1089 lines
32 KiB
C
1089 lines
32 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__1 = 1;
|
|
static complex c_b19 = {1.f,0.f};
|
|
static complex c_b20 = {0.f,0.f};
|
|
static logical c_false = FALSE_;
|
|
static integer c__3 = 3;
|
|
|
|
/* > \brief \b CTGSNA */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CTGSNA + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctgsna.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctgsna.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctgsna.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CTGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, */
|
|
/* LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK, */
|
|
/* IWORK, INFO ) */
|
|
|
|
/* CHARACTER HOWMNY, JOB */
|
|
/* INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, M, MM, N */
|
|
/* LOGICAL SELECT( * ) */
|
|
/* INTEGER IWORK( * ) */
|
|
/* REAL DIF( * ), S( * ) */
|
|
/* COMPLEX A( LDA, * ), B( LDB, * ), VL( LDVL, * ), */
|
|
/* $ VR( LDVR, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CTGSNA estimates reciprocal condition numbers for specified */
|
|
/* > eigenvalues and/or eigenvectors of a matrix pair (A, B). */
|
|
/* > */
|
|
/* > (A, B) must be in generalized Schur canonical form, that is, A and */
|
|
/* > B are both upper triangular. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOB */
|
|
/* > \verbatim */
|
|
/* > JOB is CHARACTER*1 */
|
|
/* > Specifies whether condition numbers are required for */
|
|
/* > eigenvalues (S) or eigenvectors (DIF): */
|
|
/* > = 'E': for eigenvalues only (S); */
|
|
/* > = 'V': for eigenvectors only (DIF); */
|
|
/* > = 'B': for both eigenvalues and eigenvectors (S and DIF). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] HOWMNY */
|
|
/* > \verbatim */
|
|
/* > HOWMNY is CHARACTER*1 */
|
|
/* > = 'A': compute condition numbers for all eigenpairs; */
|
|
/* > = 'S': compute condition numbers for selected eigenpairs */
|
|
/* > specified by the array SELECT. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SELECT */
|
|
/* > \verbatim */
|
|
/* > SELECT is LOGICAL array, dimension (N) */
|
|
/* > If HOWMNY = 'S', SELECT specifies the eigenpairs for which */
|
|
/* > condition numbers are required. To select condition numbers */
|
|
/* > for the corresponding j-th eigenvalue and/or eigenvector, */
|
|
/* > SELECT(j) must be set to .TRUE.. */
|
|
/* > If HOWMNY = 'A', SELECT is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the square matrix pair (A, B). N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX array, dimension (LDA,N) */
|
|
/* > The upper triangular matrix A in the pair (A,B). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX array, dimension (LDB,N) */
|
|
/* > The upper triangular matrix B in the pair (A, B). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VL */
|
|
/* > \verbatim */
|
|
/* > VL is COMPLEX array, dimension (LDVL,M) */
|
|
/* > IF JOB = 'E' or 'B', VL must contain left eigenvectors of */
|
|
/* > (A, B), corresponding to the eigenpairs specified by HOWMNY */
|
|
/* > and SELECT. The eigenvectors must be stored in consecutive */
|
|
/* > columns of VL, as returned by CTGEVC. */
|
|
/* > If JOB = 'V', VL is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVL */
|
|
/* > \verbatim */
|
|
/* > LDVL is INTEGER */
|
|
/* > The leading dimension of the array VL. LDVL >= 1; and */
|
|
/* > If JOB = 'E' or 'B', LDVL >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] VR */
|
|
/* > \verbatim */
|
|
/* > VR is COMPLEX array, dimension (LDVR,M) */
|
|
/* > IF JOB = 'E' or 'B', VR must contain right eigenvectors of */
|
|
/* > (A, B), corresponding to the eigenpairs specified by HOWMNY */
|
|
/* > and SELECT. The eigenvectors must be stored in consecutive */
|
|
/* > columns of VR, as returned by CTGEVC. */
|
|
/* > If JOB = 'V', VR is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDVR */
|
|
/* > \verbatim */
|
|
/* > LDVR is INTEGER */
|
|
/* > The leading dimension of the array VR. LDVR >= 1; */
|
|
/* > If JOB = 'E' or 'B', LDVR >= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is REAL array, dimension (MM) */
|
|
/* > If JOB = 'E' or 'B', the reciprocal condition numbers of the */
|
|
/* > selected eigenvalues, stored in consecutive elements of the */
|
|
/* > array. */
|
|
/* > If JOB = 'V', S is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DIF */
|
|
/* > \verbatim */
|
|
/* > DIF is REAL array, dimension (MM) */
|
|
/* > If JOB = 'V' or 'B', the estimated reciprocal condition */
|
|
/* > numbers of the selected eigenvectors, stored in consecutive */
|
|
/* > elements of the array. */
|
|
/* > If the eigenvalues cannot be reordered to compute DIF(j), */
|
|
/* > DIF(j) is set to 0; this can only occur when the true value */
|
|
/* > would be very small anyway. */
|
|
/* > For each eigenvalue/vector specified by SELECT, DIF stores */
|
|
/* > a Frobenius norm-based estimate of Difl. */
|
|
/* > If JOB = 'E', DIF is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] MM */
|
|
/* > \verbatim */
|
|
/* > MM is INTEGER */
|
|
/* > The number of elements in the arrays S and DIF. MM >= M. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of elements of the arrays S and DIF used to store */
|
|
/* > the specified condition numbers; for each selected eigenvalue */
|
|
/* > one element is used. If HOWMNY = 'A', M is set to N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. LWORK >= f2cmax(1,N). */
|
|
/* > If JOB = 'V' or 'B', LWORK >= f2cmax(1,2*N*N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (N+2) */
|
|
/* > If JOB = 'E', IWORK is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: Successful exit */
|
|
/* > < 0: If INFO = -i, the i-th argument had an illegal value */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complexOTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The reciprocal of the condition number of the i-th generalized */
|
|
/* > eigenvalue w = (a, b) is defined as */
|
|
/* > */
|
|
/* > S(I) = (|v**HAu|**2 + |v**HBu|**2)**(1/2) / (norm(u)*norm(v)) */
|
|
/* > */
|
|
/* > where u and v are the right and left eigenvectors of (A, B) */
|
|
/* > corresponding to w; |z| denotes the absolute value of the complex */
|
|
/* > number, and norm(u) denotes the 2-norm of the vector u. The pair */
|
|
/* > (a, b) corresponds to an eigenvalue w = a/b (= v**HAu/v**HBu) of the */
|
|
/* > matrix pair (A, B). If both a and b equal zero, then (A,B) is */
|
|
/* > singular and S(I) = -1 is returned. */
|
|
/* > */
|
|
/* > An approximate error bound on the chordal distance between the i-th */
|
|
/* > computed generalized eigenvalue w and the corresponding exact */
|
|
/* > eigenvalue lambda is */
|
|
/* > */
|
|
/* > chord(w, lambda) <= EPS * norm(A, B) / S(I), */
|
|
/* > */
|
|
/* > where EPS is the machine precision. */
|
|
/* > */
|
|
/* > The reciprocal of the condition number of the right eigenvector u */
|
|
/* > and left eigenvector v corresponding to the generalized eigenvalue w */
|
|
/* > is defined as follows. Suppose */
|
|
/* > */
|
|
/* > (A, B) = ( a * ) ( b * ) 1 */
|
|
/* > ( 0 A22 ),( 0 B22 ) n-1 */
|
|
/* > 1 n-1 1 n-1 */
|
|
/* > */
|
|
/* > Then the reciprocal condition number DIF(I) is */
|
|
/* > */
|
|
/* > Difl[(a, b), (A22, B22)] = sigma-f2cmin( Zl ) */
|
|
/* > */
|
|
/* > where sigma-f2cmin(Zl) denotes the smallest singular value of */
|
|
/* > */
|
|
/* > Zl = [ kron(a, In-1) -kron(1, A22) ] */
|
|
/* > [ kron(b, In-1) -kron(1, B22) ]. */
|
|
/* > */
|
|
/* > Here In-1 is the identity matrix of size n-1 and X**H is the conjugate */
|
|
/* > transpose of X. kron(X, Y) is the Kronecker product between the */
|
|
/* > matrices X and Y. */
|
|
/* > */
|
|
/* > We approximate the smallest singular value of Zl with an upper */
|
|
/* > bound. This is done by CLATDF. */
|
|
/* > */
|
|
/* > An approximate error bound for a computed eigenvector VL(i) or */
|
|
/* > VR(i) is given by */
|
|
/* > */
|
|
/* > EPS * norm(A, B) / DIF(i). */
|
|
/* > */
|
|
/* > See ref. [2-3] for more details and further references. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
|
|
/* > Umea University, S-901 87 Umea, Sweden. */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
|
|
/* > Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
|
|
/* > M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
|
|
/* > Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */
|
|
/* > */
|
|
/* > [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
|
|
/* > Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
|
|
/* > Estimation: Theory, Algorithms and Software, Report */
|
|
/* > UMINF - 94.04, Department of Computing Science, Umea University, */
|
|
/* > S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. */
|
|
/* > To appear in Numerical Algorithms, 1996. */
|
|
/* > */
|
|
/* > [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
|
|
/* > for Solving the Generalized Sylvester Equation and Estimating the */
|
|
/* > Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
|
|
/* > Department of Computing Science, Umea University, S-901 87 Umea, */
|
|
/* > Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
|
|
/* > Note 75. */
|
|
/* > To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void ctgsna_(char *job, char *howmny, logical *select,
|
|
integer *n, complex *a, integer *lda, complex *b, integer *ldb,
|
|
complex *vl, integer *ldvl, complex *vr, integer *ldvr, real *s, real
|
|
*dif, integer *mm, integer *m, complex *work, integer *lwork, integer
|
|
*iwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1,
|
|
vr_offset, i__1;
|
|
real r__1, r__2;
|
|
complex q__1;
|
|
|
|
/* Local variables */
|
|
real cond;
|
|
integer ierr, ifst;
|
|
real lnrm;
|
|
complex yhax, yhbx;
|
|
integer ilst;
|
|
real rnrm;
|
|
integer i__, k;
|
|
real scale;
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extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
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*, complex *, integer *);
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extern logical lsame_(char *, char *);
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extern /* Subroutine */ void cgemv_(char *, integer *, integer *, complex *
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, complex *, integer *, complex *, integer *, complex *, complex *
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, integer *);
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integer lwmin;
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logical wants;
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complex dummy[1];
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integer n1, n2;
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extern real scnrm2_(integer *, complex *, integer *), slapy2_(real *,
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real *);
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complex dummy1[1];
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extern /* Subroutine */ void slabad_(real *, real *);
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integer ks;
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extern real slamch_(char *);
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extern /* Subroutine */ void clacpy_(char *, integer *, integer *, complex
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*, integer *, complex *, integer *), ctgexc_(logical *,
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logical *, integer *, complex *, integer *, complex *, integer *,
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complex *, integer *, complex *, integer *, integer *, integer *,
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integer *);
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extern int xerbla_(char *, integer *, ftnlen);
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real bignum;
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logical wantbh, wantdf, somcon;
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extern /* Subroutine */ void ctgsyl_(char *, integer *, integer *, integer
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*, complex *, integer *, complex *, integer *, complex *, integer
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*, complex *, integer *, complex *, integer *, complex *, integer
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*, real *, real *, complex *, integer *, integer *, integer *);
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real smlnum;
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logical lquery;
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real eps;
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/* -- LAPACK computational routine (version 3.7.0) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* December 2016 */
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/* ===================================================================== */
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/* Decode and test the input parameters */
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/* Parameter adjustments */
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--select;
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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a -= a_offset;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1 * 1;
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b -= b_offset;
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vl_dim1 = *ldvl;
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vl_offset = 1 + vl_dim1 * 1;
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vl -= vl_offset;
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vr_dim1 = *ldvr;
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vr_offset = 1 + vr_dim1 * 1;
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vr -= vr_offset;
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--s;
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--dif;
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--work;
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--iwork;
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/* Function Body */
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wantbh = lsame_(job, "B");
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wants = lsame_(job, "E") || wantbh;
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wantdf = lsame_(job, "V") || wantbh;
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somcon = lsame_(howmny, "S");
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*info = 0;
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lquery = *lwork == -1;
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if (! wants && ! wantdf) {
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*info = -1;
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} else if (! lsame_(howmny, "A") && ! somcon) {
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*info = -2;
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} else if (*n < 0) {
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*info = -4;
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} else if (*lda < f2cmax(1,*n)) {
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*info = -6;
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} else if (*ldb < f2cmax(1,*n)) {
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*info = -8;
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} else if (wants && *ldvl < *n) {
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*info = -10;
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} else if (wants && *ldvr < *n) {
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*info = -12;
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} else {
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/* Set M to the number of eigenpairs for which condition numbers */
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/* are required, and test MM. */
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if (somcon) {
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*m = 0;
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i__1 = *n;
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for (k = 1; k <= i__1; ++k) {
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if (select[k]) {
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++(*m);
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}
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/* L10: */
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}
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} else {
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*m = *n;
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}
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if (*n == 0) {
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lwmin = 1;
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} else if (lsame_(job, "V") || lsame_(job,
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"B")) {
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lwmin = (*n << 1) * *n;
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} else {
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lwmin = *n;
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}
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work[1].r = (real) lwmin, work[1].i = 0.f;
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if (*mm < *m) {
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*info = -15;
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} else if (*lwork < lwmin && ! lquery) {
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*info = -18;
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}
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("CTGSNA", &i__1, (ftnlen)6);
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return;
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} else if (lquery) {
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return;
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}
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/* Quick return if possible */
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if (*n == 0) {
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return;
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}
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/* Get machine constants */
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eps = slamch_("P");
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smlnum = slamch_("S") / eps;
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bignum = 1.f / smlnum;
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slabad_(&smlnum, &bignum);
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ks = 0;
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i__1 = *n;
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for (k = 1; k <= i__1; ++k) {
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/* Determine whether condition numbers are required for the k-th */
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/* eigenpair. */
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if (somcon) {
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if (! select[k]) {
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goto L20;
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}
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}
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++ks;
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if (wants) {
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/* Compute the reciprocal condition number of the k-th */
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/* eigenvalue. */
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rnrm = scnrm2_(n, &vr[ks * vr_dim1 + 1], &c__1);
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lnrm = scnrm2_(n, &vl[ks * vl_dim1 + 1], &c__1);
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cgemv_("N", n, n, &c_b19, &a[a_offset], lda, &vr[ks * vr_dim1 + 1]
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, &c__1, &c_b20, &work[1], &c__1);
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cdotc_(&q__1, n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1);
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yhax.r = q__1.r, yhax.i = q__1.i;
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cgemv_("N", n, n, &c_b19, &b[b_offset], ldb, &vr[ks * vr_dim1 + 1]
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, &c__1, &c_b20, &work[1], &c__1);
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cdotc_(&q__1, n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1);
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yhbx.r = q__1.r, yhbx.i = q__1.i;
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r__1 = c_abs(&yhax);
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r__2 = c_abs(&yhbx);
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cond = slapy2_(&r__1, &r__2);
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if (cond == 0.f) {
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s[ks] = -1.f;
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} else {
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s[ks] = cond / (rnrm * lnrm);
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}
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}
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if (wantdf) {
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if (*n == 1) {
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r__1 = c_abs(&a[a_dim1 + 1]);
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r__2 = c_abs(&b[b_dim1 + 1]);
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dif[ks] = slapy2_(&r__1, &r__2);
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} else {
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/* Estimate the reciprocal condition number of the k-th */
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/* eigenvectors. */
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/* Copy the matrix (A, B) to the array WORK and move the */
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/* (k,k)th pair to the (1,1) position. */
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clacpy_("Full", n, n, &a[a_offset], lda, &work[1], n);
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clacpy_("Full", n, n, &b[b_offset], ldb, &work[*n * *n + 1],
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n);
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ifst = k;
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ilst = 1;
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ctgexc_(&c_false, &c_false, n, &work[1], n, &work[*n * *n + 1]
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, n, dummy, &c__1, dummy1, &c__1, &ifst, &ilst, &ierr)
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;
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if (ierr > 0) {
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/* Ill-conditioned problem - swap rejected. */
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dif[ks] = 0.f;
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} else {
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/* Reordering successful, solve generalized Sylvester */
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/* equation for R and L, */
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/* A22 * R - L * A11 = A12 */
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/* B22 * R - L * B11 = B12, */
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/* and compute estimate of Difl[(A11,B11), (A22, B22)]. */
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n1 = 1;
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n2 = *n - n1;
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i__ = *n * *n + 1;
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ctgsyl_("N", &c__3, &n2, &n1, &work[*n * n1 + n1 + 1], n,
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&work[1], n, &work[n1 + 1], n, &work[*n * n1 + n1
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+ i__], n, &work[i__], n, &work[n1 + i__], n, &
|
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scale, &dif[ks], dummy, &c__1, &iwork[1], &ierr);
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}
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}
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}
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L20:
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;
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}
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work[1].r = (real) lwmin, work[1].i = 0.f;
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return;
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/* End of CTGSNA */
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} /* ctgsna_ */
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