home | career | drupal | java | mac | mysql | perl | scala | uml | unix  

Java example source code file (LegendreGaussIntegratorTest.java)

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

Learn more about this Java project at its project page.

Java - Java tags/keywords

baseabstractunivariateintegrator, deprecated, legendregaussintegrator, legendregaussintegratortest, polynomialfunction, quinticfunction, random, test, toomanyevaluationsexception, univariatefunction, univariateintegrator, util

The LegendreGaussIntegratorTest.java Java example 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.math3.analysis.integration;

import java.util.Random;

import org.apache.commons.math3.analysis.QuinticFunction;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.function.Sin;
import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;


@Deprecated
public class LegendreGaussIntegratorTest {

    @Test
    public void testSinFunction() {
        UnivariateFunction f = new Sin();
        BaseAbstractUnivariateIntegrator integrator = new LegendreGaussIntegrator(5, 1.0e-14, 1.0e-10, 2, 15);
        double min, max, expected, result, tolerance;

        min = 0; max = FastMath.PI; expected = 2;
        tolerance = FastMath.max(integrator.getAbsoluteAccuracy(),
                             FastMath.abs(expected * integrator.getRelativeAccuracy()));
        result = integrator.integrate(10000, f, min, max);
        Assert.assertEquals(expected, result, tolerance);

        min = -FastMath.PI/3; max = 0; expected = -0.5;
        tolerance = FastMath.max(integrator.getAbsoluteAccuracy(),
                FastMath.abs(expected * integrator.getRelativeAccuracy()));
        result = integrator.integrate(10000, f, min, max);
        Assert.assertEquals(expected, result, tolerance);
    }

    @Test
    public void testQuinticFunction() {
        UnivariateFunction f = new QuinticFunction();
        UnivariateIntegrator integrator =
                new LegendreGaussIntegrator(3,
                                            BaseAbstractUnivariateIntegrator.DEFAULT_RELATIVE_ACCURACY,
                                            BaseAbstractUnivariateIntegrator.DEFAULT_ABSOLUTE_ACCURACY,
                                            BaseAbstractUnivariateIntegrator.DEFAULT_MIN_ITERATIONS_COUNT,
                                            64);
        double min, max, expected, result;

        min = 0; max = 1; expected = -1.0/48;
        result = integrator.integrate(10000, f, min, max);
        Assert.assertEquals(expected, result, 1.0e-16);

        min = 0; max = 0.5; expected = 11.0/768;
        result = integrator.integrate(10000, f, min, max);
        Assert.assertEquals(expected, result, 1.0e-16);

        min = -1; max = 4; expected = 2048/3.0 - 78 + 1.0/48;
        result = integrator.integrate(10000, f, min, max);
        Assert.assertEquals(expected, result, 1.0e-16);
    }

    @Test
    public void testExactIntegration() {
        Random random = new Random(86343623467878363l);
        for (int n = 2; n < 6; ++n) {
            LegendreGaussIntegrator integrator =
                new LegendreGaussIntegrator(n,
                                            BaseAbstractUnivariateIntegrator.DEFAULT_RELATIVE_ACCURACY,
                                            BaseAbstractUnivariateIntegrator.DEFAULT_ABSOLUTE_ACCURACY,
                                            BaseAbstractUnivariateIntegrator.DEFAULT_MIN_ITERATIONS_COUNT,
                                            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(10000, p, -5.0, 15.0);
                    double reference = exactIntegration(p, -5.0, 15.0);
                    Assert.assertEquals(n + " " + degree + " " + i, reference, result, 1.0e-12 * (1.0 + FastMath.abs(reference)));
                }
            }

        }
    }

    @Test
    public void testIssue464() {
        final double value = 0.2;
        UnivariateFunction f = new UnivariateFunction() {
            public double value(double x) {
                return (x >= 0 && x <= 5) ? value : 0.0;
            }
        };
        LegendreGaussIntegrator gauss = new LegendreGaussIntegrator(5, 3, 100);

        // due to the discontinuity, integration implies *many* calls
        double maxX = 0.32462367623786328;
        Assert.assertEquals(maxX * value, gauss.integrate(Integer.MAX_VALUE, f, -10, maxX), 1.0e-7);
        Assert.assertTrue(gauss.getEvaluations() > 37000000);
        Assert.assertTrue(gauss.getIterations() < 30);

        // setting up limits prevents such large number of calls
        try {
            gauss.integrate(1000, f, -10, maxX);
            Assert.fail("expected TooManyEvaluationsException");
        } catch (TooManyEvaluationsException tmee) {
            // expected
            Assert.assertEquals(1000, tmee.getMax());
        }

        // integrating on the two sides should be simpler
        double sum1 = gauss.integrate(1000, f, -10, 0);
        int eval1   = gauss.getEvaluations();
        double sum2 = gauss.integrate(1000, f, 0, maxX);
        int eval2   = gauss.getEvaluations();
        Assert.assertEquals(maxX * value, sum1 + sum2, 1.0e-7);
        Assert.assertTrue(eval1 + eval2 < 200);

    }

    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;
    }

}

Other Java examples (source code examples)

Here is a short list of links related to this Java LegendreGaussIntegratorTest.java source code file:



my book on functional programming

 

new blog posts

 

Copyright 1998-2019 Alvin Alexander, alvinalexander.com
All Rights Reserved.

A percentage of advertising revenue from
pages under the /java/jwarehouse URI on this website is
paid back to open source projects.