I wrote this piece of code that should make what is described here:
Conjugate Gradient from wikipedia
but after some iterations the variable denomAlpha goes to zero and so I get a NAN on alpha. So what is wrong with my algorithm?
import Jama.Matrix;
public class ConjugateGrad {
private static final int MAX_IT = 20;
private static final int MAX_SIZE = 50;
public static void main(String[] args) {
Matrix A = Matrix.random(MAX_SIZE, MAX_SIZE);
Matrix b = Matrix.random(MAX_SIZE, 1);
double[][] d = new double[MAX_SIZE][1];
for(int ii=0;ii<MAX_SIZE;ii++) {
d[ii][0] =0;
}
Matrix x = Matrix.constructWithCopy(d);
Matrix r = b.minus(A.times(x));
Matrix p = r;
Matrix rTrasp_r = r.transpose().times(p);
for (int i = 0; i < MAX_IT; i++) {
Matrix denomAlpha = p.transpose().times(A.times(p));
double numeratorAlpha = rTrasp_r.getArray()[0][0];
double Alpha = numeratorAlpha / denomAlpha.getArray()[0][0];
x = x.plus(p.times(Alpha));
r = r.minus(A.times(p));
Matrix rNew = r.transpose().times(r);
if (Math.sqrt(rNew.getArray()[0][0]) <1.0e-6) {
break;
}
double Beta = rNew.getArray()[0][0] / rTrasp_r.getArray()[0][0];
p = r.plus(p.times(Beta));
rTrasp_r = rNew;
}
}
}
it same that with those parameters :
double[][] matrixA = {{4,1},{1,3}};
Matrix A = Matrix.constructWithCopy(matrixA);
double[][] vectorb = {{1},{2}};
Matrix b = Matrix.constructWithCopy(vectorb);
double[][] d = {{2},{1}};
Matrix x = Matrix.constructWithCopy(d);
at first step of the algorithm things are good but at second step not...
r: -8.0, -3.0
Alpha: 0.22054380664652568
Beta: 12.67123287671233
x: 0.2356495468277946, 0.33836858006042303,
Second step :
Alpha: 0.0337280177221555
Beta: 159.11259655226627
x: -2.2726985108925097, -0.47156587291133856,
Ok, I have found one Error:
r = r.minus(A.times(p).times(Alpha));
Now it works:
r: -8.0, -3.0,
Alpha: 0.22054380664652568
rNew: 0.6403099643121183,
Beta: 0.008771369374138607
p: -0.3511377223647101, 0.7229306048685207,
x: 0.2356495468277946, 0.33836858006042303,
