Commons Math example source code file (LegendreGaussIntegratorTest.java)

This example Commons Math source code file (LegendreGaussIntegratorTest.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" ^TM.

Java - Commons Math tags/keywords

functionevaluationexception, legendregaussintegrator, legendregaussintegrator, legendregaussintegratortest, legendregaussintegratortest, mathexception, polynomialfunction, polynomialfunction, random, sinfunction, testcase, univariaterealfunction, univariaterealfunction, univariaterealintegrator, util

The Commons Math LegendreGaussIntegratorTest.java source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math.analysis.integration;

import java.util.Random;

import org.apache.commons.math.ConvergenceException;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.MathException;
import org.apache.commons.math.analysis.QuinticFunction;
import org.apache.commons.math.analysis.SinFunction;
import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.analysis.polynomials.PolynomialFunction;

import junit.framework.*;

public class LegendreGaussIntegratorTest
extends TestCase {

    public LegendreGaussIntegratorTest(String name) {
        super(name);
    }

    public void testSinFunction() throws MathException {
        UnivariateRealFunction f = new SinFunction();
        UnivariateRealIntegrator integrator = new LegendreGaussIntegrator(5, 64);
        integrator.setAbsoluteAccuracy(1.0e-10);
        integrator.setRelativeAccuracy(1.0e-14);
        integrator.setMinimalIterationCount(2);
        integrator.setMaximalIterationCount(15);
        double min, max, expected, result, tolerance;

        min = 0; max = Math.PI; expected = 2;
        tolerance = Math.max(integrator.getAbsoluteAccuracy(),
                             Math.abs(expected * integrator.getRelativeAccuracy()));
        result = integrator.integrate(f, min, max);
        assertEquals(expected, result, tolerance);

        min = -Math.PI/3; max = 0; expected = -0.5;
        tolerance = Math.max(integrator.getAbsoluteAccuracy(),
                Math.abs(expected * integrator.getRelativeAccuracy()));
        result = integrator.integrate(f, min, max);
        assertEquals(expected, result, tolerance);
    }

    public void testQuinticFunction() throws MathException {
        UnivariateRealFunction f = new QuinticFunction();
        UnivariateRealIntegrator integrator = new LegendreGaussIntegrator(3, 64);
        double min, max, expected, result;

        min = 0; max = 1; expected = -1.0/48;
        result = integrator.integrate(f, min, max);
        assertEquals(expected, result, 1.0e-16);

        min = 0; max = 0.5; expected = 11.0/768;
        result = integrator.integrate(f, min, max);
        assertEquals(expected, result, 1.0e-16);

        min = -1; max = 4; expected = 2048/3.0 - 78 + 1.0/48;
        result = integrator.integrate(f, min, max);
        assertEquals(expected, result, 1.0e-16);
    }

    public void testExactIntegration()
        throws ConvergenceException, FunctionEvaluationException {
        Random random = new Random(86343623467878363l);
        for (int n = 2; n < 6; ++n) {
            LegendreGaussIntegrator integrator =
                new LegendreGaussIntegrator(n, 64);

            // an n points Gauss-Legendre integrator integrates 2n-1 degree polynoms exactly
            for (int degree = 0; degree <= 2 * n - 1; ++degree) {
                for (int i = 0; i < 10; ++i) {
                    double[] coeff = new double[degree + 1];
                    for (int k = 0; k < coeff.length; ++k) {
                        coeff[k] = 2 * random.nextDouble() - 1;
                    }
                    PolynomialFunction p = new PolynomialFunction(coeff);
                    double result    = integrator.integrate(p, -5.0, 15.0);
                    double reference = exactIntegration(p, -5.0, 15.0);
                    assertEquals(n + " " + degree + " " + i, reference, result, 1.0e-12 * (1.0 + Math.abs(reference)));
                }
            }

        }
    }

    private double exactIntegration(PolynomialFunction p, double a, double b) {
        final double[] coeffs = p.getCoefficients();
        double yb = coeffs[coeffs.length - 1] / coeffs.length;
        double ya = yb;
        for (int i = coeffs.length - 2; i >= 0; --i) {
            yb = yb * b + coeffs[i] / (i + 1);
            ya = ya * a + coeffs[i] / (i + 1);
        }
        return yb * b - ya * a;
    }

}