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 * @since 1.2
036 */
037public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator {
038
039    /** Maximal number of iterations for Simpson. */
040    public static final int SIMPSON_MAX_ITERATIONS_COUNT = 64;
041
042    /**
043     * Build a Simpson integrator with given accuracies and iterations counts.
044     * @param relativeAccuracy relative accuracy of the result
045     * @param absoluteAccuracy absolute accuracy of the result
046     * @param minimalIterationCount minimum number of iterations
047     * @param maximalIterationCount maximum number of iterations
048     * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
049     * @exception NotStrictlyPositiveException if minimal number of iterations
050     * is not strictly positive
051     * @exception NumberIsTooSmallException if maximal number of iterations
052     * is lesser than or equal to the minimal number of iterations
053     * @exception NumberIsTooLargeException if maximal number of iterations
054     * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
055     */
056    public SimpsonIntegrator(final double relativeAccuracy,
057                             final double absoluteAccuracy,
058                             final int minimalIterationCount,
059                             final int maximalIterationCount)
060        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
061        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
062        if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
063            throw new NumberIsTooLargeException(maximalIterationCount,
064                                                SIMPSON_MAX_ITERATIONS_COUNT, false);
065        }
066    }
067
068    /**
069     * Build a Simpson integrator with given iteration counts.
070     * @param minimalIterationCount minimum number of iterations
071     * @param maximalIterationCount maximum number of iterations
072     * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
073     * @exception NotStrictlyPositiveException if minimal number of iterations
074     * is not strictly positive
075     * @exception NumberIsTooSmallException if maximal number of iterations
076     * is lesser than or equal to the minimal number of iterations
077     * @exception NumberIsTooLargeException if maximal number of iterations
078     * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
079     */
080    public SimpsonIntegrator(final int minimalIterationCount,
081                             final int maximalIterationCount)
082        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
083        super(minimalIterationCount, maximalIterationCount);
084        if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
085            throw new NumberIsTooLargeException(maximalIterationCount,
086                                                SIMPSON_MAX_ITERATIONS_COUNT, false);
087        }
088    }
089
090    /**
091     * Construct an integrator with default settings.
092     * (max iteration count set to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
093     */
094    public SimpsonIntegrator() {
095        super(DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT);
096    }
097
098    /** {@inheritDoc} */
099    @Override
100    protected double doIntegrate()
101        throws TooManyEvaluationsException, MaxCountExceededException {
102
103        TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
104        if (getMinimalIterationCount() == 1) {
105            return (4 * qtrap.stage(this, 1) - qtrap.stage(this, 0)) / 3.0;
106        }
107
108        // Simpson's rule requires at least two trapezoid stages.
109        double olds = 0;
110        double oldt = qtrap.stage(this, 0);
111        while (true) {
112            final double t = qtrap.stage(this, getIterations());
113            incrementCount();
114            final double s = (4 * t - oldt) / 3.0;
115            if (getIterations() >= getMinimalIterationCount()) {
116                final double delta = FastMath.abs(s - olds);
117                final double rLimit =
118                    getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
119                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
120                    return s;
121                }
122            }
123            olds = s;
124            oldt = t;
125        }
126
127    }
128
129}