001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.math4.analysis.integration.gauss;
018
019import org.apache.commons.math4.analysis.UnivariateFunction;
020import org.apache.commons.math4.util.Pair;
021
022/**
023 * This class's implements {@link #integrate(UnivariateFunction) integrate}
024 * method assuming that the integral is symmetric about 0.
025 * This allows to reduce numerical errors.
026 *
027 * @since 3.3
028 */
029public class SymmetricGaussIntegrator extends GaussIntegrator {
030    /**
031     * Creates an integrator from the given {@code points} and {@code weights}.
032     * The integration interval is defined by the first and last value of
033     * {@code points} which must be sorted in increasing order.
034     *
035     * @param points Integration points.
036     * @param weights Weights of the corresponding integration nodes.
037     * @throws org.apache.commons.math4.exception.NonMonotonicSequenceException if the {@code points} are not
038     * sorted in increasing order.
039     * @throws org.apache.commons.math4.exception.DimensionMismatchException if points and weights don't have the same length
040     */
041    public SymmetricGaussIntegrator(double[] points,
042                                    double[] weights) {
043        super(points, weights);
044    }
045
046    /**
047     * Creates an integrator from the given pair of points (first element of
048     * the pair) and weights (second element of the pair.
049     *
050     * @param pointsAndWeights Integration points and corresponding weights.
051     * @throws org.apache.commons.math4.exception.NonMonotonicSequenceException if the {@code points} are not
052     * sorted in increasing order.
053     *
054     * @see #SymmetricGaussIntegrator(double[], double[])
055     */
056    public SymmetricGaussIntegrator(Pair<double[], double[]> pointsAndWeights) {
057        this(pointsAndWeights.getFirst(), pointsAndWeights.getSecond());
058    }
059
060    /**
061     * {@inheritDoc}
062     */
063    @Override
064    public double integrate(UnivariateFunction f) {
065        final int ruleLength = getNumberOfPoints();
066
067        if (ruleLength == 1) {
068            return getWeight(0) * f.value(0d);
069        }
070
071        final int iMax = ruleLength / 2;
072        double s = 0;
073        double c = 0;
074        for (int i = 0; i < iMax; i++) {
075            final double p = getPoint(i);
076            final double w = getWeight(i);
077
078            final double f1 = f.value(p);
079            final double f2 = f.value(-p);
080
081            final double y = w * (f1 + f2) - c;
082            final double t = s + y;
083
084            c = (t - s) - y;
085            s = t;
086        }
087
088        if (ruleLength % 2 != 0) {
089            final double w = getWeight(iMax);
090
091            final double y = w * f.value(0d) - c;
092            final double t = s + y;
093
094            s = t;
095        }
096
097        return s;
098    }
099}