1294 lines
39 KiB
C
1294 lines
39 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/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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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c_n1 = -1;
|
|
static integer c__1 = 1;
|
|
static integer c__0 = 0;
|
|
static doublereal c_b36 = 0.;
|
|
static doublereal c_b37 = 1.;
|
|
|
|
/* > \brief <b> DGGES3 computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
|
|
for GE matrices (blocked algorithm)</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DGGES3 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgges3.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgges3.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgges3.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DGGES3( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB, */
|
|
/* SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, */
|
|
/* LDVSR, WORK, LWORK, BWORK, INFO ) */
|
|
|
|
/* CHARACTER JOBVSL, JOBVSR, SORT */
|
|
/* INTEGER INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N, SDIM */
|
|
/* LOGICAL BWORK( * ) */
|
|
/* DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */
|
|
/* $ B( LDB, * ), BETA( * ), VSL( LDVSL, * ), */
|
|
/* $ VSR( LDVSR, * ), WORK( * ) */
|
|
/* LOGICAL SELCTG */
|
|
/* EXTERNAL SELCTG */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DGGES3 computes for a pair of N-by-N real nonsymmetric matrices (A,B), */
|
|
/* > the generalized eigenvalues, the generalized real Schur form (S,T), */
|
|
/* > optionally, the left and/or right matrices of Schur vectors (VSL and */
|
|
/* > VSR). This gives the generalized Schur factorization */
|
|
/* > */
|
|
/* > (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T ) */
|
|
/* > */
|
|
/* > Optionally, it also orders the eigenvalues so that a selected cluster */
|
|
/* > of eigenvalues appears in the leading diagonal blocks of the upper */
|
|
/* > quasi-triangular matrix S and the upper triangular matrix T.The */
|
|
/* > leading columns of VSL and VSR then form an orthonormal basis for the */
|
|
/* > corresponding left and right eigenspaces (deflating subspaces). */
|
|
/* > */
|
|
/* > (If only the generalized eigenvalues are needed, use the driver */
|
|
/* > DGGEV 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 or both being zero. */
|
|
/* > */
|
|
/* > A pair of matrices (S,T) is in generalized real Schur form if T is */
|
|
/* > upper triangular with non-negative diagonal and S is block upper */
|
|
/* > triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond */
|
|
/* > to real generalized eigenvalues, while 2-by-2 blocks of S will be */
|
|
/* > "standardized" by making the corresponding elements of T have the */
|
|
/* > form: */
|
|
/* > [ a 0 ] */
|
|
/* > [ 0 b ] */
|
|
/* > */
|
|
/* > and the pair of corresponding 2-by-2 blocks in S and T will have a */
|
|
/* > complex conjugate pair of generalized eigenvalues. */
|
|
/* > */
|
|
/* > \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 three DOUBLE PRECISION 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 (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if */
|
|
/* > SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either */
|
|
/* > one of a complex conjugate pair of eigenvalues is selected, */
|
|
/* > then both complex eigenvalues are selected. */
|
|
/* > */
|
|
/* > Note that in the ill-conditioned case, a selected complex */
|
|
/* > eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j), */
|
|
/* > BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2 */
|
|
/* > in this case. */
|
|
/* > \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 DOUBLE PRECISION 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 DOUBLE PRECISION 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. (Complex conjugate pairs for which */
|
|
/* > SELCTG is true for either eigenvalue count as 2.) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ALPHAR */
|
|
/* > \verbatim */
|
|
/* > ALPHAR is DOUBLE PRECISION array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ALPHAI */
|
|
/* > \verbatim */
|
|
/* > ALPHAI is DOUBLE PRECISION array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BETA */
|
|
/* > \verbatim */
|
|
/* > BETA is DOUBLE PRECISION array, dimension (N) */
|
|
/* > On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */
|
|
/* > be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i, */
|
|
/* > and BETA(j),j=1,...,N are the diagonals of the complex Schur */
|
|
/* > form (S,T) that would result if the 2-by-2 diagonal blocks of */
|
|
/* > the real Schur form of (A,B) were further reduced to */
|
|
/* > triangular form using 2-by-2 complex unitary transformations. */
|
|
/* > If ALPHAI(j) is zero, then the j-th eigenvalue is real; if */
|
|
/* > positive, then the j-th and (j+1)-st eigenvalues are a */
|
|
/* > complex conjugate pair, with ALPHAI(j+1) negative. */
|
|
/* > */
|
|
/* > Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) */
|
|
/* > may easily over- or underflow, and BETA(j) may even be zero. */
|
|
/* > Thus, the user should avoid naively computing the ratio. */
|
|
/* > However, ALPHAR and ALPHAI 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] 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 ALPHAR(j), ALPHAI(j), and BETA(j) should */
|
|
/* > be correct for j=INFO+1,...,N. */
|
|
/* > > N: =N+1: other than QZ iteration failed in DHGEQZ. */
|
|
/* > =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 DTGSEN. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date January 2015 */
|
|
|
|
/* > \ingroup doubleGEeigen */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int dgges3_(char *jobvsl, char *jobvsr, char *sort, L_fp
|
|
selctg, integer *n, doublereal *a, integer *lda, doublereal *b,
|
|
integer *ldb, integer *sdim, doublereal *alphar, doublereal *alphai,
|
|
doublereal *beta, doublereal *vsl, integer *ldvsl, doublereal *vsr,
|
|
integer *ldvsr, doublereal *work, integer *lwork, 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;
|
|
doublereal d__1;
|
|
|
|
/* 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;
|
|
extern /* Subroutine */ int dgghd3_(char *, char *, integer *, integer *,
|
|
integer *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, integer *, doublereal *,
|
|
integer *, integer *);
|
|
integer irows;
|
|
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dggbak_(
|
|
char *, char *, integer *, integer *, integer *, doublereal *,
|
|
doublereal *, integer *, doublereal *, integer *, integer *), dggbal_(char *, integer *, doublereal *, integer
|
|
*, doublereal *, integer *, integer *, integer *, doublereal *,
|
|
doublereal *, doublereal *, integer *);
|
|
logical lst2sl;
|
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extern doublereal dlamch_(char *);
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integer ip;
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extern doublereal dlange_(char *, integer *, integer *, doublereal *,
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integer *, doublereal *);
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extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, integer *, doublereal *,
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integer *, integer *);
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logical ilascl, ilbscl;
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extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, integer *, integer *),
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dlacpy_(char *, integer *, integer *, doublereal *, integer *,
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doublereal *, integer *);
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doublereal safmin;
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extern /* Subroutine */ int dlaset_(char *, integer *, integer *,
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doublereal *, doublereal *, doublereal *, integer *);
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doublereal safmax;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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doublereal bignum;
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extern /* Subroutine */ int dhgeqz_(char *, char *, char *, integer *,
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integer *, integer *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, doublereal *, doublereal *,
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integer *, doublereal *, integer *, doublereal *, integer *,
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integer *), dtgsen_(integer *, logical *,
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logical *, logical *, integer *, doublereal *, integer *,
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doublereal *, integer *, doublereal *, doublereal *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, integer *,
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doublereal *, doublereal *, doublereal *, doublereal *, integer *,
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integer *, integer *, integer *);
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integer ijobvl, iright, ijobvr;
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extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *,
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doublereal *, integer *, doublereal *, doublereal *, integer *,
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integer *);
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doublereal anrmto, bnrmto;
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logical lastsl;
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extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
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integer *, doublereal *, integer *, doublereal *, doublereal *,
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integer *, doublereal *, integer *, integer *);
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doublereal smlnum;
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logical wantst, lquery;
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integer lwkopt;
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doublereal dif[2];
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integer ihi, ilo;
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doublereal eps;
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/* -- LAPACK driver routine (version 3.6.0) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* January 2015 */
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/* ===================================================================== */
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/* Decode the input arguments */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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a -= a_offset;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1 * 1;
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b -= b_offset;
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--alphar;
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--alphai;
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--beta;
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vsl_dim1 = *ldvsl;
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vsl_offset = 1 + vsl_dim1 * 1;
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vsl -= vsl_offset;
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vsr_dim1 = *ldvsr;
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vsr_offset = 1 + vsr_dim1 * 1;
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vsr -= vsr_offset;
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--work;
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--bwork;
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/* Function Body */
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if (lsame_(jobvsl, "N")) {
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ijobvl = 1;
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ilvsl = FALSE_;
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} else if (lsame_(jobvsl, "V")) {
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ijobvl = 2;
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ilvsl = TRUE_;
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} else {
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ijobvl = -1;
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ilvsl = FALSE_;
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}
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if (lsame_(jobvsr, "N")) {
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ijobvr = 1;
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ilvsr = FALSE_;
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} else if (lsame_(jobvsr, "V")) {
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ijobvr = 2;
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ilvsr = TRUE_;
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} else {
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ijobvr = -1;
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ilvsr = FALSE_;
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}
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wantst = lsame_(sort, "S");
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/* Test the input arguments */
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*info = 0;
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lquery = *lwork == -1;
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if (ijobvl <= 0) {
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*info = -1;
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} else if (ijobvr <= 0) {
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*info = -2;
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} else if (! wantst && ! lsame_(sort, "N")) {
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*info = -3;
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} else if (*n < 0) {
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*info = -5;
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} else if (*lda < f2cmax(1,*n)) {
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*info = -7;
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} else if (*ldb < f2cmax(1,*n)) {
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*info = -9;
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} else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
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*info = -15;
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} else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
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*info = -17;
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} else if (*lwork < *n * 6 + 16 && ! lquery) {
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*info = -19;
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}
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/* Compute workspace */
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if (*info == 0) {
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dgeqrf_(n, n, &b[b_offset], ldb, &work[1], &work[1], &c_n1, &ierr);
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/* Computing MAX */
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i__1 = *n * 6 + 16, i__2 = *n * 3 + (integer) work[1];
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lwkopt = f2cmax(i__1,i__2);
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dormqr_("L", "T", n, n, n, &b[b_offset], ldb, &work[1], &a[a_offset],
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lda, &work[1], &c_n1, &ierr);
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/* Computing MAX */
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i__1 = lwkopt, i__2 = *n * 3 + (integer) work[1];
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lwkopt = f2cmax(i__1,i__2);
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if (ilvsl) {
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dorgqr_(n, n, n, &vsl[vsl_offset], ldvsl, &work[1], &work[1], &
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c_n1, &ierr);
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/* Computing MAX */
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i__1 = lwkopt, i__2 = *n * 3 + (integer) work[1];
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lwkopt = f2cmax(i__1,i__2);
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}
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dgghd3_(jobvsl, jobvsr, n, &c__1, n, &a[a_offset], lda, &b[b_offset],
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ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &work[
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1], &c_n1, &ierr);
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/* Computing MAX */
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i__1 = lwkopt, i__2 = *n * 3 + (integer) work[1];
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lwkopt = f2cmax(i__1,i__2);
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dhgeqz_("S", jobvsl, jobvsr, n, &c__1, n, &a[a_offset], lda, &b[
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b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[
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vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &work[1], &c_n1,
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&ierr);
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/* Computing MAX */
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i__1 = lwkopt, i__2 = (*n << 1) + (integer) work[1];
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lwkopt = f2cmax(i__1,i__2);
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if (wantst) {
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dtgsen_(&c__0, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &
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b[b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[
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vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, sdim, &pvsl,
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&pvsr, dif, &work[1], &c_n1, idum, &c__1, &ierr);
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/* Computing MAX */
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i__1 = lwkopt, i__2 = (*n << 1) + (integer) work[1];
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lwkopt = f2cmax(i__1,i__2);
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}
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work[1] = (doublereal) lwkopt;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DGGES3 ", &i__1, (ftnlen)6);
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return 0;
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} else if (lquery) {
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return 0;
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}
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/* Quick return if possible */
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if (*n == 0) {
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*sdim = 0;
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return 0;
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}
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/* Get machine constants */
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eps = dlamch_("P");
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safmin = dlamch_("S");
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safmax = 1. / safmin;
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dlabad_(&safmin, &safmax);
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smlnum = sqrt(safmin) / eps;
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bignum = 1. / smlnum;
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/* Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */
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anrm = dlange_("M", n, n, &a[a_offset], lda, &work[1]);
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ilascl = FALSE_;
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if (anrm > 0. && anrm < smlnum) {
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anrmto = smlnum;
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ilascl = TRUE_;
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} else if (anrm > bignum) {
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anrmto = bignum;
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ilascl = TRUE_;
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}
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if (ilascl) {
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dlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
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ierr);
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}
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/* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */
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bnrm = dlange_("M", n, n, &b[b_offset], ldb, &work[1]);
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ilbscl = FALSE_;
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if (bnrm > 0. && bnrm < smlnum) {
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bnrmto = smlnum;
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ilbscl = TRUE_;
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} else if (bnrm > bignum) {
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bnrmto = bignum;
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ilbscl = TRUE_;
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}
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if (ilbscl) {
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dlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
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ierr);
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}
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/* Permute the matrix to make it more nearly triangular */
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ileft = 1;
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iright = *n + 1;
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iwrk = iright + *n;
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dggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
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ileft], &work[iright], &work[iwrk], &ierr);
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/* Reduce B to triangular form (QR decomposition of B) */
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irows = ihi + 1 - ilo;
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icols = *n + 1 - ilo;
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itau = iwrk;
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iwrk = itau + irows;
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i__1 = *lwork + 1 - iwrk;
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dgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
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iwrk], &i__1, &ierr);
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/* Apply the orthogonal transformation to matrix A */
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i__1 = *lwork + 1 - iwrk;
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dormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
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work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
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ierr);
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/* Initialize VSL */
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if (ilvsl) {
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dlaset_("Full", n, n, &c_b36, &c_b37, &vsl[vsl_offset], ldvsl);
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if (irows > 1) {
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i__1 = irows - 1;
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i__2 = irows - 1;
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dlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[
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ilo + 1 + ilo * vsl_dim1], ldvsl);
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}
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i__1 = *lwork + 1 - iwrk;
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dorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
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work[itau], &work[iwrk], &i__1, &ierr);
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}
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/* Initialize VSR */
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if (ilvsr) {
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dlaset_("Full", n, n, &c_b36, &c_b37, &vsr[vsr_offset], ldvsr);
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}
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/* Reduce to generalized Hessenberg form */
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i__1 = *lwork + 1 - iwrk;
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dgghd3_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
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ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &work[iwrk]
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, &i__1, &ierr);
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/* Perform QZ algorithm, computing Schur vectors if desired */
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iwrk = itau;
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i__1 = *lwork + 1 - iwrk;
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dhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
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b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset]
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, ldvsl, &vsr[vsr_offset], ldvsr, &work[iwrk], &i__1, &ierr);
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if (ierr != 0) {
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if (ierr > 0 && ierr <= *n) {
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*info = ierr;
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} else if (ierr > *n && ierr <= *n << 1) {
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|
*info = ierr - *n;
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} else {
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*info = *n + 1;
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}
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goto L50;
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}
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/* Sort eigenvalues ALPHA/BETA if desired */
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|
*sdim = 0;
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if (wantst) {
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/* Undo scaling on eigenvalues before SELCTGing */
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if (ilascl) {
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dlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1],
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n, &ierr);
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dlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1],
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n, &ierr);
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}
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if (ilbscl) {
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dlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n,
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&ierr);
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}
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/* Select eigenvalues */
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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bwork[i__] = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
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/* L10: */
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}
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i__1 = *lwork - iwrk + 1;
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dtgsen_(&c__0, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
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b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[
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vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, sdim, &pvsl, &
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pvsr, dif, &work[iwrk], &i__1, idum, &c__1, &ierr);
|
|
if (ierr == 1) {
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|
*info = *n + 3;
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|
}
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}
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/* Apply back-permutation to VSL and VSR */
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|
if (ilvsl) {
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|
dggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
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vsl_offset], ldvsl, &ierr);
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|
}
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if (ilvsr) {
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|
dggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
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vsr_offset], ldvsr, &ierr);
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|
}
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|
|
/* Check if unscaling would cause over/underflow, if so, rescale */
|
|
/* (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of */
|
|
/* B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I) */
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|
|
if (ilascl) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (alphai[i__] != 0.) {
|
|
if (alphar[i__] / safmax > anrmto / anrm || safmin / alphar[
|
|
i__] > anrm / anrmto) {
|
|
work[1] = (d__1 = a[i__ + i__ * a_dim1] / alphar[i__],
|
|
abs(d__1));
|
|
beta[i__] *= work[1];
|
|
alphar[i__] *= work[1];
|
|
alphai[i__] *= work[1];
|
|
} else if (alphai[i__] / safmax > anrmto / anrm || safmin /
|
|
alphai[i__] > anrm / anrmto) {
|
|
work[1] = (d__1 = a[i__ + (i__ + 1) * a_dim1] / alphai[
|
|
i__], abs(d__1));
|
|
beta[i__] *= work[1];
|
|
alphar[i__] *= work[1];
|
|
alphai[i__] *= work[1];
|
|
}
|
|
}
|
|
/* L20: */
|
|
}
|
|
}
|
|
|
|
if (ilbscl) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (alphai[i__] != 0.) {
|
|
if (beta[i__] / safmax > bnrmto / bnrm || safmin / beta[i__]
|
|
> bnrm / bnrmto) {
|
|
work[1] = (d__1 = b[i__ + i__ * b_dim1] / beta[i__], abs(
|
|
d__1));
|
|
beta[i__] *= work[1];
|
|
alphar[i__] *= work[1];
|
|
alphai[i__] *= work[1];
|
|
}
|
|
}
|
|
/* L30: */
|
|
}
|
|
}
|
|
|
|
/* Undo scaling */
|
|
|
|
if (ilascl) {
|
|
dlascl_("H", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
|
|
ierr);
|
|
dlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
|
|
ierr);
|
|
dlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
|
|
ierr);
|
|
}
|
|
|
|
if (ilbscl) {
|
|
dlascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
|
|
ierr);
|
|
dlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
|
|
ierr);
|
|
}
|
|
|
|
if (wantst) {
|
|
|
|
/* Check if reordering is correct */
|
|
|
|
lastsl = TRUE_;
|
|
lst2sl = TRUE_;
|
|
*sdim = 0;
|
|
ip = 0;
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
cursl = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
|
|
if (alphai[i__] == 0.) {
|
|
if (cursl) {
|
|
++(*sdim);
|
|
}
|
|
ip = 0;
|
|
if (cursl && ! lastsl) {
|
|
*info = *n + 2;
|
|
}
|
|
} else {
|
|
if (ip == 1) {
|
|
|
|
/* Last eigenvalue of conjugate pair */
|
|
|
|
cursl = cursl || lastsl;
|
|
lastsl = cursl;
|
|
if (cursl) {
|
|
*sdim += 2;
|
|
}
|
|
ip = -1;
|
|
if (cursl && ! lst2sl) {
|
|
*info = *n + 2;
|
|
}
|
|
} else {
|
|
|
|
/* First eigenvalue of conjugate pair */
|
|
|
|
ip = 1;
|
|
}
|
|
}
|
|
lst2sl = lastsl;
|
|
lastsl = cursl;
|
|
/* L40: */
|
|
}
|
|
|
|
}
|
|
|
|
L50:
|
|
|
|
work[1] = (doublereal) lwkopt;
|
|
|
|
return 0;
|
|
|
|
/* End of DGGES3 */
|
|
|
|
} /* dgges3_ */
|
|
|