1766 lines
53 KiB
C
1766 lines
53 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublecomplex c_b1 = {1.,0.};
|
|
static doublecomplex c_b2 = {0.,0.};
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
static integer c__2 = 2;
|
|
static integer c__3 = 3;
|
|
static integer c__16 = 16;
|
|
|
|
/* > \brief \b ZGGHD3 */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZGGHD3 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgghd3.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgghd3.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgghd3.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZGGHD3( COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, */
|
|
/* LDQ, Z, LDZ, WORK, LWORK, INFO ) */
|
|
|
|
/* CHARACTER COMPQ, COMPZ */
|
|
/* INTEGER IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, N, LWORK */
|
|
/* COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), */
|
|
/* $ Z( LDZ, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZGGHD3 reduces a pair of complex matrices (A,B) to generalized upper */
|
|
/* > Hessenberg form using unitary transformations, where A is a */
|
|
/* > general matrix and B is upper triangular. The form of the */
|
|
/* > generalized eigenvalue problem is */
|
|
/* > A*x = lambda*B*x, */
|
|
/* > and B is typically made upper triangular by computing its QR */
|
|
/* > factorization and moving the unitary matrix Q to the left side */
|
|
/* > of the equation. */
|
|
/* > */
|
|
/* > This subroutine simultaneously reduces A to a Hessenberg matrix H: */
|
|
/* > Q**H*A*Z = H */
|
|
/* > and transforms B to another upper triangular matrix T: */
|
|
/* > Q**H*B*Z = T */
|
|
/* > in order to reduce the problem to its standard form */
|
|
/* > H*y = lambda*T*y */
|
|
/* > where y = Z**H*x. */
|
|
/* > */
|
|
/* > The unitary matrices Q and Z are determined as products of Givens */
|
|
/* > rotations. They may either be formed explicitly, or they may be */
|
|
/* > postmultiplied into input matrices Q1 and Z1, so that */
|
|
/* > Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H */
|
|
/* > Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H */
|
|
/* > If Q1 is the unitary matrix from the QR factorization of B in the */
|
|
/* > original equation A*x = lambda*B*x, then ZGGHD3 reduces the original */
|
|
/* > problem to generalized Hessenberg form. */
|
|
/* > */
|
|
/* > This is a blocked variant of CGGHRD, using matrix-matrix */
|
|
/* > multiplications for parts of the computation to enhance performance. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] COMPQ */
|
|
/* > \verbatim */
|
|
/* > COMPQ is CHARACTER*1 */
|
|
/* > = 'N': do not compute Q; */
|
|
/* > = 'I': Q is initialized to the unit matrix, and the */
|
|
/* > unitary matrix Q is returned; */
|
|
/* > = 'V': Q must contain a unitary matrix Q1 on entry, */
|
|
/* > and the product Q1*Q is returned. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] COMPZ */
|
|
/* > \verbatim */
|
|
/* > COMPZ is CHARACTER*1 */
|
|
/* > = 'N': do not compute Z; */
|
|
/* > = 'I': Z is initialized to the unit matrix, and the */
|
|
/* > unitary matrix Z is returned; */
|
|
/* > = 'V': Z must contain a unitary matrix Z1 on entry, */
|
|
/* > and the product Z1*Z is returned. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrices A and B. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ILO */
|
|
/* > \verbatim */
|
|
/* > ILO is INTEGER */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IHI */
|
|
/* > \verbatim */
|
|
/* > IHI is INTEGER */
|
|
/* > */
|
|
/* > ILO and IHI mark the rows and columns of A which are to be */
|
|
/* > reduced. It is assumed that A is already upper triangular */
|
|
/* > in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are */
|
|
/* > normally set by a previous call to ZGGBAL; otherwise they */
|
|
/* > should be set to 1 and N respectively. */
|
|
/* > 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX*16 array, dimension (LDA, N) */
|
|
/* > On entry, the N-by-N general matrix to be reduced. */
|
|
/* > On exit, the upper triangle and the first subdiagonal of A */
|
|
/* > are overwritten with the upper Hessenberg matrix H, and the */
|
|
/* > rest is set to zero. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX*16 array, dimension (LDB, N) */
|
|
/* > On entry, the N-by-N upper triangular matrix B. */
|
|
/* > On exit, the upper triangular matrix T = Q**H B Z. The */
|
|
/* > elements below the diagonal are set to zero. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is COMPLEX*16 array, dimension (LDQ, N) */
|
|
/* > On entry, if COMPQ = 'V', the unitary matrix Q1, typically */
|
|
/* > from the QR factorization of B. */
|
|
/* > On exit, if COMPQ='I', the unitary matrix Q, and if */
|
|
/* > COMPQ = 'V', the product Q1*Q. */
|
|
/* > Not referenced if COMPQ='N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. */
|
|
/* > LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is COMPLEX*16 array, dimension (LDZ, N) */
|
|
/* > On entry, if COMPZ = 'V', the unitary matrix Z1. */
|
|
/* > On exit, if COMPZ='I', the unitary matrix Z, and if */
|
|
/* > COMPZ = 'V', the product Z1*Z. */
|
|
/* > Not referenced if COMPZ='N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. */
|
|
/* > LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (LWORK) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The length of the array WORK. LWORK >= 1. */
|
|
/* > For optimum performance LWORK >= 6*N*NB, where NB is the */
|
|
/* > optimal blocksize. */
|
|
/* > */
|
|
/* > 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 January 2015 */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > This routine reduces A to Hessenberg form and maintains B in */
|
|
/* > using a blocked variant of Moler and Stewart's original algorithm, */
|
|
/* > as described by Kagstrom, Kressner, Quintana-Orti, and Quintana-Orti */
|
|
/* > (BIT 2008). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zgghd3_(char *compq, char *compz, integer *n, integer *
|
|
ilo, integer *ihi, doublecomplex *a, integer *lda, doublecomplex *b,
|
|
integer *ldb, doublecomplex *q, integer *ldq, doublecomplex *z__,
|
|
integer *ldz, doublecomplex *work, integer *lwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1,
|
|
z_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9;
|
|
doublecomplex z__1, z__2, z__3, z__4;
|
|
|
|
/* Local variables */
|
|
logical blk22;
|
|
integer cola, jcol, ierr;
|
|
doublecomplex temp;
|
|
integer jrow, topq, ppwo;
|
|
extern /* Subroutine */ void zrot_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublereal *, doublecomplex *);
|
|
doublecomplex temp1, temp2, temp3;
|
|
doublereal c__;
|
|
integer kacc22, i__, j, k;
|
|
doublecomplex s;
|
|
extern logical lsame_(char *, char *);
|
|
integer nbmin;
|
|
doublecomplex ctemp;
|
|
extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *);
|
|
integer nblst;
|
|
logical initq;
|
|
doublecomplex c1, c2;
|
|
extern /* Subroutine */ void zgemv_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *);
|
|
logical wantq;
|
|
integer j0;
|
|
logical initz;
|
|
extern /* Subroutine */ void zunm22_(char *, char *, integer *, integer *,
|
|
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, integer *, integer *)
|
|
;
|
|
logical wantz;
|
|
doublecomplex s1, s2;
|
|
extern /* Subroutine */ void ztrmv_(char *, char *, char *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *);
|
|
char compq2[1], compz2[1];
|
|
integer nb, jj, nh, nx, pw;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern /* Subroutine */ void zgghrd_(char *, char *, integer *, integer *,
|
|
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *, integer *
|
|
), zlaset_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlartg_(doublecomplex *, doublecomplex *, doublereal *,
|
|
doublecomplex *, doublecomplex *), zlacpy_(char *, integer *,
|
|
integer *, doublecomplex *, integer *, doublecomplex *, integer *);
|
|
integer lwkopt;
|
|
logical lquery;
|
|
integer nnb, len, top, ppw, n2nb;
|
|
|
|
|
|
/* -- 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..-- */
|
|
/* January 2015 */
|
|
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Decode and test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
z_dim1 = *ldz;
|
|
z_offset = 1 + z_dim1 * 1;
|
|
z__ -= z_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
nb = ilaenv_(&c__1, "ZGGHD3", " ", n, ilo, ihi, &c_n1, (ftnlen)6, (ftnlen)
|
|
1);
|
|
/* Computing MAX */
|
|
i__1 = *n * 6 * nb;
|
|
lwkopt = f2cmax(i__1,1);
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
initq = lsame_(compq, "I");
|
|
wantq = initq || lsame_(compq, "V");
|
|
initz = lsame_(compz, "I");
|
|
wantz = initz || lsame_(compz, "V");
|
|
lquery = *lwork == -1;
|
|
|
|
if (! lsame_(compq, "N") && ! wantq) {
|
|
*info = -1;
|
|
} else if (! lsame_(compz, "N") && ! wantz) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*ilo < 1) {
|
|
*info = -4;
|
|
} else if (*ihi > *n || *ihi < *ilo - 1) {
|
|
*info = -5;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -7;
|
|
} else if (*ldb < f2cmax(1,*n)) {
|
|
*info = -9;
|
|
} else if (wantq && *ldq < *n || *ldq < 1) {
|
|
*info = -11;
|
|
} else if (wantz && *ldz < *n || *ldz < 1) {
|
|
*info = -13;
|
|
} else if (*lwork < 1 && ! lquery) {
|
|
*info = -15;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZGGHD3", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Initialize Q and Z if desired. */
|
|
|
|
if (initq) {
|
|
zlaset_("All", n, n, &c_b2, &c_b1, &q[q_offset], ldq);
|
|
}
|
|
if (initz) {
|
|
zlaset_("All", n, n, &c_b2, &c_b1, &z__[z_offset], ldz);
|
|
}
|
|
|
|
/* Zero out lower triangle of B. */
|
|
|
|
if (*n > 1) {
|
|
i__1 = *n - 1;
|
|
i__2 = *n - 1;
|
|
zlaset_("Lower", &i__1, &i__2, &c_b2, &c_b2, &b[b_dim1 + 2], ldb);
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
nh = *ihi - *ilo + 1;
|
|
if (nh <= 1) {
|
|
work[1].r = 1., work[1].i = 0.;
|
|
return;
|
|
}
|
|
|
|
/* Determine the blocksize. */
|
|
|
|
nbmin = ilaenv_(&c__2, "ZGGHD3", " ", n, ilo, ihi, &c_n1, (ftnlen)6, (
|
|
ftnlen)1);
|
|
if (nb > 1 && nb < nh) {
|
|
|
|
/* Determine when to use unblocked instead of blocked code. */
|
|
|
|
/* Computing MAX */
|
|
i__1 = nb, i__2 = ilaenv_(&c__3, "ZGGHD3", " ", n, ilo, ihi, &c_n1, (
|
|
ftnlen)6, (ftnlen)1);
|
|
nx = f2cmax(i__1,i__2);
|
|
if (nx < nh) {
|
|
|
|
/* Determine if workspace is large enough for blocked code. */
|
|
|
|
if (*lwork < lwkopt) {
|
|
|
|
/* Not enough workspace to use optimal NB: determine the */
|
|
/* minimum value of NB, and reduce NB or force use of */
|
|
/* unblocked code. */
|
|
|
|
/* Computing MAX */
|
|
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGGHD3", " ", n, ilo, ihi, &
|
|
c_n1, (ftnlen)6, (ftnlen)1);
|
|
nbmin = f2cmax(i__1,i__2);
|
|
if (*lwork >= *n * 6 * nbmin) {
|
|
nb = *lwork / (*n * 6);
|
|
} else {
|
|
nb = 1;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if (nb < nbmin || nb >= nh) {
|
|
|
|
/* Use unblocked code below */
|
|
|
|
jcol = *ilo;
|
|
|
|
} else {
|
|
|
|
/* Use blocked code */
|
|
|
|
kacc22 = ilaenv_(&c__16, "ZGGHD3", " ", n, ilo, ihi, &c_n1, (ftnlen)6,
|
|
(ftnlen)1);
|
|
blk22 = kacc22 == 2;
|
|
i__1 = *ihi - 2;
|
|
i__2 = nb;
|
|
for (jcol = *ilo; i__2 < 0 ? jcol >= i__1 : jcol <= i__1; jcol +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = nb, i__4 = *ihi - jcol - 1;
|
|
nnb = f2cmin(i__3,i__4);
|
|
|
|
/* Initialize small unitary factors that will hold the */
|
|
/* accumulated Givens rotations in workspace. */
|
|
/* N2NB denotes the number of 2*NNB-by-2*NNB factors */
|
|
/* NBLST denotes the (possibly smaller) order of the last */
|
|
/* factor. */
|
|
|
|
n2nb = (*ihi - jcol - 1) / nnb - 1;
|
|
nblst = *ihi - jcol - n2nb * nnb;
|
|
zlaset_("All", &nblst, &nblst, &c_b2, &c_b1, &work[1], &nblst);
|
|
pw = nblst * nblst + 1;
|
|
i__3 = n2nb;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
i__4 = nnb << 1;
|
|
i__5 = nnb << 1;
|
|
i__6 = nnb << 1;
|
|
zlaset_("All", &i__4, &i__5, &c_b2, &c_b1, &work[pw], &i__6);
|
|
pw += (nnb << 2) * nnb;
|
|
}
|
|
|
|
/* Reduce columns JCOL:JCOL+NNB-1 of A to Hessenberg form. */
|
|
|
|
i__3 = jcol + nnb - 1;
|
|
for (j = jcol; j <= i__3; ++j) {
|
|
|
|
/* Reduce Jth column of A. Store cosines and sines in Jth */
|
|
/* column of A and B, respectively. */
|
|
|
|
i__4 = j + 2;
|
|
for (i__ = *ihi; i__ >= i__4; --i__) {
|
|
i__5 = i__ - 1 + j * a_dim1;
|
|
temp.r = a[i__5].r, temp.i = a[i__5].i;
|
|
zlartg_(&temp, &a[i__ + j * a_dim1], &c__, &s, &a[i__ - 1
|
|
+ j * a_dim1]);
|
|
i__5 = i__ + j * a_dim1;
|
|
z__1.r = c__, z__1.i = 0.;
|
|
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
|
|
i__5 = i__ + j * b_dim1;
|
|
b[i__5].r = s.r, b[i__5].i = s.i;
|
|
}
|
|
|
|
/* Accumulate Givens rotations into workspace array. */
|
|
|
|
ppw = (nblst + 1) * (nblst - 2) - j + jcol + 1;
|
|
len = j + 2 - jcol;
|
|
jrow = j + n2nb * nnb + 2;
|
|
i__4 = jrow;
|
|
for (i__ = *ihi; i__ >= i__4; --i__) {
|
|
i__5 = i__ + j * a_dim1;
|
|
ctemp.r = a[i__5].r, ctemp.i = a[i__5].i;
|
|
i__5 = i__ + j * b_dim1;
|
|
s.r = b[i__5].r, s.i = b[i__5].i;
|
|
i__5 = ppw + len - 1;
|
|
for (jj = ppw; jj <= i__5; ++jj) {
|
|
i__6 = jj + nblst;
|
|
temp.r = work[i__6].r, temp.i = work[i__6].i;
|
|
i__6 = jj + nblst;
|
|
z__2.r = ctemp.r * temp.r - ctemp.i * temp.i, z__2.i =
|
|
ctemp.r * temp.i + ctemp.i * temp.r;
|
|
i__7 = jj;
|
|
z__3.r = s.r * work[i__7].r - s.i * work[i__7].i,
|
|
z__3.i = s.r * work[i__7].i + s.i * work[i__7]
|
|
.r;
|
|
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
|
|
work[i__6].r = z__1.r, work[i__6].i = z__1.i;
|
|
i__6 = jj;
|
|
d_cnjg(&z__3, &s);
|
|
z__2.r = z__3.r * temp.r - z__3.i * temp.i, z__2.i =
|
|
z__3.r * temp.i + z__3.i * temp.r;
|
|
i__7 = jj;
|
|
z__4.r = ctemp.r * work[i__7].r - ctemp.i * work[i__7]
|
|
.i, z__4.i = ctemp.r * work[i__7].i + ctemp.i
|
|
* work[i__7].r;
|
|
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
|
|
work[i__6].r = z__1.r, work[i__6].i = z__1.i;
|
|
}
|
|
++len;
|
|
ppw = ppw - nblst - 1;
|
|
}
|
|
|
|
ppwo = nblst * nblst + (nnb + j - jcol - 1 << 1) * nnb + nnb;
|
|
j0 = jrow - nnb;
|
|
i__4 = j + 2;
|
|
i__5 = -nnb;
|
|
for (jrow = j0; i__5 < 0 ? jrow >= i__4 : jrow <= i__4; jrow
|
|
+= i__5) {
|
|
ppw = ppwo;
|
|
len = j + 2 - jcol;
|
|
i__6 = jrow;
|
|
for (i__ = jrow + nnb - 1; i__ >= i__6; --i__) {
|
|
i__7 = i__ + j * a_dim1;
|
|
ctemp.r = a[i__7].r, ctemp.i = a[i__7].i;
|
|
i__7 = i__ + j * b_dim1;
|
|
s.r = b[i__7].r, s.i = b[i__7].i;
|
|
i__7 = ppw + len - 1;
|
|
for (jj = ppw; jj <= i__7; ++jj) {
|
|
i__8 = jj + (nnb << 1);
|
|
temp.r = work[i__8].r, temp.i = work[i__8].i;
|
|
i__8 = jj + (nnb << 1);
|
|
z__2.r = ctemp.r * temp.r - ctemp.i * temp.i,
|
|
z__2.i = ctemp.r * temp.i + ctemp.i *
|
|
temp.r;
|
|
i__9 = jj;
|
|
z__3.r = s.r * work[i__9].r - s.i * work[i__9].i,
|
|
z__3.i = s.r * work[i__9].i + s.i * work[
|
|
i__9].r;
|
|
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
|
|
z__3.i;
|
|
work[i__8].r = z__1.r, work[i__8].i = z__1.i;
|
|
i__8 = jj;
|
|
d_cnjg(&z__3, &s);
|
|
z__2.r = z__3.r * temp.r - z__3.i * temp.i,
|
|
z__2.i = z__3.r * temp.i + z__3.i *
|
|
temp.r;
|
|
i__9 = jj;
|
|
z__4.r = ctemp.r * work[i__9].r - ctemp.i * work[
|
|
i__9].i, z__4.i = ctemp.r * work[i__9].i
|
|
+ ctemp.i * work[i__9].r;
|
|
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i +
|
|
z__4.i;
|
|
work[i__8].r = z__1.r, work[i__8].i = z__1.i;
|
|
}
|
|
++len;
|
|
ppw = ppw - (nnb << 1) - 1;
|
|
}
|
|
ppwo += (nnb << 2) * nnb;
|
|
}
|
|
|
|
/* TOP denotes the number of top rows in A and B that will */
|
|
/* not be updated during the next steps. */
|
|
|
|
if (jcol <= 2) {
|
|
top = 0;
|
|
} else {
|
|
top = jcol;
|
|
}
|
|
|
|
/* Propagate transformations through B and replace stored */
|
|
/* left sines/cosines by right sines/cosines. */
|
|
|
|
i__5 = j + 1;
|
|
for (jj = *n; jj >= i__5; --jj) {
|
|
|
|
/* Update JJth column of B. */
|
|
|
|
/* Computing MIN */
|
|
i__4 = jj + 1;
|
|
i__6 = j + 2;
|
|
for (i__ = f2cmin(i__4,*ihi); i__ >= i__6; --i__) {
|
|
i__4 = i__ + j * a_dim1;
|
|
ctemp.r = a[i__4].r, ctemp.i = a[i__4].i;
|
|
i__4 = i__ + j * b_dim1;
|
|
s.r = b[i__4].r, s.i = b[i__4].i;
|
|
i__4 = i__ + jj * b_dim1;
|
|
temp.r = b[i__4].r, temp.i = b[i__4].i;
|
|
i__4 = i__ + jj * b_dim1;
|
|
z__2.r = ctemp.r * temp.r - ctemp.i * temp.i, z__2.i =
|
|
ctemp.r * temp.i + ctemp.i * temp.r;
|
|
d_cnjg(&z__4, &s);
|
|
i__7 = i__ - 1 + jj * b_dim1;
|
|
z__3.r = z__4.r * b[i__7].r - z__4.i * b[i__7].i,
|
|
z__3.i = z__4.r * b[i__7].i + z__4.i * b[i__7]
|
|
.r;
|
|
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
|
|
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
|
|
i__4 = i__ - 1 + jj * b_dim1;
|
|
z__2.r = s.r * temp.r - s.i * temp.i, z__2.i = s.r *
|
|
temp.i + s.i * temp.r;
|
|
i__7 = i__ - 1 + jj * b_dim1;
|
|
z__3.r = ctemp.r * b[i__7].r - ctemp.i * b[i__7].i,
|
|
z__3.i = ctemp.r * b[i__7].i + ctemp.i * b[
|
|
i__7].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
|
|
}
|
|
|
|
/* Annihilate B( JJ+1, JJ ). */
|
|
|
|
if (jj < *ihi) {
|
|
i__6 = jj + 1 + (jj + 1) * b_dim1;
|
|
temp.r = b[i__6].r, temp.i = b[i__6].i;
|
|
zlartg_(&temp, &b[jj + 1 + jj * b_dim1], &c__, &s, &b[
|
|
jj + 1 + (jj + 1) * b_dim1]);
|
|
i__6 = jj + 1 + jj * b_dim1;
|
|
b[i__6].r = 0., b[i__6].i = 0.;
|
|
i__6 = jj - top;
|
|
zrot_(&i__6, &b[top + 1 + (jj + 1) * b_dim1], &c__1, &
|
|
b[top + 1 + jj * b_dim1], &c__1, &c__, &s);
|
|
i__6 = jj + 1 + j * a_dim1;
|
|
z__1.r = c__, z__1.i = 0.;
|
|
a[i__6].r = z__1.r, a[i__6].i = z__1.i;
|
|
i__6 = jj + 1 + j * b_dim1;
|
|
d_cnjg(&z__2, &s);
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
b[i__6].r = z__1.r, b[i__6].i = z__1.i;
|
|
}
|
|
}
|
|
|
|
/* Update A by transformations from right. */
|
|
|
|
jj = (*ihi - j - 1) % 3;
|
|
i__5 = jj + 1;
|
|
for (i__ = *ihi - j - 3; i__ >= i__5; i__ += -3) {
|
|
i__6 = j + 1 + i__ + j * a_dim1;
|
|
ctemp.r = a[i__6].r, ctemp.i = a[i__6].i;
|
|
i__6 = j + 1 + i__ + j * b_dim1;
|
|
z__1.r = -b[i__6].r, z__1.i = -b[i__6].i;
|
|
s.r = z__1.r, s.i = z__1.i;
|
|
i__6 = j + 2 + i__ + j * a_dim1;
|
|
c1.r = a[i__6].r, c1.i = a[i__6].i;
|
|
i__6 = j + 2 + i__ + j * b_dim1;
|
|
z__1.r = -b[i__6].r, z__1.i = -b[i__6].i;
|
|
s1.r = z__1.r, s1.i = z__1.i;
|
|
i__6 = j + 3 + i__ + j * a_dim1;
|
|
c2.r = a[i__6].r, c2.i = a[i__6].i;
|
|
i__6 = j + 3 + i__ + j * b_dim1;
|
|
z__1.r = -b[i__6].r, z__1.i = -b[i__6].i;
|
|
s2.r = z__1.r, s2.i = z__1.i;
|
|
|
|
i__6 = *ihi;
|
|
for (k = top + 1; k <= i__6; ++k) {
|
|
i__4 = k + (j + i__) * a_dim1;
|
|
temp.r = a[i__4].r, temp.i = a[i__4].i;
|
|
i__4 = k + (j + i__ + 1) * a_dim1;
|
|
temp1.r = a[i__4].r, temp1.i = a[i__4].i;
|
|
i__4 = k + (j + i__ + 2) * a_dim1;
|
|
temp2.r = a[i__4].r, temp2.i = a[i__4].i;
|
|
i__4 = k + (j + i__ + 3) * a_dim1;
|
|
temp3.r = a[i__4].r, temp3.i = a[i__4].i;
|
|
i__4 = k + (j + i__ + 3) * a_dim1;
|
|
z__2.r = c2.r * temp3.r - c2.i * temp3.i, z__2.i =
|
|
c2.r * temp3.i + c2.i * temp3.r;
|
|
d_cnjg(&z__4, &s2);
|
|
z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i =
|
|
z__4.r * temp2.i + z__4.i * temp2.r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
a[i__4].r = z__1.r, a[i__4].i = z__1.i;
|
|
z__3.r = -s2.r, z__3.i = -s2.i;
|
|
z__2.r = z__3.r * temp3.r - z__3.i * temp3.i, z__2.i =
|
|
z__3.r * temp3.i + z__3.i * temp3.r;
|
|
z__4.r = c2.r * temp2.r - c2.i * temp2.i, z__4.i =
|
|
c2.r * temp2.i + c2.i * temp2.r;
|
|
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
|
|
temp2.r = z__1.r, temp2.i = z__1.i;
|
|
i__4 = k + (j + i__ + 2) * a_dim1;
|
|
z__2.r = c1.r * temp2.r - c1.i * temp2.i, z__2.i =
|
|
c1.r * temp2.i + c1.i * temp2.r;
|
|
d_cnjg(&z__4, &s1);
|
|
z__3.r = z__4.r * temp1.r - z__4.i * temp1.i, z__3.i =
|
|
z__4.r * temp1.i + z__4.i * temp1.r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
a[i__4].r = z__1.r, a[i__4].i = z__1.i;
|
|
z__3.r = -s1.r, z__3.i = -s1.i;
|
|
z__2.r = z__3.r * temp2.r - z__3.i * temp2.i, z__2.i =
|
|
z__3.r * temp2.i + z__3.i * temp2.r;
|
|
z__4.r = c1.r * temp1.r - c1.i * temp1.i, z__4.i =
|
|
c1.r * temp1.i + c1.i * temp1.r;
|
|
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
|
|
temp1.r = z__1.r, temp1.i = z__1.i;
|
|
i__4 = k + (j + i__ + 1) * a_dim1;
|
|
z__2.r = ctemp.r * temp1.r - ctemp.i * temp1.i,
|
|
z__2.i = ctemp.r * temp1.i + ctemp.i *
|
|
temp1.r;
|
|
d_cnjg(&z__4, &s);
|
|
z__3.r = z__4.r * temp.r - z__4.i * temp.i, z__3.i =
|
|
z__4.r * temp.i + z__4.i * temp.r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
|
|
a[i__4].r = z__1.r, a[i__4].i = z__1.i;
|
|
i__4 = k + (j + i__) * a_dim1;
|
|
z__3.r = -s.r, z__3.i = -s.i;
|
|
z__2.r = z__3.r * temp1.r - z__3.i * temp1.i, z__2.i =
|
|
z__3.r * temp1.i + z__3.i * temp1.r;
|
|
z__4.r = ctemp.r * temp.r - ctemp.i * temp.i, z__4.i =
|
|
ctemp.r * temp.i + ctemp.i * temp.r;
|
|
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
|
|
a[i__4].r = z__1.r, a[i__4].i = z__1.i;
|
|
}
|
|
}
|
|
|
|
if (jj > 0) {
|
|
for (i__ = jj; i__ >= 1; --i__) {
|
|
i__5 = j + 1 + i__ + j * a_dim1;
|
|
c__ = a[i__5].r;
|
|
i__5 = *ihi - top;
|
|
d_cnjg(&z__2, &b[j + 1 + i__ + j * b_dim1]);
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
zrot_(&i__5, &a[top + 1 + (j + i__ + 1) * a_dim1], &
|
|
c__1, &a[top + 1 + (j + i__) * a_dim1], &c__1,
|
|
&c__, &z__1);
|
|
}
|
|
}
|
|
|
|
/* Update (J+1)th column of A by transformations from left. */
|
|
|
|
if (j < jcol + nnb - 1) {
|
|
len = j + 1 - jcol;
|
|
|
|
/* Multiply with the trailing accumulated unitary */
|
|
/* matrix, which takes the form */
|
|
|
|
/* [ U11 U12 ] */
|
|
/* U = [ ], */
|
|
/* [ U21 U22 ] */
|
|
|
|
/* where U21 is a LEN-by-LEN matrix and U12 is lower */
|
|
/* triangular. */
|
|
|
|
jrow = *ihi - nblst + 1;
|
|
zgemv_("Conjugate", &nblst, &len, &c_b1, &work[1], &nblst,
|
|
&a[jrow + (j + 1) * a_dim1], &c__1, &c_b2, &work[
|
|
pw], &c__1);
|
|
ppw = pw + len;
|
|
i__5 = jrow + nblst - len - 1;
|
|
for (i__ = jrow; i__ <= i__5; ++i__) {
|
|
i__6 = ppw;
|
|
i__4 = i__ + (j + 1) * a_dim1;
|
|
work[i__6].r = a[i__4].r, work[i__6].i = a[i__4].i;
|
|
++ppw;
|
|
}
|
|
i__5 = nblst - len;
|
|
ztrmv_("Lower", "Conjugate", "Non-unit", &i__5, &work[len
|
|
* nblst + 1], &nblst, &work[pw + len], &c__1);
|
|
i__5 = nblst - len;
|
|
zgemv_("Conjugate", &len, &i__5, &c_b1, &work[(len + 1) *
|
|
nblst - len + 1], &nblst, &a[jrow + nblst - len +
|
|
(j + 1) * a_dim1], &c__1, &c_b1, &work[pw + len],
|
|
&c__1);
|
|
ppw = pw;
|
|
i__5 = jrow + nblst - 1;
|
|
for (i__ = jrow; i__ <= i__5; ++i__) {
|
|
i__6 = i__ + (j + 1) * a_dim1;
|
|
i__4 = ppw;
|
|
a[i__6].r = work[i__4].r, a[i__6].i = work[i__4].i;
|
|
++ppw;
|
|
}
|
|
|
|
/* Multiply with the other accumulated unitary */
|
|
/* matrices, which take the form */
|
|
|
|
/* [ U11 U12 0 ] */
|
|
/* [ ] */
|
|
/* U = [ U21 U22 0 ], */
|
|
/* [ ] */
|
|
/* [ 0 0 I ] */
|
|
|
|
/* where I denotes the (NNB-LEN)-by-(NNB-LEN) identity */
|
|
/* matrix, U21 is a LEN-by-LEN upper triangular matrix */
|
|
/* and U12 is an NNB-by-NNB lower triangular matrix. */
|
|
|
|
ppwo = nblst * nblst + 1;
|
|
j0 = jrow - nnb;
|
|
i__5 = jcol + 1;
|
|
i__6 = -nnb;
|
|
for (jrow = j0; i__6 < 0 ? jrow >= i__5 : jrow <= i__5;
|
|
jrow += i__6) {
|
|
ppw = pw + len;
|
|
i__4 = jrow + nnb - 1;
|
|
for (i__ = jrow; i__ <= i__4; ++i__) {
|
|
i__7 = ppw;
|
|
i__8 = i__ + (j + 1) * a_dim1;
|
|
work[i__7].r = a[i__8].r, work[i__7].i = a[i__8]
|
|
.i;
|
|
++ppw;
|
|
}
|
|
ppw = pw;
|
|
i__4 = jrow + nnb + len - 1;
|
|
for (i__ = jrow + nnb; i__ <= i__4; ++i__) {
|
|
i__7 = ppw;
|
|
i__8 = i__ + (j + 1) * a_dim1;
|
|
work[i__7].r = a[i__8].r, work[i__7].i = a[i__8]
|
|
.i;
|
|
++ppw;
|
|
}
|
|
i__4 = nnb << 1;
|
|
ztrmv_("Upper", "Conjugate", "Non-unit", &len, &work[
|
|
ppwo + nnb], &i__4, &work[pw], &c__1);
|
|
i__4 = nnb << 1;
|
|
ztrmv_("Lower", "Conjugate", "Non-unit", &nnb, &work[
|
|
ppwo + (len << 1) * nnb], &i__4, &work[pw +
|
|
len], &c__1);
|
|
i__4 = nnb << 1;
|
|
zgemv_("Conjugate", &nnb, &len, &c_b1, &work[ppwo], &
|
|
i__4, &a[jrow + (j + 1) * a_dim1], &c__1, &
|
|
c_b1, &work[pw], &c__1);
|
|
i__4 = nnb << 1;
|
|
zgemv_("Conjugate", &len, &nnb, &c_b1, &work[ppwo + (
|
|
len << 1) * nnb + nnb], &i__4, &a[jrow + nnb
|
|
+ (j + 1) * a_dim1], &c__1, &c_b1, &work[pw +
|
|
len], &c__1);
|
|
ppw = pw;
|
|
i__4 = jrow + len + nnb - 1;
|
|
for (i__ = jrow; i__ <= i__4; ++i__) {
|
|
i__7 = i__ + (j + 1) * a_dim1;
|
|
i__8 = ppw;
|
|
a[i__7].r = work[i__8].r, a[i__7].i = work[i__8]
|
|
.i;
|
|
++ppw;
|
|
}
|
|
ppwo += (nnb << 2) * nnb;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Apply accumulated unitary matrices to A. */
|
|
|
|
cola = *n - jcol - nnb + 1;
|
|
j = *ihi - nblst + 1;
|
|
zgemm_("Conjugate", "No Transpose", &nblst, &cola, &nblst, &c_b1,
|
|
&work[1], &nblst, &a[j + (jcol + nnb) * a_dim1], lda, &
|
|
c_b2, &work[pw], &nblst);
|
|
zlacpy_("All", &nblst, &cola, &work[pw], &nblst, &a[j + (jcol +
|
|
nnb) * a_dim1], lda);
|
|
ppwo = nblst * nblst + 1;
|
|
j0 = j - nnb;
|
|
i__3 = jcol + 1;
|
|
i__6 = -nnb;
|
|
for (j = j0; i__6 < 0 ? j >= i__3 : j <= i__3; j += i__6) {
|
|
if (blk22) {
|
|
|
|
/* Exploit the structure of */
|
|
|
|
/* [ U11 U12 ] */
|
|
/* U = [ ] */
|
|
/* [ U21 U22 ], */
|
|
|
|
/* where all blocks are NNB-by-NNB, U21 is upper */
|
|
/* triangular and U12 is lower triangular. */
|
|
|
|
i__5 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
i__7 = *lwork - pw + 1;
|
|
zunm22_("Left", "Conjugate", &i__5, &cola, &nnb, &nnb, &
|
|
work[ppwo], &i__4, &a[j + (jcol + nnb) * a_dim1],
|
|
lda, &work[pw], &i__7, &ierr);
|
|
} else {
|
|
|
|
/* Ignore the structure of U. */
|
|
|
|
i__5 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
i__7 = nnb << 1;
|
|
i__8 = nnb << 1;
|
|
zgemm_("Conjugate", "No Transpose", &i__5, &cola, &i__4, &
|
|
c_b1, &work[ppwo], &i__7, &a[j + (jcol + nnb) *
|
|
a_dim1], lda, &c_b2, &work[pw], &i__8);
|
|
i__5 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
zlacpy_("All", &i__5, &cola, &work[pw], &i__4, &a[j + (
|
|
jcol + nnb) * a_dim1], lda);
|
|
}
|
|
ppwo += (nnb << 2) * nnb;
|
|
}
|
|
|
|
/* Apply accumulated unitary matrices to Q. */
|
|
|
|
if (wantq) {
|
|
j = *ihi - nblst + 1;
|
|
if (initq) {
|
|
/* Computing MAX */
|
|
i__6 = 2, i__3 = j - jcol + 1;
|
|
topq = f2cmax(i__6,i__3);
|
|
nh = *ihi - topq + 1;
|
|
} else {
|
|
topq = 1;
|
|
nh = *n;
|
|
}
|
|
zgemm_("No Transpose", "No Transpose", &nh, &nblst, &nblst, &
|
|
c_b1, &q[topq + j * q_dim1], ldq, &work[1], &nblst, &
|
|
c_b2, &work[pw], &nh);
|
|
zlacpy_("All", &nh, &nblst, &work[pw], &nh, &q[topq + j *
|
|
q_dim1], ldq);
|
|
ppwo = nblst * nblst + 1;
|
|
j0 = j - nnb;
|
|
i__6 = jcol + 1;
|
|
i__3 = -nnb;
|
|
for (j = j0; i__3 < 0 ? j >= i__6 : j <= i__6; j += i__3) {
|
|
if (initq) {
|
|
/* Computing MAX */
|
|
i__5 = 2, i__4 = j - jcol + 1;
|
|
topq = f2cmax(i__5,i__4);
|
|
nh = *ihi - topq + 1;
|
|
}
|
|
if (blk22) {
|
|
|
|
/* Exploit the structure of U. */
|
|
|
|
i__5 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
i__7 = *lwork - pw + 1;
|
|
zunm22_("Right", "No Transpose", &nh, &i__5, &nnb, &
|
|
nnb, &work[ppwo], &i__4, &q[topq + j * q_dim1]
|
|
, ldq, &work[pw], &i__7, &ierr);
|
|
} else {
|
|
|
|
/* Ignore the structure of U. */
|
|
|
|
i__5 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
i__7 = nnb << 1;
|
|
zgemm_("No Transpose", "No Transpose", &nh, &i__5, &
|
|
i__4, &c_b1, &q[topq + j * q_dim1], ldq, &
|
|
work[ppwo], &i__7, &c_b2, &work[pw], &nh);
|
|
i__5 = nnb << 1;
|
|
zlacpy_("All", &nh, &i__5, &work[pw], &nh, &q[topq +
|
|
j * q_dim1], ldq);
|
|
}
|
|
ppwo += (nnb << 2) * nnb;
|
|
}
|
|
}
|
|
|
|
/* Accumulate right Givens rotations if required. */
|
|
|
|
if (wantz || top > 0) {
|
|
|
|
/* Initialize small unitary factors that will hold the */
|
|
/* accumulated Givens rotations in workspace. */
|
|
|
|
zlaset_("All", &nblst, &nblst, &c_b2, &c_b1, &work[1], &nblst);
|
|
pw = nblst * nblst + 1;
|
|
i__3 = n2nb;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
i__6 = nnb << 1;
|
|
i__5 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
zlaset_("All", &i__6, &i__5, &c_b2, &c_b1, &work[pw], &
|
|
i__4);
|
|
pw += (nnb << 2) * nnb;
|
|
}
|
|
|
|
/* Accumulate Givens rotations into workspace array. */
|
|
|
|
i__3 = jcol + nnb - 1;
|
|
for (j = jcol; j <= i__3; ++j) {
|
|
ppw = (nblst + 1) * (nblst - 2) - j + jcol + 1;
|
|
len = j + 2 - jcol;
|
|
jrow = j + n2nb * nnb + 2;
|
|
i__6 = jrow;
|
|
for (i__ = *ihi; i__ >= i__6; --i__) {
|
|
i__5 = i__ + j * a_dim1;
|
|
ctemp.r = a[i__5].r, ctemp.i = a[i__5].i;
|
|
i__5 = i__ + j * a_dim1;
|
|
a[i__5].r = 0., a[i__5].i = 0.;
|
|
i__5 = i__ + j * b_dim1;
|
|
s.r = b[i__5].r, s.i = b[i__5].i;
|
|
i__5 = i__ + j * b_dim1;
|
|
b[i__5].r = 0., b[i__5].i = 0.;
|
|
i__5 = ppw + len - 1;
|
|
for (jj = ppw; jj <= i__5; ++jj) {
|
|
i__4 = jj + nblst;
|
|
temp.r = work[i__4].r, temp.i = work[i__4].i;
|
|
i__4 = jj + nblst;
|
|
z__2.r = ctemp.r * temp.r - ctemp.i * temp.i,
|
|
z__2.i = ctemp.r * temp.i + ctemp.i *
|
|
temp.r;
|
|
d_cnjg(&z__4, &s);
|
|
i__7 = jj;
|
|
z__3.r = z__4.r * work[i__7].r - z__4.i * work[
|
|
i__7].i, z__3.i = z__4.r * work[i__7].i +
|
|
z__4.i * work[i__7].r;
|
|
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
|
|
z__3.i;
|
|
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
|
|
i__4 = jj;
|
|
z__2.r = s.r * temp.r - s.i * temp.i, z__2.i =
|
|
s.r * temp.i + s.i * temp.r;
|
|
i__7 = jj;
|
|
z__3.r = ctemp.r * work[i__7].r - ctemp.i * work[
|
|
i__7].i, z__3.i = ctemp.r * work[i__7].i
|
|
+ ctemp.i * work[i__7].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
|
|
z__3.i;
|
|
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
|
|
}
|
|
++len;
|
|
ppw = ppw - nblst - 1;
|
|
}
|
|
|
|
ppwo = nblst * nblst + (nnb + j - jcol - 1 << 1) * nnb +
|
|
nnb;
|
|
j0 = jrow - nnb;
|
|
i__6 = j + 2;
|
|
i__5 = -nnb;
|
|
for (jrow = j0; i__5 < 0 ? jrow >= i__6 : jrow <= i__6;
|
|
jrow += i__5) {
|
|
ppw = ppwo;
|
|
len = j + 2 - jcol;
|
|
i__4 = jrow;
|
|
for (i__ = jrow + nnb - 1; i__ >= i__4; --i__) {
|
|
i__7 = i__ + j * a_dim1;
|
|
ctemp.r = a[i__7].r, ctemp.i = a[i__7].i;
|
|
i__7 = i__ + j * a_dim1;
|
|
a[i__7].r = 0., a[i__7].i = 0.;
|
|
i__7 = i__ + j * b_dim1;
|
|
s.r = b[i__7].r, s.i = b[i__7].i;
|
|
i__7 = i__ + j * b_dim1;
|
|
b[i__7].r = 0., b[i__7].i = 0.;
|
|
i__7 = ppw + len - 1;
|
|
for (jj = ppw; jj <= i__7; ++jj) {
|
|
i__8 = jj + (nnb << 1);
|
|
temp.r = work[i__8].r, temp.i = work[i__8].i;
|
|
i__8 = jj + (nnb << 1);
|
|
z__2.r = ctemp.r * temp.r - ctemp.i * temp.i,
|
|
z__2.i = ctemp.r * temp.i + ctemp.i *
|
|
temp.r;
|
|
d_cnjg(&z__4, &s);
|
|
i__9 = jj;
|
|
z__3.r = z__4.r * work[i__9].r - z__4.i *
|
|
work[i__9].i, z__3.i = z__4.r * work[
|
|
i__9].i + z__4.i * work[i__9].r;
|
|
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i -
|
|
z__3.i;
|
|
work[i__8].r = z__1.r, work[i__8].i = z__1.i;
|
|
i__8 = jj;
|
|
z__2.r = s.r * temp.r - s.i * temp.i, z__2.i =
|
|
s.r * temp.i + s.i * temp.r;
|
|
i__9 = jj;
|
|
z__3.r = ctemp.r * work[i__9].r - ctemp.i *
|
|
work[i__9].i, z__3.i = ctemp.r * work[
|
|
i__9].i + ctemp.i * work[i__9].r;
|
|
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i +
|
|
z__3.i;
|
|
work[i__8].r = z__1.r, work[i__8].i = z__1.i;
|
|
}
|
|
++len;
|
|
ppw = ppw - (nnb << 1) - 1;
|
|
}
|
|
ppwo += (nnb << 2) * nnb;
|
|
}
|
|
}
|
|
} else {
|
|
|
|
i__3 = *ihi - jcol - 1;
|
|
zlaset_("Lower", &i__3, &nnb, &c_b2, &c_b2, &a[jcol + 2 +
|
|
jcol * a_dim1], lda);
|
|
i__3 = *ihi - jcol - 1;
|
|
zlaset_("Lower", &i__3, &nnb, &c_b2, &c_b2, &b[jcol + 2 +
|
|
jcol * b_dim1], ldb);
|
|
}
|
|
|
|
/* Apply accumulated unitary matrices to A and B. */
|
|
|
|
if (top > 0) {
|
|
j = *ihi - nblst + 1;
|
|
zgemm_("No Transpose", "No Transpose", &top, &nblst, &nblst, &
|
|
c_b1, &a[j * a_dim1 + 1], lda, &work[1], &nblst, &
|
|
c_b2, &work[pw], &top);
|
|
zlacpy_("All", &top, &nblst, &work[pw], &top, &a[j * a_dim1 +
|
|
1], lda);
|
|
ppwo = nblst * nblst + 1;
|
|
j0 = j - nnb;
|
|
i__3 = jcol + 1;
|
|
i__5 = -nnb;
|
|
for (j = j0; i__5 < 0 ? j >= i__3 : j <= i__3; j += i__5) {
|
|
if (blk22) {
|
|
|
|
/* Exploit the structure of U. */
|
|
|
|
i__6 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
i__7 = *lwork - pw + 1;
|
|
zunm22_("Right", "No Transpose", &top, &i__6, &nnb, &
|
|
nnb, &work[ppwo], &i__4, &a[j * a_dim1 + 1],
|
|
lda, &work[pw], &i__7, &ierr);
|
|
} else {
|
|
|
|
/* Ignore the structure of U. */
|
|
|
|
i__6 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
i__7 = nnb << 1;
|
|
zgemm_("No Transpose", "No Transpose", &top, &i__6, &
|
|
i__4, &c_b1, &a[j * a_dim1 + 1], lda, &work[
|
|
ppwo], &i__7, &c_b2, &work[pw], &top);
|
|
i__6 = nnb << 1;
|
|
zlacpy_("All", &top, &i__6, &work[pw], &top, &a[j *
|
|
a_dim1 + 1], lda);
|
|
}
|
|
ppwo += (nnb << 2) * nnb;
|
|
}
|
|
|
|
j = *ihi - nblst + 1;
|
|
zgemm_("No Transpose", "No Transpose", &top, &nblst, &nblst, &
|
|
c_b1, &b[j * b_dim1 + 1], ldb, &work[1], &nblst, &
|
|
c_b2, &work[pw], &top);
|
|
zlacpy_("All", &top, &nblst, &work[pw], &top, &b[j * b_dim1 +
|
|
1], ldb);
|
|
ppwo = nblst * nblst + 1;
|
|
j0 = j - nnb;
|
|
i__5 = jcol + 1;
|
|
i__3 = -nnb;
|
|
for (j = j0; i__3 < 0 ? j >= i__5 : j <= i__5; j += i__3) {
|
|
if (blk22) {
|
|
|
|
/* Exploit the structure of U. */
|
|
|
|
i__6 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
i__7 = *lwork - pw + 1;
|
|
zunm22_("Right", "No Transpose", &top, &i__6, &nnb, &
|
|
nnb, &work[ppwo], &i__4, &b[j * b_dim1 + 1],
|
|
ldb, &work[pw], &i__7, &ierr);
|
|
} else {
|
|
|
|
/* Ignore the structure of U. */
|
|
|
|
i__6 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
i__7 = nnb << 1;
|
|
zgemm_("No Transpose", "No Transpose", &top, &i__6, &
|
|
i__4, &c_b1, &b[j * b_dim1 + 1], ldb, &work[
|
|
ppwo], &i__7, &c_b2, &work[pw], &top);
|
|
i__6 = nnb << 1;
|
|
zlacpy_("All", &top, &i__6, &work[pw], &top, &b[j *
|
|
b_dim1 + 1], ldb);
|
|
}
|
|
ppwo += (nnb << 2) * nnb;
|
|
}
|
|
}
|
|
|
|
/* Apply accumulated unitary matrices to Z. */
|
|
|
|
if (wantz) {
|
|
j = *ihi - nblst + 1;
|
|
if (initq) {
|
|
/* Computing MAX */
|
|
i__3 = 2, i__5 = j - jcol + 1;
|
|
topq = f2cmax(i__3,i__5);
|
|
nh = *ihi - topq + 1;
|
|
} else {
|
|
topq = 1;
|
|
nh = *n;
|
|
}
|
|
zgemm_("No Transpose", "No Transpose", &nh, &nblst, &nblst, &
|
|
c_b1, &z__[topq + j * z_dim1], ldz, &work[1], &nblst,
|
|
&c_b2, &work[pw], &nh);
|
|
zlacpy_("All", &nh, &nblst, &work[pw], &nh, &z__[topq + j *
|
|
z_dim1], ldz);
|
|
ppwo = nblst * nblst + 1;
|
|
j0 = j - nnb;
|
|
i__3 = jcol + 1;
|
|
i__5 = -nnb;
|
|
for (j = j0; i__5 < 0 ? j >= i__3 : j <= i__3; j += i__5) {
|
|
if (initq) {
|
|
/* Computing MAX */
|
|
i__6 = 2, i__4 = j - jcol + 1;
|
|
topq = f2cmax(i__6,i__4);
|
|
nh = *ihi - topq + 1;
|
|
}
|
|
if (blk22) {
|
|
|
|
/* Exploit the structure of U. */
|
|
|
|
i__6 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
i__7 = *lwork - pw + 1;
|
|
zunm22_("Right", "No Transpose", &nh, &i__6, &nnb, &
|
|
nnb, &work[ppwo], &i__4, &z__[topq + j *
|
|
z_dim1], ldz, &work[pw], &i__7, &ierr);
|
|
} else {
|
|
|
|
/* Ignore the structure of U. */
|
|
|
|
i__6 = nnb << 1;
|
|
i__4 = nnb << 1;
|
|
i__7 = nnb << 1;
|
|
zgemm_("No Transpose", "No Transpose", &nh, &i__6, &
|
|
i__4, &c_b1, &z__[topq + j * z_dim1], ldz, &
|
|
work[ppwo], &i__7, &c_b2, &work[pw], &nh);
|
|
i__6 = nnb << 1;
|
|
zlacpy_("All", &nh, &i__6, &work[pw], &nh, &z__[topq
|
|
+ j * z_dim1], ldz);
|
|
}
|
|
ppwo += (nnb << 2) * nnb;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Use unblocked code to reduce the rest of the matrix */
|
|
/* Avoid re-initialization of modified Q and Z. */
|
|
|
|
*(unsigned char *)compq2 = *(unsigned char *)compq;
|
|
*(unsigned char *)compz2 = *(unsigned char *)compz;
|
|
if (jcol != *ilo) {
|
|
if (wantq) {
|
|
*(unsigned char *)compq2 = 'V';
|
|
}
|
|
if (wantz) {
|
|
*(unsigned char *)compz2 = 'V';
|
|
}
|
|
}
|
|
|
|
if (jcol < *ihi) {
|
|
zgghrd_(compq2, compz2, n, &jcol, ihi, &a[a_offset], lda, &b[b_offset]
|
|
, ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &ierr);
|
|
}
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
|
|
return;
|
|
|
|
/* End of ZGGHD3 */
|
|
|
|
} /* zgghd3_ */
|
|
|