1382 lines
43 KiB
C
1382 lines
43 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/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 {
|
|
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;
|
|
|
|
/* > \brief \b ZTGSEN */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZTGSEN + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgsen.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgsen.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgsen.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZTGSEN( IJOB, WANTQ, WANTZ, SELECT, N, A, LDA, B, LDB, */
|
|
/* ALPHA, BETA, Q, LDQ, Z, LDZ, M, PL, PR, DIF, */
|
|
/* WORK, LWORK, IWORK, LIWORK, INFO ) */
|
|
|
|
/* LOGICAL WANTQ, WANTZ */
|
|
/* INTEGER IJOB, INFO, LDA, LDB, LDQ, LDZ, LIWORK, LWORK, */
|
|
/* $ M, N */
|
|
/* DOUBLE PRECISION PL, PR */
|
|
/* LOGICAL SELECT( * ) */
|
|
/* INTEGER IWORK( * ) */
|
|
/* DOUBLE PRECISION DIF( * ) */
|
|
/* COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ), */
|
|
/* $ BETA( * ), Q( LDQ, * ), WORK( * ), Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZTGSEN reorders the generalized Schur decomposition of a complex */
|
|
/* > matrix pair (A, B) (in terms of an unitary equivalence trans- */
|
|
/* > formation Q**H * (A, B) * Z), so that a selected cluster of eigenvalues */
|
|
/* > appears in the leading diagonal blocks of the pair (A,B). The leading */
|
|
/* > columns of Q and Z form unitary bases of the corresponding left and */
|
|
/* > right eigenspaces (deflating subspaces). (A, B) must be in */
|
|
/* > generalized Schur canonical form, that is, A and B are both upper */
|
|
/* > triangular. */
|
|
/* > */
|
|
/* > ZTGSEN also computes the generalized eigenvalues */
|
|
/* > */
|
|
/* > w(j)= ALPHA(j) / BETA(j) */
|
|
/* > */
|
|
/* > of the reordered matrix pair (A, B). */
|
|
/* > */
|
|
/* > Optionally, the routine computes estimates of reciprocal condition */
|
|
/* > numbers for eigenvalues and eigenspaces. These are Difu[(A11,B11), */
|
|
/* > (A22,B22)] and Difl[(A11,B11), (A22,B22)], i.e. the separation(s) */
|
|
/* > between the matrix pairs (A11, B11) and (A22,B22) that correspond to */
|
|
/* > the selected cluster and the eigenvalues outside the cluster, resp., */
|
|
/* > and norms of "projections" onto left and right eigenspaces w.r.t. */
|
|
/* > the selected cluster in the (1,1)-block. */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] IJOB */
|
|
/* > \verbatim */
|
|
/* > IJOB is INTEGER */
|
|
/* > Specifies whether condition numbers are required for the */
|
|
/* > cluster of eigenvalues (PL and PR) or the deflating subspaces */
|
|
/* > (Difu and Difl): */
|
|
/* > =0: Only reorder w.r.t. SELECT. No extras. */
|
|
/* > =1: Reciprocal of norms of "projections" onto left and right */
|
|
/* > eigenspaces w.r.t. the selected cluster (PL and PR). */
|
|
/* > =2: Upper bounds on Difu and Difl. F-norm-based estimate */
|
|
/* > (DIF(1:2)). */
|
|
/* > =3: Estimate of Difu and Difl. 1-norm-based estimate */
|
|
/* > (DIF(1:2)). */
|
|
/* > About 5 times as expensive as IJOB = 2. */
|
|
/* > =4: Compute PL, PR and DIF (i.e. 0, 1 and 2 above): Economic */
|
|
/* > version to get it all. */
|
|
/* > =5: Compute PL, PR and DIF (i.e. 0, 1 and 3 above) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] WANTQ */
|
|
/* > \verbatim */
|
|
/* > WANTQ is LOGICAL */
|
|
/* > .TRUE. : update the left transformation matrix Q; */
|
|
/* > .FALSE.: do not update Q. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] WANTZ */
|
|
/* > \verbatim */
|
|
/* > WANTZ is LOGICAL */
|
|
/* > .TRUE. : update the right transformation matrix Z; */
|
|
/* > .FALSE.: do not update Z. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SELECT */
|
|
/* > \verbatim */
|
|
/* > SELECT is LOGICAL array, dimension (N) */
|
|
/* > SELECT specifies the eigenvalues in the selected cluster. To */
|
|
/* > select an eigenvalue w(j), SELECT(j) must be set to */
|
|
/* > .TRUE.. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrices A and B. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX*16 array, dimension(LDA,N) */
|
|
/* > On entry, the upper triangular matrix A, in generalized */
|
|
/* > Schur canonical form. */
|
|
/* > On exit, A is overwritten by the reordered matrix A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX*16 array, dimension(LDB,N) */
|
|
/* > On entry, the upper triangular matrix B, in generalized */
|
|
/* > Schur canonical form. */
|
|
/* > On exit, B is overwritten by the reordered matrix B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ALPHA */
|
|
/* > \verbatim */
|
|
/* > ALPHA is COMPLEX*16 array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BETA */
|
|
/* > \verbatim */
|
|
/* > BETA is COMPLEX*16 array, dimension (N) */
|
|
/* > */
|
|
/* > The diagonal elements of A and B, respectively, */
|
|
/* > when the pair (A,B) has been reduced to generalized Schur */
|
|
/* > form. ALPHA(i)/BETA(i) i=1,...,N are the generalized */
|
|
/* > eigenvalues. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is COMPLEX*16 array, dimension (LDQ,N) */
|
|
/* > On entry, if WANTQ = .TRUE., Q is an N-by-N matrix. */
|
|
/* > On exit, Q has been postmultiplied by the left unitary */
|
|
/* > transformation matrix which reorder (A, B); The leading M */
|
|
/* > columns of Q form orthonormal bases for the specified pair of */
|
|
/* > left eigenspaces (deflating subspaces). */
|
|
/* > If WANTQ = .FALSE., Q is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDQ */
|
|
/* > \verbatim */
|
|
/* > LDQ is INTEGER */
|
|
/* > The leading dimension of the array Q. LDQ >= 1. */
|
|
/* > If WANTQ = .TRUE., LDQ >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is COMPLEX*16 array, dimension (LDZ,N) */
|
|
/* > On entry, if WANTZ = .TRUE., Z is an N-by-N matrix. */
|
|
/* > On exit, Z has been postmultiplied by the left unitary */
|
|
/* > transformation matrix which reorder (A, B); The leading M */
|
|
/* > columns of Z form orthonormal bases for the specified pair of */
|
|
/* > left eigenspaces (deflating subspaces). */
|
|
/* > If WANTZ = .FALSE., Z is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. LDZ >= 1. */
|
|
/* > If WANTZ = .TRUE., LDZ >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The dimension of the specified pair of left and right */
|
|
/* > eigenspaces, (deflating subspaces) 0 <= M <= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] PL */
|
|
/* > \verbatim */
|
|
/* > PL is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] PR */
|
|
/* > \verbatim */
|
|
/* > PR is DOUBLE PRECISION */
|
|
/* > */
|
|
/* > If IJOB = 1, 4 or 5, PL, PR are lower bounds on the */
|
|
/* > reciprocal of the norm of "projections" onto left and right */
|
|
/* > eigenspace with respect to the selected cluster. */
|
|
/* > 0 < PL, PR <= 1. */
|
|
/* > If M = 0 or M = N, PL = PR = 1. */
|
|
/* > If IJOB = 0, 2 or 3 PL, PR are not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DIF */
|
|
/* > \verbatim */
|
|
/* > DIF is DOUBLE PRECISION array, dimension (2). */
|
|
/* > If IJOB >= 2, DIF(1:2) store the estimates of Difu and Difl. */
|
|
/* > If IJOB = 2 or 4, DIF(1:2) are F-norm-based upper bounds on */
|
|
/* > Difu and Difl. If IJOB = 3 or 5, DIF(1:2) are 1-norm-based */
|
|
/* > estimates of Difu and Difl, computed using reversed */
|
|
/* > communication with ZLACN2. */
|
|
/* > If M = 0 or N, DIF(1:2) = F-norm([A, B]). */
|
|
/* > If IJOB = 0 or 1, DIF is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 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 >= 1 */
|
|
/* > If IJOB = 1, 2 or 4, LWORK >= 2*M*(N-M) */
|
|
/* > If IJOB = 3 or 5, LWORK >= 4*M*(N-M) */
|
|
/* > */
|
|
/* > 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 (MAX(1,LIWORK)) */
|
|
/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LIWORK */
|
|
/* > \verbatim */
|
|
/* > LIWORK is INTEGER */
|
|
/* > The dimension of the array IWORK. LIWORK >= 1. */
|
|
/* > If IJOB = 1, 2 or 4, LIWORK >= N+2; */
|
|
/* > If IJOB = 3 or 5, LIWORK >= MAX(N+2, 2*M*(N-M)); */
|
|
/* > */
|
|
/* > If LIWORK = -1, then a workspace query is assumed; the */
|
|
/* > routine only calculates the optimal size of the IWORK array, */
|
|
/* > returns this value as the first entry of the IWORK array, and */
|
|
/* > no error message related to LIWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > =0: Successful exit. */
|
|
/* > <0: If INFO = -i, the i-th argument had an illegal value. */
|
|
/* > =1: Reordering of (A, B) failed because the transformed */
|
|
/* > matrix pair (A, B) would be too far from generalized */
|
|
/* > Schur form; the problem is very ill-conditioned. */
|
|
/* > (A, B) may have been partially reordered. */
|
|
/* > If requested, 0 is returned in DIF(*), PL and PR. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZTGSEN first collects the selected eigenvalues by computing unitary */
|
|
/* > U and W that move them to the top left corner of (A, B). In other */
|
|
/* > words, the selected eigenvalues are the eigenvalues of (A11, B11) in */
|
|
/* > */
|
|
/* > U**H*(A, B)*W = (A11 A12) (B11 B12) n1 */
|
|
/* > ( 0 A22),( 0 B22) n2 */
|
|
/* > n1 n2 n1 n2 */
|
|
/* > */
|
|
/* > where N = n1+n2 and U**H means the conjugate transpose of U. The first */
|
|
/* > n1 columns of U and W span the specified pair of left and right */
|
|
/* > eigenspaces (deflating subspaces) of (A, B). */
|
|
/* > */
|
|
/* > If (A, B) has been obtained from the generalized real Schur */
|
|
/* > decomposition of a matrix pair (C, D) = Q*(A, B)*Z**H, then the */
|
|
/* > reordered generalized Schur form of (C, D) is given by */
|
|
/* > */
|
|
/* > (C, D) = (Q*U)*(U**H *(A, B)*W)*(Z*W)**H, */
|
|
/* > */
|
|
/* > and the first n1 columns of Q*U and Z*W span the corresponding */
|
|
/* > deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.). */
|
|
/* > */
|
|
/* > Note that if the selected eigenvalue is sufficiently ill-conditioned, */
|
|
/* > then its value may differ significantly from its value before */
|
|
/* > reordering. */
|
|
/* > */
|
|
/* > The reciprocal condition numbers of the left and right eigenspaces */
|
|
/* > spanned by the first n1 columns of U and W (or Q*U and Z*W) may */
|
|
/* > be returned in DIF(1:2), corresponding to Difu and Difl, resp. */
|
|
/* > */
|
|
/* > The Difu and Difl are defined as: */
|
|
/* > */
|
|
/* > Difu[(A11, B11), (A22, B22)] = sigma-f2cmin( Zu ) */
|
|
/* > and */
|
|
/* > Difl[(A11, B11), (A22, B22)] = Difu[(A22, B22), (A11, B11)], */
|
|
/* > */
|
|
/* > where sigma-f2cmin(Zu) is the smallest singular value of the */
|
|
/* > (2*n1*n2)-by-(2*n1*n2) matrix */
|
|
/* > */
|
|
/* > Zu = [ kron(In2, A11) -kron(A22**H, In1) ] */
|
|
/* > [ kron(In2, B11) -kron(B22**H, In1) ]. */
|
|
/* > */
|
|
/* > Here, Inx is the identity matrix of size nx and A22**H is the */
|
|
/* > conjugate transpose of A22. kron(X, Y) is the Kronecker product between */
|
|
/* > the matrices X and Y. */
|
|
/* > */
|
|
/* > When DIF(2) is small, small changes in (A, B) can cause large changes */
|
|
/* > in the deflating subspace. An approximate (asymptotic) bound on the */
|
|
/* > maximum angular error in the computed deflating subspaces is */
|
|
/* > */
|
|
/* > EPS * norm((A, B)) / DIF(2), */
|
|
/* > */
|
|
/* > where EPS is the machine precision. */
|
|
/* > */
|
|
/* > The reciprocal norm of the projectors on the left and right */
|
|
/* > eigenspaces associated with (A11, B11) may be returned in PL and PR. */
|
|
/* > They are computed as follows. First we compute L and R so that */
|
|
/* > P*(A, B)*Q is block diagonal, where */
|
|
/* > */
|
|
/* > P = ( I -L ) n1 Q = ( I R ) n1 */
|
|
/* > ( 0 I ) n2 and ( 0 I ) n2 */
|
|
/* > n1 n2 n1 n2 */
|
|
/* > */
|
|
/* > and (L, R) is the solution to the generalized Sylvester equation */
|
|
/* > */
|
|
/* > A11*R - L*A22 = -A12 */
|
|
/* > B11*R - L*B22 = -B12 */
|
|
/* > */
|
|
/* > Then PL = (F-norm(L)**2+1)**(-1/2) and PR = (F-norm(R)**2+1)**(-1/2). */
|
|
/* > An approximate (asymptotic) bound on the average absolute error of */
|
|
/* > the selected eigenvalues is */
|
|
/* > */
|
|
/* > EPS * norm((A, B)) / PL. */
|
|
/* > */
|
|
/* > There are also global error bounds which valid for perturbations up */
|
|
/* > to a certain restriction: A lower bound (x) on the smallest */
|
|
/* > F-norm(E,F) for which an eigenvalue of (A11, B11) may move and */
|
|
/* > coalesce with an eigenvalue of (A22, B22) under perturbation (E,F), */
|
|
/* > (i.e. (A + E, B + F), is */
|
|
/* > */
|
|
/* > x = f2cmin(Difu,Difl)/((1/(PL*PL)+1/(PR*PR))**(1/2)+2*f2cmax(1/PL,1/PR)). */
|
|
/* > */
|
|
/* > An approximate bound on x can be computed from DIF(1:2), PL and PR. */
|
|
/* > */
|
|
/* > If y = ( F-norm(E,F) / x) <= 1, the angles between the perturbed */
|
|
/* > (L', R') and unperturbed (L, R) left and right deflating subspaces */
|
|
/* > associated with the selected cluster in the (1,1)-blocks can be */
|
|
/* > bounded as */
|
|
/* > */
|
|
/* > f2cmax-angle(L, L') <= arctan( y * PL / (1 - y * (1 - PL * PL)**(1/2)) */
|
|
/* > f2cmax-angle(R, R') <= arctan( y * PR / (1 - y * (1 - PR * PR)**(1/2)) */
|
|
/* > */
|
|
/* > See LAPACK User's Guide section 4.11 or the following references */
|
|
/* > for more information. */
|
|
/* > */
|
|
/* > Note that if the default method for computing the Frobenius-norm- */
|
|
/* > based estimate DIF is not wanted (see ZLATDF), then the parameter */
|
|
/* > IDIFJB (see below) should be changed from 3 to 4 (routine ZLATDF */
|
|
/* > (IJOB = 2 will be used)). See ZTGSYL for more details. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
|
|
/* > Umea University, S-901 87 Umea, Sweden. */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > [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. */
|
|
/* > \n */
|
|
/* > [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. */
|
|
/* > \n */
|
|
/* > [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. */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void ztgsen_(integer *ijob, logical *wantq, logical *wantz,
|
|
logical *select, integer *n, doublecomplex *a, integer *lda,
|
|
doublecomplex *b, integer *ldb, doublecomplex *alpha, doublecomplex *
|
|
beta, doublecomplex *q, integer *ldq, doublecomplex *z__, integer *
|
|
ldz, integer *m, doublereal *pl, doublereal *pr, doublereal *dif,
|
|
doublecomplex *work, integer *lwork, integer *iwork, integer *liwork,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1,
|
|
z_offset, i__1, i__2, i__3;
|
|
doublecomplex z__1, z__2;
|
|
|
|
/* Local variables */
|
|
integer kase, ierr;
|
|
doublereal dsum;
|
|
logical swap;
|
|
doublecomplex temp1, temp2;
|
|
integer i__, k, isave[3];
|
|
extern /* Subroutine */ void zscal_(integer *, doublecomplex *,
|
|
doublecomplex *, integer *);
|
|
logical wantd;
|
|
integer lwmin;
|
|
logical wantp;
|
|
integer n1, n2;
|
|
extern /* Subroutine */ void zlacn2_(integer *, doublecomplex *,
|
|
doublecomplex *, doublereal *, integer *, integer *);
|
|
logical wantd1, wantd2;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal dscale;
|
|
integer ks;
|
|
doublereal rdscal, safmin;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
integer liwmin;
|
|
extern /* Subroutine */ void zlacpy_(char *, integer *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *),
|
|
ztgexc_(logical *, logical *, integer *, doublecomplex *, integer
|
|
*, doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, integer *, integer *, integer *);
|
|
integer mn2;
|
|
extern /* Subroutine */ void zlassq_(integer *, doublecomplex *, integer *,
|
|
doublereal *, doublereal *);
|
|
logical lquery;
|
|
extern /* Subroutine */ void ztgsyl_(char *, integer *, integer *, integer
|
|
*, doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *,
|
|
doublereal *, doublereal *, doublecomplex *, integer *, integer *,
|
|
integer *);
|
|
integer ijb;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 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;
|
|
--alpha;
|
|
--beta;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
z_dim1 = *ldz;
|
|
z_offset = 1 + z_dim1 * 1;
|
|
z__ -= z_offset;
|
|
--dif;
|
|
--work;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
lquery = *lwork == -1 || *liwork == -1;
|
|
|
|
if (*ijob < 0 || *ijob > 5) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -5;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -7;
|
|
} else if (*ldb < f2cmax(1,*n)) {
|
|
*info = -9;
|
|
} else if (*ldq < 1 || *wantq && *ldq < *n) {
|
|
*info = -13;
|
|
} else if (*ldz < 1 || *wantz && *ldz < *n) {
|
|
*info = -15;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZTGSEN", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
ierr = 0;
|
|
|
|
wantp = *ijob == 1 || *ijob >= 4;
|
|
wantd1 = *ijob == 2 || *ijob == 4;
|
|
wantd2 = *ijob == 3 || *ijob == 5;
|
|
wantd = wantd1 || wantd2;
|
|
|
|
/* Set M to the dimension of the specified pair of deflating */
|
|
/* subspaces. */
|
|
|
|
*m = 0;
|
|
if (! lquery || *ijob != 0) {
|
|
i__1 = *n;
|
|
for (k = 1; k <= i__1; ++k) {
|
|
i__2 = k;
|
|
i__3 = k + k * a_dim1;
|
|
alpha[i__2].r = a[i__3].r, alpha[i__2].i = a[i__3].i;
|
|
i__2 = k;
|
|
i__3 = k + k * b_dim1;
|
|
beta[i__2].r = b[i__3].r, beta[i__2].i = b[i__3].i;
|
|
if (k < *n) {
|
|
if (select[k]) {
|
|
++(*m);
|
|
}
|
|
} else {
|
|
if (select[*n]) {
|
|
++(*m);
|
|
}
|
|
}
|
|
/* L10: */
|
|
}
|
|
}
|
|
|
|
if (*ijob == 1 || *ijob == 2 || *ijob == 4) {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = (*m << 1) * (*n - *m);
|
|
lwmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n + 2;
|
|
liwmin = f2cmax(i__1,i__2);
|
|
} else if (*ijob == 3 || *ijob == 5) {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = (*m << 2) * (*n - *m);
|
|
lwmin = f2cmax(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = (*m << 1) * (*n - *m), i__1 = f2cmax(i__1,i__2), i__2 =
|
|
*n + 2;
|
|
liwmin = f2cmax(i__1,i__2);
|
|
} else {
|
|
lwmin = 1;
|
|
liwmin = 1;
|
|
}
|
|
|
|
work[1].r = (doublereal) lwmin, work[1].i = 0.;
|
|
iwork[1] = liwmin;
|
|
|
|
if (*lwork < lwmin && ! lquery) {
|
|
*info = -21;
|
|
} else if (*liwork < liwmin && ! lquery) {
|
|
*info = -23;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZTGSEN", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible. */
|
|
|
|
if (*m == *n || *m == 0) {
|
|
if (wantp) {
|
|
*pl = 1.;
|
|
*pr = 1.;
|
|
}
|
|
if (wantd) {
|
|
dscale = 0.;
|
|
dsum = 1.;
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
zlassq_(n, &a[i__ * a_dim1 + 1], &c__1, &dscale, &dsum);
|
|
zlassq_(n, &b[i__ * b_dim1 + 1], &c__1, &dscale, &dsum);
|
|
/* L20: */
|
|
}
|
|
dif[1] = dscale * sqrt(dsum);
|
|
dif[2] = dif[1];
|
|
}
|
|
goto L70;
|
|
}
|
|
|
|
/* Get machine constant */
|
|
|
|
safmin = dlamch_("S");
|
|
|
|
/* Collect the selected blocks at the top-left corner of (A, B). */
|
|
|
|
ks = 0;
|
|
i__1 = *n;
|
|
for (k = 1; k <= i__1; ++k) {
|
|
swap = select[k];
|
|
if (swap) {
|
|
++ks;
|
|
|
|
/* Swap the K-th block to position KS. Compute unitary Q */
|
|
/* and Z that will swap adjacent diagonal blocks in (A, B). */
|
|
|
|
if (k != ks) {
|
|
ztgexc_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb,
|
|
&q[q_offset], ldq, &z__[z_offset], ldz, &k, &ks, &
|
|
ierr);
|
|
}
|
|
|
|
if (ierr > 0) {
|
|
|
|
/* Swap is rejected: exit. */
|
|
|
|
*info = 1;
|
|
if (wantp) {
|
|
*pl = 0.;
|
|
*pr = 0.;
|
|
}
|
|
if (wantd) {
|
|
dif[1] = 0.;
|
|
dif[2] = 0.;
|
|
}
|
|
goto L70;
|
|
}
|
|
}
|
|
/* L30: */
|
|
}
|
|
if (wantp) {
|
|
|
|
/* Solve generalized Sylvester equation for R and L: */
|
|
/* A11 * R - L * A22 = A12 */
|
|
/* B11 * R - L * B22 = B12 */
|
|
|
|
n1 = *m;
|
|
n2 = *n - *m;
|
|
i__ = n1 + 1;
|
|
zlacpy_("Full", &n1, &n2, &a[i__ * a_dim1 + 1], lda, &work[1], &n1);
|
|
zlacpy_("Full", &n1, &n2, &b[i__ * b_dim1 + 1], ldb, &work[n1 * n2 +
|
|
1], &n1);
|
|
ijb = 0;
|
|
i__1 = *lwork - (n1 << 1) * n2;
|
|
ztgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + i__ * a_dim1]
|
|
, lda, &work[1], &n1, &b[b_offset], ldb, &b[i__ + i__ *
|
|
b_dim1], ldb, &work[n1 * n2 + 1], &n1, &dscale, &dif[1], &
|
|
work[(n1 * n2 << 1) + 1], &i__1, &iwork[1], &ierr);
|
|
|
|
/* Estimate the reciprocal of norms of "projections" onto */
|
|
/* left and right eigenspaces */
|
|
|
|
rdscal = 0.;
|
|
dsum = 1.;
|
|
i__1 = n1 * n2;
|
|
zlassq_(&i__1, &work[1], &c__1, &rdscal, &dsum);
|
|
*pl = rdscal * sqrt(dsum);
|
|
if (*pl == 0.) {
|
|
*pl = 1.;
|
|
} else {
|
|
*pl = dscale / (sqrt(dscale * dscale / *pl + *pl) * sqrt(*pl));
|
|
}
|
|
rdscal = 0.;
|
|
dsum = 1.;
|
|
i__1 = n1 * n2;
|
|
zlassq_(&i__1, &work[n1 * n2 + 1], &c__1, &rdscal, &dsum);
|
|
*pr = rdscal * sqrt(dsum);
|
|
if (*pr == 0.) {
|
|
*pr = 1.;
|
|
} else {
|
|
*pr = dscale / (sqrt(dscale * dscale / *pr + *pr) * sqrt(*pr));
|
|
}
|
|
}
|
|
if (wantd) {
|
|
|
|
/* Compute estimates Difu and Difl. */
|
|
|
|
if (wantd1) {
|
|
n1 = *m;
|
|
n2 = *n - *m;
|
|
i__ = n1 + 1;
|
|
ijb = 3;
|
|
|
|
/* Frobenius norm-based Difu estimate. */
|
|
|
|
i__1 = *lwork - (n1 << 1) * n2;
|
|
ztgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ + i__ *
|
|
a_dim1], lda, &work[1], &n1, &b[b_offset], ldb, &b[i__ +
|
|
i__ * b_dim1], ldb, &work[n1 * n2 + 1], &n1, &dscale, &
|
|
dif[1], &work[(n1 * n2 << 1) + 1], &i__1, &iwork[1], &
|
|
ierr);
|
|
|
|
/* Frobenius norm-based Difl estimate. */
|
|
|
|
i__1 = *lwork - (n1 << 1) * n2;
|
|
ztgsyl_("N", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda, &a[
|
|
a_offset], lda, &work[1], &n2, &b[i__ + i__ * b_dim1],
|
|
ldb, &b[b_offset], ldb, &work[n1 * n2 + 1], &n2, &dscale,
|
|
&dif[2], &work[(n1 * n2 << 1) + 1], &i__1, &iwork[1], &
|
|
ierr);
|
|
} else {
|
|
|
|
/* Compute 1-norm-based estimates of Difu and Difl using */
|
|
/* reversed communication with ZLACN2. In each step a */
|
|
/* generalized Sylvester equation or a transposed variant */
|
|
/* is solved. */
|
|
|
|
kase = 0;
|
|
n1 = *m;
|
|
n2 = *n - *m;
|
|
i__ = n1 + 1;
|
|
ijb = 0;
|
|
mn2 = (n1 << 1) * n2;
|
|
|
|
/* 1-norm-based estimate of Difu. */
|
|
|
|
L40:
|
|
zlacn2_(&mn2, &work[mn2 + 1], &work[1], &dif[1], &kase, isave);
|
|
if (kase != 0) {
|
|
if (kase == 1) {
|
|
|
|
/* Solve generalized Sylvester equation */
|
|
|
|
i__1 = *lwork - (n1 << 1) * n2;
|
|
ztgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ +
|
|
i__ * a_dim1], lda, &work[1], &n1, &b[b_offset],
|
|
ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 +
|
|
1], &n1, &dscale, &dif[1], &work[(n1 * n2 << 1) +
|
|
1], &i__1, &iwork[1], &ierr);
|
|
} else {
|
|
|
|
/* Solve the transposed variant. */
|
|
|
|
i__1 = *lwork - (n1 << 1) * n2;
|
|
ztgsyl_("C", &ijb, &n1, &n2, &a[a_offset], lda, &a[i__ +
|
|
i__ * a_dim1], lda, &work[1], &n1, &b[b_offset],
|
|
ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 +
|
|
1], &n1, &dscale, &dif[1], &work[(n1 * n2 << 1) +
|
|
1], &i__1, &iwork[1], &ierr);
|
|
}
|
|
goto L40;
|
|
}
|
|
dif[1] = dscale / dif[1];
|
|
|
|
/* 1-norm-based estimate of Difl. */
|
|
|
|
L50:
|
|
zlacn2_(&mn2, &work[mn2 + 1], &work[1], &dif[2], &kase, isave);
|
|
if (kase != 0) {
|
|
if (kase == 1) {
|
|
|
|
/* Solve generalized Sylvester equation */
|
|
|
|
i__1 = *lwork - (n1 << 1) * n2;
|
|
ztgsyl_("N", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda,
|
|
&a[a_offset], lda, &work[1], &n2, &b[i__ + i__ *
|
|
b_dim1], ldb, &b[b_offset], ldb, &work[n1 * n2 +
|
|
1], &n2, &dscale, &dif[2], &work[(n1 * n2 << 1) +
|
|
1], &i__1, &iwork[1], &ierr);
|
|
} else {
|
|
|
|
/* Solve the transposed variant. */
|
|
|
|
i__1 = *lwork - (n1 << 1) * n2;
|
|
ztgsyl_("C", &ijb, &n2, &n1, &a[i__ + i__ * a_dim1], lda,
|
|
&a[a_offset], lda, &work[1], &n2, &b[b_offset],
|
|
ldb, &b[i__ + i__ * b_dim1], ldb, &work[n1 * n2 +
|
|
1], &n2, &dscale, &dif[2], &work[(n1 * n2 << 1) +
|
|
1], &i__1, &iwork[1], &ierr);
|
|
}
|
|
goto L50;
|
|
}
|
|
dif[2] = dscale / dif[2];
|
|
}
|
|
}
|
|
|
|
/* If B(K,K) is complex, make it real and positive (normalization */
|
|
/* of the generalized Schur form) and Store the generalized */
|
|
/* eigenvalues of reordered pair (A, B) */
|
|
|
|
i__1 = *n;
|
|
for (k = 1; k <= i__1; ++k) {
|
|
dscale = z_abs(&b[k + k * b_dim1]);
|
|
if (dscale > safmin) {
|
|
i__2 = k + k * b_dim1;
|
|
z__2.r = b[i__2].r / dscale, z__2.i = b[i__2].i / dscale;
|
|
d_cnjg(&z__1, &z__2);
|
|
temp1.r = z__1.r, temp1.i = z__1.i;
|
|
i__2 = k + k * b_dim1;
|
|
z__1.r = b[i__2].r / dscale, z__1.i = b[i__2].i / dscale;
|
|
temp2.r = z__1.r, temp2.i = z__1.i;
|
|
i__2 = k + k * b_dim1;
|
|
b[i__2].r = dscale, b[i__2].i = 0.;
|
|
i__2 = *n - k;
|
|
zscal_(&i__2, &temp1, &b[k + (k + 1) * b_dim1], ldb);
|
|
i__2 = *n - k + 1;
|
|
zscal_(&i__2, &temp1, &a[k + k * a_dim1], lda);
|
|
if (*wantq) {
|
|
zscal_(n, &temp2, &q[k * q_dim1 + 1], &c__1);
|
|
}
|
|
} else {
|
|
i__2 = k + k * b_dim1;
|
|
b[i__2].r = 0., b[i__2].i = 0.;
|
|
}
|
|
|
|
i__2 = k;
|
|
i__3 = k + k * a_dim1;
|
|
alpha[i__2].r = a[i__3].r, alpha[i__2].i = a[i__3].i;
|
|
i__2 = k;
|
|
i__3 = k + k * b_dim1;
|
|
beta[i__2].r = b[i__3].r, beta[i__2].i = b[i__3].i;
|
|
|
|
/* L60: */
|
|
}
|
|
|
|
L70:
|
|
|
|
work[1].r = (doublereal) lwmin, work[1].i = 0.;
|
|
iwork[1] = liwmin;
|
|
|
|
return;
|
|
|
|
/* End of ZTGSEN */
|
|
|
|
} /* ztgsen_ */
|
|
|