package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Computes the LU factorization of a complex matrix.</p>
 *
 * The <code>Complex</code> data structure is used to convert a real matrix to a
 * complex matrix. An LU decomposition of the 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 determinant of the input matrix is also computed.
 *
 * @see <a href="ComplexLUEx1.java">Code</a>
 * @see <a href="doc-files/ComplexLUEx1.out">Output</a>
 */
public class ComplexLUEx1 {

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

        Complex a[][] = new Complex[3][3];
        Complex b[] = new Complex[3];

        for (int i = 0; i < 3; i++) {
            b[i] = new Complex(br[i]);
            for (int j = 0; j < 3; j++) {
                a[i][j] = new Complex(ar[i][j]);
            }
        }

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

        // Check the reciprocal of the condition number of A 
        //   against machine precision
        double condition = clu.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
        Complex x[] = clu.solve(b);
        System.out.println("The solution is:");
        System.out.println(" ");
        new PrintMatrix("x").print(x);

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

        // Find the determinant of A.
        Complex determinant = clu.determinant();
        System.out.println("The determinant = " + determinant);
    }
}