| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math4.legacy.analysis.integration; |
| |
| import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException; |
| import org.apache.commons.math4.legacy.core.jdkmath.AccurateMath; |
| |
| /** |
| * Implements <a href="http://mathworld.wolfram.com/SimpsonsRule.html"> |
| * Simpson's Rule</a> for integration of real univariate functions. |
| * |
| * See <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, chapter 3. |
| * |
| * <p> |
| * This implementation employs the basic trapezoid rule to calculate Simpson's |
| * rule. |
| * |
| * <p> |
| * <em>Caveat:</em> At each iteration, the algorithm refines the estimation by |
| * evaluating the function twice as many times as in the previous iteration; |
| * When specifying a {@link #integrate(int,UnivariateFunction,double,double) |
| * maximum number of function evaluations}, the caller must ensure that it |
| * is compatible with the {@link #SimpsonIntegrator(int,int) requested minimal |
| * number of iterations}. |
| * |
| * @since 1.2 |
| */ |
| public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator { |
| /** Maximal number of iterations for Simpson. */ |
| private static final int SIMPSON_MAX_ITERATIONS_COUNT = 30; |
| |
| /** |
| * Build a Simpson integrator with given accuracies and iterations counts. |
| * @param relativeAccuracy relative accuracy of the result |
| * @param absoluteAccuracy absolute accuracy of the result |
| * @param minimalIterationCount Minimum number of iterations. |
| * @param maximalIterationCount Maximum number of iterations. |
| * It must be less than or equal to 30. |
| * @throws org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException |
| * if {@code minimalIterationCount <= 0}. |
| * @throws org.apache.commons.math4.legacy.exception.NumberIsTooSmallException |
| * if {@code maximalIterationCount < minimalIterationCount}. |
| * is lesser than or equal to the minimal number of iterations |
| * @throws NumberIsTooLargeException if {@code maximalIterationCount > 30}. |
| */ |
| public SimpsonIntegrator(final double relativeAccuracy, |
| final double absoluteAccuracy, |
| final int minimalIterationCount, |
| final int maximalIterationCount) { |
| super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount); |
| if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) { |
| throw new NumberIsTooLargeException(maximalIterationCount, |
| SIMPSON_MAX_ITERATIONS_COUNT, false); |
| } |
| } |
| |
| /** |
| * Build a Simpson integrator with given iteration counts. |
| * @param minimalIterationCount Minimum number of iterations. |
| * @param maximalIterationCount Maximum number of iterations. |
| * It must be less than or equal to 30. |
| * @throws org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException |
| * if {@code minimalIterationCount <= 0}. |
| * @throws org.apache.commons.math4.legacy.exception.NumberIsTooSmallException |
| * if {@code maximalIterationCount < minimalIterationCount}. |
| * is lesser than or equal to the minimal number of iterations |
| * @throws NumberIsTooLargeException if {@code maximalIterationCount > 30}. |
| */ |
| public SimpsonIntegrator(final int minimalIterationCount, |
| final int maximalIterationCount) { |
| super(minimalIterationCount, maximalIterationCount); |
| if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) { |
| throw new NumberIsTooLargeException(maximalIterationCount, |
| SIMPSON_MAX_ITERATIONS_COUNT, false); |
| } |
| } |
| |
| /** |
| * Construct an integrator with default settings. |
| */ |
| public SimpsonIntegrator() { |
| super(DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected double doIntegrate() { |
| // Simpson's rule requires at least two trapezoid stages. |
| // So we set the first sum using two trapezoid stages. |
| final TrapezoidIntegrator qtrap = new TrapezoidIntegrator(); |
| |
| final double s0 = qtrap.stage(this, 0); |
| double oldt = qtrap.stage(this, 1); |
| double olds = (4 * oldt - s0) / 3.0; |
| while (true) { |
| // The first iteration is the first refinement of the sum. |
| iterations.increment(); |
| final int i = getIterations(); |
| final double t = qtrap.stage(this, i + 1); // 1-stage ahead of the iteration |
| final double s = (4 * t - oldt) / 3.0; |
| if (i >= getMinimalIterationCount()) { |
| final double delta = AccurateMath.abs(s - olds); |
| final double rLimit = getRelativeAccuracy() * (AccurateMath.abs(olds) + AccurateMath.abs(s)) * 0.5; |
| if (delta <= rLimit || |
| delta <= getAbsoluteAccuracy()) { |
| return s; |
| } |
| } |
| olds = s; |
| oldt = t; |
| } |
| } |
| } |