package com.imsl.test.example.math;

import com.imsl.math.*;
import com.imsl.*;

/**
 * <p>
 * Uses the Cholesky factorization of a complex
 * sparse matrix to solve a linear system.
 * </p>
 * The Cholesky factorization of a sparse Hermitian positive definite matrix is
 * used to solve a linear system. Some additional information about the Cholesky
 * factorization is also computed.
 *
 * @see <a href="ComplexSparseCholeskyEx1.java">Code</a>
 * @see <a href="doc-files/ComplexSparseCholeskyEx1.out">Output</a>
 *
 */
public class ComplexSparseCholeskyEx1 {

    public static void main(String args[]) throws IMSLException {

        ComplexSparseMatrix A = new ComplexSparseMatrix(3, 3);

        A.set(0, 0, new Complex(2.0, 0.0));
        A.set(1, 0, new Complex(-1.0, -1.0));
        A.set(1, 1, new Complex(4.0, 0.0));
        A.set(2, 1, new Complex(1.0, -2.0));
        A.set(2, 2, new Complex(10.0, 0.0));

        Complex[] b = {
            new Complex(-2., 2.), new Complex(5., 15.), new Complex(36., 28.)
        };

        ComplexSparseCholesky cholesky = new ComplexSparseCholesky(A);

        // Choose Multifrontal method as numeric factorization method
        cholesky.setNumericFactorizationMethod(cholesky.MULTIFRONTAL_METHOD);

        // Compute solution
        Complex[] solution = cholesky.solve(b);

        PrintMatrix p = new PrintMatrix("Computed solution");
        p.print(solution);

        // Compute additional information about the factorization
        System.out.println("Smallest diagonal element of Cholesky factor: "
                + cholesky.getSmallestDiagonalElement());
        System.out.println("Largest diagonal element of Cholesky factor: "
                + cholesky.getLargestDiagonalElement());
        System.out.println("Number of nonzeros in Cholesky factor: "
                + cholesky.getNumberOfNonzeros());
    }
}