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Diffstat (limited to 'src/main/java/org/apache/commons/math3/analysis/integration/IterativeLegendreGaussIntegrator.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/analysis/integration/IterativeLegendreGaussIntegrator.java | 183 |
1 files changed, 183 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/analysis/integration/IterativeLegendreGaussIntegrator.java b/src/main/java/org/apache/commons/math3/analysis/integration/IterativeLegendreGaussIntegrator.java new file mode 100644 index 0000000..20700dd --- /dev/null +++ b/src/main/java/org/apache/commons/math3/analysis/integration/IterativeLegendreGaussIntegrator.java @@ -0,0 +1,183 @@ +/* + * 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.analysis.UnivariateFunction; +import org.apache.commons.math3.analysis.integration.gauss.GaussIntegratorFactory; +import org.apache.commons.math3.analysis.integration.gauss.GaussIntegrator; +import org.apache.commons.math3.exception.MathIllegalArgumentException; +import org.apache.commons.math3.exception.MaxCountExceededException; +import org.apache.commons.math3.exception.NotStrictlyPositiveException; +import org.apache.commons.math3.exception.NumberIsTooSmallException; +import org.apache.commons.math3.exception.TooManyEvaluationsException; +import org.apache.commons.math3.exception.util.LocalizedFormats; +import org.apache.commons.math3.util.FastMath; + +/** + * This algorithm divides the integration interval into equally-sized + * sub-interval and on each of them performs a + * <a href="http://mathworld.wolfram.com/Legendre-GaussQuadrature.html"> + * Legendre-Gauss</a> quadrature. + * Because of its <em>non-adaptive</em> nature, this algorithm can + * converge to a wrong value for the integral (for example, if the + * function is significantly different from zero toward the ends of the + * integration interval). + * In particular, a change of variables aimed at estimating integrals + * over infinite intervals as proposed + * <a href="http://en.wikipedia.org/w/index.php?title=Numerical_integration#Integrals_over_infinite_intervals"> + * here</a> should be avoided when using this class. + * + * @since 3.1 + */ + +public class IterativeLegendreGaussIntegrator + extends BaseAbstractUnivariateIntegrator { + /** Factory that computes the points and weights. */ + private static final GaussIntegratorFactory FACTORY + = new GaussIntegratorFactory(); + /** Number of integration points (per interval). */ + private final int numberOfPoints; + + /** + * Builds an integrator with given accuracies and iterations counts. + * + * @param n Number of integration points. + * @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. + * @throws NotStrictlyPositiveException if minimal number of iterations + * or number of points are not strictly positive. + * @throws NumberIsTooSmallException if maximal number of iterations + * is smaller than or equal to the minimal number of iterations. + */ + public IterativeLegendreGaussIntegrator(final int n, + final double relativeAccuracy, + final double absoluteAccuracy, + final int minimalIterationCount, + final int maximalIterationCount) + throws NotStrictlyPositiveException, NumberIsTooSmallException { + super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount); + if (n <= 0) { + throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_POINTS, n); + } + numberOfPoints = n; + } + + /** + * Builds an integrator with given accuracies. + * + * @param n Number of integration points. + * @param relativeAccuracy Relative accuracy of the result. + * @param absoluteAccuracy Absolute accuracy of the result. + * @throws NotStrictlyPositiveException if {@code n < 1}. + */ + public IterativeLegendreGaussIntegrator(final int n, + final double relativeAccuracy, + final double absoluteAccuracy) + throws NotStrictlyPositiveException { + this(n, relativeAccuracy, absoluteAccuracy, + DEFAULT_MIN_ITERATIONS_COUNT, DEFAULT_MAX_ITERATIONS_COUNT); + } + + /** + * Builds an integrator with given iteration counts. + * + * @param n Number of integration points. + * @param minimalIterationCount Minimum number of iterations. + * @param maximalIterationCount Maximum number of iterations. + * @throws NotStrictlyPositiveException if minimal number of iterations + * is not strictly positive. + * @throws NumberIsTooSmallException if maximal number of iterations + * is smaller than or equal to the minimal number of iterations. + * @throws NotStrictlyPositiveException if {@code n < 1}. + */ + public IterativeLegendreGaussIntegrator(final int n, + final int minimalIterationCount, + final int maximalIterationCount) + throws NotStrictlyPositiveException, NumberIsTooSmallException { + this(n, DEFAULT_RELATIVE_ACCURACY, DEFAULT_ABSOLUTE_ACCURACY, + minimalIterationCount, maximalIterationCount); + } + + /** {@inheritDoc} */ + @Override + protected double doIntegrate() + throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException { + // Compute first estimate with a single step. + double oldt = stage(1); + + int n = 2; + while (true) { + // Improve integral with a larger number of steps. + final double t = stage(n); + + // Estimate the error. + final double delta = FastMath.abs(t - oldt); + final double limit = + FastMath.max(getAbsoluteAccuracy(), + getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5); + + // check convergence + if (getIterations() + 1 >= getMinimalIterationCount() && + delta <= limit) { + return t; + } + + // Prepare next iteration. + final double ratio = FastMath.min(4, FastMath.pow(delta / limit, 0.5 / numberOfPoints)); + n = FastMath.max((int) (ratio * n), n + 1); + oldt = t; + incrementCount(); + } + } + + /** + * Compute the n-th stage integral. + * + * @param n Number of steps. + * @return the value of n-th stage integral. + * @throws TooManyEvaluationsException if the maximum number of evaluations + * is exceeded. + */ + private double stage(final int n) + throws TooManyEvaluationsException { + // Function to be integrated is stored in the base class. + final UnivariateFunction f = new UnivariateFunction() { + /** {@inheritDoc} */ + public double value(double x) + throws MathIllegalArgumentException, TooManyEvaluationsException { + return computeObjectiveValue(x); + } + }; + + final double min = getMin(); + final double max = getMax(); + final double step = (max - min) / n; + + double sum = 0; + for (int i = 0; i < n; i++) { + // Integrate over each sub-interval [a, b]. + final double a = min + i * step; + final double b = a + step; + final GaussIntegrator g = FACTORY.legendreHighPrecision(numberOfPoints, a, b); + sum += g.integrate(f); + } + + return sum; + } +} |