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.math.analysis.integration; 018 019 import java.util.Random; 020 021 import org.apache.commons.math.ConvergenceException; 022 import org.apache.commons.math.FunctionEvaluationException; 023 import org.apache.commons.math.MathException; 024 import org.apache.commons.math.analysis.QuinticFunction; 025 import org.apache.commons.math.analysis.SinFunction; 026 import org.apache.commons.math.analysis.UnivariateRealFunction; 027 import org.apache.commons.math.analysis.polynomials.PolynomialFunction; 028 029 import junit.framework.*; 030 031 public class LegendreGaussIntegratorTest 032 extends TestCase { 033 034 public LegendreGaussIntegratorTest(String name) { 035 super(name); 036 } 037 038 public void testSinFunction() throws MathException { 039 UnivariateRealFunction f = new SinFunction(); 040 UnivariateRealIntegrator integrator = new LegendreGaussIntegrator(5, 64); 041 integrator.setAbsoluteAccuracy(1.0e-10); 042 integrator.setRelativeAccuracy(1.0e-14); 043 integrator.setMinimalIterationCount(2); 044 integrator.setMaximalIterationCount(15); 045 double min, max, expected, result, tolerance; 046 047 min = 0; max = Math.PI; expected = 2; 048 tolerance = Math.max(integrator.getAbsoluteAccuracy(), 049 Math.abs(expected * integrator.getRelativeAccuracy())); 050 result = integrator.integrate(f, min, max); 051 assertEquals(expected, result, tolerance); 052 053 min = -Math.PI/3; max = 0; expected = -0.5; 054 tolerance = Math.max(integrator.getAbsoluteAccuracy(), 055 Math.abs(expected * integrator.getRelativeAccuracy())); 056 result = integrator.integrate(f, min, max); 057 assertEquals(expected, result, tolerance); 058 } 059 060 public void testQuinticFunction() throws MathException { 061 UnivariateRealFunction f = new QuinticFunction(); 062 UnivariateRealIntegrator integrator = new LegendreGaussIntegrator(3, 64); 063 double min, max, expected, result; 064 065 min = 0; max = 1; expected = -1.0/48; 066 result = integrator.integrate(f, min, max); 067 assertEquals(expected, result, 1.0e-16); 068 069 min = 0; max = 0.5; expected = 11.0/768; 070 result = integrator.integrate(f, min, max); 071 assertEquals(expected, result, 1.0e-16); 072 073 min = -1; max = 4; expected = 2048/3.0 - 78 + 1.0/48; 074 result = integrator.integrate(f, min, max); 075 assertEquals(expected, result, 1.0e-16); 076 } 077 078 public void testExactIntegration() 079 throws ConvergenceException, FunctionEvaluationException { 080 Random random = new Random(86343623467878363l); 081 for (int n = 2; n < 6; ++n) { 082 LegendreGaussIntegrator integrator = 083 new LegendreGaussIntegrator(n, 64); 084 085 // an n points Gauss-Legendre integrator integrates 2n-1 degree polynoms exactly 086 for (int degree = 0; degree <= 2 * n - 1; ++degree) { 087 for (int i = 0; i < 10; ++i) { 088 double[] coeff = new double[degree + 1]; 089 for (int k = 0; k < coeff.length; ++k) { 090 coeff[k] = 2 * random.nextDouble() - 1; 091 } 092 PolynomialFunction p = new PolynomialFunction(coeff); 093 double result = integrator.integrate(p, -5.0, 15.0); 094 double reference = exactIntegration(p, -5.0, 15.0); 095 assertEquals(n + " " + degree + " " + i, reference, result, 1.0e-12 * (1.0 + Math.abs(reference))); 096 } 097 } 098 099 } 100 } 101 102 private double exactIntegration(PolynomialFunction p, double a, double b) { 103 final double[] coeffs = p.getCoefficients(); 104 double yb = coeffs[coeffs.length - 1] / coeffs.length; 105 double ya = yb; 106 for (int i = coeffs.length - 2; i >= 0; --i) { 107 yb = yb * b + coeffs[i] / (i + 1); 108 ya = ya * a + coeffs[i] / (i + 1); 109 } 110 return yb * b - ya * a; 111 } 112 113 public static Test suite() { 114 return new TestSuite(LegendreGaussIntegratorTest.class); 115 } 116 117 }