Java example source code file (IterativeLegendreGaussIntegrator.java)

This example Java source code file (IterativeLegendreGaussIntegrator.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" ^TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

baseabstractunivariateintegrator, default_absolute_accuracy, default_max_iterations_count, default_min_iterations_count, default_relative_accuracy, gaussintegratorfactory, iterativelegendregaussintegrator, mathillegalargumentexception, maxcountexceededexception, notstrictlypositiveexception, numberistoosmallexception, override, toomanyevaluationsexception, univariatefunction

The IterativeLegendreGaussIntegrator.java Java example source code

/*
 * 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 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;
    }
}