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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 <a href="http://mathworld.wolfram.com/RombergIntegration.html">
* Romberg Algorithm</a> for integration of real univariate functions. For
* reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
* chapter 3.
* <p>
* Romberg integration employs k successive refinements of the trapezoid
* rule to remove error terms less than order O(N^(-2k)). Simpson's rule
* is a special case of k = 2.</p>
*
* @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $
* @since 1.2
*/
public class RombergIntegrator 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 RombergIntegrator(UnivariateRealFunction f) {
super(f, 32);
}
/**
* Construct an integrator.
*/
public RombergIntegrator() {
super(32);
}
/** {@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 {
final int m = maximalIterationCount + 1;
double previousRow[] = new double[m];
double currentRow[] = new double[m];
clearResult();
verifyInterval(min, max);
verifyIterationCount();
TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
currentRow[0] = qtrap.stage(f, min, max, 0);
double olds = currentRow[0];
for (int i = 1; i <= maximalIterationCount; ++i) {
// switch rows
final double[] tmpRow = previousRow;
previousRow = currentRow;
currentRow = tmpRow;
currentRow[0] = qtrap.stage(f, min, max, i);
for (int j = 1; j <= i; j++) {
// Richardson extrapolation coefficient
final double r = (1L << (2 * j)) - 1;
final double tIJm1 = currentRow[j - 1];
currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;
}
final double s = currentRow[i];
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;
}
throw new MaxIterationsExceededException(maximalIterationCount);
}
/** {@inheritDoc} */
@Override
protected void verifyIterationCount() throws IllegalArgumentException {
super.verifyIterationCount();
// at most 32 bisection refinements due to higher order divider
if (maximalIterationCount > 32) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.INVALID_ITERATIONS_LIMITS,
0, 32);
}
}
}
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