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Java example source code file (IterativeLegendreGaussIntegratorTest.java)

This example Java source code file (IterativeLegendreGaussIntegratorTest.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, gaussian, iterativelegendregaussintegrator, iterativelegendregaussintegratortest, polynomialfunction, quinticfunction, random, test, toomanyevaluationsexception, univariatefunction, univariateintegrator, util

The IterativeLegendreGaussIntegratorTest.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.function.Gaussian;
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;


public class IterativeLegendreGaussIntegratorTest {

    @Test
    public void testSinFunction() {
        UnivariateFunction f = new Sin();
        BaseAbstractUnivariateIntegrator integrator
            = new IterativeLegendreGaussIntegrator(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 IterativeLegendreGaussIntegrator(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) {
            IterativeLegendreGaussIntegrator integrator =
                new IterativeLegendreGaussIntegrator(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)));
                }
            }

        }
    }

    // Cf. MATH-995
    @Test
    public void testNormalDistributionWithLargeSigma() {
        final double sigma = 1000;
        final double mean = 0;
        final double factor = 1 / (sigma * FastMath.sqrt(2 * FastMath.PI));
        final UnivariateFunction normal = new Gaussian(factor, mean, sigma);

        final double tol = 1e-2;
        final IterativeLegendreGaussIntegrator integrator =
            new IterativeLegendreGaussIntegrator(5, tol, tol);

        final double a = -5000;
        final double b = 5000;
        final double s = integrator.integrate(50, normal, a, b);
        Assert.assertEquals(1, s, 1e-5);
    }

    @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;
            }
        };
        IterativeLegendreGaussIntegrator gauss
            = new IterativeLegendreGaussIntegrator(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;
    }
}

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