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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, double **s);
int main()
{
static int n,i,j;
static double **a,**s,Emin;
/* size of matrix */
n = 1000;
/* allocation of array */
a = (double**)malloc(sizeof(double*)*(n+3));
for (i=0; i<(n+3); i++){
a[i] = (double*)malloc(sizeof(double)*(n+3));
}
s = (double**)malloc(sizeof(double*)*(n+3));
for (i=0; i<(n+3); i++){
s[i] = (double*)malloc(sizeof(double)*(n+3));
}
/* initialize the matrix a */
for (i=1; i<=n; i++){
for (j=i; j<=n; j++){
a[i][j] = rnd(1.0);
a[j][i] = a[i][j];
}
}
for (i=1; i<=n; i++){
s[i][i] = 1.0;
for (j=i+1; j<=n; j++){
s[i][j] = rnd(0.1);
s[j][i] = s[i][j];
}
}
/* call find_Emin */
Emin = find_Emin(n,a,s);
printf("Emin=%18.15f\n",Emin);
/* freeing of array */
for (i=0; i<(n+3); i++){
free(a[i]);
}
free(a);
for (i=0; i<(n+3); i++){
free(s[i]);
}
free(s);
}
double find_Emin(int n, double **a, double **s)
{
static int i,j,k,k1,k2,po,num;
static double *v1,*v2;
static double tmp,e0,e1;
/* !!! change below for accuracy and efficiency !!! */
static double diff=1.0e-10;
static int nummax=10000;
/* allocation of arrays */
v1 = (double*)malloc(sizeof(double)*(n+3));
v2 = (double*)malloc(sizeof(double)*(n+3));
/* initial vector */
tmp = 1.0/sqrt((double)n);
for (i=1; i<=n; i++) v1[i] = tmp;
for (i=1; i<=n; i++){
tmp = 0.0;
for (j=1; j<=n; j++) tmp += s[i][j]*v1[j];
v2[i] = tmp;
}
tmp = 0.0;
for (i=1; i<=n; i++) tmp += v1[i]*v2[i];
tmp = 1.0/sqrt(fabs(tmp));
for (i=1; i<=n; i++) v1[i] = v1[i]*tmp;
/* steepest decent method */
e0 = 1.0e+100;
e1 = 0.0;
po = 0;
num = 0;
do {
num++;
for (i=1; i<=n; i++){
tmp = 0.0;
for (j=1; j<=n; j++) tmp += (a[i][j] - e1*s[i][j])*v1[j];
v2[i] = tmp;
}
for (i=1; i<=n; i++) v1[i] -= 0.05*v2[i];
for (i=1; i<=n; i++){
tmp = 0.0;
for (j=1; j<=n; j++) tmp += s[i][j]*v1[j];
v2[i] = tmp;
}
tmp = 0.0;
for (i=1; i<=n; i++) tmp += v1[i]*v2[i];
tmp = 1.0/sqrt(fabs(tmp));
for (i=1; i<=n; i++) v1[i] = v1[i]*tmp;
for (i=1; i<=n; i++){
tmp = 0.0;
for (j=1; j<=n; j++) tmp += a[i][j]*v1[j];
v2[i] = tmp;
}
tmp = 0.0;
for (i=1; i<=n; i++) tmp += v1[i]*v2[i];
e1 = tmp;
/* converge? */
if (fabs(e1-e0)<diff) po = 1;
else e0 = e1;
printf("num=%5d e1=%18.15f\n",num,e1);
} while(po==0 && num<nummax);
/* freeing of arrays */
free(v1);
free(v2);
/* 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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