    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    }