1106 lines
30 KiB
C
1106 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 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 doublereal c_b29 = 1.;
|
|
static doublereal c_b30 = 0.;
|
|
static doublereal c_b33 = -1.;
|
|
|
|
/* > \brief \b DLATM5 */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLATM5( PRTYPE, M, N, A, LDA, B, LDB, C, LDC, D, LDD, */
|
|
/* E, LDE, F, LDF, R, LDR, L, LDL, ALPHA, QBLCKA, */
|
|
/* QBLCKB ) */
|
|
|
|
/* INTEGER LDA, LDB, LDC, LDD, LDE, LDF, LDL, LDR, M, N, */
|
|
/* $ PRTYPE, QBLCKA, QBLCKB */
|
|
/* DOUBLE PRECISION ALPHA */
|
|
/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ), */
|
|
/* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), */
|
|
/* $ L( LDL, * ), R( LDR, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLATM5 generates matrices involved in the Generalized Sylvester */
|
|
/* > equation: */
|
|
/* > */
|
|
/* > A * R - L * B = C */
|
|
/* > D * R - L * E = F */
|
|
/* > */
|
|
/* > They also satisfy (the diagonalization condition) */
|
|
/* > */
|
|
/* > [ I -L ] ( [ A -C ], [ D -F ] ) [ I R ] = ( [ A ], [ D ] ) */
|
|
/* > [ I ] ( [ B ] [ E ] ) [ I ] ( [ B ] [ E ] ) */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] PRTYPE */
|
|
/* > \verbatim */
|
|
/* > PRTYPE is INTEGER */
|
|
/* > "Points" to a certain type of the matrices to generate */
|
|
/* > (see further details). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > Specifies the order of A and D and the number of rows in */
|
|
/* > C, F, R and L. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > Specifies the order of B and E and the number of columns in */
|
|
/* > C, F, R and L. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION array, dimension (LDA, M). */
|
|
/* > On exit A M-by-M is initialized according to PRTYPE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] B */
|
|
/* > \verbatim */
|
|
/* > B is DOUBLE PRECISION array, dimension (LDB, N). */
|
|
/* > On exit B N-by-N is initialized according to PRTYPE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of B. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] C */
|
|
/* > \verbatim */
|
|
/* > C is DOUBLE PRECISION array, dimension (LDC, N). */
|
|
/* > On exit C M-by-N is initialized according to PRTYPE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDC */
|
|
/* > \verbatim */
|
|
/* > LDC is INTEGER */
|
|
/* > The leading dimension of C. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (LDD, M). */
|
|
/* > On exit D M-by-M is initialized according to PRTYPE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDD */
|
|
/* > \verbatim */
|
|
/* > LDD is INTEGER */
|
|
/* > The leading dimension of D. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] E */
|
|
/* > \verbatim */
|
|
/* > E is DOUBLE PRECISION array, dimension (LDE, N). */
|
|
/* > On exit E N-by-N is initialized according to PRTYPE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDE */
|
|
/* > \verbatim */
|
|
/* > LDE is INTEGER */
|
|
/* > The leading dimension of E. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] F */
|
|
/* > \verbatim */
|
|
/* > F is DOUBLE PRECISION array, dimension (LDF, N). */
|
|
/* > On exit F M-by-N is initialized according to PRTYPE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDF */
|
|
/* > \verbatim */
|
|
/* > LDF is INTEGER */
|
|
/* > The leading dimension of F. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] R */
|
|
/* > \verbatim */
|
|
/* > R is DOUBLE PRECISION array, dimension (LDR, N). */
|
|
/* > On exit R M-by-N is initialized according to PRTYPE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDR */
|
|
/* > \verbatim */
|
|
/* > LDR is INTEGER */
|
|
/* > The leading dimension of R. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] L */
|
|
/* > \verbatim */
|
|
/* > L is DOUBLE PRECISION array, dimension (LDL, N). */
|
|
/* > On exit L M-by-N is initialized according to PRTYPE. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDL */
|
|
/* > \verbatim */
|
|
/* > LDL is INTEGER */
|
|
/* > The leading dimension of L. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ALPHA */
|
|
/* > \verbatim */
|
|
/* > ALPHA is DOUBLE PRECISION */
|
|
/* > Parameter used in generating PRTYPE = 1 and 5 matrices. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] QBLCKA */
|
|
/* > \verbatim */
|
|
/* > QBLCKA is INTEGER */
|
|
/* > When PRTYPE = 3, specifies the distance between 2-by-2 */
|
|
/* > blocks on the diagonal in A. Otherwise, QBLCKA is not */
|
|
/* > referenced. QBLCKA > 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] QBLCKB */
|
|
/* > \verbatim */
|
|
/* > QBLCKB is INTEGER */
|
|
/* > When PRTYPE = 3, specifies the distance between 2-by-2 */
|
|
/* > blocks on the diagonal in B. Otherwise, QBLCKB is not */
|
|
/* > referenced. QBLCKB > 1. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup double_matgen */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices */
|
|
/* > */
|
|
/* > A : if (i == j) then A(i, j) = 1.0 */
|
|
/* > if (j == i + 1) then A(i, j) = -1.0 */
|
|
/* > else A(i, j) = 0.0, i, j = 1...M */
|
|
/* > */
|
|
/* > B : if (i == j) then B(i, j) = 1.0 - ALPHA */
|
|
/* > if (j == i + 1) then B(i, j) = 1.0 */
|
|
/* > else B(i, j) = 0.0, i, j = 1...N */
|
|
/* > */
|
|
/* > D : if (i == j) then D(i, j) = 1.0 */
|
|
/* > else D(i, j) = 0.0, i, j = 1...M */
|
|
/* > */
|
|
/* > E : if (i == j) then E(i, j) = 1.0 */
|
|
/* > else E(i, j) = 0.0, i, j = 1...N */
|
|
/* > */
|
|
/* > L = R are chosen from [-10...10], */
|
|
/* > which specifies the right hand sides (C, F). */
|
|
/* > */
|
|
/* > PRTYPE = 2 or 3: Triangular and/or quasi- triangular. */
|
|
/* > */
|
|
/* > A : if (i <= j) then A(i, j) = [-1...1] */
|
|
/* > else A(i, j) = 0.0, i, j = 1...M */
|
|
/* > */
|
|
/* > if (PRTYPE = 3) then */
|
|
/* > A(k + 1, k + 1) = A(k, k) */
|
|
/* > A(k + 1, k) = [-1...1] */
|
|
/* > sign(A(k, k + 1) = -(sin(A(k + 1, k)) */
|
|
/* > k = 1, M - 1, QBLCKA */
|
|
/* > */
|
|
/* > B : if (i <= j) then B(i, j) = [-1...1] */
|
|
/* > else B(i, j) = 0.0, i, j = 1...N */
|
|
/* > */
|
|
/* > if (PRTYPE = 3) then */
|
|
/* > B(k + 1, k + 1) = B(k, k) */
|
|
/* > B(k + 1, k) = [-1...1] */
|
|
/* > sign(B(k, k + 1) = -(sign(B(k + 1, k)) */
|
|
/* > k = 1, N - 1, QBLCKB */
|
|
/* > */
|
|
/* > D : if (i <= j) then D(i, j) = [-1...1]. */
|
|
/* > else D(i, j) = 0.0, i, j = 1...M */
|
|
/* > */
|
|
/* > */
|
|
/* > E : if (i <= j) then D(i, j) = [-1...1] */
|
|
/* > else E(i, j) = 0.0, i, j = 1...N */
|
|
/* > */
|
|
/* > L, R are chosen from [-10...10], */
|
|
/* > which specifies the right hand sides (C, F). */
|
|
/* > */
|
|
/* > PRTYPE = 4 Full */
|
|
/* > A(i, j) = [-10...10] */
|
|
/* > D(i, j) = [-1...1] i,j = 1...M */
|
|
/* > B(i, j) = [-10...10] */
|
|
/* > E(i, j) = [-1...1] i,j = 1...N */
|
|
/* > R(i, j) = [-10...10] */
|
|
/* > L(i, j) = [-1...1] i = 1..M ,j = 1...N */
|
|
/* > */
|
|
/* > L, R specifies the right hand sides (C, F). */
|
|
/* > */
|
|
/* > PRTYPE = 5 special case common and/or close eigs. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlatm5_(integer *prtype, integer *m, integer *n,
|
|
doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
|
|
c__, integer *ldc, doublereal *d__, integer *ldd, doublereal *e,
|
|
integer *lde, doublereal *f, integer *ldf, doublereal *r__, integer *
|
|
ldr, doublereal *l, integer *ldl, doublereal *alpha, integer *qblcka,
|
|
integer *qblckb)
|
|
{
|
|
/* 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, l_dim1, l_offset,
|
|
r_dim1, r_offset, i__1, i__2;
|
|
|
|
/* Local variables */
|
|
integer i__, j, k;
|
|
extern /* Subroutine */ void dgemm_(char *, char *, integer *, integer *,
|
|
integer *, doublereal *, doublereal *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, integer *);
|
|
doublereal imeps, reeps;
|
|
|
|
|
|
/* -- 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..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* 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;
|
|
r_dim1 = *ldr;
|
|
r_offset = 1 + r_dim1 * 1;
|
|
r__ -= r_offset;
|
|
l_dim1 = *ldl;
|
|
l_offset = 1 + l_dim1 * 1;
|
|
l -= l_offset;
|
|
|
|
/* Function Body */
|
|
if (*prtype == 1) {
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *m;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
if (i__ == j) {
|
|
a[i__ + j * a_dim1] = 1.;
|
|
d__[i__ + j * d_dim1] = 1.;
|
|
} else if (i__ == j - 1) {
|
|
a[i__ + j * a_dim1] = -1.;
|
|
d__[i__ + j * d_dim1] = 0.;
|
|
} else {
|
|
a[i__ + j * a_dim1] = 0.;
|
|
d__[i__ + j * d_dim1] = 0.;
|
|
}
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *n;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
if (i__ == j) {
|
|
b[i__ + j * b_dim1] = 1. - *alpha;
|
|
e[i__ + j * e_dim1] = 1.;
|
|
} else if (i__ == j - 1) {
|
|
b[i__ + j * b_dim1] = 1.;
|
|
e[i__ + j * e_dim1] = 0.;
|
|
} else {
|
|
b[i__ + j * b_dim1] = 0.;
|
|
e[i__ + j * e_dim1] = 0.;
|
|
}
|
|
/* L30: */
|
|
}
|
|
/* L40: */
|
|
}
|
|
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *n;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
r__[i__ + j * r_dim1] = (.5 - sin((doublereal) (i__ / j))) *
|
|
20.;
|
|
l[i__ + j * l_dim1] = r__[i__ + j * r_dim1];
|
|
/* L50: */
|
|
}
|
|
/* L60: */
|
|
}
|
|
|
|
} else if (*prtype == 2 || *prtype == 3) {
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *m;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
if (i__ <= j) {
|
|
a[i__ + j * a_dim1] = (.5 - sin((doublereal) i__)) * 2.;
|
|
d__[i__ + j * d_dim1] = (.5 - sin((doublereal) (i__ * j)))
|
|
* 2.;
|
|
} else {
|
|
a[i__ + j * a_dim1] = 0.;
|
|
d__[i__ + j * d_dim1] = 0.;
|
|
}
|
|
/* L70: */
|
|
}
|
|
/* L80: */
|
|
}
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *n;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
if (i__ <= j) {
|
|
b[i__ + j * b_dim1] = (.5 - sin((doublereal) (i__ + j))) *
|
|
2.;
|
|
e[i__ + j * e_dim1] = (.5 - sin((doublereal) j)) * 2.;
|
|
} else {
|
|
b[i__ + j * b_dim1] = 0.;
|
|
e[i__ + j * e_dim1] = 0.;
|
|
}
|
|
/* L90: */
|
|
}
|
|
/* L100: */
|
|
}
|
|
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *n;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
r__[i__ + j * r_dim1] = (.5 - sin((doublereal) (i__ * j))) *
|
|
20.;
|
|
l[i__ + j * l_dim1] = (.5 - sin((doublereal) (i__ + j))) *
|
|
20.;
|
|
/* L110: */
|
|
}
|
|
/* L120: */
|
|
}
|
|
|
|
if (*prtype == 3) {
|
|
if (*qblcka <= 1) {
|
|
*qblcka = 2;
|
|
}
|
|
i__1 = *m - 1;
|
|
i__2 = *qblcka;
|
|
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
|
|
a[k + 1 + (k + 1) * a_dim1] = a[k + k * a_dim1];
|
|
a[k + 1 + k * a_dim1] = -sin(a[k + (k + 1) * a_dim1]);
|
|
/* L130: */
|
|
}
|
|
|
|
if (*qblckb <= 1) {
|
|
*qblckb = 2;
|
|
}
|
|
i__2 = *n - 1;
|
|
i__1 = *qblckb;
|
|
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
|
|
b[k + 1 + (k + 1) * b_dim1] = b[k + k * b_dim1];
|
|
b[k + 1 + k * b_dim1] = -sin(b[k + (k + 1) * b_dim1]);
|
|
/* L140: */
|
|
}
|
|
}
|
|
|
|
} else if (*prtype == 4) {
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *m;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
a[i__ + j * a_dim1] = (.5 - sin((doublereal) (i__ * j))) *
|
|
20.;
|
|
d__[i__ + j * d_dim1] = (.5 - sin((doublereal) (i__ + j))) *
|
|
2.;
|
|
/* L150: */
|
|
}
|
|
/* L160: */
|
|
}
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *n;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
b[i__ + j * b_dim1] = (.5 - sin((doublereal) (i__ + j))) *
|
|
20.;
|
|
e[i__ + j * e_dim1] = (.5 - sin((doublereal) (i__ * j))) * 2.;
|
|
/* L170: */
|
|
}
|
|
/* L180: */
|
|
}
|
|
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *n;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
r__[i__ + j * r_dim1] = (.5 - sin((doublereal) (j / i__))) *
|
|
20.;
|
|
l[i__ + j * l_dim1] = (.5 - sin((doublereal) (i__ * j))) * 2.;
|
|
/* L190: */
|
|
}
|
|
/* L200: */
|
|
}
|
|
|
|
} else if (*prtype >= 5) {
|
|
reeps = 20. / *alpha;
|
|
imeps = -1.5 / *alpha;
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *n;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
r__[i__ + j * r_dim1] = (.5 - sin((doublereal) (i__ * j))) * *
|
|
alpha / 20.;
|
|
l[i__ + j * l_dim1] = (.5 - sin((doublereal) (i__ + j))) * *
|
|
alpha / 20.;
|
|
/* L210: */
|
|
}
|
|
/* L220: */
|
|
}
|
|
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
d__[i__ + i__ * d_dim1] = 1.;
|
|
/* L230: */
|
|
}
|
|
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (i__ <= 4) {
|
|
a[i__ + i__ * a_dim1] = 1.;
|
|
if (i__ > 2) {
|
|
a[i__ + i__ * a_dim1] = reeps + 1.;
|
|
}
|
|
if (i__ % 2 != 0 && i__ < *m) {
|
|
a[i__ + (i__ + 1) * a_dim1] = imeps;
|
|
} else if (i__ > 1) {
|
|
a[i__ + (i__ - 1) * a_dim1] = -imeps;
|
|
}
|
|
} else if (i__ <= 8) {
|
|
if (i__ <= 6) {
|
|
a[i__ + i__ * a_dim1] = reeps;
|
|
} else {
|
|
a[i__ + i__ * a_dim1] = -reeps;
|
|
}
|
|
if (i__ % 2 != 0 && i__ < *m) {
|
|
a[i__ + (i__ + 1) * a_dim1] = 1.;
|
|
} else if (i__ > 1) {
|
|
a[i__ + (i__ - 1) * a_dim1] = -1.;
|
|
}
|
|
} else {
|
|
a[i__ + i__ * a_dim1] = 1.;
|
|
if (i__ % 2 != 0 && i__ < *m) {
|
|
a[i__ + (i__ + 1) * a_dim1] = imeps * 2;
|
|
} else if (i__ > 1) {
|
|
a[i__ + (i__ - 1) * a_dim1] = -imeps * 2;
|
|
}
|
|
}
|
|
/* L240: */
|
|
}
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
e[i__ + i__ * e_dim1] = 1.;
|
|
if (i__ <= 4) {
|
|
b[i__ + i__ * b_dim1] = -1.;
|
|
if (i__ > 2) {
|
|
b[i__ + i__ * b_dim1] = 1. - reeps;
|
|
}
|
|
if (i__ % 2 != 0 && i__ < *n) {
|
|
b[i__ + (i__ + 1) * b_dim1] = imeps;
|
|
} else if (i__ > 1) {
|
|
b[i__ + (i__ - 1) * b_dim1] = -imeps;
|
|
}
|
|
} else if (i__ <= 8) {
|
|
if (i__ <= 6) {
|
|
b[i__ + i__ * b_dim1] = reeps;
|
|
} else {
|
|
b[i__ + i__ * b_dim1] = -reeps;
|
|
}
|
|
if (i__ % 2 != 0 && i__ < *n) {
|
|
b[i__ + (i__ + 1) * b_dim1] = imeps + 1.;
|
|
} else if (i__ > 1) {
|
|
b[i__ + (i__ - 1) * b_dim1] = -1. - imeps;
|
|
}
|
|
} else {
|
|
b[i__ + i__ * b_dim1] = 1. - reeps;
|
|
if (i__ % 2 != 0 && i__ < *n) {
|
|
b[i__ + (i__ + 1) * b_dim1] = imeps * 2;
|
|
} else if (i__ > 1) {
|
|
b[i__ + (i__ - 1) * b_dim1] = -imeps * 2;
|
|
}
|
|
}
|
|
/* L250: */
|
|
}
|
|
}
|
|
|
|
/* Compute rhs (C, F) */
|
|
|
|
dgemm_("N", "N", m, n, m, &c_b29, &a[a_offset], lda, &r__[r_offset], ldr,
|
|
&c_b30, &c__[c_offset], ldc);
|
|
dgemm_("N", "N", m, n, n, &c_b33, &l[l_offset], ldl, &b[b_offset], ldb, &
|
|
c_b29, &c__[c_offset], ldc);
|
|
dgemm_("N", "N", m, n, m, &c_b29, &d__[d_offset], ldd, &r__[r_offset],
|
|
ldr, &c_b30, &f[f_offset], ldf);
|
|
dgemm_("N", "N", m, n, n, &c_b33, &l[l_offset], ldl, &e[e_offset], lde, &
|
|
c_b29, &f[f_offset], ldf);
|
|
|
|
/* End of DLATM5 */
|
|
|
|
return;
|
|
} /* dlatm5_ */
|
|
|