package com.imsl.test.example.math;

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

/**
 * <p>
 * Approximates the gradient with a combination of
 * numerical derivatives and analytic derivatives.</p>
 *
 * This example uses the same data as in {@link NumericalDerivativesEx2}. An
 * examination of the function 
 * $$f(y_1 ,y_2 ) = a\exp (by_1 ) + cy_1 y_2^2$$ 
 * shows that the first term on the right-hand side does not depend on
 * the second variable, and therefore can be left out of the evaluation of the
 * first partial of \( f \) with respect to \( y_2 \), potentially avoiding
 * cancellation errors. Also, \( cy_2^2 \) appears as an additive term when 
 * computing the partial with respect to \(y_1\). This examples shows how different
 * terms in a derivative can be used explicitly and then added to approximated 
 * terms.
 * The input values of array
 * <code>options</code> allow <code>NumericalDerivatives</code> to use these
 * facts and obtain greater accuracy using fewer evaluations of
 * the exponential function.
 *
 * @see <a href="NumericalDerivativesEx3.java">Code</a>
 * @see <a href="doc-files/NumericalDerivativesEx3.out">Output</a>
 */
public class NumericalDerivativesEx3 {

    static private int m = 1, n = 2;
    static private double a, b, c, f2 = 0.0;

    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.ACCUMULATE;
        options[1] = NumericalDerivatives.ONE_SIDED;

        valueF[0] = a * Math.exp(b * y[0]);
        scale[1] = 1.e0;

        NumericalDerivatives.Jacobian fcn
                = new NumericalDerivatives.Jacobian() {
            
                    @Override
            public double[] f(int varIndex, double[] y) {
                double[] tmp = new double[m];

                if (varIndex != 2) {
                    tmp[0] = a * Math.exp(b * y[0]);
                } else {
                    // This is the function value for the partial wrt y_2.
                    tmp[0] = c * y[0] * y[1] * y[1];
                }

                return tmp;
            }

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

                // Start with part of the derivative that is known.
                tmp[0][0] = c * y[1] * 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]);
    }
}