package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Performs the LU factorization of a matrix.
 * </p>
 *
 * The LU Factorization of a Matrix is performed. The reciprocal of the
 * condition number of the Matrix is then computed and checked against machine
 * precision to determine whether or not to issue a Warning about the results. A
 * linear system is then solved using the factorization. The inverse and
 * determinant of the input matrix are also computed.
 *
 * @see <a href="LUEx1.java">Code</a>
 * @see <a href="doc-files/LUEx1.out">Output</a>
 */
public class LUEx1 {

    public static void main(String args[]) throws SingularMatrixException {
        double a[][] = {
            {1, 3, 3},
            {1, 3, 4},
            {1, 4, 3}
        };
        double b[] = {12, 13, 14};

        // Compute the LU factorization of A
        LU lu = new LU(a);

        // Check the reciprocal of the condition number of
        // A against machine precision
        double condition = lu.condition(a);
        if (condition <= 2.220446049250313e-16) {
            System.out.println("WARNING. The matrix is too ill-conditioned.");
            System.out.println("An estimate of the reciprocal of its L1 "
                    + "condition number is " + condition + ".");
            System.out.println("Results based on this factorization "
                    + "may not be accurate.");
        }

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

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

        // Print the condition number of A.
        System.out.println("condition number = " + condition);
        System.out.println();

        // Find the determinant of A.
        double determinant = lu.determinant();
        System.out.println("determinant = " + determinant);
    }
}