1061 lines
28 KiB
C
1061 lines
28 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
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 doublecomplex c_b2 = {0.,0.};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZHPTRI */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZHPTRI + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhptri.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhptri.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhptri.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, INFO ) */
|
|
|
|
/* CHARACTER UPLO */
|
|
/* INTEGER INFO, N */
|
|
/* INTEGER IPIV( * ) */
|
|
/* COMPLEX*16 AP( * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZHPTRI computes the inverse of a complex Hermitian indefinite matrix */
|
|
/* > A in packed storage using the factorization A = U*D*U**H or */
|
|
/* > A = L*D*L**H computed by ZHPTRF. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > Specifies whether the details of the factorization are stored */
|
|
/* > as an upper or lower triangular matrix. */
|
|
/* > = 'U': Upper triangular, form is A = U*D*U**H; */
|
|
/* > = 'L': Lower triangular, form is A = L*D*L**H. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AP */
|
|
/* > \verbatim */
|
|
/* > AP is COMPLEX*16 array, dimension (N*(N+1)/2) */
|
|
/* > On entry, the block diagonal matrix D and the multipliers */
|
|
/* > used to obtain the factor U or L as computed by ZHPTRF, */
|
|
/* > stored as a packed triangular matrix. */
|
|
/* > */
|
|
/* > On exit, if INFO = 0, the (Hermitian) inverse of the original */
|
|
/* > matrix, stored as a packed triangular matrix. The j-th column */
|
|
/* > of inv(A) is stored in the array AP as follows: */
|
|
/* > if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; */
|
|
/* > if UPLO = 'L', */
|
|
/* > AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IPIV */
|
|
/* > \verbatim */
|
|
/* > IPIV is INTEGER array, dimension (N) */
|
|
/* > Details of the interchanges and the block structure of D */
|
|
/* > as determined by ZHPTRF. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its */
|
|
/* > inverse could not be computed. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zhptri_(char *uplo, integer *n, doublecomplex *ap,
|
|
integer *ipiv, doublecomplex *work, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer i__1, i__2, i__3;
|
|
doublereal d__1;
|
|
doublecomplex z__1, z__2;
|
|
|
|
/* Local variables */
|
|
doublecomplex temp, akkp1;
|
|
doublereal d__;
|
|
integer j, k;
|
|
doublereal t;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *);
|
|
integer kstep;
|
|
logical upper;
|
|
extern /* Subroutine */ void zcopy_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *), zhpmv_(char *, integer *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
|
|
doublecomplex *, doublecomplex *, integer *), zswap_(
|
|
integer *, doublecomplex *, integer *, doublecomplex *, integer *)
|
|
;
|
|
doublereal ak;
|
|
integer kc, kp, kx;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
integer kcnext, kpc, npp;
|
|
doublereal akp1;
|
|
|
|
|
|
/* -- 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 */
|
|
--work;
|
|
--ipiv;
|
|
--ap;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
upper = lsame_(uplo, "U");
|
|
if (! upper && ! lsame_(uplo, "L")) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZHPTRI", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Check that the diagonal matrix D is nonsingular. */
|
|
|
|
if (upper) {
|
|
|
|
/* Upper triangular storage: examine D from bottom to top */
|
|
|
|
kp = *n * (*n + 1) / 2;
|
|
for (*info = *n; *info >= 1; --(*info)) {
|
|
i__1 = kp;
|
|
if (ipiv[*info] > 0 && (ap[i__1].r == 0. && ap[i__1].i == 0.)) {
|
|
return;
|
|
}
|
|
kp -= *info;
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
|
|
/* Lower triangular storage: examine D from top to bottom. */
|
|
|
|
kp = 1;
|
|
i__1 = *n;
|
|
for (*info = 1; *info <= i__1; ++(*info)) {
|
|
i__2 = kp;
|
|
if (ipiv[*info] > 0 && (ap[i__2].r == 0. && ap[i__2].i == 0.)) {
|
|
return;
|
|
}
|
|
kp = kp + *n - *info + 1;
|
|
/* L20: */
|
|
}
|
|
}
|
|
*info = 0;
|
|
|
|
if (upper) {
|
|
|
|
/* Compute inv(A) from the factorization A = U*D*U**H. */
|
|
|
|
/* K is the main loop index, increasing from 1 to N in steps of */
|
|
/* 1 or 2, depending on the size of the diagonal blocks. */
|
|
|
|
k = 1;
|
|
kc = 1;
|
|
L30:
|
|
|
|
/* If K > N, exit from loop. */
|
|
|
|
if (k > *n) {
|
|
goto L50;
|
|
}
|
|
|
|
kcnext = kc + k;
|
|
if (ipiv[k] > 0) {
|
|
|
|
/* 1 x 1 diagonal block */
|
|
|
|
/* Invert the diagonal block. */
|
|
|
|
i__1 = kc + k - 1;
|
|
i__2 = kc + k - 1;
|
|
d__1 = 1. / ap[i__2].r;
|
|
ap[i__1].r = d__1, ap[i__1].i = 0.;
|
|
|
|
/* Compute column K of the inverse. */
|
|
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
zcopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
|
|
i__1 = k - 1;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zhpmv_(uplo, &i__1, &z__1, &ap[1], &work[1], &c__1, &c_b2, &
|
|
ap[kc], &c__1);
|
|
i__1 = kc + k - 1;
|
|
i__2 = kc + k - 1;
|
|
i__3 = k - 1;
|
|
zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kc], &c__1);
|
|
d__1 = z__2.r;
|
|
z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
}
|
|
kstep = 1;
|
|
} else {
|
|
|
|
/* 2 x 2 diagonal block */
|
|
|
|
/* Invert the diagonal block. */
|
|
|
|
t = z_abs(&ap[kcnext + k - 1]);
|
|
i__1 = kc + k - 1;
|
|
ak = ap[i__1].r / t;
|
|
i__1 = kcnext + k;
|
|
akp1 = ap[i__1].r / t;
|
|
i__1 = kcnext + k - 1;
|
|
z__1.r = ap[i__1].r / t, z__1.i = ap[i__1].i / t;
|
|
akkp1.r = z__1.r, akkp1.i = z__1.i;
|
|
d__ = t * (ak * akp1 - 1.);
|
|
i__1 = kc + k - 1;
|
|
d__1 = akp1 / d__;
|
|
ap[i__1].r = d__1, ap[i__1].i = 0.;
|
|
i__1 = kcnext + k;
|
|
d__1 = ak / d__;
|
|
ap[i__1].r = d__1, ap[i__1].i = 0.;
|
|
i__1 = kcnext + k - 1;
|
|
z__2.r = -akkp1.r, z__2.i = -akkp1.i;
|
|
z__1.r = z__2.r / d__, z__1.i = z__2.i / d__;
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
|
|
/* Compute columns K and K+1 of the inverse. */
|
|
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
zcopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
|
|
i__1 = k - 1;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zhpmv_(uplo, &i__1, &z__1, &ap[1], &work[1], &c__1, &c_b2, &
|
|
ap[kc], &c__1);
|
|
i__1 = kc + k - 1;
|
|
i__2 = kc + k - 1;
|
|
i__3 = k - 1;
|
|
zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kc], &c__1);
|
|
d__1 = z__2.r;
|
|
z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
i__1 = kcnext + k - 1;
|
|
i__2 = kcnext + k - 1;
|
|
i__3 = k - 1;
|
|
zdotc_(&z__2, &i__3, &ap[kc], &c__1, &ap[kcnext], &c__1);
|
|
z__1.r = ap[i__2].r - z__2.r, z__1.i = ap[i__2].i - z__2.i;
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
i__1 = k - 1;
|
|
zcopy_(&i__1, &ap[kcnext], &c__1, &work[1], &c__1);
|
|
i__1 = k - 1;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zhpmv_(uplo, &i__1, &z__1, &ap[1], &work[1], &c__1, &c_b2, &
|
|
ap[kcnext], &c__1);
|
|
i__1 = kcnext + k;
|
|
i__2 = kcnext + k;
|
|
i__3 = k - 1;
|
|
zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kcnext], &c__1);
|
|
d__1 = z__2.r;
|
|
z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
}
|
|
kstep = 2;
|
|
kcnext = kcnext + k + 1;
|
|
}
|
|
|
|
kp = (i__1 = ipiv[k], abs(i__1));
|
|
if (kp != k) {
|
|
|
|
/* Interchange rows and columns K and KP in the leading */
|
|
/* submatrix A(1:k+1,1:k+1) */
|
|
|
|
kpc = (kp - 1) * kp / 2 + 1;
|
|
i__1 = kp - 1;
|
|
zswap_(&i__1, &ap[kc], &c__1, &ap[kpc], &c__1);
|
|
kx = kpc + kp - 1;
|
|
i__1 = k - 1;
|
|
for (j = kp + 1; j <= i__1; ++j) {
|
|
kx = kx + j - 1;
|
|
d_cnjg(&z__1, &ap[kc + j - 1]);
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
i__2 = kc + j - 1;
|
|
d_cnjg(&z__1, &ap[kx]);
|
|
ap[i__2].r = z__1.r, ap[i__2].i = z__1.i;
|
|
i__2 = kx;
|
|
ap[i__2].r = temp.r, ap[i__2].i = temp.i;
|
|
/* L40: */
|
|
}
|
|
i__1 = kc + kp - 1;
|
|
d_cnjg(&z__1, &ap[kc + kp - 1]);
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
i__1 = kc + k - 1;
|
|
temp.r = ap[i__1].r, temp.i = ap[i__1].i;
|
|
i__1 = kc + k - 1;
|
|
i__2 = kpc + kp - 1;
|
|
ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
|
|
i__1 = kpc + kp - 1;
|
|
ap[i__1].r = temp.r, ap[i__1].i = temp.i;
|
|
if (kstep == 2) {
|
|
i__1 = kc + k + k - 1;
|
|
temp.r = ap[i__1].r, temp.i = ap[i__1].i;
|
|
i__1 = kc + k + k - 1;
|
|
i__2 = kc + k + kp - 1;
|
|
ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
|
|
i__1 = kc + k + kp - 1;
|
|
ap[i__1].r = temp.r, ap[i__1].i = temp.i;
|
|
}
|
|
}
|
|
|
|
k += kstep;
|
|
kc = kcnext;
|
|
goto L30;
|
|
L50:
|
|
|
|
;
|
|
} else {
|
|
|
|
/* Compute inv(A) from the factorization A = L*D*L**H. */
|
|
|
|
/* K is the main loop index, increasing from 1 to N in steps of */
|
|
/* 1 or 2, depending on the size of the diagonal blocks. */
|
|
|
|
npp = *n * (*n + 1) / 2;
|
|
k = *n;
|
|
kc = npp;
|
|
L60:
|
|
|
|
/* If K < 1, exit from loop. */
|
|
|
|
if (k < 1) {
|
|
goto L80;
|
|
}
|
|
|
|
kcnext = kc - (*n - k + 2);
|
|
if (ipiv[k] > 0) {
|
|
|
|
/* 1 x 1 diagonal block */
|
|
|
|
/* Invert the diagonal block. */
|
|
|
|
i__1 = kc;
|
|
i__2 = kc;
|
|
d__1 = 1. / ap[i__2].r;
|
|
ap[i__1].r = d__1, ap[i__1].i = 0.;
|
|
|
|
/* Compute column K of the inverse. */
|
|
|
|
if (k < *n) {
|
|
i__1 = *n - k;
|
|
zcopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
|
|
i__1 = *n - k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zhpmv_(uplo, &i__1, &z__1, &ap[kc + *n - k + 1], &work[1], &
|
|
c__1, &c_b2, &ap[kc + 1], &c__1);
|
|
i__1 = kc;
|
|
i__2 = kc;
|
|
i__3 = *n - k;
|
|
zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kc + 1], &c__1);
|
|
d__1 = z__2.r;
|
|
z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
}
|
|
kstep = 1;
|
|
} else {
|
|
|
|
/* 2 x 2 diagonal block */
|
|
|
|
/* Invert the diagonal block. */
|
|
|
|
t = z_abs(&ap[kcnext + 1]);
|
|
i__1 = kcnext;
|
|
ak = ap[i__1].r / t;
|
|
i__1 = kc;
|
|
akp1 = ap[i__1].r / t;
|
|
i__1 = kcnext + 1;
|
|
z__1.r = ap[i__1].r / t, z__1.i = ap[i__1].i / t;
|
|
akkp1.r = z__1.r, akkp1.i = z__1.i;
|
|
d__ = t * (ak * akp1 - 1.);
|
|
i__1 = kcnext;
|
|
d__1 = akp1 / d__;
|
|
ap[i__1].r = d__1, ap[i__1].i = 0.;
|
|
i__1 = kc;
|
|
d__1 = ak / d__;
|
|
ap[i__1].r = d__1, ap[i__1].i = 0.;
|
|
i__1 = kcnext + 1;
|
|
z__2.r = -akkp1.r, z__2.i = -akkp1.i;
|
|
z__1.r = z__2.r / d__, z__1.i = z__2.i / d__;
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
|
|
/* Compute columns K-1 and K of the inverse. */
|
|
|
|
if (k < *n) {
|
|
i__1 = *n - k;
|
|
zcopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
|
|
i__1 = *n - k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zhpmv_(uplo, &i__1, &z__1, &ap[kc + (*n - k + 1)], &work[1], &
|
|
c__1, &c_b2, &ap[kc + 1], &c__1);
|
|
i__1 = kc;
|
|
i__2 = kc;
|
|
i__3 = *n - k;
|
|
zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kc + 1], &c__1);
|
|
d__1 = z__2.r;
|
|
z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
i__1 = kcnext + 1;
|
|
i__2 = kcnext + 1;
|
|
i__3 = *n - k;
|
|
zdotc_(&z__2, &i__3, &ap[kc + 1], &c__1, &ap[kcnext + 2], &
|
|
c__1);
|
|
z__1.r = ap[i__2].r - z__2.r, z__1.i = ap[i__2].i - z__2.i;
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
i__1 = *n - k;
|
|
zcopy_(&i__1, &ap[kcnext + 2], &c__1, &work[1], &c__1);
|
|
i__1 = *n - k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zhpmv_(uplo, &i__1, &z__1, &ap[kc + (*n - k + 1)], &work[1], &
|
|
c__1, &c_b2, &ap[kcnext + 2], &c__1);
|
|
i__1 = kcnext;
|
|
i__2 = kcnext;
|
|
i__3 = *n - k;
|
|
zdotc_(&z__2, &i__3, &work[1], &c__1, &ap[kcnext + 2], &c__1);
|
|
d__1 = z__2.r;
|
|
z__1.r = ap[i__2].r - d__1, z__1.i = ap[i__2].i;
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
}
|
|
kstep = 2;
|
|
kcnext -= *n - k + 3;
|
|
}
|
|
|
|
kp = (i__1 = ipiv[k], abs(i__1));
|
|
if (kp != k) {
|
|
|
|
/* Interchange rows and columns K and KP in the trailing */
|
|
/* submatrix A(k-1:n,k-1:n) */
|
|
|
|
kpc = npp - (*n - kp + 1) * (*n - kp + 2) / 2 + 1;
|
|
if (kp < *n) {
|
|
i__1 = *n - kp;
|
|
zswap_(&i__1, &ap[kc + kp - k + 1], &c__1, &ap[kpc + 1], &
|
|
c__1);
|
|
}
|
|
kx = kc + kp - k;
|
|
i__1 = kp - 1;
|
|
for (j = k + 1; j <= i__1; ++j) {
|
|
kx = kx + *n - j + 1;
|
|
d_cnjg(&z__1, &ap[kc + j - k]);
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
i__2 = kc + j - k;
|
|
d_cnjg(&z__1, &ap[kx]);
|
|
ap[i__2].r = z__1.r, ap[i__2].i = z__1.i;
|
|
i__2 = kx;
|
|
ap[i__2].r = temp.r, ap[i__2].i = temp.i;
|
|
/* L70: */
|
|
}
|
|
i__1 = kc + kp - k;
|
|
d_cnjg(&z__1, &ap[kc + kp - k]);
|
|
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
|
|
i__1 = kc;
|
|
temp.r = ap[i__1].r, temp.i = ap[i__1].i;
|
|
i__1 = kc;
|
|
i__2 = kpc;
|
|
ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
|
|
i__1 = kpc;
|
|
ap[i__1].r = temp.r, ap[i__1].i = temp.i;
|
|
if (kstep == 2) {
|
|
i__1 = kc - *n + k - 1;
|
|
temp.r = ap[i__1].r, temp.i = ap[i__1].i;
|
|
i__1 = kc - *n + k - 1;
|
|
i__2 = kc - *n + kp - 1;
|
|
ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
|
|
i__1 = kc - *n + kp - 1;
|
|
ap[i__1].r = temp.r, ap[i__1].i = temp.i;
|
|
}
|
|
}
|
|
|
|
k -= kstep;
|
|
kc = kcnext;
|
|
goto L60;
|
|
L80:
|
|
;
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZHPTRI */
|
|
|
|
} /* zhptri_ */
|
|
|