001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017 package org.apache.commons.math3.analysis.integration;
018
019 import java.util.Random;
020
021 import org.apache.commons.math3.analysis.QuinticFunction;
022 import org.apache.commons.math3.analysis.UnivariateFunction;
023 import org.apache.commons.math3.analysis.function.Sin;
024 import org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
025 import org.apache.commons.math3.exception.TooManyEvaluationsException;
026 import org.apache.commons.math3.util.FastMath;
027 import org.junit.Assert;
028 import org.junit.Test;
029
030
031 @Deprecated
032 public class LegendreGaussIntegratorTest {
033
034 @Test
035 public void testSinFunction() {
036 UnivariateFunction f = new Sin();
037 BaseAbstractUnivariateIntegrator integrator = new LegendreGaussIntegrator(5, 1.0e-14, 1.0e-10, 2, 15);
038 double min, max, expected, result, tolerance;
039
040 min = 0; max = FastMath.PI; expected = 2;
041 tolerance = FastMath.max(integrator.getAbsoluteAccuracy(),
042 FastMath.abs(expected * integrator.getRelativeAccuracy()));
043 result = integrator.integrate(10000, f, min, max);
044 Assert.assertEquals(expected, result, tolerance);
045
046 min = -FastMath.PI/3; max = 0; expected = -0.5;
047 tolerance = FastMath.max(integrator.getAbsoluteAccuracy(),
048 FastMath.abs(expected * integrator.getRelativeAccuracy()));
049 result = integrator.integrate(10000, f, min, max);
050 Assert.assertEquals(expected, result, tolerance);
051 }
052
053 @Test
054 public void testQuinticFunction() {
055 UnivariateFunction f = new QuinticFunction();
056 UnivariateIntegrator integrator =
057 new LegendreGaussIntegrator(3,
058 BaseAbstractUnivariateIntegrator.DEFAULT_RELATIVE_ACCURACY,
059 BaseAbstractUnivariateIntegrator.DEFAULT_ABSOLUTE_ACCURACY,
060 BaseAbstractUnivariateIntegrator.DEFAULT_MIN_ITERATIONS_COUNT,
061 64);
062 double min, max, expected, result;
063
064 min = 0; max = 1; expected = -1.0/48;
065 result = integrator.integrate(10000, f, min, max);
066 Assert.assertEquals(expected, result, 1.0e-16);
067
068 min = 0; max = 0.5; expected = 11.0/768;
069 result = integrator.integrate(10000, f, min, max);
070 Assert.assertEquals(expected, result, 1.0e-16);
071
072 min = -1; max = 4; expected = 2048/3.0 - 78 + 1.0/48;
073 result = integrator.integrate(10000, f, min, max);
074 Assert.assertEquals(expected, result, 1.0e-16);
075 }
076
077 @Test
078 public void testExactIntegration() {
079 Random random = new Random(86343623467878363l);
080 for (int n = 2; n < 6; ++n) {
081 LegendreGaussIntegrator integrator =
082 new LegendreGaussIntegrator(n,
083 BaseAbstractUnivariateIntegrator.DEFAULT_RELATIVE_ACCURACY,
084 BaseAbstractUnivariateIntegrator.DEFAULT_ABSOLUTE_ACCURACY,
085 BaseAbstractUnivariateIntegrator.DEFAULT_MIN_ITERATIONS_COUNT,
086 64);
087
088 // an n points Gauss-Legendre integrator integrates 2n-1 degree polynoms exactly
089 for (int degree = 0; degree <= 2 * n - 1; ++degree) {
090 for (int i = 0; i < 10; ++i) {
091 double[] coeff = new double[degree + 1];
092 for (int k = 0; k < coeff.length; ++k) {
093 coeff[k] = 2 * random.nextDouble() - 1;
094 }
095 PolynomialFunction p = new PolynomialFunction(coeff);
096 double result = integrator.integrate(10000, p, -5.0, 15.0);
097 double reference = exactIntegration(p, -5.0, 15.0);
098 Assert.assertEquals(n + " " + degree + " " + i, reference, result, 1.0e-12 * (1.0 + FastMath.abs(reference)));
099 }
100 }
101
102 }
103 }
104
105 @Test
106 public void testIssue464() {
107 final double value = 0.2;
108 UnivariateFunction f = new UnivariateFunction() {
109 public double value(double x) {
110 return (x >= 0 && x <= 5) ? value : 0.0;
111 }
112 };
113 LegendreGaussIntegrator gauss = new LegendreGaussIntegrator(5, 3, 100);
114
115 // due to the discontinuity, integration implies *many* calls
116 double maxX = 0.32462367623786328;
117 Assert.assertEquals(maxX * value, gauss.integrate(Integer.MAX_VALUE, f, -10, maxX), 1.0e-7);
118 Assert.assertTrue(gauss.getEvaluations() > 37000000);
119 Assert.assertTrue(gauss.getIterations() < 30);
120
121 // setting up limits prevents such large number of calls
122 try {
123 gauss.integrate(1000, f, -10, maxX);
124 Assert.fail("expected TooManyEvaluationsException");
125 } catch (TooManyEvaluationsException tmee) {
126 // expected
127 Assert.assertEquals(1000, tmee.getMax());
128 }
129
130 // integrating on the two sides should be simpler
131 double sum1 = gauss.integrate(1000, f, -10, 0);
132 int eval1 = gauss.getEvaluations();
133 double sum2 = gauss.integrate(1000, f, 0, maxX);
134 int eval2 = gauss.getEvaluations();
135 Assert.assertEquals(maxX * value, sum1 + sum2, 1.0e-7);
136 Assert.assertTrue(eval1 + eval2 < 200);
137
138 }
139
140 private double exactIntegration(PolynomialFunction p, double a, double b) {
141 final double[] coeffs = p.getCoefficients();
142 double yb = coeffs[coeffs.length - 1] / coeffs.length;
143 double ya = yb;
144 for (int i = coeffs.length - 2; i >= 0; --i) {
145 yb = yb * b + coeffs[i] / (i + 1);
146 ya = ya * a + coeffs[i] / (i + 1);
147 }
148 return yb * b - ya * a;
149 }
150
151 }