1383 lines
39 KiB
C
1383 lines
39 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 complex c_b1 = {1.f,0.f};
|
|
static complex c_b2 = {0.f,0.f};
|
|
|
|
/* > \brief \b CSYTRI2X */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CSYTRI2X + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csytri2
|
|
x.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csytri2
|
|
x.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csytri2
|
|
x.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO ) */
|
|
|
|
/* CHARACTER UPLO */
|
|
/* INTEGER INFO, LDA, N, NB */
|
|
/* INTEGER IPIV( * ) */
|
|
/* COMPLEX A( LDA, * ), WORK( N+NB+1,* ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CSYTRI2X computes the inverse of a real symmetric indefinite matrix */
|
|
/* > A using the factorization A = U*D*U**T or A = L*D*L**T computed by */
|
|
/* > CSYTRF. */
|
|
/* > \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**T; */
|
|
/* > = 'L': Lower triangular, form is A = L*D*L**T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX array, dimension (LDA,N) */
|
|
/* > On entry, the NNB diagonal matrix D and the multipliers */
|
|
/* > used to obtain the factor U or L as computed by CSYTRF. */
|
|
/* > */
|
|
/* > On exit, if INFO = 0, the (symmetric) inverse of the original */
|
|
/* > matrix. If UPLO = 'U', the upper triangular part of the */
|
|
/* > inverse is formed and the part of A below the diagonal is not */
|
|
/* > referenced; if UPLO = 'L' the lower triangular part of the */
|
|
/* > inverse is formed and the part of A above the diagonal is */
|
|
/* > not referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IPIV */
|
|
/* > \verbatim */
|
|
/* > IPIV is INTEGER array, dimension (N) */
|
|
/* > Details of the interchanges and the NNB structure of D */
|
|
/* > as determined by CSYTRF. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX array, dimension (N+NB+1,NB+3) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NB */
|
|
/* > \verbatim */
|
|
/* > NB is INTEGER */
|
|
/* > Block size */
|
|
/* > \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 June 2017 */
|
|
|
|
/* > \ingroup complexSYcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void csytri2x_(char *uplo, integer *n, complex *a, integer *
|
|
lda, integer *ipiv, complex *work, integer *nb, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, work_dim1, work_offset, i__1, i__2, i__3, i__4,
|
|
i__5, i__6;
|
|
complex q__1, q__2, q__3;
|
|
|
|
/* Local variables */
|
|
integer invd;
|
|
complex akkp1;
|
|
extern /* Subroutine */ void csyswapr_(char *, integer *, complex *,
|
|
integer *, integer *, integer *);
|
|
complex d__;
|
|
integer i__, j, k;
|
|
complex t;
|
|
extern /* Subroutine */ void cgemm_(char *, char *, integer *, integer *,
|
|
integer *, complex *, complex *, integer *, complex *, integer *,
|
|
complex *, complex *, integer *);
|
|
extern logical lsame_(char *, char *);
|
|
integer iinfo;
|
|
extern /* Subroutine */ void ctrmm_(char *, char *, char *, char *,
|
|
integer *, integer *, complex *, complex *, integer *, complex *,
|
|
integer *);
|
|
integer count;
|
|
logical upper;
|
|
complex ak, u01_i_j__;
|
|
integer u11;
|
|
complex u11_i_j__;
|
|
integer ip;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern int ctrtri_(
|
|
char *, char *, integer *, complex *, integer *, integer *);
|
|
integer nnb, cut;
|
|
complex akp1;
|
|
extern /* Subroutine */ void csyconv_(char *, char *, integer *, complex *,
|
|
integer *, integer *, complex *, integer *);
|
|
complex u01_ip1_j__, u11_ip1_j__;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2017 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--ipiv;
|
|
work_dim1 = *n + *nb + 1;
|
|
work_offset = 1 + work_dim1 * 1;
|
|
work -= work_offset;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
upper = lsame_(uplo, "U");
|
|
if (! upper && ! lsame_(uplo, "L")) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*lda < f2cmax(1,*n)) {
|
|
*info = -4;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CSYTRI2X", &i__1, (ftnlen)8);
|
|
return;
|
|
}
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Convert A */
|
|
/* Workspace got Non-diag elements of D */
|
|
|
|
csyconv_(uplo, "C", n, &a[a_offset], lda, &ipiv[1], &work[work_offset], &
|
|
iinfo);
|
|
|
|
/* Check that the diagonal matrix D is nonsingular. */
|
|
|
|
if (upper) {
|
|
|
|
/* Upper triangular storage: examine D from bottom to top */
|
|
|
|
for (*info = *n; *info >= 1; --(*info)) {
|
|
i__1 = *info + *info * a_dim1;
|
|
if (ipiv[*info] > 0 && (a[i__1].r == 0.f && a[i__1].i == 0.f)) {
|
|
return;
|
|
}
|
|
}
|
|
} else {
|
|
|
|
/* Lower triangular storage: examine D from top to bottom. */
|
|
|
|
i__1 = *n;
|
|
for (*info = 1; *info <= i__1; ++(*info)) {
|
|
i__2 = *info + *info * a_dim1;
|
|
if (ipiv[*info] > 0 && (a[i__2].r == 0.f && a[i__2].i == 0.f)) {
|
|
return;
|
|
}
|
|
}
|
|
}
|
|
*info = 0;
|
|
|
|
/* Splitting Workspace */
|
|
/* U01 is a block (N,NB+1) */
|
|
/* The first element of U01 is in WORK(1,1) */
|
|
/* U11 is a block (NB+1,NB+1) */
|
|
/* The first element of U11 is in WORK(N+1,1) */
|
|
u11 = *n;
|
|
/* INVD is a block (N,2) */
|
|
/* The first element of INVD is in WORK(1,INVD) */
|
|
invd = *nb + 2;
|
|
if (upper) {
|
|
|
|
/* invA = P * inv(U**T)*inv(D)*inv(U)*P**T. */
|
|
|
|
ctrtri_(uplo, "U", n, &a[a_offset], lda, info);
|
|
|
|
/* inv(D) and inv(D)*inv(U) */
|
|
|
|
k = 1;
|
|
while(k <= *n) {
|
|
if (ipiv[k] > 0) {
|
|
/* 1 x 1 diagonal NNB */
|
|
i__1 = k + invd * work_dim1;
|
|
c_div(&q__1, &c_b1, &a[k + k * a_dim1]);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
i__1 = k + (invd + 1) * work_dim1;
|
|
work[i__1].r = 0.f, work[i__1].i = 0.f;
|
|
++k;
|
|
} else {
|
|
/* 2 x 2 diagonal NNB */
|
|
i__1 = k + 1 + work_dim1;
|
|
t.r = work[i__1].r, t.i = work[i__1].i;
|
|
c_div(&q__1, &a[k + k * a_dim1], &t);
|
|
ak.r = q__1.r, ak.i = q__1.i;
|
|
c_div(&q__1, &a[k + 1 + (k + 1) * a_dim1], &t);
|
|
akp1.r = q__1.r, akp1.i = q__1.i;
|
|
c_div(&q__1, &work[k + 1 + work_dim1], &t);
|
|
akkp1.r = q__1.r, akkp1.i = q__1.i;
|
|
q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r *
|
|
akp1.i + ak.i * akp1.r;
|
|
q__2.r = q__3.r - 1.f, q__2.i = q__3.i + 0.f;
|
|
q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i +
|
|
t.i * q__2.r;
|
|
d__.r = q__1.r, d__.i = q__1.i;
|
|
i__1 = k + invd * work_dim1;
|
|
c_div(&q__1, &akp1, &d__);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
i__1 = k + 1 + (invd + 1) * work_dim1;
|
|
c_div(&q__1, &ak, &d__);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
i__1 = k + (invd + 1) * work_dim1;
|
|
q__2.r = -akkp1.r, q__2.i = -akkp1.i;
|
|
c_div(&q__1, &q__2, &d__);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
i__1 = k + 1 + invd * work_dim1;
|
|
q__2.r = -akkp1.r, q__2.i = -akkp1.i;
|
|
c_div(&q__1, &q__2, &d__);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
k += 2;
|
|
}
|
|
}
|
|
|
|
/* inv(U**T) = (inv(U))**T */
|
|
|
|
/* inv(U**T)*inv(D)*inv(U) */
|
|
|
|
cut = *n;
|
|
while(cut > 0) {
|
|
nnb = *nb;
|
|
if (cut <= nnb) {
|
|
nnb = cut;
|
|
} else {
|
|
count = 0;
|
|
/* count negative elements, */
|
|
i__1 = cut;
|
|
for (i__ = cut + 1 - nnb; i__ <= i__1; ++i__) {
|
|
if (ipiv[i__] < 0) {
|
|
++count;
|
|
}
|
|
}
|
|
/* need a even number for a clear cut */
|
|
if (count % 2 == 1) {
|
|
++nnb;
|
|
}
|
|
}
|
|
cut -= nnb;
|
|
|
|
/* U01 Block */
|
|
|
|
i__1 = cut;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = nnb;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = i__ + j * work_dim1;
|
|
i__4 = i__ + (cut + j) * a_dim1;
|
|
work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
|
|
}
|
|
}
|
|
|
|
/* U11 Block */
|
|
|
|
i__1 = nnb;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = u11 + i__ + i__ * work_dim1;
|
|
work[i__2].r = 1.f, work[i__2].i = 0.f;
|
|
i__2 = i__ - 1;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = u11 + i__ + j * work_dim1;
|
|
work[i__3].r = 0.f, work[i__3].i = 0.f;
|
|
}
|
|
i__2 = nnb;
|
|
for (j = i__ + 1; j <= i__2; ++j) {
|
|
i__3 = u11 + i__ + j * work_dim1;
|
|
i__4 = cut + i__ + (cut + j) * a_dim1;
|
|
work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
|
|
}
|
|
}
|
|
|
|
/* invD*U01 */
|
|
|
|
i__ = 1;
|
|
while(i__ <= cut) {
|
|
if (ipiv[i__] > 0) {
|
|
i__1 = nnb;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = i__ + j * work_dim1;
|
|
i__3 = i__ + invd * work_dim1;
|
|
i__4 = i__ + j * work_dim1;
|
|
q__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
|
|
work[i__4].i, q__1.i = work[i__3].r * work[
|
|
i__4].i + work[i__3].i * work[i__4].r;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
}
|
|
++i__;
|
|
} else {
|
|
i__1 = nnb;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = i__ + j * work_dim1;
|
|
u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2]
|
|
.i;
|
|
i__2 = i__ + 1 + j * work_dim1;
|
|
u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[
|
|
i__2].i;
|
|
i__2 = i__ + j * work_dim1;
|
|
i__3 = i__ + invd * work_dim1;
|
|
q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
|
|
u01_i_j__.i, q__2.i = work[i__3].r *
|
|
u01_i_j__.i + work[i__3].i * u01_i_j__.r;
|
|
i__4 = i__ + (invd + 1) * work_dim1;
|
|
q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
|
|
u01_ip1_j__.i, q__3.i = work[i__4].r *
|
|
u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
|
|
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
i__2 = i__ + 1 + j * work_dim1;
|
|
i__3 = i__ + 1 + invd * work_dim1;
|
|
q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
|
|
u01_i_j__.i, q__2.i = work[i__3].r *
|
|
u01_i_j__.i + work[i__3].i * u01_i_j__.r;
|
|
i__4 = i__ + 1 + (invd + 1) * work_dim1;
|
|
q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
|
|
u01_ip1_j__.i, q__3.i = work[i__4].r *
|
|
u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
|
|
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
}
|
|
i__ += 2;
|
|
}
|
|
}
|
|
|
|
/* invD1*U11 */
|
|
|
|
i__ = 1;
|
|
while(i__ <= nnb) {
|
|
if (ipiv[cut + i__] > 0) {
|
|
i__1 = nnb;
|
|
for (j = i__; j <= i__1; ++j) {
|
|
i__2 = u11 + i__ + j * work_dim1;
|
|
i__3 = cut + i__ + invd * work_dim1;
|
|
i__4 = u11 + i__ + j * work_dim1;
|
|
q__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
|
|
work[i__4].i, q__1.i = work[i__3].r * work[
|
|
i__4].i + work[i__3].i * work[i__4].r;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
}
|
|
++i__;
|
|
} else {
|
|
i__1 = nnb;
|
|
for (j = i__; j <= i__1; ++j) {
|
|
i__2 = u11 + i__ + j * work_dim1;
|
|
u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2]
|
|
.i;
|
|
i__2 = u11 + i__ + 1 + j * work_dim1;
|
|
u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[
|
|
i__2].i;
|
|
i__2 = u11 + i__ + j * work_dim1;
|
|
i__3 = cut + i__ + invd * work_dim1;
|
|
i__4 = u11 + i__ + j * work_dim1;
|
|
q__2.r = work[i__3].r * work[i__4].r - work[i__3].i *
|
|
work[i__4].i, q__2.i = work[i__3].r * work[
|
|
i__4].i + work[i__3].i * work[i__4].r;
|
|
i__5 = cut + i__ + (invd + 1) * work_dim1;
|
|
i__6 = u11 + i__ + 1 + j * work_dim1;
|
|
q__3.r = work[i__5].r * work[i__6].r - work[i__5].i *
|
|
work[i__6].i, q__3.i = work[i__5].r * work[
|
|
i__6].i + work[i__5].i * work[i__6].r;
|
|
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
i__2 = u11 + i__ + 1 + j * work_dim1;
|
|
i__3 = cut + i__ + 1 + invd * work_dim1;
|
|
q__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i *
|
|
u11_i_j__.i, q__2.i = work[i__3].r *
|
|
u11_i_j__.i + work[i__3].i * u11_i_j__.r;
|
|
i__4 = cut + i__ + 1 + (invd + 1) * work_dim1;
|
|
q__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i *
|
|
u11_ip1_j__.i, q__3.i = work[i__4].r *
|
|
u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r;
|
|
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
}
|
|
i__ += 2;
|
|
}
|
|
}
|
|
|
|
/* U11**T*invD1*U11->U11 */
|
|
|
|
i__1 = *n + *nb + 1;
|
|
ctrmm_("L", "U", "T", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut +
|
|
1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
|
|
|
|
i__1 = nnb;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = nnb;
|
|
for (j = i__; j <= i__2; ++j) {
|
|
i__3 = cut + i__ + (cut + j) * a_dim1;
|
|
i__4 = u11 + i__ + j * work_dim1;
|
|
a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
|
|
}
|
|
}
|
|
|
|
/* U01**T*invD*U01->A(CUT+I,CUT+J) */
|
|
|
|
i__1 = *n + *nb + 1;
|
|
i__2 = *n + *nb + 1;
|
|
cgemm_("T", "N", &nnb, &nnb, &cut, &c_b1, &a[(cut + 1) * a_dim1 +
|
|
1], lda, &work[work_offset], &i__1, &c_b2, &work[u11 + 1
|
|
+ work_dim1], &i__2);
|
|
|
|
/* U11 = U11**T*invD1*U11 + U01**T*invD*U01 */
|
|
|
|
i__1 = nnb;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = nnb;
|
|
for (j = i__; j <= i__2; ++j) {
|
|
i__3 = cut + i__ + (cut + j) * a_dim1;
|
|
i__4 = cut + i__ + (cut + j) * a_dim1;
|
|
i__5 = u11 + i__ + j * work_dim1;
|
|
q__1.r = a[i__4].r + work[i__5].r, q__1.i = a[i__4].i +
|
|
work[i__5].i;
|
|
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
|
|
}
|
|
}
|
|
|
|
/* U01 = U00**T*invD0*U01 */
|
|
|
|
i__1 = *n + *nb + 1;
|
|
ctrmm_("L", uplo, "T", "U", &cut, &nnb, &c_b1, &a[a_offset], lda,
|
|
&work[work_offset], &i__1);
|
|
|
|
/* Update U01 */
|
|
|
|
i__1 = cut;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = nnb;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = i__ + (cut + j) * a_dim1;
|
|
i__4 = i__ + j * work_dim1;
|
|
a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
|
|
}
|
|
}
|
|
|
|
/* Next Block */
|
|
|
|
}
|
|
|
|
/* Apply PERMUTATIONS P and P**T: P * inv(U**T)*inv(D)*inv(U) *P**T */
|
|
|
|
i__ = 1;
|
|
while(i__ <= *n) {
|
|
if (ipiv[i__] > 0) {
|
|
ip = ipiv[i__];
|
|
if (i__ < ip) {
|
|
csyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
|
|
}
|
|
if (i__ > ip) {
|
|
csyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
|
|
}
|
|
} else {
|
|
ip = -ipiv[i__];
|
|
++i__;
|
|
if (i__ - 1 < ip) {
|
|
i__1 = i__ - 1;
|
|
csyswapr_(uplo, n, &a[a_offset], lda, &i__1, &ip);
|
|
}
|
|
if (i__ - 1 > ip) {
|
|
i__1 = i__ - 1;
|
|
csyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__1);
|
|
}
|
|
}
|
|
++i__;
|
|
}
|
|
} else {
|
|
|
|
/* LOWER... */
|
|
|
|
/* invA = P * inv(U**T)*inv(D)*inv(U)*P**T. */
|
|
|
|
ctrtri_(uplo, "U", n, &a[a_offset], lda, info);
|
|
|
|
/* inv(D) and inv(D)*inv(U) */
|
|
|
|
k = *n;
|
|
while(k >= 1) {
|
|
if (ipiv[k] > 0) {
|
|
/* 1 x 1 diagonal NNB */
|
|
i__1 = k + invd * work_dim1;
|
|
c_div(&q__1, &c_b1, &a[k + k * a_dim1]);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
i__1 = k + (invd + 1) * work_dim1;
|
|
work[i__1].r = 0.f, work[i__1].i = 0.f;
|
|
--k;
|
|
} else {
|
|
/* 2 x 2 diagonal NNB */
|
|
i__1 = k - 1 + work_dim1;
|
|
t.r = work[i__1].r, t.i = work[i__1].i;
|
|
c_div(&q__1, &a[k - 1 + (k - 1) * a_dim1], &t);
|
|
ak.r = q__1.r, ak.i = q__1.i;
|
|
c_div(&q__1, &a[k + k * a_dim1], &t);
|
|
akp1.r = q__1.r, akp1.i = q__1.i;
|
|
c_div(&q__1, &work[k - 1 + work_dim1], &t);
|
|
akkp1.r = q__1.r, akkp1.i = q__1.i;
|
|
q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r *
|
|
akp1.i + ak.i * akp1.r;
|
|
q__2.r = q__3.r - 1.f, q__2.i = q__3.i + 0.f;
|
|
q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i +
|
|
t.i * q__2.r;
|
|
d__.r = q__1.r, d__.i = q__1.i;
|
|
i__1 = k - 1 + invd * work_dim1;
|
|
c_div(&q__1, &akp1, &d__);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
i__1 = k + invd * work_dim1;
|
|
c_div(&q__1, &ak, &d__);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
i__1 = k + (invd + 1) * work_dim1;
|
|
q__2.r = -akkp1.r, q__2.i = -akkp1.i;
|
|
c_div(&q__1, &q__2, &d__);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
i__1 = k - 1 + (invd + 1) * work_dim1;
|
|
q__2.r = -akkp1.r, q__2.i = -akkp1.i;
|
|
c_div(&q__1, &q__2, &d__);
|
|
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
|
|
k += -2;
|
|
}
|
|
}
|
|
|
|
/* inv(U**T) = (inv(U))**T */
|
|
|
|
/* inv(U**T)*inv(D)*inv(U) */
|
|
|
|
cut = 0;
|
|
while(cut < *n) {
|
|
nnb = *nb;
|
|
if (cut + nnb >= *n) {
|
|
nnb = *n - cut;
|
|
} else {
|
|
count = 0;
|
|
/* count negative elements, */
|
|
i__1 = cut + nnb;
|
|
for (i__ = cut + 1; i__ <= i__1; ++i__) {
|
|
if (ipiv[i__] < 0) {
|
|
++count;
|
|
}
|
|
}
|
|
/* need a even number for a clear cut */
|
|
if (count % 2 == 1) {
|
|
++nnb;
|
|
}
|
|
}
|
|
/* L21 Block */
|
|
i__1 = *n - cut - nnb;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = nnb;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = i__ + j * work_dim1;
|
|
i__4 = cut + nnb + i__ + (cut + j) * a_dim1;
|
|
work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
|
|
}
|
|
}
|
|
/* L11 Block */
|
|
i__1 = nnb;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = u11 + i__ + i__ * work_dim1;
|
|
work[i__2].r = 1.f, work[i__2].i = 0.f;
|
|
i__2 = nnb;
|
|
for (j = i__ + 1; j <= i__2; ++j) {
|
|
i__3 = u11 + i__ + j * work_dim1;
|
|
work[i__3].r = 0.f, work[i__3].i = 0.f;
|
|
}
|
|
i__2 = i__ - 1;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = u11 + i__ + j * work_dim1;
|
|
i__4 = cut + i__ + (cut + j) * a_dim1;
|
|
work[i__3].r = a[i__4].r, work[i__3].i = a[i__4].i;
|
|
}
|
|
}
|
|
|
|
/* invD*L21 */
|
|
|
|
i__ = *n - cut - nnb;
|
|
while(i__ >= 1) {
|
|
if (ipiv[cut + nnb + i__] > 0) {
|
|
i__1 = nnb;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = i__ + j * work_dim1;
|
|
i__3 = cut + nnb + i__ + invd * work_dim1;
|
|
i__4 = i__ + j * work_dim1;
|
|
q__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
|
|
work[i__4].i, q__1.i = work[i__3].r * work[
|
|
i__4].i + work[i__3].i * work[i__4].r;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
}
|
|
--i__;
|
|
} else {
|
|
i__1 = nnb;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = i__ + j * work_dim1;
|
|
u01_i_j__.r = work[i__2].r, u01_i_j__.i = work[i__2]
|
|
.i;
|
|
i__2 = i__ - 1 + j * work_dim1;
|
|
u01_ip1_j__.r = work[i__2].r, u01_ip1_j__.i = work[
|
|
i__2].i;
|
|
i__2 = i__ + j * work_dim1;
|
|
i__3 = cut + nnb + i__ + invd * work_dim1;
|
|
q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
|
|
u01_i_j__.i, q__2.i = work[i__3].r *
|
|
u01_i_j__.i + work[i__3].i * u01_i_j__.r;
|
|
i__4 = cut + nnb + i__ + (invd + 1) * work_dim1;
|
|
q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
|
|
u01_ip1_j__.i, q__3.i = work[i__4].r *
|
|
u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
|
|
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
i__2 = i__ - 1 + j * work_dim1;
|
|
i__3 = cut + nnb + i__ - 1 + (invd + 1) * work_dim1;
|
|
q__2.r = work[i__3].r * u01_i_j__.r - work[i__3].i *
|
|
u01_i_j__.i, q__2.i = work[i__3].r *
|
|
u01_i_j__.i + work[i__3].i * u01_i_j__.r;
|
|
i__4 = cut + nnb + i__ - 1 + invd * work_dim1;
|
|
q__3.r = work[i__4].r * u01_ip1_j__.r - work[i__4].i *
|
|
u01_ip1_j__.i, q__3.i = work[i__4].r *
|
|
u01_ip1_j__.i + work[i__4].i * u01_ip1_j__.r;
|
|
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
}
|
|
i__ += -2;
|
|
}
|
|
}
|
|
|
|
/* invD1*L11 */
|
|
|
|
i__ = nnb;
|
|
while(i__ >= 1) {
|
|
if (ipiv[cut + i__] > 0) {
|
|
i__1 = nnb;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = u11 + i__ + j * work_dim1;
|
|
i__3 = cut + i__ + invd * work_dim1;
|
|
i__4 = u11 + i__ + j * work_dim1;
|
|
q__1.r = work[i__3].r * work[i__4].r - work[i__3].i *
|
|
work[i__4].i, q__1.i = work[i__3].r * work[
|
|
i__4].i + work[i__3].i * work[i__4].r;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
}
|
|
--i__;
|
|
} else {
|
|
i__1 = nnb;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = u11 + i__ + j * work_dim1;
|
|
u11_i_j__.r = work[i__2].r, u11_i_j__.i = work[i__2]
|
|
.i;
|
|
i__2 = u11 + i__ - 1 + j * work_dim1;
|
|
u11_ip1_j__.r = work[i__2].r, u11_ip1_j__.i = work[
|
|
i__2].i;
|
|
i__2 = u11 + i__ + j * work_dim1;
|
|
i__3 = cut + i__ + invd * work_dim1;
|
|
i__4 = u11 + i__ + j * work_dim1;
|
|
q__2.r = work[i__3].r * work[i__4].r - work[i__3].i *
|
|
work[i__4].i, q__2.i = work[i__3].r * work[
|
|
i__4].i + work[i__3].i * work[i__4].r;
|
|
i__5 = cut + i__ + (invd + 1) * work_dim1;
|
|
q__3.r = work[i__5].r * u11_ip1_j__.r - work[i__5].i *
|
|
u11_ip1_j__.i, q__3.i = work[i__5].r *
|
|
u11_ip1_j__.i + work[i__5].i * u11_ip1_j__.r;
|
|
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
i__2 = u11 + i__ - 1 + j * work_dim1;
|
|
i__3 = cut + i__ - 1 + (invd + 1) * work_dim1;
|
|
q__2.r = work[i__3].r * u11_i_j__.r - work[i__3].i *
|
|
u11_i_j__.i, q__2.i = work[i__3].r *
|
|
u11_i_j__.i + work[i__3].i * u11_i_j__.r;
|
|
i__4 = cut + i__ - 1 + invd * work_dim1;
|
|
q__3.r = work[i__4].r * u11_ip1_j__.r - work[i__4].i *
|
|
u11_ip1_j__.i, q__3.i = work[i__4].r *
|
|
u11_ip1_j__.i + work[i__4].i * u11_ip1_j__.r;
|
|
q__1.r = q__2.r + q__3.r, q__1.i = q__2.i + q__3.i;
|
|
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
|
|
}
|
|
i__ += -2;
|
|
}
|
|
}
|
|
|
|
/* L11**T*invD1*L11->L11 */
|
|
|
|
i__1 = *n + *nb + 1;
|
|
ctrmm_("L", uplo, "T", "U", &nnb, &nnb, &c_b1, &a[cut + 1 + (cut
|
|
+ 1) * a_dim1], lda, &work[u11 + 1 + work_dim1], &i__1);
|
|
|
|
i__1 = nnb;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = cut + i__ + (cut + j) * a_dim1;
|
|
i__4 = u11 + i__ + j * work_dim1;
|
|
a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
|
|
}
|
|
}
|
|
|
|
if (cut + nnb < *n) {
|
|
|
|
/* L21**T*invD2*L21->A(CUT+I,CUT+J) */
|
|
|
|
i__1 = *n - nnb - cut;
|
|
i__2 = *n + *nb + 1;
|
|
i__3 = *n + *nb + 1;
|
|
cgemm_("T", "N", &nnb, &nnb, &i__1, &c_b1, &a[cut + nnb + 1 +
|
|
(cut + 1) * a_dim1], lda, &work[work_offset], &i__2, &
|
|
c_b2, &work[u11 + 1 + work_dim1], &i__3);
|
|
|
|
/* L11 = L11**T*invD1*L11 + U01**T*invD*U01 */
|
|
|
|
i__1 = nnb;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = cut + i__ + (cut + j) * a_dim1;
|
|
i__4 = cut + i__ + (cut + j) * a_dim1;
|
|
i__5 = u11 + i__ + j * work_dim1;
|
|
q__1.r = a[i__4].r + work[i__5].r, q__1.i = a[i__4].i
|
|
+ work[i__5].i;
|
|
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
|
|
}
|
|
}
|
|
|
|
/* L01 = L22**T*invD2*L21 */
|
|
|
|
i__1 = *n - nnb - cut;
|
|
i__2 = *n + *nb + 1;
|
|
ctrmm_("L", uplo, "T", "U", &i__1, &nnb, &c_b1, &a[cut + nnb
|
|
+ 1 + (cut + nnb + 1) * a_dim1], lda, &work[
|
|
work_offset], &i__2);
|
|
/* Update L21 */
|
|
i__1 = *n - cut - nnb;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = nnb;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = cut + nnb + i__ + (cut + j) * a_dim1;
|
|
i__4 = i__ + j * work_dim1;
|
|
a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
|
|
}
|
|
}
|
|
} else {
|
|
|
|
/* L11 = L11**T*invD1*L11 */
|
|
|
|
i__1 = nnb;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
i__3 = cut + i__ + (cut + j) * a_dim1;
|
|
i__4 = u11 + i__ + j * work_dim1;
|
|
a[i__3].r = work[i__4].r, a[i__3].i = work[i__4].i;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Next Block */
|
|
|
|
cut += nnb;
|
|
}
|
|
|
|
/* Apply PERMUTATIONS P and P**T: P * inv(U**T)*inv(D)*inv(U) *P**T */
|
|
|
|
i__ = *n;
|
|
while(i__ >= 1) {
|
|
if (ipiv[i__] > 0) {
|
|
ip = ipiv[i__];
|
|
if (i__ < ip) {
|
|
csyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
|
|
}
|
|
if (i__ > ip) {
|
|
csyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
|
|
}
|
|
} else {
|
|
ip = -ipiv[i__];
|
|
if (i__ < ip) {
|
|
csyswapr_(uplo, n, &a[a_offset], lda, &i__, &ip);
|
|
}
|
|
if (i__ > ip) {
|
|
csyswapr_(uplo, n, &a[a_offset], lda, &ip, &i__);
|
|
}
|
|
--i__;
|
|
}
|
|
--i__;
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of CSYTRI2X */
|
|
|
|
} /* csytri2x_ */
|
|
|