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Diffstat (limited to 'src/main/java/org/apache/commons/math/analysis/integration/SimpsonIntegrator.java')
-rw-r--r-- | src/main/java/org/apache/commons/math/analysis/integration/SimpsonIntegrator.java | 112 |
1 files changed, 112 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/analysis/integration/SimpsonIntegrator.java b/src/main/java/org/apache/commons/math/analysis/integration/SimpsonIntegrator.java new file mode 100644 index 0000000..045b54e --- /dev/null +++ b/src/main/java/org/apache/commons/math/analysis/integration/SimpsonIntegrator.java @@ -0,0 +1,112 @@ +/* + * 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/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 basic trapezoid rule as building blocks to + * calculate the Simpson's rule of alternating 2/3 and 4/3.</p> + * + * @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); + } + } +} |