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Java example source code file (RombergIntegrator.java)

This example Java source code file (RombergIntegrator.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, maxcountexceededexception, notstrictlypositiveexception, numberistoolargeexception, numberistoosmallexception, override, romberg_max_iterations_count, rombergintegrator, toomanyevaluationsexception, trapezoidintegrator

The RombergIntegrator.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.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://mathworld.wolfram.com/RombergIntegration.html">
 * Romberg Algorithm</a> for integration of real univariate functions. For
 * reference, see <b>Introduction to Numerical Analysis, ISBN 038795452X,
 * chapter 3.
 * <p>
 * Romberg integration employs k successive refinements of the trapezoid
 * rule to remove error terms less than order O(N^(-2k)). Simpson's rule
 * is a special case of k = 2.</p>
 *
 * @since 1.2
 */
public class RombergIntegrator extends BaseAbstractUnivariateIntegrator {

    /** Maximal number of iterations for Romberg. */
    public static final int ROMBERG_MAX_ITERATIONS_COUNT = 32;

    /**
     * Build a Romberg 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 #ROMBERG_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 #ROMBERG_MAX_ITERATIONS_COUNT}
     */
    public RombergIntegrator(final double relativeAccuracy,
                             final double absoluteAccuracy,
                             final int minimalIterationCount,
                             final int maximalIterationCount)
        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
        if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
            throw new NumberIsTooLargeException(maximalIterationCount,
                                                ROMBERG_MAX_ITERATIONS_COUNT, false);
        }
    }

    /**
     * Build a Romberg 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 #ROMBERG_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 #ROMBERG_MAX_ITERATIONS_COUNT}
     */
    public RombergIntegrator(final int minimalIterationCount,
                             final int maximalIterationCount)
        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
        super(minimalIterationCount, maximalIterationCount);
        if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
            throw new NumberIsTooLargeException(maximalIterationCount,
                                                ROMBERG_MAX_ITERATIONS_COUNT, false);
        }
    }

    /**
     * Construct a Romberg integrator with default settings
     * (max iteration count set to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
     */
    public RombergIntegrator() {
        super(DEFAULT_MIN_ITERATIONS_COUNT, ROMBERG_MAX_ITERATIONS_COUNT);
    }

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

        final int m = getMaximalIterationCount() + 1;
        double previousRow[] = new double[m];
        double currentRow[]  = new double[m];

        TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
        currentRow[0] = qtrap.stage(this, 0);
        incrementCount();
        double olds = currentRow[0];
        while (true) {

            final int i = getIterations();

            // switch rows
            final double[] tmpRow = previousRow;
            previousRow = currentRow;
            currentRow = tmpRow;

            currentRow[0] = qtrap.stage(this, i);
            incrementCount();
            for (int j = 1; j <= i; j++) {
                // Richardson extrapolation coefficient
                final double r = (1L << (2 * j)) - 1;
                final double tIJm1 = currentRow[j - 1];
                currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;
            }
            final double s = currentRow[i];
            if (i >= getMinimalIterationCount()) {
                final double delta  = FastMath.abs(s - olds);
                final double rLimit = getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
                    return s;
                }
            }
            olds = s;
        }

    }

}

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