SimpsonIntegrator.java

/*
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 * 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
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 *
 *      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
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package org.apache.commons.math4.legacy.analysis.integration;

import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
import org.apache.commons.math4.core.jdkmath.JdkMath;

/**
 * Implements <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
 * Simpson's Rule</a> for integration of real univariate functions.
 *
 * See <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, chapter 3.
 *
 * <p>
 * This implementation employs the basic trapezoid rule to calculate Simpson's
 * rule.
 *
 * <p>
 * <em>Caveat:</em> At each iteration, the algorithm refines the estimation by
 * evaluating the function twice as many times as in the previous iteration;
 * When specifying a {@link #integrate(int,UnivariateFunction,double,double)
 * maximum number of function evaluations}, the caller must ensure that it
 * is compatible with the {@link #SimpsonIntegrator(int,int) requested minimal
 * number of iterations}.
 *
 * @since 1.2
 */
public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator {
    /** Maximal number of iterations for Simpson. */
    private static final int SIMPSON_MAX_ITERATIONS_COUNT = 30;

    /**
     * Build a Simpson integrator with given accuracies and iterations counts.
     * @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.
     * It must be less than or equal to 30.
     * @throws org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException
     * if {@code minimalIterationCount <= 0}.
     * @throws org.apache.commons.math4.legacy.exception.NumberIsTooSmallException
     * if {@code maximalIterationCount < minimalIterationCount}.
     * is lesser than or equal to the minimal number of iterations
     * @throws NumberIsTooLargeException if {@code maximalIterationCount > 30}.
     */
    public SimpsonIntegrator(final double relativeAccuracy,
                             final double absoluteAccuracy,
                             final int minimalIterationCount,
                             final int maximalIterationCount) {
        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
        if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
            throw new NumberIsTooLargeException(maximalIterationCount,
                                                SIMPSON_MAX_ITERATIONS_COUNT, false);
        }
    }

    /**
     * Build a Simpson integrator with given iteration counts.
     * @param minimalIterationCount Minimum number of iterations.
     * @param maximalIterationCount Maximum number of iterations.
     * It must be less than or equal to 30.
     * @throws org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException
     * if {@code minimalIterationCount <= 0}.
     * @throws org.apache.commons.math4.legacy.exception.NumberIsTooSmallException
     * if {@code maximalIterationCount < minimalIterationCount}.
     * is lesser than or equal to the minimal number of iterations
     * @throws NumberIsTooLargeException if {@code maximalIterationCount > 30}.
     */
    public SimpsonIntegrator(final int minimalIterationCount,
                             final int maximalIterationCount) {
        super(minimalIterationCount, maximalIterationCount);
        if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
            throw new NumberIsTooLargeException(maximalIterationCount,
                                                SIMPSON_MAX_ITERATIONS_COUNT, false);
        }
    }

    /**
     * Construct an integrator with default settings.
     */
    public SimpsonIntegrator() {
        super(DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT);
    }

    /** {@inheritDoc} */
    @Override
    protected double doIntegrate() {
        // Simpson's rule requires at least two trapezoid stages.
        // So we set the first sum using two trapezoid stages.
        final TrapezoidIntegrator qtrap = new TrapezoidIntegrator();

        final double s0 = qtrap.stage(this, 0);
        double oldt = qtrap.stage(this, 1);
        double olds = (4 * oldt - s0) / 3.0;
        while (true) {
            // The first iteration is the first refinement of the sum.
            iterations.increment();
            final int i = getIterations();
            final double t = qtrap.stage(this, i + 1); // 1-stage ahead of the iteration
            final double s = (4 * t - oldt) / 3.0;
            if (i >= getMinimalIterationCount()) {
                final double delta = JdkMath.abs(s - olds);
                final double rLimit = getRelativeAccuracy() * (JdkMath.abs(olds) + JdkMath.abs(s)) * 0.5;
                if (delta <= rLimit ||
                    delta <= getAbsoluteAccuracy()) {
                    return s;
                }
            }
            olds = s;
            oldt = t;
        }
    }
}