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Commons Math example source code file (SimpsonIntegrator.java)
The Commons Math SimpsonIntegrator.java source code/* * 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.math.analysis.integration; import org.apache.commons.math.FunctionEvaluationException; import org.apache.commons.math.MathRuntimeException; import org.apache.commons.math.MaxIterationsExceededException; import org.apache.commons.math.analysis.UnivariateRealFunction; /** * Implements the <a href="http://mathworld.wolfram.com/SimpsonsRule.html"> * Simpson's Rule</a> for integration of real univariate functions. For * reference, see <b>Introduction to Numerical Analysis, ISBN 038795452X, * chapter 3. * <p> * This implementation employs basic trapezoid rule as building blocks to * calculate the Simpson's rule of alternating 2/3 and 4/3.</p> * * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $ * @since 1.2 */ public class SimpsonIntegrator extends UnivariateRealIntegratorImpl { /** * Construct an integrator for the given function. * * @param f function to integrate * @deprecated as of 2.0 the integrand function is passed as an argument * to the {@link #integrate(UnivariateRealFunction, double, double)}method. */ @Deprecated public SimpsonIntegrator(UnivariateRealFunction f) { super(f, 64); } /** * Construct an integrator. */ public SimpsonIntegrator() { super(64); } /** {@inheritDoc} */ @Deprecated public double integrate(final double min, final double max) throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { return integrate(f, min, max); } /** {@inheritDoc} */ public double integrate(final UnivariateRealFunction f, final double min, final double max) throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { clearResult(); verifyInterval(min, max); verifyIterationCount(); TrapezoidIntegrator qtrap = new TrapezoidIntegrator(); if (minimalIterationCount == 1) { final double s = (4 * qtrap.stage(f, min, max, 1) - qtrap.stage(f, min, max, 0)) / 3.0; setResult(s, 1); return result; } // Simpson's rule requires at least two trapezoid stages. double olds = 0; double oldt = qtrap.stage(f, min, max, 0); for (int i = 1; i <= maximalIterationCount; ++i) { final double t = qtrap.stage(f, min, max, i); final double s = (4 * t - oldt) / 3.0; if (i >= minimalIterationCount) { final double delta = Math.abs(s - olds); final double rLimit = relativeAccuracy * (Math.abs(olds) + Math.abs(s)) * 0.5; if ((delta <= rLimit) || (delta <= absoluteAccuracy)) { setResult(s, i); return result; } } olds = s; oldt = t; } throw new MaxIterationsExceededException(maximalIterationCount); } /** {@inheritDoc} */ @Override protected void verifyIterationCount() throws IllegalArgumentException { super.verifyIterationCount(); // at most 64 bisection refinements if (maximalIterationCount > 64) { throw MathRuntimeException.createIllegalArgumentException( "invalid iteration limits: min={0}, max={1}", 0, 64); } } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math SimpsonIntegrator.java source code file: |
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