package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Solves a linear programming problem. </p>
 *
 * The linear programming problem in the standard form
 * <p>
 * $${\rm {min}} \,\, f(x) = -x_1 + -3x_2$$</p>
 * <p>
 * subject to:</p>
 *
 * <p align="center">
 * \(x_1 + x_2 + x_3 = 1.5\)<br/>
 * \(x_1 + x_2 - x_4 = 0.5\)<br/>
 * \(x_1 + x_5 = 1.0\)<br/>
 * \(x_2 + x_6 = 1.0\)<br/>
 * \(x_i \ge 0, \,\,\,\, {\rm {for}} \,\,\, i = 1, \ldots , 6\)</p>
 * <p>
 * is solved.</p>
 *
 *
 * @see <a href="DenseLPEx1.java">Code</a>
 * @see <a href="doc-files/DenseLPEx1.out">Output</a>
 *
 */
public class DenseLPEx1 {

    public static void main(String args[]) throws Exception {
        double[][] a = {
            {1.0, 1.0, 1.0, 0.0, 0.0, 0.0},
            {1.0, 1.0, 0.0, -1.0, 0.0, 0.0},
            {1.0, 0.0, 0.0, 0.0, 1.0, 0.0},
            {0.0, 1.0, 0.0, 0.0, 0.0, 1.0}
        };
        double[] b = {1.5, 0.5, 1.0, 1.0};
        double[] c = {-1.0, -3.0, 0.0, 0.0, 0.0, 0.0};

        DenseLP zf = new DenseLP(a, b, c);

        zf.solve();
        new PrintMatrix("Solution").print(zf.getPrimalSolution());
    }
}