1971 lines
54 KiB
C
1971 lines
54 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 {
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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 logical c_true = TRUE_;
|
|
static integer c__2 = 2;
|
|
static doublereal c_b34 = 1.;
|
|
static integer c__1 = 1;
|
|
static doublereal c_b36 = 0.;
|
|
static logical c_false = FALSE_;
|
|
|
|
/* > \brief \b DTGEVC */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DTGEVC + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgevc.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgevc.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgevc.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, */
|
|
/* LDVL, VR, LDVR, MM, M, WORK, INFO ) */
|
|
|
|
/* CHARACTER HOWMNY, SIDE */
|
|
/* INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N */
|
|
/* LOGICAL SELECT( * ) */
|
|
/* DOUBLE PRECISION P( LDP, * ), S( LDS, * ), VL( LDVL, * ), */
|
|
/* $ VR( LDVR, * ), WORK( * ) */
|
|
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DTGEVC computes some or all of the right and/or left eigenvectors of */
|
|
/* > a pair of real matrices (S,P), where S is a quasi-triangular matrix */
|
|
/* > and P is upper triangular. Matrix pairs of this type are produced by */
|
|
/* > the generalized Schur factorization of a matrix pair (A,B): */
|
|
/* > */
|
|
/* > A = Q*S*Z**T, B = Q*P*Z**T */
|
|
/* > */
|
|
/* > as computed by DGGHRD + DHGEQZ. */
|
|
/* > */
|
|
/* > The right eigenvector x and the left eigenvector y of (S,P) */
|
|
/* > corresponding to an eigenvalue w are defined by: */
|
|
/* > */
|
|
/* > S*x = w*P*x, (y**H)*S = w*(y**H)*P, */
|
|
/* > */
|
|
/* > where y**H denotes the conjugate tranpose of y. */
|
|
/* > The eigenvalues are not input to this routine, but are computed */
|
|
/* > directly from the diagonal blocks of S and P. */
|
|
/* > */
|
|
/* > This routine returns the matrices X and/or Y of right and left */
|
|
/* > eigenvectors of (S,P), or the products Z*X and/or Q*Y, */
|
|
/* > where Z and Q are input matrices. */
|
|
/* > If Q and Z are the orthogonal factors from the generalized Schur */
|
|
/* > factorization of a matrix pair (A,B), then Z*X and Q*Y */
|
|
/* > are the matrices of right and left eigenvectors of (A,B). */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] SIDE */
|
|
/* > \verbatim */
|
|
/* > SIDE is CHARACTER*1 */
|
|
/* > = 'R': compute right eigenvectors only; */
|
|
/* > = 'L': compute left eigenvectors only; */
|
|
/* > = 'B': compute both right and left eigenvectors. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] HOWMNY */
|
|
/* > \verbatim */
|
|
/* > HOWMNY is CHARACTER*1 */
|
|
/* > = 'A': compute all right and/or left eigenvectors; */
|
|
/* > = 'B': compute all right and/or left eigenvectors, */
|
|
/* > backtransformed by the matrices in VR and/or VL; */
|
|
/* > = 'S': compute selected right and/or left eigenvectors, */
|
|
/* > specified by the logical array SELECT. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SELECT */
|
|
/* > \verbatim */
|
|
/* > SELECT is LOGICAL array, dimension (N) */
|
|
/* > If HOWMNY='S', SELECT specifies the eigenvectors to be */
|
|
/* > computed. If w(j) is a real eigenvalue, the corresponding */
|
|
/* > real eigenvector is computed if SELECT(j) is .TRUE.. */
|
|
/* > If w(j) and w(j+1) are the real and imaginary parts of a */
|
|
/* > complex eigenvalue, the corresponding complex eigenvector */
|
|
/* > is computed if either SELECT(j) or SELECT(j+1) is .TRUE., */
|
|
/* > and on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is */
|
|
/* > set to .FALSE.. */
|
|
/* > Not referenced if HOWMNY = 'A' or 'B'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrices S and P. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] S */
|
|
/* > \verbatim */
|
|
/* > S is DOUBLE PRECISION array, dimension (LDS,N) */
|
|
/* > The upper quasi-triangular matrix S from a generalized Schur */
|
|
/* > factorization, as computed by DHGEQZ. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDS */
|
|
/* > \verbatim */
|
|
/* > LDS is INTEGER */
|
|
/* > The leading dimension of array S. LDS >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] P */
|
|
/* > \verbatim */
|
|
/* > P is DOUBLE PRECISION array, dimension (LDP,N) */
|
|
/* > The upper triangular matrix P from a generalized Schur */
|
|
/* > factorization, as computed by DHGEQZ. */
|
|
/* > 2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks */
|
|
/* > of S must be in positive diagonal form. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDP */
|
|
/* > \verbatim */
|
|
/* > LDP is INTEGER */
|
|
/* > The leading dimension of array P. LDP >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] VL */
|
|
/* > \verbatim */
|
|
/* > VL is DOUBLE PRECISION array, dimension (LDVL,MM) */
|
|
/* > On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */
|
|
/* > contain an N-by-N matrix Q (usually the orthogonal matrix Q */
|
|
/* > of left Schur vectors returned by DHGEQZ). */
|
|
/* > On exit, if SIDE = 'L' or 'B', VL contains: */
|
|
/* > if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); */
|
|
/* > if HOWMNY = 'B', the matrix Q*Y; */
|
|
/* > if HOWMNY = 'S', the left eigenvectors of (S,P) specified by */
|
|
/* > SELECT, stored consecutively in the columns of */
|
|
/* > VL, in the same order as their eigenvalues. */
|
|
/* > */
|
|
/* > A complex eigenvector corresponding to a complex eigenvalue */
|
|
/* > is stored in two consecutive columns, the first holding the */
|
|
/* > real part, and the second the imaginary part. */
|
|
/* > */
|
|
/* > Not referenced if SIDE = 'R'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVL */
|
|
/* > \verbatim */
|
|
/* > LDVL is INTEGER */
|
|
/* > The leading dimension of array VL. LDVL >= 1, and if */
|
|
/* > SIDE = 'L' or 'B', LDVL >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] VR */
|
|
/* > \verbatim */
|
|
/* > VR is DOUBLE PRECISION array, dimension (LDVR,MM) */
|
|
/* > On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */
|
|
/* > contain an N-by-N matrix Z (usually the orthogonal matrix Z */
|
|
/* > of right Schur vectors returned by DHGEQZ). */
|
|
/* > */
|
|
/* > On exit, if SIDE = 'R' or 'B', VR contains: */
|
|
/* > if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); */
|
|
/* > if HOWMNY = 'B' or 'b', the matrix Z*X; */
|
|
/* > if HOWMNY = 'S' or 's', the right eigenvectors of (S,P) */
|
|
/* > specified by SELECT, stored consecutively in the */
|
|
/* > columns of VR, in the same order as their */
|
|
/* > eigenvalues. */
|
|
/* > */
|
|
/* > A complex eigenvector corresponding to a complex eigenvalue */
|
|
/* > is stored in two consecutive columns, the first holding the */
|
|
/* > real part and the second the imaginary part. */
|
|
/* > */
|
|
/* > Not referenced if SIDE = 'L'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVR */
|
|
/* > \verbatim */
|
|
/* > LDVR is INTEGER */
|
|
/* > The leading dimension of the array VR. LDVR >= 1, and if */
|
|
/* > SIDE = 'R' or 'B', LDVR >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] MM */
|
|
/* > \verbatim */
|
|
/* > MM is INTEGER */
|
|
/* > The number of columns in the arrays VL and/or VR. MM >= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of columns in the arrays VL and/or VR actually */
|
|
/* > used to store the eigenvectors. If HOWMNY = 'A' or 'B', M */
|
|
/* > is set to N. Each selected real eigenvector occupies one */
|
|
/* > column and each selected complex eigenvector occupies two */
|
|
/* > columns. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (6*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: the 2-by-2 block (INFO:INFO+1) does not have a complex */
|
|
/* > eigenvalue. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleGEcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > Allocation of workspace: */
|
|
/* > ---------- -- --------- */
|
|
/* > */
|
|
/* > WORK( j ) = 1-norm of j-th column of A, above the diagonal */
|
|
/* > WORK( N+j ) = 1-norm of j-th column of B, above the diagonal */
|
|
/* > WORK( 2*N+1:3*N ) = real part of eigenvector */
|
|
/* > WORK( 3*N+1:4*N ) = imaginary part of eigenvector */
|
|
/* > WORK( 4*N+1:5*N ) = real part of back-transformed eigenvector */
|
|
/* > WORK( 5*N+1:6*N ) = imaginary part of back-transformed eigenvector */
|
|
/* > */
|
|
/* > Rowwise vs. columnwise solution methods: */
|
|
/* > ------- -- ---------- -------- ------- */
|
|
/* > */
|
|
/* > Finding a generalized eigenvector consists basically of solving the */
|
|
/* > singular triangular system */
|
|
/* > */
|
|
/* > (A - w B) x = 0 (for right) or: (A - w B)**H y = 0 (for left) */
|
|
/* > */
|
|
/* > Consider finding the i-th right eigenvector (assume all eigenvalues */
|
|
/* > are real). The equation to be solved is: */
|
|
/* > n i */
|
|
/* > 0 = sum C(j,k) v(k) = sum C(j,k) v(k) for j = i,. . .,1 */
|
|
/* > k=j k=j */
|
|
/* > */
|
|
/* > where C = (A - w B) (The components v(i+1:n) are 0.) */
|
|
/* > */
|
|
/* > The "rowwise" method is: */
|
|
/* > */
|
|
/* > (1) v(i) := 1 */
|
|
/* > for j = i-1,. . .,1: */
|
|
/* > i */
|
|
/* > (2) compute s = - sum C(j,k) v(k) and */
|
|
/* > k=j+1 */
|
|
/* > */
|
|
/* > (3) v(j) := s / C(j,j) */
|
|
/* > */
|
|
/* > Step 2 is sometimes called the "dot product" step, since it is an */
|
|
/* > inner product between the j-th row and the portion of the eigenvector */
|
|
/* > that has been computed so far. */
|
|
/* > */
|
|
/* > The "columnwise" method consists basically in doing the sums */
|
|
/* > for all the rows in parallel. As each v(j) is computed, the */
|
|
/* > contribution of v(j) times the j-th column of C is added to the */
|
|
/* > partial sums. Since FORTRAN arrays are stored columnwise, this has */
|
|
/* > the advantage that at each step, the elements of C that are accessed */
|
|
/* > are adjacent to one another, whereas with the rowwise method, the */
|
|
/* > elements accessed at a step are spaced LDS (and LDP) words apart. */
|
|
/* > */
|
|
/* > When finding left eigenvectors, the matrix in question is the */
|
|
/* > transpose of the one in storage, so the rowwise method then */
|
|
/* > actually accesses columns of A and B at each step, and so is the */
|
|
/* > preferred method. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dtgevc_(char *side, char *howmny, logical *select,
|
|
integer *n, doublereal *s, integer *lds, doublereal *p, integer *ldp,
|
|
doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, integer
|
|
*mm, integer *m, doublereal *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1,
|
|
vr_offset, i__1, i__2, i__3, i__4, i__5;
|
|
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
|
|
|
|
/* Local variables */
|
|
integer ibeg, ieig, iend;
|
|
doublereal dmin__, temp, xmax, sump[4] /* was [2][2] */, sums[4]
|
|
/* was [2][2] */;
|
|
extern /* Subroutine */ void dlag2_(doublereal *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *, doublereal *);
|
|
doublereal cim2a, cim2b, cre2a, cre2b, temp2, bdiag[2];
|
|
integer i__, j;
|
|
doublereal acoef, scale;
|
|
logical ilall;
|
|
integer iside;
|
|
doublereal sbeta;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void dgemv_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, doublereal *, integer *);
|
|
logical il2by2;
|
|
integer iinfo;
|
|
doublereal small;
|
|
logical compl;
|
|
doublereal anorm, bnorm;
|
|
logical compr;
|
|
extern /* Subroutine */ void dlaln2_(logical *, integer *, integer *,
|
|
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
|
|
doublereal *, doublereal *, integer *, doublereal *, doublereal *
|
|
, doublereal *, integer *, doublereal *, doublereal *, integer *);
|
|
doublereal temp2i;
|
|
extern /* Subroutine */ void dlabad_(doublereal *, doublereal *);
|
|
doublereal temp2r;
|
|
integer ja;
|
|
logical ilabad, ilbbad;
|
|
integer jc, je, na;
|
|
doublereal acoefa, bcoefa, cimaga, cimagb;
|
|
logical ilback;
|
|
integer im;
|
|
doublereal bcoefi, ascale, bscale, creala;
|
|
integer jr;
|
|
doublereal crealb;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal bcoefr;
|
|
integer jw, nw;
|
|
doublereal salfar, safmin;
|
|
extern /* Subroutine */ void dlacpy_(char *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, integer *);
|
|
doublereal xscale, bignum;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
logical ilcomp, ilcplx;
|
|
integer ihwmny;
|
|
doublereal big;
|
|
logical lsa, lsb;
|
|
doublereal ulp, sum[4] /* was [2][2] */;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Decode and Test the input parameters */
|
|
|
|
/* Parameter adjustments */
|
|
--select;
|
|
s_dim1 = *lds;
|
|
s_offset = 1 + s_dim1 * 1;
|
|
s -= s_offset;
|
|
p_dim1 = *ldp;
|
|
p_offset = 1 + p_dim1 * 1;
|
|
p -= p_offset;
|
|
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_(howmny, "A")) {
|
|
ihwmny = 1;
|
|
ilall = TRUE_;
|
|
ilback = FALSE_;
|
|
} else if (lsame_(howmny, "S")) {
|
|
ihwmny = 2;
|
|
ilall = FALSE_;
|
|
ilback = FALSE_;
|
|
} else if (lsame_(howmny, "B")) {
|
|
ihwmny = 3;
|
|
ilall = TRUE_;
|
|
ilback = TRUE_;
|
|
} else {
|
|
ihwmny = -1;
|
|
ilall = TRUE_;
|
|
}
|
|
|
|
if (lsame_(side, "R")) {
|
|
iside = 1;
|
|
compl = FALSE_;
|
|
compr = TRUE_;
|
|
} else if (lsame_(side, "L")) {
|
|
iside = 2;
|
|
compl = TRUE_;
|
|
compr = FALSE_;
|
|
} else if (lsame_(side, "B")) {
|
|
iside = 3;
|
|
compl = TRUE_;
|
|
compr = TRUE_;
|
|
} else {
|
|
iside = -1;
|
|
}
|
|
|
|
*info = 0;
|
|
if (iside < 0) {
|
|
*info = -1;
|
|
} else if (ihwmny < 0) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -4;
|
|
} else if (*lds < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
} else if (*ldp < f2cmax(1,*n)) {
|
|
*info = -8;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DTGEVC", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Count the number of eigenvectors to be computed */
|
|
|
|
if (! ilall) {
|
|
im = 0;
|
|
ilcplx = FALSE_;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (ilcplx) {
|
|
ilcplx = FALSE_;
|
|
goto L10;
|
|
}
|
|
if (j < *n) {
|
|
if (s[j + 1 + j * s_dim1] != 0.) {
|
|
ilcplx = TRUE_;
|
|
}
|
|
}
|
|
if (ilcplx) {
|
|
if (select[j] || select[j + 1]) {
|
|
im += 2;
|
|
}
|
|
} else {
|
|
if (select[j]) {
|
|
++im;
|
|
}
|
|
}
|
|
L10:
|
|
;
|
|
}
|
|
} else {
|
|
im = *n;
|
|
}
|
|
|
|
/* Check 2-by-2 diagonal blocks of A, B */
|
|
|
|
ilabad = FALSE_;
|
|
ilbbad = FALSE_;
|
|
i__1 = *n - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (s[j + 1 + j * s_dim1] != 0.) {
|
|
if (p[j + j * p_dim1] == 0. || p[j + 1 + (j + 1) * p_dim1] == 0.
|
|
|| p[j + (j + 1) * p_dim1] != 0.) {
|
|
ilbbad = TRUE_;
|
|
}
|
|
if (j < *n - 1) {
|
|
if (s[j + 2 + (j + 1) * s_dim1] != 0.) {
|
|
ilabad = TRUE_;
|
|
}
|
|
}
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
if (ilabad) {
|
|
*info = -5;
|
|
} else if (ilbbad) {
|
|
*info = -7;
|
|
} else if (compl && *ldvl < *n || *ldvl < 1) {
|
|
*info = -10;
|
|
} else if (compr && *ldvr < *n || *ldvr < 1) {
|
|
*info = -12;
|
|
} else if (*mm < im) {
|
|
*info = -13;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DTGEVC", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
*m = im;
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Machine Constants */
|
|
|
|
safmin = dlamch_("Safe minimum");
|
|
big = 1. / safmin;
|
|
dlabad_(&safmin, &big);
|
|
ulp = dlamch_("Epsilon") * dlamch_("Base");
|
|
small = safmin * *n / ulp;
|
|
big = 1. / small;
|
|
bignum = 1. / (safmin * *n);
|
|
|
|
/* Compute the 1-norm of each column of the strictly upper triangular */
|
|
/* part (i.e., excluding all elements belonging to the diagonal */
|
|
/* blocks) of A and B to check for possible overflow in the */
|
|
/* triangular solver. */
|
|
|
|
anorm = (d__1 = s[s_dim1 + 1], abs(d__1));
|
|
if (*n > 1) {
|
|
anorm += (d__1 = s[s_dim1 + 2], abs(d__1));
|
|
}
|
|
bnorm = (d__1 = p[p_dim1 + 1], abs(d__1));
|
|
work[1] = 0.;
|
|
work[*n + 1] = 0.;
|
|
|
|
i__1 = *n;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
temp = 0.;
|
|
temp2 = 0.;
|
|
if (s[j + (j - 1) * s_dim1] == 0.) {
|
|
iend = j - 1;
|
|
} else {
|
|
iend = j - 2;
|
|
}
|
|
i__2 = iend;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
temp += (d__1 = s[i__ + j * s_dim1], abs(d__1));
|
|
temp2 += (d__1 = p[i__ + j * p_dim1], abs(d__1));
|
|
/* L30: */
|
|
}
|
|
work[j] = temp;
|
|
work[*n + j] = temp2;
|
|
/* Computing MIN */
|
|
i__3 = j + 1;
|
|
i__2 = f2cmin(i__3,*n);
|
|
for (i__ = iend + 1; i__ <= i__2; ++i__) {
|
|
temp += (d__1 = s[i__ + j * s_dim1], abs(d__1));
|
|
temp2 += (d__1 = p[i__ + j * p_dim1], abs(d__1));
|
|
/* L40: */
|
|
}
|
|
anorm = f2cmax(anorm,temp);
|
|
bnorm = f2cmax(bnorm,temp2);
|
|
/* L50: */
|
|
}
|
|
|
|
ascale = 1. / f2cmax(anorm,safmin);
|
|
bscale = 1. / f2cmax(bnorm,safmin);
|
|
|
|
/* Left eigenvectors */
|
|
|
|
if (compl) {
|
|
ieig = 0;
|
|
|
|
/* Main loop over eigenvalues */
|
|
|
|
ilcplx = FALSE_;
|
|
i__1 = *n;
|
|
for (je = 1; je <= i__1; ++je) {
|
|
|
|
/* Skip this iteration if (a) HOWMNY='S' and SELECT=.FALSE., or */
|
|
/* (b) this would be the second of a complex pair. */
|
|
/* Check for complex eigenvalue, so as to be sure of which */
|
|
/* entry(-ies) of SELECT to look at. */
|
|
|
|
if (ilcplx) {
|
|
ilcplx = FALSE_;
|
|
goto L220;
|
|
}
|
|
nw = 1;
|
|
if (je < *n) {
|
|
if (s[je + 1 + je * s_dim1] != 0.) {
|
|
ilcplx = TRUE_;
|
|
nw = 2;
|
|
}
|
|
}
|
|
if (ilall) {
|
|
ilcomp = TRUE_;
|
|
} else if (ilcplx) {
|
|
ilcomp = select[je] || select[je + 1];
|
|
} else {
|
|
ilcomp = select[je];
|
|
}
|
|
if (! ilcomp) {
|
|
goto L220;
|
|
}
|
|
|
|
/* Decide if (a) singular pencil, (b) real eigenvalue, or */
|
|
/* (c) complex eigenvalue. */
|
|
|
|
if (! ilcplx) {
|
|
if ((d__1 = s[je + je * s_dim1], abs(d__1)) <= safmin && (
|
|
d__2 = p[je + je * p_dim1], abs(d__2)) <= safmin) {
|
|
|
|
/* Singular matrix pencil -- return unit eigenvector */
|
|
|
|
++ieig;
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
vl[jr + ieig * vl_dim1] = 0.;
|
|
/* L60: */
|
|
}
|
|
vl[ieig + ieig * vl_dim1] = 1.;
|
|
goto L220;
|
|
}
|
|
}
|
|
|
|
/* Clear vector */
|
|
|
|
i__2 = nw * *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
work[(*n << 1) + jr] = 0.;
|
|
/* L70: */
|
|
}
|
|
/* T */
|
|
/* Compute coefficients in ( a A - b B ) y = 0 */
|
|
/* a is ACOEF */
|
|
/* b is BCOEFR + i*BCOEFI */
|
|
|
|
if (! ilcplx) {
|
|
|
|
/* Real eigenvalue */
|
|
|
|
/* Computing MAX */
|
|
d__3 = (d__1 = s[je + je * s_dim1], abs(d__1)) * ascale, d__4
|
|
= (d__2 = p[je + je * p_dim1], abs(d__2)) * bscale,
|
|
d__3 = f2cmax(d__3,d__4);
|
|
temp = 1. / f2cmax(d__3,safmin);
|
|
salfar = temp * s[je + je * s_dim1] * ascale;
|
|
sbeta = temp * p[je + je * p_dim1] * bscale;
|
|
acoef = sbeta * ascale;
|
|
bcoefr = salfar * bscale;
|
|
bcoefi = 0.;
|
|
|
|
/* Scale to avoid underflow */
|
|
|
|
scale = 1.;
|
|
lsa = abs(sbeta) >= safmin && abs(acoef) < small;
|
|
lsb = abs(salfar) >= safmin && abs(bcoefr) < small;
|
|
if (lsa) {
|
|
scale = small / abs(sbeta) * f2cmin(anorm,big);
|
|
}
|
|
if (lsb) {
|
|
/* Computing MAX */
|
|
d__1 = scale, d__2 = small / abs(salfar) * f2cmin(bnorm,big);
|
|
scale = f2cmax(d__1,d__2);
|
|
}
|
|
if (lsa || lsb) {
|
|
/* Computing MIN */
|
|
/* Computing MAX */
|
|
d__3 = 1., d__4 = abs(acoef), d__3 = f2cmax(d__3,d__4), d__4
|
|
= abs(bcoefr);
|
|
d__1 = scale, d__2 = 1. / (safmin * f2cmax(d__3,d__4));
|
|
scale = f2cmin(d__1,d__2);
|
|
if (lsa) {
|
|
acoef = ascale * (scale * sbeta);
|
|
} else {
|
|
acoef = scale * acoef;
|
|
}
|
|
if (lsb) {
|
|
bcoefr = bscale * (scale * salfar);
|
|
} else {
|
|
bcoefr = scale * bcoefr;
|
|
}
|
|
}
|
|
acoefa = abs(acoef);
|
|
bcoefa = abs(bcoefr);
|
|
|
|
/* First component is 1 */
|
|
|
|
work[(*n << 1) + je] = 1.;
|
|
xmax = 1.;
|
|
} else {
|
|
|
|
/* Complex eigenvalue */
|
|
|
|
d__1 = safmin * 100.;
|
|
dlag2_(&s[je + je * s_dim1], lds, &p[je + je * p_dim1], ldp, &
|
|
d__1, &acoef, &temp, &bcoefr, &temp2, &bcoefi);
|
|
bcoefi = -bcoefi;
|
|
if (bcoefi == 0.) {
|
|
*info = je;
|
|
return;
|
|
}
|
|
|
|
/* Scale to avoid over/underflow */
|
|
|
|
acoefa = abs(acoef);
|
|
bcoefa = abs(bcoefr) + abs(bcoefi);
|
|
scale = 1.;
|
|
if (acoefa * ulp < safmin && acoefa >= safmin) {
|
|
scale = safmin / ulp / acoefa;
|
|
}
|
|
if (bcoefa * ulp < safmin && bcoefa >= safmin) {
|
|
/* Computing MAX */
|
|
d__1 = scale, d__2 = safmin / ulp / bcoefa;
|
|
scale = f2cmax(d__1,d__2);
|
|
}
|
|
if (safmin * acoefa > ascale) {
|
|
scale = ascale / (safmin * acoefa);
|
|
}
|
|
if (safmin * bcoefa > bscale) {
|
|
/* Computing MIN */
|
|
d__1 = scale, d__2 = bscale / (safmin * bcoefa);
|
|
scale = f2cmin(d__1,d__2);
|
|
}
|
|
if (scale != 1.) {
|
|
acoef = scale * acoef;
|
|
acoefa = abs(acoef);
|
|
bcoefr = scale * bcoefr;
|
|
bcoefi = scale * bcoefi;
|
|
bcoefa = abs(bcoefr) + abs(bcoefi);
|
|
}
|
|
|
|
/* Compute first two components of eigenvector */
|
|
|
|
temp = acoef * s[je + 1 + je * s_dim1];
|
|
temp2r = acoef * s[je + je * s_dim1] - bcoefr * p[je + je *
|
|
p_dim1];
|
|
temp2i = -bcoefi * p[je + je * p_dim1];
|
|
if (abs(temp) > abs(temp2r) + abs(temp2i)) {
|
|
work[(*n << 1) + je] = 1.;
|
|
work[*n * 3 + je] = 0.;
|
|
work[(*n << 1) + je + 1] = -temp2r / temp;
|
|
work[*n * 3 + je + 1] = -temp2i / temp;
|
|
} else {
|
|
work[(*n << 1) + je + 1] = 1.;
|
|
work[*n * 3 + je + 1] = 0.;
|
|
temp = acoef * s[je + (je + 1) * s_dim1];
|
|
work[(*n << 1) + je] = (bcoefr * p[je + 1 + (je + 1) *
|
|
p_dim1] - acoef * s[je + 1 + (je + 1) * s_dim1]) /
|
|
temp;
|
|
work[*n * 3 + je] = bcoefi * p[je + 1 + (je + 1) * p_dim1]
|
|
/ temp;
|
|
}
|
|
/* Computing MAX */
|
|
d__5 = (d__1 = work[(*n << 1) + je], abs(d__1)) + (d__2 =
|
|
work[*n * 3 + je], abs(d__2)), d__6 = (d__3 = work[(*
|
|
n << 1) + je + 1], abs(d__3)) + (d__4 = work[*n * 3 +
|
|
je + 1], abs(d__4));
|
|
xmax = f2cmax(d__5,d__6);
|
|
}
|
|
|
|
/* Computing MAX */
|
|
d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, d__1 =
|
|
f2cmax(d__1,d__2);
|
|
dmin__ = f2cmax(d__1,safmin);
|
|
|
|
/* T */
|
|
/* Triangular solve of (a A - b B) y = 0 */
|
|
|
|
/* T */
|
|
/* (rowwise in (a A - b B) , or columnwise in (a A - b B) ) */
|
|
|
|
il2by2 = FALSE_;
|
|
|
|
i__2 = *n;
|
|
for (j = je + nw; j <= i__2; ++j) {
|
|
if (il2by2) {
|
|
il2by2 = FALSE_;
|
|
goto L160;
|
|
}
|
|
|
|
na = 1;
|
|
bdiag[0] = p[j + j * p_dim1];
|
|
if (j < *n) {
|
|
if (s[j + 1 + j * s_dim1] != 0.) {
|
|
il2by2 = TRUE_;
|
|
bdiag[1] = p[j + 1 + (j + 1) * p_dim1];
|
|
na = 2;
|
|
}
|
|
}
|
|
|
|
/* Check whether scaling is necessary for dot products */
|
|
|
|
xscale = 1. / f2cmax(1.,xmax);
|
|
/* Computing MAX */
|
|
d__1 = work[j], d__2 = work[*n + j], d__1 = f2cmax(d__1,d__2),
|
|
d__2 = acoefa * work[j] + bcoefa * work[*n + j];
|
|
temp = f2cmax(d__1,d__2);
|
|
if (il2by2) {
|
|
/* Computing MAX */
|
|
d__1 = temp, d__2 = work[j + 1], d__1 = f2cmax(d__1,d__2),
|
|
d__2 = work[*n + j + 1], d__1 = f2cmax(d__1,d__2),
|
|
d__2 = acoefa * work[j + 1] + bcoefa * work[*n +
|
|
j + 1];
|
|
temp = f2cmax(d__1,d__2);
|
|
}
|
|
if (temp > bignum * xscale) {
|
|
i__3 = nw - 1;
|
|
for (jw = 0; jw <= i__3; ++jw) {
|
|
i__4 = j - 1;
|
|
for (jr = je; jr <= i__4; ++jr) {
|
|
work[(jw + 2) * *n + jr] = xscale * work[(jw + 2)
|
|
* *n + jr];
|
|
/* L80: */
|
|
}
|
|
/* L90: */
|
|
}
|
|
xmax *= xscale;
|
|
}
|
|
|
|
/* Compute dot products */
|
|
|
|
/* j-1 */
|
|
/* SUM = sum conjg( a*S(k,j) - b*P(k,j) )*x(k) */
|
|
/* k=je */
|
|
|
|
/* To reduce the op count, this is done as */
|
|
|
|
/* _ j-1 _ j-1 */
|
|
/* a*conjg( sum S(k,j)*x(k) ) - b*conjg( sum P(k,j)*x(k) ) */
|
|
/* k=je k=je */
|
|
|
|
/* which may cause underflow problems if A or B are close */
|
|
/* to underflow. (E.g., less than SMALL.) */
|
|
|
|
|
|
i__3 = nw;
|
|
for (jw = 1; jw <= i__3; ++jw) {
|
|
i__4 = na;
|
|
for (ja = 1; ja <= i__4; ++ja) {
|
|
sums[ja + (jw << 1) - 3] = 0.;
|
|
sump[ja + (jw << 1) - 3] = 0.;
|
|
|
|
i__5 = j - 1;
|
|
for (jr = je; jr <= i__5; ++jr) {
|
|
sums[ja + (jw << 1) - 3] += s[jr + (j + ja - 1) *
|
|
s_dim1] * work[(jw + 1) * *n + jr];
|
|
sump[ja + (jw << 1) - 3] += p[jr + (j + ja - 1) *
|
|
p_dim1] * work[(jw + 1) * *n + jr];
|
|
/* L100: */
|
|
}
|
|
/* L110: */
|
|
}
|
|
/* L120: */
|
|
}
|
|
|
|
i__3 = na;
|
|
for (ja = 1; ja <= i__3; ++ja) {
|
|
if (ilcplx) {
|
|
sum[ja - 1] = -acoef * sums[ja - 1] + bcoefr * sump[
|
|
ja - 1] - bcoefi * sump[ja + 1];
|
|
sum[ja + 1] = -acoef * sums[ja + 1] + bcoefr * sump[
|
|
ja + 1] + bcoefi * sump[ja - 1];
|
|
} else {
|
|
sum[ja - 1] = -acoef * sums[ja - 1] + bcoefr * sump[
|
|
ja - 1];
|
|
}
|
|
/* L130: */
|
|
}
|
|
|
|
/* T */
|
|
/* Solve ( a A - b B ) y = SUM(,) */
|
|
/* with scaling and perturbation of the denominator */
|
|
|
|
dlaln2_(&c_true, &na, &nw, &dmin__, &acoef, &s[j + j * s_dim1]
|
|
, lds, bdiag, &bdiag[1], sum, &c__2, &bcoefr, &bcoefi,
|
|
&work[(*n << 1) + j], n, &scale, &temp, &iinfo);
|
|
if (scale < 1.) {
|
|
i__3 = nw - 1;
|
|
for (jw = 0; jw <= i__3; ++jw) {
|
|
i__4 = j - 1;
|
|
for (jr = je; jr <= i__4; ++jr) {
|
|
work[(jw + 2) * *n + jr] = scale * work[(jw + 2) *
|
|
*n + jr];
|
|
/* L140: */
|
|
}
|
|
/* L150: */
|
|
}
|
|
xmax = scale * xmax;
|
|
}
|
|
xmax = f2cmax(xmax,temp);
|
|
L160:
|
|
;
|
|
}
|
|
|
|
/* Copy eigenvector to VL, back transforming if */
|
|
/* HOWMNY='B'. */
|
|
|
|
++ieig;
|
|
if (ilback) {
|
|
i__2 = nw - 1;
|
|
for (jw = 0; jw <= i__2; ++jw) {
|
|
i__3 = *n + 1 - je;
|
|
dgemv_("N", n, &i__3, &c_b34, &vl[je * vl_dim1 + 1], ldvl,
|
|
&work[(jw + 2) * *n + je], &c__1, &c_b36, &work[(
|
|
jw + 4) * *n + 1], &c__1);
|
|
/* L170: */
|
|
}
|
|
dlacpy_(" ", n, &nw, &work[(*n << 2) + 1], n, &vl[je *
|
|
vl_dim1 + 1], ldvl);
|
|
ibeg = 1;
|
|
} else {
|
|
dlacpy_(" ", n, &nw, &work[(*n << 1) + 1], n, &vl[ieig *
|
|
vl_dim1 + 1], ldvl);
|
|
ibeg = je;
|
|
}
|
|
|
|
/* Scale eigenvector */
|
|
|
|
xmax = 0.;
|
|
if (ilcplx) {
|
|
i__2 = *n;
|
|
for (j = ibeg; j <= i__2; ++j) {
|
|
/* Computing MAX */
|
|
d__3 = xmax, d__4 = (d__1 = vl[j + ieig * vl_dim1], abs(
|
|
d__1)) + (d__2 = vl[j + (ieig + 1) * vl_dim1],
|
|
abs(d__2));
|
|
xmax = f2cmax(d__3,d__4);
|
|
/* L180: */
|
|
}
|
|
} else {
|
|
i__2 = *n;
|
|
for (j = ibeg; j <= i__2; ++j) {
|
|
/* Computing MAX */
|
|
d__2 = xmax, d__3 = (d__1 = vl[j + ieig * vl_dim1], abs(
|
|
d__1));
|
|
xmax = f2cmax(d__2,d__3);
|
|
/* L190: */
|
|
}
|
|
}
|
|
|
|
if (xmax > safmin) {
|
|
xscale = 1. / xmax;
|
|
|
|
i__2 = nw - 1;
|
|
for (jw = 0; jw <= i__2; ++jw) {
|
|
i__3 = *n;
|
|
for (jr = ibeg; jr <= i__3; ++jr) {
|
|
vl[jr + (ieig + jw) * vl_dim1] = xscale * vl[jr + (
|
|
ieig + jw) * vl_dim1];
|
|
/* L200: */
|
|
}
|
|
/* L210: */
|
|
}
|
|
}
|
|
ieig = ieig + nw - 1;
|
|
|
|
L220:
|
|
;
|
|
}
|
|
}
|
|
|
|
/* Right eigenvectors */
|
|
|
|
if (compr) {
|
|
ieig = im + 1;
|
|
|
|
/* Main loop over eigenvalues */
|
|
|
|
ilcplx = FALSE_;
|
|
for (je = *n; je >= 1; --je) {
|
|
|
|
/* Skip this iteration if (a) HOWMNY='S' and SELECT=.FALSE., or */
|
|
/* (b) this would be the second of a complex pair. */
|
|
/* Check for complex eigenvalue, so as to be sure of which */
|
|
/* entry(-ies) of SELECT to look at -- if complex, SELECT(JE) */
|
|
/* or SELECT(JE-1). */
|
|
/* If this is a complex pair, the 2-by-2 diagonal block */
|
|
/* corresponding to the eigenvalue is in rows/columns JE-1:JE */
|
|
|
|
if (ilcplx) {
|
|
ilcplx = FALSE_;
|
|
goto L500;
|
|
}
|
|
nw = 1;
|
|
if (je > 1) {
|
|
if (s[je + (je - 1) * s_dim1] != 0.) {
|
|
ilcplx = TRUE_;
|
|
nw = 2;
|
|
}
|
|
}
|
|
if (ilall) {
|
|
ilcomp = TRUE_;
|
|
} else if (ilcplx) {
|
|
ilcomp = select[je] || select[je - 1];
|
|
} else {
|
|
ilcomp = select[je];
|
|
}
|
|
if (! ilcomp) {
|
|
goto L500;
|
|
}
|
|
|
|
/* Decide if (a) singular pencil, (b) real eigenvalue, or */
|
|
/* (c) complex eigenvalue. */
|
|
|
|
if (! ilcplx) {
|
|
if ((d__1 = s[je + je * s_dim1], abs(d__1)) <= safmin && (
|
|
d__2 = p[je + je * p_dim1], abs(d__2)) <= safmin) {
|
|
|
|
/* Singular matrix pencil -- unit eigenvector */
|
|
|
|
--ieig;
|
|
i__1 = *n;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
vr[jr + ieig * vr_dim1] = 0.;
|
|
/* L230: */
|
|
}
|
|
vr[ieig + ieig * vr_dim1] = 1.;
|
|
goto L500;
|
|
}
|
|
}
|
|
|
|
/* Clear vector */
|
|
|
|
i__1 = nw - 1;
|
|
for (jw = 0; jw <= i__1; ++jw) {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
work[(jw + 2) * *n + jr] = 0.;
|
|
/* L240: */
|
|
}
|
|
/* L250: */
|
|
}
|
|
|
|
/* Compute coefficients in ( a A - b B ) x = 0 */
|
|
/* a is ACOEF */
|
|
/* b is BCOEFR + i*BCOEFI */
|
|
|
|
if (! ilcplx) {
|
|
|
|
/* Real eigenvalue */
|
|
|
|
/* Computing MAX */
|
|
d__3 = (d__1 = s[je + je * s_dim1], abs(d__1)) * ascale, d__4
|
|
= (d__2 = p[je + je * p_dim1], abs(d__2)) * bscale,
|
|
d__3 = f2cmax(d__3,d__4);
|
|
temp = 1. / f2cmax(d__3,safmin);
|
|
salfar = temp * s[je + je * s_dim1] * ascale;
|
|
sbeta = temp * p[je + je * p_dim1] * bscale;
|
|
acoef = sbeta * ascale;
|
|
bcoefr = salfar * bscale;
|
|
bcoefi = 0.;
|
|
|
|
/* Scale to avoid underflow */
|
|
|
|
scale = 1.;
|
|
lsa = abs(sbeta) >= safmin && abs(acoef) < small;
|
|
lsb = abs(salfar) >= safmin && abs(bcoefr) < small;
|
|
if (lsa) {
|
|
scale = small / abs(sbeta) * f2cmin(anorm,big);
|
|
}
|
|
if (lsb) {
|
|
/* Computing MAX */
|
|
d__1 = scale, d__2 = small / abs(salfar) * f2cmin(bnorm,big);
|
|
scale = f2cmax(d__1,d__2);
|
|
}
|
|
if (lsa || lsb) {
|
|
/* Computing MIN */
|
|
/* Computing MAX */
|
|
d__3 = 1., d__4 = abs(acoef), d__3 = f2cmax(d__3,d__4), d__4
|
|
= abs(bcoefr);
|
|
d__1 = scale, d__2 = 1. / (safmin * f2cmax(d__3,d__4));
|
|
scale = f2cmin(d__1,d__2);
|
|
if (lsa) {
|
|
acoef = ascale * (scale * sbeta);
|
|
} else {
|
|
acoef = scale * acoef;
|
|
}
|
|
if (lsb) {
|
|
bcoefr = bscale * (scale * salfar);
|
|
} else {
|
|
bcoefr = scale * bcoefr;
|
|
}
|
|
}
|
|
acoefa = abs(acoef);
|
|
bcoefa = abs(bcoefr);
|
|
|
|
/* First component is 1 */
|
|
|
|
work[(*n << 1) + je] = 1.;
|
|
xmax = 1.;
|
|
|
|
/* Compute contribution from column JE of A and B to sum */
|
|
/* (See "Further Details", above.) */
|
|
|
|
i__1 = je - 1;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
work[(*n << 1) + jr] = bcoefr * p[jr + je * p_dim1] -
|
|
acoef * s[jr + je * s_dim1];
|
|
/* L260: */
|
|
}
|
|
} else {
|
|
|
|
/* Complex eigenvalue */
|
|
|
|
d__1 = safmin * 100.;
|
|
dlag2_(&s[je - 1 + (je - 1) * s_dim1], lds, &p[je - 1 + (je -
|
|
1) * p_dim1], ldp, &d__1, &acoef, &temp, &bcoefr, &
|
|
temp2, &bcoefi);
|
|
if (bcoefi == 0.) {
|
|
*info = je - 1;
|
|
return;
|
|
}
|
|
|
|
/* Scale to avoid over/underflow */
|
|
|
|
acoefa = abs(acoef);
|
|
bcoefa = abs(bcoefr) + abs(bcoefi);
|
|
scale = 1.;
|
|
if (acoefa * ulp < safmin && acoefa >= safmin) {
|
|
scale = safmin / ulp / acoefa;
|
|
}
|
|
if (bcoefa * ulp < safmin && bcoefa >= safmin) {
|
|
/* Computing MAX */
|
|
d__1 = scale, d__2 = safmin / ulp / bcoefa;
|
|
scale = f2cmax(d__1,d__2);
|
|
}
|
|
if (safmin * acoefa > ascale) {
|
|
scale = ascale / (safmin * acoefa);
|
|
}
|
|
if (safmin * bcoefa > bscale) {
|
|
/* Computing MIN */
|
|
d__1 = scale, d__2 = bscale / (safmin * bcoefa);
|
|
scale = f2cmin(d__1,d__2);
|
|
}
|
|
if (scale != 1.) {
|
|
acoef = scale * acoef;
|
|
acoefa = abs(acoef);
|
|
bcoefr = scale * bcoefr;
|
|
bcoefi = scale * bcoefi;
|
|
bcoefa = abs(bcoefr) + abs(bcoefi);
|
|
}
|
|
|
|
/* Compute first two components of eigenvector */
|
|
/* and contribution to sums */
|
|
|
|
temp = acoef * s[je + (je - 1) * s_dim1];
|
|
temp2r = acoef * s[je + je * s_dim1] - bcoefr * p[je + je *
|
|
p_dim1];
|
|
temp2i = -bcoefi * p[je + je * p_dim1];
|
|
if (abs(temp) >= abs(temp2r) + abs(temp2i)) {
|
|
work[(*n << 1) + je] = 1.;
|
|
work[*n * 3 + je] = 0.;
|
|
work[(*n << 1) + je - 1] = -temp2r / temp;
|
|
work[*n * 3 + je - 1] = -temp2i / temp;
|
|
} else {
|
|
work[(*n << 1) + je - 1] = 1.;
|
|
work[*n * 3 + je - 1] = 0.;
|
|
temp = acoef * s[je - 1 + je * s_dim1];
|
|
work[(*n << 1) + je] = (bcoefr * p[je - 1 + (je - 1) *
|
|
p_dim1] - acoef * s[je - 1 + (je - 1) * s_dim1]) /
|
|
temp;
|
|
work[*n * 3 + je] = bcoefi * p[je - 1 + (je - 1) * p_dim1]
|
|
/ temp;
|
|
}
|
|
|
|
/* Computing MAX */
|
|
d__5 = (d__1 = work[(*n << 1) + je], abs(d__1)) + (d__2 =
|
|
work[*n * 3 + je], abs(d__2)), d__6 = (d__3 = work[(*
|
|
n << 1) + je - 1], abs(d__3)) + (d__4 = work[*n * 3 +
|
|
je - 1], abs(d__4));
|
|
xmax = f2cmax(d__5,d__6);
|
|
|
|
/* Compute contribution from columns JE and JE-1 */
|
|
/* of A and B to the sums. */
|
|
|
|
creala = acoef * work[(*n << 1) + je - 1];
|
|
cimaga = acoef * work[*n * 3 + je - 1];
|
|
crealb = bcoefr * work[(*n << 1) + je - 1] - bcoefi * work[*n
|
|
* 3 + je - 1];
|
|
cimagb = bcoefi * work[(*n << 1) + je - 1] + bcoefr * work[*n
|
|
* 3 + je - 1];
|
|
cre2a = acoef * work[(*n << 1) + je];
|
|
cim2a = acoef * work[*n * 3 + je];
|
|
cre2b = bcoefr * work[(*n << 1) + je] - bcoefi * work[*n * 3
|
|
+ je];
|
|
cim2b = bcoefi * work[(*n << 1) + je] + bcoefr * work[*n * 3
|
|
+ je];
|
|
i__1 = je - 2;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
work[(*n << 1) + jr] = -creala * s[jr + (je - 1) * s_dim1]
|
|
+ crealb * p[jr + (je - 1) * p_dim1] - cre2a * s[
|
|
jr + je * s_dim1] + cre2b * p[jr + je * p_dim1];
|
|
work[*n * 3 + jr] = -cimaga * s[jr + (je - 1) * s_dim1] +
|
|
cimagb * p[jr + (je - 1) * p_dim1] - cim2a * s[jr
|
|
+ je * s_dim1] + cim2b * p[jr + je * p_dim1];
|
|
/* L270: */
|
|
}
|
|
}
|
|
|
|
/* Computing MAX */
|
|
d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, d__1 =
|
|
f2cmax(d__1,d__2);
|
|
dmin__ = f2cmax(d__1,safmin);
|
|
|
|
/* Columnwise triangular solve of (a A - b B) x = 0 */
|
|
|
|
il2by2 = FALSE_;
|
|
for (j = je - nw; j >= 1; --j) {
|
|
|
|
/* If a 2-by-2 block, is in position j-1:j, wait until */
|
|
/* next iteration to process it (when it will be j:j+1) */
|
|
|
|
if (! il2by2 && j > 1) {
|
|
if (s[j + (j - 1) * s_dim1] != 0.) {
|
|
il2by2 = TRUE_;
|
|
goto L370;
|
|
}
|
|
}
|
|
bdiag[0] = p[j + j * p_dim1];
|
|
if (il2by2) {
|
|
na = 2;
|
|
bdiag[1] = p[j + 1 + (j + 1) * p_dim1];
|
|
} else {
|
|
na = 1;
|
|
}
|
|
|
|
/* Compute x(j) (and x(j+1), if 2-by-2 block) */
|
|
|
|
dlaln2_(&c_false, &na, &nw, &dmin__, &acoef, &s[j + j *
|
|
s_dim1], lds, bdiag, &bdiag[1], &work[(*n << 1) + j],
|
|
n, &bcoefr, &bcoefi, sum, &c__2, &scale, &temp, &
|
|
iinfo);
|
|
if (scale < 1.) {
|
|
|
|
i__1 = nw - 1;
|
|
for (jw = 0; jw <= i__1; ++jw) {
|
|
i__2 = je;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
work[(jw + 2) * *n + jr] = scale * work[(jw + 2) *
|
|
*n + jr];
|
|
/* L280: */
|
|
}
|
|
/* L290: */
|
|
}
|
|
}
|
|
/* Computing MAX */
|
|
d__1 = scale * xmax;
|
|
xmax = f2cmax(d__1,temp);
|
|
|
|
i__1 = nw;
|
|
for (jw = 1; jw <= i__1; ++jw) {
|
|
i__2 = na;
|
|
for (ja = 1; ja <= i__2; ++ja) {
|
|
work[(jw + 1) * *n + j + ja - 1] = sum[ja + (jw << 1)
|
|
- 3];
|
|
/* L300: */
|
|
}
|
|
/* L310: */
|
|
}
|
|
|
|
/* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */
|
|
|
|
if (j > 1) {
|
|
|
|
/* Check whether scaling is necessary for sum. */
|
|
|
|
xscale = 1. / f2cmax(1.,xmax);
|
|
temp = acoefa * work[j] + bcoefa * work[*n + j];
|
|
if (il2by2) {
|
|
/* Computing MAX */
|
|
d__1 = temp, d__2 = acoefa * work[j + 1] + bcoefa *
|
|
work[*n + j + 1];
|
|
temp = f2cmax(d__1,d__2);
|
|
}
|
|
/* Computing MAX */
|
|
d__1 = f2cmax(temp,acoefa);
|
|
temp = f2cmax(d__1,bcoefa);
|
|
if (temp > bignum * xscale) {
|
|
|
|
i__1 = nw - 1;
|
|
for (jw = 0; jw <= i__1; ++jw) {
|
|
i__2 = je;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
work[(jw + 2) * *n + jr] = xscale * work[(jw
|
|
+ 2) * *n + jr];
|
|
/* L320: */
|
|
}
|
|
/* L330: */
|
|
}
|
|
xmax *= xscale;
|
|
}
|
|
|
|
/* Compute the contributions of the off-diagonals of */
|
|
/* column j (and j+1, if 2-by-2 block) of A and B to the */
|
|
/* sums. */
|
|
|
|
|
|
i__1 = na;
|
|
for (ja = 1; ja <= i__1; ++ja) {
|
|
if (ilcplx) {
|
|
creala = acoef * work[(*n << 1) + j + ja - 1];
|
|
cimaga = acoef * work[*n * 3 + j + ja - 1];
|
|
crealb = bcoefr * work[(*n << 1) + j + ja - 1] -
|
|
bcoefi * work[*n * 3 + j + ja - 1];
|
|
cimagb = bcoefi * work[(*n << 1) + j + ja - 1] +
|
|
bcoefr * work[*n * 3 + j + ja - 1];
|
|
i__2 = j - 1;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
work[(*n << 1) + jr] = work[(*n << 1) + jr] -
|
|
creala * s[jr + (j + ja - 1) * s_dim1]
|
|
+ crealb * p[jr + (j + ja - 1) *
|
|
p_dim1];
|
|
work[*n * 3 + jr] = work[*n * 3 + jr] -
|
|
cimaga * s[jr + (j + ja - 1) * s_dim1]
|
|
+ cimagb * p[jr + (j + ja - 1) *
|
|
p_dim1];
|
|
/* L340: */
|
|
}
|
|
} else {
|
|
creala = acoef * work[(*n << 1) + j + ja - 1];
|
|
crealb = bcoefr * work[(*n << 1) + j + ja - 1];
|
|
i__2 = j - 1;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
work[(*n << 1) + jr] = work[(*n << 1) + jr] -
|
|
creala * s[jr + (j + ja - 1) * s_dim1]
|
|
+ crealb * p[jr + (j + ja - 1) *
|
|
p_dim1];
|
|
/* L350: */
|
|
}
|
|
}
|
|
/* L360: */
|
|
}
|
|
}
|
|
|
|
il2by2 = FALSE_;
|
|
L370:
|
|
;
|
|
}
|
|
|
|
/* Copy eigenvector to VR, back transforming if */
|
|
/* HOWMNY='B'. */
|
|
|
|
ieig -= nw;
|
|
if (ilback) {
|
|
|
|
i__1 = nw - 1;
|
|
for (jw = 0; jw <= i__1; ++jw) {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
work[(jw + 4) * *n + jr] = work[(jw + 2) * *n + 1] *
|
|
vr[jr + vr_dim1];
|
|
/* L380: */
|
|
}
|
|
|
|
/* A series of compiler directives to defeat */
|
|
/* vectorization for the next loop */
|
|
|
|
|
|
i__2 = je;
|
|
for (jc = 2; jc <= i__2; ++jc) {
|
|
i__3 = *n;
|
|
for (jr = 1; jr <= i__3; ++jr) {
|
|
work[(jw + 4) * *n + jr] += work[(jw + 2) * *n +
|
|
jc] * vr[jr + jc * vr_dim1];
|
|
/* L390: */
|
|
}
|
|
/* L400: */
|
|
}
|
|
/* L410: */
|
|
}
|
|
|
|
i__1 = nw - 1;
|
|
for (jw = 0; jw <= i__1; ++jw) {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
vr[jr + (ieig + jw) * vr_dim1] = work[(jw + 4) * *n +
|
|
jr];
|
|
/* L420: */
|
|
}
|
|
/* L430: */
|
|
}
|
|
|
|
iend = *n;
|
|
} else {
|
|
i__1 = nw - 1;
|
|
for (jw = 0; jw <= i__1; ++jw) {
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
vr[jr + (ieig + jw) * vr_dim1] = work[(jw + 2) * *n +
|
|
jr];
|
|
/* L440: */
|
|
}
|
|
/* L450: */
|
|
}
|
|
|
|
iend = je;
|
|
}
|
|
|
|
/* Scale eigenvector */
|
|
|
|
xmax = 0.;
|
|
if (ilcplx) {
|
|
i__1 = iend;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
/* Computing MAX */
|
|
d__3 = xmax, d__4 = (d__1 = vr[j + ieig * vr_dim1], abs(
|
|
d__1)) + (d__2 = vr[j + (ieig + 1) * vr_dim1],
|
|
abs(d__2));
|
|
xmax = f2cmax(d__3,d__4);
|
|
/* L460: */
|
|
}
|
|
} else {
|
|
i__1 = iend;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
/* Computing MAX */
|
|
d__2 = xmax, d__3 = (d__1 = vr[j + ieig * vr_dim1], abs(
|
|
d__1));
|
|
xmax = f2cmax(d__2,d__3);
|
|
/* L470: */
|
|
}
|
|
}
|
|
|
|
if (xmax > safmin) {
|
|
xscale = 1. / xmax;
|
|
i__1 = nw - 1;
|
|
for (jw = 0; jw <= i__1; ++jw) {
|
|
i__2 = iend;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
vr[jr + (ieig + jw) * vr_dim1] = xscale * vr[jr + (
|
|
ieig + jw) * vr_dim1];
|
|
/* L480: */
|
|
}
|
|
/* L490: */
|
|
}
|
|
}
|
|
L500:
|
|
;
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of DTGEVC */
|
|
|
|
} /* dtgevc_ */
|
|
|