1039 lines
28 KiB
C
1039 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 int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__2 = 2;
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
|
|
/* > \brief \b CSTEIN */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CSTEIN + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cstein.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cstein.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cstein.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, */
|
|
/* IWORK, IFAIL, INFO ) */
|
|
|
|
/* INTEGER INFO, LDZ, M, N */
|
|
/* INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), */
|
|
/* $ IWORK( * ) */
|
|
/* REAL D( * ), E( * ), W( * ), WORK( * ) */
|
|
/* COMPLEX Z( LDZ, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CSTEIN computes the eigenvectors of a real symmetric tridiagonal */
|
|
/* > matrix T corresponding to specified eigenvalues, using inverse */
|
|
/* > iteration. */
|
|
/* > */
|
|
/* > The maximum number of iterations allowed for each eigenvector is */
|
|
/* > specified by an internal parameter MAXITS (currently set to 5). */
|
|
/* > */
|
|
/* > Although the eigenvectors are real, they are stored in a complex */
|
|
/* > array, which may be passed to CUNMTR or CUPMTR for back */
|
|
/* > transformation to the eigenvectors of a complex Hermitian matrix */
|
|
/* > which was reduced to tridiagonal form. */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D */
|
|
/* > \verbatim */
|
|
/* > D is REAL array, dimension (N) */
|
|
/* > The n diagonal elements of the tridiagonal matrix T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] E */
|
|
/* > \verbatim */
|
|
/* > E is REAL array, dimension (N-1) */
|
|
/* > The (n-1) subdiagonal elements of the tridiagonal matrix */
|
|
/* > T, stored in elements 1 to N-1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of eigenvectors to be found. 0 <= M <= N. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] W */
|
|
/* > \verbatim */
|
|
/* > W is REAL array, dimension (N) */
|
|
/* > The first M elements of W contain the eigenvalues for */
|
|
/* > which eigenvectors are to be computed. The eigenvalues */
|
|
/* > should be grouped by split-off block and ordered from */
|
|
/* > smallest to largest within the block. ( The output array */
|
|
/* > W from SSTEBZ with ORDER = 'B' is expected here. ) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IBLOCK */
|
|
/* > \verbatim */
|
|
/* > IBLOCK is INTEGER array, dimension (N) */
|
|
/* > The submatrix indices associated with the corresponding */
|
|
/* > eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to */
|
|
/* > the first submatrix from the top, =2 if W(i) belongs to */
|
|
/* > the second submatrix, etc. ( The output array IBLOCK */
|
|
/* > from SSTEBZ is expected here. ) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ISPLIT */
|
|
/* > \verbatim */
|
|
/* > ISPLIT is INTEGER array, dimension (N) */
|
|
/* > The splitting points, at which T breaks up into submatrices. */
|
|
/* > The first submatrix consists of rows/columns 1 to */
|
|
/* > ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 */
|
|
/* > through ISPLIT( 2 ), etc. */
|
|
/* > ( The output array ISPLIT from SSTEBZ is expected here. ) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] Z */
|
|
/* > \verbatim */
|
|
/* > Z is COMPLEX array, dimension (LDZ, M) */
|
|
/* > The computed eigenvectors. The eigenvector associated */
|
|
/* > with the eigenvalue W(i) is stored in the i-th column of */
|
|
/* > Z. Any vector which fails to converge is set to its current */
|
|
/* > iterate after MAXITS iterations. */
|
|
/* > The imaginary parts of the eigenvectors are set to zero. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDZ */
|
|
/* > \verbatim */
|
|
/* > LDZ is INTEGER */
|
|
/* > The leading dimension of the array Z. LDZ >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension (5*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IFAIL */
|
|
/* > \verbatim */
|
|
/* > IFAIL is INTEGER array, dimension (M) */
|
|
/* > On normal exit, all elements of IFAIL are zero. */
|
|
/* > If one or more eigenvectors fail to converge after */
|
|
/* > MAXITS iterations, then their indices are stored in */
|
|
/* > array IFAIL. */
|
|
/* > \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, then i eigenvectors failed to converge */
|
|
/* > in MAXITS iterations. Their indices are stored in */
|
|
/* > array IFAIL. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Internal Parameters: */
|
|
/* ========================= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > MAXITS INTEGER, default = 5 */
|
|
/* > The maximum number of iterations performed. */
|
|
/* > */
|
|
/* > EXTRA INTEGER, default = 2 */
|
|
/* > The number of iterations performed after norm growth */
|
|
/* > criterion is satisfied, should be at least 1. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complexOTHERcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void cstein_(integer *n, real *d__, real *e, integer *m, real
|
|
*w, integer *iblock, integer *isplit, complex *z__, integer *ldz,
|
|
real *work, integer *iwork, integer *ifail, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5;
|
|
real r__1, r__2, r__3, r__4, r__5;
|
|
complex q__1;
|
|
|
|
/* Local variables */
|
|
integer jblk, nblk, jmax;
|
|
extern real snrm2_(integer *, real *, integer *);
|
|
integer i__, j, iseed[4], gpind, iinfo;
|
|
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
|
|
integer b1, j1;
|
|
extern /* Subroutine */ void scopy_(integer *, real *, integer *, real *,
|
|
integer *);
|
|
real ortol;
|
|
integer indrv1, indrv2, indrv3, indrv4, indrv5, bn, jr;
|
|
real xj;
|
|
extern real slamch_(char *);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern void slagtf_(
|
|
integer *, real *, real *, real *, real *, real *, real *,
|
|
integer *, integer *);
|
|
integer nrmchk;
|
|
extern integer isamax_(integer *, real *, integer *);
|
|
extern /* Subroutine */ void slagts_(integer *, integer *, real *, real *,
|
|
real *, real *, integer *, real *, real *, integer *);
|
|
integer blksiz;
|
|
real onenrm, pertol;
|
|
extern /* Subroutine */ void slarnv_(integer *, integer *, integer *, real
|
|
*);
|
|
real stpcrt, scl, eps, ctr, sep, nrm, tol;
|
|
integer its;
|
|
real xjm, eps1;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
--d__;
|
|
--e;
|
|
--w;
|
|
--iblock;
|
|
--isplit;
|
|
z_dim1 = *ldz;
|
|
z_offset = 1 + z_dim1 * 1;
|
|
z__ -= z_offset;
|
|
--work;
|
|
--iwork;
|
|
--ifail;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
ifail[i__] = 0;
|
|
/* L10: */
|
|
}
|
|
|
|
if (*n < 0) {
|
|
*info = -1;
|
|
} else if (*m < 0 || *m > *n) {
|
|
*info = -4;
|
|
} else if (*ldz < f2cmax(1,*n)) {
|
|
*info = -9;
|
|
} else {
|
|
i__1 = *m;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
if (iblock[j] < iblock[j - 1]) {
|
|
*info = -6;
|
|
goto L30;
|
|
}
|
|
if (iblock[j] == iblock[j - 1] && w[j] < w[j - 1]) {
|
|
*info = -5;
|
|
goto L30;
|
|
}
|
|
/* L20: */
|
|
}
|
|
L30:
|
|
;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CSTEIN", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0 || *m == 0) {
|
|
return;
|
|
} else if (*n == 1) {
|
|
i__1 = z_dim1 + 1;
|
|
z__[i__1].r = 1.f, z__[i__1].i = 0.f;
|
|
return;
|
|
}
|
|
|
|
/* Get machine constants. */
|
|
|
|
eps = slamch_("Precision");
|
|
|
|
/* Initialize seed for random number generator SLARNV. */
|
|
|
|
for (i__ = 1; i__ <= 4; ++i__) {
|
|
iseed[i__ - 1] = 1;
|
|
/* L40: */
|
|
}
|
|
|
|
/* Initialize pointers. */
|
|
|
|
indrv1 = 0;
|
|
indrv2 = indrv1 + *n;
|
|
indrv3 = indrv2 + *n;
|
|
indrv4 = indrv3 + *n;
|
|
indrv5 = indrv4 + *n;
|
|
|
|
/* Compute eigenvectors of matrix blocks. */
|
|
|
|
j1 = 1;
|
|
i__1 = iblock[*m];
|
|
for (nblk = 1; nblk <= i__1; ++nblk) {
|
|
|
|
/* Find starting and ending indices of block nblk. */
|
|
|
|
if (nblk == 1) {
|
|
b1 = 1;
|
|
} else {
|
|
b1 = isplit[nblk - 1] + 1;
|
|
}
|
|
bn = isplit[nblk];
|
|
blksiz = bn - b1 + 1;
|
|
if (blksiz == 1) {
|
|
goto L60;
|
|
}
|
|
gpind = j1;
|
|
|
|
/* Compute reorthogonalization criterion and stopping criterion. */
|
|
|
|
onenrm = (r__1 = d__[b1], abs(r__1)) + (r__2 = e[b1], abs(r__2));
|
|
/* Computing MAX */
|
|
r__3 = onenrm, r__4 = (r__1 = d__[bn], abs(r__1)) + (r__2 = e[bn - 1],
|
|
abs(r__2));
|
|
onenrm = f2cmax(r__3,r__4);
|
|
i__2 = bn - 1;
|
|
for (i__ = b1 + 1; i__ <= i__2; ++i__) {
|
|
/* Computing MAX */
|
|
r__4 = onenrm, r__5 = (r__1 = d__[i__], abs(r__1)) + (r__2 = e[
|
|
i__ - 1], abs(r__2)) + (r__3 = e[i__], abs(r__3));
|
|
onenrm = f2cmax(r__4,r__5);
|
|
/* L50: */
|
|
}
|
|
ortol = onenrm * .001f;
|
|
|
|
stpcrt = sqrt(.1f / blksiz);
|
|
|
|
/* Loop through eigenvalues of block nblk. */
|
|
|
|
L60:
|
|
jblk = 0;
|
|
i__2 = *m;
|
|
for (j = j1; j <= i__2; ++j) {
|
|
if (iblock[j] != nblk) {
|
|
j1 = j;
|
|
goto L180;
|
|
}
|
|
++jblk;
|
|
xj = w[j];
|
|
|
|
/* Skip all the work if the block size is one. */
|
|
|
|
if (blksiz == 1) {
|
|
work[indrv1 + 1] = 1.f;
|
|
goto L140;
|
|
}
|
|
|
|
/* If eigenvalues j and j-1 are too close, add a relatively */
|
|
/* small perturbation. */
|
|
|
|
if (jblk > 1) {
|
|
eps1 = (r__1 = eps * xj, abs(r__1));
|
|
pertol = eps1 * 10.f;
|
|
sep = xj - xjm;
|
|
if (sep < pertol) {
|
|
xj = xjm + pertol;
|
|
}
|
|
}
|
|
|
|
its = 0;
|
|
nrmchk = 0;
|
|
|
|
/* Get random starting vector. */
|
|
|
|
slarnv_(&c__2, iseed, &blksiz, &work[indrv1 + 1]);
|
|
|
|
/* Copy the matrix T so it won't be destroyed in factorization. */
|
|
|
|
scopy_(&blksiz, &d__[b1], &c__1, &work[indrv4 + 1], &c__1);
|
|
i__3 = blksiz - 1;
|
|
scopy_(&i__3, &e[b1], &c__1, &work[indrv2 + 2], &c__1);
|
|
i__3 = blksiz - 1;
|
|
scopy_(&i__3, &e[b1], &c__1, &work[indrv3 + 1], &c__1);
|
|
|
|
/* Compute LU factors with partial pivoting ( PT = LU ) */
|
|
|
|
tol = 0.f;
|
|
slagtf_(&blksiz, &work[indrv4 + 1], &xj, &work[indrv2 + 2], &work[
|
|
indrv3 + 1], &tol, &work[indrv5 + 1], &iwork[1], &iinfo);
|
|
|
|
/* Update iteration count. */
|
|
|
|
L70:
|
|
++its;
|
|
if (its > 5) {
|
|
goto L120;
|
|
}
|
|
|
|
/* Normalize and scale the righthand side vector Pb. */
|
|
|
|
jmax = isamax_(&blksiz, &work[indrv1 + 1], &c__1);
|
|
/* Computing MAX */
|
|
r__3 = eps, r__4 = (r__1 = work[indrv4 + blksiz], abs(r__1));
|
|
scl = blksiz * onenrm * f2cmax(r__3,r__4) / (r__2 = work[indrv1 +
|
|
jmax], abs(r__2));
|
|
sscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
|
|
|
|
/* Solve the system LU = Pb. */
|
|
|
|
slagts_(&c_n1, &blksiz, &work[indrv4 + 1], &work[indrv2 + 2], &
|
|
work[indrv3 + 1], &work[indrv5 + 1], &iwork[1], &work[
|
|
indrv1 + 1], &tol, &iinfo);
|
|
|
|
/* Reorthogonalize by modified Gram-Schmidt if eigenvalues are */
|
|
/* close enough. */
|
|
|
|
if (jblk == 1) {
|
|
goto L110;
|
|
}
|
|
if ((r__1 = xj - xjm, abs(r__1)) > ortol) {
|
|
gpind = j;
|
|
}
|
|
if (gpind != j) {
|
|
i__3 = j - 1;
|
|
for (i__ = gpind; i__ <= i__3; ++i__) {
|
|
ctr = 0.f;
|
|
i__4 = blksiz;
|
|
for (jr = 1; jr <= i__4; ++jr) {
|
|
i__5 = b1 - 1 + jr + i__ * z_dim1;
|
|
ctr += work[indrv1 + jr] * z__[i__5].r;
|
|
/* L80: */
|
|
}
|
|
i__4 = blksiz;
|
|
for (jr = 1; jr <= i__4; ++jr) {
|
|
i__5 = b1 - 1 + jr + i__ * z_dim1;
|
|
work[indrv1 + jr] -= ctr * z__[i__5].r;
|
|
/* L90: */
|
|
}
|
|
/* L100: */
|
|
}
|
|
}
|
|
|
|
/* Check the infinity norm of the iterate. */
|
|
|
|
L110:
|
|
jmax = isamax_(&blksiz, &work[indrv1 + 1], &c__1);
|
|
nrm = (r__1 = work[indrv1 + jmax], abs(r__1));
|
|
|
|
/* Continue for additional iterations after norm reaches */
|
|
/* stopping criterion. */
|
|
|
|
if (nrm < stpcrt) {
|
|
goto L70;
|
|
}
|
|
++nrmchk;
|
|
if (nrmchk < 3) {
|
|
goto L70;
|
|
}
|
|
|
|
goto L130;
|
|
|
|
/* If stopping criterion was not satisfied, update info and */
|
|
/* store eigenvector number in array ifail. */
|
|
|
|
L120:
|
|
++(*info);
|
|
ifail[*info] = j;
|
|
|
|
/* Accept iterate as jth eigenvector. */
|
|
|
|
L130:
|
|
scl = 1.f / snrm2_(&blksiz, &work[indrv1 + 1], &c__1);
|
|
jmax = isamax_(&blksiz, &work[indrv1 + 1], &c__1);
|
|
if (work[indrv1 + jmax] < 0.f) {
|
|
scl = -scl;
|
|
}
|
|
sscal_(&blksiz, &scl, &work[indrv1 + 1], &c__1);
|
|
L140:
|
|
i__3 = *n;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
i__4 = i__ + j * z_dim1;
|
|
z__[i__4].r = 0.f, z__[i__4].i = 0.f;
|
|
/* L150: */
|
|
}
|
|
i__3 = blksiz;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
i__4 = b1 + i__ - 1 + j * z_dim1;
|
|
i__5 = indrv1 + i__;
|
|
q__1.r = work[i__5], q__1.i = 0.f;
|
|
z__[i__4].r = q__1.r, z__[i__4].i = q__1.i;
|
|
/* L160: */
|
|
}
|
|
|
|
/* Save the shift to check eigenvalue spacing at next */
|
|
/* iteration. */
|
|
|
|
xjm = xj;
|
|
|
|
/* L170: */
|
|
}
|
|
L180:
|
|
;
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of CSTEIN */
|
|
|
|
} /* cstein_ */
|
|
|