1194 lines
30 KiB
C
1194 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 integer c__1 = 1;
|
|
static real c_b35 = 10.f;
|
|
static real c_b71 = .5f;
|
|
|
|
/* > \brief \b SGGBAL */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SGGBAL + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sggbal.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sggbal.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sggbal.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SGGBAL( JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE, */
|
|
/* RSCALE, WORK, INFO ) */
|
|
|
|
/* CHARACTER JOB */
|
|
/* INTEGER IHI, ILO, INFO, LDA, LDB, N */
|
|
/* REAL A( LDA, * ), B( LDB, * ), LSCALE( * ), */
|
|
/* $ RSCALE( * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SGGBAL balances a pair of general real matrices (A,B). This */
|
|
/* > involves, first, permuting A and B by similarity transformations to */
|
|
/* > isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N */
|
|
/* > elements on the diagonal; and second, applying a diagonal similarity */
|
|
/* > transformation to rows and columns ILO to IHI to make the rows */
|
|
/* > and columns as close in norm as possible. Both steps are optional. */
|
|
/* > */
|
|
/* > Balancing may reduce the 1-norm of the matrices, and improve the */
|
|
/* > accuracy of the computed eigenvalues and/or eigenvectors in the */
|
|
/* > generalized eigenvalue problem A*x = lambda*B*x. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] JOB */
|
|
/* > \verbatim */
|
|
/* > JOB is CHARACTER*1 */
|
|
/* > Specifies the operations to be performed on A and B: */
|
|
/* > = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0 */
|
|
/* > and RSCALE(I) = 1.0 for i = 1,...,N. */
|
|
/* > = 'P': permute only; */
|
|
/* > = 'S': scale only; */
|
|
/* > = 'B': both permute and scale. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrices A and B. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is REAL array, dimension (LDA,N) */
|
|
/* > On entry, the input matrix A. */
|
|
/* > On exit, A is overwritten by the balanced matrix. */
|
|
/* > If JOB = 'N', A is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is REAL array, dimension (LDB,N) */
|
|
/* > On entry, the input matrix B. */
|
|
/* > On exit, B is overwritten by the balanced matrix. */
|
|
/* > If JOB = 'N', B is not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ILO */
|
|
/* > \verbatim */
|
|
/* > ILO is INTEGER */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IHI */
|
|
/* > \verbatim */
|
|
/* > IHI is INTEGER */
|
|
/* > ILO and IHI are set to integers such that on exit */
|
|
/* > A(i,j) = 0 and B(i,j) = 0 if i > j and */
|
|
/* > j = 1,...,ILO-1 or i = IHI+1,...,N. */
|
|
/* > If JOB = 'N' or 'S', ILO = 1 and IHI = N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] LSCALE */
|
|
/* > \verbatim */
|
|
/* > LSCALE is REAL array, dimension (N) */
|
|
/* > Details of the permutations and scaling factors applied */
|
|
/* > to the left side of A and B. If P(j) is the index of the */
|
|
/* > row interchanged with row j, and D(j) */
|
|
/* > is the scaling factor applied to row j, then */
|
|
/* > LSCALE(j) = P(j) for J = 1,...,ILO-1 */
|
|
/* > = D(j) for J = ILO,...,IHI */
|
|
/* > = P(j) for J = IHI+1,...,N. */
|
|
/* > The order in which the interchanges are made is N to IHI+1, */
|
|
/* > then 1 to ILO-1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RSCALE */
|
|
/* > \verbatim */
|
|
/* > RSCALE is REAL array, dimension (N) */
|
|
/* > Details of the permutations and scaling factors applied */
|
|
/* > to the right side of A and B. If P(j) is the index of the */
|
|
/* > column interchanged with column j, and D(j) */
|
|
/* > is the scaling factor applied to column j, then */
|
|
/* > LSCALE(j) = P(j) for J = 1,...,ILO-1 */
|
|
/* > = D(j) for J = ILO,...,IHI */
|
|
/* > = P(j) for J = IHI+1,...,N. */
|
|
/* > The order in which the interchanges are made is N to IHI+1, */
|
|
/* > then 1 to ILO-1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension (lwork) */
|
|
/* > lwork must be at least f2cmax(1,6*N) when JOB = 'S' or 'B', and */
|
|
/* > at least 1 when JOB = 'N' or 'P'. */
|
|
/* > \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 realGBcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > See R.C. WARD, Balancing the generalized eigenvalue problem, */
|
|
/* > SIAM J. Sci. Stat. Comp. 2 (1981), 141-152. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void sggbal_(char *job, integer *n, real *a, integer *lda,
|
|
real *b, integer *ldb, integer *ilo, integer *ihi, real *lscale, real
|
|
*rscale, real *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
|
|
real r__1, r__2, r__3;
|
|
|
|
/* Local variables */
|
|
integer lcab;
|
|
real beta, coef;
|
|
integer irab, lrab;
|
|
real basl, cmax;
|
|
extern real sdot_(integer *, real *, integer *, real *, integer *);
|
|
real coef2, coef5;
|
|
integer i__, j, k, l, m;
|
|
real gamma, t, alpha;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
|
|
real sfmin, sfmax;
|
|
integer iflow;
|
|
extern /* Subroutine */ void sswap_(integer *, real *, integer *, real *,
|
|
integer *);
|
|
integer kount;
|
|
extern /* Subroutine */ void saxpy_(integer *, real *, real *, integer *,
|
|
real *, integer *);
|
|
integer jc;
|
|
real ta, tb, tc;
|
|
integer ir, it;
|
|
real ew;
|
|
integer nr;
|
|
real pgamma;
|
|
extern real slamch_(char *);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer isamax_(integer *, real *, integer *);
|
|
integer lsfmin, lsfmax, ip1, jp1, lm1;
|
|
real cab, rab, ewc, cor, sum;
|
|
integer nrp2, icab;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
--lscale;
|
|
--rscale;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S")
|
|
&& ! lsame_(job, "B")) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -4;
|
|
} else if (*ldb < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SGGBAL", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
*ilo = 1;
|
|
*ihi = *n;
|
|
return;
|
|
}
|
|
|
|
if (*n == 1) {
|
|
*ilo = 1;
|
|
*ihi = *n;
|
|
lscale[1] = 1.f;
|
|
rscale[1] = 1.f;
|
|
return;
|
|
}
|
|
|
|
if (lsame_(job, "N")) {
|
|
*ilo = 1;
|
|
*ihi = *n;
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
lscale[i__] = 1.f;
|
|
rscale[i__] = 1.f;
|
|
/* L10: */
|
|
}
|
|
return;
|
|
}
|
|
|
|
k = 1;
|
|
l = *n;
|
|
if (lsame_(job, "S")) {
|
|
goto L190;
|
|
}
|
|
|
|
goto L30;
|
|
|
|
/* Permute the matrices A and B to isolate the eigenvalues. */
|
|
|
|
/* Find row with one nonzero in columns 1 through L */
|
|
|
|
L20:
|
|
l = lm1;
|
|
if (l != 1) {
|
|
goto L30;
|
|
}
|
|
|
|
rscale[1] = 1.f;
|
|
lscale[1] = 1.f;
|
|
goto L190;
|
|
|
|
L30:
|
|
lm1 = l - 1;
|
|
for (i__ = l; i__ >= 1; --i__) {
|
|
i__1 = lm1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
jp1 = j + 1;
|
|
if (a[i__ + j * a_dim1] != 0.f || b[i__ + j * b_dim1] != 0.f) {
|
|
goto L50;
|
|
}
|
|
/* L40: */
|
|
}
|
|
j = l;
|
|
goto L70;
|
|
|
|
L50:
|
|
i__1 = l;
|
|
for (j = jp1; j <= i__1; ++j) {
|
|
if (a[i__ + j * a_dim1] != 0.f || b[i__ + j * b_dim1] != 0.f) {
|
|
goto L80;
|
|
}
|
|
/* L60: */
|
|
}
|
|
j = jp1 - 1;
|
|
|
|
L70:
|
|
m = l;
|
|
iflow = 1;
|
|
goto L160;
|
|
L80:
|
|
;
|
|
}
|
|
goto L100;
|
|
|
|
/* Find column with one nonzero in rows K through N */
|
|
|
|
L90:
|
|
++k;
|
|
|
|
L100:
|
|
i__1 = l;
|
|
for (j = k; j <= i__1; ++j) {
|
|
i__2 = lm1;
|
|
for (i__ = k; i__ <= i__2; ++i__) {
|
|
ip1 = i__ + 1;
|
|
if (a[i__ + j * a_dim1] != 0.f || b[i__ + j * b_dim1] != 0.f) {
|
|
goto L120;
|
|
}
|
|
/* L110: */
|
|
}
|
|
i__ = l;
|
|
goto L140;
|
|
L120:
|
|
i__2 = l;
|
|
for (i__ = ip1; i__ <= i__2; ++i__) {
|
|
if (a[i__ + j * a_dim1] != 0.f || b[i__ + j * b_dim1] != 0.f) {
|
|
goto L150;
|
|
}
|
|
/* L130: */
|
|
}
|
|
i__ = ip1 - 1;
|
|
L140:
|
|
m = k;
|
|
iflow = 2;
|
|
goto L160;
|
|
L150:
|
|
;
|
|
}
|
|
goto L190;
|
|
|
|
/* Permute rows M and I */
|
|
|
|
L160:
|
|
lscale[m] = (real) i__;
|
|
if (i__ == m) {
|
|
goto L170;
|
|
}
|
|
i__1 = *n - k + 1;
|
|
sswap_(&i__1, &a[i__ + k * a_dim1], lda, &a[m + k * a_dim1], lda);
|
|
i__1 = *n - k + 1;
|
|
sswap_(&i__1, &b[i__ + k * b_dim1], ldb, &b[m + k * b_dim1], ldb);
|
|
|
|
/* Permute columns M and J */
|
|
|
|
L170:
|
|
rscale[m] = (real) j;
|
|
if (j == m) {
|
|
goto L180;
|
|
}
|
|
sswap_(&l, &a[j * a_dim1 + 1], &c__1, &a[m * a_dim1 + 1], &c__1);
|
|
sswap_(&l, &b[j * b_dim1 + 1], &c__1, &b[m * b_dim1 + 1], &c__1);
|
|
|
|
L180:
|
|
switch (iflow) {
|
|
case 1: goto L20;
|
|
case 2: goto L90;
|
|
}
|
|
|
|
L190:
|
|
*ilo = k;
|
|
*ihi = l;
|
|
|
|
if (lsame_(job, "P")) {
|
|
i__1 = *ihi;
|
|
for (i__ = *ilo; i__ <= i__1; ++i__) {
|
|
lscale[i__] = 1.f;
|
|
rscale[i__] = 1.f;
|
|
/* L195: */
|
|
}
|
|
return;
|
|
}
|
|
|
|
if (*ilo == *ihi) {
|
|
return;
|
|
}
|
|
|
|
/* Balance the submatrix in rows ILO to IHI. */
|
|
|
|
nr = *ihi - *ilo + 1;
|
|
i__1 = *ihi;
|
|
for (i__ = *ilo; i__ <= i__1; ++i__) {
|
|
rscale[i__] = 0.f;
|
|
lscale[i__] = 0.f;
|
|
|
|
work[i__] = 0.f;
|
|
work[i__ + *n] = 0.f;
|
|
work[i__ + (*n << 1)] = 0.f;
|
|
work[i__ + *n * 3] = 0.f;
|
|
work[i__ + (*n << 2)] = 0.f;
|
|
work[i__ + *n * 5] = 0.f;
|
|
/* L200: */
|
|
}
|
|
|
|
/* Compute right side vector in resulting linear equations */
|
|
|
|
basl = r_lg10(&c_b35);
|
|
i__1 = *ihi;
|
|
for (i__ = *ilo; i__ <= i__1; ++i__) {
|
|
i__2 = *ihi;
|
|
for (j = *ilo; j <= i__2; ++j) {
|
|
tb = b[i__ + j * b_dim1];
|
|
ta = a[i__ + j * a_dim1];
|
|
if (ta == 0.f) {
|
|
goto L210;
|
|
}
|
|
r__1 = abs(ta);
|
|
ta = r_lg10(&r__1) / basl;
|
|
L210:
|
|
if (tb == 0.f) {
|
|
goto L220;
|
|
}
|
|
r__1 = abs(tb);
|
|
tb = r_lg10(&r__1) / basl;
|
|
L220:
|
|
work[i__ + (*n << 2)] = work[i__ + (*n << 2)] - ta - tb;
|
|
work[j + *n * 5] = work[j + *n * 5] - ta - tb;
|
|
/* L230: */
|
|
}
|
|
/* L240: */
|
|
}
|
|
|
|
coef = 1.f / (real) (nr << 1);
|
|
coef2 = coef * coef;
|
|
coef5 = coef2 * .5f;
|
|
nrp2 = nr + 2;
|
|
beta = 0.f;
|
|
it = 1;
|
|
|
|
/* Start generalized conjugate gradient iteration */
|
|
|
|
L250:
|
|
|
|
gamma = sdot_(&nr, &work[*ilo + (*n << 2)], &c__1, &work[*ilo + (*n << 2)]
|
|
, &c__1) + sdot_(&nr, &work[*ilo + *n * 5], &c__1, &work[*ilo + *
|
|
n * 5], &c__1);
|
|
|
|
ew = 0.f;
|
|
ewc = 0.f;
|
|
i__1 = *ihi;
|
|
for (i__ = *ilo; i__ <= i__1; ++i__) {
|
|
ew += work[i__ + (*n << 2)];
|
|
ewc += work[i__ + *n * 5];
|
|
/* L260: */
|
|
}
|
|
|
|
/* Computing 2nd power */
|
|
r__1 = ew;
|
|
/* Computing 2nd power */
|
|
r__2 = ewc;
|
|
/* Computing 2nd power */
|
|
r__3 = ew - ewc;
|
|
gamma = coef * gamma - coef2 * (r__1 * r__1 + r__2 * r__2) - coef5 * (
|
|
r__3 * r__3);
|
|
if (gamma == 0.f) {
|
|
goto L350;
|
|
}
|
|
if (it != 1) {
|
|
beta = gamma / pgamma;
|
|
}
|
|
t = coef5 * (ewc - ew * 3.f);
|
|
tc = coef5 * (ew - ewc * 3.f);
|
|
|
|
sscal_(&nr, &beta, &work[*ilo], &c__1);
|
|
sscal_(&nr, &beta, &work[*ilo + *n], &c__1);
|
|
|
|
saxpy_(&nr, &coef, &work[*ilo + (*n << 2)], &c__1, &work[*ilo + *n], &
|
|
c__1);
|
|
saxpy_(&nr, &coef, &work[*ilo + *n * 5], &c__1, &work[*ilo], &c__1);
|
|
|
|
i__1 = *ihi;
|
|
for (i__ = *ilo; i__ <= i__1; ++i__) {
|
|
work[i__] += tc;
|
|
work[i__ + *n] += t;
|
|
/* L270: */
|
|
}
|
|
|
|
/* Apply matrix to vector */
|
|
|
|
i__1 = *ihi;
|
|
for (i__ = *ilo; i__ <= i__1; ++i__) {
|
|
kount = 0;
|
|
sum = 0.f;
|
|
i__2 = *ihi;
|
|
for (j = *ilo; j <= i__2; ++j) {
|
|
if (a[i__ + j * a_dim1] == 0.f) {
|
|
goto L280;
|
|
}
|
|
++kount;
|
|
sum += work[j];
|
|
L280:
|
|
if (b[i__ + j * b_dim1] == 0.f) {
|
|
goto L290;
|
|
}
|
|
++kount;
|
|
sum += work[j];
|
|
L290:
|
|
;
|
|
}
|
|
work[i__ + (*n << 1)] = (real) kount * work[i__ + *n] + sum;
|
|
/* L300: */
|
|
}
|
|
|
|
i__1 = *ihi;
|
|
for (j = *ilo; j <= i__1; ++j) {
|
|
kount = 0;
|
|
sum = 0.f;
|
|
i__2 = *ihi;
|
|
for (i__ = *ilo; i__ <= i__2; ++i__) {
|
|
if (a[i__ + j * a_dim1] == 0.f) {
|
|
goto L310;
|
|
}
|
|
++kount;
|
|
sum += work[i__ + *n];
|
|
L310:
|
|
if (b[i__ + j * b_dim1] == 0.f) {
|
|
goto L320;
|
|
}
|
|
++kount;
|
|
sum += work[i__ + *n];
|
|
L320:
|
|
;
|
|
}
|
|
work[j + *n * 3] = (real) kount * work[j] + sum;
|
|
/* L330: */
|
|
}
|
|
|
|
sum = sdot_(&nr, &work[*ilo + *n], &c__1, &work[*ilo + (*n << 1)], &c__1)
|
|
+ sdot_(&nr, &work[*ilo], &c__1, &work[*ilo + *n * 3], &c__1);
|
|
alpha = gamma / sum;
|
|
|
|
/* Determine correction to current iteration */
|
|
|
|
cmax = 0.f;
|
|
i__1 = *ihi;
|
|
for (i__ = *ilo; i__ <= i__1; ++i__) {
|
|
cor = alpha * work[i__ + *n];
|
|
if (abs(cor) > cmax) {
|
|
cmax = abs(cor);
|
|
}
|
|
lscale[i__] += cor;
|
|
cor = alpha * work[i__];
|
|
if (abs(cor) > cmax) {
|
|
cmax = abs(cor);
|
|
}
|
|
rscale[i__] += cor;
|
|
/* L340: */
|
|
}
|
|
if (cmax < .5f) {
|
|
goto L350;
|
|
}
|
|
|
|
r__1 = -alpha;
|
|
saxpy_(&nr, &r__1, &work[*ilo + (*n << 1)], &c__1, &work[*ilo + (*n << 2)]
|
|
, &c__1);
|
|
r__1 = -alpha;
|
|
saxpy_(&nr, &r__1, &work[*ilo + *n * 3], &c__1, &work[*ilo + *n * 5], &
|
|
c__1);
|
|
|
|
pgamma = gamma;
|
|
++it;
|
|
if (it <= nrp2) {
|
|
goto L250;
|
|
}
|
|
|
|
/* End generalized conjugate gradient iteration */
|
|
|
|
L350:
|
|
sfmin = slamch_("S");
|
|
sfmax = 1.f / sfmin;
|
|
lsfmin = (integer) (r_lg10(&sfmin) / basl + 1.f);
|
|
lsfmax = (integer) (r_lg10(&sfmax) / basl);
|
|
i__1 = *ihi;
|
|
for (i__ = *ilo; i__ <= i__1; ++i__) {
|
|
i__2 = *n - *ilo + 1;
|
|
irab = isamax_(&i__2, &a[i__ + *ilo * a_dim1], lda);
|
|
rab = (r__1 = a[i__ + (irab + *ilo - 1) * a_dim1], abs(r__1));
|
|
i__2 = *n - *ilo + 1;
|
|
irab = isamax_(&i__2, &b[i__ + *ilo * b_dim1], ldb);
|
|
/* Computing MAX */
|
|
r__2 = rab, r__3 = (r__1 = b[i__ + (irab + *ilo - 1) * b_dim1], abs(
|
|
r__1));
|
|
rab = f2cmax(r__2,r__3);
|
|
r__1 = rab + sfmin;
|
|
lrab = (integer) (r_lg10(&r__1) / basl + 1.f);
|
|
ir = lscale[i__] + r_sign(&c_b71, &lscale[i__]);
|
|
/* Computing MIN */
|
|
i__2 = f2cmax(ir,lsfmin), i__2 = f2cmin(i__2,lsfmax), i__3 = lsfmax - lrab;
|
|
ir = f2cmin(i__2,i__3);
|
|
lscale[i__] = pow_ri(&c_b35, &ir);
|
|
icab = isamax_(ihi, &a[i__ * a_dim1 + 1], &c__1);
|
|
cab = (r__1 = a[icab + i__ * a_dim1], abs(r__1));
|
|
icab = isamax_(ihi, &b[i__ * b_dim1 + 1], &c__1);
|
|
/* Computing MAX */
|
|
r__2 = cab, r__3 = (r__1 = b[icab + i__ * b_dim1], abs(r__1));
|
|
cab = f2cmax(r__2,r__3);
|
|
r__1 = cab + sfmin;
|
|
lcab = (integer) (r_lg10(&r__1) / basl + 1.f);
|
|
jc = rscale[i__] + r_sign(&c_b71, &rscale[i__]);
|
|
/* Computing MIN */
|
|
i__2 = f2cmax(jc,lsfmin), i__2 = f2cmin(i__2,lsfmax), i__3 = lsfmax - lcab;
|
|
jc = f2cmin(i__2,i__3);
|
|
rscale[i__] = pow_ri(&c_b35, &jc);
|
|
/* L360: */
|
|
}
|
|
|
|
/* Row scaling of matrices A and B */
|
|
|
|
i__1 = *ihi;
|
|
for (i__ = *ilo; i__ <= i__1; ++i__) {
|
|
i__2 = *n - *ilo + 1;
|
|
sscal_(&i__2, &lscale[i__], &a[i__ + *ilo * a_dim1], lda);
|
|
i__2 = *n - *ilo + 1;
|
|
sscal_(&i__2, &lscale[i__], &b[i__ + *ilo * b_dim1], ldb);
|
|
/* L370: */
|
|
}
|
|
|
|
/* Column scaling of matrices A and B */
|
|
|
|
i__1 = *ihi;
|
|
for (j = *ilo; j <= i__1; ++j) {
|
|
sscal_(ihi, &rscale[j], &a[j * a_dim1 + 1], &c__1);
|
|
sscal_(ihi, &rscale[j], &b[j * b_dim1 + 1], &c__1);
|
|
/* L380: */
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of SGGBAL */
|
|
|
|
} /* sggbal_ */
|
|
|