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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
static double rnd(double width);
static double find_Emin(int n, double **a);
int main()
{
static int n,i,j;
static double **a,Emin;
/* size of matrix */
n = 2000;
/* allocation of array */
a = (double**)malloc(sizeof(double*)*(n+1));
for (i=0; i<(n+1); i++){
a[i] = (double*)malloc(sizeof(double)*(n+1));
}
/* initialize the matrix a */
for (i=1; i<=n; i++){
for (j=1; j<=n; j++){
a[i][j] = rnd(1.0);
a[j][i] = a[i][j];
}
}
/* initialize the matrix a */
Emin = find_Emin(n,a);
printf("Emin=%18.15f\n",Emin);
/* freeing of array */
for (i=0; i<(n+1); i++){
free(a[i]);
}
free(a);
}
double find_Emin(int n, double **a)
{
static int i,j,po,num;
static double *v1,*v2,tmp,e0,e1;
static double diff=1.0e-13;
static double shiftE=35.0;
static int nummax=31000;
/* allocation of arrays */
v1 = (double*)malloc(sizeof(double)*(n+1));
v2 = (double*)malloc(sizeof(double)*(n+1));
/* shift diagonal parts */
for (i=1; i<=n; i++) a[i][i] -= shiftE;
/* initial vector */
tmp = 1.0/sqrt((double)n);
for (i=1; i<=n; i++) v1[i] = tmp;
/* power method */
e0 = 1.0e+100;
po = 0;
num = 0;
do {
num++;
/* a by v1 -> v2 */
for (i=1; i<=n; i++){
tmp = 0.0;
for (j=1; j<=n; j++){
tmp += a[i][j]*v1[j];
}
v2[i] = tmp;
}
/* e1 = <v1|v2> */
e1 = 0.0;
for (i=1; i<=n; i++){
e1 += v1[i]*v2[i];
}
/* converge? */
if (fabs(e1-e0)<diff) po = 1;
else e0 = e1;
/* normalize v2 -> v1 */
tmp = 0.0;
for (i=1; i<=n; i++){
tmp += v2[i]*v2[i];
}
tmp = 1.0/sqrt(tmp);
for (i=1; i<=n; i++){
v1[i] = tmp*v2[i];
}
printf("num=%6d e1=%18.15f\n",num,e1);
} while(po==0 && num<nummax);
/* freeing of arrays */
free(v1);
free(v2);
/* back shift */
for (i=1; i<=n; i++) a[i][i] += shiftE;
e1 += shiftE;
/* return */
return e1;
}
double rnd(double width)
{
/****************************************************
This rnd() function generates random number
-width/2 to width/2
****************************************************/
static double result;
result = rand();
while (width<result){
result = result/2.0;
}
result = result - width*0.75;
return result;
}
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