1031 lines
29 KiB
C
1031 lines
29 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b DLARRF finds a new relatively robust representation such that at least one of the eigenvalues i
|
|
s relatively isolated. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLARRF + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrf.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrf.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrf.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLARRF( N, D, L, LD, CLSTRT, CLEND, */
|
|
/* W, WGAP, WERR, */
|
|
/* SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, */
|
|
/* DPLUS, LPLUS, WORK, INFO ) */
|
|
|
|
/* INTEGER CLSTRT, CLEND, INFO, N */
|
|
/* DOUBLE PRECISION CLGAPL, CLGAPR, PIVMIN, SIGMA, SPDIAM */
|
|
/* DOUBLE PRECISION D( * ), DPLUS( * ), L( * ), LD( * ), */
|
|
/* $ LPLUS( * ), W( * ), WGAP( * ), WERR( * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > Given the initial representation L D L^T and its cluster of close */
|
|
/* > eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ... */
|
|
/* > W( CLEND ), DLARRF finds a new relatively robust representation */
|
|
/* > L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the */
|
|
/* > eigenvalues of L(+) D(+) L(+)^T is relatively isolated. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix (subblock, if the matrix split). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D */
|
|
/* > \verbatim */
|
|
/* > D is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The N diagonal elements of the diagonal matrix D. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] L */
|
|
/* > \verbatim */
|
|
/* > L is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The (N-1) subdiagonal elements of the unit bidiagonal */
|
|
/* > matrix L. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LD */
|
|
/* > \verbatim */
|
|
/* > LD is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The (N-1) elements L(i)*D(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] CLSTRT */
|
|
/* > \verbatim */
|
|
/* > CLSTRT is INTEGER */
|
|
/* > The index of the first eigenvalue in the cluster. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] CLEND */
|
|
/* > \verbatim */
|
|
/* > CLEND is INTEGER */
|
|
/* > The index of the last eigenvalue in the cluster. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] W */
|
|
/* > \verbatim */
|
|
/* > W is DOUBLE PRECISION array, dimension */
|
|
/* > dimension is >= (CLEND-CLSTRT+1) */
|
|
/* > The eigenvalue APPROXIMATIONS of L D L^T in ascending order. */
|
|
/* > W( CLSTRT ) through W( CLEND ) form the cluster of relatively */
|
|
/* > close eigenalues. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] WGAP */
|
|
/* > \verbatim */
|
|
/* > WGAP is DOUBLE PRECISION array, dimension */
|
|
/* > dimension is >= (CLEND-CLSTRT+1) */
|
|
/* > The separation from the right neighbor eigenvalue in W. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] WERR */
|
|
/* > \verbatim */
|
|
/* > WERR is DOUBLE PRECISION array, dimension */
|
|
/* > dimension is >= (CLEND-CLSTRT+1) */
|
|
/* > WERR contain the semiwidth of the uncertainty */
|
|
/* > interval of the corresponding eigenvalue APPROXIMATION in W */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SPDIAM */
|
|
/* > \verbatim */
|
|
/* > SPDIAM is DOUBLE PRECISION */
|
|
/* > estimate of the spectral diameter obtained from the */
|
|
/* > Gerschgorin intervals */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] CLGAPL */
|
|
/* > \verbatim */
|
|
/* > CLGAPL is DOUBLE PRECISION */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] CLGAPR */
|
|
/* > \verbatim */
|
|
/* > CLGAPR is DOUBLE PRECISION */
|
|
/* > absolute gap on each end of the cluster. */
|
|
/* > Set by the calling routine to protect against shifts too close */
|
|
/* > to eigenvalues outside the cluster. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] PIVMIN */
|
|
/* > \verbatim */
|
|
/* > PIVMIN is DOUBLE PRECISION */
|
|
/* > The minimum pivot allowed in the Sturm sequence. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SIGMA */
|
|
/* > \verbatim */
|
|
/* > SIGMA is DOUBLE PRECISION */
|
|
/* > The shift used to form L(+) D(+) L(+)^T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] DPLUS */
|
|
/* > \verbatim */
|
|
/* > DPLUS is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The N diagonal elements of the diagonal matrix D(+). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] LPLUS */
|
|
/* > \verbatim */
|
|
/* > LPLUS is DOUBLE PRECISION array, dimension (N-1) */
|
|
/* > The first (N-1) elements of LPLUS contain the subdiagonal */
|
|
/* > elements of the unit bidiagonal matrix L(+). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is DOUBLE PRECISION array, dimension (2*N) */
|
|
/* > Workspace. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > Signals processing OK (=0) or failure (=1) */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2016 */
|
|
|
|
/* > \ingroup OTHERauxiliary */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Beresford Parlett, University of California, Berkeley, USA \n */
|
|
/* > Jim Demmel, University of California, Berkeley, USA \n */
|
|
/* > Inderjit Dhillon, University of Texas, Austin, USA \n */
|
|
/* > Osni Marques, LBNL/NERSC, USA \n */
|
|
/* > Christof Voemel, University of California, Berkeley, USA */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlarrf_(integer *n, doublereal *d__, doublereal *l,
|
|
doublereal *ld, integer *clstrt, integer *clend, doublereal *w,
|
|
doublereal *wgap, doublereal *werr, doublereal *spdiam, doublereal *
|
|
clgapl, doublereal *clgapr, doublereal *pivmin, doublereal *sigma,
|
|
doublereal *dplus, doublereal *lplus, doublereal *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer i__1;
|
|
doublereal d__1, d__2, d__3;
|
|
|
|
/* Local variables */
|
|
doublereal growthbound, fail, fact, oldp;
|
|
integer indx;
|
|
doublereal prod;
|
|
integer ktry;
|
|
doublereal fail2;
|
|
integer i__;
|
|
doublereal s, avgap, ldmax, rdmax;
|
|
integer shift;
|
|
extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
|
|
doublereal *, integer *);
|
|
doublereal bestshift, smlgrowth;
|
|
logical dorrr1;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal ldelta;
|
|
logical nofail;
|
|
doublereal mingap, lsigma, rdelta;
|
|
extern logical disnan_(doublereal *);
|
|
logical forcer;
|
|
doublereal rsigma, clwdth;
|
|
logical sawnan1, sawnan2;
|
|
doublereal eps, tmp;
|
|
logical tryrrr1;
|
|
doublereal max1, max2, rrr1, rrr2, znm2;
|
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Parameter adjustments */
|
|
--work;
|
|
--lplus;
|
|
--dplus;
|
|
--werr;
|
|
--wgap;
|
|
--w;
|
|
--ld;
|
|
--l;
|
|
--d__;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n <= 0) {
|
|
return;
|
|
}
|
|
|
|
fact = 2.;
|
|
eps = dlamch_("Precision");
|
|
shift = 0;
|
|
forcer = FALSE_;
|
|
/* Note that we cannot guarantee that for any of the shifts tried, */
|
|
/* the factorization has a small or even moderate element growth. */
|
|
/* There could be Ritz values at both ends of the cluster and despite */
|
|
/* backing off, there are examples where all factorizations tried */
|
|
/* (in IEEE mode, allowing zero pivots & infinities) have INFINITE */
|
|
/* element growth. */
|
|
/* For this reason, we should use PIVMIN in this subroutine so that at */
|
|
/* least the L D L^T factorization exists. It can be checked afterwards */
|
|
/* whether the element growth caused bad residuals/orthogonality. */
|
|
/* Decide whether the code should accept the best among all */
|
|
/* representations despite large element growth or signal INFO=1 */
|
|
/* Setting NOFAIL to .FALSE. for quick fix for bug 113 */
|
|
nofail = FALSE_;
|
|
|
|
/* Compute the average gap length of the cluster */
|
|
clwdth = (d__1 = w[*clend] - w[*clstrt], abs(d__1)) + werr[*clend] + werr[
|
|
*clstrt];
|
|
avgap = clwdth / (doublereal) (*clend - *clstrt);
|
|
mingap = f2cmin(*clgapl,*clgapr);
|
|
/* Initial values for shifts to both ends of cluster */
|
|
/* Computing MIN */
|
|
d__1 = w[*clstrt], d__2 = w[*clend];
|
|
lsigma = f2cmin(d__1,d__2) - werr[*clstrt];
|
|
/* Computing MAX */
|
|
d__1 = w[*clstrt], d__2 = w[*clend];
|
|
rsigma = f2cmax(d__1,d__2) + werr[*clend];
|
|
/* Use a small fudge to make sure that we really shift to the outside */
|
|
lsigma -= abs(lsigma) * 4. * eps;
|
|
rsigma += abs(rsigma) * 4. * eps;
|
|
/* Compute upper bounds for how much to back off the initial shifts */
|
|
ldmax = mingap * .25 + *pivmin * 2.;
|
|
rdmax = mingap * .25 + *pivmin * 2.;
|
|
/* Computing MAX */
|
|
d__1 = avgap, d__2 = wgap[*clstrt];
|
|
ldelta = f2cmax(d__1,d__2) / fact;
|
|
/* Computing MAX */
|
|
d__1 = avgap, d__2 = wgap[*clend - 1];
|
|
rdelta = f2cmax(d__1,d__2) / fact;
|
|
|
|
/* Initialize the record of the best representation found */
|
|
|
|
s = dlamch_("S");
|
|
smlgrowth = 1. / s;
|
|
fail = (doublereal) (*n - 1) * mingap / (*spdiam * eps);
|
|
fail2 = (doublereal) (*n - 1) * mingap / (*spdiam * sqrt(eps));
|
|
bestshift = lsigma;
|
|
|
|
/* while (KTRY <= KTRYMAX) */
|
|
ktry = 0;
|
|
growthbound = *spdiam * 8.;
|
|
L5:
|
|
sawnan1 = FALSE_;
|
|
sawnan2 = FALSE_;
|
|
/* Ensure that we do not back off too much of the initial shifts */
|
|
ldelta = f2cmin(ldmax,ldelta);
|
|
rdelta = f2cmin(rdmax,rdelta);
|
|
/* Compute the element growth when shifting to both ends of the cluster */
|
|
/* accept the shift if there is no element growth at one of the two ends */
|
|
/* Left end */
|
|
s = -lsigma;
|
|
dplus[1] = d__[1] + s;
|
|
if (abs(dplus[1]) < *pivmin) {
|
|
dplus[1] = -(*pivmin);
|
|
/* Need to set SAWNAN1 because refined RRR test should not be used */
|
|
/* in this case */
|
|
sawnan1 = TRUE_;
|
|
}
|
|
max1 = abs(dplus[1]);
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
lplus[i__] = ld[i__] / dplus[i__];
|
|
s = s * lplus[i__] * l[i__] - lsigma;
|
|
dplus[i__ + 1] = d__[i__ + 1] + s;
|
|
if ((d__1 = dplus[i__ + 1], abs(d__1)) < *pivmin) {
|
|
dplus[i__ + 1] = -(*pivmin);
|
|
/* Need to set SAWNAN1 because refined RRR test should not be used */
|
|
/* in this case */
|
|
sawnan1 = TRUE_;
|
|
}
|
|
/* Computing MAX */
|
|
d__2 = max1, d__3 = (d__1 = dplus[i__ + 1], abs(d__1));
|
|
max1 = f2cmax(d__2,d__3);
|
|
/* L6: */
|
|
}
|
|
sawnan1 = sawnan1 || disnan_(&max1);
|
|
if (forcer || max1 <= growthbound && ! sawnan1) {
|
|
*sigma = lsigma;
|
|
shift = 1;
|
|
goto L100;
|
|
}
|
|
/* Right end */
|
|
s = -rsigma;
|
|
work[1] = d__[1] + s;
|
|
if (abs(work[1]) < *pivmin) {
|
|
work[1] = -(*pivmin);
|
|
/* Need to set SAWNAN2 because refined RRR test should not be used */
|
|
/* in this case */
|
|
sawnan2 = TRUE_;
|
|
}
|
|
max2 = abs(work[1]);
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
work[*n + i__] = ld[i__] / work[i__];
|
|
s = s * work[*n + i__] * l[i__] - rsigma;
|
|
work[i__ + 1] = d__[i__ + 1] + s;
|
|
if ((d__1 = work[i__ + 1], abs(d__1)) < *pivmin) {
|
|
work[i__ + 1] = -(*pivmin);
|
|
/* Need to set SAWNAN2 because refined RRR test should not be used */
|
|
/* in this case */
|
|
sawnan2 = TRUE_;
|
|
}
|
|
/* Computing MAX */
|
|
d__2 = max2, d__3 = (d__1 = work[i__ + 1], abs(d__1));
|
|
max2 = f2cmax(d__2,d__3);
|
|
/* L7: */
|
|
}
|
|
sawnan2 = sawnan2 || disnan_(&max2);
|
|
if (forcer || max2 <= growthbound && ! sawnan2) {
|
|
*sigma = rsigma;
|
|
shift = 2;
|
|
goto L100;
|
|
}
|
|
/* If we are at this point, both shifts led to too much element growth */
|
|
/* Record the better of the two shifts (provided it didn't lead to NaN) */
|
|
if (sawnan1 && sawnan2) {
|
|
/* both MAX1 and MAX2 are NaN */
|
|
goto L50;
|
|
} else {
|
|
if (! sawnan1) {
|
|
indx = 1;
|
|
if (max1 <= smlgrowth) {
|
|
smlgrowth = max1;
|
|
bestshift = lsigma;
|
|
}
|
|
}
|
|
if (! sawnan2) {
|
|
if (sawnan1 || max2 <= max1) {
|
|
indx = 2;
|
|
}
|
|
if (max2 <= smlgrowth) {
|
|
smlgrowth = max2;
|
|
bestshift = rsigma;
|
|
}
|
|
}
|
|
}
|
|
/* If we are here, both the left and the right shift led to */
|
|
/* element growth. If the element growth is moderate, then */
|
|
/* we may still accept the representation, if it passes a */
|
|
/* refined test for RRR. This test supposes that no NaN occurred. */
|
|
/* Moreover, we use the refined RRR test only for isolated clusters. */
|
|
if (clwdth < mingap / 128. && f2cmin(max1,max2) < fail2 && ! sawnan1 && !
|
|
sawnan2) {
|
|
dorrr1 = TRUE_;
|
|
} else {
|
|
dorrr1 = FALSE_;
|
|
}
|
|
tryrrr1 = TRUE_;
|
|
if (tryrrr1 && dorrr1) {
|
|
if (indx == 1) {
|
|
tmp = (d__1 = dplus[*n], abs(d__1));
|
|
znm2 = 1.;
|
|
prod = 1.;
|
|
oldp = 1.;
|
|
for (i__ = *n - 1; i__ >= 1; --i__) {
|
|
if (prod <= eps) {
|
|
prod = dplus[i__ + 1] * work[*n + i__ + 1] / (dplus[i__] *
|
|
work[*n + i__]) * oldp;
|
|
} else {
|
|
prod *= (d__1 = work[*n + i__], abs(d__1));
|
|
}
|
|
oldp = prod;
|
|
/* Computing 2nd power */
|
|
d__1 = prod;
|
|
znm2 += d__1 * d__1;
|
|
/* Computing MAX */
|
|
d__2 = tmp, d__3 = (d__1 = dplus[i__] * prod, abs(d__1));
|
|
tmp = f2cmax(d__2,d__3);
|
|
/* L15: */
|
|
}
|
|
rrr1 = tmp / (*spdiam * sqrt(znm2));
|
|
if (rrr1 <= 8.) {
|
|
*sigma = lsigma;
|
|
shift = 1;
|
|
goto L100;
|
|
}
|
|
} else if (indx == 2) {
|
|
tmp = (d__1 = work[*n], abs(d__1));
|
|
znm2 = 1.;
|
|
prod = 1.;
|
|
oldp = 1.;
|
|
for (i__ = *n - 1; i__ >= 1; --i__) {
|
|
if (prod <= eps) {
|
|
prod = work[i__ + 1] * lplus[i__ + 1] / (work[i__] *
|
|
lplus[i__]) * oldp;
|
|
} else {
|
|
prod *= (d__1 = lplus[i__], abs(d__1));
|
|
}
|
|
oldp = prod;
|
|
/* Computing 2nd power */
|
|
d__1 = prod;
|
|
znm2 += d__1 * d__1;
|
|
/* Computing MAX */
|
|
d__2 = tmp, d__3 = (d__1 = work[i__] * prod, abs(d__1));
|
|
tmp = f2cmax(d__2,d__3);
|
|
/* L16: */
|
|
}
|
|
rrr2 = tmp / (*spdiam * sqrt(znm2));
|
|
if (rrr2 <= 8.) {
|
|
*sigma = rsigma;
|
|
shift = 2;
|
|
goto L100;
|
|
}
|
|
}
|
|
}
|
|
L50:
|
|
if (ktry < 1) {
|
|
/* If we are here, both shifts failed also the RRR test. */
|
|
/* Back off to the outside */
|
|
/* Computing MAX */
|
|
d__1 = lsigma - ldelta, d__2 = lsigma - ldmax;
|
|
lsigma = f2cmax(d__1,d__2);
|
|
/* Computing MIN */
|
|
d__1 = rsigma + rdelta, d__2 = rsigma + rdmax;
|
|
rsigma = f2cmin(d__1,d__2);
|
|
ldelta *= 2.;
|
|
rdelta *= 2.;
|
|
++ktry;
|
|
goto L5;
|
|
} else {
|
|
/* None of the representations investigated satisfied our */
|
|
/* criteria. Take the best one we found. */
|
|
if (smlgrowth < fail || nofail) {
|
|
lsigma = bestshift;
|
|
rsigma = bestshift;
|
|
forcer = TRUE_;
|
|
goto L5;
|
|
} else {
|
|
*info = 1;
|
|
return;
|
|
}
|
|
}
|
|
L100:
|
|
if (shift == 1) {
|
|
} else if (shift == 2) {
|
|
/* store new L and D back into DPLUS, LPLUS */
|
|
dcopy_(n, &work[1], &c__1, &dplus[1], &c__1);
|
|
i__1 = *n - 1;
|
|
dcopy_(&i__1, &work[*n + 1], &c__1, &lplus[1], &c__1);
|
|
}
|
|
return;
|
|
|
|
/* End of DLARRF */
|
|
|
|
} /* dlarrf_ */
|
|
|