1304 lines
39 KiB
C
1304 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__4 = 4;
|
|
static doublereal c_b5 = 0.;
|
|
static integer c__1 = 1;
|
|
static integer c__2 = 2;
|
|
static doublereal c_b42 = 1.;
|
|
static doublereal c_b48 = -1.;
|
|
static integer c__0 = 0;
|
|
|
|
/* > \brief \b DTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogon
|
|
al equivalence transformation. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DTGEX2 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgex2.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgex2.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgex2.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, */
|
|
/* LDZ, J1, N1, N2, WORK, LWORK, INFO ) */
|
|
|
|
/* LOGICAL WANTQ, WANTZ */
|
|
/* INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2 */
|
|
/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), */
|
|
/* $ WORK( * ), Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) */
|
|
/* > of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair */
|
|
/* > (A, B) by an orthogonal equivalence transformation. */
|
|
/* > */
|
|
/* > (A, B) must be in generalized real Schur canonical form (as returned */
|
|
/* > by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 */
|
|
/* > diagonal blocks. B is upper triangular. */
|
|
/* > */
|
|
/* > Optionally, the matrices Q and Z of generalized Schur vectors are */
|
|
/* > updated. */
|
|
/* > */
|
|
/* > Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T */
|
|
/* > Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \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] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrices A and B. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION array, dimensions (LDA,N) */
|
|
/* > On entry, the matrix A in the pair (A, B). */
|
|
/* > On exit, the updated 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 DOUBLE PRECISION array, dimensions (LDB,N) */
|
|
/* > On entry, the matrix B in the pair (A, B). */
|
|
/* > On exit, the updated matrix B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Q */
|
|
/* > \verbatim */
|
|
/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
|
|
/* > On entry, if WANTQ = .TRUE., the orthogonal matrix Q. */
|
|
/* > On exit, the updated matrix Q. */
|
|
/* > Not referenced if WANTQ = .FALSE.. */
|
|
/* > \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 DOUBLE PRECISION array, dimension (LDZ,N) */
|
|
/* > On entry, if WANTZ =.TRUE., the orthogonal matrix Z. */
|
|
/* > On exit, the updated matrix Z. */
|
|
/* > Not referenced if WANTZ = .FALSE.. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. LDZ >= 1. */
|
|
/* > If WANTZ = .TRUE., LDZ >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] J1 */
|
|
/* > \verbatim */
|
|
/* > J1 is INTEGER */
|
|
/* > The index to the first block (A11, B11). 1 <= J1 <= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N1 */
|
|
/* > \verbatim */
|
|
/* > N1 is INTEGER */
|
|
/* > The order of the first block (A11, B11). N1 = 0, 1 or 2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N2 */
|
|
/* > \verbatim */
|
|
/* > N2 is INTEGER */
|
|
/* > The order of the second block (A22, B22). N2 = 0, 1 or 2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. */
|
|
/* > LWORK >= MAX( 1, N*(N2+N1), (N2+N1)*(N2+N1)*2 ) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > =0: Successful exit */
|
|
/* > >0: If INFO = 1, the transformed matrix (A, B) would be */
|
|
/* > too far from generalized Schur form; the blocks are */
|
|
/* > not swapped and (A, B) and (Q, Z) are unchanged. */
|
|
/* > The problem of swapping is too ill-conditioned. */
|
|
/* > <0: If INFO = -16: LWORK is too small. Appropriate value */
|
|
/* > for LWORK is returned in WORK(1). */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleGEauxiliary */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > In the current code both weak and strong stability tests are */
|
|
/* > performed. The user can omit the strong stability test by changing */
|
|
/* > the internal logical parameter WANDS to .FALSE.. See ref. [2] for */
|
|
/* > details. */
|
|
|
|
/* > \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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dtgex2_(logical *wantq, logical *wantz, integer *n,
|
|
doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
|
|
q, integer *ldq, doublereal *z__, integer *ldz, integer *j1, integer *
|
|
n1, integer *n2, doublereal *work, integer *lwork, 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;
|
|
doublereal d__1;
|
|
|
|
/* Local variables */
|
|
logical weak;
|
|
doublereal ddum;
|
|
integer idum;
|
|
doublereal taul[4], dsum;
|
|
extern /* Subroutine */ void drot_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *);
|
|
doublereal taur[4], scpy[16] /* was [4][4] */, tcpy[16] /*
|
|
was [4][4] */, f, g;
|
|
integer i__, m;
|
|
doublereal s[16] /* was [4][4] */, t[16] /* was [4][4] */;
|
|
extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
|
|
integer *);
|
|
doublereal scale, bqra21, brqa21;
|
|
extern /* Subroutine */ void dgemm_(char *, char *, integer *, integer *,
|
|
integer *, doublereal *, doublereal *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, integer *);
|
|
doublereal licop[16] /* was [4][4] */;
|
|
integer linfo;
|
|
doublereal ircop[16] /* was [4][4] */, dnorm;
|
|
integer iwork[4];
|
|
extern /* Subroutine */ void dlagv2_(doublereal *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, doublereal *, doublereal *
|
|
, doublereal *, doublereal *, doublereal *), dgeqr2_(integer *,
|
|
integer *, doublereal *, integer *, doublereal *, doublereal *,
|
|
integer *), dgerq2_(integer *, integer *, doublereal *, integer *,
|
|
doublereal *, doublereal *, integer *), dorg2r_(integer *,
|
|
integer *, integer *, doublereal *, integer *, doublereal *,
|
|
doublereal *, integer *), dorgr2_(integer *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *),
|
|
dorm2r_(char *, char *, integer *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, integer *), dormr2_(char *, char *,
|
|
integer *, integer *, integer *, doublereal *, integer *,
|
|
doublereal *, doublereal *, integer *, doublereal *, integer *);
|
|
doublereal be[2], ai[2];
|
|
extern /* Subroutine */ void dtgsy2_(char *, integer *, integer *, integer
|
|
*, doublereal *, integer *, doublereal *, integer *, doublereal *,
|
|
integer *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
|
|
integer *, integer *, integer *);
|
|
doublereal ar[2], sa, sb, li[16] /* was [4][4] */;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal dscale, ir[16] /* was [4][4] */, ss, ws;
|
|
extern /* Subroutine */ void dlacpy_(char *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, integer *),
|
|
dlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
|
|
doublereal *), dlaset_(char *, integer *, integer *, doublereal *,
|
|
doublereal *, doublereal *, integer *), dlassq_(integer *
|
|
, doublereal *, integer *, doublereal *, doublereal *);
|
|
logical dtrong;
|
|
doublereal thresh, smlnum, eps;
|
|
|
|
|
|
/* -- LAPACK auxiliary 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
/* Replaced various illegal calls to DCOPY by calls to DLASET, or by DO */
|
|
/* loops. Sven Hammarling, 1/5/02. */
|
|
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
q_dim1 = *ldq;
|
|
q_offset = 1 + q_dim1 * 1;
|
|
q -= q_offset;
|
|
z_dim1 = *ldz;
|
|
z_offset = 1 + z_dim1 * 1;
|
|
z__ -= z_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n <= 1 || *n1 <= 0 || *n2 <= 0) {
|
|
return;
|
|
}
|
|
if (*n1 > *n || *j1 + *n1 > *n) {
|
|
return;
|
|
}
|
|
m = *n1 + *n2;
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n * m, i__1 = f2cmax(i__1,i__2), i__2 = m * m << 1;
|
|
if (*lwork < f2cmax(i__1,i__2)) {
|
|
*info = -16;
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = *n * m, i__1 = f2cmax(i__1,i__2), i__2 = m * m << 1;
|
|
work[1] = (doublereal) f2cmax(i__1,i__2);
|
|
return;
|
|
}
|
|
|
|
weak = FALSE_;
|
|
dtrong = FALSE_;
|
|
|
|
/* Make a local copy of selected block */
|
|
|
|
dlaset_("Full", &c__4, &c__4, &c_b5, &c_b5, li, &c__4);
|
|
dlaset_("Full", &c__4, &c__4, &c_b5, &c_b5, ir, &c__4);
|
|
dlacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, s, &c__4);
|
|
dlacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, t, &c__4);
|
|
|
|
/* Compute threshold for testing acceptance of swapping. */
|
|
|
|
eps = dlamch_("P");
|
|
smlnum = dlamch_("S") / eps;
|
|
dscale = 0.;
|
|
dsum = 1.;
|
|
dlacpy_("Full", &m, &m, s, &c__4, &work[1], &m);
|
|
i__1 = m * m;
|
|
dlassq_(&i__1, &work[1], &c__1, &dscale, &dsum);
|
|
dlacpy_("Full", &m, &m, t, &c__4, &work[1], &m);
|
|
i__1 = m * m;
|
|
dlassq_(&i__1, &work[1], &c__1, &dscale, &dsum);
|
|
dnorm = dscale * sqrt(dsum);
|
|
|
|
/* THRES has been changed from */
|
|
/* THRESH = MAX( TEN*EPS*SA, SMLNUM ) */
|
|
/* to */
|
|
/* THRESH = MAX( TWENTY*EPS*SA, SMLNUM ) */
|
|
/* on 04/01/10. */
|
|
/* "Bug" reported by Ondra Kamenik, confirmed by Julie Langou, fixed by */
|
|
/* Jim Demmel and Guillaume Revy. See forum post 1783. */
|
|
|
|
/* Computing MAX */
|
|
d__1 = eps * 20. * dnorm;
|
|
thresh = f2cmax(d__1,smlnum);
|
|
|
|
if (m == 2) {
|
|
|
|
/* CASE 1: Swap 1-by-1 and 1-by-1 blocks. */
|
|
|
|
/* Compute orthogonal QL and RQ that swap 1-by-1 and 1-by-1 blocks */
|
|
/* using Givens rotations and perform the swap tentatively. */
|
|
|
|
f = s[5] * t[0] - t[5] * s[0];
|
|
g = s[5] * t[4] - t[5] * s[4];
|
|
sb = abs(t[5]);
|
|
sa = abs(s[5]);
|
|
dlartg_(&f, &g, &ir[4], ir, &ddum);
|
|
ir[1] = -ir[4];
|
|
ir[5] = ir[0];
|
|
drot_(&c__2, s, &c__1, &s[4], &c__1, ir, &ir[1]);
|
|
drot_(&c__2, t, &c__1, &t[4], &c__1, ir, &ir[1]);
|
|
if (sa >= sb) {
|
|
dlartg_(s, &s[1], li, &li[1], &ddum);
|
|
} else {
|
|
dlartg_(t, &t[1], li, &li[1], &ddum);
|
|
}
|
|
drot_(&c__2, s, &c__4, &s[1], &c__4, li, &li[1]);
|
|
drot_(&c__2, t, &c__4, &t[1], &c__4, li, &li[1]);
|
|
li[5] = li[0];
|
|
li[4] = -li[1];
|
|
|
|
/* Weak stability test: */
|
|
/* |S21| + |T21| <= O(EPS * F-norm((S, T))) */
|
|
|
|
ws = abs(s[1]) + abs(t[1]);
|
|
weak = ws <= thresh;
|
|
if (! weak) {
|
|
goto L70;
|
|
}
|
|
|
|
if (TRUE_) {
|
|
|
|
/* Strong stability test: */
|
|
/* F-norm((A-QL**T*S*QR, B-QL**T*T*QR)) <= O(EPS*F-norm((A,B))) */
|
|
|
|
dlacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, &work[m * m
|
|
+ 1], &m);
|
|
dgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, &
|
|
work[1], &m);
|
|
dgemm_("N", "T", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
|
|
c_b42, &work[m * m + 1], &m);
|
|
dscale = 0.;
|
|
dsum = 1.;
|
|
i__1 = m * m;
|
|
dlassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
|
|
|
|
dlacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, &work[m * m
|
|
+ 1], &m);
|
|
dgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, &
|
|
work[1], &m);
|
|
dgemm_("N", "T", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
|
|
c_b42, &work[m * m + 1], &m);
|
|
i__1 = m * m;
|
|
dlassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
|
|
ss = dscale * sqrt(dsum);
|
|
dtrong = ss <= thresh;
|
|
if (! dtrong) {
|
|
goto L70;
|
|
}
|
|
}
|
|
|
|
/* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and */
|
|
/* (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */
|
|
|
|
i__1 = *j1 + 1;
|
|
drot_(&i__1, &a[*j1 * a_dim1 + 1], &c__1, &a[(*j1 + 1) * a_dim1 + 1],
|
|
&c__1, ir, &ir[1]);
|
|
i__1 = *j1 + 1;
|
|
drot_(&i__1, &b[*j1 * b_dim1 + 1], &c__1, &b[(*j1 + 1) * b_dim1 + 1],
|
|
&c__1, ir, &ir[1]);
|
|
i__1 = *n - *j1 + 1;
|
|
drot_(&i__1, &a[*j1 + *j1 * a_dim1], lda, &a[*j1 + 1 + *j1 * a_dim1],
|
|
lda, li, &li[1]);
|
|
i__1 = *n - *j1 + 1;
|
|
drot_(&i__1, &b[*j1 + *j1 * b_dim1], ldb, &b[*j1 + 1 + *j1 * b_dim1],
|
|
ldb, li, &li[1]);
|
|
|
|
/* Set N1-by-N2 (2,1) - blocks to ZERO. */
|
|
|
|
a[*j1 + 1 + *j1 * a_dim1] = 0.;
|
|
b[*j1 + 1 + *j1 * b_dim1] = 0.;
|
|
|
|
/* Accumulate transformations into Q and Z if requested. */
|
|
|
|
if (*wantz) {
|
|
drot_(n, &z__[*j1 * z_dim1 + 1], &c__1, &z__[(*j1 + 1) * z_dim1 +
|
|
1], &c__1, ir, &ir[1]);
|
|
}
|
|
if (*wantq) {
|
|
drot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[(*j1 + 1) * q_dim1 + 1],
|
|
&c__1, li, &li[1]);
|
|
}
|
|
|
|
/* Exit with INFO = 0 if swap was successfully performed. */
|
|
|
|
return;
|
|
|
|
} else {
|
|
|
|
/* CASE 2: Swap 1-by-1 and 2-by-2 blocks, or 2-by-2 */
|
|
/* and 2-by-2 blocks. */
|
|
|
|
/* Solve the generalized Sylvester equation */
|
|
/* S11 * R - L * S22 = SCALE * S12 */
|
|
/* T11 * R - L * T22 = SCALE * T12 */
|
|
/* for R and L. Solutions in LI and IR. */
|
|
|
|
dlacpy_("Full", n1, n2, &t[(*n1 + 1 << 2) - 4], &c__4, li, &c__4);
|
|
dlacpy_("Full", n1, n2, &s[(*n1 + 1 << 2) - 4], &c__4, &ir[*n2 + 1 + (
|
|
*n1 + 1 << 2) - 5], &c__4);
|
|
dtgsy2_("N", &c__0, n1, n2, s, &c__4, &s[*n1 + 1 + (*n1 + 1 << 2) - 5]
|
|
, &c__4, &ir[*n2 + 1 + (*n1 + 1 << 2) - 5], &c__4, t, &c__4, &
|
|
t[*n1 + 1 + (*n1 + 1 << 2) - 5], &c__4, li, &c__4, &scale, &
|
|
dsum, &dscale, iwork, &idum, &linfo);
|
|
|
|
/* Compute orthogonal matrix QL: */
|
|
|
|
/* QL**T * LI = [ TL ] */
|
|
/* [ 0 ] */
|
|
/* where */
|
|
/* LI = [ -L ] */
|
|
/* [ SCALE * identity(N2) ] */
|
|
|
|
i__1 = *n2;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
dscal_(n1, &c_b48, &li[(i__ << 2) - 4], &c__1);
|
|
li[*n1 + i__ + (i__ << 2) - 5] = scale;
|
|
/* L10: */
|
|
}
|
|
dgeqr2_(&m, n2, li, &c__4, taul, &work[1], &linfo);
|
|
if (linfo != 0) {
|
|
goto L70;
|
|
}
|
|
dorg2r_(&m, &m, n2, li, &c__4, taul, &work[1], &linfo);
|
|
if (linfo != 0) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Compute orthogonal matrix RQ: */
|
|
|
|
/* IR * RQ**T = [ 0 TR], */
|
|
|
|
/* where IR = [ SCALE * identity(N1), R ] */
|
|
|
|
i__1 = *n1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
ir[*n2 + i__ + (i__ << 2) - 5] = scale;
|
|
/* L20: */
|
|
}
|
|
dgerq2_(n1, &m, &ir[*n2], &c__4, taur, &work[1], &linfo);
|
|
if (linfo != 0) {
|
|
goto L70;
|
|
}
|
|
dorgr2_(&m, &m, n1, ir, &c__4, taur, &work[1], &linfo);
|
|
if (linfo != 0) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Perform the swapping tentatively: */
|
|
|
|
dgemm_("T", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, &
|
|
work[1], &m);
|
|
dgemm_("N", "T", &m, &m, &m, &c_b42, &work[1], &m, ir, &c__4, &c_b5,
|
|
s, &c__4);
|
|
dgemm_("T", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, &
|
|
work[1], &m);
|
|
dgemm_("N", "T", &m, &m, &m, &c_b42, &work[1], &m, ir, &c__4, &c_b5,
|
|
t, &c__4);
|
|
dlacpy_("F", &m, &m, s, &c__4, scpy, &c__4);
|
|
dlacpy_("F", &m, &m, t, &c__4, tcpy, &c__4);
|
|
dlacpy_("F", &m, &m, ir, &c__4, ircop, &c__4);
|
|
dlacpy_("F", &m, &m, li, &c__4, licop, &c__4);
|
|
|
|
/* Triangularize the B-part by an RQ factorization. */
|
|
/* Apply transformation (from left) to A-part, giving S. */
|
|
|
|
dgerq2_(&m, &m, t, &c__4, taur, &work[1], &linfo);
|
|
if (linfo != 0) {
|
|
goto L70;
|
|
}
|
|
dormr2_("R", "T", &m, &m, &m, t, &c__4, taur, s, &c__4, &work[1], &
|
|
linfo);
|
|
if (linfo != 0) {
|
|
goto L70;
|
|
}
|
|
dormr2_("L", "N", &m, &m, &m, t, &c__4, taur, ir, &c__4, &work[1], &
|
|
linfo);
|
|
if (linfo != 0) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Compute F-norm(S21) in BRQA21. (T21 is 0.) */
|
|
|
|
dscale = 0.;
|
|
dsum = 1.;
|
|
i__1 = *n2;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
dlassq_(n1, &s[*n2 + 1 + (i__ << 2) - 5], &c__1, &dscale, &dsum);
|
|
/* L30: */
|
|
}
|
|
brqa21 = dscale * sqrt(dsum);
|
|
|
|
/* Triangularize the B-part by a QR factorization. */
|
|
/* Apply transformation (from right) to A-part, giving S. */
|
|
|
|
dgeqr2_(&m, &m, tcpy, &c__4, taul, &work[1], &linfo);
|
|
if (linfo != 0) {
|
|
goto L70;
|
|
}
|
|
dorm2r_("L", "T", &m, &m, &m, tcpy, &c__4, taul, scpy, &c__4, &work[1]
|
|
, info);
|
|
dorm2r_("R", "N", &m, &m, &m, tcpy, &c__4, taul, licop, &c__4, &work[
|
|
1], info);
|
|
if (linfo != 0) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Compute F-norm(S21) in BQRA21. (T21 is 0.) */
|
|
|
|
dscale = 0.;
|
|
dsum = 1.;
|
|
i__1 = *n2;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
dlassq_(n1, &scpy[*n2 + 1 + (i__ << 2) - 5], &c__1, &dscale, &
|
|
dsum);
|
|
/* L40: */
|
|
}
|
|
bqra21 = dscale * sqrt(dsum);
|
|
|
|
/* Decide which method to use. */
|
|
/* Weak stability test: */
|
|
/* F-norm(S21) <= O(EPS * F-norm((S, T))) */
|
|
|
|
if (bqra21 <= brqa21 && bqra21 <= thresh) {
|
|
dlacpy_("F", &m, &m, scpy, &c__4, s, &c__4);
|
|
dlacpy_("F", &m, &m, tcpy, &c__4, t, &c__4);
|
|
dlacpy_("F", &m, &m, ircop, &c__4, ir, &c__4);
|
|
dlacpy_("F", &m, &m, licop, &c__4, li, &c__4);
|
|
} else if (brqa21 >= thresh) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Set lower triangle of B-part to zero */
|
|
|
|
i__1 = m - 1;
|
|
i__2 = m - 1;
|
|
dlaset_("Lower", &i__1, &i__2, &c_b5, &c_b5, &t[1], &c__4);
|
|
|
|
if (TRUE_) {
|
|
|
|
/* Strong stability test: */
|
|
/* F-norm((A-QL*S*QR**T, B-QL*T*QR**T)) <= O(EPS*F-norm((A,B))) */
|
|
|
|
dlacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, &work[m * m
|
|
+ 1], &m);
|
|
dgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, s, &c__4, &c_b5, &
|
|
work[1], &m);
|
|
dgemm_("N", "N", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
|
|
c_b42, &work[m * m + 1], &m);
|
|
dscale = 0.;
|
|
dsum = 1.;
|
|
i__1 = m * m;
|
|
dlassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
|
|
|
|
dlacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, &work[m * m
|
|
+ 1], &m);
|
|
dgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, t, &c__4, &c_b5, &
|
|
work[1], &m);
|
|
dgemm_("N", "N", &m, &m, &m, &c_b48, &work[1], &m, ir, &c__4, &
|
|
c_b42, &work[m * m + 1], &m);
|
|
i__1 = m * m;
|
|
dlassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
|
|
ss = dscale * sqrt(dsum);
|
|
dtrong = ss <= thresh;
|
|
if (! dtrong) {
|
|
goto L70;
|
|
}
|
|
|
|
}
|
|
|
|
/* If the swap is accepted ("weakly" and "strongly"), apply the */
|
|
/* transformations and set N1-by-N2 (2,1)-block to zero. */
|
|
|
|
dlaset_("Full", n1, n2, &c_b5, &c_b5, &s[*n2], &c__4);
|
|
|
|
/* copy back M-by-M diagonal block starting at index J1 of (A, B) */
|
|
|
|
dlacpy_("F", &m, &m, s, &c__4, &a[*j1 + *j1 * a_dim1], lda)
|
|
;
|
|
dlacpy_("F", &m, &m, t, &c__4, &b[*j1 + *j1 * b_dim1], ldb)
|
|
;
|
|
dlaset_("Full", &c__4, &c__4, &c_b5, &c_b5, t, &c__4);
|
|
|
|
/* Standardize existing 2-by-2 blocks. */
|
|
|
|
dlaset_("Full", &m, &m, &c_b5, &c_b5, &work[1], &m);
|
|
work[1] = 1.;
|
|
t[0] = 1.;
|
|
idum = *lwork - m * m - 2;
|
|
if (*n2 > 1) {
|
|
dlagv2_(&a[*j1 + *j1 * a_dim1], lda, &b[*j1 + *j1 * b_dim1], ldb,
|
|
ar, ai, be, &work[1], &work[2], t, &t[1]);
|
|
work[m + 1] = -work[2];
|
|
work[m + 2] = work[1];
|
|
t[*n2 + (*n2 << 2) - 5] = t[0];
|
|
t[4] = -t[1];
|
|
}
|
|
work[m * m] = 1.;
|
|
t[m + (m << 2) - 5] = 1.;
|
|
|
|
if (*n1 > 1) {
|
|
dlagv2_(&a[*j1 + *n2 + (*j1 + *n2) * a_dim1], lda, &b[*j1 + *n2 +
|
|
(*j1 + *n2) * b_dim1], ldb, taur, taul, &work[m * m + 1],
|
|
&work[*n2 * m + *n2 + 1], &work[*n2 * m + *n2 + 2], &t[*
|
|
n2 + 1 + (*n2 + 1 << 2) - 5], &t[m + (m - 1 << 2) - 5]);
|
|
work[m * m] = work[*n2 * m + *n2 + 1];
|
|
work[m * m - 1] = -work[*n2 * m + *n2 + 2];
|
|
t[m + (m << 2) - 5] = t[*n2 + 1 + (*n2 + 1 << 2) - 5];
|
|
t[m - 1 + (m << 2) - 5] = -t[m + (m - 1 << 2) - 5];
|
|
}
|
|
dgemm_("T", "N", n2, n1, n2, &c_b42, &work[1], &m, &a[*j1 + (*j1 + *
|
|
n2) * a_dim1], lda, &c_b5, &work[m * m + 1], n2);
|
|
dlacpy_("Full", n2, n1, &work[m * m + 1], n2, &a[*j1 + (*j1 + *n2) *
|
|
a_dim1], lda);
|
|
dgemm_("T", "N", n2, n1, n2, &c_b42, &work[1], &m, &b[*j1 + (*j1 + *
|
|
n2) * b_dim1], ldb, &c_b5, &work[m * m + 1], n2);
|
|
dlacpy_("Full", n2, n1, &work[m * m + 1], n2, &b[*j1 + (*j1 + *n2) *
|
|
b_dim1], ldb);
|
|
dgemm_("N", "N", &m, &m, &m, &c_b42, li, &c__4, &work[1], &m, &c_b5, &
|
|
work[m * m + 1], &m);
|
|
dlacpy_("Full", &m, &m, &work[m * m + 1], &m, li, &c__4);
|
|
dgemm_("N", "N", n2, n1, n1, &c_b42, &a[*j1 + (*j1 + *n2) * a_dim1],
|
|
lda, &t[*n2 + 1 + (*n2 + 1 << 2) - 5], &c__4, &c_b5, &work[1],
|
|
n2);
|
|
dlacpy_("Full", n2, n1, &work[1], n2, &a[*j1 + (*j1 + *n2) * a_dim1],
|
|
lda);
|
|
dgemm_("N", "N", n2, n1, n1, &c_b42, &b[*j1 + (*j1 + *n2) * b_dim1],
|
|
ldb, &t[*n2 + 1 + (*n2 + 1 << 2) - 5], &c__4, &c_b5, &work[1],
|
|
n2);
|
|
dlacpy_("Full", n2, n1, &work[1], n2, &b[*j1 + (*j1 + *n2) * b_dim1],
|
|
ldb);
|
|
dgemm_("T", "N", &m, &m, &m, &c_b42, ir, &c__4, t, &c__4, &c_b5, &
|
|
work[1], &m);
|
|
dlacpy_("Full", &m, &m, &work[1], &m, ir, &c__4);
|
|
|
|
/* Accumulate transformations into Q and Z if requested. */
|
|
|
|
if (*wantq) {
|
|
dgemm_("N", "N", n, &m, &m, &c_b42, &q[*j1 * q_dim1 + 1], ldq, li,
|
|
&c__4, &c_b5, &work[1], n);
|
|
dlacpy_("Full", n, &m, &work[1], n, &q[*j1 * q_dim1 + 1], ldq);
|
|
|
|
}
|
|
|
|
if (*wantz) {
|
|
dgemm_("N", "N", n, &m, &m, &c_b42, &z__[*j1 * z_dim1 + 1], ldz,
|
|
ir, &c__4, &c_b5, &work[1], n);
|
|
dlacpy_("Full", n, &m, &work[1], n, &z__[*j1 * z_dim1 + 1], ldz);
|
|
|
|
}
|
|
|
|
/* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and */
|
|
/* (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */
|
|
|
|
i__ = *j1 + m;
|
|
if (i__ <= *n) {
|
|
i__1 = *n - i__ + 1;
|
|
dgemm_("T", "N", &m, &i__1, &m, &c_b42, li, &c__4, &a[*j1 + i__ *
|
|
a_dim1], lda, &c_b5, &work[1], &m);
|
|
i__1 = *n - i__ + 1;
|
|
dlacpy_("Full", &m, &i__1, &work[1], &m, &a[*j1 + i__ * a_dim1],
|
|
lda);
|
|
i__1 = *n - i__ + 1;
|
|
dgemm_("T", "N", &m, &i__1, &m, &c_b42, li, &c__4, &b[*j1 + i__ *
|
|
b_dim1], ldb, &c_b5, &work[1], &m);
|
|
i__1 = *n - i__ + 1;
|
|
dlacpy_("Full", &m, &i__1, &work[1], &m, &b[*j1 + i__ * b_dim1],
|
|
ldb);
|
|
}
|
|
i__ = *j1 - 1;
|
|
if (i__ > 0) {
|
|
dgemm_("N", "N", &i__, &m, &m, &c_b42, &a[*j1 * a_dim1 + 1], lda,
|
|
ir, &c__4, &c_b5, &work[1], &i__);
|
|
dlacpy_("Full", &i__, &m, &work[1], &i__, &a[*j1 * a_dim1 + 1],
|
|
lda);
|
|
dgemm_("N", "N", &i__, &m, &m, &c_b42, &b[*j1 * b_dim1 + 1], ldb,
|
|
ir, &c__4, &c_b5, &work[1], &i__);
|
|
dlacpy_("Full", &i__, &m, &work[1], &i__, &b[*j1 * b_dim1 + 1],
|
|
ldb);
|
|
}
|
|
|
|
/* Exit with INFO = 0 if swap was successfully performed. */
|
|
|
|
return;
|
|
|
|
}
|
|
|
|
/* Exit with INFO = 1 if swap was rejected. */
|
|
|
|
L70:
|
|
|
|
*info = 1;
|
|
return;
|
|
|
|
/* End of DTGEX2 */
|
|
|
|
} /* dtgex2_ */
|
|
|