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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.math3.analysis.integration;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.util.FastMath;
/**
* Implements <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</b>, ISBN 038795452X,
* chapter 3.
* <p>
* This implementation employs the basic trapezoid rule to calculate Simpson's
* rule.</p>
*
* @since 1.2
*/
public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator {
/** Maximal number of iterations for Simpson. */
public static final int SIMPSON_MAX_ITERATIONS_COUNT = 64;
/**
* 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
* (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
* @exception NotStrictlyPositiveException if minimal number of iterations
* is not strictly positive
* @exception NumberIsTooSmallException if maximal number of iterations
* is lesser than or equal to the minimal number of iterations
* @exception NumberIsTooLargeException if maximal number of iterations
* is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
*/
public SimpsonIntegrator(final double relativeAccuracy,
final double absoluteAccuracy,
final int minimalIterationCount,
final int maximalIterationCount)
throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
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
* (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
* @exception NotStrictlyPositiveException if minimal number of iterations
* is not strictly positive
* @exception NumberIsTooSmallException if maximal number of iterations
* is lesser than or equal to the minimal number of iterations
* @exception NumberIsTooLargeException if maximal number of iterations
* is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
*/
public SimpsonIntegrator(final int minimalIterationCount,
final int maximalIterationCount)
throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
super(minimalIterationCount, maximalIterationCount);
if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
throw new NumberIsTooLargeException(maximalIterationCount,
SIMPSON_MAX_ITERATIONS_COUNT, false);
}
}
/**
* Construct an integrator with default settings.
* (max iteration count set to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
*/
public SimpsonIntegrator() {
super(DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT);
}
/** {@inheritDoc} */
@Override
protected double doIntegrate()
throws TooManyEvaluationsException, MaxCountExceededException {
TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
if (getMinimalIterationCount() == 1) {
return (4 * qtrap.stage(this, 1) - qtrap.stage(this, 0)) / 3.0;
}
// Simpson's rule requires at least two trapezoid stages.
double olds = 0;
double oldt = qtrap.stage(this, 0);
while (true) {
final double t = qtrap.stage(this, getIterations());
incrementCount();
final double s = (4 * t - oldt) / 3.0;
if (getIterations() >= getMinimalIterationCount()) {
final double delta = FastMath.abs(s - olds);
final double rLimit =
getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
return s;
}
}
olds = s;
oldt = t;
}
}
}
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