1248 lines
36 KiB
C
1248 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 integer c_n1 = -1;
|
|
static integer c__1 = 1;
|
|
static integer c__0 = 0;
|
|
static doublereal c_b38 = 0.;
|
|
static doublereal c_b39 = 1.;
|
|
|
|
/* > \brief <b> DGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE mat
|
|
rices (blocked algorithm)</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DGGEV3 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggev3.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggev3.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggev3.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR, */
|
|
/* $ ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK, */
|
|
/* $ INFO ) */
|
|
|
|
/* CHARACTER JOBVL, JOBVR */
|
|
/* INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N */
|
|
/* DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), */
|
|
/* $ B( LDB, * ), BETA( * ), VL( LDVL, * ), */
|
|
/* $ VR( LDVR, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DGGEV3 computes for a pair of N-by-N real nonsymmetric matrices (A,B) */
|
|
/* > the generalized eigenvalues, and optionally, the left and/or right */
|
|
/* > generalized eigenvectors. */
|
|
/* > */
|
|
/* > A generalized eigenvalue for a pair of matrices (A,B) is a scalar */
|
|
/* > lambda or a ratio alpha/beta = lambda, such that A - lambda*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. */
|
|
/* > */
|
|
/* > The right eigenvector v(j) corresponding to the eigenvalue lambda(j) */
|
|
/* > of (A,B) satisfies */
|
|
/* > */
|
|
/* > A * v(j) = lambda(j) * B * v(j). */
|
|
/* > */
|
|
/* > The left eigenvector u(j) corresponding to the eigenvalue lambda(j) */
|
|
/* > of (A,B) satisfies */
|
|
/* > */
|
|
/* > u(j)**H * A = lambda(j) * u(j)**H * B . */
|
|
/* > */
|
|
/* > where u(j)**H is the conjugate-transpose of u(j). */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOBVL */
|
|
/* > \verbatim */
|
|
/* > JOBVL is CHARACTER*1 */
|
|
/* > = 'N': do not compute the left generalized eigenvectors; */
|
|
/* > = 'V': compute the left generalized eigenvectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] JOBVR */
|
|
/* > \verbatim */
|
|
/* > JOBVR is CHARACTER*1 */
|
|
/* > = 'N': do not compute the right generalized eigenvectors; */
|
|
/* > = 'V': compute the right generalized eigenvectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrices A, B, VL, and VR. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION array, dimension (LDA, N) */
|
|
/* > On entry, the matrix A in the pair (A,B). */
|
|
/* > On exit, A has been overwritten. */
|
|
/* > \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 matrix B in the pair (A,B). */
|
|
/* > On exit, B has been overwritten. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of B. LDB >= f2cmax(1,N). */
|
|
/* > \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. 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 */
|
|
/* > alpha/beta. 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] VL */
|
|
/* > \verbatim */
|
|
/* > VL is DOUBLE PRECISION array, dimension (LDVL,N) */
|
|
/* > If JOBVL = 'V', the left eigenvectors u(j) are stored one */
|
|
/* > after another in the columns of VL, in the same order as */
|
|
/* > their eigenvalues. If the j-th eigenvalue is real, then */
|
|
/* > u(j) = VL(:,j), the j-th column of VL. If the j-th and */
|
|
/* > (j+1)-th eigenvalues form a complex conjugate pair, then */
|
|
/* > u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1). */
|
|
/* > Each eigenvector is scaled so the largest component has */
|
|
/* > abs(real part)+abs(imag. part)=1. */
|
|
/* > Not referenced if JOBVL = 'N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVL */
|
|
/* > \verbatim */
|
|
/* > LDVL is INTEGER */
|
|
/* > The leading dimension of the matrix VL. LDVL >= 1, and */
|
|
/* > if JOBVL = 'V', LDVL >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] VR */
|
|
/* > \verbatim */
|
|
/* > VR is DOUBLE PRECISION array, dimension (LDVR,N) */
|
|
/* > If JOBVR = 'V', the right eigenvectors v(j) are stored one */
|
|
/* > after another in the columns of VR, in the same order as */
|
|
/* > their eigenvalues. If the j-th eigenvalue is real, then */
|
|
/* > v(j) = VR(:,j), the j-th column of VR. If the j-th and */
|
|
/* > (j+1)-th eigenvalues form a complex conjugate pair, then */
|
|
/* > v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1). */
|
|
/* > Each eigenvector is scaled so the largest component has */
|
|
/* > abs(real part)+abs(imag. part)=1. */
|
|
/* > Not referenced if JOBVR = 'N'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVR */
|
|
/* > \verbatim */
|
|
/* > LDVR is INTEGER */
|
|
/* > The leading dimension of the matrix VR. LDVR >= 1, and */
|
|
/* > if JOBVR = 'V', LDVR >= 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 */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > = 1,...,N: */
|
|
/* > The QZ iteration failed. No eigenvectors have been */
|
|
/* > calculated, 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: error return from DTGEVC. */
|
|
/* > \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 */ void dggev3_(char *jobvl, char *jobvr, integer *n, doublereal
|
|
*a, integer *lda, doublereal *b, integer *ldb, doublereal *alphar,
|
|
doublereal *alphai, doublereal *beta, doublereal *vl, integer *ldvl,
|
|
doublereal *vr, integer *ldvr, doublereal *work, integer *lwork,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
|
|
vr_offset, i__1, i__2;
|
|
doublereal d__1, d__2, d__3, d__4;
|
|
|
|
/* Local variables */
|
|
doublereal anrm, bnrm;
|
|
integer ierr, itau;
|
|
doublereal temp;
|
|
logical ilvl, ilvr;
|
|
integer iwrk;
|
|
extern logical lsame_(char *, char *);
|
|
integer ileft, icols;
|
|
extern /* Subroutine */ void dgghd3_(char *, char *, integer *, integer *,
|
|
integer *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, integer *, doublereal *,
|
|
integer *, integer *);
|
|
integer irows;
|
|
extern /* Subroutine */ void dlabad_(doublereal *, doublereal *);
|
|
integer jc;
|
|
extern /* Subroutine */ void 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 *);
|
|
integer in;
|
|
extern doublereal dlamch_(char *), dlange_(char *, integer *,
|
|
integer *, doublereal *, integer *, doublereal *);
|
|
integer jr;
|
|
extern /* Subroutine */ void dlascl_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, integer *, doublereal *,
|
|
integer *, integer *);
|
|
logical ilascl, ilbscl;
|
|
extern /* Subroutine */ void dgeqrf_(integer *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, integer *, integer *),
|
|
dlacpy_(char *, integer *, integer *, doublereal *, integer *,
|
|
doublereal *, integer *), dlaset_(char *, integer *,
|
|
integer *, doublereal *, doublereal *, doublereal *, integer *), dtgevc_(char *, char *, logical *, integer *, doublereal
|
|
*, integer *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, integer *, integer *, integer *, doublereal *,
|
|
integer *);
|
|
logical ldumma[1];
|
|
char chtemp[1];
|
|
doublereal bignum;
|
|
extern /* Subroutine */ void dhgeqz_(char *, char *, char *, integer *,
|
|
integer *, integer *, doublereal *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
|
|
integer *, doublereal *, integer *, doublereal *, integer *,
|
|
integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
integer ijobvl, iright, ijobvr;
|
|
extern /* Subroutine */ void dorgqr_(integer *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
|
integer *);
|
|
doublereal anrmto, bnrmto;
|
|
extern /* Subroutine */ void dormqr_(char *, char *, integer *, integer *,
|
|
integer *, doublereal *, integer *, doublereal *, doublereal *,
|
|
integer *, doublereal *, integer *, integer *);
|
|
doublereal smlnum;
|
|
integer lwkopt;
|
|
logical lquery;
|
|
integer ihi, ilo;
|
|
doublereal eps;
|
|
logical ilv;
|
|
|
|
|
|
/* -- LAPACK driver routine (version 3.6.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* January 2015 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Decode 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;
|
|
--alphar;
|
|
--alphai;
|
|
--beta;
|
|
vl_dim1 = *ldvl;
|
|
vl_offset = 1 + vl_dim1 * 1;
|
|
vl -= vl_offset;
|
|
vr_dim1 = *ldvr;
|
|
vr_offset = 1 + vr_dim1 * 1;
|
|
vr -= vr_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
if (lsame_(jobvl, "N")) {
|
|
ijobvl = 1;
|
|
ilvl = FALSE_;
|
|
} else if (lsame_(jobvl, "V")) {
|
|
ijobvl = 2;
|
|
ilvl = TRUE_;
|
|
} else {
|
|
ijobvl = -1;
|
|
ilvl = FALSE_;
|
|
}
|
|
|
|
if (lsame_(jobvr, "N")) {
|
|
ijobvr = 1;
|
|
ilvr = FALSE_;
|
|
} else if (lsame_(jobvr, "V")) {
|
|
ijobvr = 2;
|
|
ilvr = TRUE_;
|
|
} else {
|
|
ijobvr = -1;
|
|
ilvr = FALSE_;
|
|
}
|
|
ilv = ilvl || ilvr;
|
|
|
|
/* Test the input arguments */
|
|
|
|
*info = 0;
|
|
lquery = *lwork == -1;
|
|
if (ijobvl <= 0) {
|
|
*info = -1;
|
|
} else if (ijobvr <= 0) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -5;
|
|
} else if (*ldb < f2cmax(1,*n)) {
|
|
*info = -7;
|
|
} else if (*ldvl < 1 || ilvl && *ldvl < *n) {
|
|
*info = -12;
|
|
} else if (*ldvr < 1 || ilvr && *ldvr < *n) {
|
|
*info = -14;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n << 3;
|
|
if (*lwork < f2cmax(i__1,i__2) && ! lquery) {
|
|
*info = -16;
|
|
}
|
|
}
|
|
|
|
/* Compute workspace */
|
|
|
|
if (*info == 0) {
|
|
dgeqrf_(n, n, &b[b_offset], ldb, &work[1], &work[1], &c_n1, &ierr);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n << 3, i__1 = f2cmax(i__1,i__2), i__2 = *n * 3 + (
|
|
integer) work[1];
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
dormqr_("L", "T", n, n, n, &b[b_offset], ldb, &work[1], &a[a_offset],
|
|
lda, &work[1], &c_n1, &ierr);
|
|
/* Computing MAX */
|
|
i__1 = lwkopt, i__2 = *n * 3 + (integer) work[1];
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
if (ilvl) {
|
|
dorgqr_(n, n, n, &vl[vl_offset], ldvl, &work[1], &work[1], &c_n1,
|
|
&ierr);
|
|
/* Computing MAX */
|
|
i__1 = lwkopt, i__2 = *n * 3 + (integer) work[1];
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
}
|
|
if (ilv) {
|
|
dgghd3_(jobvl, jobvr, n, &c__1, n, &a[a_offset], lda, &b[b_offset]
|
|
, ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &work[
|
|
1], &c_n1, &ierr);
|
|
/* Computing MAX */
|
|
i__1 = lwkopt, i__2 = *n * 3 + (integer) work[1];
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
dhgeqz_("S", jobvl, jobvr, n, &c__1, n, &a[a_offset], lda, &b[
|
|
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[
|
|
vl_offset], ldvl, &vr[vr_offset], ldvr, &work[1], &c_n1, &
|
|
ierr);
|
|
/* Computing MAX */
|
|
i__1 = lwkopt, i__2 = (*n << 1) + (integer) work[1];
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
} else {
|
|
dgghd3_("N", "N", n, &c__1, n, &a[a_offset], lda, &b[b_offset],
|
|
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &work[1],
|
|
&c_n1, &ierr);
|
|
/* Computing MAX */
|
|
i__1 = lwkopt, i__2 = *n * 3 + (integer) work[1];
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
dhgeqz_("E", jobvl, jobvr, n, &c__1, n, &a[a_offset], lda, &b[
|
|
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[
|
|
vl_offset], ldvl, &vr[vr_offset], ldvr, &work[1], &c_n1, &
|
|
ierr);
|
|
/* Computing MAX */
|
|
i__1 = lwkopt, i__2 = (*n << 1) + (integer) work[1];
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
}
|
|
work[1] = (doublereal) lwkopt;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DGGEV3 ", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 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 = dlange_("M", n, n, &a[a_offset], lda, &work[1]);
|
|
ilascl = FALSE_;
|
|
if (anrm > 0. && anrm < smlnum) {
|
|
anrmto = smlnum;
|
|
ilascl = TRUE_;
|
|
} else if (anrm > bignum) {
|
|
anrmto = bignum;
|
|
ilascl = TRUE_;
|
|
}
|
|
if (ilascl) {
|
|
dlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
|
|
ierr);
|
|
}
|
|
|
|
/* Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */
|
|
|
|
bnrm = dlange_("M", n, n, &b[b_offset], ldb, &work[1]);
|
|
ilbscl = FALSE_;
|
|
if (bnrm > 0. && bnrm < smlnum) {
|
|
bnrmto = smlnum;
|
|
ilbscl = TRUE_;
|
|
} else if (bnrm > bignum) {
|
|
bnrmto = bignum;
|
|
ilbscl = TRUE_;
|
|
}
|
|
if (ilbscl) {
|
|
dlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
|
|
ierr);
|
|
}
|
|
|
|
/* Permute the matrices A, B to isolate eigenvalues if possible */
|
|
|
|
ileft = 1;
|
|
iright = *n + 1;
|
|
iwrk = iright + *n;
|
|
dggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
|
|
ileft], &work[iright], &work[iwrk], &ierr);
|
|
|
|
/* Reduce B to triangular form (QR decomposition of B) */
|
|
|
|
irows = ihi + 1 - ilo;
|
|
if (ilv) {
|
|
icols = *n + 1 - ilo;
|
|
} else {
|
|
icols = irows;
|
|
}
|
|
itau = iwrk;
|
|
iwrk = itau + irows;
|
|
i__1 = *lwork + 1 - iwrk;
|
|
dgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
|
|
iwrk], &i__1, &ierr);
|
|
|
|
/* Apply the orthogonal transformation to matrix A */
|
|
|
|
i__1 = *lwork + 1 - iwrk;
|
|
dormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
|
|
work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
|
|
ierr);
|
|
|
|
/* Initialize VL */
|
|
|
|
if (ilvl) {
|
|
dlaset_("Full", n, n, &c_b38, &c_b39, &vl[vl_offset], ldvl)
|
|
;
|
|
if (irows > 1) {
|
|
i__1 = irows - 1;
|
|
i__2 = irows - 1;
|
|
dlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[
|
|
ilo + 1 + ilo * vl_dim1], ldvl);
|
|
}
|
|
i__1 = *lwork + 1 - iwrk;
|
|
dorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
|
|
itau], &work[iwrk], &i__1, &ierr);
|
|
}
|
|
|
|
/* Initialize VR */
|
|
|
|
if (ilvr) {
|
|
dlaset_("Full", n, n, &c_b38, &c_b39, &vr[vr_offset], ldvr)
|
|
;
|
|
}
|
|
|
|
/* Reduce to generalized Hessenberg form */
|
|
|
|
if (ilv) {
|
|
|
|
/* Eigenvectors requested -- work on whole matrix. */
|
|
|
|
i__1 = *lwork + 1 - iwrk;
|
|
dgghd3_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset],
|
|
ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &work[iwrk],
|
|
&i__1, &ierr);
|
|
} else {
|
|
i__1 = *lwork + 1 - iwrk;
|
|
dgghd3_("N", "N", &irows, &c__1, &irows, &a[ilo + ilo * a_dim1], lda,
|
|
&b[ilo + ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[
|
|
vr_offset], ldvr, &work[iwrk], &i__1, &ierr);
|
|
}
|
|
|
|
/* Perform QZ algorithm (Compute eigenvalues, and optionally, the */
|
|
/* Schur forms and Schur vectors) */
|
|
|
|
iwrk = itau;
|
|
if (ilv) {
|
|
*(unsigned char *)chtemp = 'S';
|
|
} else {
|
|
*(unsigned char *)chtemp = 'E';
|
|
}
|
|
i__1 = *lwork + 1 - iwrk;
|
|
dhgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
|
|
b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset],
|
|
ldvl, &vr[vr_offset], ldvr, &work[iwrk], &i__1, &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 L110;
|
|
}
|
|
|
|
/* Compute Eigenvectors */
|
|
|
|
if (ilv) {
|
|
if (ilvl) {
|
|
if (ilvr) {
|
|
*(unsigned char *)chtemp = 'B';
|
|
} else {
|
|
*(unsigned char *)chtemp = 'L';
|
|
}
|
|
} else {
|
|
*(unsigned char *)chtemp = 'R';
|
|
}
|
|
dtgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb,
|
|
&vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
|
|
iwrk], &ierr);
|
|
if (ierr != 0) {
|
|
*info = *n + 2;
|
|
goto L110;
|
|
}
|
|
|
|
/* Undo balancing on VL and VR and normalization */
|
|
|
|
if (ilvl) {
|
|
dggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
|
|
vl[vl_offset], ldvl, &ierr);
|
|
i__1 = *n;
|
|
for (jc = 1; jc <= i__1; ++jc) {
|
|
if (alphai[jc] < 0.) {
|
|
goto L50;
|
|
}
|
|
temp = 0.;
|
|
if (alphai[jc] == 0.) {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
/* Computing MAX */
|
|
d__2 = temp, d__3 = (d__1 = vl[jr + jc * vl_dim1],
|
|
abs(d__1));
|
|
temp = f2cmax(d__2,d__3);
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
/* Computing MAX */
|
|
d__3 = temp, d__4 = (d__1 = vl[jr + jc * vl_dim1],
|
|
abs(d__1)) + (d__2 = vl[jr + (jc + 1) *
|
|
vl_dim1], abs(d__2));
|
|
temp = f2cmax(d__3,d__4);
|
|
/* L20: */
|
|
}
|
|
}
|
|
if (temp < smlnum) {
|
|
goto L50;
|
|
}
|
|
temp = 1. / temp;
|
|
if (alphai[jc] == 0.) {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
vl[jr + jc * vl_dim1] *= temp;
|
|
/* L30: */
|
|
}
|
|
} else {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
vl[jr + jc * vl_dim1] *= temp;
|
|
vl[jr + (jc + 1) * vl_dim1] *= temp;
|
|
/* L40: */
|
|
}
|
|
}
|
|
L50:
|
|
;
|
|
}
|
|
}
|
|
if (ilvr) {
|
|
dggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
|
|
vr[vr_offset], ldvr, &ierr);
|
|
i__1 = *n;
|
|
for (jc = 1; jc <= i__1; ++jc) {
|
|
if (alphai[jc] < 0.) {
|
|
goto L100;
|
|
}
|
|
temp = 0.;
|
|
if (alphai[jc] == 0.) {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
/* Computing MAX */
|
|
d__2 = temp, d__3 = (d__1 = vr[jr + jc * vr_dim1],
|
|
abs(d__1));
|
|
temp = f2cmax(d__2,d__3);
|
|
/* L60: */
|
|
}
|
|
} else {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
/* Computing MAX */
|
|
d__3 = temp, d__4 = (d__1 = vr[jr + jc * vr_dim1],
|
|
abs(d__1)) + (d__2 = vr[jr + (jc + 1) *
|
|
vr_dim1], abs(d__2));
|
|
temp = f2cmax(d__3,d__4);
|
|
/* L70: */
|
|
}
|
|
}
|
|
if (temp < smlnum) {
|
|
goto L100;
|
|
}
|
|
temp = 1. / temp;
|
|
if (alphai[jc] == 0.) {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
vr[jr + jc * vr_dim1] *= temp;
|
|
/* L80: */
|
|
}
|
|
} else {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
vr[jr + jc * vr_dim1] *= temp;
|
|
vr[jr + (jc + 1) * vr_dim1] *= temp;
|
|
/* L90: */
|
|
}
|
|
}
|
|
L100:
|
|
;
|
|
}
|
|
}
|
|
|
|
/* End of eigenvector calculation */
|
|
|
|
}
|
|
|
|
/* Undo scaling if necessary */
|
|
|
|
L110:
|
|
|
|
if (ilascl) {
|
|
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_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
|
|
ierr);
|
|
}
|
|
|
|
work[1] = (doublereal) lwkopt;
|
|
return;
|
|
|
|
/* End of DGGEV3 */
|
|
|
|
} /* dggev3_ */
|
|
|