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    
024    /**
025     * Implements the <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
026     * Simpson's Rule</a> for integration of real univariate functions. For
027     * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
028     * chapter 3.
029     * <p>
030     * This implementation employs basic trapezoid rule as building blocks to
031     * calculate the Simpson's rule of alternating 2/3 and 4/3.</p>
032     *
033     * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $
034     * @since 1.2
035     */
036    public class SimpsonIntegrator extends UnivariateRealIntegratorImpl {
037    
038        /**
039         * Construct an integrator for the given function.
040         *
041         * @param f function to integrate
042         * @deprecated as of 2.0 the integrand function is passed as an argument
043         * to the {@link #integrate(UnivariateRealFunction, double, double)}method.
044         */
045        @Deprecated
046        public SimpsonIntegrator(UnivariateRealFunction f) {
047            super(f, 64);
048        }
049    
050        /**
051         * Construct an integrator.
052         */
053        public SimpsonIntegrator() {
054            super(64);
055        }
056    
057        /** {@inheritDoc} */
058        @Deprecated
059        public double integrate(final double min, final double max)
060            throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
061            return integrate(f, min, max);
062        }
063    
064        /** {@inheritDoc} */
065        public double integrate(final UnivariateRealFunction f,
066                                final double min, final double max)
067            throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
068    
069            clearResult();
070            verifyInterval(min, max);
071            verifyIterationCount();
072    
073            TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
074            if (minimalIterationCount == 1) {
075                final double s = (4 * qtrap.stage(f, min, max, 1) - qtrap.stage(f, min, max, 0)) / 3.0;
076                setResult(s, 1);
077                return result;
078            }
079            // Simpson's rule requires at least two trapezoid stages.
080            double olds = 0;
081            double oldt = qtrap.stage(f, min, max, 0);
082            for (int i = 1; i <= maximalIterationCount; ++i) {
083                final double t = qtrap.stage(f, min, max, i);
084                final double s = (4 * t - oldt) / 3.0;
085                if (i >= minimalIterationCount) {
086                    final double delta = Math.abs(s - olds);
087                    final double rLimit =
088                        relativeAccuracy * (Math.abs(olds) + Math.abs(s)) * 0.5;
089                    if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
090                        setResult(s, i);
091                        return result;
092                    }
093                }
094                olds = s;
095                oldt = t;
096            }
097            throw new MaxIterationsExceededException(maximalIterationCount);
098        }
099    
100        /** {@inheritDoc} */
101        @Override
102        protected void verifyIterationCount() throws IllegalArgumentException {
103            super.verifyIterationCount();
104            // at most 64 bisection refinements
105            if (maximalIterationCount > 64) {
106                throw MathRuntimeException.createIllegalArgumentException(
107                        "invalid iteration limits: min={0}, max={1}",
108                        0, 64);
109            }
110        }
111    }