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 import org.apache.commons.math.exception.util.LocalizedFormats;
024 import org.apache.commons.math.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 $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 f??vr. 2011) $
037 * @since 1.2
038 */
039 public class RombergIntegrator extends UnivariateRealIntegratorImpl {
040
041 /**
042 * Construct an integrator for the given function.
043 *
044 * @param f function to integrate
045 * @deprecated as of 2.0 the integrand function is passed as an argument
046 * to the {@link #integrate(UnivariateRealFunction, double, double)}method.
047 */
048 @Deprecated
049 public RombergIntegrator(UnivariateRealFunction f) {
050 super(f, 32);
051 }
052
053 /**
054 * Construct an integrator.
055 */
056 public RombergIntegrator() {
057 super(32);
058 }
059
060 /** {@inheritDoc} */
061 @Deprecated
062 public double integrate(final double min, final double max)
063 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
064 return integrate(f, min, max);
065 }
066
067 /** {@inheritDoc} */
068 public double integrate(final UnivariateRealFunction f, final double min, final double max)
069 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
070
071 final int m = maximalIterationCount + 1;
072 double previousRow[] = new double[m];
073 double currentRow[] = new double[m];
074
075 clearResult();
076 verifyInterval(min, max);
077 verifyIterationCount();
078
079 TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
080 currentRow[0] = qtrap.stage(f, min, max, 0);
081 double olds = currentRow[0];
082 for (int i = 1; i <= maximalIterationCount; ++i) {
083
084 // switch rows
085 final double[] tmpRow = previousRow;
086 previousRow = currentRow;
087 currentRow = tmpRow;
088
089 currentRow[0] = qtrap.stage(f, min, max, i);
090 for (int j = 1; j <= i; j++) {
091 // Richardson extrapolation coefficient
092 final double r = (1L << (2 * j)) - 1;
093 final double tIJm1 = currentRow[j - 1];
094 currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;
095 }
096 final double s = currentRow[i];
097 if (i >= minimalIterationCount) {
098 final double delta = FastMath.abs(s - olds);
099 final double rLimit = relativeAccuracy * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
100 if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
101 setResult(s, i);
102 return result;
103 }
104 }
105 olds = s;
106 }
107 throw new MaxIterationsExceededException(maximalIterationCount);
108 }
109
110 /** {@inheritDoc} */
111 @Override
112 protected void verifyIterationCount() throws IllegalArgumentException {
113 super.verifyIterationCount();
114 // at most 32 bisection refinements due to higher order divider
115 if (maximalIterationCount > 32) {
116 throw MathRuntimeException.createIllegalArgumentException(
117 LocalizedFormats.INVALID_ITERATIONS_LIMITS,
118 0, 32);
119 }
120 }
121 }