1553 lines
43 KiB
C
1553 lines
43 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static complex c_b1 = {0.f,0.f};
|
|
static complex c_b2 = {1.f,0.f};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b CTGEVC */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CTGEVC + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctgevc.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctgevc.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctgevc.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, */
|
|
/* LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO ) */
|
|
|
|
/* CHARACTER HOWMNY, SIDE */
|
|
/* INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N */
|
|
/* LOGICAL SELECT( * ) */
|
|
/* REAL RWORK( * ) */
|
|
/* COMPLEX P( LDP, * ), S( LDS, * ), VL( LDVL, * ), */
|
|
/* $ VR( LDVR, * ), WORK( * ) */
|
|
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CTGEVC computes some or all of the right and/or left eigenvectors of */
|
|
/* > a pair of complex matrices (S,P), where S and P are upper triangular. */
|
|
/* > Matrix pairs of this type are produced by the generalized Schur */
|
|
/* > factorization of a complex matrix pair (A,B): */
|
|
/* > */
|
|
/* > A = Q*S*Z**H, B = Q*P*Z**H */
|
|
/* > */
|
|
/* > as computed by CGGHRD + CHGEQZ. */
|
|
/* > */
|
|
/* > 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 elements 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 unitary 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. The eigenvector corresponding to the j-th */
|
|
/* > eigenvalue is computed if SELECT(j) = .TRUE.. */
|
|
/* > 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 COMPLEX array, dimension (LDS,N) */
|
|
/* > The upper triangular matrix S from a generalized Schur */
|
|
/* > factorization, as computed by CHGEQZ. */
|
|
/* > \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 COMPLEX array, dimension (LDP,N) */
|
|
/* > The upper triangular matrix P from a generalized Schur */
|
|
/* > factorization, as computed by CHGEQZ. P must have real */
|
|
/* > diagonal elements. */
|
|
/* > \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 COMPLEX 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 unitary matrix Q */
|
|
/* > of left Schur vectors returned by CHGEQZ). */
|
|
/* > 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. */
|
|
/* > 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 'l' or 'B' or 'b', LDVL >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] VR */
|
|
/* > \verbatim */
|
|
/* > VR is COMPLEX array, dimension (LDVR,MM) */
|
|
/* > On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */
|
|
/* > contain an N-by-N matrix Q (usually the unitary matrix Z */
|
|
/* > of right Schur vectors returned by CHGEQZ). */
|
|
/* > On exit, if SIDE = 'R' or 'B', VR contains: */
|
|
/* > if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); */
|
|
/* > if HOWMNY = 'B', the matrix Z*X; */
|
|
/* > if HOWMNY = 'S', the right eigenvectors of (S,P) specified by */
|
|
/* > SELECT, stored consecutively in the columns of */
|
|
/* > VR, in the same order as their eigenvalues. */
|
|
/* > 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 eigenvector occupies one column. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is REAL array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complexGEcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int ctgevc_(char *side, char *howmny, logical *select,
|
|
integer *n, complex *s, integer *lds, complex *p, integer *ldp,
|
|
complex *vl, integer *ldvl, complex *vr, integer *ldvr, integer *mm,
|
|
integer *m, complex *work, real *rwork, 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;
|
|
real r__1, r__2, r__3, r__4, r__5, r__6;
|
|
complex q__1, q__2, q__3, q__4;
|
|
|
|
/* Local variables */
|
|
integer ibeg, ieig, iend;
|
|
real dmin__;
|
|
integer isrc;
|
|
real temp;
|
|
complex suma, sumb;
|
|
real xmax;
|
|
complex d__;
|
|
integer i__, j;
|
|
real scale;
|
|
logical ilall;
|
|
integer iside;
|
|
real sbeta;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
|
|
, complex *, integer *, complex *, integer *, complex *, complex *
|
|
, integer *);
|
|
real small;
|
|
logical compl;
|
|
real anorm, bnorm;
|
|
logical compr;
|
|
complex ca, cb;
|
|
logical ilbbad;
|
|
real acoefa;
|
|
integer je;
|
|
real bcoefa, acoeff;
|
|
complex bcoeff;
|
|
logical ilback;
|
|
integer im;
|
|
extern /* Subroutine */ int slabad_(real *, real *);
|
|
real ascale, bscale;
|
|
integer jr;
|
|
extern /* Complex */ VOID cladiv_(complex *, complex *, complex *);
|
|
extern real slamch_(char *);
|
|
complex salpha;
|
|
real safmin;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
real bignum;
|
|
logical ilcomp;
|
|
integer ihwmny;
|
|
real big;
|
|
logical lsa, lsb;
|
|
real ulp;
|
|
complex sum;
|
|
|
|
|
|
/* -- 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;
|
|
--rwork;
|
|
|
|
/* 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;
|
|
}
|
|
|
|
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_("CTGEVC", &i__1, (ftnlen)6);
|
|
return 0;
|
|
}
|
|
|
|
/* Count the number of eigenvectors */
|
|
|
|
if (! ilall) {
|
|
im = 0;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (select[j]) {
|
|
++im;
|
|
}
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
im = *n;
|
|
}
|
|
|
|
/* Check diagonal of B */
|
|
|
|
ilbbad = FALSE_;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (r_imag(&p[j + j * p_dim1]) != 0.f) {
|
|
ilbbad = TRUE_;
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
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_("CTGEVC", &i__1, (ftnlen)6);
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
*m = im;
|
|
if (*n == 0) {
|
|
return 0;
|
|
}
|
|
|
|
/* Machine Constants */
|
|
|
|
safmin = slamch_("Safe minimum");
|
|
big = 1.f / safmin;
|
|
slabad_(&safmin, &big);
|
|
ulp = slamch_("Epsilon") * slamch_("Base");
|
|
small = safmin * *n / ulp;
|
|
big = 1.f / small;
|
|
bignum = 1.f / (safmin * *n);
|
|
|
|
/* Compute the 1-norm of each column of the strictly upper triangular */
|
|
/* part of A and B to check for possible overflow in the triangular */
|
|
/* solver. */
|
|
|
|
i__1 = s_dim1 + 1;
|
|
anorm = (r__1 = s[i__1].r, abs(r__1)) + (r__2 = r_imag(&s[s_dim1 + 1]),
|
|
abs(r__2));
|
|
i__1 = p_dim1 + 1;
|
|
bnorm = (r__1 = p[i__1].r, abs(r__1)) + (r__2 = r_imag(&p[p_dim1 + 1]),
|
|
abs(r__2));
|
|
rwork[1] = 0.f;
|
|
rwork[*n + 1] = 0.f;
|
|
i__1 = *n;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
rwork[j] = 0.f;
|
|
rwork[*n + j] = 0.f;
|
|
i__2 = j - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * s_dim1;
|
|
rwork[j] += (r__1 = s[i__3].r, abs(r__1)) + (r__2 = r_imag(&s[i__
|
|
+ j * s_dim1]), abs(r__2));
|
|
i__3 = i__ + j * p_dim1;
|
|
rwork[*n + j] += (r__1 = p[i__3].r, abs(r__1)) + (r__2 = r_imag(&
|
|
p[i__ + j * p_dim1]), abs(r__2));
|
|
/* L30: */
|
|
}
|
|
/* Computing MAX */
|
|
i__2 = j + j * s_dim1;
|
|
r__3 = anorm, r__4 = rwork[j] + ((r__1 = s[i__2].r, abs(r__1)) + (
|
|
r__2 = r_imag(&s[j + j * s_dim1]), abs(r__2)));
|
|
anorm = f2cmax(r__3,r__4);
|
|
/* Computing MAX */
|
|
i__2 = j + j * p_dim1;
|
|
r__3 = bnorm, r__4 = rwork[*n + j] + ((r__1 = p[i__2].r, abs(r__1)) +
|
|
(r__2 = r_imag(&p[j + j * p_dim1]), abs(r__2)));
|
|
bnorm = f2cmax(r__3,r__4);
|
|
/* L40: */
|
|
}
|
|
|
|
ascale = 1.f / f2cmax(anorm,safmin);
|
|
bscale = 1.f / f2cmax(bnorm,safmin);
|
|
|
|
/* Left eigenvectors */
|
|
|
|
if (compl) {
|
|
ieig = 0;
|
|
|
|
/* Main loop over eigenvalues */
|
|
|
|
i__1 = *n;
|
|
for (je = 1; je <= i__1; ++je) {
|
|
if (ilall) {
|
|
ilcomp = TRUE_;
|
|
} else {
|
|
ilcomp = select[je];
|
|
}
|
|
if (ilcomp) {
|
|
++ieig;
|
|
|
|
i__2 = je + je * s_dim1;
|
|
i__3 = je + je * p_dim1;
|
|
if ((r__2 = s[i__2].r, abs(r__2)) + (r__3 = r_imag(&s[je + je
|
|
* s_dim1]), abs(r__3)) <= safmin && (r__1 = p[i__3].r,
|
|
abs(r__1)) <= safmin) {
|
|
|
|
/* Singular matrix pencil -- return unit eigenvector */
|
|
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
i__3 = jr + ieig * vl_dim1;
|
|
vl[i__3].r = 0.f, vl[i__3].i = 0.f;
|
|
/* L50: */
|
|
}
|
|
i__2 = ieig + ieig * vl_dim1;
|
|
vl[i__2].r = 1.f, vl[i__2].i = 0.f;
|
|
goto L140;
|
|
}
|
|
|
|
/* Non-singular eigenvalue: */
|
|
/* Compute coefficients a and b in */
|
|
/* H */
|
|
/* y ( a A - b B ) = 0 */
|
|
|
|
/* Computing MAX */
|
|
i__2 = je + je * s_dim1;
|
|
i__3 = je + je * p_dim1;
|
|
r__4 = ((r__2 = s[i__2].r, abs(r__2)) + (r__3 = r_imag(&s[je
|
|
+ je * s_dim1]), abs(r__3))) * ascale, r__5 = (r__1 =
|
|
p[i__3].r, abs(r__1)) * bscale, r__4 = f2cmax(r__4,r__5);
|
|
temp = 1.f / f2cmax(r__4,safmin);
|
|
i__2 = je + je * s_dim1;
|
|
q__2.r = temp * s[i__2].r, q__2.i = temp * s[i__2].i;
|
|
q__1.r = ascale * q__2.r, q__1.i = ascale * q__2.i;
|
|
salpha.r = q__1.r, salpha.i = q__1.i;
|
|
i__2 = je + je * p_dim1;
|
|
sbeta = temp * p[i__2].r * bscale;
|
|
acoeff = sbeta * ascale;
|
|
q__1.r = bscale * salpha.r, q__1.i = bscale * salpha.i;
|
|
bcoeff.r = q__1.r, bcoeff.i = q__1.i;
|
|
|
|
/* Scale to avoid underflow */
|
|
|
|
lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
|
|
lsb = (r__1 = salpha.r, abs(r__1)) + (r__2 = r_imag(&salpha),
|
|
abs(r__2)) >= safmin && (r__3 = bcoeff.r, abs(r__3))
|
|
+ (r__4 = r_imag(&bcoeff), abs(r__4)) < small;
|
|
|
|
scale = 1.f;
|
|
if (lsa) {
|
|
scale = small / abs(sbeta) * f2cmin(anorm,big);
|
|
}
|
|
if (lsb) {
|
|
/* Computing MAX */
|
|
r__3 = scale, r__4 = small / ((r__1 = salpha.r, abs(r__1))
|
|
+ (r__2 = r_imag(&salpha), abs(r__2))) * f2cmin(
|
|
bnorm,big);
|
|
scale = f2cmax(r__3,r__4);
|
|
}
|
|
if (lsa || lsb) {
|
|
/* Computing MIN */
|
|
/* Computing MAX */
|
|
r__5 = 1.f, r__6 = abs(acoeff), r__5 = f2cmax(r__5,r__6),
|
|
r__6 = (r__1 = bcoeff.r, abs(r__1)) + (r__2 =
|
|
r_imag(&bcoeff), abs(r__2));
|
|
r__3 = scale, r__4 = 1.f / (safmin * f2cmax(r__5,r__6));
|
|
scale = f2cmin(r__3,r__4);
|
|
if (lsa) {
|
|
acoeff = ascale * (scale * sbeta);
|
|
} else {
|
|
acoeff = scale * acoeff;
|
|
}
|
|
if (lsb) {
|
|
q__2.r = scale * salpha.r, q__2.i = scale * salpha.i;
|
|
q__1.r = bscale * q__2.r, q__1.i = bscale * q__2.i;
|
|
bcoeff.r = q__1.r, bcoeff.i = q__1.i;
|
|
} else {
|
|
q__1.r = scale * bcoeff.r, q__1.i = scale * bcoeff.i;
|
|
bcoeff.r = q__1.r, bcoeff.i = q__1.i;
|
|
}
|
|
}
|
|
|
|
acoefa = abs(acoeff);
|
|
bcoefa = (r__1 = bcoeff.r, abs(r__1)) + (r__2 = r_imag(&
|
|
bcoeff), abs(r__2));
|
|
xmax = 1.f;
|
|
i__2 = *n;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
i__3 = jr;
|
|
work[i__3].r = 0.f, work[i__3].i = 0.f;
|
|
/* L60: */
|
|
}
|
|
i__2 = je;
|
|
work[i__2].r = 1.f, work[i__2].i = 0.f;
|
|
/* Computing MAX */
|
|
r__1 = ulp * acoefa * anorm, r__2 = ulp * bcoefa * bnorm,
|
|
r__1 = f2cmax(r__1,r__2);
|
|
dmin__ = f2cmax(r__1,safmin);
|
|
|
|
/* H */
|
|
/* Triangular solve of (a A - b B) y = 0 */
|
|
|
|
/* H */
|
|
/* (rowwise in (a A - b B) , or columnwise in a A - b B) */
|
|
|
|
i__2 = *n;
|
|
for (j = je + 1; j <= i__2; ++j) {
|
|
|
|
/* Compute */
|
|
/* j-1 */
|
|
/* SUM = sum conjg( a*S(k,j) - b*P(k,j) )*x(k) */
|
|
/* k=je */
|
|
/* (Scale if necessary) */
|
|
|
|
temp = 1.f / xmax;
|
|
if (acoefa * rwork[j] + bcoefa * rwork[*n + j] > bignum *
|
|
temp) {
|
|
i__3 = j - 1;
|
|
for (jr = je; jr <= i__3; ++jr) {
|
|
i__4 = jr;
|
|
i__5 = jr;
|
|
q__1.r = temp * work[i__5].r, q__1.i = temp *
|
|
work[i__5].i;
|
|
work[i__4].r = q__1.r, work[i__4].i = q__1.i;
|
|
/* L70: */
|
|
}
|
|
xmax = 1.f;
|
|
}
|
|
suma.r = 0.f, suma.i = 0.f;
|
|
sumb.r = 0.f, sumb.i = 0.f;
|
|
|
|
i__3 = j - 1;
|
|
for (jr = je; jr <= i__3; ++jr) {
|
|
r_cnjg(&q__3, &s[jr + j * s_dim1]);
|
|
i__4 = jr;
|
|
q__2.r = q__3.r * work[i__4].r - q__3.i * work[i__4]
|
|
.i, q__2.i = q__3.r * work[i__4].i + q__3.i *
|
|
work[i__4].r;
|
|
q__1.r = suma.r + q__2.r, q__1.i = suma.i + q__2.i;
|
|
suma.r = q__1.r, suma.i = q__1.i;
|
|
r_cnjg(&q__3, &p[jr + j * p_dim1]);
|
|
i__4 = jr;
|
|
q__2.r = q__3.r * work[i__4].r - q__3.i * work[i__4]
|
|
.i, q__2.i = q__3.r * work[i__4].i + q__3.i *
|
|
work[i__4].r;
|
|
q__1.r = sumb.r + q__2.r, q__1.i = sumb.i + q__2.i;
|
|
sumb.r = q__1.r, sumb.i = q__1.i;
|
|
/* L80: */
|
|
}
|
|
q__2.r = acoeff * suma.r, q__2.i = acoeff * suma.i;
|
|
r_cnjg(&q__4, &bcoeff);
|
|
q__3.r = q__4.r * sumb.r - q__4.i * sumb.i, q__3.i =
|
|
q__4.r * sumb.i + q__4.i * sumb.r;
|
|
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
|
|
sum.r = q__1.r, sum.i = q__1.i;
|
|
|
|
/* Form x(j) = - SUM / conjg( a*S(j,j) - b*P(j,j) ) */
|
|
|
|
/* with scaling and perturbation of the denominator */
|
|
|
|
i__3 = j + j * s_dim1;
|
|
q__3.r = acoeff * s[i__3].r, q__3.i = acoeff * s[i__3].i;
|
|
i__4 = j + j * p_dim1;
|
|
q__4.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i,
|
|
q__4.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
|
|
.r;
|
|
q__2.r = q__3.r - q__4.r, q__2.i = q__3.i - q__4.i;
|
|
r_cnjg(&q__1, &q__2);
|
|
d__.r = q__1.r, d__.i = q__1.i;
|
|
if ((r__1 = d__.r, abs(r__1)) + (r__2 = r_imag(&d__), abs(
|
|
r__2)) <= dmin__) {
|
|
q__1.r = dmin__, q__1.i = 0.f;
|
|
d__.r = q__1.r, d__.i = q__1.i;
|
|
}
|
|
|
|
if ((r__1 = d__.r, abs(r__1)) + (r__2 = r_imag(&d__), abs(
|
|
r__2)) < 1.f) {
|
|
if ((r__1 = sum.r, abs(r__1)) + (r__2 = r_imag(&sum),
|
|
abs(r__2)) >= bignum * ((r__3 = d__.r, abs(
|
|
r__3)) + (r__4 = r_imag(&d__), abs(r__4)))) {
|
|
temp = 1.f / ((r__1 = sum.r, abs(r__1)) + (r__2 =
|
|
r_imag(&sum), abs(r__2)));
|
|
i__3 = j - 1;
|
|
for (jr = je; jr <= i__3; ++jr) {
|
|
i__4 = jr;
|
|
i__5 = jr;
|
|
q__1.r = temp * work[i__5].r, q__1.i = temp *
|
|
work[i__5].i;
|
|
work[i__4].r = q__1.r, work[i__4].i = q__1.i;
|
|
/* L90: */
|
|
}
|
|
xmax = temp * xmax;
|
|
q__1.r = temp * sum.r, q__1.i = temp * sum.i;
|
|
sum.r = q__1.r, sum.i = q__1.i;
|
|
}
|
|
}
|
|
i__3 = j;
|
|
q__2.r = -sum.r, q__2.i = -sum.i;
|
|
cladiv_(&q__1, &q__2, &d__);
|
|
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
|
|
/* Computing MAX */
|
|
i__3 = j;
|
|
r__3 = xmax, r__4 = (r__1 = work[i__3].r, abs(r__1)) + (
|
|
r__2 = r_imag(&work[j]), abs(r__2));
|
|
xmax = f2cmax(r__3,r__4);
|
|
/* L100: */
|
|
}
|
|
|
|
/* Back transform eigenvector if HOWMNY='B'. */
|
|
|
|
if (ilback) {
|
|
i__2 = *n + 1 - je;
|
|
cgemv_("N", n, &i__2, &c_b2, &vl[je * vl_dim1 + 1], ldvl,
|
|
&work[je], &c__1, &c_b1, &work[*n + 1], &c__1);
|
|
isrc = 2;
|
|
ibeg = 1;
|
|
} else {
|
|
isrc = 1;
|
|
ibeg = je;
|
|
}
|
|
|
|
/* Copy and scale eigenvector into column of VL */
|
|
|
|
xmax = 0.f;
|
|
i__2 = *n;
|
|
for (jr = ibeg; jr <= i__2; ++jr) {
|
|
/* Computing MAX */
|
|
i__3 = (isrc - 1) * *n + jr;
|
|
r__3 = xmax, r__4 = (r__1 = work[i__3].r, abs(r__1)) + (
|
|
r__2 = r_imag(&work[(isrc - 1) * *n + jr]), abs(
|
|
r__2));
|
|
xmax = f2cmax(r__3,r__4);
|
|
/* L110: */
|
|
}
|
|
|
|
if (xmax > safmin) {
|
|
temp = 1.f / xmax;
|
|
i__2 = *n;
|
|
for (jr = ibeg; jr <= i__2; ++jr) {
|
|
i__3 = jr + ieig * vl_dim1;
|
|
i__4 = (isrc - 1) * *n + jr;
|
|
q__1.r = temp * work[i__4].r, q__1.i = temp * work[
|
|
i__4].i;
|
|
vl[i__3].r = q__1.r, vl[i__3].i = q__1.i;
|
|
/* L120: */
|
|
}
|
|
} else {
|
|
ibeg = *n + 1;
|
|
}
|
|
|
|
i__2 = ibeg - 1;
|
|
for (jr = 1; jr <= i__2; ++jr) {
|
|
i__3 = jr + ieig * vl_dim1;
|
|
vl[i__3].r = 0.f, vl[i__3].i = 0.f;
|
|
/* L130: */
|
|
}
|
|
|
|
}
|
|
L140:
|
|
;
|
|
}
|
|
}
|
|
|
|
/* Right eigenvectors */
|
|
|
|
if (compr) {
|
|
ieig = im + 1;
|
|
|
|
/* Main loop over eigenvalues */
|
|
|
|
for (je = *n; je >= 1; --je) {
|
|
if (ilall) {
|
|
ilcomp = TRUE_;
|
|
} else {
|
|
ilcomp = select[je];
|
|
}
|
|
if (ilcomp) {
|
|
--ieig;
|
|
|
|
i__1 = je + je * s_dim1;
|
|
i__2 = je + je * p_dim1;
|
|
if ((r__2 = s[i__1].r, abs(r__2)) + (r__3 = r_imag(&s[je + je
|
|
* s_dim1]), abs(r__3)) <= safmin && (r__1 = p[i__2].r,
|
|
abs(r__1)) <= safmin) {
|
|
|
|
/* Singular matrix pencil -- return unit eigenvector */
|
|
|
|
i__1 = *n;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
i__2 = jr + ieig * vr_dim1;
|
|
vr[i__2].r = 0.f, vr[i__2].i = 0.f;
|
|
/* L150: */
|
|
}
|
|
i__1 = ieig + ieig * vr_dim1;
|
|
vr[i__1].r = 1.f, vr[i__1].i = 0.f;
|
|
goto L250;
|
|
}
|
|
|
|
/* Non-singular eigenvalue: */
|
|
/* Compute coefficients a and b in */
|
|
|
|
/* ( a A - b B ) x = 0 */
|
|
|
|
/* Computing MAX */
|
|
i__1 = je + je * s_dim1;
|
|
i__2 = je + je * p_dim1;
|
|
r__4 = ((r__2 = s[i__1].r, abs(r__2)) + (r__3 = r_imag(&s[je
|
|
+ je * s_dim1]), abs(r__3))) * ascale, r__5 = (r__1 =
|
|
p[i__2].r, abs(r__1)) * bscale, r__4 = f2cmax(r__4,r__5);
|
|
temp = 1.f / f2cmax(r__4,safmin);
|
|
i__1 = je + je * s_dim1;
|
|
q__2.r = temp * s[i__1].r, q__2.i = temp * s[i__1].i;
|
|
q__1.r = ascale * q__2.r, q__1.i = ascale * q__2.i;
|
|
salpha.r = q__1.r, salpha.i = q__1.i;
|
|
i__1 = je + je * p_dim1;
|
|
sbeta = temp * p[i__1].r * bscale;
|
|
acoeff = sbeta * ascale;
|
|
q__1.r = bscale * salpha.r, q__1.i = bscale * salpha.i;
|
|
bcoeff.r = q__1.r, bcoeff.i = q__1.i;
|
|
|
|
/* Scale to avoid underflow */
|
|
|
|
lsa = abs(sbeta) >= safmin && abs(acoeff) < small;
|
|
lsb = (r__1 = salpha.r, abs(r__1)) + (r__2 = r_imag(&salpha),
|
|
abs(r__2)) >= safmin && (r__3 = bcoeff.r, abs(r__3))
|
|
+ (r__4 = r_imag(&bcoeff), abs(r__4)) < small;
|
|
|
|
scale = 1.f;
|
|
if (lsa) {
|
|
scale = small / abs(sbeta) * f2cmin(anorm,big);
|
|
}
|
|
if (lsb) {
|
|
/* Computing MAX */
|
|
r__3 = scale, r__4 = small / ((r__1 = salpha.r, abs(r__1))
|
|
+ (r__2 = r_imag(&salpha), abs(r__2))) * f2cmin(
|
|
bnorm,big);
|
|
scale = f2cmax(r__3,r__4);
|
|
}
|
|
if (lsa || lsb) {
|
|
/* Computing MIN */
|
|
/* Computing MAX */
|
|
r__5 = 1.f, r__6 = abs(acoeff), r__5 = f2cmax(r__5,r__6),
|
|
r__6 = (r__1 = bcoeff.r, abs(r__1)) + (r__2 =
|
|
r_imag(&bcoeff), abs(r__2));
|
|
r__3 = scale, r__4 = 1.f / (safmin * f2cmax(r__5,r__6));
|
|
scale = f2cmin(r__3,r__4);
|
|
if (lsa) {
|
|
acoeff = ascale * (scale * sbeta);
|
|
} else {
|
|
acoeff = scale * acoeff;
|
|
}
|
|
if (lsb) {
|
|
q__2.r = scale * salpha.r, q__2.i = scale * salpha.i;
|
|
q__1.r = bscale * q__2.r, q__1.i = bscale * q__2.i;
|
|
bcoeff.r = q__1.r, bcoeff.i = q__1.i;
|
|
} else {
|
|
q__1.r = scale * bcoeff.r, q__1.i = scale * bcoeff.i;
|
|
bcoeff.r = q__1.r, bcoeff.i = q__1.i;
|
|
}
|
|
}
|
|
|
|
acoefa = abs(acoeff);
|
|
bcoefa = (r__1 = bcoeff.r, abs(r__1)) + (r__2 = r_imag(&
|
|
bcoeff), abs(r__2));
|
|
xmax = 1.f;
|
|
i__1 = *n;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
i__2 = jr;
|
|
work[i__2].r = 0.f, work[i__2].i = 0.f;
|
|
/* L160: */
|
|
}
|
|
i__1 = je;
|
|
work[i__1].r = 1.f, work[i__1].i = 0.f;
|
|
/* Computing MAX */
|
|
r__1 = ulp * acoefa * anorm, r__2 = ulp * bcoefa * bnorm,
|
|
r__1 = f2cmax(r__1,r__2);
|
|
dmin__ = f2cmax(r__1,safmin);
|
|
|
|
/* Triangular solve of (a A - b B) x = 0 (columnwise) */
|
|
|
|
/* WORK(1:j-1) contains sums w, */
|
|
/* WORK(j+1:JE) contains x */
|
|
|
|
i__1 = je - 1;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
i__2 = jr;
|
|
i__3 = jr + je * s_dim1;
|
|
q__2.r = acoeff * s[i__3].r, q__2.i = acoeff * s[i__3].i;
|
|
i__4 = jr + je * p_dim1;
|
|
q__3.r = bcoeff.r * p[i__4].r - bcoeff.i * p[i__4].i,
|
|
q__3.i = bcoeff.r * p[i__4].i + bcoeff.i * p[i__4]
|
|
.r;
|
|
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
/* L170: */
|
|
}
|
|
i__1 = je;
|
|
work[i__1].r = 1.f, work[i__1].i = 0.f;
|
|
|
|
for (j = je - 1; j >= 1; --j) {
|
|
|
|
/* Form x(j) := - w(j) / d */
|
|
/* with scaling and perturbation of the denominator */
|
|
|
|
i__1 = j + j * s_dim1;
|
|
q__2.r = acoeff * s[i__1].r, q__2.i = acoeff * s[i__1].i;
|
|
i__2 = j + j * p_dim1;
|
|
q__3.r = bcoeff.r * p[i__2].r - bcoeff.i * p[i__2].i,
|
|
q__3.i = bcoeff.r * p[i__2].i + bcoeff.i * p[i__2]
|
|
.r;
|
|
q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
|
|
d__.r = q__1.r, d__.i = q__1.i;
|
|
if ((r__1 = d__.r, abs(r__1)) + (r__2 = r_imag(&d__), abs(
|
|
r__2)) <= dmin__) {
|
|
q__1.r = dmin__, q__1.i = 0.f;
|
|
d__.r = q__1.r, d__.i = q__1.i;
|
|
}
|
|
|
|
if ((r__1 = d__.r, abs(r__1)) + (r__2 = r_imag(&d__), abs(
|
|
r__2)) < 1.f) {
|
|
i__1 = j;
|
|
if ((r__1 = work[i__1].r, abs(r__1)) + (r__2 = r_imag(
|
|
&work[j]), abs(r__2)) >= bignum * ((r__3 =
|
|
d__.r, abs(r__3)) + (r__4 = r_imag(&d__), abs(
|
|
r__4)))) {
|
|
i__1 = j;
|
|
temp = 1.f / ((r__1 = work[i__1].r, abs(r__1)) + (
|
|
r__2 = r_imag(&work[j]), abs(r__2)));
|
|
i__1 = je;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
i__2 = jr;
|
|
i__3 = jr;
|
|
q__1.r = temp * work[i__3].r, q__1.i = temp *
|
|
work[i__3].i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
/* L180: */
|
|
}
|
|
}
|
|
}
|
|
|
|
i__1 = j;
|
|
i__2 = j;
|
|
q__2.r = -work[i__2].r, q__2.i = -work[i__2].i;
|
|
cladiv_(&q__1, &q__2, &d__);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
|
|
if (j > 1) {
|
|
|
|
/* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */
|
|
|
|
i__1 = j;
|
|
if ((r__1 = work[i__1].r, abs(r__1)) + (r__2 = r_imag(
|
|
&work[j]), abs(r__2)) > 1.f) {
|
|
i__1 = j;
|
|
temp = 1.f / ((r__1 = work[i__1].r, abs(r__1)) + (
|
|
r__2 = r_imag(&work[j]), abs(r__2)));
|
|
if (acoefa * rwork[j] + bcoefa * rwork[*n + j] >=
|
|
bignum * temp) {
|
|
i__1 = je;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
i__2 = jr;
|
|
i__3 = jr;
|
|
q__1.r = temp * work[i__3].r, q__1.i =
|
|
temp * work[i__3].i;
|
|
work[i__2].r = q__1.r, work[i__2].i =
|
|
q__1.i;
|
|
/* L190: */
|
|
}
|
|
}
|
|
}
|
|
|
|
i__1 = j;
|
|
q__1.r = acoeff * work[i__1].r, q__1.i = acoeff *
|
|
work[i__1].i;
|
|
ca.r = q__1.r, ca.i = q__1.i;
|
|
i__1 = j;
|
|
q__1.r = bcoeff.r * work[i__1].r - bcoeff.i * work[
|
|
i__1].i, q__1.i = bcoeff.r * work[i__1].i +
|
|
bcoeff.i * work[i__1].r;
|
|
cb.r = q__1.r, cb.i = q__1.i;
|
|
i__1 = j - 1;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
i__2 = jr;
|
|
i__3 = jr;
|
|
i__4 = jr + j * s_dim1;
|
|
q__3.r = ca.r * s[i__4].r - ca.i * s[i__4].i,
|
|
q__3.i = ca.r * s[i__4].i + ca.i * s[i__4]
|
|
.r;
|
|
q__2.r = work[i__3].r + q__3.r, q__2.i = work[
|
|
i__3].i + q__3.i;
|
|
i__5 = jr + j * p_dim1;
|
|
q__4.r = cb.r * p[i__5].r - cb.i * p[i__5].i,
|
|
q__4.i = cb.r * p[i__5].i + cb.i * p[i__5]
|
|
.r;
|
|
q__1.r = q__2.r - q__4.r, q__1.i = q__2.i -
|
|
q__4.i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
/* L200: */
|
|
}
|
|
}
|
|
/* L210: */
|
|
}
|
|
|
|
/* Back transform eigenvector if HOWMNY='B'. */
|
|
|
|
if (ilback) {
|
|
cgemv_("N", n, &je, &c_b2, &vr[vr_offset], ldvr, &work[1],
|
|
&c__1, &c_b1, &work[*n + 1], &c__1);
|
|
isrc = 2;
|
|
iend = *n;
|
|
} else {
|
|
isrc = 1;
|
|
iend = je;
|
|
}
|
|
|
|
/* Copy and scale eigenvector into column of VR */
|
|
|
|
xmax = 0.f;
|
|
i__1 = iend;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
/* Computing MAX */
|
|
i__2 = (isrc - 1) * *n + jr;
|
|
r__3 = xmax, r__4 = (r__1 = work[i__2].r, abs(r__1)) + (
|
|
r__2 = r_imag(&work[(isrc - 1) * *n + jr]), abs(
|
|
r__2));
|
|
xmax = f2cmax(r__3,r__4);
|
|
/* L220: */
|
|
}
|
|
|
|
if (xmax > safmin) {
|
|
temp = 1.f / xmax;
|
|
i__1 = iend;
|
|
for (jr = 1; jr <= i__1; ++jr) {
|
|
i__2 = jr + ieig * vr_dim1;
|
|
i__3 = (isrc - 1) * *n + jr;
|
|
q__1.r = temp * work[i__3].r, q__1.i = temp * work[
|
|
i__3].i;
|
|
vr[i__2].r = q__1.r, vr[i__2].i = q__1.i;
|
|
/* L230: */
|
|
}
|
|
} else {
|
|
iend = 0;
|
|
}
|
|
|
|
i__1 = *n;
|
|
for (jr = iend + 1; jr <= i__1; ++jr) {
|
|
i__2 = jr + ieig * vr_dim1;
|
|
vr[i__2].r = 0.f, vr[i__2].i = 0.f;
|
|
/* L240: */
|
|
}
|
|
|
|
}
|
|
L250:
|
|
;
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of CTGEVC */
|
|
|
|
} /* ctgevc_ */
|
|
|