1dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/* 2dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Licensed to the Apache Software Foundation (ASF) under one or more 3dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * contributor license agreements. See the NOTICE file distributed with 4dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * this work for additional information regarding copyright ownership. 5dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The ASF licenses this file to You under the Apache License, Version 2.0 6dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * (the "License"); you may not use this file except in compliance with 7dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * the License. You may obtain a copy of the License at 8dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 9dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * http://www.apache.org/licenses/LICENSE-2.0 10dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 11dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Unless required by applicable law or agreed to in writing, software 12dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * distributed under the License is distributed on an "AS IS" BASIS, 13dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * See the License for the specific language governing permissions and 15dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * limitations under the License. 16dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 17dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpackage org.apache.commons.math.analysis.integration; 18dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 19dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.FunctionEvaluationException; 20dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.MathRuntimeException; 21dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.MaxIterationsExceededException; 22dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.analysis.UnivariateRealFunction; 23dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.exception.util.LocalizedFormats; 24dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.util.FastMath; 25dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 26dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/** 27dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Implements the <a href="http://mathworld.wolfram.com/SimpsonsRule.html"> 28dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Simpson's Rule</a> for integration of real univariate functions. For 29dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, 30dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * chapter 3. 31dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 32dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * This implementation employs basic trapezoid rule as building blocks to 33dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * calculate the Simpson's rule of alternating 2/3 and 4/3.</p> 34dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 35dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $ 36dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @since 1.2 37dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 38dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpublic class SimpsonIntegrator extends UnivariateRealIntegratorImpl { 39dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 40dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 41dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Construct an integrator for the given function. 42dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 43dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param f function to integrate 44dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @deprecated as of 2.0 the integrand function is passed as an argument 45dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * to the {@link #integrate(UnivariateRealFunction, double, double)}method. 46dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 47dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Deprecated 48dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public SimpsonIntegrator(UnivariateRealFunction f) { 49dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond super(f, 64); 50dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 51dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 52dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 53dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Construct an integrator. 54dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 55dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public SimpsonIntegrator() { 56dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond super(64); 57dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 58dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 59dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 60dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Deprecated 61dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public double integrate(final double min, final double max) 62dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { 63dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return integrate(f, min, max); 64dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 65dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 66dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 67dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public double integrate(final UnivariateRealFunction f, final double min, final double max) 68dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { 69dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 70dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond clearResult(); 71dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond verifyInterval(min, max); 72dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond verifyIterationCount(); 73dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 74dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond TrapezoidIntegrator qtrap = new TrapezoidIntegrator(); 75dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (minimalIterationCount == 1) { 76dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double s = (4 * qtrap.stage(f, min, max, 1) - qtrap.stage(f, min, max, 0)) / 3.0; 77dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond setResult(s, 1); 78dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return result; 79dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 80dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // Simpson's rule requires at least two trapezoid stages. 81dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double olds = 0; 82dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double oldt = qtrap.stage(f, min, max, 0); 83dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 1; i <= maximalIterationCount; ++i) { 84dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double t = qtrap.stage(f, min, max, i); 85dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double s = (4 * t - oldt) / 3.0; 86dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (i >= minimalIterationCount) { 87dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double delta = FastMath.abs(s - olds); 88dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double rLimit = 89dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond relativeAccuracy * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5; 90dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if ((delta <= rLimit) || (delta <= absoluteAccuracy)) { 91dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond setResult(s, i); 92dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return result; 93dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 94dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 95dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond olds = s; 96dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond oldt = t; 97dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 98dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw new MaxIterationsExceededException(maximalIterationCount); 99dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 100dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 101dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 102dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 103dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond protected void verifyIterationCount() throws IllegalArgumentException { 104dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond super.verifyIterationCount(); 105dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // at most 64 bisection refinements 106dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (maximalIterationCount > 64) { 107dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw MathRuntimeException.createIllegalArgumentException( 108dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond LocalizedFormats.INVALID_ITERATIONS_LIMITS, 109dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 0, 64); 110dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 111dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 112dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond} 113