711 lines
18 KiB
C
711 lines
18 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 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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#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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/* -- translated by f2c (version 20000121).
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You must link the resulting object file with the libraries:
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-lf2c -lm (in that order)
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*/
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/* Table of constant values */
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static integer c__1 = 1;
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/* > \brief \b SGEBAL */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download SGEBAL + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgebal.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgebal.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgebal.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE SGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO ) */
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/* CHARACTER JOB */
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/* INTEGER IHI, ILO, INFO, LDA, N */
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/* REAL A( LDA, * ), SCALE( * ) */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > SGEBAL balances a general real matrix A. This involves, first, */
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/* > permuting A by a similarity transformation to isolate eigenvalues */
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/* > in the first 1 to ILO-1 and last IHI+1 to N elements on the */
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/* > diagonal; and second, applying a diagonal similarity transformation */
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/* > to rows and columns ILO to IHI to make the rows and columns as */
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/* > close in norm as possible. Both steps are optional. */
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/* > */
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/* > Balancing may reduce the 1-norm of the matrix, and improve the */
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/* > accuracy of the computed eigenvalues and/or eigenvectors. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] JOB */
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/* > \verbatim */
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/* > JOB is CHARACTER*1 */
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/* > Specifies the operations to be performed on A: */
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/* > = 'N': none: simply set ILO = 1, IHI = N, SCALE(I) = 1.0 */
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/* > for i = 1,...,N; */
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/* > = 'P': permute only; */
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/* > = 'S': scale only; */
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/* > = 'B': both permute and scale. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The order of the matrix A. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] A */
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/* > \verbatim */
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/* > A is REAL array, dimension (LDA,N) */
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/* > On entry, the input matrix A. */
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/* > On exit, A is overwritten by the balanced matrix. */
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/* > If JOB = 'N', A is not referenced. */
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/* > See Further Details. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] ILO */
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/* > \verbatim */
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/* > ILO is INTEGER */
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/* > \endverbatim */
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/* > \param[out] IHI */
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/* > \verbatim */
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/* > IHI is INTEGER */
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/* > ILO and IHI are set to integers such that on exit */
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/* > A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N. */
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/* > If JOB = 'N' or 'S', ILO = 1 and IHI = N. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] SCALE */
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/* > \verbatim */
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/* > SCALE is REAL array, dimension (N) */
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/* > Details of the permutations and scaling factors applied to */
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/* > A. If P(j) is the index of the row and column interchanged */
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/* > with row and column j and D(j) is the scaling factor */
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/* > applied to row and column j, then */
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/* > SCALE(j) = P(j) for j = 1,...,ILO-1 */
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/* > = D(j) for j = ILO,...,IHI */
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/* > = P(j) for j = IHI+1,...,N. */
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/* > The order in which the interchanges are made is N to IHI+1, */
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/* > then 1 to ILO-1. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit. */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \date December 2016 */
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/* > \ingroup realGEcomputational */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > \verbatim */
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/* > */
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/* > The permutations consist of row and column interchanges which put */
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/* > the matrix in the form */
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/* > */
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/* > ( T1 X Y ) */
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/* > P A P = ( 0 B Z ) */
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/* > ( 0 0 T2 ) */
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/* > */
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/* > where T1 and T2 are upper triangular matrices whose eigenvalues lie */
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/* > along the diagonal. The column indices ILO and IHI mark the starting */
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/* > and ending columns of the submatrix B. Balancing consists of applying */
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/* > a diagonal similarity transformation inv(D) * B * D to make the */
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/* > 1-norms of each row of B and its corresponding column nearly equal. */
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/* > The output matrix is */
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/* > */
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/* > ( T1 X*D Y ) */
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/* > ( 0 inv(D)*B*D inv(D)*Z ). */
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/* > ( 0 0 T2 ) */
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/* > */
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/* > Information about the permutations P and the diagonal matrix D is */
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/* > returned in the vector SCALE. */
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/* > */
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/* > This subroutine is based on the EISPACK routine BALANC. */
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/* > */
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/* > Modified by Tzu-Yi Chen, Computer Science Division, University of */
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/* > California at Berkeley, USA */
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/* > \endverbatim */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ void sgebal_(char *job, integer *n, real *a, integer *lda,
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integer *ilo, integer *ihi, real *scale, integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2;
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real r__1, r__2;
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/* Local variables */
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integer iexc;
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extern real snrm2_(integer *, real *, integer *);
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real c__, f, g;
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integer i__, j, k, l, m;
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real r__, s;
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extern logical lsame_(char *, char *);
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extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *),
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sswap_(integer *, real *, integer *, real *, integer *);
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real sfmin1, sfmin2, sfmax1, sfmax2, ca, ra;
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extern real slamch_(char *);
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extern /* Subroutine */ int xerbla_(char *, integer *,ftnlen);
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extern integer isamax_(integer *, real *, integer *);
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extern logical sisnan_(real *);
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logical noconv;
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integer ica, ira;
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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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/* Test the input parameters */
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/* Parameter adjustments */
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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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--scale;
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/* Function Body */
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*info = 0;
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if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S")
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&& ! lsame_(job, "B")) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*lda < f2cmax(1,*n)) {
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*info = -4;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SGEBAL", &i__1,(ftnlen)6);
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return;
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}
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k = 1;
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l = *n;
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if (*n == 0) {
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goto L210;
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}
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if (lsame_(job, "N")) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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scale[i__] = 1.f;
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/* L10: */
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}
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goto L210;
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}
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if (lsame_(job, "S")) {
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goto L120;
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}
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/* Permutation to isolate eigenvalues if possible */
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goto L50;
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/* Row and column exchange. */
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L20:
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scale[m] = (real) j;
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if (j == m) {
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goto L30;
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}
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sswap_(&l, &a[j * a_dim1 + 1], &c__1, &a[m * a_dim1 + 1], &c__1);
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i__1 = *n - k + 1;
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sswap_(&i__1, &a[j + k * a_dim1], lda, &a[m + k * a_dim1], lda);
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L30:
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switch (iexc) {
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case 1: goto L40;
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case 2: goto L80;
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}
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/* Search for rows isolating an eigenvalue and push them down. */
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L40:
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if (l == 1) {
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goto L210;
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}
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--l;
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L50:
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for (j = l; j >= 1; --j) {
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i__1 = l;
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for (i__ = 1; i__ <= i__1; ++i__) {
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if (i__ == j) {
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goto L60;
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}
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if (a[j + i__ * a_dim1] != 0.f) {
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goto L70;
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}
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L60:
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;
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}
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m = l;
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iexc = 1;
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goto L20;
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L70:
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;
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}
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goto L90;
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/* Search for columns isolating an eigenvalue and push them left. */
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L80:
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++k;
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L90:
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i__1 = l;
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for (j = k; j <= i__1; ++j) {
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i__2 = l;
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for (i__ = k; i__ <= i__2; ++i__) {
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if (i__ == j) {
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goto L100;
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}
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if (a[i__ + j * a_dim1] != 0.f) {
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goto L110;
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}
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L100:
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;
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}
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m = k;
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iexc = 2;
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goto L20;
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L110:
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;
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}
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L120:
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i__1 = l;
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for (i__ = k; i__ <= i__1; ++i__) {
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scale[i__] = 1.f;
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/* L130: */
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}
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if (lsame_(job, "P")) {
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goto L210;
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}
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/* Balance the submatrix in rows K to L. */
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/* Iterative loop for norm reduction */
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sfmin1 = slamch_("S") / slamch_("P");
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sfmax1 = 1.f / sfmin1;
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sfmin2 = sfmin1 * 2.f;
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sfmax2 = 1.f / sfmin2;
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L140:
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noconv = FALSE_;
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i__1 = l;
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for (i__ = k; i__ <= i__1; ++i__) {
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i__2 = l - k + 1;
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c__ = snrm2_(&i__2, &a[k + i__ * a_dim1], &c__1);
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i__2 = l - k + 1;
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r__ = snrm2_(&i__2, &a[i__ + k * a_dim1], lda);
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ica = isamax_(&l, &a[i__ * a_dim1 + 1], &c__1);
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ca = (r__1 = a[ica + i__ * a_dim1], abs(r__1));
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i__2 = *n - k + 1;
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ira = isamax_(&i__2, &a[i__ + k * a_dim1], lda);
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ra = (r__1 = a[i__ + (ira + k - 1) * a_dim1], abs(r__1));
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/* Guard against zero C or R due to underflow. */
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if (c__ == 0.f || r__ == 0.f) {
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goto L200;
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}
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g = r__ / 2.f;
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|
f = 1.f;
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s = c__ + r__;
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L160:
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/* Computing MAX */
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r__1 = f2cmax(f,c__);
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/* Computing MIN */
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r__2 = f2cmin(r__,g);
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if (c__ >= g || f2cmax(r__1,ca) >= sfmax2 || f2cmin(r__2,ra) <= sfmin2) {
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goto L170;
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}
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f *= 2.f;
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c__ *= 2.f;
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|
ca *= 2.f;
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r__ /= 2.f;
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g /= 2.f;
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|
ra /= 2.f;
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goto L160;
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L170:
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|
g = c__ / 2.f;
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L180:
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/* Computing MIN */
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r__1 = f2cmin(f,c__), r__1 = f2cmin(r__1,g);
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if (g < r__ || f2cmax(r__,ra) >= sfmax2 || f2cmin(r__1,ca) <= sfmin2) {
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goto L190;
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}
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|
r__1 = c__ + f + ca + r__ + g + ra;
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|
if (sisnan_(&r__1)) {
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|
|
|
/* Exit if NaN to avoid infinite loop */
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|
|
|
*info = -3;
|
|
i__2 = -(*info);
|
|
xerbla_("SGEBAL", &i__2, (ftnlen)6);
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|
return;
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|
}
|
|
f /= 2.f;
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|
c__ /= 2.f;
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|
g /= 2.f;
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|
ca /= 2.f;
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|
r__ *= 2.f;
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|
ra *= 2.f;
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goto L180;
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|
|
/* Now balance. */
|
|
|
|
L190:
|
|
if (c__ + r__ >= s * .95f) {
|
|
goto L200;
|
|
}
|
|
if (f < 1.f && scale[i__] < 1.f) {
|
|
if (f * scale[i__] <= sfmin1) {
|
|
goto L200;
|
|
}
|
|
}
|
|
if (f > 1.f && scale[i__] > 1.f) {
|
|
if (scale[i__] >= sfmax1 / f) {
|
|
goto L200;
|
|
}
|
|
}
|
|
g = 1.f / f;
|
|
scale[i__] *= f;
|
|
noconv = TRUE_;
|
|
|
|
i__2 = *n - k + 1;
|
|
sscal_(&i__2, &g, &a[i__ + k * a_dim1], lda);
|
|
sscal_(&l, &f, &a[i__ * a_dim1 + 1], &c__1);
|
|
|
|
L200:
|
|
;
|
|
}
|
|
|
|
if (noconv) {
|
|
goto L140;
|
|
}
|
|
|
|
L210:
|
|
*ilo = k;
|
|
*ihi = l;
|
|
|
|
return;
|
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|
|
/* End of SGEBAL */
|
|
|
|
} /* sgebal_ */
|
|
|