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.math3.analysis.integration;
018
019import org.apache.commons.math3.exception.MaxCountExceededException;
020import org.apache.commons.math3.exception.NotStrictlyPositiveException;
021import org.apache.commons.math3.exception.NumberIsTooLargeException;
022import org.apache.commons.math3.exception.NumberIsTooSmallException;
023import org.apache.commons.math3.exception.TooManyEvaluationsException;
024import 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 */
038public 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}