package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Solves a nonnegative least squares problem.
 * </p>
 * Consider the following problem: $$ \begin{bmatrix}1 & -3 & 2\\ -3 & 10 & -5\\
 * 2 & -5 & 6\end{bmatrix} \begin{bmatrix}x_1\\ x_2\\ x_3\end{bmatrix} =
 * \begin{bmatrix}27\\ -78\\ 64\end{bmatrix}$$
 * <p>
 * Subject to the constraint \(x \ge 0\). The NonNegativeLeastSquares class is
 * used to compute a solution, which is compared to the exact solution of \([1, -4, 7]\).
 * </p>
 *
 * @see <a href="NonNegativeLeastSquaresEx1.java">Code</a>
 * @see <a href="doc-files/NonNegativeLeastSquaresEx1.out">Output</a>
 */
public class NonNegativeLeastSquaresEx1 {

    public static void main(String args[]) throws Exception {
        double a[][] = {
            {1, -3, 2},
            {-3, 10, -5},
            {2, -5, 6}
        };
        double b[] = {27, -78, 64};

        NonNegativeLeastSquares nnls = new NonNegativeLeastSquares(a, b);
        nnls.solve();
        double[] x = nnls.getSolution();

        new PrintMatrix("Solution").print(x);

        // compare solution with exact answer
        double[][] compare = new double[2][];
        compare[0] = Matrix.multiply(a, x);
        compare[1] = Matrix.multiply(a, new double[]{1, -4, 7});

        PrintMatrixFormat pmf = new PrintMatrixFormat();
        pmf.setColumnLabels(new String[]{"x >= 0", "exact"});
        PrintMatrix pm = new PrintMatrix("Comparison of 'b'");
        pm.print(pmf, Matrix.transpose(compare));
    }
}