Eigenvectors and Eigenvalues

 1//powermethod.c
 2//A program to find the largest eigenvector of a matrix
 3//By David Isaacson, 2003
 4//Released into the Public Domain
 5
 6#include <stdio.h>
 7#include <math.h>
 8
 9int main ()
10{
11    float A[4][4]={{.8,.6,.4,.2},{.6,1.2,.8,.4},{.4,.8,1.2,.6},{.2,.4,.6,.8}};
12    float newx[4]={1,1,1,1};
13    float oldx[4]={0,0,0,0};
14    float eigen;
15    int i,j,done=0;			
16
17    while (!done)
18    //repeat until all values within 10%
19    {
20	//set old=new
21	for(i=0;i<4;i++)
22	    oldx[i]=newx[i];
23
24	
25	//multiply
26	for(i=0;i<4;i++)
27	{
28	    newx[i]=0;
29	    for(j=0;j<4;j++)
30	    {
31		newx[i]=newx[i]+(A[i][j])*(oldx[j]);
32	    }
33	}
34
35	//normalize
36	j=0;		//j=smallest value
37	for(i=1;i<4;i++)
38	{
39	    if (fabs(newx[j])>fabs(newx[i])&&newx[1]!=0)
40		j=i;
41	}
42	eigen=fabs(newx[j]);
43	for(i=0;i<4;i++)
44	    newx[i]=newx[i]/eigen;
45
46	if ((fabs(((newx[0]-oldx[0])/oldx[0]))<=0.1)
47          &&(fabs(((newx[1]-oldx[1])/oldx[1]))<=0.1)
48          &&(fabs(((newx[2]-oldx[2])/oldx[2]))<=0.1)
49          &&(fabs(((newx[3]-oldx[3])/oldx[3]))<=0.1))
50	{
51	    done=1;
52	}
53	
54	    
55    }
56    
57    printf("The eigenvector is about ");
58    printf("{%f,%f,%f,%f}^T\n",newx[0],newx[1],newx[2],newx[3]);
59    printf("The largest eigenvalue is about %f",eigen);
60
61    return 0;
62}
63
64/*OUTPUT:
65
66The eigenvector is about {1.000000,1.600000,1.600000,1.000000}^T
67The largest eigenvalue is about 2.500000
68
69*/
70