1295 lines
39 KiB
C
1295 lines
39 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static real c_b19 = 1.f;
|
|
static real c_b21 = 0.f;
|
|
static integer c__2 = 2;
|
|
static logical c_false = FALSE_;
|
|
static integer c__3 = 3;
|
|
|
|
/* > \brief \b STGSNA */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download STGSNA + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stgsna.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stgsna.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stgsna.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE STGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, */
|
|
/* LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK, */
|
|
/* IWORK, INFO ) */
|
|
|
|
/* CHARACTER HOWMNY, JOB */
|
|
/* INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, M, MM, N */
|
|
/* LOGICAL SELECT( * ) */
|
|
/* INTEGER IWORK( * ) */
|
|
/* REAL A( LDA, * ), B( LDB, * ), DIF( * ), S( * ), */
|
|
/* $ VL( LDVL, * ), VR( LDVR, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > STGSNA estimates reciprocal condition numbers for specified */
|
|
/* > eigenvalues and/or eigenvectors of a matrix pair (A, B) in */
|
|
/* > generalized real Schur canonical form (or of any matrix pair */
|
|
/* > (Q*A*Z**T, Q*B*Z**T) with orthogonal matrices Q and Z, where */
|
|
/* > Z**T denotes the transpose of Z. */
|
|
/* > */
|
|
/* > (A, B) must be in generalized real Schur form (as returned by SGGES), */
|
|
/* > i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal */
|
|
/* > blocks. B is upper triangular. */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOB */
|
|
/* > \verbatim */
|
|
/* > JOB is CHARACTER*1 */
|
|
/* > Specifies whether condition numbers are required for */
|
|
/* > eigenvalues (S) or eigenvectors (DIF): */
|
|
/* > = 'E': for eigenvalues only (S); */
|
|
/* > = 'V': for eigenvectors only (DIF); */
|
|
/* > = 'B': for both eigenvalues and eigenvectors (S and DIF). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] HOWMNY */
|
|
/* > \verbatim */
|
|
/* > HOWMNY is CHARACTER*1 */
|
|
/* > = 'A': compute condition numbers for all eigenpairs; */
|
|
/* > = 'S': compute condition numbers for selected eigenpairs */
|
|
/* > specified by the array SELECT. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SELECT */
|
|
/* > \verbatim */
|
|
/* > SELECT is LOGICAL array, dimension (N) */
|
|
/* > If HOWMNY = 'S', SELECT specifies the eigenpairs for which */
|
|
/* > condition numbers are required. To select condition numbers */
|
|
/* > for the eigenpair corresponding to a real eigenvalue w(j), */
|
|
/* > SELECT(j) must be set to .TRUE.. To select condition numbers */
|
|
/* > corresponding to a complex conjugate pair of eigenvalues w(j) */
|
|
/* > and w(j+1), either SELECT(j) or SELECT(j+1) or both, must be */
|
|
/* > set to .TRUE.. */
|
|
/* > If HOWMNY = 'A', SELECT is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the square matrix pair (A, B). N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A */
|
|
/* > \verbatim */
|
|
/* > A is REAL array, dimension (LDA,N) */
|
|
/* > The upper quasi-triangular matrix A in the pair (A,B). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B */
|
|
/* > \verbatim */
|
|
/* > B is REAL array, dimension (LDB,N) */
|
|
/* > The upper triangular matrix B in the pair (A,B). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VL */
|
|
/* > \verbatim */
|
|
/* > VL is REAL array, dimension (LDVL,M) */
|
|
/* > If JOB = 'E' or 'B', VL must contain left eigenvectors of */
|
|
/* > (A, B), corresponding to the eigenpairs specified by HOWMNY */
|
|
/* > and SELECT. The eigenvectors must be stored in consecutive */
|
|
/* > columns of VL, as returned by STGEVC. */
|
|
/* > If JOB = 'V', VL is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVL */
|
|
/* > \verbatim */
|
|
/* > LDVL is INTEGER */
|
|
/* > The leading dimension of the array VL. LDVL >= 1. */
|
|
/* > If JOB = 'E' or 'B', LDVL >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VR */
|
|
/* > \verbatim */
|
|
/* > VR is REAL array, dimension (LDVR,M) */
|
|
/* > If JOB = 'E' or 'B', VR must contain right eigenvectors of */
|
|
/* > (A, B), corresponding to the eigenpairs specified by HOWMNY */
|
|
/* > and SELECT. The eigenvectors must be stored in consecutive */
|
|
/* > columns ov VR, as returned by STGEVC. */
|
|
/* > If JOB = 'V', VR is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVR */
|
|
/* > \verbatim */
|
|
/* > LDVR is INTEGER */
|
|
/* > The leading dimension of the array VR. LDVR >= 1. */
|
|
/* > If JOB = 'E' or 'B', LDVR >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is REAL array, dimension (MM) */
|
|
/* > If JOB = 'E' or 'B', the reciprocal condition numbers of the */
|
|
/* > selected eigenvalues, stored in consecutive elements of the */
|
|
/* > array. For a complex conjugate pair of eigenvalues two */
|
|
/* > consecutive elements of S are set to the same value. Thus */
|
|
/* > S(j), DIF(j), and the j-th columns of VL and VR all */
|
|
/* > correspond to the same eigenpair (but not in general the */
|
|
/* > j-th eigenpair, unless all eigenpairs are selected). */
|
|
/* > If JOB = 'V', S is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DIF */
|
|
/* > \verbatim */
|
|
/* > DIF is REAL array, dimension (MM) */
|
|
/* > If JOB = 'V' or 'B', the estimated reciprocal condition */
|
|
/* > numbers of the selected eigenvectors, stored in consecutive */
|
|
/* > elements of the array. For a complex eigenvector two */
|
|
/* > consecutive elements of DIF are set to the same value. If */
|
|
/* > the eigenvalues cannot be reordered to compute DIF(j), DIF(j) */
|
|
/* > is set to 0; this can only occur when the true value would be */
|
|
/* > very small anyway. */
|
|
/* > If JOB = 'E', DIF is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] MM */
|
|
/* > \verbatim */
|
|
/* > MM is INTEGER */
|
|
/* > The number of elements in the arrays S and DIF. MM >= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of elements of the arrays S and DIF used to store */
|
|
/* > the specified condition numbers; for each selected real */
|
|
/* > eigenvalue one element is used, and for each selected complex */
|
|
/* > conjugate pair of eigenvalues, two elements are used. */
|
|
/* > If HOWMNY = 'A', M is set to N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= f2cmax(1,N). */
|
|
/* > If JOB = 'V' or 'B' LWORK >= 2*N*(N+2)+16. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (N + 6) */
|
|
/* > If JOB = 'E', IWORK is not referenced. */
|
|
/* > \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 realOTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The reciprocal of the condition number of a generalized eigenvalue */
|
|
/* > w = (a, b) is defined as */
|
|
/* > */
|
|
/* > S(w) = (|u**TAv|**2 + |u**TBv|**2)**(1/2) / (norm(u)*norm(v)) */
|
|
/* > */
|
|
/* > where u and v are the left and right eigenvectors of (A, B) */
|
|
/* > corresponding to w; |z| denotes the absolute value of the complex */
|
|
/* > number, and norm(u) denotes the 2-norm of the vector u. */
|
|
/* > The pair (a, b) corresponds to an eigenvalue w = a/b (= u**TAv/u**TBv) */
|
|
/* > of the matrix pair (A, B). If both a and b equal zero, then (A B) is */
|
|
/* > singular and S(I) = -1 is returned. */
|
|
/* > */
|
|
/* > An approximate error bound on the chordal distance between the i-th */
|
|
/* > computed generalized eigenvalue w and the corresponding exact */
|
|
/* > eigenvalue lambda is */
|
|
/* > */
|
|
/* > chord(w, lambda) <= EPS * norm(A, B) / S(I) */
|
|
/* > */
|
|
/* > where EPS is the machine precision. */
|
|
/* > */
|
|
/* > The reciprocal of the condition number DIF(i) of right eigenvector u */
|
|
/* > and left eigenvector v corresponding to the generalized eigenvalue w */
|
|
/* > is defined as follows: */
|
|
/* > */
|
|
/* > a) If the i-th eigenvalue w = (a,b) is real */
|
|
/* > */
|
|
/* > Suppose U and V are orthogonal transformations such that */
|
|
/* > */
|
|
/* > U**T*(A, B)*V = (S, T) = ( a * ) ( b * ) 1 */
|
|
/* > ( 0 S22 ),( 0 T22 ) n-1 */
|
|
/* > 1 n-1 1 n-1 */
|
|
/* > */
|
|
/* > Then the reciprocal condition number DIF(i) is */
|
|
/* > */
|
|
/* > Difl((a, b), (S22, T22)) = sigma-f2cmin( Zl ), */
|
|
/* > */
|
|
/* > where sigma-f2cmin(Zl) denotes the smallest singular value of the */
|
|
/* > 2(n-1)-by-2(n-1) matrix */
|
|
/* > */
|
|
/* > Zl = [ kron(a, In-1) -kron(1, S22) ] */
|
|
/* > [ kron(b, In-1) -kron(1, T22) ] . */
|
|
/* > */
|
|
/* > Here In-1 is the identity matrix of size n-1. kron(X, Y) is the */
|
|
/* > Kronecker product between the matrices X and Y. */
|
|
/* > */
|
|
/* > Note that if the default method for computing DIF(i) is wanted */
|
|
/* > (see SLATDF), then the parameter DIFDRI (see below) should be */
|
|
/* > changed from 3 to 4 (routine SLATDF(IJOB = 2 will be used)). */
|
|
/* > See STGSYL for more details. */
|
|
/* > */
|
|
/* > b) If the i-th and (i+1)-th eigenvalues are complex conjugate pair, */
|
|
/* > */
|
|
/* > Suppose U and V are orthogonal transformations such that */
|
|
/* > */
|
|
/* > U**T*(A, B)*V = (S, T) = ( S11 * ) ( T11 * ) 2 */
|
|
/* > ( 0 S22 ),( 0 T22) n-2 */
|
|
/* > 2 n-2 2 n-2 */
|
|
/* > */
|
|
/* > and (S11, T11) corresponds to the complex conjugate eigenvalue */
|
|
/* > pair (w, conjg(w)). There exist unitary matrices U1 and V1 such */
|
|
/* > that */
|
|
/* > */
|
|
/* > U1**T*S11*V1 = ( s11 s12 ) and U1**T*T11*V1 = ( t11 t12 ) */
|
|
/* > ( 0 s22 ) ( 0 t22 ) */
|
|
/* > */
|
|
/* > where the generalized eigenvalues w = s11/t11 and */
|
|
/* > conjg(w) = s22/t22. */
|
|
/* > */
|
|
/* > Then the reciprocal condition number DIF(i) is bounded by */
|
|
/* > */
|
|
/* > f2cmin( d1, f2cmax( 1, |real(s11)/real(s22)| )*d2 ) */
|
|
/* > */
|
|
/* > where, d1 = Difl((s11, t11), (s22, t22)) = sigma-f2cmin(Z1), where */
|
|
/* > Z1 is the complex 2-by-2 matrix */
|
|
/* > */
|
|
/* > Z1 = [ s11 -s22 ] */
|
|
/* > [ t11 -t22 ], */
|
|
/* > */
|
|
/* > This is done by computing (using real arithmetic) the */
|
|
/* > roots of the characteristical polynomial det(Z1**T * Z1 - lambda I), */
|
|
/* > where Z1**T denotes the transpose of Z1 and det(X) denotes */
|
|
/* > the determinant of X. */
|
|
/* > */
|
|
/* > and d2 is an upper bound on Difl((S11, T11), (S22, T22)), i.e. an */
|
|
/* > upper bound on sigma-f2cmin(Z2), where Z2 is (2n-2)-by-(2n-2) */
|
|
/* > */
|
|
/* > Z2 = [ kron(S11**T, In-2) -kron(I2, S22) ] */
|
|
/* > [ kron(T11**T, In-2) -kron(I2, T22) ] */
|
|
/* > */
|
|
/* > Note that if the default method for computing DIF is wanted (see */
|
|
/* > SLATDF), then the parameter DIFDRI (see below) should be changed */
|
|
/* > from 3 to 4 (routine SLATDF(IJOB = 2 will be used)). See STGSYL */
|
|
/* > for more details. */
|
|
/* > */
|
|
/* > For each eigenvalue/vector specified by SELECT, DIF stores a */
|
|
/* > Frobenius norm-based estimate of Difl. */
|
|
/* > */
|
|
/* > An approximate error bound for the i-th computed eigenvector VL(i) or */
|
|
/* > VR(i) is given by */
|
|
/* > */
|
|
/* > EPS * norm(A, B) / DIF(i). */
|
|
/* > */
|
|
/* > See ref. [2-3] for more details and further references. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
|
|
/* > Umea University, S-901 87 Umea, Sweden. */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
|
|
/* > Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
|
|
/* > M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
|
|
/* > Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */
|
|
/* > */
|
|
/* > [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
|
|
/* > Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
|
|
/* > Estimation: Theory, Algorithms and Software, */
|
|
/* > Report UMINF - 94.04, Department of Computing Science, Umea */
|
|
/* > University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working */
|
|
/* > Note 87. To appear in Numerical Algorithms, 1996. */
|
|
/* > */
|
|
/* > [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
|
|
/* > for Solving the Generalized Sylvester Equation and Estimating the */
|
|
/* > Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
|
|
/* > Department of Computing Science, Umea University, S-901 87 Umea, */
|
|
/* > Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
|
|
/* > Note 75. To appear in ACM Trans. on Math. Software, Vol 22, */
|
|
/* > No 1, 1996. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void stgsna_(char *job, char *howmny, logical *select,
|
|
integer *n, real *a, integer *lda, real *b, integer *ldb, real *vl,
|
|
integer *ldvl, real *vr, integer *ldvr, real *s, real *dif, integer *
|
|
mm, integer *m, real *work, integer *lwork, integer *iwork, integer *
|
|
info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
|
|
vr_offset, i__1, i__2;
|
|
real r__1, r__2;
|
|
|
|
/* Local variables */
|
|
real beta, cond;
|
|
logical pair;
|
|
integer ierr;
|
|
real uhav, uhbv;
|
|
integer ifst;
|
|
real lnrm;
|
|
extern real sdot_(integer *, real *, integer *, real *, integer *);
|
|
integer ilst;
|
|
real rnrm;
|
|
extern /* Subroutine */ void slag2_(real *, integer *, real *, integer *,
|
|
real *, real *, real *, real *, real *, real *);
|
|
extern real snrm2_(integer *, real *, integer *);
|
|
real root1, root2;
|
|
integer i__, k;
|
|
real scale;
|
|
extern logical lsame_(char *, char *);
|
|
real uhavi, uhbvi;
|
|
extern /* Subroutine */ void sgemv_(char *, integer *, integer *, real *,
|
|
real *, integer *, real *, integer *, real *, real *, integer *);
|
|
real tmpii, c1, c2;
|
|
integer lwmin;
|
|
logical wants;
|
|
real tmpir;
|
|
integer n1, n2;
|
|
real tmpri, dummy[1], tmprr;
|
|
extern real slapy2_(real *, real *);
|
|
real dummy1[1];
|
|
integer ks;
|
|
real alphai;
|
|
integer iz;
|
|
real alphar;
|
|
extern real slamch_(char *);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
logical wantbh, wantdf;
|
|
extern /* Subroutine */ void slacpy_(char *, integer *, integer *, real *,
|
|
integer *, real *, integer *), stgexc_(logical *, logical
|
|
*, integer *, real *, integer *, real *, integer *, real *,
|
|
integer *, real *, integer *, integer *, integer *, real *,
|
|
integer *, integer *);
|
|
logical somcon;
|
|
real alprqt, smlnum;
|
|
logical lquery;
|
|
extern /* Subroutine */ void stgsyl_(char *, integer *, integer *, integer
|
|
*, real *, integer *, real *, integer *, real *, integer *, real *
|
|
, integer *, real *, integer *, real *, integer *, real *, real *,
|
|
real *, integer *, integer *, integer *);
|
|
real eps;
|
|
|
|
|
|
/* -- 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;
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_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;
|
|
--s;
|
|
--dif;
|
|
--work;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
wantbh = lsame_(job, "B");
|
|
wants = lsame_(job, "E") || wantbh;
|
|
wantdf = lsame_(job, "V") || wantbh;
|
|
|
|
somcon = lsame_(howmny, "S");
|
|
|
|
*info = 0;
|
|
lquery = *lwork == -1;
|
|
|
|
if (! wants && ! wantdf) {
|
|
*info = -1;
|
|
} else if (! lsame_(howmny, "A") && ! somcon) {
|
|
*info = -2;
|
|
} else if (*n < 0) {
|
|
*info = -4;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
} else if (*ldb < f2cmax(1,*n)) {
|
|
*info = -8;
|
|
} else if (wants && *ldvl < *n) {
|
|
*info = -10;
|
|
} else if (wants && *ldvr < *n) {
|
|
*info = -12;
|
|
} else {
|
|
|
|
/* Set M to the number of eigenpairs for which condition numbers */
|
|
/* are required, and test MM. */
|
|
|
|
if (somcon) {
|
|
*m = 0;
|
|
pair = FALSE_;
|
|
i__1 = *n;
|
|
for (k = 1; k <= i__1; ++k) {
|
|
if (pair) {
|
|
pair = FALSE_;
|
|
} else {
|
|
if (k < *n) {
|
|
if (a[k + 1 + k * a_dim1] == 0.f) {
|
|
if (select[k]) {
|
|
++(*m);
|
|
}
|
|
} else {
|
|
pair = TRUE_;
|
|
if (select[k] || select[k + 1]) {
|
|
*m += 2;
|
|
}
|
|
}
|
|
} else {
|
|
if (select[*n]) {
|
|
++(*m);
|
|
}
|
|
}
|
|
}
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
*m = *n;
|
|
}
|
|
|
|
if (*n == 0) {
|
|
lwmin = 1;
|
|
} else if (lsame_(job, "V") || lsame_(job,
|
|
"B")) {
|
|
lwmin = (*n << 1) * (*n + 2) + 16;
|
|
} else {
|
|
lwmin = *n;
|
|
}
|
|
work[1] = (real) lwmin;
|
|
|
|
if (*mm < *m) {
|
|
*info = -15;
|
|
} else if (*lwork < lwmin && ! lquery) {
|
|
*info = -18;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("STGSNA", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Get machine constants */
|
|
|
|
eps = slamch_("P");
|
|
smlnum = slamch_("S") / eps;
|
|
ks = 0;
|
|
pair = FALSE_;
|
|
|
|
i__1 = *n;
|
|
for (k = 1; k <= i__1; ++k) {
|
|
|
|
/* Determine whether A(k,k) begins a 1-by-1 or 2-by-2 block. */
|
|
|
|
if (pair) {
|
|
pair = FALSE_;
|
|
goto L20;
|
|
} else {
|
|
if (k < *n) {
|
|
pair = a[k + 1 + k * a_dim1] != 0.f;
|
|
}
|
|
}
|
|
|
|
/* Determine whether condition numbers are required for the k-th */
|
|
/* eigenpair. */
|
|
|
|
if (somcon) {
|
|
if (pair) {
|
|
if (! select[k] && ! select[k + 1]) {
|
|
goto L20;
|
|
}
|
|
} else {
|
|
if (! select[k]) {
|
|
goto L20;
|
|
}
|
|
}
|
|
}
|
|
|
|
++ks;
|
|
|
|
if (wants) {
|
|
|
|
/* Compute the reciprocal condition number of the k-th */
|
|
/* eigenvalue. */
|
|
|
|
if (pair) {
|
|
|
|
/* Complex eigenvalue pair. */
|
|
|
|
r__1 = snrm2_(n, &vr[ks * vr_dim1 + 1], &c__1);
|
|
r__2 = snrm2_(n, &vr[(ks + 1) * vr_dim1 + 1], &c__1);
|
|
rnrm = slapy2_(&r__1, &r__2);
|
|
r__1 = snrm2_(n, &vl[ks * vl_dim1 + 1], &c__1);
|
|
r__2 = snrm2_(n, &vl[(ks + 1) * vl_dim1 + 1], &c__1);
|
|
lnrm = slapy2_(&r__1, &r__2);
|
|
sgemv_("N", n, n, &c_b19, &a[a_offset], lda, &vr[ks * vr_dim1
|
|
+ 1], &c__1, &c_b21, &work[1], &c__1);
|
|
tmprr = sdot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &
|
|
c__1);
|
|
tmpri = sdot_(n, &work[1], &c__1, &vl[(ks + 1) * vl_dim1 + 1],
|
|
&c__1);
|
|
sgemv_("N", n, n, &c_b19, &a[a_offset], lda, &vr[(ks + 1) *
|
|
vr_dim1 + 1], &c__1, &c_b21, &work[1], &c__1);
|
|
tmpii = sdot_(n, &work[1], &c__1, &vl[(ks + 1) * vl_dim1 + 1],
|
|
&c__1);
|
|
tmpir = sdot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &
|
|
c__1);
|
|
uhav = tmprr + tmpii;
|
|
uhavi = tmpir - tmpri;
|
|
sgemv_("N", n, n, &c_b19, &b[b_offset], ldb, &vr[ks * vr_dim1
|
|
+ 1], &c__1, &c_b21, &work[1], &c__1);
|
|
tmprr = sdot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &
|
|
c__1);
|
|
tmpri = sdot_(n, &work[1], &c__1, &vl[(ks + 1) * vl_dim1 + 1],
|
|
&c__1);
|
|
sgemv_("N", n, n, &c_b19, &b[b_offset], ldb, &vr[(ks + 1) *
|
|
vr_dim1 + 1], &c__1, &c_b21, &work[1], &c__1);
|
|
tmpii = sdot_(n, &work[1], &c__1, &vl[(ks + 1) * vl_dim1 + 1],
|
|
&c__1);
|
|
tmpir = sdot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &
|
|
c__1);
|
|
uhbv = tmprr + tmpii;
|
|
uhbvi = tmpir - tmpri;
|
|
uhav = slapy2_(&uhav, &uhavi);
|
|
uhbv = slapy2_(&uhbv, &uhbvi);
|
|
cond = slapy2_(&uhav, &uhbv);
|
|
s[ks] = cond / (rnrm * lnrm);
|
|
s[ks + 1] = s[ks];
|
|
|
|
} else {
|
|
|
|
/* Real eigenvalue. */
|
|
|
|
rnrm = snrm2_(n, &vr[ks * vr_dim1 + 1], &c__1);
|
|
lnrm = snrm2_(n, &vl[ks * vl_dim1 + 1], &c__1);
|
|
sgemv_("N", n, n, &c_b19, &a[a_offset], lda, &vr[ks * vr_dim1
|
|
+ 1], &c__1, &c_b21, &work[1], &c__1);
|
|
uhav = sdot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1)
|
|
;
|
|
sgemv_("N", n, n, &c_b19, &b[b_offset], ldb, &vr[ks * vr_dim1
|
|
+ 1], &c__1, &c_b21, &work[1], &c__1);
|
|
uhbv = sdot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1)
|
|
;
|
|
cond = slapy2_(&uhav, &uhbv);
|
|
if (cond == 0.f) {
|
|
s[ks] = -1.f;
|
|
} else {
|
|
s[ks] = cond / (rnrm * lnrm);
|
|
}
|
|
}
|
|
}
|
|
|
|
if (wantdf) {
|
|
if (*n == 1) {
|
|
dif[ks] = slapy2_(&a[a_dim1 + 1], &b[b_dim1 + 1]);
|
|
goto L20;
|
|
}
|
|
|
|
/* Estimate the reciprocal condition number of the k-th */
|
|
/* eigenvectors. */
|
|
if (pair) {
|
|
|
|
/* Copy the 2-by 2 pencil beginning at (A(k,k), B(k, k)). */
|
|
/* Compute the eigenvalue(s) at position K. */
|
|
|
|
work[1] = a[k + k * a_dim1];
|
|
work[2] = a[k + 1 + k * a_dim1];
|
|
work[3] = a[k + (k + 1) * a_dim1];
|
|
work[4] = a[k + 1 + (k + 1) * a_dim1];
|
|
work[5] = b[k + k * b_dim1];
|
|
work[6] = b[k + 1 + k * b_dim1];
|
|
work[7] = b[k + (k + 1) * b_dim1];
|
|
work[8] = b[k + 1 + (k + 1) * b_dim1];
|
|
r__1 = smlnum * eps;
|
|
slag2_(&work[1], &c__2, &work[5], &c__2, &r__1, &beta, dummy1,
|
|
&alphar, dummy, &alphai);
|
|
alprqt = 1.f;
|
|
c1 = (alphar * alphar + alphai * alphai + beta * beta) * 2.f;
|
|
c2 = beta * 4.f * beta * alphai * alphai;
|
|
root1 = c1 + sqrt(c1 * c1 - c2 * 4.f);
|
|
root2 = c2 / root1;
|
|
root1 /= 2.f;
|
|
/* Computing MIN */
|
|
r__1 = sqrt(root1), r__2 = sqrt(root2);
|
|
cond = f2cmin(r__1,r__2);
|
|
}
|
|
|
|
/* Copy the matrix (A, B) to the array WORK and swap the */
|
|
/* diagonal block beginning at A(k,k) to the (1,1) position. */
|
|
|
|
slacpy_("Full", n, n, &a[a_offset], lda, &work[1], n);
|
|
slacpy_("Full", n, n, &b[b_offset], ldb, &work[*n * *n + 1], n);
|
|
ifst = k;
|
|
ilst = 1;
|
|
|
|
i__2 = *lwork - (*n << 1) * *n;
|
|
stgexc_(&c_false, &c_false, n, &work[1], n, &work[*n * *n + 1], n,
|
|
dummy, &c__1, dummy1, &c__1, &ifst, &ilst, &work[(*n * *
|
|
n << 1) + 1], &i__2, &ierr);
|
|
|
|
if (ierr > 0) {
|
|
|
|
/* Ill-conditioned problem - swap rejected. */
|
|
|
|
dif[ks] = 0.f;
|
|
} else {
|
|
|
|
/* Reordering successful, solve generalized Sylvester */
|
|
/* equation for R and L, */
|
|
/* A22 * R - L * A11 = A12 */
|
|
/* B22 * R - L * B11 = B12, */
|
|
/* and compute estimate of Difl((A11,B11), (A22, B22)). */
|
|
|
|
n1 = 1;
|
|
if (work[2] != 0.f) {
|
|
n1 = 2;
|
|
}
|
|
n2 = *n - n1;
|
|
if (n2 == 0) {
|
|
dif[ks] = cond;
|
|
} else {
|
|
i__ = *n * *n + 1;
|
|
iz = (*n << 1) * *n + 1;
|
|
i__2 = *lwork - (*n << 1) * *n;
|
|
stgsyl_("N", &c__3, &n2, &n1, &work[*n * n1 + n1 + 1], n,
|
|
&work[1], n, &work[n1 + 1], n, &work[*n * n1 + n1
|
|
+ i__], n, &work[i__], n, &work[n1 + i__], n, &
|
|
scale, &dif[ks], &work[iz + 1], &i__2, &iwork[1],
|
|
&ierr);
|
|
|
|
if (pair) {
|
|
/* Computing MIN */
|
|
r__1 = f2cmax(1.f,alprqt) * dif[ks];
|
|
dif[ks] = f2cmin(r__1,cond);
|
|
}
|
|
}
|
|
}
|
|
if (pair) {
|
|
dif[ks + 1] = dif[ks];
|
|
}
|
|
}
|
|
if (pair) {
|
|
++ks;
|
|
}
|
|
|
|
L20:
|
|
;
|
|
}
|
|
work[1] = (real) lwmin;
|
|
return;
|
|
|
|
/* End of STGSNA */
|
|
|
|
} /* stgsna_ */
|
|
|