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 org.apache.commons.math.FunctionEvaluationException; 020 import org.apache.commons.math.MathRuntimeException; 021 import org.apache.commons.math.MaxIterationsExceededException; 022 import org.apache.commons.math.analysis.UnivariateRealFunction; 023 import org.apache.commons.math.exception.util.LocalizedFormats; 024 import org.apache.commons.math.util.FastMath; 025 026 /** 027 * Implements the <a href="http://mathworld.wolfram.com/SimpsonsRule.html"> 028 * Simpson's Rule</a> for integration of real univariate functions. For 029 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, 030 * chapter 3. 031 * <p> 032 * This implementation employs basic trapezoid rule as building blocks to 033 * calculate the Simpson's rule of alternating 2/3 and 4/3.</p> 034 * 035 * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 f??vr. 2011) $ 036 * @since 1.2 037 */ 038 public class SimpsonIntegrator extends UnivariateRealIntegratorImpl { 039 040 /** 041 * Construct an integrator for the given function. 042 * 043 * @param f function to integrate 044 * @deprecated as of 2.0 the integrand function is passed as an argument 045 * to the {@link #integrate(UnivariateRealFunction, double, double)}method. 046 */ 047 @Deprecated 048 public SimpsonIntegrator(UnivariateRealFunction f) { 049 super(f, 64); 050 } 051 052 /** 053 * Construct an integrator. 054 */ 055 public SimpsonIntegrator() { 056 super(64); 057 } 058 059 /** {@inheritDoc} */ 060 @Deprecated 061 public double integrate(final double min, final double max) 062 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { 063 return integrate(f, min, max); 064 } 065 066 /** {@inheritDoc} */ 067 public double integrate(final UnivariateRealFunction f, final double min, final double max) 068 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { 069 070 clearResult(); 071 verifyInterval(min, max); 072 verifyIterationCount(); 073 074 TrapezoidIntegrator qtrap = new TrapezoidIntegrator(); 075 if (minimalIterationCount == 1) { 076 final double s = (4 * qtrap.stage(f, min, max, 1) - qtrap.stage(f, min, max, 0)) / 3.0; 077 setResult(s, 1); 078 return result; 079 } 080 // Simpson's rule requires at least two trapezoid stages. 081 double olds = 0; 082 double oldt = qtrap.stage(f, min, max, 0); 083 for (int i = 1; i <= maximalIterationCount; ++i) { 084 final double t = qtrap.stage(f, min, max, i); 085 final double s = (4 * t - oldt) / 3.0; 086 if (i >= minimalIterationCount) { 087 final double delta = FastMath.abs(s - olds); 088 final double rLimit = 089 relativeAccuracy * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5; 090 if ((delta <= rLimit) || (delta <= absoluteAccuracy)) { 091 setResult(s, i); 092 return result; 093 } 094 } 095 olds = s; 096 oldt = t; 097 } 098 throw new MaxIterationsExceededException(maximalIterationCount); 099 } 100 101 /** {@inheritDoc} */ 102 @Override 103 protected void verifyIterationCount() throws IllegalArgumentException { 104 super.verifyIterationCount(); 105 // at most 64 bisection refinements 106 if (maximalIterationCount > 64) { 107 throw MathRuntimeException.createIllegalArgumentException( 108 LocalizedFormats.INVALID_ITERATIONS_LIMITS, 109 0, 64); 110 } 111 } 112 }