery) {
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return;
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}
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/* Get machine constants */
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eps = dlamch_("Epsilon");
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unfl = dlamch_("Safe minimum");
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/* Computing MAX */
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/* Computing MIN */
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d__3 = 100., d__4 = pow_dd(&eps, &c_b11);
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d__1 = 10., d__2 = f2cmin(d__3,d__4);
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tolmul = f2cmax(d__1,d__2);
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tol = tolmul * eps;
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/* Computing MAX */
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d__1 = tol, d__2 = *q * 6 * *q * unfl;
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thresh = f2cmax(d__1,d__2);
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/* Test for negligible sines or cosines */
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i__1 = *q;
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for (i__ = 1; i__ <= i__1; ++i__) {
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if (theta[i__] < thresh) {
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theta[i__] = 0.;
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} else if (theta[i__] > 1.57079632679489662 - thresh) {
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theta[i__] = 1.57079632679489662;
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}
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}
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i__1 = *q - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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if (phi[i__] < thresh) {
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phi[i__] = 0.;
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} else if (phi[i__] > 1.57079632679489662 - thresh) {
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phi[i__] = 1.57079632679489662;
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}
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}
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/* Initial deflation */
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imax = *q;
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while(imax > 1) {
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if (phi[imax - 1] != 0.) {
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myexit_();
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}
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--imax;
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}
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imin = imax - 1;
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if (imin > 1) {
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while(phi[imin - 1] != 0.) {
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--imin;
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if (imin <= 1) {
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myexit_();
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}
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}
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}
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/* Initialize iteration counter */
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maxit = *q * 6 * *q;
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iter = 0;
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/* Begin main iteration loop */
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while(imax > 1) {
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/* Compute the matrix entries */
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b11d[imin] = cos(theta[imin]);
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b21d[imin] = -sin(theta[imin]);
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i__1 = imax - 1;
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for (i__ = imin; i__ <= i__1; ++i__) {
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b11e[i__] = -sin(theta[i__]) * sin(phi[i__]);
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b11d[i__ + 1] = cos(theta[i__ + 1]) * cos(phi[i__]);
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b12d[i__] = sin(theta[i__]) * cos(phi[i__]);
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b12e[i__] = cos(theta[i__ + 1]) * sin(phi[i__]);
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b21e[i__] = -cos(theta[i__]) * sin(phi[i__]);
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b21d[i__ + 1] = -sin(theta[i__ + 1]) * cos(phi[i__]);
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b22d[i__] = cos(theta[i__]) * cos(phi[i__]);
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b22e[i__] = -sin(theta[i__ + 1]) * sin(phi[i__]);
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}
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b12d[imax] = sin(theta[imax]);
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b22d[imax] = cos(theta[imax]);
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/* Abort if not converging; otherwise, increment ITER */
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if (iter > maxit) {
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*info = 0;
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i__1 = *q;
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for (i__ = 1; i__ <= i__1; ++i__) {
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if (phi[i__] != 0.) {
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++(*info);
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}
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}
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return;
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}
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iter = iter + imax - imin;
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/* Compute shifts */
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thetamax = theta[imin];
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thetamin = theta[imin];
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i__1 = imax;
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for (i__ = imin + 1; i__ <= i__1; ++i__) {
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if (theta[i__] > thetamax) {
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thetamax = theta[i__];
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}
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if (theta[i__] < thetamin) {
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thetamin = theta[i__];
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}
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}
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if (thetamax > 1.57079632679489662 - thresh) {
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/* Zero on diagonals of B11 and B22; induce deflation with a */
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/* zero shift */
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mu = 0.;
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nu = 1.;
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} else if (thetamin < thresh) {
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/* Zero on diagonals of B12 and B22; induce deflation with a */
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/* zero shift */
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mu = 1.;
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nu = 0.;
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} else {
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/* Compute shifts for B11 and B21 and use the lesser */
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dlas2_(&b11d[imax - 1], &b11e[imax - 1], &b11d[imax], &sigma11, &
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dummy);
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dlas2_(&b21d[imax - 1], &b21e[imax - 1], &b21d[imax], &sigma21, &
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dummy);
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if (sigma11 <= sigma21) {
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mu = sigma11;
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/* Computing 2nd power */
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d__1 = mu;
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nu = sqrt(1. - d__1 * d__1);
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if (mu < thresh) {
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mu = 0.;
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nu = 1.;
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}
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} else {
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nu = sigma21;
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/* Computing 2nd power */
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d__1 = nu;
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mu = sqrt(1.f - d__1 * d__1);
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if (nu < thresh) {
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mu = 1.;
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nu = 0.;
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}
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}
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}
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/* Rotate to produce bulges in B11 and B21 */
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if (mu <= nu) {
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dlartgs_(&b11d[imin], &b11e[imin], &mu, &rwork[iv1tcs + imin - 1],
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&rwork[iv1tsn + imin - 1]);
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} else {
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dlartgs_(&b21d[imin], &b21e[imin], &nu, &rwork[iv1tcs + imin - 1],
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&rwork[iv1tsn + imin - 1]);
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}
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temp = rwork[iv1tcs + imin - 1] * b11d[imin] + rwork[iv1tsn + imin -
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1] * b11e[imin];
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b11e[imin] = rwork[iv1tcs + imin - 1] * b11e[imin] - rwork[iv1tsn +
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imin - 1] * b11d[imin];
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b11d[imin] = temp;
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b11bulge = rwork[iv1tsn + imin - 1] * b11d[imin + 1];
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b11d[imin + 1] = rwork[iv1tcs + imin - 1] * b11d[imin + 1];
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temp = rwork[iv1tcs + imin - 1] * b21d[imin] + rwork[iv1tsn + imin -
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1] * b21e[imin];
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b21e[imin] = rwork[iv1tcs + imin - 1] * b21e[imin] - rwork[iv1tsn +
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imin - 1] * b21d[imin];
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b21d[imin] = temp;
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b21bulge = rwork[iv1tsn + imin - 1] * b21d[imin + 1];
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b21d[imin + 1] = rwork[iv1tcs + imin - 1] * b21d[imin + 1];
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/* Compute THETA(IMIN) */
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/* Computing 2nd power */
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d__1 = b21d[imin];
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/* Computing 2nd power */
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d__2 = b21bulge;
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/* Computing 2nd power */
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d__3 = b11d[imin];
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/* Computing 2nd power */
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d__4 = b11bulge;
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theta[imin] = atan2(sqrt(d__1 * d__1 + d__2 * d__2), sqrt(d__3 * d__3
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+ d__4 * d__4));
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/* Chase the bulges in B11(IMIN+1,IMIN) and B21(IMIN+1,IMIN) */
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/* Computing 2nd power */
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d__1 = b11d[imin];
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/* Computing 2nd power */
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d__2 = b11bulge;
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/* Computing 2nd power */
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d__3 = thresh;
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if (d__1 * d__1 + d__2 * d__2 > d__3 * d__3) {
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dlartgp_(&b11bulge, &b11d[imin], &rwork[iu1sn + imin - 1], &rwork[
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iu1cs + imin - 1], &r__);
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} else if (mu <= nu) {
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dlartgs_(&b11e[imin], &b11d[imin + 1], &mu, &rwork[iu1cs + imin -
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1], &rwork[iu1sn + imin - 1]);
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} else {
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dlartgs_(&b12d[imin], &b12e[imin], &nu, &rwork[iu1cs + imin - 1],
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&rwork[iu1sn + imin - 1]);
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}
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/* Computing 2nd power */
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d__1 = b21d[imin];
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/* Computing 2nd power */
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d__2 = b21bulge;
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/* Computing 2nd power */
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d__3 = thresh;
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if (d__1 * d__1 + d__2 * d__2 > d__3 * d__3) {
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dlartgp_(&b21bulge, &b21d[imin], &rwork[iu2sn + imin - 1], &rwork[
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iu2cs + imin - 1], &r__);
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} else if (nu < mu) {
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dlartgs_(&b21e[imin], &b21d[imin + 1], &nu, &rwork[iu2cs + imin -
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1], &rwork[iu2sn + imin - 1]);
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} else {
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dlartgs_(&b22d[imin], &b22e[imin], &mu, &rwork[iu2cs + imin - 1],
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&rwork[iu2sn + imin - 1]);
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}
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rwork[iu2cs + imin - 1] = -rwork[iu2cs + imin - 1];
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rwork[iu2sn + imin - 1] = -rwork[iu2sn + imin - 1];
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temp = rwork[iu1cs + imin - 1] * b11e[imin] + rwork[iu1sn + imin - 1]
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* b11d[imin + 1];
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b11d[imin + 1] = rwork[iu1cs + imin - 1] * b11d[imin + 1] - rwork[
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iu1sn + imin - 1] * b11e[imin];
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b11e[imin] = temp;
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if (imax > imin + 1) {
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b11bulge = rwork[iu1sn + imin - 1] * b11e[imin + 1];
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b11e[imin + 1] = rwork[iu1cs + imin - 1] * b11e[imin + 1];
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}
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temp = rwork[iu1cs + imin - 1] * b12d[imin] + rwork[iu1sn + imin - 1]
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* b12e[imin];
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b12e[imin] = rwork[iu1cs + imin - 1] * b12e[imin] - rwork[iu1sn +
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imin - 1] * b12d[imin];
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b12d[imin] = temp;
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b12bulge = rwork[iu1sn + imin - 1] * b12d[imin + 1];
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b12d[imin + 1] = rwork[iu1cs + imin - 1] * b12d[imin + 1];
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temp = rwork[iu2cs + imin - 1] * b21e[imin] + rwork[iu2sn + imin - 1]
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* b21d[imin + 1];
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b21d[imin + 1] = rwork[iu2cs + imin - 1] * b21d[imin + 1] - rwork[
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iu2sn + imin - 1] * b21e[imin];
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b21e[imin] = temp;
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if (imax > imin + 1) {
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b21bulge = rwork[iu2sn + imin - 1] * b21e[imin + 1];
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b21e[imin + 1] = rwork[iu2cs + imin - 1] * b21e[imin + 1];
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}
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temp = rwork[iu2cs + imin - 1] * b22d[imin] + rwork[iu2sn + imin - 1]
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* b22e[imin];
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b22e[imin] = rwork[iu2cs + imin - 1] * b22e[imin] - rwork[iu2sn +
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imin - 1] * b22d[imin];
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b22d[imin] = temp;
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b22bulge = rwork[iu2sn + imin - 1] * b22d[imin + 1];
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b22d[imin + 1] = rwork[iu2cs + imin - 1] * b22d[imin + 1];
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/* Inner loop: chase bulges from B11(IMIN,IMIN+2), */
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/* B12(IMIN,IMIN+1), B21(IMIN,IMIN+2), and B22(IMIN,IMIN+1) to */
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/* bottom-right */
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i__1 = imax - 1;
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for (i__ = imin + 1; i__ <= i__1; ++i__) {
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/* Compute PHI(I-1) */
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x1 = sin(theta[i__ - 1]) * b11e[i__ - 1] + cos(theta[i__ - 1]) *
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b21e[i__ - 1];
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x2 = sin(theta[i__ - 1]) * b11bulge + cos(theta[i__ - 1]) *
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b21bulge;
|
|
y1 = sin(theta[i__ - 1]) * b12d[i__ - 1] + cos(theta[i__ - 1]) *
|
|
b22d[i__ - 1];
|
|
y2 = sin(theta[i__ - 1]) * b12bulge + cos(theta[i__ - 1]) *
|
|
b22bulge;
|
|
|
|
/* Computing 2nd power */
|
|
d__1 = x1;
|
|
/* Computing 2nd power */
|
|
d__2 = x2;
|
|
/* Computing 2nd power */
|
|
d__3 = y1;
|
|
/* Computing 2nd power */
|
|
d__4 = y2;
|
|
phi[i__ - 1] = atan2(sqrt(d__1 * d__1 + d__2 * d__2), sqrt(d__3 *
|
|
d__3 + d__4 * d__4));
|
|
|
|
/* Determine if there are bulges to chase or if a new direct */
|
|
/* summand has been reached */
|
|
|
|
/* Computing 2nd power */
|
|
d__1 = b11e[i__ - 1];
|
|
/* Computing 2nd power */
|
|
d__2 = b11bulge;
|
|
/* Computing 2nd power */
|
|
d__3 = thresh;
|
|
restart11 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
|
|
/* Computing 2nd power */
|
|
d__1 = b21e[i__ - 1];
|
|
/* Computing 2nd power */
|
|
d__2 = b21bulge;
|
|
/* Computing 2nd power */
|
|
d__3 = thresh;
|
|
restart21 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
|
|
/* Computing 2nd power */
|
|
d__1 = b12d[i__ - 1];
|
|
/* Computing 2nd power */
|
|
d__2 = b12bulge;
|
|
/* Computing 2nd power */
|
|
d__3 = thresh;
|
|
restart12 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
|
|
/* Computing 2nd power */
|
|
d__1 = b22d[i__ - 1];
|
|
/* Computing 2nd power */
|
|
d__2 = b22bulge;
|
|
/* Computing 2nd power */
|
|
d__3 = thresh;
|
|
restart22 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
|
|
|
|
/* If possible, chase bulges from B11(I-1,I+1), B12(I-1,I), */
|
|
/* B21(I-1,I+1), and B22(I-1,I). If necessary, restart bulge- */
|
|
/* chasing by applying the original shift again. */
|
|
|
|
if (! restart11 && ! restart21) {
|
|
dlartgp_(&x2, &x1, &rwork[iv1tsn + i__ - 1], &rwork[iv1tcs +
|
|
i__ - 1], &r__);
|
|
} else if (! restart11 && restart21) {
|
|
dlartgp_(&b11bulge, &b11e[i__ - 1], &rwork[iv1tsn + i__ - 1],
|
|
&rwork[iv1tcs + i__ - 1], &r__);
|
|
} else if (restart11 && ! restart21) {
|
|
dlartgp_(&b21bulge, &b21e[i__ - 1], &rwork[iv1tsn + i__ - 1],
|
|
&rwork[iv1tcs + i__ - 1], &r__);
|
|
} else if (mu <= nu) {
|
|
dlartgs_(&b11d[i__], &b11e[i__], &mu, &rwork[iv1tcs + i__ - 1]
|
|
, &rwork[iv1tsn + i__ - 1]);
|
|
} else {
|
|
dlartgs_(&b21d[i__], &b21e[i__], &nu, &rwork[iv1tcs + i__ - 1]
|
|
, &rwork[iv1tsn + i__ - 1]);
|
|
}
|
|
rwork[iv1tcs + i__ - 1] = -rwork[iv1tcs + i__ - 1];
|
|
rwork[iv1tsn + i__ - 1] = -rwork[iv1tsn + i__ - 1];
|
|
if (! restart12 && ! restart22) {
|
|
dlartgp_(&y2, &y1, &rwork[iv2tsn + i__ - 2], &rwork[iv2tcs +
|
|
i__ - 2], &r__);
|
|
} else if (! restart12 && restart22) {
|
|
dlartgp_(&b12bulge, &b12d[i__ - 1], &rwork[iv2tsn + i__ - 2],
|
|
&rwork[iv2tcs + i__ - 2], &r__);
|
|
} else if (restart12 && ! restart22) {
|
|
dlartgp_(&b22bulge, &b22d[i__ - 1], &rwork[iv2tsn + i__ - 2],
|
|
&rwork[iv2tcs + i__ - 2], &r__);
|
|
} else if (nu < mu) {
|
|
dlartgs_(&b12e[i__ - 1], &b12d[i__], &nu, &rwork[iv2tcs + i__
|
|
- 2], &rwork[iv2tsn + i__ - 2]);
|
|
} else {
|
|
dlartgs_(&b22e[i__ - 1], &b22d[i__], &mu, &rwork[iv2tcs + i__
|
|
- 2], &rwork[iv2tsn + i__ - 2]);
|
|
}
|
|
|
|
temp = rwork[iv1tcs + i__ - 1] * b11d[i__] + rwork[iv1tsn + i__ -
|
|
1] * b11e[i__];
|
|
b11e[i__] = rwork[iv1tcs + i__ - 1] * b11e[i__] - rwork[iv1tsn +
|
|
i__ - 1] * b11d[i__];
|
|
b11d[i__] = temp;
|
|
b11bulge = rwork[iv1tsn + i__ - 1] * b11d[i__ + 1];
|
|
b11d[i__ + 1] = rwork[iv1tcs + i__ - 1] * b11d[i__ + 1];
|
|
temp = rwork[iv1tcs + i__ - 1] * b21d[i__] + rwork[iv1tsn + i__ -
|
|
1] * b21e[i__];
|
|
b21e[i__] = rwork[iv1tcs + i__ - 1] * b21e[i__] - rwork[iv1tsn +
|
|
i__ - 1] * b21d[i__];
|
|
b21d[i__] = temp;
|
|
b21bulge = rwork[iv1tsn + i__ - 1] * b21d[i__ + 1];
|
|
b21d[i__ + 1] = rwork[iv1tcs + i__ - 1] * b21d[i__ + 1];
|
|
temp = rwork[iv2tcs + i__ - 2] * b12e[i__ - 1] + rwork[iv2tsn +
|
|
i__ - 2] * b12d[i__];
|
|
b12d[i__] = rwork[iv2tcs + i__ - 2] * b12d[i__] - rwork[iv2tsn +
|
|
i__ - 2] * b12e[i__ - 1];
|
|
b12e[i__ - 1] = temp;
|
|
b12bulge = rwork[iv2tsn + i__ - 2] * b12e[i__];
|
|
b12e[i__] = rwork[iv2tcs + i__ - 2] * b12e[i__];
|
|
temp = rwork[iv2tcs + i__ - 2] * b22e[i__ - 1] + rwork[iv2tsn +
|
|
i__ - 2] * b22d[i__];
|
|
b22d[i__] = rwork[iv2tcs + i__ - 2] * b22d[i__] - rwork[iv2tsn +
|
|
i__ - 2] * b22e[i__ - 1];
|
|
b22e[i__ - 1] = temp;
|
|
b22bulge = rwork[iv2tsn + i__ - 2] * b22e[i__];
|
|
b22e[i__] = rwork[iv2tcs + i__ - 2] * b22e[i__];
|
|
|
|
/* Compute THETA(I) */
|
|
|
|
x1 = cos(phi[i__ - 1]) * b11d[i__] + sin(phi[i__ - 1]) * b12e[i__
|
|
- 1];
|
|
x2 = cos(phi[i__ - 1]) * b11bulge + sin(phi[i__ - 1]) * b12bulge;
|
|
y1 = cos(phi[i__ - 1]) * b21d[i__] + sin(phi[i__ - 1]) * b22e[i__
|
|
- 1];
|
|
y2 = cos(phi[i__ - 1]) * b21bulge + sin(phi[i__ - 1]) * b22bulge;
|
|
|
|
/* Computing 2nd power */
|
|
d__1 = y1;
|
|
/* Computing 2nd power */
|
|
d__2 = y2;
|
|
/* Computing 2nd power */
|
|
d__3 = x1;
|
|
/* Computing 2nd power */
|
|
d__4 = x2;
|
|
theta[i__] = atan2(sqrt(d__1 * d__1 + d__2 * d__2), sqrt(d__3 *
|
|
d__3 + d__4 * d__4));
|
|
|
|
/* Determine if there are bulges to chase or if a new direct */
|
|
/* summand has been reached */
|
|
|
|
/* Computing 2nd power */
|
|
d__1 = b11d[i__];
|
|
/* Computing 2nd power */
|
|
d__2 = b11bulge;
|
|
/* Computing 2nd power */
|
|
d__3 = thresh;
|
|
restart11 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
|
|
/* Computing 2nd power */
|
|
d__1 = b12e[i__ - 1];
|
|
/* Computing 2nd power */
|
|
d__2 = b12bulge;
|
|
/* Computing 2nd power */
|
|
d__3 = thresh;
|
|
restart12 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
|
|
/* Computing 2nd power */
|
|
d__1 = b21d[i__];
|
|
/* Computing 2nd power */
|
|
d__2 = b21bulge;
|
|
/* Computing 2nd power */
|
|
d__3 = thresh;
|
|
restart21 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
|
|
/* Computing 2nd power */
|
|
d__1 = b22e[i__ - 1];
|
|
/* Computing 2nd power */
|
|
d__2 = b22bulge;
|
|
/* Computing 2nd power */
|
|
d__3 = thresh;
|
|
restart22 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
|
|
|
|
/* If possible, chase bulges from B11(I+1,I), B12(I+1,I-1), */
|
|
/* B21(I+1,I), and B22(I+1,I-1). If necessary, restart bulge- */
|
|
/* chasing by applying the original shift again. */
|
|
|
|
if (! restart11 && ! restart12) {
|
|
dlartgp_(&x2, &x1, &rwork[iu1sn + i__ - 1], &rwork[iu1cs +
|
|
i__ - 1], &r__);
|
|
} else if (! restart11 && restart12) {
|
|
dlartgp_(&b11bulge, &b11d[i__], &rwork[iu1sn + i__ - 1], &
|
|
rwork[iu1cs + i__ - 1], &r__);
|
|
} else if (restart11 && ! restart12) {
|
|
dlartgp_(&b12bulge, &b12e[i__ - 1], &rwork[iu1sn + i__ - 1], &
|
|
rwork[iu1cs + i__ - 1], &r__);
|
|
} else if (mu <= nu) {
|
|
dlartgs_(&b11e[i__], &b11d[i__ + 1], &mu, &rwork[iu1cs + i__
|
|
- 1], &rwork[iu1sn + i__ - 1]);
|
|
} else {
|
|
dlartgs_(&b12d[i__], &b12e[i__], &nu, &rwork[iu1cs + i__ - 1],
|
|
&rwork[iu1sn + i__ - 1]);
|
|
}
|
|
if (! restart21 && ! restart22) {
|
|
dlartgp_(&y2, &y1, &rwork[iu2sn + i__ - 1], &rwork[iu2cs +
|
|
i__ - 1], &r__);
|
|
} else if (! restart21 && restart22) {
|
|
dlartgp_(&b21bulge, &b21d[i__], &rwork[iu2sn + i__ - 1], &
|
|
rwork[iu2cs + i__ - 1], &r__);
|
|
} else if (restart21 && ! restart22) {
|
|
dlartgp_(&b22bulge, &b22e[i__ - 1], &rwork[iu2sn + i__ - 1], &
|
|
rwork[iu2cs + i__ - 1], &r__);
|
|
} else if (nu < mu) {
|
|
dlartgs_(&b21e[i__], &b21e[i__ + 1], &nu, &rwork[iu2cs + i__
|
|
- 1], &rwork[iu2sn + i__ - 1]);
|
|
} else {
|
|
dlartgs_(&b22d[i__], &b22e[i__], &mu, &rwork[iu2cs + i__ - 1],
|
|
&rwork[iu2sn + i__ - 1]);
|
|
}
|
|
rwork[iu2cs + i__ - 1] = -rwork[iu2cs + i__ - 1];
|
|
rwork[iu2sn + i__ - 1] = -rwork[iu2sn + i__ - 1];
|
|
|
|
temp = rwork[iu1cs + i__ - 1] * b11e[i__] + rwork[iu1sn + i__ - 1]
|
|
* b11d[i__ + 1];
|
|
b11d[i__ + 1] = rwork[iu1cs + i__ - 1] * b11d[i__ + 1] - rwork[
|
|
iu1sn + i__ - 1] * b11e[i__];
|
|
b11e[i__] = temp;
|
|
if (i__ < imax - 1) {
|
|
b11bulge = rwork[iu1sn + i__ - 1] * b11e[i__ + 1];
|
|
b11e[i__ + 1] = rwork[iu1cs + i__ - 1] * b11e[i__ + 1];
|
|
}
|
|
temp = rwork[iu2cs + i__ - 1] * b21e[i__] + rwork[iu2sn + i__ - 1]
|
|
* b21d[i__ + 1];
|
|
b21d[i__ + 1] = rwork[iu2cs + i__ - 1] * b21d[i__ + 1] - rwork[
|
|
iu2sn + i__ - 1] * b21e[i__];
|
|
b21e[i__] = temp;
|
|
if (i__ < imax - 1) {
|
|
b21bulge = rwork[iu2sn + i__ - 1] * b21e[i__ + 1];
|
|
b21e[i__ + 1] = rwork[iu2cs + i__ - 1] * b21e[i__ + 1];
|
|
}
|
|
temp = rwork[iu1cs + i__ - 1] * b12d[i__] + rwork[iu1sn + i__ - 1]
|
|
* b12e[i__];
|
|
b12e[i__] = rwork[iu1cs + i__ - 1] * b12e[i__] - rwork[iu1sn +
|
|
i__ - 1] * b12d[i__];
|
|
b12d[i__] = temp;
|
|
b12bulge = rwork[iu1sn + i__ - 1] * b12d[i__ + 1];
|
|
b12d[i__ + 1] = rwork[iu1cs + i__ - 1] * b12d[i__ + 1];
|
|
temp = rwork[iu2cs + i__ - 1] * b22d[i__] + rwork[iu2sn + i__ - 1]
|
|
* b22e[i__];
|
|
b22e[i__] = rwork[iu2cs + i__ - 1] * b22e[i__] - rwork[iu2sn +
|
|
i__ - 1] * b22d[i__];
|
|
b22d[i__] = temp;
|
|
b22bulge = rwork[iu2sn + i__ - 1] * b22d[i__ + 1];
|
|
b22d[i__ + 1] = rwork[iu2cs + i__ - 1] * b22d[i__ + 1];
|
|
|
|
}
|
|
|
|
/* Compute PHI(IMAX-1) */
|
|
|
|
x1 = sin(theta[imax - 1]) * b11e[imax - 1] + cos(theta[imax - 1]) *
|
|
b21e[imax - 1];
|
|
y1 = sin(theta[imax - 1]) * b12d[imax - 1] + cos(theta[imax - 1]) *
|
|
b22d[imax - 1];
|
|
y2 = sin(theta[imax - 1]) * b12bulge + cos(theta[imax - 1]) *
|
|
b22bulge;
|
|
|
|
/* Computing 2nd power */
|
|
d__1 = y1;
|
|
/* Computing 2nd power */
|
|
d__2 = y2;
|
|
phi[imax - 1] = atan2((abs(x1)), sqrt(d__1 * d__1 + d__2 * d__2));
|
|
|
|
/* Chase bulges from B12(IMAX-1,IMAX) and B22(IMAX-1,IMAX) */
|
|
|
|
/* Computing 2nd power */
|
|
d__1 = b12d[imax - 1];
|
|
/* Computing 2nd power */
|
|
d__2 = b12bulge;
|
|
/* Computing 2nd power */
|
|
d__3 = thresh;
|
|
restart12 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
|
|
/* Computing 2nd power */
|
|
d__1 = b22d[imax - 1];
|
|
/* Computing 2nd power */
|
|
d__2 = b22bulge;
|
|
/* Computing 2nd power */
|
|
d__3 = thresh;
|
|
restart22 = d__1 * d__1 + d__2 * d__2 <= d__3 * d__3;
|
|
|
|
if (! restart12 && ! restart22) {
|
|
dlartgp_(&y2, &y1, &rwork[iv2tsn + imax - 2], &rwork[iv2tcs +
|
|
imax - 2], &r__);
|
|
} else if (! restart12 && restart22) {
|
|
dlartgp_(&b12bulge, &b12d[imax - 1], &rwork[iv2tsn + imax - 2], &
|
|
rwork[iv2tcs + imax - 2], &r__);
|
|
} else if (restart12 && ! restart22) {
|
|
dlartgp_(&b22bulge, &b22d[imax - 1], &rwork[iv2tsn + imax - 2], &
|
|
rwork[iv2tcs + imax - 2], &r__);
|
|
} else if (nu < mu) {
|
|
dlartgs_(&b12e[imax - 1], &b12d[imax], &nu, &rwork[iv2tcs + imax
|
|
- 2], &rwork[iv2tsn + imax - 2]);
|
|
} else {
|
|
dlartgs_(&b22e[imax - 1], &b22d[imax], &mu, &rwork[iv2tcs + imax
|
|
- 2], &rwork[iv2tsn + imax - 2]);
|
|
}
|
|
|
|
temp = rwork[iv2tcs + imax - 2] * b12e[imax - 1] + rwork[iv2tsn +
|
|
imax - 2] * b12d[imax];
|
|
b12d[imax] = rwork[iv2tcs + imax - 2] * b12d[imax] - rwork[iv2tsn +
|
|
imax - 2] * b12e[imax - 1];
|
|
b12e[imax - 1] = temp;
|
|
temp = rwork[iv2tcs + imax - 2] * b22e[imax - 1] + rwork[iv2tsn +
|
|
imax - 2] * b22d[imax];
|
|
b22d[imax] = rwork[iv2tcs + imax - 2] * b22d[imax] - rwork[iv2tsn +
|
|
imax - 2] * b22e[imax - 1];
|
|
b22e[imax - 1] = temp;
|
|
|
|
/* Update singular vectors */
|
|
|
|
if (wantu1) {
|
|
if (colmajor) {
|
|
i__1 = imax - imin + 1;
|
|
zlasr_("R", "V", "F", p, &i__1, &rwork[iu1cs + imin - 1], &
|
|
rwork[iu1sn + imin - 1], &u1[imin * u1_dim1 + 1],
|
|
ldu1);
|
|
} else {
|
|
i__1 = imax - imin + 1;
|
|
zlasr_("L", "V", "F", &i__1, p, &rwork[iu1cs + imin - 1], &
|
|
rwork[iu1sn + imin - 1], &u1[imin + u1_dim1], ldu1);
|
|
}
|
|
}
|
|
if (wantu2) {
|
|
if (colmajor) {
|
|
i__1 = *m - *p;
|
|
i__2 = imax - imin + 1;
|
|
zlasr_("R", "V", "F", &i__1, &i__2, &rwork[iu2cs + imin - 1],
|
|
&rwork[iu2sn + imin - 1], &u2[imin * u2_dim1 + 1],
|
|
ldu2);
|
|
} else {
|
|
i__1 = imax - imin + 1;
|
|
i__2 = *m - *p;
|
|
zlasr_("L", "V", "F", &i__1, &i__2, &rwork[iu2cs + imin - 1],
|
|
&rwork[iu2sn + imin - 1], &u2[imin + u2_dim1], ldu2);
|
|
}
|
|
}
|
|
if (wantv1t) {
|
|
if (colmajor) {
|
|
i__1 = imax - imin + 1;
|
|
zlasr_("L", "V", "F", &i__1, q, &rwork[iv1tcs + imin - 1], &
|
|
rwork[iv1tsn + imin - 1], &v1t[imin + v1t_dim1],
|
|
ldv1t);
|
|
} else {
|
|
i__1 = imax - imin + 1;
|
|
zlasr_("R", "V", "F", q, &i__1, &rwork[iv1tcs + imin - 1], &
|
|
rwork[iv1tsn + imin - 1], &v1t[imin * v1t_dim1 + 1],
|
|
ldv1t);
|
|
}
|
|
}
|
|
if (wantv2t) {
|
|
if (colmajor) {
|
|
i__1 = imax - imin + 1;
|
|
i__2 = *m - *q;
|
|
zlasr_("L", "V", "F", &i__1, &i__2, &rwork[iv2tcs + imin - 1],
|
|
&rwork[iv2tsn + imin - 1], &v2t[imin + v2t_dim1],
|
|
ldv2t);
|
|
} else {
|
|
i__1 = *m - *q;
|
|
i__2 = imax - imin + 1;
|
|
zlasr_("R", "V", "F", &i__1, &i__2, &rwork[iv2tcs + imin - 1],
|
|
&rwork[iv2tsn + imin - 1], &v2t[imin * v2t_dim1 + 1],
|
|
ldv2t);
|
|
}
|
|
}
|
|
|
|
/* Fix signs on B11(IMAX-1,IMAX) and B21(IMAX-1,IMAX) */
|
|
|
|
if (b11e[imax - 1] + b21e[imax - 1] > 0.) {
|
|
b11d[imax] = -b11d[imax];
|
|
b21d[imax] = -b21d[imax];
|
|
if (wantv1t) {
|
|
if (colmajor) {
|
|
zscal_(q, &c_b1, &v1t[imax + v1t_dim1], ldv1t);
|
|
} else {
|
|
zscal_(q, &c_b1, &v1t[imax * v1t_dim1 + 1], &c__1);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Compute THETA(IMAX) */
|
|
|
|
x1 = cos(phi[imax - 1]) * b11d[imax] + sin(phi[imax - 1]) * b12e[imax
|
|
- 1];
|
|
y1 = cos(phi[imax - 1]) * b21d[imax] + sin(phi[imax - 1]) * b22e[imax
|
|
- 1];
|
|
|
|
theta[imax] = atan2((abs(y1)), (abs(x1)));
|
|
|
|
/* Fix signs on B11(IMAX,IMAX), B12(IMAX,IMAX-1), B21(IMAX,IMAX), */
|
|
/* and B22(IMAX,IMAX-1) */
|
|
|
|
if (b11d[imax] + b12e[imax - 1] < 0.) {
|
|
b12d[imax] = -b12d[imax];
|
|
if (wantu1) {
|
|
if (colmajor) {
|
|
zscal_(p, &c_b1, &u1[imax * u1_dim1 + 1], &c__1);
|
|
} else {
|
|
zscal_(p, &c_b1, &u1[imax + u1_dim1], ldu1);
|
|
}
|
|
}
|
|
}
|
|
if (b21d[imax] + b22e[imax - 1] > 0.) {
|
|
b22d[imax] = -b22d[imax];
|
|
if (wantu2) {
|
|
if (colmajor) {
|
|
i__1 = *m - *p;
|
|
zscal_(&i__1, &c_b1, &u2[imax * u2_dim1 + 1], &c__1);
|
|
} else {
|
|
i__1 = *m - *p;
|
|
zscal_(&i__1, &c_b1, &u2[imax + u2_dim1], ldu2);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Fix signs on B12(IMAX,IMAX) and B22(IMAX,IMAX) */
|
|
|
|
if (b12d[imax] + b22d[imax] < 0.) {
|
|
if (wantv2t) {
|
|
if (colmajor) {
|
|
i__1 = *m - *q;
|
|
zscal_(&i__1, &c_b1, &v2t[imax + v2t_dim1], ldv2t);
|
|
} else {
|
|
i__1 = *m - *q;
|
|
zscal_(&i__1, &c_b1, &v2t[imax * v2t_dim1 + 1], &c__1);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Test for negligible sines or cosines */
|
|
|
|
i__1 = imax;
|
|
for (i__ = imin; i__ <= i__1; ++i__) {
|
|
if (theta[i__] < thresh) {
|
|
theta[i__] = 0.;
|
|
} else if (theta[i__] > 1.57079632679489662 - thresh) {
|
|
theta[i__] = 1.57079632679489662;
|
|
}
|
|
}
|
|
i__1 = imax - 1;
|
|
for (i__ = imin; i__ <= i__1; ++i__) {
|
|
if (phi[i__] < thresh) {
|
|
phi[i__] = 0.;
|
|
} else if (phi[i__] > 1.57079632679489662 - thresh) {
|
|
phi[i__] = 1.57079632679489662;
|
|
}
|
|
}
|
|
|
|
/* Deflate */
|
|
|
|
if (imax > 1) {
|
|
while(phi[imax - 1] == 0.) {
|
|
--imax;
|
|
if (imax <= 1) {
|
|
myexit_();
|
|
}
|
|
}
|
|
}
|
|
if (imin > imax - 1) {
|
|
imin = imax - 1;
|
|
}
|
|
if (imin > 1) {
|
|
while(phi[imin - 1] != 0.) {
|
|
--imin;
|
|
if (imin <= 1) {
|
|
myexit_();
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Repeat main iteration loop */
|
|
|
|
}
|
|
|
|
/* Postprocessing: order THETA from least to greatest */
|
|
|
|
i__1 = *q;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
|
|
mini = i__;
|
|
thetamin = theta[i__];
|
|
i__2 = *q;
|
|
for (j = i__ + 1; j <= i__2; ++j) {
|
|
if (theta[j] < thetamin) {
|
|
mini = j;
|
|
thetamin = theta[j];
|
|
}
|
|
}
|
|
|
|
if (mini != i__) {
|
|
theta[mini] = theta[i__];
|
|
theta[i__] = thetamin;
|
|
if (colmajor) {
|
|
if (wantu1) {
|
|
zswap_(p, &u1[i__ * u1_dim1 + 1], &c__1, &u1[mini *
|
|
u1_dim1 + 1], &c__1);
|
|
}
|
|
if (wantu2) {
|
|
i__2 = *m - *p;
|
|
zswap_(&i__2, &u2[i__ * u2_dim1 + 1], &c__1, &u2[mini *
|
|
u2_dim1 + 1], &c__1);
|
|
}
|
|
if (wantv1t) {
|
|
zswap_(q, &v1t[i__ + v1t_dim1], ldv1t, &v1t[mini +
|
|
v1t_dim1], ldv1t);
|
|
}
|
|
if (wantv2t) {
|
|
i__2 = *m - *q;
|
|
zswap_(&i__2, &v2t[i__ + v2t_dim1], ldv2t, &v2t[mini +
|
|
v2t_dim1], ldv2t);
|
|
}
|
|
} else {
|
|
if (wantu1) {
|
|
zswap_(p, &u1[i__ + u1_dim1], ldu1, &u1[mini + u1_dim1],
|
|
ldu1);
|
|
}
|
|
if (wantu2) {
|
|
i__2 = *m - *p;
|
|
zswap_(&i__2, &u2[i__ + u2_dim1], ldu2, &u2[mini +
|
|
u2_dim1], ldu2);
|
|
}
|
|
if (wantv1t) {
|
|
zswap_(q, &v1t[i__ * v1t_dim1 + 1], &c__1, &v1t[mini *
|
|
v1t_dim1 + 1], &c__1);
|
|
}
|
|
if (wantv2t) {
|
|
i__2 = *m - *q;
|
|
zswap_(&i__2, &v2t[i__ * v2t_dim1 + 1], &c__1, &v2t[mini *
|
|
v2t_dim1 + 1], &c__1);
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZBBCSD */
|
|
|
|
} /* zbbcsd_ */
|
|
|