package com.imsl.test.example.math;

import com.imsl.math.*;
/**
 * <p>Solves a system using Cholesky factorization.</p>
  *
  * This example uses the Cholesky factorization of \(A\) to solve \(Ax=b\) 
  * and to find the inverse, \( A^{-1}\).
  * 
  * @see <a href="CholeskyEx1.java">Code</a>
  * @see <a href="doc-files/CholeskyEx1.out">Output</a>
*/
public class CholeskyEx1 {

    public static void main(String args[]) throws com.imsl.IMSLException {
        double a[][] = {
            {1, -3, 2},
            {-3, 10, -5},
            {2, -5, 6}
        };
        double b[] = {27, -78, 64};

        // Compute the Cholesky factorization of A
        Cholesky cholesky = new Cholesky(a);

        // Solve Ax = b
        double x[] = cholesky.solve(b);
        new PrintMatrix("x").print(x);

        // Find the inverse of A.
        double ainv[][] = cholesky.inverse();
        new PrintMatrix("ainv").print(ainv);
    }
}