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Java example source code file (MidPointIntegrator.java)

This example Java source code file (MidPointIntegrator.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, mathillegalargumentexception, maxcountexceededexception, midpoint_max_iterations_count, midpointintegrator, notstrictlypositiveexception, numberistoolargeexception, numberistoosmallexception, override, toomanyevaluationsexception

The MidPointIntegrator.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.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.util.FastMath;

/**
 * Implements the <a href="http://en.wikipedia.org/wiki/Midpoint_method">
 * Midpoint Rule</a> for integration of real univariate functions. For
 * reference, see <b>Numerical Mathematics, ISBN 0387989595,
 * chapter 9.2.
 * <p>
 * The function should be integrable.</p>
 *
 * @since 3.3
 */
public class MidPointIntegrator extends BaseAbstractUnivariateIntegrator {

    /** Maximum number of iterations for midpoint. */
    public static final int MIDPOINT_MAX_ITERATIONS_COUNT = 64;

    /**
     * Build a midpoint 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
     * (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
     * @exception NotStrictlyPositiveException if minimal number of iterations
     * is not strictly positive
     * @exception NumberIsTooSmallException if maximal number of iterations
     * is lesser than or equal to the minimal number of iterations
     * @exception NumberIsTooLargeException if maximal number of iterations
     * is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
     */
    public MidPointIntegrator(final double relativeAccuracy,
                              final double absoluteAccuracy,
                              final int minimalIterationCount,
                              final int maximalIterationCount)
        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
        if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
            throw new NumberIsTooLargeException(maximalIterationCount,
                                                MIDPOINT_MAX_ITERATIONS_COUNT, false);
        }
    }

    /**
     * Build a midpoint integrator with given iteration counts.
     * @param minimalIterationCount minimum number of iterations
     * @param maximalIterationCount maximum number of iterations
     * (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
     * @exception NotStrictlyPositiveException if minimal number of iterations
     * is not strictly positive
     * @exception NumberIsTooSmallException if maximal number of iterations
     * is lesser than or equal to the minimal number of iterations
     * @exception NumberIsTooLargeException if maximal number of iterations
     * is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
     */
    public MidPointIntegrator(final int minimalIterationCount,
                              final int maximalIterationCount)
        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
        super(minimalIterationCount, maximalIterationCount);
        if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
            throw new NumberIsTooLargeException(maximalIterationCount,
                                                MIDPOINT_MAX_ITERATIONS_COUNT, false);
        }
    }

    /**
     * Construct a midpoint integrator with default settings.
     * (max iteration count set to {@link #MIDPOINT_MAX_ITERATIONS_COUNT})
     */
    public MidPointIntegrator() {
        super(DEFAULT_MIN_ITERATIONS_COUNT, MIDPOINT_MAX_ITERATIONS_COUNT);
    }

    /**
     * Compute the n-th stage integral of midpoint rule.
     * This function should only be called by API <code>integrate() in the package.
     * To save time it does not verify arguments - caller does.
     * <p>
     * The interval is divided equally into 2^n sections rather than an
     * arbitrary m sections because this configuration can best utilize the
     * already computed values.</p>
     *
     * @param n the stage of 1/2 refinement. Must be larger than 0.
     * @param previousStageResult Result from the previous call to the
     * {@code stage} method.
     * @param min Lower bound of the integration interval.
     * @param diffMaxMin Difference between the lower bound and upper bound
     * of the integration interval.
     * @return the value of n-th stage integral
     * @throws TooManyEvaluationsException if the maximal number of evaluations
     * is exceeded.
     */
    private double stage(final int n,
                         double previousStageResult,
                         double min,
                         double diffMaxMin)
        throws TooManyEvaluationsException {

        // number of new points in this stage
        final long np = 1L << (n - 1);
        double sum = 0;

        // spacing between adjacent new points
        final double spacing = diffMaxMin / np;

        // the first new point
        double x = min + 0.5 * spacing;
        for (long i = 0; i < np; i++) {
            sum += computeObjectiveValue(x);
            x += spacing;
        }
        // add the new sum to previously calculated result
        return 0.5 * (previousStageResult + sum * spacing);
    }


    /** {@inheritDoc} */
    @Override
    protected double doIntegrate()
        throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {

        final double min = getMin();
        final double diff = getMax() - min;
        final double midPoint = min + 0.5 * diff;

        double oldt = diff * computeObjectiveValue(midPoint);

        while (true) {
            incrementCount();
            final int i = getIterations();
            final double t = stage(i, oldt, min, diff);
            if (i >= getMinimalIterationCount()) {
                final double delta = FastMath.abs(t - oldt);
                final double rLimit =
                        getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
                    return t;
                }
            }
            oldt = t;
        }

    }

}

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