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 */ 017package org.apache.commons.math4.legacy.analysis.integration; 018 019import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException; 020import org.apache.commons.math4.core.jdkmath.JdkMath; 021 022/** 023 * Implements <a href="http://mathworld.wolfram.com/SimpsonsRule.html"> 024 * Simpson's Rule</a> for integration of real univariate functions. 025 * 026 * See <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, chapter 3. 027 * 028 * <p> 029 * This implementation employs the basic trapezoid rule to calculate Simpson's 030 * rule. 031 * 032 * <p> 033 * <em>Caveat:</em> At each iteration, the algorithm refines the estimation by 034 * evaluating the function twice as many times as in the previous iteration; 035 * When specifying a {@link #integrate(int,UnivariateFunction,double,double) 036 * maximum number of function evaluations}, the caller must ensure that it 037 * is compatible with the {@link #SimpsonIntegrator(int,int) requested minimal 038 * number of iterations}. 039 * 040 * @since 1.2 041 */ 042public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator { 043 /** Maximal number of iterations for Simpson. */ 044 private static final int SIMPSON_MAX_ITERATIONS_COUNT = 30; 045 046 /** 047 * Build a Simpson integrator with given accuracies and iterations counts. 048 * @param relativeAccuracy relative accuracy of the result 049 * @param absoluteAccuracy absolute accuracy of the result 050 * @param minimalIterationCount Minimum number of iterations. 051 * @param maximalIterationCount Maximum number of iterations. 052 * It must be less than or equal to 30. 053 * @throws org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException 054 * if {@code minimalIterationCount <= 0}. 055 * @throws org.apache.commons.math4.legacy.exception.NumberIsTooSmallException 056 * if {@code maximalIterationCount < minimalIterationCount}. 057 * is lesser than or equal to the minimal number of iterations 058 * @throws NumberIsTooLargeException if {@code maximalIterationCount > 30}. 059 */ 060 public SimpsonIntegrator(final double relativeAccuracy, 061 final double absoluteAccuracy, 062 final int minimalIterationCount, 063 final int maximalIterationCount) { 064 super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount); 065 if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) { 066 throw new NumberIsTooLargeException(maximalIterationCount, 067 SIMPSON_MAX_ITERATIONS_COUNT, false); 068 } 069 } 070 071 /** 072 * Build a Simpson integrator with given iteration counts. 073 * @param minimalIterationCount Minimum number of iterations. 074 * @param maximalIterationCount Maximum number of iterations. 075 * It must be less than or equal to 30. 076 * @throws org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException 077 * if {@code minimalIterationCount <= 0}. 078 * @throws org.apache.commons.math4.legacy.exception.NumberIsTooSmallException 079 * if {@code maximalIterationCount < minimalIterationCount}. 080 * is lesser than or equal to the minimal number of iterations 081 * @throws NumberIsTooLargeException if {@code maximalIterationCount > 30}. 082 */ 083 public SimpsonIntegrator(final int minimalIterationCount, 084 final int maximalIterationCount) { 085 super(minimalIterationCount, maximalIterationCount); 086 if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) { 087 throw new NumberIsTooLargeException(maximalIterationCount, 088 SIMPSON_MAX_ITERATIONS_COUNT, false); 089 } 090 } 091 092 /** 093 * Construct an integrator with default settings. 094 */ 095 public SimpsonIntegrator() { 096 super(DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT); 097 } 098 099 /** {@inheritDoc} */ 100 @Override 101 protected double doIntegrate() { 102 // Simpson's rule requires at least two trapezoid stages. 103 // So we set the first sum using two trapezoid stages. 104 final TrapezoidIntegrator qtrap = new TrapezoidIntegrator(); 105 106 final double s0 = qtrap.stage(this, 0); 107 double oldt = qtrap.stage(this, 1); 108 double olds = (4 * oldt - s0) / 3.0; 109 while (true) { 110 // The first iteration is the first refinement of the sum. 111 iterations.increment(); 112 final int i = getIterations(); 113 final double t = qtrap.stage(this, i + 1); // 1-stage ahead of the iteration 114 final double s = (4 * t - oldt) / 3.0; 115 if (i >= getMinimalIterationCount()) { 116 final double delta = JdkMath.abs(s - olds); 117 final double rLimit = getRelativeAccuracy() * (JdkMath.abs(olds) + JdkMath.abs(s)) * 0.5; 118 if (delta <= rLimit || 119 delta <= getAbsoluteAccuracy()) { 120 return s; 121 } 122 } 123 olds = s; 124 oldt = t; 125 } 126 } 127}