package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Solves a linear least squares problem
 * with bounds on the variables. </p>
 *
 * The following example solves a linear least squares problem with bounds on
 * the variables and compares the result to its unbounded solution. The system
 * is \( Ax = b \) where $$A =\begin{pmatrix} 1.0 & -3.0 & 2.0 \\ -3.0 & 10.0 &
 * -5.0 \\ 2.0 & -5.0 & 6.0 \end{pmatrix} $$
 * <p>
 * \( b = (27.0, -78.0, 64.0)^T\) and \( -1.0 \le x_i \le 5.0, i=1,2,3\).
 * </p>
 *
 * @see <a href="BoundedVariableLeastSquaresEx1.java">Code</a>
 * @see <a href="doc-files/BoundedVariableLeastSquaresEx1.out">Output</a>
 */
public class BoundedVariableLeastSquaresEx1 {

    public static void main(String args[]) throws Exception {
        double a[][] = {
            {1, -3, 2},
            {-3, 10, -5},
            {2, -5, 6}
        };
        double b[] = {27, -78, 64};
        double xlb[] = {-1, -1, -1};
        double xub[] = {5, 5, 5};
        double xl_ub[] = {Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY,
            Double.NEGATIVE_INFINITY};
        double xu_ub[] = {Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY,
            Double.POSITIVE_INFINITY};

        // compute the bounded solution
        BoundedVariableLeastSquares bvls
                = new BoundedVariableLeastSquares(a, b, xlb, xub);
        bvls.solve();
        double[] x_bounded = bvls.getSolution();
        new PrintMatrix("Bounded Solution").print(x_bounded);
        System.out.println("Norm of the Residuals = " + bvls.getResidualNorm());

        // compute the unbounded solution
        bvls = new BoundedVariableLeastSquares(a, b, xl_ub, xu_ub);
        bvls.solve();
        double[] x_unbounded = bvls.getSolution();
        new PrintMatrix("\nUnbounded Solution").print(x_unbounded);
        System.out.println("Norm of the Residuals = " + bvls.getResidualNorm());
    }
}