package com.imsl.test.example.math;

import com.imsl.math.*;
import java.text.*;

/**
 * <p>
 * Approximates one component of the gradient using numerical differentiation.</p>
 *
 * <p>
 * This example uses the same data as in example
 * {@link NumericalDerivativesEx1}. In this case, numerical differentiation is
 * used for \(y_1\) and the analytical derivative is used for \(y_2\). The input
 * array <code>options</code> specifies that numerical differentiation with
 * respect to \(y_2\) is skipped. This example illustrates using mixed numerical
 * and analytical derivatives. Using analytical derivatives where possible helps
 * improve accuracy.
 * </p>
 *
 * @see <a href="NumericalDerivativesEx2.java">Code</a>
 * @see <a href="doc-files/NumericalDerivativesEx2.out">Output</a>
 */
public class NumericalDerivativesEx2 {

    static private int m = 1, n = 2;
    static private double a, b, c;

    public static void main(String args[]) {
        int[] options = new int[n];
        double u;
        double[] y = new double[n];
        double[] valueF = new double[m];
        double[] scale = new double[n];
        double[][] actual = new double[m][n];
        double[] re = new double[2];

        // Define data and point of evaluation:
        a = 2.5e6;
        b = 3.4e0;
        c = 4.5e0;
        y[0] = 2.1e0;
        y[1] = 3.2e0;

        // Precision, for measuring errors
        u = Math.sqrt(2.220446049250313e-016);

        // Set scaling:
        scale[0] = 1.e0;
        // Increase scale to account for large value of a.
        scale[1] = 8.e3;

        // compute true values of partials.
        actual[0][0] = a * b * Math.exp(b * y[0]) + c * y[1] * y[1];
        actual[0][1] = 2 * c * y[0] * y[1];

        options[0] = NumericalDerivatives.ONE_SIDED;
        options[1] = NumericalDerivatives.SKIP;

        valueF[0] = a * Math.exp(b * y[0]) + c * y[0] * y[1] * y[1];

        NumericalDerivatives.Jacobian fcn
                = new NumericalDerivatives.Jacobian() {

            @Override
            public double[] f(int varIndex, double[] y) {
                double[] tmp = new double[m];
                tmp[0] = a * Math.exp(b * y[0]) + c * y[0] * y[1] * y[1];
                return tmp;
            }

            @Override
            public double[][] jacobian(double[] y) {
                double[][] tmp = new double[m][n];

                // The second component partial is skipped,
                // since it is known analytically
                tmp[0][1] = 2.e0 * c * y[0] * y[1];

                return tmp;
            }
        };

        NumericalDerivatives derv = new NumericalDerivatives(fcn);
        derv.setDifferencingMethods(options);
        derv.setScalingFactors(scale);
        derv.setInitialF(valueF);
        double[][] jacobian = derv.evaluateJ(y);

        NumberFormat nf = NumberFormat.getInstance();
        nf.setMaximumFractionDigits(2);
        nf.setMinimumFractionDigits(2);

        PrintMatrixFormat pmf = new PrintMatrixFormat();
        pmf.setNumberFormat(nf);
        new PrintMatrix("Numerical gradient:").print(pmf, jacobian);
        new PrintMatrix("Analytic gradient:").print(pmf, actual);

        jacobian[0][0] = (jacobian[0][0] - actual[0][0]) / actual[0][0];
        jacobian[0][1] = (jacobian[0][1] - actual[0][1]) / actual[0][1];
        re[0] = jacobian[0][0];
        re[1] = jacobian[0][1];

        System.out.println("Relative accuracy:");
        System.out.println("df/dy_1       df/dy_2");
        System.out.printf(" %.2fu        %.2fu\n", re[0] / u, re[1] / u);
        System.out.printf("(%.3e)  (%.3e)\n", re[0], re[1]);
    }
}