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/*
 * 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;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.util.FastMath;

/**
 * Implements the 
 * Simpson's Rule for integration of real univariate functions. For
 * reference, see Introduction to Numerical Analysis, ISBN 038795452X,
 * chapter 3.
 * 

* This implementation employs basic trapezoid rule as building blocks to * calculate the Simpson's rule of alternating 2/3 and 4/3.

* * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $ * @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 = FastMath.abs(s - olds); final double rLimit = relativeAccuracy * (FastMath.abs(olds) + FastMath.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( LocalizedFormats.INVALID_ITERATIONS_LIMITS, 0, 64); } } }




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