926 lines
27 KiB
C
926 lines
27 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/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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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublecomplex c_b1 = {-1.,0.};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZUNBDB2 */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZUNBDB2 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunbdb2
|
|
.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunbdb2
|
|
.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunbdb2
|
|
.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, */
|
|
/* TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO ) */
|
|
|
|
/* INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21 */
|
|
/* DOUBLE PRECISION PHI(*), THETA(*) */
|
|
/* COMPLEX*16 TAUP1(*), TAUP2(*), TAUQ1(*), WORK(*), */
|
|
/* $ X11(LDX11,*), X21(LDX21,*) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* >\verbatim */
|
|
/* > */
|
|
/* > ZUNBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny */
|
|
/* > matrix X with orthonomal columns: */
|
|
/* > */
|
|
/* > [ B11 ] */
|
|
/* > [ X11 ] [ P1 | ] [ 0 ] */
|
|
/* > [-----] = [---------] [-----] Q1**T . */
|
|
/* > [ X21 ] [ | P2 ] [ B21 ] */
|
|
/* > [ 0 ] */
|
|
/* > */
|
|
/* > X11 is P-by-Q, and X21 is (M-P)-by-Q. P must be no larger than M-P, */
|
|
/* > Q, or M-Q. Routines ZUNBDB1, ZUNBDB3, and ZUNBDB4 handle cases in */
|
|
/* > which P is not the minimum dimension. */
|
|
/* > */
|
|
/* > The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P), */
|
|
/* > and (M-Q)-by-(M-Q), respectively. They are represented implicitly by */
|
|
/* > Householder vectors. */
|
|
/* > */
|
|
/* > B11 and B12 are P-by-P bidiagonal matrices represented implicitly by */
|
|
/* > angles THETA, PHI. */
|
|
/* > */
|
|
/* >\endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows X11 plus the number of rows in X21. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] P */
|
|
/* > \verbatim */
|
|
/* > P is INTEGER */
|
|
/* > The number of rows in X11. 0 <= P <= f2cmin(M-P,Q,M-Q). */
|
|
/* > \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, the top block of the matrix X to be reduced. On */
|
|
/* > exit, the columns of tril(X11) specify reflectors for P1 and */
|
|
/* > the rows of triu(X11,1) specify reflectors for Q1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDX11 */
|
|
/* > \verbatim */
|
|
/* > LDX11 is INTEGER */
|
|
/* > The leading dimension of X11. LDX11 >= P. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] X21 */
|
|
/* > \verbatim */
|
|
/* > X21 is COMPLEX*16 array, dimension (LDX21,Q) */
|
|
/* > On entry, the bottom block of the matrix X to be reduced. On */
|
|
/* > exit, the columns of tril(X21) specify reflectors for P2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDX21 */
|
|
/* > \verbatim */
|
|
/* > LDX21 is INTEGER */
|
|
/* > The leading dimension of X21. LDX21 >= M-P. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] THETA */
|
|
/* > \verbatim */
|
|
/* > THETA is DOUBLE PRECISION array, dimension (Q) */
|
|
/* > The entries of the bidiagonal blocks B11, B21 are defined by */
|
|
/* > THETA and PHI. See Further Details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] PHI */
|
|
/* > \verbatim */
|
|
/* > PHI is DOUBLE PRECISION array, dimension (Q-1) */
|
|
/* > The entries of the bidiagonal blocks B11, B21 are defined by */
|
|
/* > THETA and PHI. See Further Details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] TAUP1 */
|
|
/* > \verbatim */
|
|
/* > TAUP1 is COMPLEX*16 array, dimension (P) */
|
|
/* > The scalar factors of the elementary reflectors that define */
|
|
/* > P1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] TAUP2 */
|
|
/* > \verbatim */
|
|
/* > TAUP2 is COMPLEX*16 array, dimension (M-P) */
|
|
/* > The scalar factors of the elementary reflectors that define */
|
|
/* > P2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] TAUQ1 */
|
|
/* > \verbatim */
|
|
/* > TAUQ1 is COMPLEX*16 array, dimension (Q) */
|
|
/* > The scalar factors of the elementary reflectors that define */
|
|
/* > Q1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (LWORK) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= M-Q. */
|
|
/* > */
|
|
/* > 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] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date July 2012 */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The upper-bidiagonal blocks B11, B21 are represented implicitly by */
|
|
/* > angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry */
|
|
/* > in each bidiagonal band is a product of a sine or cosine of a THETA */
|
|
/* > with a sine or cosine of a PHI. See [1] or ZUNCSD for details. */
|
|
/* > */
|
|
/* > P1, P2, and Q1 are represented as products of elementary reflectors. */
|
|
/* > See ZUNCSD2BY1 for details on generating P1, P2, and Q1 using ZUNGQR */
|
|
/* > and ZUNGLQ. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. */
|
|
/* > Algorithms, 50(1):33-65, 2009. */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zunbdb2_(integer *m, integer *p, integer *q,
|
|
doublecomplex *x11, integer *ldx11, doublecomplex *x21, integer *
|
|
ldx21, doublereal *theta, doublereal *phi, doublecomplex *taup1,
|
|
doublecomplex *taup2, doublecomplex *tauq1, doublecomplex *work,
|
|
integer *lwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer x11_dim1, x11_offset, x21_dim1, x21_offset, i__1, i__2, i__3,
|
|
i__4;
|
|
doublereal d__1, d__2;
|
|
doublecomplex z__1;
|
|
|
|
/* Local variables */
|
|
integer lworkmin, lworkopt;
|
|
doublereal c__;
|
|
integer i__;
|
|
doublereal s;
|
|
integer ilarf, llarf;
|
|
extern /* Subroutine */ void zscal_(integer *, doublecomplex *,
|
|
doublecomplex *, integer *);
|
|
integer childinfo;
|
|
extern /* Subroutine */ void zlarf_(char *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *, doublecomplex *), zdrot_(integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublereal *, doublereal *);
|
|
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern void zlacgv_(
|
|
integer *, doublecomplex *, integer *);
|
|
logical lquery;
|
|
integer iorbdb5, lorbdb5;
|
|
extern /* Subroutine */ void zunbdb5_(integer *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, integer *), zlarfgp_(integer *,
|
|
doublecomplex *, doublecomplex *, integer *, doublecomplex *);
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.8.0) -- */
|
|
/* -- 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;
|
|
--phi;
|
|
--taup1;
|
|
--taup2;
|
|
--tauq1;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
lquery = *lwork == -1;
|
|
|
|
if (*m < 0) {
|
|
*info = -1;
|
|
} else if (*p < 0 || *p > *m - *p) {
|
|
*info = -2;
|
|
} else if (*q < 0 || *q < *p || *m - *q < *p) {
|
|
*info = -3;
|
|
} else if (*ldx11 < f2cmax(1,*p)) {
|
|
*info = -5;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *m - *p;
|
|
if (*ldx21 < f2cmax(i__1,i__2)) {
|
|
*info = -7;
|
|
}
|
|
}
|
|
|
|
/* Compute workspace */
|
|
|
|
if (*info == 0) {
|
|
ilarf = 2;
|
|
/* Computing MAX */
|
|
i__1 = *p - 1, i__2 = *m - *p, i__1 = f2cmax(i__1,i__2), i__2 = *q - 1;
|
|
llarf = f2cmax(i__1,i__2);
|
|
iorbdb5 = 2;
|
|
lorbdb5 = *q - 1;
|
|
/* Computing MAX */
|
|
i__1 = ilarf + llarf - 1, i__2 = iorbdb5 + lorbdb5 - 1;
|
|
lworkopt = f2cmax(i__1,i__2);
|
|
lworkmin = lworkopt;
|
|
work[1].r = (doublereal) lworkopt, work[1].i = 0.;
|
|
if (*lwork < lworkmin && ! lquery) {
|
|
*info = -14;
|
|
}
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZUNBDB2", &i__1, (ftnlen)7);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Reduce rows 1, ..., P of X11 and X21 */
|
|
|
|
i__1 = *p;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
|
|
if (i__ > 1) {
|
|
i__2 = *q - i__ + 1;
|
|
zdrot_(&i__2, &x11[i__ + i__ * x11_dim1], ldx11, &x21[i__ - 1 +
|
|
i__ * x21_dim1], ldx21, &c__, &s);
|
|
}
|
|
i__2 = *q - i__ + 1;
|
|
zlacgv_(&i__2, &x11[i__ + i__ * x11_dim1], ldx11);
|
|
i__2 = *q - i__ + 1;
|
|
zlarfgp_(&i__2, &x11[i__ + i__ * x11_dim1], &x11[i__ + (i__ + 1) *
|
|
x11_dim1], ldx11, &tauq1[i__]);
|
|
i__2 = i__ + i__ * x11_dim1;
|
|
c__ = x11[i__2].r;
|
|
i__2 = i__ + i__ * x11_dim1;
|
|
x11[i__2].r = 1., x11[i__2].i = 0.;
|
|
i__2 = *p - i__;
|
|
i__3 = *q - i__ + 1;
|
|
zlarf_("R", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], ldx11, &tauq1[
|
|
i__], &x11[i__ + 1 + i__ * x11_dim1], ldx11, &work[ilarf]);
|
|
i__2 = *m - *p - i__ + 1;
|
|
i__3 = *q - i__ + 1;
|
|
zlarf_("R", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], ldx11, &tauq1[
|
|
i__], &x21[i__ + i__ * x21_dim1], ldx21, &work[ilarf]);
|
|
i__2 = *q - i__ + 1;
|
|
zlacgv_(&i__2, &x11[i__ + i__ * x11_dim1], ldx11);
|
|
i__2 = *p - i__;
|
|
/* Computing 2nd power */
|
|
d__1 = dznrm2_(&i__2, &x11[i__ + 1 + i__ * x11_dim1], &c__1);
|
|
i__3 = *m - *p - i__ + 1;
|
|
/* Computing 2nd power */
|
|
d__2 = dznrm2_(&i__3, &x21[i__ + i__ * x21_dim1], &c__1);
|
|
s = sqrt(d__1 * d__1 + d__2 * d__2);
|
|
theta[i__] = atan2(s, c__);
|
|
|
|
i__2 = *p - i__;
|
|
i__3 = *m - *p - i__ + 1;
|
|
i__4 = *q - i__;
|
|
zunbdb5_(&i__2, &i__3, &i__4, &x11[i__ + 1 + i__ * x11_dim1], &c__1, &
|
|
x21[i__ + i__ * x21_dim1], &c__1, &x11[i__ + 1 + (i__ + 1) *
|
|
x11_dim1], ldx11, &x21[i__ + (i__ + 1) * x21_dim1], ldx21, &
|
|
work[iorbdb5], &lorbdb5, &childinfo);
|
|
i__2 = *p - i__;
|
|
zscal_(&i__2, &c_b1, &x11[i__ + 1 + i__ * x11_dim1], &c__1);
|
|
i__2 = *m - *p - i__ + 1;
|
|
zlarfgp_(&i__2, &x21[i__ + i__ * x21_dim1], &x21[i__ + 1 + i__ *
|
|
x21_dim1], &c__1, &taup2[i__]);
|
|
if (i__ < *p) {
|
|
i__2 = *p - i__;
|
|
zlarfgp_(&i__2, &x11[i__ + 1 + i__ * x11_dim1], &x11[i__ + 2 +
|
|
i__ * x11_dim1], &c__1, &taup1[i__]);
|
|
phi[i__] = atan2((doublereal) x11[i__ + 1 + i__ * x11_dim1].r, (
|
|
doublereal) x21[i__ + i__ * x21_dim1].r);
|
|
c__ = cos(phi[i__]);
|
|
s = sin(phi[i__]);
|
|
i__2 = i__ + 1 + i__ * x11_dim1;
|
|
x11[i__2].r = 1., x11[i__2].i = 0.;
|
|
i__2 = *p - i__;
|
|
i__3 = *q - i__;
|
|
d_cnjg(&z__1, &taup1[i__]);
|
|
zlarf_("L", &i__2, &i__3, &x11[i__ + 1 + i__ * x11_dim1], &c__1, &
|
|
z__1, &x11[i__ + 1 + (i__ + 1) * x11_dim1], ldx11, &work[
|
|
ilarf]);
|
|
}
|
|
i__2 = i__ + i__ * x21_dim1;
|
|
x21[i__2].r = 1., x21[i__2].i = 0.;
|
|
i__2 = *m - *p - i__ + 1;
|
|
i__3 = *q - i__;
|
|
d_cnjg(&z__1, &taup2[i__]);
|
|
zlarf_("L", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], &c__1, &z__1, &
|
|
x21[i__ + (i__ + 1) * x21_dim1], ldx21, &work[ilarf]);
|
|
|
|
}
|
|
|
|
/* Reduce the bottom-right portion of X21 to the identity matrix */
|
|
|
|
i__1 = *q;
|
|
for (i__ = *p + 1; i__ <= i__1; ++i__) {
|
|
i__2 = *m - *p - i__ + 1;
|
|
zlarfgp_(&i__2, &x21[i__ + i__ * x21_dim1], &x21[i__ + 1 + i__ *
|
|
x21_dim1], &c__1, &taup2[i__]);
|
|
i__2 = i__ + i__ * x21_dim1;
|
|
x21[i__2].r = 1., x21[i__2].i = 0.;
|
|
i__2 = *m - *p - i__ + 1;
|
|
i__3 = *q - i__;
|
|
d_cnjg(&z__1, &taup2[i__]);
|
|
zlarf_("L", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], &c__1, &z__1, &
|
|
x21[i__ + (i__ + 1) * x21_dim1], ldx21, &work[ilarf]);
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZUNBDB2 */
|
|
|
|
} /* zunbdb2_ */
|
|
|