    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    import org.apache.commons.math.exception.util.LocalizedFormats;
    024    import org.apache.commons.math.util.FastMath;
    025
    026    /**
    027     * Implements the <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 basic trapezoid rule as building blocks to
    033     * calculate the Simpson's rule of alternating 2/3 and 4/3.</p>
    034     *
    035     * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 f??vr. 2011) $
    036     * @since 1.2
    037     */
    038    public class SimpsonIntegrator extends UnivariateRealIntegratorImpl {
    039
    040        /**
    041         * Construct an integrator for the given function.
    042         *
    043         * @param f function to integrate
    044         * @deprecated as of 2.0 the integrand function is passed as an argument
    045         * to the {@link #integrate(UnivariateRealFunction, double, double)}method.
    046         */
    047        @Deprecated
    048        public SimpsonIntegrator(UnivariateRealFunction f) {
    049            super(f, 64);
    050        }
    051
    052        /**
    053         * Construct an integrator.
    054         */
    055        public SimpsonIntegrator() {
    056            super(64);
    057        }
    058
    059        /** {@inheritDoc} */
    060        @Deprecated
    061        public double integrate(final double min, final double max)
    062            throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
    063            return integrate(f, min, max);
    064        }
    065
    066        /** {@inheritDoc} */
    067        public double integrate(final UnivariateRealFunction f, final double min, final double max)
    068            throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
    069
    070            clearResult();
    071            verifyInterval(min, max);
    072            verifyIterationCount();
    073
    074            TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
    075            if (minimalIterationCount == 1) {
    076                final double s = (4 * qtrap.stage(f, min, max, 1) - qtrap.stage(f, min, max, 0)) / 3.0;
    077                setResult(s, 1);
    078                return result;
    079            }
    080            // Simpson's rule requires at least two trapezoid stages.
    081            double olds = 0;
    082            double oldt = qtrap.stage(f, min, max, 0);
    083            for (int i = 1; i <= maximalIterationCount; ++i) {
    084                final double t = qtrap.stage(f, min, max, i);
    085                final double s = (4 * t - oldt) / 3.0;
    086                if (i >= minimalIterationCount) {
    087                    final double delta = FastMath.abs(s - olds);
    088                    final double rLimit =
    089                        relativeAccuracy * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
    090                    if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
    091                        setResult(s, i);
    092                        return result;
    093                    }
    094                }
    095                olds = s;
    096                oldt = t;
    097            }
    098            throw new MaxIterationsExceededException(maximalIterationCount);
    099        }
    100
    101        /** {@inheritDoc} */
    102        @Override
    103        protected void verifyIterationCount() throws IllegalArgumentException {
    104            super.verifyIterationCount();
    105            // at most 64 bisection refinements
    106            if (maximalIterationCount > 64) {
    107                throw MathRuntimeException.createIllegalArgumentException(
    108                        LocalizedFormats.INVALID_ITERATIONS_LIMITS,
    109                        0, 64);
    110            }
    111        }
    112    }