999 lines
28 KiB
C
999 lines
28 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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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;
|
|
|
|
/* > \brief \b ZHEEQUB */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZHEEQUB + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zheequb
|
|
.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zheequb
|
|
.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zheequb
|
|
.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZHEEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO ) */
|
|
|
|
/* INTEGER INFO, LDA, N */
|
|
/* DOUBLE PRECISION AMAX, SCOND */
|
|
/* CHARACTER UPLO */
|
|
/* COMPLEX*16 A( LDA, * ), WORK( * ) */
|
|
/* DOUBLE PRECISION S( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZHEEQUB computes row and column scalings intended to equilibrate a */
|
|
/* > Hermitian matrix A (with respect to the Euclidean norm) and reduce */
|
|
/* > its condition number. The scale factors S are computed by the BIN */
|
|
/* > algorithm (see references) so that the scaled matrix B with elements */
|
|
/* > B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of */
|
|
/* > the smallest possible condition number over all possible diagonal */
|
|
/* > scalings. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > = 'U': Upper triangle of A is stored; */
|
|
/* > = 'L': Lower triangle of A is stored. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX*16 array, dimension (LDA,N) */
|
|
/* > The N-by-N Hermitian matrix whose scaling factors are to be */
|
|
/* > computed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] S */
|
|
/* > \verbatim */
|
|
/* > S is DOUBLE PRECISION array, dimension (N) */
|
|
/* > If INFO = 0, S contains the scale factors for A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SCOND */
|
|
/* > \verbatim */
|
|
/* > SCOND is DOUBLE PRECISION */
|
|
/* > If INFO = 0, S contains the ratio of the smallest S(i) to */
|
|
/* > the largest S(i). If SCOND >= 0.1 and AMAX is neither too */
|
|
/* > large nor too small, it is not worth scaling by S. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] AMAX */
|
|
/* > \verbatim */
|
|
/* > AMAX is DOUBLE PRECISION */
|
|
/* > Largest absolute value of any matrix element. If AMAX is */
|
|
/* > very close to overflow or very close to underflow, the */
|
|
/* > matrix should be scaled. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > > 0: if INFO = i, the i-th diagonal element is nonpositive. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date April 2012 */
|
|
|
|
/* > \ingroup complex16HEcomputational */
|
|
|
|
/* > \par References: */
|
|
/* ================ */
|
|
/* > */
|
|
/* > Livne, O.E. and Golub, G.H., "Scaling by Binormalization", \n */
|
|
/* > Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004. \n */
|
|
/* > DOI 10.1023/B:NUMA.0000016606.32820.69 \n */
|
|
/* > Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zheequb_(char *uplo, integer *n, doublecomplex *a,
|
|
integer *lda, doublereal *s, doublereal *scond, doublereal *amax,
|
|
doublecomplex *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
|
|
doublereal d__1, d__2, d__3, d__4;
|
|
doublecomplex z__1, z__2, z__3, z__4;
|
|
|
|
/* Local variables */
|
|
doublereal base;
|
|
integer iter;
|
|
doublereal smin, smax, d__;
|
|
integer i__, j;
|
|
doublereal t, u, scale;
|
|
extern logical lsame_(char *, char *);
|
|
doublereal c0, c1, c2, sumsq;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal si;
|
|
logical up;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
doublereal bignum, smlnum;
|
|
extern /* Subroutine */ void zlassq_(integer *, doublecomplex *, integer *,
|
|
doublereal *, doublereal *);
|
|
doublereal avg, std, tol;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.8.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* April 2012 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--s;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
if (! (lsame_(uplo, "U") || lsame_(uplo, "L"))) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -4;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZHEEQUB", &i__1, (ftnlen)7);
|
|
return;
|
|
}
|
|
up = lsame_(uplo, "U");
|
|
*amax = 0.;
|
|
|
|
/* Quick return if possible. */
|
|
|
|
if (*n == 0) {
|
|
*scond = 1.;
|
|
return;
|
|
}
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
s[i__] = 0.;
|
|
}
|
|
*amax = 0.;
|
|
if (up) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
/* Computing MAX */
|
|
i__3 = i__ + j * a_dim1;
|
|
d__3 = s[i__], d__4 = (d__1 = a[i__3].r, abs(d__1)) + (d__2 =
|
|
d_imag(&a[i__ + j * a_dim1]), abs(d__2));
|
|
s[i__] = f2cmax(d__3,d__4);
|
|
/* Computing MAX */
|
|
i__3 = i__ + j * a_dim1;
|
|
d__3 = s[j], d__4 = (d__1 = a[i__3].r, abs(d__1)) + (d__2 =
|
|
d_imag(&a[i__ + j * a_dim1]), abs(d__2));
|
|
s[j] = f2cmax(d__3,d__4);
|
|
/* Computing MAX */
|
|
i__3 = i__ + j * a_dim1;
|
|
d__3 = *amax, d__4 = (d__1 = a[i__3].r, abs(d__1)) + (d__2 =
|
|
d_imag(&a[i__ + j * a_dim1]), abs(d__2));
|
|
*amax = f2cmax(d__3,d__4);
|
|
}
|
|
/* Computing MAX */
|
|
i__2 = j + j * a_dim1;
|
|
d__3 = s[j], d__4 = (d__1 = a[i__2].r, abs(d__1)) + (d__2 =
|
|
d_imag(&a[j + j * a_dim1]), abs(d__2));
|
|
s[j] = f2cmax(d__3,d__4);
|
|
/* Computing MAX */
|
|
i__2 = j + j * a_dim1;
|
|
d__3 = *amax, d__4 = (d__1 = a[i__2].r, abs(d__1)) + (d__2 =
|
|
d_imag(&a[j + j * a_dim1]), abs(d__2));
|
|
*amax = f2cmax(d__3,d__4);
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
/* Computing MAX */
|
|
i__2 = j + j * a_dim1;
|
|
d__3 = s[j], d__4 = (d__1 = a[i__2].r, abs(d__1)) + (d__2 =
|
|
d_imag(&a[j + j * a_dim1]), abs(d__2));
|
|
s[j] = f2cmax(d__3,d__4);
|
|
/* Computing MAX */
|
|
i__2 = j + j * a_dim1;
|
|
d__3 = *amax, d__4 = (d__1 = a[i__2].r, abs(d__1)) + (d__2 =
|
|
d_imag(&a[j + j * a_dim1]), abs(d__2));
|
|
*amax = f2cmax(d__3,d__4);
|
|
i__2 = *n;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
/* Computing MAX */
|
|
i__3 = i__ + j * a_dim1;
|
|
d__3 = s[i__], d__4 = (d__1 = a[i__3].r, abs(d__1)) + (d__2 =
|
|
d_imag(&a[i__ + j * a_dim1]), abs(d__2));
|
|
s[i__] = f2cmax(d__3,d__4);
|
|
/* Computing MAX */
|
|
i__3 = i__ + j * a_dim1;
|
|
d__3 = s[j], d__4 = (d__1 = a[i__3].r, abs(d__1)) + (d__2 =
|
|
d_imag(&a[i__ + j * a_dim1]), abs(d__2));
|
|
s[j] = f2cmax(d__3,d__4);
|
|
/* Computing MAX */
|
|
i__3 = i__ + j * a_dim1;
|
|
d__3 = *amax, d__4 = (d__1 = a[i__3].r, abs(d__1)) + (d__2 =
|
|
d_imag(&a[i__ + j * a_dim1]), abs(d__2));
|
|
*amax = f2cmax(d__3,d__4);
|
|
}
|
|
}
|
|
}
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
s[j] = 1. / s[j];
|
|
}
|
|
tol = 1. / sqrt(*n * 2.);
|
|
for (iter = 1; iter <= 100; ++iter) {
|
|
scale = 0.;
|
|
sumsq = 0.;
|
|
/* beta = |A|s */
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__;
|
|
work[i__2].r = 0., work[i__2].i = 0.;
|
|
}
|
|
if (up) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__;
|
|
i__4 = i__;
|
|
i__5 = i__ + j * a_dim1;
|
|
d__3 = ((d__1 = a[i__5].r, abs(d__1)) + (d__2 = d_imag(&a[
|
|
i__ + j * a_dim1]), abs(d__2))) * s[j];
|
|
z__1.r = work[i__4].r + d__3, z__1.i = work[i__4].i;
|
|
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
|
|
i__3 = j;
|
|
i__4 = j;
|
|
i__5 = i__ + j * a_dim1;
|
|
d__3 = ((d__1 = a[i__5].r, abs(d__1)) + (d__2 = d_imag(&a[
|
|
i__ + j * a_dim1]), abs(d__2))) * s[i__];
|
|
z__1.r = work[i__4].r + d__3, z__1.i = work[i__4].i;
|
|
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
|
|
}
|
|
i__2 = j;
|
|
i__3 = j;
|
|
i__4 = j + j * a_dim1;
|
|
d__3 = ((d__1 = a[i__4].r, abs(d__1)) + (d__2 = d_imag(&a[j +
|
|
j * a_dim1]), abs(d__2))) * s[j];
|
|
z__1.r = work[i__3].r + d__3, z__1.i = work[i__3].i;
|
|
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
i__3 = j;
|
|
i__4 = j + j * a_dim1;
|
|
d__3 = ((d__1 = a[i__4].r, abs(d__1)) + (d__2 = d_imag(&a[j +
|
|
j * a_dim1]), abs(d__2))) * s[j];
|
|
z__1.r = work[i__3].r + d__3, z__1.i = work[i__3].i;
|
|
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
|
|
i__2 = *n;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__;
|
|
i__4 = i__;
|
|
i__5 = i__ + j * a_dim1;
|
|
d__3 = ((d__1 = a[i__5].r, abs(d__1)) + (d__2 = d_imag(&a[
|
|
i__ + j * a_dim1]), abs(d__2))) * s[j];
|
|
z__1.r = work[i__4].r + d__3, z__1.i = work[i__4].i;
|
|
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
|
|
i__3 = j;
|
|
i__4 = j;
|
|
i__5 = i__ + j * a_dim1;
|
|
d__3 = ((d__1 = a[i__5].r, abs(d__1)) + (d__2 = d_imag(&a[
|
|
i__ + j * a_dim1]), abs(d__2))) * s[i__];
|
|
z__1.r = work[i__4].r + d__3, z__1.i = work[i__4].i;
|
|
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
|
|
}
|
|
}
|
|
}
|
|
/* avg = s^T beta / n */
|
|
avg = 0.;
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__;
|
|
i__3 = i__;
|
|
z__2.r = s[i__2] * work[i__3].r, z__2.i = s[i__2] * work[i__3].i;
|
|
z__1.r = avg + z__2.r, z__1.i = z__2.i;
|
|
avg = z__1.r;
|
|
}
|
|
avg /= *n;
|
|
std = 0.;
|
|
i__1 = *n << 1;
|
|
for (i__ = *n + 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__;
|
|
i__3 = i__ - *n;
|
|
i__4 = i__ - *n;
|
|
z__2.r = s[i__3] * work[i__4].r, z__2.i = s[i__3] * work[i__4].i;
|
|
z__1.r = z__2.r - avg, z__1.i = z__2.i;
|
|
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
|
|
}
|
|
zlassq_(n, &work[*n + 1], &c__1, &scale, &sumsq);
|
|
std = scale * sqrt(sumsq / *n);
|
|
if (std < tol * avg) {
|
|
goto L999;
|
|
}
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__ + i__ * a_dim1;
|
|
t = (d__1 = a[i__2].r, abs(d__1)) + (d__2 = d_imag(&a[i__ + i__ *
|
|
a_dim1]), abs(d__2));
|
|
si = s[i__];
|
|
c2 = (*n - 1) * t;
|
|
i__2 = *n - 2;
|
|
i__3 = i__;
|
|
d__1 = t * si;
|
|
z__2.r = work[i__3].r - d__1, z__2.i = work[i__3].i;
|
|
d__2 = (doublereal) i__2;
|
|
z__1.r = d__2 * z__2.r, z__1.i = d__2 * z__2.i;
|
|
c1 = z__1.r;
|
|
d__1 = -(t * si) * si;
|
|
i__2 = i__;
|
|
d__2 = 2.;
|
|
z__4.r = d__2 * work[i__2].r, z__4.i = d__2 * work[i__2].i;
|
|
z__3.r = si * z__4.r, z__3.i = si * z__4.i;
|
|
z__2.r = d__1 + z__3.r, z__2.i = z__3.i;
|
|
d__3 = *n * avg;
|
|
z__1.r = z__2.r - d__3, z__1.i = z__2.i;
|
|
c0 = z__1.r;
|
|
d__ = c1 * c1 - c0 * 4 * c2;
|
|
if (d__ <= 0.) {
|
|
*info = -1;
|
|
return;
|
|
}
|
|
si = c0 * -2 / (c1 + sqrt(d__));
|
|
d__ = si - s[i__];
|
|
u = 0.;
|
|
if (up) {
|
|
i__2 = i__;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = j + i__ * a_dim1;
|
|
t = (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[j +
|
|
i__ * a_dim1]), abs(d__2));
|
|
u += s[j] * t;
|
|
i__3 = j;
|
|
i__4 = j;
|
|
d__1 = d__ * t;
|
|
z__1.r = work[i__4].r + d__1, z__1.i = work[i__4].i;
|
|
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
|
|
}
|
|
i__2 = *n;
|
|
for (j = i__ + 1; j <= i__2; ++j) {
|
|
i__3 = i__ + j * a_dim1;
|
|
t = (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[i__
|
|
+ j * a_dim1]), abs(d__2));
|
|
u += s[j] * t;
|
|
i__3 = j;
|
|
i__4 = j;
|
|
d__1 = d__ * t;
|
|
z__1.r = work[i__4].r + d__1, z__1.i = work[i__4].i;
|
|
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
|
|
}
|
|
} else {
|
|
i__2 = i__;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = i__ + j * a_dim1;
|
|
t = (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[i__
|
|
+ j * a_dim1]), abs(d__2));
|
|
u += s[j] * t;
|
|
i__3 = j;
|
|
i__4 = j;
|
|
d__1 = d__ * t;
|
|
z__1.r = work[i__4].r + d__1, z__1.i = work[i__4].i;
|
|
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
|
|
}
|
|
i__2 = *n;
|
|
for (j = i__ + 1; j <= i__2; ++j) {
|
|
i__3 = j + i__ * a_dim1;
|
|
t = (d__1 = a[i__3].r, abs(d__1)) + (d__2 = d_imag(&a[j +
|
|
i__ * a_dim1]), abs(d__2));
|
|
u += s[j] * t;
|
|
i__3 = j;
|
|
i__4 = j;
|
|
d__1 = d__ * t;
|
|
z__1.r = work[i__4].r + d__1, z__1.i = work[i__4].i;
|
|
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
|
|
}
|
|
}
|
|
i__2 = i__;
|
|
z__4.r = u + work[i__2].r, z__4.i = work[i__2].i;
|
|
z__3.r = d__ * z__4.r, z__3.i = d__ * z__4.i;
|
|
d__1 = (doublereal) (*n);
|
|
z__2.r = z__3.r / d__1, z__2.i = z__3.i / d__1;
|
|
z__1.r = avg + z__2.r, z__1.i = z__2.i;
|
|
avg = z__1.r;
|
|
s[i__] = si;
|
|
}
|
|
}
|
|
L999:
|
|
smlnum = dlamch_("SAFEMIN");
|
|
bignum = 1. / smlnum;
|
|
smin = bignum;
|
|
smax = 0.;
|
|
t = 1. / sqrt(avg);
|
|
base = dlamch_("B");
|
|
u = 1. / log(base);
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = (integer) (u * log(s[i__] * t));
|
|
s[i__] = pow_di(&base, &i__2);
|
|
/* Computing MIN */
|
|
d__1 = smin, d__2 = s[i__];
|
|
smin = f2cmin(d__1,d__2);
|
|
/* Computing MAX */
|
|
d__1 = smax, d__2 = s[i__];
|
|
smax = f2cmax(d__1,d__2);
|
|
}
|
|
*scond = f2cmax(smin,smlnum) / f2cmin(smax,bignum);
|
|
|
|
return;
|
|
} /* zheequb_ */
|
|
|