1111 lines
31 KiB
C
1111 lines
31 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]/Cd(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 doublecomplex c_b2 = {1.,0.};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZTREVC */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZTREVC + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrevc.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztrevc.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrevc.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, */
|
|
/* LDVR, MM, M, WORK, RWORK, INFO ) */
|
|
|
|
/* CHARACTER HOWMNY, SIDE */
|
|
/* INTEGER INFO, LDT, LDVL, LDVR, M, MM, N */
|
|
/* LOGICAL SELECT( * ) */
|
|
/* DOUBLE PRECISION RWORK( * ) */
|
|
/* COMPLEX*16 T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), */
|
|
/* $ WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZTREVC computes some or all of the right and/or left eigenvectors of */
|
|
/* > a complex upper triangular matrix T. */
|
|
/* > Matrices of this type are produced by the Schur factorization of */
|
|
/* > a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR. */
|
|
/* > */
|
|
/* > The right eigenvector x and the left eigenvector y of T corresponding */
|
|
/* > to an eigenvalue w are defined by: */
|
|
/* > */
|
|
/* > T*x = w*x, (y**H)*T = w*(y**H) */
|
|
/* > */
|
|
/* > where y**H denotes the conjugate transpose of the vector y. */
|
|
/* > The eigenvalues are not input to this routine, but are read directly */
|
|
/* > from the diagonal of T. */
|
|
/* > */
|
|
/* > This routine returns the matrices X and/or Y of right and left */
|
|
/* > eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an */
|
|
/* > input matrix. If Q is the unitary factor that reduces a matrix A to */
|
|
/* > Schur form T, then Q*X and Q*Y are the matrices of right and left */
|
|
/* > eigenvectors of A. */
|
|
/* > \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 using the matrices supplied in */
|
|
/* > VR and/or VL; */
|
|
/* > = 'S': compute selected right and/or left eigenvectors, */
|
|
/* > as indicated 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 matrix T. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] T */
|
|
/* > \verbatim */
|
|
/* > T is COMPLEX*16 array, dimension (LDT,N) */
|
|
/* > The upper triangular matrix T. T is modified, but restored */
|
|
/* > on exit. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of the array T. LDT >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] VL */
|
|
/* > \verbatim */
|
|
/* > VL is COMPLEX*16 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 */
|
|
/* > Schur vectors returned by ZHSEQR). */
|
|
/* > On exit, if SIDE = 'L' or 'B', VL contains: */
|
|
/* > if HOWMNY = 'A', the matrix Y of left eigenvectors of T; */
|
|
/* > if HOWMNY = 'B', the matrix Q*Y; */
|
|
/* > if HOWMNY = 'S', the left eigenvectors of T 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 the array VL. LDVL >= 1, and if */
|
|
/* > SIDE = 'L' or 'B', LDVL >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] VR */
|
|
/* > \verbatim */
|
|
/* > VR is COMPLEX*16 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 Q of */
|
|
/* > Schur vectors returned by ZHSEQR). */
|
|
/* > On exit, if SIDE = 'R' or 'B', VR contains: */
|
|
/* > if HOWMNY = 'A', the matrix X of right eigenvectors of T; */
|
|
/* > if HOWMNY = 'B', the matrix Q*X; */
|
|
/* > if HOWMNY = 'S', the right eigenvectors of T 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*16 array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (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 November 2017 */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The algorithm used in this program is basically backward (forward) */
|
|
/* > substitution, with scaling to make the the code robust against */
|
|
/* > possible overflow. */
|
|
/* > */
|
|
/* > Each eigenvector is normalized so that the element of largest */
|
|
/* > magnitude has magnitude 1; here the magnitude of a complex number */
|
|
/* > (x,y) is taken to be |x| + |y|. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void ztrevc_(char *side, char *howmny, logical *select,
|
|
integer *n, doublecomplex *t, integer *ldt, doublecomplex *vl,
|
|
integer *ldvl, doublecomplex *vr, integer *ldvr, integer *mm, integer
|
|
*m, doublecomplex *work, doublereal *rwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer t_dim1, t_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;
|
|
doublecomplex z__1, z__2;
|
|
|
|
/* Local variables */
|
|
logical allv;
|
|
doublereal unfl, ovfl, smin;
|
|
logical over;
|
|
integer i__, j, k;
|
|
doublereal scale;
|
|
extern logical lsame_(char *, char *);
|
|
doublereal remax;
|
|
logical leftv, bothv;
|
|
extern /* Subroutine */ void zgemv_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *);
|
|
logical somev;
|
|
extern /* Subroutine */ void zcopy_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
|
|
integer ii, ki;
|
|
extern doublereal dlamch_(char *);
|
|
integer is;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern void zdscal_(
|
|
integer *, doublereal *, doublecomplex *, integer *);
|
|
extern integer izamax_(integer *, doublecomplex *, integer *);
|
|
logical rightv;
|
|
extern doublereal dzasum_(integer *, doublecomplex *, integer *);
|
|
doublereal smlnum;
|
|
extern /* Subroutine */ void zlatrs_(char *, char *, char *, char *,
|
|
integer *, doublecomplex *, integer *, doublecomplex *,
|
|
doublereal *, doublereal *, integer *);
|
|
doublereal ulp;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.8.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* November 2017 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Decode and test the input parameters */
|
|
|
|
/* Parameter adjustments */
|
|
--select;
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1 * 1;
|
|
t -= t_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 */
|
|
bothv = lsame_(side, "B");
|
|
rightv = lsame_(side, "R") || bothv;
|
|
leftv = lsame_(side, "L") || bothv;
|
|
|
|
allv = lsame_(howmny, "A");
|
|
over = lsame_(howmny, "B");
|
|
somev = lsame_(howmny, "S");
|
|
|
|
/* Set M to the number of columns required to store the selected */
|
|
/* eigenvectors. */
|
|
|
|
if (somev) {
|
|
*m = 0;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (select[j]) {
|
|
++(*m);
|
|
}
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
*m = *n;
|
|
}
|
|
|
|
*info = 0;
|
|
if (! rightv && ! leftv) {
|
|
*info = -1;
|
|
} else if (! allv && ! over && ! somev) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -4;
|
|
} else if (*ldt < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
} else if (*ldvl < 1 || leftv && *ldvl < *n) {
|
|
*info = -8;
|
|
} else if (*ldvr < 1 || rightv && *ldvr < *n) {
|
|
*info = -10;
|
|
} else if (*mm < *m) {
|
|
*info = -11;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZTREVC", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible. */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Set the constants to control overflow. */
|
|
|
|
unfl = dlamch_("Safe minimum");
|
|
ovfl = 1. / unfl;
|
|
dlabad_(&unfl, &ovfl);
|
|
ulp = dlamch_("Precision");
|
|
smlnum = unfl * (*n / ulp);
|
|
|
|
/* Store the diagonal elements of T in working array WORK. */
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__ + *n;
|
|
i__3 = i__ + i__ * t_dim1;
|
|
work[i__2].r = t[i__3].r, work[i__2].i = t[i__3].i;
|
|
/* L20: */
|
|
}
|
|
|
|
/* Compute 1-norm of each column of strictly upper triangular */
|
|
/* part of T to control overflow in triangular solver. */
|
|
|
|
rwork[1] = 0.;
|
|
i__1 = *n;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
i__2 = j - 1;
|
|
rwork[j] = dzasum_(&i__2, &t[j * t_dim1 + 1], &c__1);
|
|
/* L30: */
|
|
}
|
|
|
|
if (rightv) {
|
|
|
|
/* Compute right eigenvectors. */
|
|
|
|
is = *m;
|
|
for (ki = *n; ki >= 1; --ki) {
|
|
|
|
if (somev) {
|
|
if (! select[ki]) {
|
|
goto L80;
|
|
}
|
|
}
|
|
/* Computing MAX */
|
|
i__1 = ki + ki * t_dim1;
|
|
d__3 = ulp * ((d__1 = t[i__1].r, abs(d__1)) + (d__2 = d_imag(&t[
|
|
ki + ki * t_dim1]), abs(d__2)));
|
|
smin = f2cmax(d__3,smlnum);
|
|
|
|
work[1].r = 1., work[1].i = 0.;
|
|
|
|
/* Form right-hand side. */
|
|
|
|
i__1 = ki - 1;
|
|
for (k = 1; k <= i__1; ++k) {
|
|
i__2 = k;
|
|
i__3 = k + ki * t_dim1;
|
|
z__1.r = -t[i__3].r, z__1.i = -t[i__3].i;
|
|
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
|
|
/* L40: */
|
|
}
|
|
|
|
/* Solve the triangular system: */
|
|
/* (T(1:KI-1,1:KI-1) - T(KI,KI))*X = SCALE*WORK. */
|
|
|
|
i__1 = ki - 1;
|
|
for (k = 1; k <= i__1; ++k) {
|
|
i__2 = k + k * t_dim1;
|
|
i__3 = k + k * t_dim1;
|
|
i__4 = ki + ki * t_dim1;
|
|
z__1.r = t[i__3].r - t[i__4].r, z__1.i = t[i__3].i - t[i__4]
|
|
.i;
|
|
t[i__2].r = z__1.r, t[i__2].i = z__1.i;
|
|
i__2 = k + k * t_dim1;
|
|
if ((d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[k + k *
|
|
t_dim1]), abs(d__2)) < smin) {
|
|
i__3 = k + k * t_dim1;
|
|
t[i__3].r = smin, t[i__3].i = 0.;
|
|
}
|
|
/* L50: */
|
|
}
|
|
|
|
if (ki > 1) {
|
|
i__1 = ki - 1;
|
|
zlatrs_("Upper", "No transpose", "Non-unit", "Y", &i__1, &t[
|
|
t_offset], ldt, &work[1], &scale, &rwork[1], info);
|
|
i__1 = ki;
|
|
work[i__1].r = scale, work[i__1].i = 0.;
|
|
}
|
|
|
|
/* Copy the vector x or Q*x to VR and normalize. */
|
|
|
|
if (! over) {
|
|
zcopy_(&ki, &work[1], &c__1, &vr[is * vr_dim1 + 1], &c__1);
|
|
|
|
ii = izamax_(&ki, &vr[is * vr_dim1 + 1], &c__1);
|
|
i__1 = ii + is * vr_dim1;
|
|
remax = 1. / ((d__1 = vr[i__1].r, abs(d__1)) + (d__2 = d_imag(
|
|
&vr[ii + is * vr_dim1]), abs(d__2)));
|
|
zdscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);
|
|
|
|
i__1 = *n;
|
|
for (k = ki + 1; k <= i__1; ++k) {
|
|
i__2 = k + is * vr_dim1;
|
|
vr[i__2].r = 0., vr[i__2].i = 0.;
|
|
/* L60: */
|
|
}
|
|
} else {
|
|
if (ki > 1) {
|
|
i__1 = ki - 1;
|
|
z__1.r = scale, z__1.i = 0.;
|
|
zgemv_("N", n, &i__1, &c_b2, &vr[vr_offset], ldvr, &work[
|
|
1], &c__1, &z__1, &vr[ki * vr_dim1 + 1], &c__1);
|
|
}
|
|
|
|
ii = izamax_(n, &vr[ki * vr_dim1 + 1], &c__1);
|
|
i__1 = ii + ki * vr_dim1;
|
|
remax = 1. / ((d__1 = vr[i__1].r, abs(d__1)) + (d__2 = d_imag(
|
|
&vr[ii + ki * vr_dim1]), abs(d__2)));
|
|
zdscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);
|
|
}
|
|
|
|
/* Set back the original diagonal elements of T. */
|
|
|
|
i__1 = ki - 1;
|
|
for (k = 1; k <= i__1; ++k) {
|
|
i__2 = k + k * t_dim1;
|
|
i__3 = k + *n;
|
|
t[i__2].r = work[i__3].r, t[i__2].i = work[i__3].i;
|
|
/* L70: */
|
|
}
|
|
|
|
--is;
|
|
L80:
|
|
;
|
|
}
|
|
}
|
|
|
|
if (leftv) {
|
|
|
|
/* Compute left eigenvectors. */
|
|
|
|
is = 1;
|
|
i__1 = *n;
|
|
for (ki = 1; ki <= i__1; ++ki) {
|
|
|
|
if (somev) {
|
|
if (! select[ki]) {
|
|
goto L130;
|
|
}
|
|
}
|
|
/* Computing MAX */
|
|
i__2 = ki + ki * t_dim1;
|
|
d__3 = ulp * ((d__1 = t[i__2].r, abs(d__1)) + (d__2 = d_imag(&t[
|
|
ki + ki * t_dim1]), abs(d__2)));
|
|
smin = f2cmax(d__3,smlnum);
|
|
|
|
i__2 = *n;
|
|
work[i__2].r = 1., work[i__2].i = 0.;
|
|
|
|
/* Form right-hand side. */
|
|
|
|
i__2 = *n;
|
|
for (k = ki + 1; k <= i__2; ++k) {
|
|
i__3 = k;
|
|
d_cnjg(&z__2, &t[ki + k * t_dim1]);
|
|
z__1.r = -z__2.r, z__1.i = -z__2.i;
|
|
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
|
|
/* L90: */
|
|
}
|
|
|
|
/* Solve the triangular system: */
|
|
/* (T(KI+1:N,KI+1:N) - T(KI,KI))**H * X = SCALE*WORK. */
|
|
|
|
i__2 = *n;
|
|
for (k = ki + 1; k <= i__2; ++k) {
|
|
i__3 = k + k * t_dim1;
|
|
i__4 = k + k * t_dim1;
|
|
i__5 = ki + ki * t_dim1;
|
|
z__1.r = t[i__4].r - t[i__5].r, z__1.i = t[i__4].i - t[i__5]
|
|
.i;
|
|
t[i__3].r = z__1.r, t[i__3].i = z__1.i;
|
|
i__3 = k + k * t_dim1;
|
|
if ((d__1 = t[i__3].r, abs(d__1)) + (d__2 = d_imag(&t[k + k *
|
|
t_dim1]), abs(d__2)) < smin) {
|
|
i__4 = k + k * t_dim1;
|
|
t[i__4].r = smin, t[i__4].i = 0.;
|
|
}
|
|
/* L100: */
|
|
}
|
|
|
|
if (ki < *n) {
|
|
i__2 = *n - ki;
|
|
zlatrs_("Upper", "Conjugate transpose", "Non-unit", "Y", &
|
|
i__2, &t[ki + 1 + (ki + 1) * t_dim1], ldt, &work[ki +
|
|
1], &scale, &rwork[1], info);
|
|
i__2 = ki;
|
|
work[i__2].r = scale, work[i__2].i = 0.;
|
|
}
|
|
|
|
/* Copy the vector x or Q*x to VL and normalize. */
|
|
|
|
if (! over) {
|
|
i__2 = *n - ki + 1;
|
|
zcopy_(&i__2, &work[ki], &c__1, &vl[ki + is * vl_dim1], &c__1)
|
|
;
|
|
|
|
i__2 = *n - ki + 1;
|
|
ii = izamax_(&i__2, &vl[ki + is * vl_dim1], &c__1) + ki - 1;
|
|
i__2 = ii + is * vl_dim1;
|
|
remax = 1. / ((d__1 = vl[i__2].r, abs(d__1)) + (d__2 = d_imag(
|
|
&vl[ii + is * vl_dim1]), abs(d__2)));
|
|
i__2 = *n - ki + 1;
|
|
zdscal_(&i__2, &remax, &vl[ki + is * vl_dim1], &c__1);
|
|
|
|
i__2 = ki - 1;
|
|
for (k = 1; k <= i__2; ++k) {
|
|
i__3 = k + is * vl_dim1;
|
|
vl[i__3].r = 0., vl[i__3].i = 0.;
|
|
/* L110: */
|
|
}
|
|
} else {
|
|
if (ki < *n) {
|
|
i__2 = *n - ki;
|
|
z__1.r = scale, z__1.i = 0.;
|
|
zgemv_("N", n, &i__2, &c_b2, &vl[(ki + 1) * vl_dim1 + 1],
|
|
ldvl, &work[ki + 1], &c__1, &z__1, &vl[ki *
|
|
vl_dim1 + 1], &c__1);
|
|
}
|
|
|
|
ii = izamax_(n, &vl[ki * vl_dim1 + 1], &c__1);
|
|
i__2 = ii + ki * vl_dim1;
|
|
remax = 1. / ((d__1 = vl[i__2].r, abs(d__1)) + (d__2 = d_imag(
|
|
&vl[ii + ki * vl_dim1]), abs(d__2)));
|
|
zdscal_(n, &remax, &vl[ki * vl_dim1 + 1], &c__1);
|
|
}
|
|
|
|
/* Set back the original diagonal elements of T. */
|
|
|
|
i__2 = *n;
|
|
for (k = ki + 1; k <= i__2; ++k) {
|
|
i__3 = k + k * t_dim1;
|
|
i__4 = k + *n;
|
|
t[i__3].r = work[i__4].r, t[i__3].i = work[i__4].i;
|
|
/* L120: */
|
|
}
|
|
|
|
++is;
|
|
L130:
|
|
;
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZTREVC */
|
|
|
|
} /* ztrevc_ */
|
|
|