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Diffstat (limited to 'src/main/java/org/apache/commons/math/analysis/integration/RombergIntegrator.java')
-rw-r--r-- | src/main/java/org/apache/commons/math/analysis/integration/RombergIntegrator.java | 121 |
1 files changed, 121 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/analysis/integration/RombergIntegrator.java b/src/main/java/org/apache/commons/math/analysis/integration/RombergIntegrator.java new file mode 100644 index 0000000..9650af5 --- /dev/null +++ b/src/main/java/org/apache/commons/math/analysis/integration/RombergIntegrator.java @@ -0,0 +1,121 @@ +/* + * 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); + } + } +} |