package com.imsl.test.example.math;

import com.imsl.math.*;
/** <p>Solves a linear programming problem with sparse representation. </p>
 * 
 * $$\min{f(x) = 2x_1 - 8x_2 + 3x_3}$$
 * 
 * <p>subject to</p>
 *
 * $$\begin{array}{rlr}
 * 2x_2 + 3x_3 \leq 6 \\
 * x_1 + x_2 + x_3 \geq 2 \\
 * -1 \leq x_1 \leq 5 \\
 * 0 \leq x_2 \leq 7 \\
 * 0 \leq x_3 \leq 9
 * \end{array}$$
 * 
 * <p>is solved.</p>
 * 
 * @see <a href="SparseLPEx1.java">Code</a>
 * @see <a href="doc-files/SparseLPEx1.out">Output</a>
 */

public class SparseLPEx1 {

    public static void main(String args[]) throws Exception {
        double[] b = {3.0, 6.0, 2.0};
        double[] c = {2.0, -8.0, 3.0};
        double[] xlb = {-1.0, 0.0, 0.0};
        double[] xub = {5.0, 7.0, 9.0};
        int[] irtype = {1, 1, 2};

        SparseMatrix a = new SparseMatrix(3, 3);
        a.set(0, 0, 1.0);
        a.set(0, 1, 3.0);
        a.set(1, 1, 2.0);
        a.set(1, 2, 3.0);
        a.set(2, 0, 1.0);
        a.set(2, 1, 1.0);
        a.set(2, 2, 1.0);

        // Solve problem.
        SparseLP lp = new SparseLP(a, b, c);
        lp.setLowerBound(xlb);
        lp.setUpperBound(xub);
        lp.setConstraintType(irtype);
        lp.solve();

        // Print solution.
        PrintMatrixFormat mf = new PrintMatrixFormat();
        mf.setNoColumnLabels();
        new PrintMatrix("Solution").print(mf, lp.getSolution());

        System.out.printf("Objective:  %.2f\n", lp.getOptimalValue());
    }
}