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.math3.analysis.integration;
018
019import org.apache.commons.math3.exception.MaxCountExceededException;
020import org.apache.commons.math3.exception.NotStrictlyPositiveException;
021import org.apache.commons.math3.exception.NumberIsTooLargeException;
022import org.apache.commons.math3.exception.NumberIsTooSmallException;
023import org.apache.commons.math3.exception.TooManyEvaluationsException;
024import org.apache.commons.math3.util.FastMath;
025
026/**
027 * Implements the <a href="http://mathworld.wolfram.com/RombergIntegration.html">
028 * Romberg Algorithm</a> for integration of real univariate functions. For
029 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
030 * chapter 3.
031 * <p>
032 * Romberg integration employs k successive refinements of the trapezoid
033 * rule to remove error terms less than order O(N^(-2k)). Simpson's rule
034 * is a special case of k = 2.</p>
035 *
036 * @version $Id: RombergIntegrator.java 1364387 2012-07-22 18:14:11Z tn $
037 * @since 1.2
038 */
039public class RombergIntegrator extends BaseAbstractUnivariateIntegrator {
040
041    /** Maximal number of iterations for Romberg. */
042    public static final int ROMBERG_MAX_ITERATIONS_COUNT = 32;
043
044    /**
045     * Build a Romberg integrator with given accuracies and iterations counts.
046     * @param relativeAccuracy relative accuracy of the result
047     * @param absoluteAccuracy absolute accuracy of the result
048     * @param minimalIterationCount minimum number of iterations
049     * @param maximalIterationCount maximum number of iterations
050     * (must be less than or equal to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
051     * @exception NotStrictlyPositiveException if minimal number of iterations
052     * is not strictly positive
053     * @exception NumberIsTooSmallException if maximal number of iterations
054     * is lesser than or equal to the minimal number of iterations
055     * @exception NumberIsTooLargeException if maximal number of iterations
056     * is greater than {@link #ROMBERG_MAX_ITERATIONS_COUNT}
057     */
058    public RombergIntegrator(final double relativeAccuracy,
059                             final double absoluteAccuracy,
060                             final int minimalIterationCount,
061                             final int maximalIterationCount)
062        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
063        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
064        if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
065            throw new NumberIsTooLargeException(maximalIterationCount,
066                                                ROMBERG_MAX_ITERATIONS_COUNT, false);
067        }
068    }
069
070    /**
071     * Build a Romberg integrator with given iteration counts.
072     * @param minimalIterationCount minimum number of iterations
073     * @param maximalIterationCount maximum number of iterations
074     * (must be less than or equal to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
075     * @exception NotStrictlyPositiveException if minimal number of iterations
076     * is not strictly positive
077     * @exception NumberIsTooSmallException if maximal number of iterations
078     * is lesser than or equal to the minimal number of iterations
079     * @exception NumberIsTooLargeException if maximal number of iterations
080     * is greater than {@link #ROMBERG_MAX_ITERATIONS_COUNT}
081     */
082    public RombergIntegrator(final int minimalIterationCount,
083                             final int maximalIterationCount)
084        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
085        super(minimalIterationCount, maximalIterationCount);
086        if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
087            throw new NumberIsTooLargeException(maximalIterationCount,
088                                                ROMBERG_MAX_ITERATIONS_COUNT, false);
089        }
090    }
091
092    /**
093     * Construct a Romberg integrator with default settings
094     * (max iteration count set to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
095     */
096    public RombergIntegrator() {
097        super(DEFAULT_MIN_ITERATIONS_COUNT, ROMBERG_MAX_ITERATIONS_COUNT);
098    }
099
100    /** {@inheritDoc} */
101    @Override
102    protected double doIntegrate()
103        throws TooManyEvaluationsException, MaxCountExceededException {
104
105        final int m = iterations.getMaximalCount() + 1;
106        double previousRow[] = new double[m];
107        double currentRow[]  = new double[m];
108
109        TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
110        currentRow[0] = qtrap.stage(this, 0);
111        iterations.incrementCount();
112        double olds = currentRow[0];
113        while (true) {
114
115            final int i = iterations.getCount();
116
117            // switch rows
118            final double[] tmpRow = previousRow;
119            previousRow = currentRow;
120            currentRow = tmpRow;
121
122            currentRow[0] = qtrap.stage(this, i);
123            iterations.incrementCount();
124            for (int j = 1; j <= i; j++) {
125                // Richardson extrapolation coefficient
126                final double r = (1L << (2 * j)) - 1;
127                final double tIJm1 = currentRow[j - 1];
128                currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;
129            }
130            final double s = currentRow[i];
131            if (i >= getMinimalIterationCount()) {
132                final double delta  = FastMath.abs(s - olds);
133                final double rLimit = getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
134                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
135                    return s;
136                }
137            }
138            olds = s;
139        }
140
141    }
142
143}