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 */
017 package org.apache.commons.math3.analysis.integration;
018
019 import org.apache.commons.math3.exception.MaxCountExceededException;
020 import org.apache.commons.math3.exception.NotStrictlyPositiveException;
021 import org.apache.commons.math3.exception.NumberIsTooLargeException;
022 import org.apache.commons.math3.exception.NumberIsTooSmallException;
023 import org.apache.commons.math3.exception.TooManyEvaluationsException;
024 import 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 */
039 public 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 }