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
024 /**
025 * Implements the <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
026 * Simpson's Rule</a> for integration of real univariate functions. For
027 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
028 * chapter 3.
029 * <p>
030 * This implementation employs basic trapezoid rule as building blocks to
031 * calculate the Simpson's rule of alternating 2/3 and 4/3.</p>
032 *
033 * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $
034 * @since 1.2
035 */
036 public class SimpsonIntegrator extends UnivariateRealIntegratorImpl {
037
038 /**
039 * Construct an integrator for the given function.
040 *
041 * @param f function to integrate
042 * @deprecated as of 2.0 the integrand function is passed as an argument
043 * to the {@link #integrate(UnivariateRealFunction, double, double)}method.
044 */
045 @Deprecated
046 public SimpsonIntegrator(UnivariateRealFunction f) {
047 super(f, 64);
048 }
049
050 /**
051 * Construct an integrator.
052 */
053 public SimpsonIntegrator() {
054 super(64);
055 }
056
057 /** {@inheritDoc} */
058 @Deprecated
059 public double integrate(final double min, final double max)
060 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
061 return integrate(f, min, max);
062 }
063
064 /** {@inheritDoc} */
065 public double integrate(final UnivariateRealFunction f,
066 final double min, final double max)
067 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
068
069 clearResult();
070 verifyInterval(min, max);
071 verifyIterationCount();
072
073 TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
074 if (minimalIterationCount == 1) {
075 final double s = (4 * qtrap.stage(f, min, max, 1) - qtrap.stage(f, min, max, 0)) / 3.0;
076 setResult(s, 1);
077 return result;
078 }
079 // Simpson's rule requires at least two trapezoid stages.
080 double olds = 0;
081 double oldt = qtrap.stage(f, min, max, 0);
082 for (int i = 1; i <= maximalIterationCount; ++i) {
083 final double t = qtrap.stage(f, min, max, i);
084 final double s = (4 * t - oldt) / 3.0;
085 if (i >= minimalIterationCount) {
086 final double delta = Math.abs(s - olds);
087 final double rLimit =
088 relativeAccuracy * (Math.abs(olds) + Math.abs(s)) * 0.5;
089 if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
090 setResult(s, i);
091 return result;
092 }
093 }
094 olds = s;
095 oldt = t;
096 }
097 throw new MaxIterationsExceededException(maximalIterationCount);
098 }
099
100 /** {@inheritDoc} */
101 @Override
102 protected void verifyIterationCount() throws IllegalArgumentException {
103 super.verifyIterationCount();
104 // at most 64 bisection refinements
105 if (maximalIterationCount > 64) {
106 throw MathRuntimeException.createIllegalArgumentException(
107 "invalid iteration limits: min={0}, max={1}",
108 0, 64);
109 }
110 }
111 }