1302 lines
37 KiB
C
1302 lines
37 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/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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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__2 = 2;
|
|
static integer c_n1 = -1;
|
|
static integer c__5 = 5;
|
|
static real c_b14 = 0.f;
|
|
static integer c__1 = 1;
|
|
static real c_b51 = -1.f;
|
|
static real c_b52 = 1.f;
|
|
|
|
/* > \brief \b STGSYL */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download STGSYL + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stgsyl.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stgsyl.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stgsyl.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE STGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, */
|
|
/* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK, */
|
|
/* IWORK, INFO ) */
|
|
|
|
/* CHARACTER TRANS */
|
|
/* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, */
|
|
/* $ LWORK, M, N */
|
|
/* REAL DIF, SCALE */
|
|
/* INTEGER IWORK( * ) */
|
|
/* REAL A( LDA, * ), B( LDB, * ), C( LDC, * ), */
|
|
/* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), */
|
|
/* $ WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > STGSYL solves the generalized Sylvester equation: */
|
|
/* > */
|
|
/* > A * R - L * B = scale * C (1) */
|
|
/* > D * R - L * E = scale * F */
|
|
/* > */
|
|
/* > 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, with real entries. (A, D) and (B, E) must be in */
|
|
/* > generalized (real) Schur canonical form, i.e. A, B are upper quasi */
|
|
/* > triangular and D, E are upper triangular. */
|
|
/* > */
|
|
/* > The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output */
|
|
/* > scaling factor chosen to avoid overflow. */
|
|
/* > */
|
|
/* > In matrix notation (1) is equivalent to solve Zx = scale b, where */
|
|
/* > Z is defined as */
|
|
/* > */
|
|
/* > Z = [ kron(In, A) -kron(B**T, Im) ] (2) */
|
|
/* > [ kron(In, D) -kron(E**T, Im) ]. */
|
|
/* > */
|
|
/* > Here Ik is the identity matrix of size k and X**T is the transpose of */
|
|
/* > X. kron(X, Y) is the Kronecker product between the matrices X and Y. */
|
|
/* > */
|
|
/* > If TRANS = 'T', STGSYL solves the transposed system Z**T*y = scale*b, */
|
|
/* > which is equivalent to solve for R and L in */
|
|
/* > */
|
|
/* > A**T * R + D**T * L = scale * C (3) */
|
|
/* > R * B**T + L * E**T = scale * -F */
|
|
/* > */
|
|
/* > This case (TRANS = 'T') is used to compute an one-norm-based estimate */
|
|
/* > of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) */
|
|
/* > and (B,E), using SLACON. */
|
|
/* > */
|
|
/* > If IJOB >= 1, STGSYL computes a Frobenius norm-based estimate */
|
|
/* > of Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the */
|
|
/* > reciprocal of the smallest singular value of Z. See [1-2] for more */
|
|
/* > information. */
|
|
/* > */
|
|
/* > This is a level 3 BLAS algorithm. */
|
|
/* > \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: The functionality of 0 and 3. */
|
|
/* > = 2: The functionality of 0 and 4. */
|
|
/* > = 3: Only an estimate of Dif[(A,D), (B,E)] is computed. */
|
|
/* > (look ahead strategy IJOB = 1 is used). */
|
|
/* > = 4: Only an estimate of Dif[(A,D), (B,E)] is computed. */
|
|
/* > ( SGECON on sub-systems is used ). */
|
|
/* > Not referenced if TRANS = 'T'. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The order of the matrices A and D, and the row dimension of */
|
|
/* > the matrices C, F, R and L. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrices B and E, and the column dimension */
|
|
/* > of the matrices C, F, R and L. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A */
|
|
/* > \verbatim */
|
|
/* > A is REAL array, dimension (LDA, M) */
|
|
/* > The upper quasi triangular matrix A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1, M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B */
|
|
/* > \verbatim */
|
|
/* > B is REAL array, dimension (LDB, N) */
|
|
/* > The upper quasi triangular 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] C */
|
|
/* > \verbatim */
|
|
/* > C is REAL array, dimension (LDC, N) */
|
|
/* > On entry, C contains the right-hand-side of the first matrix */
|
|
/* > equation in (1) or (3). */
|
|
/* > On exit, if IJOB = 0, 1 or 2, C has been overwritten by */
|
|
/* > the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R, */
|
|
/* > the solution achieved during the computation of the */
|
|
/* > Dif-estimate. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDC */
|
|
/* > \verbatim */
|
|
/* > LDC is INTEGER */
|
|
/* > The leading dimension of the array C. LDC >= f2cmax(1, M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D */
|
|
/* > \verbatim */
|
|
/* > D is REAL array, dimension (LDD, M) */
|
|
/* > The upper triangular matrix D. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDD */
|
|
/* > \verbatim */
|
|
/* > LDD is INTEGER */
|
|
/* > The leading dimension of the array D. LDD >= f2cmax(1, M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] E */
|
|
/* > \verbatim */
|
|
/* > E is REAL array, dimension (LDE, N) */
|
|
/* > The upper triangular matrix E. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDE */
|
|
/* > \verbatim */
|
|
/* > LDE is INTEGER */
|
|
/* > The leading dimension of the array E. LDE >= f2cmax(1, N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] F */
|
|
/* > \verbatim */
|
|
/* > F is REAL array, dimension (LDF, N) */
|
|
/* > On entry, F contains the right-hand-side of the second matrix */
|
|
/* > equation in (1) or (3). */
|
|
/* > On exit, if IJOB = 0, 1 or 2, F has been overwritten by */
|
|
/* > the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L, */
|
|
/* > the solution achieved during the computation of the */
|
|
/* > Dif-estimate. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDF */
|
|
/* > \verbatim */
|
|
/* > LDF is INTEGER */
|
|
/* > The leading dimension of the array F. LDF >= f2cmax(1, M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DIF */
|
|
/* > \verbatim */
|
|
/* > DIF is REAL */
|
|
/* > On exit DIF is the reciprocal of a lower bound of the */
|
|
/* > reciprocal of the Dif-function, i.e. DIF is an upper bound of */
|
|
/* > Dif[(A,D), (B,E)] = sigma_min(Z), where Z as in (2). */
|
|
/* > IF IJOB = 0 or TRANS = 'T', DIF is not touched. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SCALE */
|
|
/* > \verbatim */
|
|
/* > SCALE is REAL */
|
|
/* > On exit SCALE is the scaling factor in (1) or (3). */
|
|
/* > If 0 < SCALE < 1, C and F hold the solutions R and L, resp., */
|
|
/* > to a slightly perturbed system but the input matrices A, B, D */
|
|
/* > and E have not been changed. If SCALE = 0, C and F hold the */
|
|
/* > solutions R and L, respectively, to the homogeneous system */
|
|
/* > with C = F = 0. Normally, SCALE = 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK > = 1. */
|
|
/* > If IJOB = 1 or 2 and TRANS = 'N', LWORK >= f2cmax(1,2*M*N). */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (M+N+6) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > =0: successful exit */
|
|
/* > <0: If INFO = -i, the i-th argument had an illegal value. */
|
|
/* > >0: (A, D) and (B, E) have common or 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 realSYcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
|
|
/* > Umea University, S-901 87 Umea, Sweden. */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
|
|
/* > for Solving the Generalized Sylvester Equation and Estimating the */
|
|
/* > Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
|
|
/* > Department of Computing Science, Umea University, S-901 87 Umea, */
|
|
/* > Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
|
|
/* > Note 75. To appear in ACM Trans. on Math. Software, Vol 22, */
|
|
/* > No 1, 1996. */
|
|
/* > */
|
|
/* > [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester */
|
|
/* > Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal. */
|
|
/* > Appl., 15(4):1045-1060, 1994 */
|
|
/* > */
|
|
/* > [3] B. Kagstrom and L. Westin, Generalized Schur Methods with */
|
|
/* > Condition Estimators for Solving the Generalized Sylvester */
|
|
/* > Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, */
|
|
/* > July 1989, pp 745-751. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void stgsyl_(char *trans, integer *ijob, integer *m, integer *
|
|
n, real *a, integer *lda, real *b, integer *ldb, real *c__, integer *
|
|
ldc, real *d__, integer *ldd, real *e, integer *lde, real *f, integer
|
|
*ldf, real *scale, real *dif, real *work, integer *lwork, integer *
|
|
iwork, 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;
|
|
|
|
/* Local variables */
|
|
real dsum;
|
|
integer ppqq, i__, j, k, p, q;
|
|
extern logical lsame_(char *, char *);
|
|
integer ifunc;
|
|
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
|
|
integer linfo;
|
|
extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *,
|
|
integer *, real *, real *, integer *, real *, integer *, real *,
|
|
real *, integer *);
|
|
integer lwmin;
|
|
real scale2;
|
|
integer ie, je, mb, nb;
|
|
real dscale;
|
|
integer is, js;
|
|
extern /* Subroutine */ void stgsy2_(char *, integer *, integer *, integer
|
|
*, real *, integer *, real *, integer *, real *, integer *, real *
|
|
, integer *, real *, integer *, real *, integer *, real *, real *,
|
|
real *, integer *, integer *, integer *);
|
|
integer pq;
|
|
real scaloc;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern /* Subroutine */ void slacpy_(char *, integer *, integer *, real *,
|
|
integer *, real *, integer *), slaset_(char *, integer *,
|
|
integer *, real *, real *, real *, integer *);
|
|
integer iround;
|
|
logical notran;
|
|
integer isolve;
|
|
logical lquery;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
/* Replaced various illegal calls to SCOPY by calls to SLASET. */
|
|
/* Sven Hammarling, 1/5/02. */
|
|
|
|
|
|
/* 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;
|
|
--work;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
notran = lsame_(trans, "N");
|
|
lquery = *lwork == -1;
|
|
|
|
if (! notran && ! lsame_(trans, "T")) {
|
|
*info = -1;
|
|
} else if (notran) {
|
|
if (*ijob < 0 || *ijob > 4) {
|
|
*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) {
|
|
if (notran) {
|
|
if (*ijob == 1 || *ijob == 2) {
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = (*m << 1) * *n;
|
|
lwmin = f2cmax(i__1,i__2);
|
|
} else {
|
|
lwmin = 1;
|
|
}
|
|
} else {
|
|
lwmin = 1;
|
|
}
|
|
work[1] = (real) lwmin;
|
|
|
|
if (*lwork < lwmin && ! lquery) {
|
|
*info = -20;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("STGSYL", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*m == 0 || *n == 0) {
|
|
*scale = 1.f;
|
|
if (notran) {
|
|
if (*ijob != 0) {
|
|
*dif = 0.f;
|
|
}
|
|
}
|
|
return;
|
|
}
|
|
|
|
/* Determine optimal block sizes MB and NB */
|
|
|
|
mb = ilaenv_(&c__2, "STGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, (
|
|
ftnlen)1);
|
|
nb = ilaenv_(&c__5, "STGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, (
|
|
ftnlen)1);
|
|
|
|
isolve = 1;
|
|
ifunc = 0;
|
|
if (notran) {
|
|
if (*ijob >= 3) {
|
|
ifunc = *ijob - 2;
|
|
slaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc)
|
|
;
|
|
slaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
|
|
} else if (*ijob >= 1 && notran) {
|
|
isolve = 2;
|
|
}
|
|
}
|
|
|
|
if (mb <= 1 && nb <= 1 || mb >= *m && nb >= *n) {
|
|
|
|
i__1 = isolve;
|
|
for (iround = 1; iround <= i__1; ++iround) {
|
|
|
|
/* Use unblocked Level 2 solver */
|
|
|
|
dscale = 0.f;
|
|
dsum = 1.f;
|
|
pq = 0;
|
|
stgsy2_(trans, &ifunc, m, n, &a[a_offset], lda, &b[b_offset], ldb,
|
|
&c__[c_offset], ldc, &d__[d_offset], ldd, &e[e_offset],
|
|
lde, &f[f_offset], ldf, scale, &dsum, &dscale, &iwork[1],
|
|
&pq, info);
|
|
if (dscale != 0.f) {
|
|
if (*ijob == 1 || *ijob == 3) {
|
|
*dif = sqrt((real) ((*m << 1) * *n)) / (dscale * sqrt(
|
|
dsum));
|
|
} else {
|
|
*dif = sqrt((real) pq) / (dscale * sqrt(dsum));
|
|
}
|
|
}
|
|
|
|
if (isolve == 2 && iround == 1) {
|
|
if (notran) {
|
|
ifunc = *ijob;
|
|
}
|
|
scale2 = *scale;
|
|
slacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
|
|
slacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
|
|
slaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc);
|
|
slaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
|
|
} else if (isolve == 2 && iround == 2) {
|
|
slacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
|
|
slacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf);
|
|
*scale = scale2;
|
|
}
|
|
/* L30: */
|
|
}
|
|
|
|
return;
|
|
}
|
|
|
|
/* Determine block structure of A */
|
|
|
|
p = 0;
|
|
i__ = 1;
|
|
L40:
|
|
if (i__ > *m) {
|
|
goto L50;
|
|
}
|
|
++p;
|
|
iwork[p] = i__;
|
|
i__ += mb;
|
|
if (i__ >= *m) {
|
|
goto L50;
|
|
}
|
|
if (a[i__ + (i__ - 1) * a_dim1] != 0.f) {
|
|
++i__;
|
|
}
|
|
goto L40;
|
|
L50:
|
|
|
|
iwork[p + 1] = *m + 1;
|
|
if (iwork[p] == iwork[p + 1]) {
|
|
--p;
|
|
}
|
|
|
|
/* Determine block structure of B */
|
|
|
|
q = p + 1;
|
|
j = 1;
|
|
L60:
|
|
if (j > *n) {
|
|
goto L70;
|
|
}
|
|
++q;
|
|
iwork[q] = j;
|
|
j += nb;
|
|
if (j >= *n) {
|
|
goto L70;
|
|
}
|
|
if (b[j + (j - 1) * b_dim1] != 0.f) {
|
|
++j;
|
|
}
|
|
goto L60;
|
|
L70:
|
|
|
|
iwork[q + 1] = *n + 1;
|
|
if (iwork[q] == iwork[q + 1]) {
|
|
--q;
|
|
}
|
|
|
|
if (notran) {
|
|
|
|
i__1 = isolve;
|
|
for (iround = 1; iround <= i__1; ++iround) {
|
|
|
|
/* Solve (I, J)-subsystem */
|
|
/* 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 = P, P - 1,..., 1; J = 1, 2,..., Q */
|
|
|
|
dscale = 0.f;
|
|
dsum = 1.f;
|
|
pq = 0;
|
|
*scale = 1.f;
|
|
i__2 = q;
|
|
for (j = p + 2; j <= i__2; ++j) {
|
|
js = iwork[j];
|
|
je = iwork[j + 1] - 1;
|
|
nb = je - js + 1;
|
|
for (i__ = p; i__ >= 1; --i__) {
|
|
is = iwork[i__];
|
|
ie = iwork[i__ + 1] - 1;
|
|
mb = ie - is + 1;
|
|
ppqq = 0;
|
|
stgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1],
|
|
lda, &b[js + js * b_dim1], ldb, &c__[is + js *
|
|
c_dim1], ldc, &d__[is + is * d_dim1], ldd, &e[js
|
|
+ js * e_dim1], lde, &f[is + js * f_dim1], ldf, &
|
|
scaloc, &dsum, &dscale, &iwork[q + 2], &ppqq, &
|
|
linfo);
|
|
if (linfo > 0) {
|
|
*info = linfo;
|
|
}
|
|
|
|
pq += ppqq;
|
|
if (scaloc != 1.f) {
|
|
i__3 = js - 1;
|
|
for (k = 1; k <= i__3; ++k) {
|
|
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
|
|
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
|
|
/* L80: */
|
|
}
|
|
i__3 = je;
|
|
for (k = js; k <= i__3; ++k) {
|
|
i__4 = is - 1;
|
|
sscal_(&i__4, &scaloc, &c__[k * c_dim1 + 1], &
|
|
c__1);
|
|
i__4 = is - 1;
|
|
sscal_(&i__4, &scaloc, &f[k * f_dim1 + 1], &c__1);
|
|
/* L90: */
|
|
}
|
|
i__3 = je;
|
|
for (k = js; k <= i__3; ++k) {
|
|
i__4 = *m - ie;
|
|
sscal_(&i__4, &scaloc, &c__[ie + 1 + k * c_dim1],
|
|
&c__1);
|
|
i__4 = *m - ie;
|
|
sscal_(&i__4, &scaloc, &f[ie + 1 + k * f_dim1], &
|
|
c__1);
|
|
/* L100: */
|
|
}
|
|
i__3 = *n;
|
|
for (k = je + 1; k <= i__3; ++k) {
|
|
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
|
|
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
|
|
/* L110: */
|
|
}
|
|
*scale *= scaloc;
|
|
}
|
|
|
|
/* Substitute R(I, J) and L(I, J) into remaining */
|
|
/* equation. */
|
|
|
|
if (i__ > 1) {
|
|
i__3 = is - 1;
|
|
sgemm_("N", "N", &i__3, &nb, &mb, &c_b51, &a[is *
|
|
a_dim1 + 1], lda, &c__[is + js * c_dim1], ldc,
|
|
&c_b52, &c__[js * c_dim1 + 1], ldc);
|
|
i__3 = is - 1;
|
|
sgemm_("N", "N", &i__3, &nb, &mb, &c_b51, &d__[is *
|
|
d_dim1 + 1], ldd, &c__[is + js * c_dim1], ldc,
|
|
&c_b52, &f[js * f_dim1 + 1], ldf);
|
|
}
|
|
if (j < q) {
|
|
i__3 = *n - je;
|
|
sgemm_("N", "N", &mb, &i__3, &nb, &c_b52, &f[is + js *
|
|
f_dim1], ldf, &b[js + (je + 1) * b_dim1],
|
|
ldb, &c_b52, &c__[is + (je + 1) * c_dim1],
|
|
ldc);
|
|
i__3 = *n - je;
|
|
sgemm_("N", "N", &mb, &i__3, &nb, &c_b52, &f[is + js *
|
|
f_dim1], ldf, &e[js + (je + 1) * e_dim1],
|
|
lde, &c_b52, &f[is + (je + 1) * f_dim1], ldf);
|
|
}
|
|
/* L120: */
|
|
}
|
|
/* L130: */
|
|
}
|
|
if (dscale != 0.f) {
|
|
if (*ijob == 1 || *ijob == 3) {
|
|
*dif = sqrt((real) ((*m << 1) * *n)) / (dscale * sqrt(
|
|
dsum));
|
|
} else {
|
|
*dif = sqrt((real) pq) / (dscale * sqrt(dsum));
|
|
}
|
|
}
|
|
if (isolve == 2 && iround == 1) {
|
|
if (notran) {
|
|
ifunc = *ijob;
|
|
}
|
|
scale2 = *scale;
|
|
slacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
|
|
slacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
|
|
slaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc);
|
|
slaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
|
|
} else if (isolve == 2 && iround == 2) {
|
|
slacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
|
|
slacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf);
|
|
*scale = scale2;
|
|
}
|
|
/* L150: */
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Solve transposed (I, J)-subsystem */
|
|
/* A(I, I)**T * R(I, J) + D(I, I)**T * L(I, J) = C(I, J) */
|
|
/* R(I, J) * B(J, J)**T + L(I, J) * E(J, J)**T = -F(I, J) */
|
|
/* for I = 1,2,..., P; J = Q, Q-1,..., 1 */
|
|
|
|
*scale = 1.f;
|
|
i__1 = p;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
is = iwork[i__];
|
|
ie = iwork[i__ + 1] - 1;
|
|
mb = ie - is + 1;
|
|
i__2 = p + 2;
|
|
for (j = q; j >= i__2; --j) {
|
|
js = iwork[j];
|
|
je = iwork[j + 1] - 1;
|
|
nb = je - js + 1;
|
|
stgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1], lda, &
|
|
b[js + js * b_dim1], ldb, &c__[is + js * c_dim1], ldc,
|
|
&d__[is + is * d_dim1], ldd, &e[js + js * e_dim1],
|
|
lde, &f[is + js * f_dim1], ldf, &scaloc, &dsum, &
|
|
dscale, &iwork[q + 2], &ppqq, &linfo);
|
|
if (linfo > 0) {
|
|
*info = linfo;
|
|
}
|
|
if (scaloc != 1.f) {
|
|
i__3 = js - 1;
|
|
for (k = 1; k <= i__3; ++k) {
|
|
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
|
|
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
|
|
/* L160: */
|
|
}
|
|
i__3 = je;
|
|
for (k = js; k <= i__3; ++k) {
|
|
i__4 = is - 1;
|
|
sscal_(&i__4, &scaloc, &c__[k * c_dim1 + 1], &c__1);
|
|
i__4 = is - 1;
|
|
sscal_(&i__4, &scaloc, &f[k * f_dim1 + 1], &c__1);
|
|
/* L170: */
|
|
}
|
|
i__3 = je;
|
|
for (k = js; k <= i__3; ++k) {
|
|
i__4 = *m - ie;
|
|
sscal_(&i__4, &scaloc, &c__[ie + 1 + k * c_dim1], &
|
|
c__1);
|
|
i__4 = *m - ie;
|
|
sscal_(&i__4, &scaloc, &f[ie + 1 + k * f_dim1], &c__1)
|
|
;
|
|
/* L180: */
|
|
}
|
|
i__3 = *n;
|
|
for (k = je + 1; k <= i__3; ++k) {
|
|
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
|
|
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
|
|
/* L190: */
|
|
}
|
|
*scale *= scaloc;
|
|
}
|
|
|
|
/* Substitute R(I, J) and L(I, J) into remaining equation. */
|
|
|
|
if (j > p + 2) {
|
|
i__3 = js - 1;
|
|
sgemm_("N", "T", &mb, &i__3, &nb, &c_b52, &c__[is + js *
|
|
c_dim1], ldc, &b[js * b_dim1 + 1], ldb, &c_b52, &
|
|
f[is + f_dim1], ldf);
|
|
i__3 = js - 1;
|
|
sgemm_("N", "T", &mb, &i__3, &nb, &c_b52, &f[is + js *
|
|
f_dim1], ldf, &e[js * e_dim1 + 1], lde, &c_b52, &
|
|
f[is + f_dim1], ldf);
|
|
}
|
|
if (i__ < p) {
|
|
i__3 = *m - ie;
|
|
sgemm_("T", "N", &i__3, &nb, &mb, &c_b51, &a[is + (ie + 1)
|
|
* a_dim1], lda, &c__[is + js * c_dim1], ldc, &
|
|
c_b52, &c__[ie + 1 + js * c_dim1], ldc);
|
|
i__3 = *m - ie;
|
|
sgemm_("T", "N", &i__3, &nb, &mb, &c_b51, &d__[is + (ie +
|
|
1) * d_dim1], ldd, &f[is + js * f_dim1], ldf, &
|
|
c_b52, &c__[ie + 1 + js * c_dim1], ldc);
|
|
}
|
|
/* L200: */
|
|
}
|
|
/* L210: */
|
|
}
|
|
|
|
}
|
|
|
|
work[1] = (real) lwmin;
|
|
|
|
return;
|
|
|
|
/* End of STGSYL */
|
|
|
|
} /* stgsyl_ */
|
|
|