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.math3.analysis.integration;
018
019 import org.apache.commons.math3.exception.MaxCountExceededException;
020 import org.apache.commons.math3.exception.NotStrictlyPositiveException;
021 import org.apache.commons.math3.exception.NumberIsTooLargeException;
022 import org.apache.commons.math3.exception.NumberIsTooSmallException;
023 import org.apache.commons.math3.exception.TooManyEvaluationsException;
024 import org.apache.commons.math3.util.FastMath;
025
026 /**
027 * Implements <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 the basic trapezoid rule to calculate Simpson's
033 * rule.</p>
034 *
035 * @version $Id: SimpsonIntegrator.java 1364387 2012-07-22 18:14:11Z tn $
036 * @since 1.2
037 */
038 public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator {
039
040 /** Maximal number of iterations for Simpson. */
041 public static final int SIMPSON_MAX_ITERATIONS_COUNT = 64;
042
043 /**
044 * Build a Simpson integrator with given accuracies and iterations counts.
045 * @param relativeAccuracy relative accuracy of the result
046 * @param absoluteAccuracy absolute accuracy of the result
047 * @param minimalIterationCount minimum number of iterations
048 * @param maximalIterationCount maximum number of iterations
049 * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
050 * @exception NotStrictlyPositiveException if minimal number of iterations
051 * is not strictly positive
052 * @exception NumberIsTooSmallException if maximal number of iterations
053 * is lesser than or equal to the minimal number of iterations
054 * @exception NumberIsTooLargeException if maximal number of iterations
055 * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
056 */
057 public SimpsonIntegrator(final double relativeAccuracy,
058 final double absoluteAccuracy,
059 final int minimalIterationCount,
060 final int maximalIterationCount)
061 throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
062 super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
063 if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
064 throw new NumberIsTooLargeException(maximalIterationCount,
065 SIMPSON_MAX_ITERATIONS_COUNT, false);
066 }
067 }
068
069 /**
070 * Build a Simpson integrator with given iteration counts.
071 * @param minimalIterationCount minimum number of iterations
072 * @param maximalIterationCount maximum number of iterations
073 * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
074 * @exception NotStrictlyPositiveException if minimal number of iterations
075 * is not strictly positive
076 * @exception NumberIsTooSmallException if maximal number of iterations
077 * is lesser than or equal to the minimal number of iterations
078 * @exception NumberIsTooLargeException if maximal number of iterations
079 * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
080 */
081 public SimpsonIntegrator(final int minimalIterationCount,
082 final int maximalIterationCount)
083 throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
084 super(minimalIterationCount, maximalIterationCount);
085 if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
086 throw new NumberIsTooLargeException(maximalIterationCount,
087 SIMPSON_MAX_ITERATIONS_COUNT, false);
088 }
089 }
090
091 /**
092 * Construct an integrator with default settings.
093 * (max iteration count set to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
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 throws TooManyEvaluationsException, MaxCountExceededException {
103
104 TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
105 if (getMinimalIterationCount() == 1) {
106 return (4 * qtrap.stage(this, 1) - qtrap.stage(this, 0)) / 3.0;
107 }
108
109 // Simpson's rule requires at least two trapezoid stages.
110 double olds = 0;
111 double oldt = qtrap.stage(this, 0);
112 while (true) {
113 final double t = qtrap.stage(this, iterations.getCount());
114 iterations.incrementCount();
115 final double s = (4 * t - oldt) / 3.0;
116 if (iterations.getCount() >= getMinimalIterationCount()) {
117 final double delta = FastMath.abs(s - olds);
118 final double rLimit =
119 getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
120 if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
121 return s;
122 }
123 }
124 olds = s;
125 oldt = t;
126 }
127
128 }
129
130 }