1202 lines
36 KiB
C
1202 lines
36 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 = {0.,0.};
|
|
static doublecomplex c_b2 = {1.,0.};
|
|
static integer c__1 = 1;
|
|
static integer c__0 = 0;
|
|
static integer c_n1 = -1;
|
|
|
|
/* > \brief <b> ZGGES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors f
|
|
or GE matrices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZGGES + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgges.f
|
|
"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgges.f
|
|
"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgges.f
|
|
"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB, */
|
|
/* SDIM, ALPHA, BETA, VSL, LDVSL, VSR, LDVSR, WORK, */
|
|
/* LWORK, RWORK, BWORK, INFO ) */
|
|
|
|
/* CHARACTER JOBVSL, JOBVSR, SORT */
|
|
/* INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM */
|
|
/* LOGICAL BWORK( * ) */
|
|
/* DOUBLE PRECISION RWORK( * ) */
|
|
/* COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ), */
|
|
/* $ BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ), */
|
|
/* $ WORK( * ) */
|
|
/* LOGICAL SELCTG */
|
|
/* EXTERNAL SELCTG */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZGGES computes for a pair of N-by-N complex nonsymmetric matrices */
|
|
/* > (A,B), the generalized eigenvalues, the generalized complex Schur */
|
|
/* > form (S, T), and optionally left and/or right Schur vectors (VSL */
|
|
/* > and VSR). This gives the generalized Schur factorization */
|
|
/* > */
|
|
/* > (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H ) */
|
|
/* > */
|
|
/* > where (VSR)**H is the conjugate-transpose of VSR. */
|
|
/* > */
|
|
/* > Optionally, it also orders the eigenvalues so that a selected cluster */
|
|
/* > of eigenvalues appears in the leading diagonal blocks of the upper */
|
|
/* > triangular matrix S and the upper triangular matrix T. The leading */
|
|
/* > columns of VSL and VSR then form an unitary basis for the */
|
|
/* > corresponding left and right eigenspaces (deflating subspaces). */
|
|
/* > */
|
|
/* > (If only the generalized eigenvalues are needed, use the driver */
|
|
/* > ZGGEV instead, which is faster.) */
|
|
/* > */
|
|
/* > A generalized eigenvalue for a pair of matrices (A,B) is a scalar w */
|
|
/* > or a ratio alpha/beta = w, such that A - w*B is singular. It is */
|
|
/* > usually represented as the pair (alpha,beta), as there is a */
|
|
/* > reasonable interpretation for beta=0, and even for both being zero. */
|
|
/* > */
|
|
/* > A pair of matrices (S,T) is in generalized complex Schur form if S */
|
|
/* > and T are upper triangular and, in addition, the diagonal elements */
|
|
/* > of T are non-negative real numbers. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBVSL */
|
|
/* > \verbatim */
|
|
/* > JOBVSL is CHARACTER*1 */
|
|
/* > = 'N': do not compute the left Schur vectors; */
|
|
/* > = 'V': compute the left Schur vectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBVSR */
|
|
/* > \verbatim */
|
|
/* > JOBVSR is CHARACTER*1 */
|
|
/* > = 'N': do not compute the right Schur vectors; */
|
|
/* > = 'V': compute the right Schur vectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SORT */
|
|
/* > \verbatim */
|
|
/* > SORT is CHARACTER*1 */
|
|
/* > Specifies whether or not to order the eigenvalues on the */
|
|
/* > diagonal of the generalized Schur form. */
|
|
/* > = 'N': Eigenvalues are not ordered; */
|
|
/* > = 'S': Eigenvalues are ordered (see SELCTG). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SELCTG */
|
|
/* > \verbatim */
|
|
/* > SELCTG is a LOGICAL FUNCTION of two COMPLEX*16 arguments */
|
|
/* > SELCTG must be declared EXTERNAL in the calling subroutine. */
|
|
/* > If SORT = 'N', SELCTG is not referenced. */
|
|
/* > If SORT = 'S', SELCTG is used to select eigenvalues to sort */
|
|
/* > to the top left of the Schur form. */
|
|
/* > An eigenvalue ALPHA(j)/BETA(j) is selected if */
|
|
/* > SELCTG(ALPHA(j),BETA(j)) is true. */
|
|
/* > */
|
|
/* > Note that a selected complex eigenvalue may no longer satisfy */
|
|
/* > SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since */
|
|
/* > ordering may change the value of complex eigenvalues */
|
|
/* > (especially if the eigenvalue is ill-conditioned), in this */
|
|
/* > case INFO is set to N+2 (See INFO below). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrices A, B, VSL, and VSR. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX*16 array, dimension (LDA, N) */
|
|
/* > On entry, the first of the pair of matrices. */
|
|
/* > On exit, A has been overwritten by its generalized Schur */
|
|
/* > form S. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX*16 array, dimension (LDB, N) */
|
|
/* > On entry, the second of the pair of matrices. */
|
|
/* > On exit, B has been overwritten by its generalized Schur */
|
|
/* > form T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of B. LDB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SDIM */
|
|
/* > \verbatim */
|
|
/* > SDIM is INTEGER */
|
|
/* > If SORT = 'N', SDIM = 0. */
|
|
/* > If SORT = 'S', SDIM = number of eigenvalues (after sorting) */
|
|
/* > for which SELCTG is true. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ALPHA */
|
|
/* > \verbatim */
|
|
/* > ALPHA is COMPLEX*16 array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BETA */
|
|
/* > \verbatim */
|
|
/* > BETA is COMPLEX*16 array, dimension (N) */
|
|
/* > On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the */
|
|
/* > generalized eigenvalues. ALPHA(j), j=1,...,N and BETA(j), */
|
|
/* > j=1,...,N are the diagonals of the complex Schur form (A,B) */
|
|
/* > output by ZGGES. The BETA(j) will be non-negative real. */
|
|
/* > */
|
|
/* > Note: the quotients ALPHA(j)/BETA(j) may easily over- or */
|
|
/* > underflow, and BETA(j) may even be zero. Thus, the user */
|
|
/* > should avoid naively computing the ratio alpha/beta. */
|
|
/* > However, ALPHA will be always less than and usually */
|
|
/* > comparable with norm(A) in magnitude, and BETA always less */
|
|
/* > than and usually comparable with norm(B). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VSL */
|
|
/* > \verbatim */
|
|
/* > VSL is COMPLEX*16 array, dimension (LDVSL,N) */
|
|
/* > If JOBVSL = 'V', VSL will contain the left Schur vectors. */
|
|
/* > Not referenced if JOBVSL = 'N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVSL */
|
|
/* > \verbatim */
|
|
/* > LDVSL is INTEGER */
|
|
/* > The leading dimension of the matrix VSL. LDVSL >= 1, and */
|
|
/* > if JOBVSL = 'V', LDVSL >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VSR */
|
|
/* > \verbatim */
|
|
/* > VSR is COMPLEX*16 array, dimension (LDVSR,N) */
|
|
/* > If JOBVSR = 'V', VSR will contain the right Schur vectors. */
|
|
/* > Not referenced if JOBVSR = 'N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVSR */
|
|
/* > \verbatim */
|
|
/* > LDVSR is INTEGER */
|
|
/* > The leading dimension of the matrix VSR. LDVSR >= 1, and */
|
|
/* > if JOBVSR = 'V', LDVSR >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= f2cmax(1,2*N). */
|
|
/* > For good performance, LWORK must generally be larger. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (8*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BWORK */
|
|
/* > \verbatim */
|
|
/* > BWORK is LOGICAL array, dimension (N) */
|
|
/* > Not referenced if SORT = 'N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > =1,...,N: */
|
|
/* > The QZ iteration failed. (A,B) are not in Schur */
|
|
/* > form, but ALPHA(j) and BETA(j) should be correct for */
|
|
/* > j=INFO+1,...,N. */
|
|
/* > > N: =N+1: other than QZ iteration failed in ZHGEQZ */
|
|
/* > =N+2: after reordering, roundoff changed values of */
|
|
/* > some complex eigenvalues so that leading */
|
|
/* > eigenvalues in the Generalized Schur form no */
|
|
/* > longer satisfy SELCTG=.TRUE. This could also */
|
|
/* > be caused due to scaling. */
|
|
/* > =N+3: reordering failed in ZTGSEN. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complex16GEeigen */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zgges_(char *jobvsl, char *jobvsr, char *sort, L_fp
|
|
selctg, integer *n, doublecomplex *a, integer *lda, doublecomplex *b,
|
|
integer *ldb, integer *sdim, doublecomplex *alpha, doublecomplex *
|
|
beta, doublecomplex *vsl, integer *ldvsl, doublecomplex *vsr, integer
|
|
*ldvsr, doublecomplex *work, integer *lwork, doublereal *rwork,
|
|
logical *bwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset,
|
|
vsr_dim1, vsr_offset, i__1, i__2;
|
|
|
|
/* Local variables */
|
|
doublereal anrm, bnrm;
|
|
integer idum[1], ierr, itau, iwrk;
|
|
doublereal pvsl, pvsr;
|
|
integer i__;
|
|
extern logical lsame_(char *, char *);
|
|
integer ileft, icols;
|
|
logical cursl, ilvsl, ilvsr;
|
|
integer irwrk, irows;
|
|
extern /* Subroutine */ void dlabad_(doublereal *, doublereal *);
|
|
extern doublereal dlamch_(char *);
|
|
extern /* Subroutine */ void zggbak_(char *, char *, integer *, integer *,
|
|
integer *, doublereal *, doublereal *, integer *, doublecomplex *,
|
|
integer *, integer *), zggbal_(char *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *, integer *
|
|
, integer *, doublereal *, doublereal *, doublereal *, integer *);
|
|
logical ilascl, ilbscl;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
|
|
integer *, doublereal *);
|
|
doublereal bignum;
|
|
integer ijobvl, iright;
|
|
extern /* Subroutine */ void zgghrd_(char *, char *, integer *, integer *,
|
|
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *, integer *
|
|
), zlascl_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
|
|
integer *, integer *);
|
|
integer ijobvr;
|
|
extern /* Subroutine */ void zgeqrf_(integer *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *, integer *
|
|
);
|
|
doublereal anrmto;
|
|
integer lwkmin;
|
|
logical lastsl;
|
|
doublereal bnrmto;
|
|
extern /* Subroutine */ void zlacpy_(char *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *),
|
|
zlaset_(char *, integer *, integer *, doublecomplex *,
|
|
doublecomplex *, doublecomplex *, integer *), zhgeqz_(
|
|
char *, char *, char *, integer *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublereal *, integer *), ztgsen_(integer
|
|
*, logical *, logical *, logical *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, integer *, doublecomplex *,
|
|
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
|
|
integer *, integer *, doublereal *, doublereal *, doublereal *,
|
|
doublecomplex *, integer *, integer *, integer *, integer *);
|
|
doublereal smlnum;
|
|
logical wantst, lquery;
|
|
integer lwkopt;
|
|
extern /* Subroutine */ void zungqr_(integer *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *, integer *), zunmqr_(char *, char *, integer *, integer
|
|
*, integer *, doublecomplex *, integer *, doublecomplex *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
|
|
doublereal dif[2];
|
|
integer ihi, ilo;
|
|
doublereal eps;
|
|
|
|
|
|
/* -- LAPACK driver routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Decode the input arguments */
|
|
|
|
/* 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;
|
|
--alpha;
|
|
--beta;
|
|
vsl_dim1 = *ldvsl;
|
|
vsl_offset = 1 + vsl_dim1 * 1;
|
|
vsl -= vsl_offset;
|
|
vsr_dim1 = *ldvsr;
|
|
vsr_offset = 1 + vsr_dim1 * 1;
|
|
vsr -= vsr_offset;
|
|
--work;
|
|
--rwork;
|
|
--bwork;
|
|
|
|
/* Function Body */
|
|
if (lsame_(jobvsl, "N")) {
|
|
ijobvl = 1;
|
|
ilvsl = FALSE_;
|
|
} else if (lsame_(jobvsl, "V")) {
|
|
ijobvl = 2;
|
|
ilvsl = TRUE_;
|
|
} else {
|
|
ijobvl = -1;
|
|
ilvsl = FALSE_;
|
|
}
|
|
|
|
if (lsame_(jobvsr, "N")) {
|
|
ijobvr = 1;
|
|
ilvsr = FALSE_;
|
|
} else if (lsame_(jobvsr, "V")) {
|
|
ijobvr = 2;
|
|
ilvsr = TRUE_;
|
|
} else {
|
|
ijobvr = -1;
|
|
ilvsr = FALSE_;
|
|
}
|
|
|
|
wantst = lsame_(sort, "S");
|
|
|
|
/* Test the input arguments */
|
|
|
|
*info = 0;
|
|
lquery = *lwork == -1;
|
|
if (ijobvl <= 0) {
|
|
*info = -1;
|
|
} else if (ijobvr <= 0) {
|
|
*info = -2;
|
|
} else if (! wantst && ! lsame_(sort, "N")) {
|
|
*info = -3;
|
|
} else if (*n < 0) {
|
|
*info = -5;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -7;
|
|
} else if (*ldb < f2cmax(1,*n)) {
|
|
*info = -9;
|
|
} else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
|
|
*info = -14;
|
|
} else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
|
|
*info = -16;
|
|
}
|
|
|
|
/* Compute workspace */
|
|
/* (Note: Comments in the code beginning "Workspace:" describe the */
|
|
/* minimal amount of workspace needed at that point in the code, */
|
|
/* as well as the preferred amount for good performance. */
|
|
/* NB refers to the optimal block size for the immediately */
|
|
/* following subroutine, as returned by ILAENV.) */
|
|
|
|
if (*info == 0) {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n << 1;
|
|
lwkmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", n, &c__1, n,
|
|
&c__0, (ftnlen)6, (ftnlen)1);
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = lwkopt, i__2 = *n + *n * ilaenv_(&c__1, "ZUNMQR", " ", n, &
|
|
c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
if (ilvsl) {
|
|
/* Computing MAX */
|
|
i__1 = lwkopt, i__2 = *n + *n * ilaenv_(&c__1, "ZUNGQR", " ", n, &
|
|
c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
}
|
|
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
|
|
|
|
if (*lwork < lwkmin && ! lquery) {
|
|
*info = -18;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZGGES ", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
*sdim = 0;
|
|
return;
|
|
}
|
|
|
|
/* Get machine constants */
|
|
|
|
eps = dlamch_("P");
|
|
smlnum = dlamch_("S");
|
|
bignum = 1. / smlnum;
|
|
dlabad_(&smlnum, &bignum);
|
|
smlnum = sqrt(smlnum) / eps;
|
|
bignum = 1. / smlnum;
|
|
|
|
/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
|
|
|
|
anrm = zlange_("M", n, n, &a[a_offset], lda, &rwork[1]);
|
|
ilascl = FALSE_;
|
|
if (anrm > 0. && anrm < smlnum) {
|
|
anrmto = smlnum;
|
|
ilascl = TRUE_;
|
|
} else if (anrm > bignum) {
|
|
anrmto = bignum;
|
|
ilascl = TRUE_;
|
|
}
|
|
|
|
if (ilascl) {
|
|
zlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
|
|
ierr);
|
|
}
|
|
|
|
/* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */
|
|
|
|
bnrm = zlange_("M", n, n, &b[b_offset], ldb, &rwork[1]);
|
|
ilbscl = FALSE_;
|
|
if (bnrm > 0. && bnrm < smlnum) {
|
|
bnrmto = smlnum;
|
|
ilbscl = TRUE_;
|
|
} else if (bnrm > bignum) {
|
|
bnrmto = bignum;
|
|
ilbscl = TRUE_;
|
|
}
|
|
|
|
if (ilbscl) {
|
|
zlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
|
|
ierr);
|
|
}
|
|
|
|
/* Permute the matrix to make it more nearly triangular */
|
|
/* (Real Workspace: need 6*N) */
|
|
|
|
ileft = 1;
|
|
iright = *n + 1;
|
|
irwrk = iright + *n;
|
|
zggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[
|
|
ileft], &rwork[iright], &rwork[irwrk], &ierr);
|
|
|
|
/* Reduce B to triangular form (QR decomposition of B) */
|
|
/* (Complex Workspace: need N, prefer N*NB) */
|
|
|
|
irows = ihi + 1 - ilo;
|
|
icols = *n + 1 - ilo;
|
|
itau = 1;
|
|
iwrk = itau + irows;
|
|
i__1 = *lwork + 1 - iwrk;
|
|
zgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
|
|
iwrk], &i__1, &ierr);
|
|
|
|
/* Apply the orthogonal transformation to matrix A */
|
|
/* (Complex Workspace: need N, prefer N*NB) */
|
|
|
|
i__1 = *lwork + 1 - iwrk;
|
|
zunmqr_("L", "C", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
|
|
work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
|
|
ierr);
|
|
|
|
/* Initialize VSL */
|
|
/* (Complex Workspace: need N, prefer N*NB) */
|
|
|
|
if (ilvsl) {
|
|
zlaset_("Full", n, n, &c_b1, &c_b2, &vsl[vsl_offset], ldvsl);
|
|
if (irows > 1) {
|
|
i__1 = irows - 1;
|
|
i__2 = irows - 1;
|
|
zlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[
|
|
ilo + 1 + ilo * vsl_dim1], ldvsl);
|
|
}
|
|
i__1 = *lwork + 1 - iwrk;
|
|
zungqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
|
|
work[itau], &work[iwrk], &i__1, &ierr);
|
|
}
|
|
|
|
/* Initialize VSR */
|
|
|
|
if (ilvsr) {
|
|
zlaset_("Full", n, n, &c_b1, &c_b2, &vsr[vsr_offset], ldvsr);
|
|
}
|
|
|
|
/* Reduce to generalized Hessenberg form */
|
|
/* (Workspace: none needed) */
|
|
|
|
zgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
|
|
ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &ierr);
|
|
|
|
*sdim = 0;
|
|
|
|
/* Perform QZ algorithm, computing Schur vectors if desired */
|
|
/* (Complex Workspace: need N) */
|
|
/* (Real Workspace: need N) */
|
|
|
|
iwrk = itau;
|
|
i__1 = *lwork + 1 - iwrk;
|
|
zhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
|
|
b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl, &
|
|
vsr[vsr_offset], ldvsr, &work[iwrk], &i__1, &rwork[irwrk], &ierr);
|
|
if (ierr != 0) {
|
|
if (ierr > 0 && ierr <= *n) {
|
|
*info = ierr;
|
|
} else if (ierr > *n && ierr <= *n << 1) {
|
|
*info = ierr - *n;
|
|
} else {
|
|
*info = *n + 1;
|
|
}
|
|
goto L30;
|
|
}
|
|
|
|
/* Sort eigenvalues ALPHA/BETA if desired */
|
|
/* (Workspace: none needed) */
|
|
|
|
if (wantst) {
|
|
|
|
/* Undo scaling on eigenvalues before selecting */
|
|
|
|
if (ilascl) {
|
|
zlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, &c__1, &alpha[1], n,
|
|
&ierr);
|
|
}
|
|
if (ilbscl) {
|
|
zlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, &c__1, &beta[1], n,
|
|
&ierr);
|
|
}
|
|
|
|
/* Select eigenvalues */
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
bwork[i__] = (*selctg)(&alpha[i__], &beta[i__]);
|
|
/* L10: */
|
|
}
|
|
|
|
i__1 = *lwork - iwrk + 1;
|
|
ztgsen_(&c__0, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
|
|
b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl,
|
|
&vsr[vsr_offset], ldvsr, sdim, &pvsl, &pvsr, dif, &work[iwrk],
|
|
&i__1, idum, &c__1, &ierr);
|
|
if (ierr == 1) {
|
|
*info = *n + 3;
|
|
}
|
|
|
|
}
|
|
|
|
/* Apply back-permutation to VSL and VSR */
|
|
/* (Workspace: none needed) */
|
|
|
|
if (ilvsl) {
|
|
zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
|
|
vsl[vsl_offset], ldvsl, &ierr);
|
|
}
|
|
if (ilvsr) {
|
|
zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
|
|
vsr[vsr_offset], ldvsr, &ierr);
|
|
}
|
|
|
|
/* Undo scaling */
|
|
|
|
if (ilascl) {
|
|
zlascl_("U", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
|
|
ierr);
|
|
zlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
|
|
ierr);
|
|
}
|
|
|
|
if (ilbscl) {
|
|
zlascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
|
|
ierr);
|
|
zlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
|
|
ierr);
|
|
}
|
|
|
|
if (wantst) {
|
|
|
|
/* Check if reordering is correct */
|
|
|
|
lastsl = TRUE_;
|
|
*sdim = 0;
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
cursl = (*selctg)(&alpha[i__], &beta[i__]);
|
|
if (cursl) {
|
|
++(*sdim);
|
|
}
|
|
if (cursl && ! lastsl) {
|
|
*info = *n + 2;
|
|
}
|
|
lastsl = cursl;
|
|
/* L20: */
|
|
}
|
|
|
|
}
|
|
|
|
L30:
|
|
|
|
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
|
|
|
|
return;
|
|
|
|
/* End of ZGGES */
|
|
|
|
} /* zgges_ */
|
|
|