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/******************************************************************
zero_fermi.c generates zero points and associated residues
of a continued fraction expansion terminated at M level
which is derived from a hypergeometric function.
This code is distributed under the constitution of GNU-GPL.
(C) Taisuke Ozaki (AIST-RICS)
The code and tables for the poles and residues can be downloadable
from http://staff.aist.go.jp/t-ozaki/
Log of zero_fermi.c:
26/Nov/2006 Released by T.Ozaki
**** HOW TO COMPILE *****
For example, if there is an ATLAS library, libatlas_p4.a,
in a directory, /home/ozaki/lib, then compile.
% gcc zero_fermi.c -lm -L/home/ozaki/lib -latlas_p4 -o zero_fermi
Binary files for ATLAS can be found in
http://www.theochem.ruhr-uni-bochum.de/~axel.kohlmeyer/cpmd-linux.html
**** USAGE ****
% ./zero_fermi 4
where '4' means the number of poles of the continued fraction of
the Fermi-Dirac function on the upper half complex plane.
**** OUTPUT ****
[ozaki@vtpcc01 exp]$ ./zero_fermi 4
pole residue
1 3.14159265364309e+00 -1.00000000028333e+00
2 9.42675965413364e+00 -1.00295747791527e+00
3 1.66063154702243e+01 -1.56204667295638e+00
4 4.63195086818196e+01 -1.44349958488449e+01
The 1st column: serial number
The 2nd column: the imaginary part of pole,
note that the real is zero.
The 3rd column: residue
******************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <search.h>
#include <string.h>
int main(int argc, char *argv[])
{
int i,j,N,M;
double **A,**B,*zp,*Rp;
/* check input parameters */
if (argc!=2){
printf("\ncould not find the number of zeros\n\n");
exit(0);
}
/* find the number of zeros */
N = (int)atof(argv[1]);
M = 2*N;
/* allocation of arrays */
A = (double**)malloc(sizeof(double*)*(M+2));
for (i=0; i<(M+2); i++){
A[i] = (double*)malloc(sizeof(double)*(M+2));
}
B = (double**)malloc(sizeof(double*)*(M+2));
for (i=0; i<(M+2); i++){
B[i] = (double*)malloc(sizeof(double)*(M+2));
}
zp = (double*)malloc(sizeof(double)*(M+2));
Rp = (double*)malloc(sizeof(double)*(M+2));
/* initialize arrays */
for (i=0; i<(M+2); i++){
for (j=0; j<(M+2); j++){
A[i][j] = 0.0;
B[i][j] = 0.0;
}
}
/* set matrix elements */
for (i=1; i<=M; i++){
B[i][i] = (2.0*(double)i - 1.0);
}
for (i=1; i<=(M-1); i++){
A[i][i+1] = -0.5;
A[i+1][i] = -0.5;
}
/* diagonalization */
{
int i,j;
char jobz = 'V';
char uplo ='U';
static long int itype=1;
static long int n,lda,ldb,lwork,info;
double *a,*b;
double *work;
n = M;
lda = M;
ldb = M;
lwork = 3*M;
a = (double*)malloc(sizeof(double)*n*n);
b = (double*)malloc(sizeof(double)*n*n);
work = (double*)malloc(sizeof(double)*3*n);
for (i=0; i<n; i++) {
for (j=0; j<n; j++) {
a[j*n+i] = A[i+1][j+1];
b[j*n+i] = B[i+1][j+1];
}
}
dsygv_( &itype, &jobz, &uplo, &n, a, &lda, b, &ldb, zp, work, &lwork, &info);
/*
printf("info=%2d\n",info);
*/
/* shift zp by 1 */
for (i=n; i>=1; i--){
zp[i]= zp[i-1];
}
/* store residue */
for (i=1; i<=n; i++){
zp[i] = 1.0/zp[i];
}
for (i=0; i<n; i++) {
Rp[i+1] = -a[i*n]*a[i*n]*zp[i+1]*zp[i+1]*0.250;
}
free(a);
free(b);
free(work);
}
/* print result */
printf("\n pole residue\n\n");
for (i=1; i<=N; i++){
printf("%5d %18.14e %18.14e\n",i,-zp[i],Rp[i]);
}
/* free of arrays */
for (i=0; i<(M+2); i++){
free(A[i]);
}
free(A);
for (i=0; i<(M+2); i++){
free(B[i]);
}
free(B);
free(zp);
free(Rp);
return 0;
}
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