1066 lines
31 KiB
C
1066 lines
31 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef 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__2 = 2;
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b CTGSY2 solves the generalized Sylvester equation (unblocked algorithm). */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CTGSY2 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctgsy2.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctgsy2.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctgsy2.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CTGSY2( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, */
|
|
/* LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL, */
|
|
/* INFO ) */
|
|
|
|
/* CHARACTER TRANS */
|
|
/* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, M, N */
|
|
/* REAL RDSCAL, RDSUM, SCALE */
|
|
/* COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * ), */
|
|
/* $ D( LDD, * ), E( LDE, * ), F( LDF, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CTGSY2 solves the generalized Sylvester equation */
|
|
/* > */
|
|
/* > A * R - L * B = scale * C (1) */
|
|
/* > D * R - L * E = scale * F */
|
|
/* > */
|
|
/* > using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices, */
|
|
/* > (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M, */
|
|
/* > N-by-N and M-by-N, respectively. A, B, D and E are upper triangular */
|
|
/* > (i.e., (A,D) and (B,E) in generalized Schur form). */
|
|
/* > */
|
|
/* > The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output */
|
|
/* > scaling factor chosen to avoid overflow. */
|
|
/* > */
|
|
/* > In matrix notation solving equation (1) corresponds to solve */
|
|
/* > Zx = scale * b, where Z is defined as */
|
|
/* > */
|
|
/* > Z = [ kron(In, A) -kron(B**H, Im) ] (2) */
|
|
/* > [ kron(In, D) -kron(E**H, Im) ], */
|
|
/* > */
|
|
/* > Ik is the identity matrix of size k and X**H is the transpose of X. */
|
|
/* > kron(X, Y) is the Kronecker product between the matrices X and Y. */
|
|
/* > */
|
|
/* > If TRANS = 'C', y in the conjugate transposed system Z**H*y = scale*b */
|
|
/* > is solved for, which is equivalent to solve for R and L in */
|
|
/* > */
|
|
/* > A**H * R + D**H * L = scale * C (3) */
|
|
/* > R * B**H + L * E**H = scale * -F */
|
|
/* > */
|
|
/* > This case is used to compute an estimate of Dif[(A, D), (B, E)] = */
|
|
/* > = sigma_min(Z) using reverse communication with CLACON. */
|
|
/* > */
|
|
/* > CTGSY2 also (IJOB >= 1) contributes to the computation in CTGSYL */
|
|
/* > of an upper bound on the separation between to matrix pairs. Then */
|
|
/* > the input (A, D), (B, E) are sub-pencils of two matrix pairs in */
|
|
/* > CTGSYL. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] TRANS */
|
|
/* > \verbatim */
|
|
/* > TRANS is CHARACTER*1 */
|
|
/* > = 'N': solve the generalized Sylvester equation (1). */
|
|
/* > = 'T': solve the 'transposed' system (3). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IJOB */
|
|
/* > \verbatim */
|
|
/* > IJOB is INTEGER */
|
|
/* > Specifies what kind of functionality to be performed. */
|
|
/* > = 0: solve (1) only. */
|
|
/* > = 1: A contribution from this subsystem to a Frobenius */
|
|
/* > norm-based estimate of the separation between two matrix */
|
|
/* > pairs is computed. (look ahead strategy is used). */
|
|
/* > = 2: A contribution from this subsystem to a Frobenius */
|
|
/* > norm-based estimate of the separation between two matrix */
|
|
/* > pairs is computed. (SGECON on sub-systems is used.) */
|
|
/* > Not referenced if TRANS = 'T'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > On entry, M specifies the order of A and D, and the row */
|
|
/* > dimension of C, F, R and L. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > On entry, N specifies the order of B and E, and the column */
|
|
/* > dimension of C, F, R and L. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX array, dimension (LDA, M) */
|
|
/* > On entry, A contains an upper triangular matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the matrix A. LDA >= f2cmax(1, M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX array, dimension (LDB, N) */
|
|
/* > On entry, B contains an upper triangular matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the matrix B. LDB >= f2cmax(1, N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] C */
|
|
/* > \verbatim */
|
|
/* > C is COMPLEX array, dimension (LDC, N) */
|
|
/* > On entry, C contains the right-hand-side of the first matrix */
|
|
/* > equation in (1). */
|
|
/* > On exit, if IJOB = 0, C has been overwritten by the solution */
|
|
/* > R. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDC */
|
|
/* > \verbatim */
|
|
/* > LDC is INTEGER */
|
|
/* > The leading dimension of the matrix C. LDC >= f2cmax(1, M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D */
|
|
/* > \verbatim */
|
|
/* > D is COMPLEX array, dimension (LDD, M) */
|
|
/* > On entry, D contains an upper triangular matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDD */
|
|
/* > \verbatim */
|
|
/* > LDD is INTEGER */
|
|
/* > The leading dimension of the matrix D. LDD >= f2cmax(1, M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] E */
|
|
/* > \verbatim */
|
|
/* > E is COMPLEX array, dimension (LDE, N) */
|
|
/* > On entry, E contains an upper triangular matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDE */
|
|
/* > \verbatim */
|
|
/* > LDE is INTEGER */
|
|
/* > The leading dimension of the matrix E. LDE >= f2cmax(1, N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] F */
|
|
/* > \verbatim */
|
|
/* > F is COMPLEX array, dimension (LDF, N) */
|
|
/* > On entry, F contains the right-hand-side of the second matrix */
|
|
/* > equation in (1). */
|
|
/* > On exit, if IJOB = 0, F has been overwritten by the solution */
|
|
/* > L. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDF */
|
|
/* > \verbatim */
|
|
/* > LDF is INTEGER */
|
|
/* > The leading dimension of the matrix F. LDF >= f2cmax(1, M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SCALE */
|
|
/* > \verbatim */
|
|
/* > SCALE is REAL */
|
|
/* > On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions */
|
|
/* > R and L (C and F on entry) will hold the solutions to a */
|
|
/* > slightly perturbed system but the input matrices A, B, D and */
|
|
/* > E have not been changed. If SCALE = 0, R and L will hold the */
|
|
/* > solutions to the homogeneous system with C = F = 0. */
|
|
/* > Normally, SCALE = 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] RDSUM */
|
|
/* > \verbatim */
|
|
/* > RDSUM is REAL */
|
|
/* > On entry, the sum of squares of computed contributions to */
|
|
/* > the Dif-estimate under computation by CTGSYL, where the */
|
|
/* > scaling factor RDSCAL (see below) has been factored out. */
|
|
/* > On exit, the corresponding sum of squares updated with the */
|
|
/* > contributions from the current sub-system. */
|
|
/* > If TRANS = 'T' RDSUM is not touched. */
|
|
/* > NOTE: RDSUM only makes sense when CTGSY2 is called by */
|
|
/* > CTGSYL. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] RDSCAL */
|
|
/* > \verbatim */
|
|
/* > RDSCAL is REAL */
|
|
/* > On entry, scaling factor used to prevent overflow in RDSUM. */
|
|
/* > On exit, RDSCAL is updated w.r.t. the current contributions */
|
|
/* > in RDSUM. */
|
|
/* > If TRANS = 'T', RDSCAL is not touched. */
|
|
/* > NOTE: RDSCAL only makes sense when CTGSY2 is called by */
|
|
/* > CTGSYL. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > On exit, if INFO is set to */
|
|
/* > =0: Successful exit */
|
|
/* > <0: If INFO = -i, input argument number i is illegal. */
|
|
/* > >0: The matrix pairs (A, D) and (B, E) have common or very */
|
|
/* > close eigenvalues. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complexSYauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
|
|
/* > Umea University, S-901 87 Umea, Sweden. */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void ctgsy2_(char *trans, integer *ijob, integer *m, integer *
|
|
n, complex *a, integer *lda, complex *b, integer *ldb, complex *c__,
|
|
integer *ldc, complex *d__, integer *ldd, complex *e, integer *lde,
|
|
complex *f, integer *ldf, real *scale, real *rdsum, real *rdscal,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1,
|
|
d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3,
|
|
i__4;
|
|
complex q__1, q__2, q__3, q__4, q__5, q__6;
|
|
|
|
/* Local variables */
|
|
integer ierr, ipiv[2], jpiv[2], i__, j, k;
|
|
complex alpha;
|
|
extern /* Subroutine */ void cscal_(integer *, complex *, complex *,
|
|
integer *);
|
|
complex z__[4] /* was [2][2] */;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void caxpy_(integer *, complex *, complex *,
|
|
integer *, complex *, integer *), cgesc2_(integer *, complex *,
|
|
integer *, complex *, integer *, integer *, real *), cgetc2_(
|
|
integer *, complex *, integer *, integer *, integer *, integer *),
|
|
clatdf_(integer *, integer *, complex *, integer *, complex *,
|
|
real *, real *, integer *, integer *);
|
|
real scaloc;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
logical notran;
|
|
complex rhs[2];
|
|
|
|
|
|
/* -- 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Decode and test input parameters */
|
|
|
|
/* 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;
|
|
c_dim1 = *ldc;
|
|
c_offset = 1 + c_dim1 * 1;
|
|
c__ -= c_offset;
|
|
d_dim1 = *ldd;
|
|
d_offset = 1 + d_dim1 * 1;
|
|
d__ -= d_offset;
|
|
e_dim1 = *lde;
|
|
e_offset = 1 + e_dim1 * 1;
|
|
e -= e_offset;
|
|
f_dim1 = *ldf;
|
|
f_offset = 1 + f_dim1 * 1;
|
|
f -= f_offset;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
ierr = 0;
|
|
notran = lsame_(trans, "N");
|
|
if (! notran && ! lsame_(trans, "C")) {
|
|
*info = -1;
|
|
} else if (notran) {
|
|
if (*ijob < 0 || *ijob > 2) {
|
|
*info = -2;
|
|
}
|
|
}
|
|
if (*info == 0) {
|
|
if (*m <= 0) {
|
|
*info = -3;
|
|
} else if (*n <= 0) {
|
|
*info = -4;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -6;
|
|
} else if (*ldb < f2cmax(1,*n)) {
|
|
*info = -8;
|
|
} else if (*ldc < f2cmax(1,*m)) {
|
|
*info = -10;
|
|
} else if (*ldd < f2cmax(1,*m)) {
|
|
*info = -12;
|
|
} else if (*lde < f2cmax(1,*n)) {
|
|
*info = -14;
|
|
} else if (*ldf < f2cmax(1,*m)) {
|
|
*info = -16;
|
|
}
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CTGSY2", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
if (notran) {
|
|
|
|
/* Solve (I, J) - system */
|
|
/* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */
|
|
/* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */
|
|
/* for I = M, M - 1, ..., 1; J = 1, 2, ..., N */
|
|
|
|
*scale = 1.f;
|
|
scaloc = 1.f;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
for (i__ = *m; i__ >= 1; --i__) {
|
|
|
|
/* Build 2 by 2 system */
|
|
|
|
i__2 = i__ + i__ * a_dim1;
|
|
z__[0].r = a[i__2].r, z__[0].i = a[i__2].i;
|
|
i__2 = i__ + i__ * d_dim1;
|
|
z__[1].r = d__[i__2].r, z__[1].i = d__[i__2].i;
|
|
i__2 = j + j * b_dim1;
|
|
q__1.r = -b[i__2].r, q__1.i = -b[i__2].i;
|
|
z__[2].r = q__1.r, z__[2].i = q__1.i;
|
|
i__2 = j + j * e_dim1;
|
|
q__1.r = -e[i__2].r, q__1.i = -e[i__2].i;
|
|
z__[3].r = q__1.r, z__[3].i = q__1.i;
|
|
|
|
/* Set up right hand side(s) */
|
|
|
|
i__2 = i__ + j * c_dim1;
|
|
rhs[0].r = c__[i__2].r, rhs[0].i = c__[i__2].i;
|
|
i__2 = i__ + j * f_dim1;
|
|
rhs[1].r = f[i__2].r, rhs[1].i = f[i__2].i;
|
|
|
|
/* Solve Z * x = RHS */
|
|
|
|
cgetc2_(&c__2, z__, &c__2, ipiv, jpiv, &ierr);
|
|
if (ierr > 0) {
|
|
*info = ierr;
|
|
}
|
|
if (*ijob == 0) {
|
|
cgesc2_(&c__2, z__, &c__2, rhs, ipiv, jpiv, &scaloc);
|
|
if (scaloc != 1.f) {
|
|
i__2 = *n;
|
|
for (k = 1; k <= i__2; ++k) {
|
|
q__1.r = scaloc, q__1.i = 0.f;
|
|
cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1);
|
|
q__1.r = scaloc, q__1.i = 0.f;
|
|
cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1);
|
|
/* L10: */
|
|
}
|
|
*scale *= scaloc;
|
|
}
|
|
} else {
|
|
clatdf_(ijob, &c__2, z__, &c__2, rhs, rdsum, rdscal, ipiv,
|
|
jpiv);
|
|
}
|
|
|
|
/* Unpack solution vector(s) */
|
|
|
|
i__2 = i__ + j * c_dim1;
|
|
c__[i__2].r = rhs[0].r, c__[i__2].i = rhs[0].i;
|
|
i__2 = i__ + j * f_dim1;
|
|
f[i__2].r = rhs[1].r, f[i__2].i = rhs[1].i;
|
|
|
|
/* Substitute R(I, J) and L(I, J) into remaining equation. */
|
|
|
|
if (i__ > 1) {
|
|
q__1.r = -rhs[0].r, q__1.i = -rhs[0].i;
|
|
alpha.r = q__1.r, alpha.i = q__1.i;
|
|
i__2 = i__ - 1;
|
|
caxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &c__[j
|
|
* c_dim1 + 1], &c__1);
|
|
i__2 = i__ - 1;
|
|
caxpy_(&i__2, &alpha, &d__[i__ * d_dim1 + 1], &c__1, &f[j
|
|
* f_dim1 + 1], &c__1);
|
|
}
|
|
if (j < *n) {
|
|
i__2 = *n - j;
|
|
caxpy_(&i__2, &rhs[1], &b[j + (j + 1) * b_dim1], ldb, &
|
|
c__[i__ + (j + 1) * c_dim1], ldc);
|
|
i__2 = *n - j;
|
|
caxpy_(&i__2, &rhs[1], &e[j + (j + 1) * e_dim1], lde, &f[
|
|
i__ + (j + 1) * f_dim1], ldf);
|
|
}
|
|
|
|
/* L20: */
|
|
}
|
|
/* L30: */
|
|
}
|
|
} else {
|
|
|
|
/* Solve transposed (I, J) - system: */
|
|
/* A(I, I)**H * R(I, J) + D(I, I)**H * L(J, J) = C(I, J) */
|
|
/* R(I, I) * B(J, J) + L(I, J) * E(J, J) = -F(I, J) */
|
|
/* for I = 1, 2, ..., M, J = N, N - 1, ..., 1 */
|
|
|
|
*scale = 1.f;
|
|
scaloc = 1.f;
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
for (j = *n; j >= 1; --j) {
|
|
|
|
/* Build 2 by 2 system Z**H */
|
|
|
|
r_cnjg(&q__1, &a[i__ + i__ * a_dim1]);
|
|
z__[0].r = q__1.r, z__[0].i = q__1.i;
|
|
r_cnjg(&q__2, &b[j + j * b_dim1]);
|
|
q__1.r = -q__2.r, q__1.i = -q__2.i;
|
|
z__[1].r = q__1.r, z__[1].i = q__1.i;
|
|
r_cnjg(&q__1, &d__[i__ + i__ * d_dim1]);
|
|
z__[2].r = q__1.r, z__[2].i = q__1.i;
|
|
r_cnjg(&q__2, &e[j + j * e_dim1]);
|
|
q__1.r = -q__2.r, q__1.i = -q__2.i;
|
|
z__[3].r = q__1.r, z__[3].i = q__1.i;
|
|
|
|
|
|
/* Set up right hand side(s) */
|
|
|
|
i__2 = i__ + j * c_dim1;
|
|
rhs[0].r = c__[i__2].r, rhs[0].i = c__[i__2].i;
|
|
i__2 = i__ + j * f_dim1;
|
|
rhs[1].r = f[i__2].r, rhs[1].i = f[i__2].i;
|
|
|
|
/* Solve Z**H * x = RHS */
|
|
|
|
cgetc2_(&c__2, z__, &c__2, ipiv, jpiv, &ierr);
|
|
if (ierr > 0) {
|
|
*info = ierr;
|
|
}
|
|
cgesc2_(&c__2, z__, &c__2, rhs, ipiv, jpiv, &scaloc);
|
|
if (scaloc != 1.f) {
|
|
i__2 = *n;
|
|
for (k = 1; k <= i__2; ++k) {
|
|
q__1.r = scaloc, q__1.i = 0.f;
|
|
cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1);
|
|
q__1.r = scaloc, q__1.i = 0.f;
|
|
cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1);
|
|
/* L40: */
|
|
}
|
|
*scale *= scaloc;
|
|
}
|
|
|
|
/* Unpack solution vector(s) */
|
|
|
|
i__2 = i__ + j * c_dim1;
|
|
c__[i__2].r = rhs[0].r, c__[i__2].i = rhs[0].i;
|
|
i__2 = i__ + j * f_dim1;
|
|
f[i__2].r = rhs[1].r, f[i__2].i = rhs[1].i;
|
|
|
|
/* Substitute R(I, J) and L(I, J) into remaining equation. */
|
|
|
|
i__2 = j - 1;
|
|
for (k = 1; k <= i__2; ++k) {
|
|
i__3 = i__ + k * f_dim1;
|
|
i__4 = i__ + k * f_dim1;
|
|
r_cnjg(&q__4, &b[k + j * b_dim1]);
|
|
q__3.r = rhs[0].r * q__4.r - rhs[0].i * q__4.i, q__3.i =
|
|
rhs[0].r * q__4.i + rhs[0].i * q__4.r;
|
|
q__2.r = f[i__4].r + q__3.r, q__2.i = f[i__4].i + q__3.i;
|
|
r_cnjg(&q__6, &e[k + j * e_dim1]);
|
|
q__5.r = rhs[1].r * q__6.r - rhs[1].i * q__6.i, q__5.i =
|
|
rhs[1].r * q__6.i + rhs[1].i * q__6.r;
|
|
q__1.r = q__2.r + q__5.r, q__1.i = q__2.i + q__5.i;
|
|
f[i__3].r = q__1.r, f[i__3].i = q__1.i;
|
|
/* L50: */
|
|
}
|
|
i__2 = *m;
|
|
for (k = i__ + 1; k <= i__2; ++k) {
|
|
i__3 = k + j * c_dim1;
|
|
i__4 = k + j * c_dim1;
|
|
r_cnjg(&q__4, &a[i__ + k * a_dim1]);
|
|
q__3.r = q__4.r * rhs[0].r - q__4.i * rhs[0].i, q__3.i =
|
|
q__4.r * rhs[0].i + q__4.i * rhs[0].r;
|
|
q__2.r = c__[i__4].r - q__3.r, q__2.i = c__[i__4].i -
|
|
q__3.i;
|
|
r_cnjg(&q__6, &d__[i__ + k * d_dim1]);
|
|
q__5.r = q__6.r * rhs[1].r - q__6.i * rhs[1].i, q__5.i =
|
|
q__6.r * rhs[1].i + q__6.i * rhs[1].r;
|
|
q__1.r = q__2.r - q__5.r, q__1.i = q__2.i - q__5.i;
|
|
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
|
|
/* L60: */
|
|
}
|
|
|
|
/* L70: */
|
|
}
|
|
/* L80: */
|
|
}
|
|
}
|
|
return;
|
|
|
|
/* End of CTGSY2 */
|
|
|
|
} /* ctgsy2_ */
|
|
|