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.math.analysis.integration;
018
019 import org.apache.commons.math.FunctionEvaluationException;
020 import org.apache.commons.math.MathRuntimeException;
021 import org.apache.commons.math.MaxIterationsExceededException;
022 import org.apache.commons.math.analysis.UnivariateRealFunction;
023
024 /**
025 * Implements the <a href="http://mathworld.wolfram.com/RombergIntegration.html">
026 * Romberg Algorithm</a> for integration of real univariate functions. For
027 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
028 * chapter 3.
029 * <p>
030 * Romberg integration employs k successive refinements of the trapezoid
031 * rule to remove error terms less than order O(N^(-2k)). Simpson's rule
032 * is a special case of k = 2.</p>
033 *
034 * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $
035 * @since 1.2
036 */
037 public class RombergIntegrator extends UnivariateRealIntegratorImpl {
038
039 /**
040 * Construct an integrator for the given function.
041 *
042 * @param f function to integrate
043 * @deprecated as of 2.0 the integrand function is passed as an argument
044 * to the {@link #integrate(UnivariateRealFunction, double, double)}method.
045 */
046 @Deprecated
047 public RombergIntegrator(UnivariateRealFunction f) {
048 super(f, 32);
049 }
050
051 /**
052 * Construct an integrator.
053 */
054 public RombergIntegrator() {
055 super(32);
056 }
057
058 /** {@inheritDoc} */
059 @Deprecated
060 public double integrate(final double min, final double max)
061 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
062 return integrate(f, min, max);
063 }
064
065 /** {@inheritDoc} */
066 public double integrate(final UnivariateRealFunction f,
067 final double min, final double max)
068 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
069
070 int i = 1, j, m = maximalIterationCount + 1;
071 // Array structure here can be improved for better space
072 // efficiency because only the lower triangle is used.
073 double r, t[][] = new double[m][m], s, olds;
074
075 clearResult();
076 verifyInterval(min, max);
077 verifyIterationCount();
078
079 TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
080 t[0][0] = qtrap.stage(f, min, max, 0);
081 olds = t[0][0];
082 while (i <= maximalIterationCount) {
083 t[i][0] = qtrap.stage(f, min, max, i);
084 for (j = 1; j <= i; j++) {
085 // Richardson extrapolation coefficient
086 r = (1L << (2 * j)) -1;
087 t[i][j] = t[i][j-1] + (t[i][j-1] - t[i-1][j-1]) / r;
088 }
089 s = t[i][i];
090 if (i >= minimalIterationCount) {
091 final double delta = Math.abs(s - olds);
092 final double rLimit =
093 relativeAccuracy * (Math.abs(olds) + Math.abs(s)) * 0.5;
094 if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
095 setResult(s, i);
096 return result;
097 }
098 }
099 olds = s;
100 i++;
101 }
102 throw new MaxIterationsExceededException(maximalIterationCount);
103 }
104
105 /** {@inheritDoc} */
106 @Override
107 protected void verifyIterationCount() throws IllegalArgumentException {
108 super.verifyIterationCount();
109 // at most 32 bisection refinements due to higher order divider
110 if (maximalIterationCount > 32) {
111 throw MathRuntimeException.createIllegalArgumentException(
112 "invalid iteration limits: min={0}, max={1}",
113 0, 32);
114 }
115 }
116 }