RombergIntegrator.java

/*
 * 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
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 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
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 * See the License for the specific language governing permissions and
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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</b>, 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 = iterations.getMaximalCount() + 1;
        double previousRow[] = new double[m];
        double currentRow[]  = new double[m];

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

            final int i = iterations.getCount();

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

            currentRow[0] = qtrap.stage(this, i);
            iterations.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;
        }

    }

}