Eigen values and vectors

[Mr. Eigen]

I have an assignment where I have to determine both the eigen values and vectors of a 3 x 3 array :

3
2 -1 4
1 3 2
8 1 3

First number is the dimension of the array. This is what I have reached to:

#include <iostream.h>
#include <iomanip.h>
#include <fstream.h>
#include <math.h>
#include <stdlib.h>
int main ()
{
ifstream inFile ("ineigen.txt" , ios::in);
ofstream outFile ("outeigen.txt" , ios:ut);

int i,j,dim,x[3]={1,0,0},y[3],A[3][3];

float product,lambda,newx[3],oldx[3],tol=2,tolarray[3];

inFile>>dim;

for (i=0 ; i<dim ; i++)
for (j=0 ; j<dim ; j++)
inFile>>A[i][j];

for (i=0 ; i<dim ; i++)
newx[i]=x[i];


for (i=0 ; i<dim ; i++)
oldx[i]=x[i];

while (tol>=0.0001){




for (i=0 ; i<dim ; i++){
product=0;
for (j=0 ; j<dim ; j++)
product += A[i][j] * newx[j];
y[i]=product;
}



product=0;

for(i=0 ; i<dim ; i++)
product += y[i] * y[i];
cout<<product<<endl;

lambda = pow(product , 0.5);


for (i=0 ; i<dim ; i++)
newx[i]=y[i]/lambda;


for(i=0 ; i<dim ; i++)
outFile<<setprecision (4)<<setiosflags (ios::fixed | ios::showpoint)<<newx[i]<<" ";

outFile<<lambda<<" ";

for (i=0 ; i<dim ; i++)
tolarray[i]=abs (newx[i]-oldx[i]);

for (i=0 ; i<dim ; i++)
tol += tolarray[i]/3;


for(i=0 ; i<dim ; i++)
oldx[i]=newx[i];



}









return 0;

}


________________________

I just cant get the tolerance right, its supposed to be the average of all components of | x - x1 |.

Thnxx

[Salem]

Dunno - but when I compiled it, I got a couple of warnings which don't look too good in the light of trying to converge floating point values

#include <iostream.h>
#include <iomanip.h>
#include <fstream.h>
#include <math.h>
#include <stdlib.h>
int main()
{
    ifstream inFile( "ineigen.txt" , ios::in );
    ofstream outFile( "outeigen.txt" , ios::out );
    int i,j,dim,x[3]={1,0,0},y[3],A[3][3];
    float product,lambda,newx[3],oldx[3],tol=2,tolarray[3];
    inFile>>dim;
    for (i=0 ; i<dim ; i++) {
        for (j=0 ; j<dim ; j++)
            inFile>>A[i][j];
    }
    for (i=0 ; i<dim ; i++)
        newx[i]=x[i];
    for (i=0 ; i<dim ; i++)
        oldx[i]=x[i];
    while (tol>=0.0001){
        for (i=0 ; i<dim ; i++){
            product=0;
            for (j=0 ; j<dim ; j++)
                product += A[i][j] * newx[j];
            y[i]=product; // warning: assignment to `int' from `float'
        }
        product=0;
        for(i=0 ; i<dim ; i++)
            product += y[i] * y[i];
        cout<<product<<endl;
        lambda = pow( product , 0.5 );
        for (i=0 ; i<dim ; i++)			
            newx[i]=y[i]/lambda;
        for(i=0 ; i<dim ; i++)
            outFile<<setprecision( 4 )<<setiosflags( ios::fixed | ios::showpoint )<<newx[i]<<"  ";
        outFile<<lambda<<" ";
        for (i=0 ; i<dim ; i++)
            tolarray[i]=abs( newx[i]-oldx[i] ); // warning: `float' used for argument 1 of `abs(int)'
        for (i=0 ; i<dim ; i++)
            tol += tolarray[i]/3;
        for(i=0 ; i<dim ; i++)
            oldx[i]=newx[i];
    }
    return 0;
}