1491 lines
46 KiB
C
1491 lines
46 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]/Cd(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle_() continue;
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#define myceiling_(w) {ceil(w)}
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#define myhuge_(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c_n1 = -1;
|
|
static integer c__1 = 1;
|
|
static logical c_false = FALSE_;
|
|
|
|
/* > \brief \b ZUNCSD2BY1 */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZUNCSD2BY1 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zuncsd2
|
|
by1.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zuncsd2
|
|
by1.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zuncsd2
|
|
by1.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, */
|
|
/* X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, */
|
|
/* LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, */
|
|
/* INFO ) */
|
|
|
|
/* CHARACTER JOBU1, JOBU2, JOBV1T */
|
|
/* INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21, */
|
|
/* $ M, P, Q */
|
|
/* INTEGER LRWORK, LRWORKMIN, LRWORKOPT */
|
|
/* DOUBLE PRECISION RWORK(*) */
|
|
/* DOUBLE PRECISION THETA(*) */
|
|
/* COMPLEX*16 U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*), */
|
|
/* $ X11(LDX11,*), X21(LDX21,*) */
|
|
/* INTEGER IWORK(*) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* >\verbatim */
|
|
/* > */
|
|
/* > ZUNCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with */
|
|
/* > orthonormal columns that has been partitioned into a 2-by-1 block */
|
|
/* > structure: */
|
|
/* > */
|
|
/* > [ I1 0 0 ] */
|
|
/* > [ 0 C 0 ] */
|
|
/* > [ X11 ] [ U1 | ] [ 0 0 0 ] */
|
|
/* > X = [-----] = [---------] [----------] V1**T . */
|
|
/* > [ X21 ] [ | U2 ] [ 0 0 0 ] */
|
|
/* > [ 0 S 0 ] */
|
|
/* > [ 0 0 I2] */
|
|
/* > */
|
|
/* > X11 is P-by-Q. The unitary matrices U1, U2, and V1 are P-by-P, */
|
|
/* > (M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R */
|
|
/* > nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which */
|
|
/* > R = MIN(P,M-P,Q,M-Q). I1 is a K1-by-K1 identity matrix and I2 is a */
|
|
/* > K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0). */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBU1 */
|
|
/* > \verbatim */
|
|
/* > JOBU1 is CHARACTER */
|
|
/* > = 'Y': U1 is computed; */
|
|
/* > otherwise: U1 is not computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBU2 */
|
|
/* > \verbatim */
|
|
/* > JOBU2 is CHARACTER */
|
|
/* > = 'Y': U2 is computed; */
|
|
/* > otherwise: U2 is not computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBV1T */
|
|
/* > \verbatim */
|
|
/* > JOBV1T is CHARACTER */
|
|
/* > = 'Y': V1T is computed; */
|
|
/* > otherwise: V1T is not computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows in X. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] P */
|
|
/* > \verbatim */
|
|
/* > P is INTEGER */
|
|
/* > The number of rows in X11. 0 <= P <= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] Q */
|
|
/* > \verbatim */
|
|
/* > Q is INTEGER */
|
|
/* > The number of columns in X11 and X21. 0 <= Q <= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] X11 */
|
|
/* > \verbatim */
|
|
/* > X11 is COMPLEX*16 array, dimension (LDX11,Q) */
|
|
/* > On entry, part of the unitary matrix whose CSD is desired. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDX11 */
|
|
/* > \verbatim */
|
|
/* > LDX11 is INTEGER */
|
|
/* > The leading dimension of X11. LDX11 >= MAX(1,P). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] X21 */
|
|
/* > \verbatim */
|
|
/* > X21 is COMPLEX*16 array, dimension (LDX21,Q) */
|
|
/* > On entry, part of the unitary matrix whose CSD is desired. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDX21 */
|
|
/* > \verbatim */
|
|
/* > LDX21 is INTEGER */
|
|
/* > The leading dimension of X21. LDX21 >= MAX(1,M-P). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] THETA */
|
|
/* > \verbatim */
|
|
/* > THETA is DOUBLE PRECISION array, dimension (R), in which R = */
|
|
/* > MIN(P,M-P,Q,M-Q). */
|
|
/* > C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and */
|
|
/* > S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] U1 */
|
|
/* > \verbatim */
|
|
/* > U1 is COMPLEX*16 array, dimension (P) */
|
|
/* > If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU1 */
|
|
/* > \verbatim */
|
|
/* > LDU1 is INTEGER */
|
|
/* > The leading dimension of U1. If JOBU1 = 'Y', LDU1 >= */
|
|
/* > MAX(1,P). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] U2 */
|
|
/* > \verbatim */
|
|
/* > U2 is COMPLEX*16 array, dimension (M-P) */
|
|
/* > If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary */
|
|
/* > matrix U2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDU2 */
|
|
/* > \verbatim */
|
|
/* > LDU2 is INTEGER */
|
|
/* > The leading dimension of U2. If JOBU2 = 'Y', LDU2 >= */
|
|
/* > MAX(1,M-P). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] V1T */
|
|
/* > \verbatim */
|
|
/* > V1T is COMPLEX*16 array, dimension (Q) */
|
|
/* > If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary */
|
|
/* > matrix V1**T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDV1T */
|
|
/* > \verbatim */
|
|
/* > LDV1T is INTEGER */
|
|
/* > The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >= */
|
|
/* > MAX(1,Q). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the work array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \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. */
|
|
/* > If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1), */
|
|
/* > ..., PHI(R-1) that, together with THETA(1), ..., THETA(R), */
|
|
/* > define the matrix in intermediate bidiagonal-block form */
|
|
/* > remaining after nonconvergence. INFO specifies the number */
|
|
/* > of nonzero PHI's. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LRWORK */
|
|
/* > \verbatim */
|
|
/* > LRWORK is INTEGER */
|
|
/* > The dimension of the array RWORK. */
|
|
/* > */
|
|
/* > 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] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q)) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: ZBBCSD did not converge. See the description of WORK */
|
|
/* > above for details. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. */
|
|
/* > Algorithms, 50(1):33-65, 2009. */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date July 2012 */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zuncsd2by1_(char *jobu1, char *jobu2, char *jobv1t,
|
|
integer *m, integer *p, integer *q, doublecomplex *x11, integer *
|
|
ldx11, doublecomplex *x21, integer *ldx21, doublereal *theta,
|
|
doublecomplex *u1, integer *ldu1, doublecomplex *u2, integer *ldu2,
|
|
doublecomplex *v1t, integer *ldv1t, doublecomplex *work, integer *
|
|
lwork, doublereal *rwork, integer *lrwork, integer *iwork, integer *
|
|
info)
|
|
{
|
|
/* System generated locals */
|
|
integer u1_dim1, u1_offset, u2_dim1, u2_offset, v1t_dim1, v1t_offset,
|
|
x11_dim1, x11_offset, x21_dim1, x21_offset, i__1, i__2, i__3;
|
|
|
|
/* Local variables */
|
|
integer ib11d, ib11e, ib12d, ib12e, ib21d, ib21e, ib22d, ib22e;
|
|
doublecomplex cdum[1] /* was [1][1] */;
|
|
integer iphi, lworkmin, lworkopt, i__, j, r__;
|
|
extern logical lsame_(char *, char *);
|
|
integer childinfo;
|
|
extern /* Subroutine */ void zcopy_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *);
|
|
integer lorglqmin, lorgqrmin, lorglqopt, lrworkmin, itaup1, itaup2,
|
|
itauq1, lorgqropt;
|
|
logical wantu1, wantu2;
|
|
integer lrworkopt, ibbcsd, lbbcsd, iorbdb, lorbdb;
|
|
extern /* Subroutine */ void zbbcsd_(char *, char *, char *, char *, char *
|
|
, integer *, integer *, integer *, doublereal *, doublereal *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, integer *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
integer iorglq, lorglq;
|
|
extern /* Subroutine */ void zlacpy_(char *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *);
|
|
integer iorgqr;
|
|
extern /* Subroutine */ void zlapmr_(logical *, integer *, integer *,
|
|
doublecomplex *, integer *, integer *);
|
|
integer lorgqr;
|
|
extern /* Subroutine */ void zlapmt_(logical *, integer *, integer *,
|
|
doublecomplex *, integer *, integer *);
|
|
logical lquery;
|
|
extern /* Subroutine */ void zunglq_(integer *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *, integer *), zungqr_(integer *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *, integer *), zunbdb1_(integer *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublereal *, doublereal *, doublecomplex *, doublecomplex *,
|
|
doublecomplex *, doublecomplex *, integer *, integer *), zunbdb2_(
|
|
integer *, integer *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublereal *, doublereal *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
|
|
, integer *, integer *), zunbdb3_(integer *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublereal *, doublereal *, doublecomplex *, doublecomplex *,
|
|
doublecomplex *, doublecomplex *, integer *, integer *), zunbdb4_(
|
|
integer *, integer *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublereal *, doublereal *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
|
|
, doublecomplex *, integer *, integer *);
|
|
logical wantv1t;
|
|
doublereal dum[1];
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* July 2012 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test input arguments */
|
|
|
|
/* Parameter adjustments */
|
|
x11_dim1 = *ldx11;
|
|
x11_offset = 1 + x11_dim1 * 1;
|
|
x11 -= x11_offset;
|
|
x21_dim1 = *ldx21;
|
|
x21_offset = 1 + x21_dim1 * 1;
|
|
x21 -= x21_offset;
|
|
--theta;
|
|
u1_dim1 = *ldu1;
|
|
u1_offset = 1 + u1_dim1 * 1;
|
|
u1 -= u1_offset;
|
|
u2_dim1 = *ldu2;
|
|
u2_offset = 1 + u2_dim1 * 1;
|
|
u2 -= u2_offset;
|
|
v1t_dim1 = *ldv1t;
|
|
v1t_offset = 1 + v1t_dim1 * 1;
|
|
v1t -= v1t_offset;
|
|
--work;
|
|
--rwork;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
wantu1 = lsame_(jobu1, "Y");
|
|
wantu2 = lsame_(jobu2, "Y");
|
|
wantv1t = lsame_(jobv1t, "Y");
|
|
lquery = *lwork == -1;
|
|
|
|
if (*m < 0) {
|
|
*info = -4;
|
|
} else if (*p < 0 || *p > *m) {
|
|
*info = -5;
|
|
} else if (*q < 0 || *q > *m) {
|
|
*info = -6;
|
|
} else if (*ldx11 < f2cmax(1,*p)) {
|
|
*info = -8;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *m - *p;
|
|
if (*ldx21 < f2cmax(i__1,i__2)) {
|
|
*info = -10;
|
|
} else if (wantu1 && *ldu1 < f2cmax(1,*p)) {
|
|
*info = -13;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *m - *p;
|
|
if (wantu2 && *ldu2 < f2cmax(i__1,i__2)) {
|
|
*info = -15;
|
|
} else if (wantv1t && *ldv1t < f2cmax(1,*q)) {
|
|
*info = -17;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Computing MIN */
|
|
i__1 = *p, i__2 = *m - *p, i__1 = f2cmin(i__1,i__2), i__1 = f2cmin(i__1,*q),
|
|
i__2 = *m - *q;
|
|
r__ = f2cmin(i__1,i__2);
|
|
|
|
/* Compute workspace */
|
|
|
|
/* WORK layout: */
|
|
/* |-----------------------------------------| */
|
|
/* | LWORKOPT (1) | */
|
|
/* |-----------------------------------------| */
|
|
/* | TAUP1 (MAX(1,P)) | */
|
|
/* | TAUP2 (MAX(1,M-P)) | */
|
|
/* | TAUQ1 (MAX(1,Q)) | */
|
|
/* |-----------------------------------------| */
|
|
/* | ZUNBDB WORK | ZUNGQR WORK | ZUNGLQ WORK | */
|
|
/* | | | | */
|
|
/* | | | | */
|
|
/* | | | | */
|
|
/* | | | | */
|
|
/* |-----------------------------------------| */
|
|
/* RWORK layout: */
|
|
/* |------------------| */
|
|
/* | LRWORKOPT (1) | */
|
|
/* |------------------| */
|
|
/* | PHI (MAX(1,R-1)) | */
|
|
/* |------------------| */
|
|
/* | B11D (R) | */
|
|
/* | B11E (R-1) | */
|
|
/* | B12D (R) | */
|
|
/* | B12E (R-1) | */
|
|
/* | B21D (R) | */
|
|
/* | B21E (R-1) | */
|
|
/* | B22D (R) | */
|
|
/* | B22E (R-1) | */
|
|
/* | ZBBCSD RWORK | */
|
|
/* |------------------| */
|
|
|
|
if (*info == 0) {
|
|
iphi = 2;
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = r__ - 1;
|
|
ib11d = iphi + f2cmax(i__1,i__2);
|
|
ib11e = ib11d + f2cmax(1,r__);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = r__ - 1;
|
|
ib12d = ib11e + f2cmax(i__1,i__2);
|
|
ib12e = ib12d + f2cmax(1,r__);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = r__ - 1;
|
|
ib21d = ib12e + f2cmax(i__1,i__2);
|
|
ib21e = ib21d + f2cmax(1,r__);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = r__ - 1;
|
|
ib22d = ib21e + f2cmax(i__1,i__2);
|
|
ib22e = ib22d + f2cmax(1,r__);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = r__ - 1;
|
|
ibbcsd = ib22e + f2cmax(i__1,i__2);
|
|
itaup1 = 2;
|
|
itaup2 = itaup1 + f2cmax(1,*p);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *m - *p;
|
|
itauq1 = itaup2 + f2cmax(i__1,i__2);
|
|
iorbdb = itauq1 + f2cmax(1,*q);
|
|
iorgqr = itauq1 + f2cmax(1,*q);
|
|
iorglq = itauq1 + f2cmax(1,*q);
|
|
lorgqrmin = 1;
|
|
lorgqropt = 1;
|
|
lorglqmin = 1;
|
|
lorglqopt = 1;
|
|
if (r__ == *q) {
|
|
zunbdb1_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset],
|
|
ldx21, &theta[1], dum, cdum, cdum, cdum, &work[1], &c_n1,
|
|
&childinfo);
|
|
lorbdb = (integer) work[1].r;
|
|
if (wantu1 && *p > 0) {
|
|
zungqr_(p, p, q, &u1[u1_offset], ldu1, cdum, &work[1], &c_n1,
|
|
&childinfo);
|
|
lorgqrmin = f2cmax(lorgqrmin,*p);
|
|
/* Computing MAX */
|
|
i__1 = lorgqropt, i__2 = (integer) work[1].r;
|
|
lorgqropt = f2cmax(i__1,i__2);
|
|
}
|
|
if (wantu2 && *m - *p > 0) {
|
|
i__1 = *m - *p;
|
|
i__2 = *m - *p;
|
|
zungqr_(&i__1, &i__2, q, &u2[u2_offset], ldu2, cdum, &work[1],
|
|
&c_n1, &childinfo);
|
|
/* Computing MAX */
|
|
i__1 = lorgqrmin, i__2 = *m - *p;
|
|
lorgqrmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = lorgqropt, i__2 = (integer) work[1].r;
|
|
lorgqropt = f2cmax(i__1,i__2);
|
|
}
|
|
if (wantv1t && *q > 0) {
|
|
i__1 = *q - 1;
|
|
i__2 = *q - 1;
|
|
i__3 = *q - 1;
|
|
zunglq_(&i__1, &i__2, &i__3, &v1t[v1t_offset], ldv1t, cdum, &
|
|
work[1], &c_n1, &childinfo);
|
|
/* Computing MAX */
|
|
i__1 = lorglqmin, i__2 = *q - 1;
|
|
lorglqmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = lorglqopt, i__2 = (integer) work[1].r;
|
|
lorglqopt = f2cmax(i__1,i__2);
|
|
}
|
|
zbbcsd_(jobu1, jobu2, jobv1t, "N", "N", m, p, q, &theta[1], dum, &
|
|
u1[u1_offset], ldu1, &u2[u2_offset], ldu2, &v1t[
|
|
v1t_offset], ldv1t, cdum, &c__1, dum, dum, dum, dum, dum,
|
|
dum, dum, dum, &rwork[1], &c_n1, &childinfo);
|
|
lbbcsd = (integer) rwork[1];
|
|
} else if (r__ == *p) {
|
|
zunbdb2_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset],
|
|
ldx21, &theta[1], dum, cdum, cdum, cdum, &work[1], &c_n1,
|
|
&childinfo);
|
|
lorbdb = (integer) work[1].r;
|
|
if (wantu1 && *p > 0) {
|
|
i__1 = *p - 1;
|
|
i__2 = *p - 1;
|
|
i__3 = *p - 1;
|
|
zungqr_(&i__1, &i__2, &i__3, &u1[(u1_dim1 << 1) + 2], ldu1,
|
|
cdum, &work[1], &c_n1, &childinfo);
|
|
/* Computing MAX */
|
|
i__1 = lorgqrmin, i__2 = *p - 1;
|
|
lorgqrmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = lorgqropt, i__2 = (integer) work[1].r;
|
|
lorgqropt = f2cmax(i__1,i__2);
|
|
}
|
|
if (wantu2 && *m - *p > 0) {
|
|
i__1 = *m - *p;
|
|
i__2 = *m - *p;
|
|
zungqr_(&i__1, &i__2, q, &u2[u2_offset], ldu2, cdum, &work[1],
|
|
&c_n1, &childinfo);
|
|
/* Computing MAX */
|
|
i__1 = lorgqrmin, i__2 = *m - *p;
|
|
lorgqrmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = lorgqropt, i__2 = (integer) work[1].r;
|
|
lorgqropt = f2cmax(i__1,i__2);
|
|
}
|
|
if (wantv1t && *q > 0) {
|
|
zunglq_(q, q, &r__, &v1t[v1t_offset], ldv1t, cdum, &work[1], &
|
|
c_n1, &childinfo);
|
|
lorglqmin = f2cmax(lorglqmin,*q);
|
|
/* Computing MAX */
|
|
i__1 = lorglqopt, i__2 = (integer) work[1].r;
|
|
lorglqopt = f2cmax(i__1,i__2);
|
|
}
|
|
zbbcsd_(jobv1t, "N", jobu1, jobu2, "T", m, q, p, &theta[1], dum, &
|
|
v1t[v1t_offset], ldv1t, cdum, &c__1, &u1[u1_offset], ldu1,
|
|
&u2[u2_offset], ldu2, dum, dum, dum, dum, dum, dum, dum,
|
|
dum, &rwork[1], &c_n1, &childinfo);
|
|
lbbcsd = (integer) rwork[1];
|
|
} else if (r__ == *m - *p) {
|
|
zunbdb3_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset],
|
|
ldx21, &theta[1], dum, cdum, cdum, cdum, &work[1], &c_n1,
|
|
&childinfo);
|
|
lorbdb = (integer) work[1].r;
|
|
if (wantu1 && *p > 0) {
|
|
zungqr_(p, p, q, &u1[u1_offset], ldu1, cdum, &work[1], &c_n1,
|
|
&childinfo);
|
|
lorgqrmin = f2cmax(lorgqrmin,*p);
|
|
/* Computing MAX */
|
|
i__1 = lorgqropt, i__2 = (integer) work[1].r;
|
|
lorgqropt = f2cmax(i__1,i__2);
|
|
}
|
|
if (wantu2 && *m - *p > 0) {
|
|
i__1 = *m - *p - 1;
|
|
i__2 = *m - *p - 1;
|
|
i__3 = *m - *p - 1;
|
|
zungqr_(&i__1, &i__2, &i__3, &u2[(u2_dim1 << 1) + 2], ldu2,
|
|
cdum, &work[1], &c_n1, &childinfo);
|
|
/* Computing MAX */
|
|
i__1 = lorgqrmin, i__2 = *m - *p - 1;
|
|
lorgqrmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = lorgqropt, i__2 = (integer) work[1].r;
|
|
lorgqropt = f2cmax(i__1,i__2);
|
|
}
|
|
if (wantv1t && *q > 0) {
|
|
zunglq_(q, q, &r__, &v1t[v1t_offset], ldv1t, cdum, &work[1], &
|
|
c_n1, &childinfo);
|
|
lorglqmin = f2cmax(lorglqmin,*q);
|
|
/* Computing MAX */
|
|
i__1 = lorglqopt, i__2 = (integer) work[1].r;
|
|
lorglqopt = f2cmax(i__1,i__2);
|
|
}
|
|
i__1 = *m - *q;
|
|
i__2 = *m - *p;
|
|
zbbcsd_("N", jobv1t, jobu2, jobu1, "T", m, &i__1, &i__2, &theta[1]
|
|
, dum, cdum, &c__1, &v1t[v1t_offset], ldv1t, &u2[
|
|
u2_offset], ldu2, &u1[u1_offset], ldu1, dum, dum, dum,
|
|
dum, dum, dum, dum, dum, &rwork[1], &c_n1, &childinfo);
|
|
lbbcsd = (integer) rwork[1];
|
|
} else {
|
|
zunbdb4_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset],
|
|
ldx21, &theta[1], dum, cdum, cdum, cdum, cdum, &work[1], &
|
|
c_n1, &childinfo);
|
|
lorbdb = *m + (integer) work[1].r;
|
|
if (wantu1 && *p > 0) {
|
|
i__1 = *m - *q;
|
|
zungqr_(p, p, &i__1, &u1[u1_offset], ldu1, cdum, &work[1], &
|
|
c_n1, &childinfo);
|
|
lorgqrmin = f2cmax(lorgqrmin,*p);
|
|
/* Computing MAX */
|
|
i__1 = lorgqropt, i__2 = (integer) work[1].r;
|
|
lorgqropt = f2cmax(i__1,i__2);
|
|
}
|
|
if (wantu2 && *m - *p > 0) {
|
|
i__1 = *m - *p;
|
|
i__2 = *m - *p;
|
|
i__3 = *m - *q;
|
|
zungqr_(&i__1, &i__2, &i__3, &u2[u2_offset], ldu2, cdum, &
|
|
work[1], &c_n1, &childinfo);
|
|
/* Computing MAX */
|
|
i__1 = lorgqrmin, i__2 = *m - *p;
|
|
lorgqrmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = lorgqropt, i__2 = (integer) work[1].r;
|
|
lorgqropt = f2cmax(i__1,i__2);
|
|
}
|
|
if (wantv1t && *q > 0) {
|
|
zunglq_(q, q, q, &v1t[v1t_offset], ldv1t, cdum, &work[1], &
|
|
c_n1, &childinfo);
|
|
lorglqmin = f2cmax(lorglqmin,*q);
|
|
/* Computing MAX */
|
|
i__1 = lorglqopt, i__2 = (integer) work[1].r;
|
|
lorglqopt = f2cmax(i__1,i__2);
|
|
}
|
|
i__1 = *m - *p;
|
|
i__2 = *m - *q;
|
|
zbbcsd_(jobu2, jobu1, "N", jobv1t, "N", m, &i__1, &i__2, &theta[1]
|
|
, dum, &u2[u2_offset], ldu2, &u1[u1_offset], ldu1, cdum, &
|
|
c__1, &v1t[v1t_offset], ldv1t, dum, dum, dum, dum, dum,
|
|
dum, dum, dum, &rwork[1], &c_n1, &childinfo);
|
|
lbbcsd = (integer) rwork[1];
|
|
}
|
|
lrworkmin = ibbcsd + lbbcsd - 1;
|
|
lrworkopt = lrworkmin;
|
|
rwork[1] = (doublereal) lrworkopt;
|
|
/* Computing MAX */
|
|
i__1 = iorbdb + lorbdb - 1, i__2 = iorgqr + lorgqrmin - 1, i__1 = f2cmax(
|
|
i__1,i__2), i__2 = iorglq + lorglqmin - 1;
|
|
lworkmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = iorbdb + lorbdb - 1, i__2 = iorgqr + lorgqropt - 1, i__1 = f2cmax(
|
|
i__1,i__2), i__2 = iorglq + lorglqopt - 1;
|
|
lworkopt = f2cmax(i__1,i__2);
|
|
work[1].r = (doublereal) lworkopt, work[1].i = 0.;
|
|
if (*lwork < lworkmin && ! lquery) {
|
|
*info = -19;
|
|
}
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZUNCSD2BY1", &i__1, (ftnlen)10);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
lorgqr = *lwork - iorgqr + 1;
|
|
lorglq = *lwork - iorglq + 1;
|
|
|
|
/* Handle four cases separately: R = Q, R = P, R = M-P, and R = M-Q, */
|
|
/* in which R = MIN(P,M-P,Q,M-Q) */
|
|
|
|
if (r__ == *q) {
|
|
|
|
/* Case 1: R = Q */
|
|
|
|
/* Simultaneously bidiagonalize X11 and X21 */
|
|
|
|
zunbdb1_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &
|
|
theta[1], &rwork[iphi], &work[itaup1], &work[itaup2], &work[
|
|
itauq1], &work[iorbdb], &lorbdb, &childinfo);
|
|
|
|
/* Accumulate Householder reflectors */
|
|
|
|
if (wantu1 && *p > 0) {
|
|
zlacpy_("L", p, q, &x11[x11_offset], ldx11, &u1[u1_offset], ldu1);
|
|
zungqr_(p, p, q, &u1[u1_offset], ldu1, &work[itaup1], &work[
|
|
iorgqr], &lorgqr, &childinfo);
|
|
}
|
|
if (wantu2 && *m - *p > 0) {
|
|
i__1 = *m - *p;
|
|
zlacpy_("L", &i__1, q, &x21[x21_offset], ldx21, &u2[u2_offset],
|
|
ldu2);
|
|
i__1 = *m - *p;
|
|
i__2 = *m - *p;
|
|
zungqr_(&i__1, &i__2, q, &u2[u2_offset], ldu2, &work[itaup2], &
|
|
work[iorgqr], &lorgqr, &childinfo);
|
|
}
|
|
if (wantv1t && *q > 0) {
|
|
i__1 = v1t_dim1 + 1;
|
|
v1t[i__1].r = 1., v1t[i__1].i = 0.;
|
|
i__1 = *q;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
i__2 = j * v1t_dim1 + 1;
|
|
v1t[i__2].r = 0., v1t[i__2].i = 0.;
|
|
i__2 = j + v1t_dim1;
|
|
v1t[i__2].r = 0., v1t[i__2].i = 0.;
|
|
}
|
|
i__1 = *q - 1;
|
|
i__2 = *q - 1;
|
|
zlacpy_("U", &i__1, &i__2, &x21[(x21_dim1 << 1) + 1], ldx21, &v1t[
|
|
(v1t_dim1 << 1) + 2], ldv1t);
|
|
i__1 = *q - 1;
|
|
i__2 = *q - 1;
|
|
i__3 = *q - 1;
|
|
zunglq_(&i__1, &i__2, &i__3, &v1t[(v1t_dim1 << 1) + 2], ldv1t, &
|
|
work[itauq1], &work[iorglq], &lorglq, &childinfo);
|
|
}
|
|
|
|
/* Simultaneously diagonalize X11 and X21. */
|
|
|
|
zbbcsd_(jobu1, jobu2, jobv1t, "N", "N", m, p, q, &theta[1], &rwork[
|
|
iphi], &u1[u1_offset], ldu1, &u2[u2_offset], ldu2, &v1t[
|
|
v1t_offset], ldv1t, cdum, &c__1, &rwork[ib11d], &rwork[ib11e],
|
|
&rwork[ib12d], &rwork[ib12e], &rwork[ib21d], &rwork[ib21e], &
|
|
rwork[ib22d], &rwork[ib22e], &rwork[ibbcsd], &lbbcsd, &
|
|
childinfo);
|
|
|
|
/* Permute rows and columns to place zero submatrices in */
|
|
/* preferred positions */
|
|
|
|
if (*q > 0 && wantu2) {
|
|
i__1 = *q;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
iwork[i__] = *m - *p - *q + i__;
|
|
}
|
|
i__1 = *m - *p;
|
|
for (i__ = *q + 1; i__ <= i__1; ++i__) {
|
|
iwork[i__] = i__ - *q;
|
|
}
|
|
i__1 = *m - *p;
|
|
i__2 = *m - *p;
|
|
zlapmt_(&c_false, &i__1, &i__2, &u2[u2_offset], ldu2, &iwork[1]);
|
|
}
|
|
} else if (r__ == *p) {
|
|
|
|
/* Case 2: R = P */
|
|
|
|
/* Simultaneously bidiagonalize X11 and X21 */
|
|
|
|
zunbdb2_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &
|
|
theta[1], &rwork[iphi], &work[itaup1], &work[itaup2], &work[
|
|
itauq1], &work[iorbdb], &lorbdb, &childinfo);
|
|
|
|
/* Accumulate Householder reflectors */
|
|
|
|
if (wantu1 && *p > 0) {
|
|
i__1 = u1_dim1 + 1;
|
|
u1[i__1].r = 1., u1[i__1].i = 0.;
|
|
i__1 = *p;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
i__2 = j * u1_dim1 + 1;
|
|
u1[i__2].r = 0., u1[i__2].i = 0.;
|
|
i__2 = j + u1_dim1;
|
|
u1[i__2].r = 0., u1[i__2].i = 0.;
|
|
}
|
|
i__1 = *p - 1;
|
|
i__2 = *p - 1;
|
|
zlacpy_("L", &i__1, &i__2, &x11[x11_dim1 + 2], ldx11, &u1[(
|
|
u1_dim1 << 1) + 2], ldu1);
|
|
i__1 = *p - 1;
|
|
i__2 = *p - 1;
|
|
i__3 = *p - 1;
|
|
zungqr_(&i__1, &i__2, &i__3, &u1[(u1_dim1 << 1) + 2], ldu1, &work[
|
|
itaup1], &work[iorgqr], &lorgqr, &childinfo);
|
|
}
|
|
if (wantu2 && *m - *p > 0) {
|
|
i__1 = *m - *p;
|
|
zlacpy_("L", &i__1, q, &x21[x21_offset], ldx21, &u2[u2_offset],
|
|
ldu2);
|
|
i__1 = *m - *p;
|
|
i__2 = *m - *p;
|
|
zungqr_(&i__1, &i__2, q, &u2[u2_offset], ldu2, &work[itaup2], &
|
|
work[iorgqr], &lorgqr, &childinfo);
|
|
}
|
|
if (wantv1t && *q > 0) {
|
|
zlacpy_("U", p, q, &x11[x11_offset], ldx11, &v1t[v1t_offset],
|
|
ldv1t);
|
|
zunglq_(q, q, &r__, &v1t[v1t_offset], ldv1t, &work[itauq1], &work[
|
|
iorglq], &lorglq, &childinfo);
|
|
}
|
|
|
|
/* Simultaneously diagonalize X11 and X21. */
|
|
|
|
zbbcsd_(jobv1t, "N", jobu1, jobu2, "T", m, q, p, &theta[1], &rwork[
|
|
iphi], &v1t[v1t_offset], ldv1t, cdum, &c__1, &u1[u1_offset],
|
|
ldu1, &u2[u2_offset], ldu2, &rwork[ib11d], &rwork[ib11e], &
|
|
rwork[ib12d], &rwork[ib12e], &rwork[ib21d], &rwork[ib21e], &
|
|
rwork[ib22d], &rwork[ib22e], &rwork[ibbcsd], &lbbcsd, &
|
|
childinfo);
|
|
|
|
/* Permute rows and columns to place identity submatrices in */
|
|
/* preferred positions */
|
|
|
|
if (*q > 0 && wantu2) {
|
|
i__1 = *q;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
iwork[i__] = *m - *p - *q + i__;
|
|
}
|
|
i__1 = *m - *p;
|
|
for (i__ = *q + 1; i__ <= i__1; ++i__) {
|
|
iwork[i__] = i__ - *q;
|
|
}
|
|
i__1 = *m - *p;
|
|
i__2 = *m - *p;
|
|
zlapmt_(&c_false, &i__1, &i__2, &u2[u2_offset], ldu2, &iwork[1]);
|
|
}
|
|
} else if (r__ == *m - *p) {
|
|
|
|
/* Case 3: R = M-P */
|
|
|
|
/* Simultaneously bidiagonalize X11 and X21 */
|
|
|
|
zunbdb3_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &
|
|
theta[1], &rwork[iphi], &work[itaup1], &work[itaup2], &work[
|
|
itauq1], &work[iorbdb], &lorbdb, &childinfo);
|
|
|
|
/* Accumulate Householder reflectors */
|
|
|
|
if (wantu1 && *p > 0) {
|
|
zlacpy_("L", p, q, &x11[x11_offset], ldx11, &u1[u1_offset], ldu1);
|
|
zungqr_(p, p, q, &u1[u1_offset], ldu1, &work[itaup1], &work[
|
|
iorgqr], &lorgqr, &childinfo);
|
|
}
|
|
if (wantu2 && *m - *p > 0) {
|
|
i__1 = u2_dim1 + 1;
|
|
u2[i__1].r = 1., u2[i__1].i = 0.;
|
|
i__1 = *m - *p;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
i__2 = j * u2_dim1 + 1;
|
|
u2[i__2].r = 0., u2[i__2].i = 0.;
|
|
i__2 = j + u2_dim1;
|
|
u2[i__2].r = 0., u2[i__2].i = 0.;
|
|
}
|
|
i__1 = *m - *p - 1;
|
|
i__2 = *m - *p - 1;
|
|
zlacpy_("L", &i__1, &i__2, &x21[x21_dim1 + 2], ldx21, &u2[(
|
|
u2_dim1 << 1) + 2], ldu2);
|
|
i__1 = *m - *p - 1;
|
|
i__2 = *m - *p - 1;
|
|
i__3 = *m - *p - 1;
|
|
zungqr_(&i__1, &i__2, &i__3, &u2[(u2_dim1 << 1) + 2], ldu2, &work[
|
|
itaup2], &work[iorgqr], &lorgqr, &childinfo);
|
|
}
|
|
if (wantv1t && *q > 0) {
|
|
i__1 = *m - *p;
|
|
zlacpy_("U", &i__1, q, &x21[x21_offset], ldx21, &v1t[v1t_offset],
|
|
ldv1t);
|
|
zunglq_(q, q, &r__, &v1t[v1t_offset], ldv1t, &work[itauq1], &work[
|
|
iorglq], &lorglq, &childinfo);
|
|
}
|
|
|
|
/* Simultaneously diagonalize X11 and X21. */
|
|
|
|
i__1 = *m - *q;
|
|
i__2 = *m - *p;
|
|
zbbcsd_("N", jobv1t, jobu2, jobu1, "T", m, &i__1, &i__2, &theta[1], &
|
|
rwork[iphi], cdum, &c__1, &v1t[v1t_offset], ldv1t, &u2[
|
|
u2_offset], ldu2, &u1[u1_offset], ldu1, &rwork[ib11d], &rwork[
|
|
ib11e], &rwork[ib12d], &rwork[ib12e], &rwork[ib21d], &rwork[
|
|
ib21e], &rwork[ib22d], &rwork[ib22e], &rwork[ibbcsd], &lbbcsd,
|
|
&childinfo);
|
|
|
|
/* Permute rows and columns to place identity submatrices in */
|
|
/* preferred positions */
|
|
|
|
if (*q > r__) {
|
|
i__1 = r__;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
iwork[i__] = *q - r__ + i__;
|
|
}
|
|
i__1 = *q;
|
|
for (i__ = r__ + 1; i__ <= i__1; ++i__) {
|
|
iwork[i__] = i__ - r__;
|
|
}
|
|
if (wantu1) {
|
|
zlapmt_(&c_false, p, q, &u1[u1_offset], ldu1, &iwork[1]);
|
|
}
|
|
if (wantv1t) {
|
|
zlapmr_(&c_false, q, q, &v1t[v1t_offset], ldv1t, &iwork[1]);
|
|
}
|
|
}
|
|
} else {
|
|
|
|
/* Case 4: R = M-Q */
|
|
|
|
/* Simultaneously bidiagonalize X11 and X21 */
|
|
|
|
i__1 = lorbdb - *m;
|
|
zunbdb4_(m, p, q, &x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &
|
|
theta[1], &rwork[iphi], &work[itaup1], &work[itaup2], &work[
|
|
itauq1], &work[iorbdb], &work[iorbdb + *m], &i__1, &childinfo)
|
|
;
|
|
|
|
/* Accumulate Householder reflectors */
|
|
|
|
if (wantu1 && *p > 0) {
|
|
zcopy_(p, &work[iorbdb], &c__1, &u1[u1_offset], &c__1);
|
|
i__1 = *p;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
i__2 = j * u1_dim1 + 1;
|
|
u1[i__2].r = 0., u1[i__2].i = 0.;
|
|
}
|
|
i__1 = *p - 1;
|
|
i__2 = *m - *q - 1;
|
|
zlacpy_("L", &i__1, &i__2, &x11[x11_dim1 + 2], ldx11, &u1[(
|
|
u1_dim1 << 1) + 2], ldu1);
|
|
i__1 = *m - *q;
|
|
zungqr_(p, p, &i__1, &u1[u1_offset], ldu1, &work[itaup1], &work[
|
|
iorgqr], &lorgqr, &childinfo);
|
|
}
|
|
if (wantu2 && *m - *p > 0) {
|
|
i__1 = *m - *p;
|
|
zcopy_(&i__1, &work[iorbdb + *p], &c__1, &u2[u2_offset], &c__1);
|
|
i__1 = *m - *p;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
i__2 = j * u2_dim1 + 1;
|
|
u2[i__2].r = 0., u2[i__2].i = 0.;
|
|
}
|
|
i__1 = *m - *p - 1;
|
|
i__2 = *m - *q - 1;
|
|
zlacpy_("L", &i__1, &i__2, &x21[x21_dim1 + 2], ldx21, &u2[(
|
|
u2_dim1 << 1) + 2], ldu2);
|
|
i__1 = *m - *p;
|
|
i__2 = *m - *p;
|
|
i__3 = *m - *q;
|
|
zungqr_(&i__1, &i__2, &i__3, &u2[u2_offset], ldu2, &work[itaup2],
|
|
&work[iorgqr], &lorgqr, &childinfo);
|
|
}
|
|
if (wantv1t && *q > 0) {
|
|
i__1 = *m - *q;
|
|
zlacpy_("U", &i__1, q, &x21[x21_offset], ldx21, &v1t[v1t_offset],
|
|
ldv1t);
|
|
i__1 = *p - (*m - *q);
|
|
i__2 = *q - (*m - *q);
|
|
zlacpy_("U", &i__1, &i__2, &x11[*m - *q + 1 + (*m - *q + 1) *
|
|
x11_dim1], ldx11, &v1t[*m - *q + 1 + (*m - *q + 1) *
|
|
v1t_dim1], ldv1t);
|
|
i__1 = -(*p) + *q;
|
|
i__2 = *q - *p;
|
|
zlacpy_("U", &i__1, &i__2, &x21[*m - *q + 1 + (*p + 1) * x21_dim1]
|
|
, ldx21, &v1t[*p + 1 + (*p + 1) * v1t_dim1], ldv1t);
|
|
zunglq_(q, q, q, &v1t[v1t_offset], ldv1t, &work[itauq1], &work[
|
|
iorglq], &lorglq, &childinfo);
|
|
}
|
|
|
|
/* Simultaneously diagonalize X11 and X21. */
|
|
|
|
i__1 = *m - *p;
|
|
i__2 = *m - *q;
|
|
zbbcsd_(jobu2, jobu1, "N", jobv1t, "N", m, &i__1, &i__2, &theta[1], &
|
|
rwork[iphi], &u2[u2_offset], ldu2, &u1[u1_offset], ldu1, cdum,
|
|
&c__1, &v1t[v1t_offset], ldv1t, &rwork[ib11d], &rwork[ib11e],
|
|
&rwork[ib12d], &rwork[ib12e], &rwork[ib21d], &rwork[ib21e], &
|
|
rwork[ib22d], &rwork[ib22e], &rwork[ibbcsd], &lbbcsd, &
|
|
childinfo);
|
|
|
|
/* Permute rows and columns to place identity submatrices in */
|
|
/* preferred positions */
|
|
|
|
if (*p > r__) {
|
|
i__1 = r__;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
iwork[i__] = *p - r__ + i__;
|
|
}
|
|
i__1 = *p;
|
|
for (i__ = r__ + 1; i__ <= i__1; ++i__) {
|
|
iwork[i__] = i__ - r__;
|
|
}
|
|
if (wantu1) {
|
|
zlapmt_(&c_false, p, p, &u1[u1_offset], ldu1, &iwork[1]);
|
|
}
|
|
if (wantv1t) {
|
|
zlapmr_(&c_false, p, q, &v1t[v1t_offset], ldv1t, &iwork[1]);
|
|
}
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZUNCSD2BY1 */
|
|
|
|
} /* zuncsd2by1_ */
|
|
|