1056 lines
30 KiB
C
1056 lines
30 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__4 = 4;
|
|
static integer c__1 = 1;
|
|
static integer c__16 = 16;
|
|
static integer c__0 = 0;
|
|
|
|
/* > \brief \b DLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLASY2 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasy2.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasy2.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasy2.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLASY2( LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR, */
|
|
/* LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO ) */
|
|
|
|
/* LOGICAL LTRANL, LTRANR */
|
|
/* INTEGER INFO, ISGN, LDB, LDTL, LDTR, LDX, N1, N2 */
|
|
/* DOUBLE PRECISION SCALE, XNORM */
|
|
/* DOUBLE PRECISION B( LDB, * ), TL( LDTL, * ), TR( LDTR, * ), */
|
|
/* $ X( LDX, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLASY2 solves for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in */
|
|
/* > */
|
|
/* > op(TL)*X + ISGN*X*op(TR) = SCALE*B, */
|
|
/* > */
|
|
/* > where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or */
|
|
/* > -1. op(T) = T or T**T, where T**T denotes the transpose of T. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] LTRANL */
|
|
/* > \verbatim */
|
|
/* > LTRANL is LOGICAL */
|
|
/* > On entry, LTRANL specifies the op(TL): */
|
|
/* > = .FALSE., op(TL) = TL, */
|
|
/* > = .TRUE., op(TL) = TL**T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LTRANR */
|
|
/* > \verbatim */
|
|
/* > LTRANR is LOGICAL */
|
|
/* > On entry, LTRANR specifies the op(TR): */
|
|
/* > = .FALSE., op(TR) = TR, */
|
|
/* > = .TRUE., op(TR) = TR**T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ISGN */
|
|
/* > \verbatim */
|
|
/* > ISGN is INTEGER */
|
|
/* > On entry, ISGN specifies the sign of the equation */
|
|
/* > as described before. ISGN may only be 1 or -1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N1 */
|
|
/* > \verbatim */
|
|
/* > N1 is INTEGER */
|
|
/* > On entry, N1 specifies the order of matrix TL. */
|
|
/* > N1 may only be 0, 1 or 2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N2 */
|
|
/* > \verbatim */
|
|
/* > N2 is INTEGER */
|
|
/* > On entry, N2 specifies the order of matrix TR. */
|
|
/* > N2 may only be 0, 1 or 2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TL */
|
|
/* > \verbatim */
|
|
/* > TL is DOUBLE PRECISION array, dimension (LDTL,2) */
|
|
/* > On entry, TL contains an N1 by N1 matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDTL */
|
|
/* > \verbatim */
|
|
/* > LDTL is INTEGER */
|
|
/* > The leading dimension of the matrix TL. LDTL >= f2cmax(1,N1). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TR */
|
|
/* > \verbatim */
|
|
/* > TR is DOUBLE PRECISION array, dimension (LDTR,2) */
|
|
/* > On entry, TR contains an N2 by N2 matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDTR */
|
|
/* > \verbatim */
|
|
/* > LDTR is INTEGER */
|
|
/* > The leading dimension of the matrix TR. LDTR >= f2cmax(1,N2). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B */
|
|
/* > \verbatim */
|
|
/* > B is DOUBLE PRECISION array, dimension (LDB,2) */
|
|
/* > On entry, the N1 by N2 matrix B contains the right-hand */
|
|
/* > side of the equation. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the matrix B. LDB >= f2cmax(1,N1). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SCALE */
|
|
/* > \verbatim */
|
|
/* > SCALE is DOUBLE PRECISION */
|
|
/* > On exit, SCALE contains the scale factor. SCALE is chosen */
|
|
/* > less than or equal to 1 to prevent the solution overflowing. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] X */
|
|
/* > \verbatim */
|
|
/* > X is DOUBLE PRECISION array, dimension (LDX,2) */
|
|
/* > On exit, X contains the N1 by N2 solution. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDX */
|
|
/* > \verbatim */
|
|
/* > LDX is INTEGER */
|
|
/* > The leading dimension of the matrix X. LDX >= f2cmax(1,N1). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] XNORM */
|
|
/* > \verbatim */
|
|
/* > XNORM is DOUBLE PRECISION */
|
|
/* > On exit, XNORM is the infinity-norm of the solution. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > On exit, INFO is set to */
|
|
/* > 0: successful exit. */
|
|
/* > 1: TL and TR have too close eigenvalues, so TL or */
|
|
/* > TR is perturbed to get a nonsingular equation. */
|
|
/* > NOTE: In the interests of speed, this routine does not */
|
|
/* > check the inputs for errors. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup doubleSYauxiliary */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlasy2_(logical *ltranl, logical *ltranr, integer *isgn,
|
|
integer *n1, integer *n2, doublereal *tl, integer *ldtl, doublereal *
|
|
tr, integer *ldtr, doublereal *b, integer *ldb, doublereal *scale,
|
|
doublereal *x, integer *ldx, doublereal *xnorm, integer *info)
|
|
{
|
|
/* Initialized data */
|
|
|
|
static integer locu12[4] = { 3,4,1,2 };
|
|
static integer locl21[4] = { 2,1,4,3 };
|
|
static integer locu22[4] = { 4,3,2,1 };
|
|
static logical xswpiv[4] = { FALSE_,FALSE_,TRUE_,TRUE_ };
|
|
static logical bswpiv[4] = { FALSE_,TRUE_,FALSE_,TRUE_ };
|
|
|
|
/* System generated locals */
|
|
integer b_dim1, b_offset, tl_dim1, tl_offset, tr_dim1, tr_offset, x_dim1,
|
|
x_offset;
|
|
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8;
|
|
|
|
/* Local variables */
|
|
doublereal btmp[4], smin;
|
|
integer ipiv;
|
|
doublereal temp;
|
|
integer jpiv[4];
|
|
doublereal xmax;
|
|
integer ipsv, jpsv, i__, j, k;
|
|
logical bswap;
|
|
extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *), dswap_(integer *, doublereal *, integer
|
|
*, doublereal *, integer *);
|
|
logical xswap;
|
|
doublereal x2[2], l21, u11, u12;
|
|
integer ip, jp;
|
|
doublereal u22, t16[16] /* was [4][4] */;
|
|
extern doublereal dlamch_(char *);
|
|
extern integer idamax_(integer *, doublereal *, integer *);
|
|
doublereal smlnum, gam, bet, eps, sgn, tmp[4], tau1;
|
|
|
|
|
|
/* -- 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..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
/* Parameter adjustments */
|
|
tl_dim1 = *ldtl;
|
|
tl_offset = 1 + tl_dim1 * 1;
|
|
tl -= tl_offset;
|
|
tr_dim1 = *ldtr;
|
|
tr_offset = 1 + tr_dim1 * 1;
|
|
tr -= tr_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
x_dim1 = *ldx;
|
|
x_offset = 1 + x_dim1 * 1;
|
|
x -= x_offset;
|
|
|
|
/* Function Body */
|
|
|
|
/* Do not check the input parameters for errors */
|
|
|
|
*info = 0;
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n1 == 0 || *n2 == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Set constants to control overflow */
|
|
|
|
eps = dlamch_("P");
|
|
smlnum = dlamch_("S") / eps;
|
|
sgn = (doublereal) (*isgn);
|
|
|
|
k = *n1 + *n1 + *n2 - 2;
|
|
switch (k) {
|
|
case 1: goto L10;
|
|
case 2: goto L20;
|
|
case 3: goto L30;
|
|
case 4: goto L50;
|
|
}
|
|
|
|
/* 1 by 1: TL11*X + SGN*X*TR11 = B11 */
|
|
|
|
L10:
|
|
tau1 = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
|
|
bet = abs(tau1);
|
|
if (bet <= smlnum) {
|
|
tau1 = smlnum;
|
|
bet = smlnum;
|
|
*info = 1;
|
|
}
|
|
|
|
*scale = 1.;
|
|
gam = (d__1 = b[b_dim1 + 1], abs(d__1));
|
|
if (smlnum * gam > bet) {
|
|
*scale = 1. / gam;
|
|
}
|
|
|
|
x[x_dim1 + 1] = b[b_dim1 + 1] * *scale / tau1;
|
|
*xnorm = (d__1 = x[x_dim1 + 1], abs(d__1));
|
|
return;
|
|
|
|
/* 1 by 2: */
|
|
/* TL11*[X11 X12] + ISGN*[X11 X12]*op[TR11 TR12] = [B11 B12] */
|
|
/* [TR21 TR22] */
|
|
|
|
L20:
|
|
|
|
/* Computing MAX */
|
|
/* Computing MAX */
|
|
d__7 = (d__1 = tl[tl_dim1 + 1], abs(d__1)), d__8 = (d__2 = tr[tr_dim1 + 1]
|
|
, abs(d__2)), d__7 = f2cmax(d__7,d__8), d__8 = (d__3 = tr[(tr_dim1 <<
|
|
1) + 1], abs(d__3)), d__7 = f2cmax(d__7,d__8), d__8 = (d__4 = tr[
|
|
tr_dim1 + 2], abs(d__4)), d__7 = f2cmax(d__7,d__8), d__8 = (d__5 =
|
|
tr[(tr_dim1 << 1) + 2], abs(d__5));
|
|
d__6 = eps * f2cmax(d__7,d__8);
|
|
smin = f2cmax(d__6,smlnum);
|
|
tmp[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
|
|
tmp[3] = tl[tl_dim1 + 1] + sgn * tr[(tr_dim1 << 1) + 2];
|
|
if (*ltranr) {
|
|
tmp[1] = sgn * tr[tr_dim1 + 2];
|
|
tmp[2] = sgn * tr[(tr_dim1 << 1) + 1];
|
|
} else {
|
|
tmp[1] = sgn * tr[(tr_dim1 << 1) + 1];
|
|
tmp[2] = sgn * tr[tr_dim1 + 2];
|
|
}
|
|
btmp[0] = b[b_dim1 + 1];
|
|
btmp[1] = b[(b_dim1 << 1) + 1];
|
|
goto L40;
|
|
|
|
/* 2 by 1: */
|
|
/* op[TL11 TL12]*[X11] + ISGN* [X11]*TR11 = [B11] */
|
|
/* [TL21 TL22] [X21] [X21] [B21] */
|
|
|
|
L30:
|
|
/* Computing MAX */
|
|
/* Computing MAX */
|
|
d__7 = (d__1 = tr[tr_dim1 + 1], abs(d__1)), d__8 = (d__2 = tl[tl_dim1 + 1]
|
|
, abs(d__2)), d__7 = f2cmax(d__7,d__8), d__8 = (d__3 = tl[(tl_dim1 <<
|
|
1) + 1], abs(d__3)), d__7 = f2cmax(d__7,d__8), d__8 = (d__4 = tl[
|
|
tl_dim1 + 2], abs(d__4)), d__7 = f2cmax(d__7,d__8), d__8 = (d__5 =
|
|
tl[(tl_dim1 << 1) + 2], abs(d__5));
|
|
d__6 = eps * f2cmax(d__7,d__8);
|
|
smin = f2cmax(d__6,smlnum);
|
|
tmp[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
|
|
tmp[3] = tl[(tl_dim1 << 1) + 2] + sgn * tr[tr_dim1 + 1];
|
|
if (*ltranl) {
|
|
tmp[1] = tl[(tl_dim1 << 1) + 1];
|
|
tmp[2] = tl[tl_dim1 + 2];
|
|
} else {
|
|
tmp[1] = tl[tl_dim1 + 2];
|
|
tmp[2] = tl[(tl_dim1 << 1) + 1];
|
|
}
|
|
btmp[0] = b[b_dim1 + 1];
|
|
btmp[1] = b[b_dim1 + 2];
|
|
L40:
|
|
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/* Solve 2 by 2 system using complete pivoting. */
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/* Set pivots less than SMIN to SMIN. */
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|
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|
ipiv = idamax_(&c__4, tmp, &c__1);
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u11 = tmp[ipiv - 1];
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if (abs(u11) <= smin) {
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*info = 1;
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u11 = smin;
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|
}
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u12 = tmp[locu12[ipiv - 1] - 1];
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l21 = tmp[locl21[ipiv - 1] - 1] / u11;
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u22 = tmp[locu22[ipiv - 1] - 1] - u12 * l21;
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xswap = xswpiv[ipiv - 1];
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bswap = bswpiv[ipiv - 1];
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if (abs(u22) <= smin) {
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|
*info = 1;
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|
u22 = smin;
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|
}
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|
if (bswap) {
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temp = btmp[1];
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btmp[1] = btmp[0] - l21 * temp;
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btmp[0] = temp;
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} else {
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|
btmp[1] -= l21 * btmp[0];
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|
}
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|
*scale = 1.;
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if (smlnum * 2. * abs(btmp[1]) > abs(u22) || smlnum * 2. * abs(btmp[0]) >
|
|
abs(u11)) {
|
|
/* Computing MAX */
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|
d__1 = abs(btmp[0]), d__2 = abs(btmp[1]);
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|
*scale = .5 / f2cmax(d__1,d__2);
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|
btmp[0] *= *scale;
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btmp[1] *= *scale;
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}
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x2[1] = btmp[1] / u22;
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|
x2[0] = btmp[0] / u11 - u12 / u11 * x2[1];
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|
if (xswap) {
|
|
temp = x2[1];
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|
x2[1] = x2[0];
|
|
x2[0] = temp;
|
|
}
|
|
x[x_dim1 + 1] = x2[0];
|
|
if (*n1 == 1) {
|
|
x[(x_dim1 << 1) + 1] = x2[1];
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|
*xnorm = (d__1 = x[x_dim1 + 1], abs(d__1)) + (d__2 = x[(x_dim1 << 1)
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+ 1], abs(d__2));
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} else {
|
|
x[x_dim1 + 2] = x2[1];
|
|
/* Computing MAX */
|
|
d__3 = (d__1 = x[x_dim1 + 1], abs(d__1)), d__4 = (d__2 = x[x_dim1 + 2]
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, abs(d__2));
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*xnorm = f2cmax(d__3,d__4);
|
|
}
|
|
return;
|
|
|
|
/* 2 by 2: */
|
|
/* op[TL11 TL12]*[X11 X12] +ISGN* [X11 X12]*op[TR11 TR12] = [B11 B12] */
|
|
/* [TL21 TL22] [X21 X22] [X21 X22] [TR21 TR22] [B21 B22] */
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|
|
|
/* Solve equivalent 4 by 4 system using complete pivoting. */
|
|
/* Set pivots less than SMIN to SMIN. */
|
|
|
|
L50:
|
|
/* Computing MAX */
|
|
d__5 = (d__1 = tr[tr_dim1 + 1], abs(d__1)), d__6 = (d__2 = tr[(tr_dim1 <<
|
|
1) + 1], abs(d__2)), d__5 = f2cmax(d__5,d__6), d__6 = (d__3 = tr[
|
|
tr_dim1 + 2], abs(d__3)), d__5 = f2cmax(d__5,d__6), d__6 = (d__4 =
|
|
tr[(tr_dim1 << 1) + 2], abs(d__4));
|
|
smin = f2cmax(d__5,d__6);
|
|
/* Computing MAX */
|
|
d__5 = smin, d__6 = (d__1 = tl[tl_dim1 + 1], abs(d__1)), d__5 = f2cmax(d__5,
|
|
d__6), d__6 = (d__2 = tl[(tl_dim1 << 1) + 1], abs(d__2)), d__5 =
|
|
f2cmax(d__5,d__6), d__6 = (d__3 = tl[tl_dim1 + 2], abs(d__3)), d__5 =
|
|
f2cmax(d__5,d__6), d__6 = (d__4 = tl[(tl_dim1 << 1) + 2], abs(d__4))
|
|
;
|
|
smin = f2cmax(d__5,d__6);
|
|
/* Computing MAX */
|
|
d__1 = eps * smin;
|
|
smin = f2cmax(d__1,smlnum);
|
|
btmp[0] = 0.;
|
|
dcopy_(&c__16, btmp, &c__0, t16, &c__1);
|
|
t16[0] = tl[tl_dim1 + 1] + sgn * tr[tr_dim1 + 1];
|
|
t16[5] = tl[(tl_dim1 << 1) + 2] + sgn * tr[tr_dim1 + 1];
|
|
t16[10] = tl[tl_dim1 + 1] + sgn * tr[(tr_dim1 << 1) + 2];
|
|
t16[15] = tl[(tl_dim1 << 1) + 2] + sgn * tr[(tr_dim1 << 1) + 2];
|
|
if (*ltranl) {
|
|
t16[4] = tl[tl_dim1 + 2];
|
|
t16[1] = tl[(tl_dim1 << 1) + 1];
|
|
t16[14] = tl[tl_dim1 + 2];
|
|
t16[11] = tl[(tl_dim1 << 1) + 1];
|
|
} else {
|
|
t16[4] = tl[(tl_dim1 << 1) + 1];
|
|
t16[1] = tl[tl_dim1 + 2];
|
|
t16[14] = tl[(tl_dim1 << 1) + 1];
|
|
t16[11] = tl[tl_dim1 + 2];
|
|
}
|
|
if (*ltranr) {
|
|
t16[8] = sgn * tr[(tr_dim1 << 1) + 1];
|
|
t16[13] = sgn * tr[(tr_dim1 << 1) + 1];
|
|
t16[2] = sgn * tr[tr_dim1 + 2];
|
|
t16[7] = sgn * tr[tr_dim1 + 2];
|
|
} else {
|
|
t16[8] = sgn * tr[tr_dim1 + 2];
|
|
t16[13] = sgn * tr[tr_dim1 + 2];
|
|
t16[2] = sgn * tr[(tr_dim1 << 1) + 1];
|
|
t16[7] = sgn * tr[(tr_dim1 << 1) + 1];
|
|
}
|
|
btmp[0] = b[b_dim1 + 1];
|
|
btmp[1] = b[b_dim1 + 2];
|
|
btmp[2] = b[(b_dim1 << 1) + 1];
|
|
btmp[3] = b[(b_dim1 << 1) + 2];
|
|
|
|
/* Perform elimination */
|
|
|
|
for (i__ = 1; i__ <= 3; ++i__) {
|
|
xmax = 0.;
|
|
for (ip = i__; ip <= 4; ++ip) {
|
|
for (jp = i__; jp <= 4; ++jp) {
|
|
if ((d__1 = t16[ip + (jp << 2) - 5], abs(d__1)) >= xmax) {
|
|
xmax = (d__1 = t16[ip + (jp << 2) - 5], abs(d__1));
|
|
ipsv = ip;
|
|
jpsv = jp;
|
|
}
|
|
/* L60: */
|
|
}
|
|
/* L70: */
|
|
}
|
|
if (ipsv != i__) {
|
|
dswap_(&c__4, &t16[ipsv - 1], &c__4, &t16[i__ - 1], &c__4);
|
|
temp = btmp[i__ - 1];
|
|
btmp[i__ - 1] = btmp[ipsv - 1];
|
|
btmp[ipsv - 1] = temp;
|
|
}
|
|
if (jpsv != i__) {
|
|
dswap_(&c__4, &t16[(jpsv << 2) - 4], &c__1, &t16[(i__ << 2) - 4],
|
|
&c__1);
|
|
}
|
|
jpiv[i__ - 1] = jpsv;
|
|
if ((d__1 = t16[i__ + (i__ << 2) - 5], abs(d__1)) < smin) {
|
|
*info = 1;
|
|
t16[i__ + (i__ << 2) - 5] = smin;
|
|
}
|
|
for (j = i__ + 1; j <= 4; ++j) {
|
|
t16[j + (i__ << 2) - 5] /= t16[i__ + (i__ << 2) - 5];
|
|
btmp[j - 1] -= t16[j + (i__ << 2) - 5] * btmp[i__ - 1];
|
|
for (k = i__ + 1; k <= 4; ++k) {
|
|
t16[j + (k << 2) - 5] -= t16[j + (i__ << 2) - 5] * t16[i__ + (
|
|
k << 2) - 5];
|
|
/* L80: */
|
|
}
|
|
/* L90: */
|
|
}
|
|
/* L100: */
|
|
}
|
|
if (abs(t16[15]) < smin) {
|
|
*info = 1;
|
|
t16[15] = smin;
|
|
}
|
|
*scale = 1.;
|
|
if (smlnum * 8. * abs(btmp[0]) > abs(t16[0]) || smlnum * 8. * abs(btmp[1])
|
|
> abs(t16[5]) || smlnum * 8. * abs(btmp[2]) > abs(t16[10]) ||
|
|
smlnum * 8. * abs(btmp[3]) > abs(t16[15])) {
|
|
/* Computing MAX */
|
|
d__1 = abs(btmp[0]), d__2 = abs(btmp[1]), d__1 = f2cmax(d__1,d__2), d__2
|
|
= abs(btmp[2]), d__1 = f2cmax(d__1,d__2), d__2 = abs(btmp[3]);
|
|
*scale = .125 / f2cmax(d__1,d__2);
|
|
btmp[0] *= *scale;
|
|
btmp[1] *= *scale;
|
|
btmp[2] *= *scale;
|
|
btmp[3] *= *scale;
|
|
}
|
|
for (i__ = 1; i__ <= 4; ++i__) {
|
|
k = 5 - i__;
|
|
temp = 1. / t16[k + (k << 2) - 5];
|
|
tmp[k - 1] = btmp[k - 1] * temp;
|
|
for (j = k + 1; j <= 4; ++j) {
|
|
tmp[k - 1] -= temp * t16[k + (j << 2) - 5] * tmp[j - 1];
|
|
/* L110: */
|
|
}
|
|
/* L120: */
|
|
}
|
|
for (i__ = 1; i__ <= 3; ++i__) {
|
|
if (jpiv[4 - i__ - 1] != 4 - i__) {
|
|
temp = tmp[4 - i__ - 1];
|
|
tmp[4 - i__ - 1] = tmp[jpiv[4 - i__ - 1] - 1];
|
|
tmp[jpiv[4 - i__ - 1] - 1] = temp;
|
|
}
|
|
/* L130: */
|
|
}
|
|
x[x_dim1 + 1] = tmp[0];
|
|
x[x_dim1 + 2] = tmp[1];
|
|
x[(x_dim1 << 1) + 1] = tmp[2];
|
|
x[(x_dim1 << 1) + 2] = tmp[3];
|
|
/* Computing MAX */
|
|
d__1 = abs(tmp[0]) + abs(tmp[2]), d__2 = abs(tmp[1]) + abs(tmp[3]);
|
|
*xnorm = f2cmax(d__1,d__2);
|
|
return;
|
|
|
|
/* End of DLASY2 */
|
|
|
|
} /* dlasy2_ */
|
|
|