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Diffstat (limited to 'src/main/java/org/apache/commons/math3/analysis/integration/RombergIntegrator.java')
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1 files changed, 142 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/analysis/integration/RombergIntegrator.java b/src/main/java/org/apache/commons/math3/analysis/integration/RombergIntegrator.java new file mode 100644 index 0000000..125d251 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/analysis/integration/RombergIntegrator.java @@ -0,0 +1,142 @@ +/* + * 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 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> + * + * @since 1.2 + */ +public class RombergIntegrator extends BaseAbstractUnivariateIntegrator { + + /** Maximal number of iterations for Romberg. */ + public static final int ROMBERG_MAX_ITERATIONS_COUNT = 32; + + /** + * Build a Romberg 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 #ROMBERG_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 #ROMBERG_MAX_ITERATIONS_COUNT} + */ + public RombergIntegrator(final double relativeAccuracy, + final double absoluteAccuracy, + final int minimalIterationCount, + final int maximalIterationCount) + throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException { + super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount); + if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) { + throw new NumberIsTooLargeException(maximalIterationCount, + ROMBERG_MAX_ITERATIONS_COUNT, false); + } + } + + /** + * Build a Romberg 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 #ROMBERG_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 #ROMBERG_MAX_ITERATIONS_COUNT} + */ + public RombergIntegrator(final int minimalIterationCount, + final int maximalIterationCount) + throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException { + super(minimalIterationCount, maximalIterationCount); + if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) { + throw new NumberIsTooLargeException(maximalIterationCount, + ROMBERG_MAX_ITERATIONS_COUNT, false); + } + } + + /** + * Construct a Romberg integrator with default settings + * (max iteration count set to {@link #ROMBERG_MAX_ITERATIONS_COUNT}) + */ + public RombergIntegrator() { + super(DEFAULT_MIN_ITERATIONS_COUNT, ROMBERG_MAX_ITERATIONS_COUNT); + } + + /** {@inheritDoc} */ + @Override + protected double doIntegrate() + throws TooManyEvaluationsException, MaxCountExceededException { + + final int m = getMaximalIterationCount() + 1; + double previousRow[] = new double[m]; + double currentRow[] = new double[m]; + + TrapezoidIntegrator qtrap = new TrapezoidIntegrator(); + currentRow[0] = qtrap.stage(this, 0); + incrementCount(); + double olds = currentRow[0]; + while (true) { + + final int i = getIterations(); + + // switch rows + final double[] tmpRow = previousRow; + previousRow = currentRow; + currentRow = tmpRow; + + currentRow[0] = qtrap.stage(this, i); + incrementCount(); + 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 >= 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; + } + + } + +} |