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view libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/analysis/integration/RombergIntegrator.html @ 13:cbf34dd4d7e6
commons-math-2.1 added
| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.analysis.integration;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import org.apache.commons.math.FunctionEvaluationException;<a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.MaxIterationsExceededException;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.22"></a> <FONT color="green">023</FONT> <a name="line.23"></a> <FONT color="green">024</FONT> /**<a name="line.24"></a> <FONT color="green">025</FONT> * Implements the <a href="http://mathworld.wolfram.com/RombergIntegration.html"><a name="line.25"></a> <FONT color="green">026</FONT> * Romberg Algorithm</a> for integration of real univariate functions. For<a name="line.26"></a> <FONT color="green">027</FONT> * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,<a name="line.27"></a> <FONT color="green">028</FONT> * chapter 3.<a name="line.28"></a> <FONT color="green">029</FONT> * <p><a name="line.29"></a> <FONT color="green">030</FONT> * Romberg integration employs k successive refinements of the trapezoid<a name="line.30"></a> <FONT color="green">031</FONT> * rule to remove error terms less than order O(N^(-2k)). Simpson's rule<a name="line.31"></a> <FONT color="green">032</FONT> * is a special case of k = 2.</p><a name="line.32"></a> <FONT color="green">033</FONT> *<a name="line.33"></a> <FONT color="green">034</FONT> * @version $Revision: 824822 $ $Date: 2009-10-13 11:56:51 -0400 (Tue, 13 Oct 2009) $<a name="line.34"></a> <FONT color="green">035</FONT> * @since 1.2<a name="line.35"></a> <FONT color="green">036</FONT> */<a name="line.36"></a> <FONT color="green">037</FONT> public class RombergIntegrator extends UnivariateRealIntegratorImpl {<a name="line.37"></a> <FONT color="green">038</FONT> <a name="line.38"></a> <FONT color="green">039</FONT> /**<a name="line.39"></a> <FONT color="green">040</FONT> * Construct an integrator for the given function.<a name="line.40"></a> <FONT color="green">041</FONT> *<a name="line.41"></a> <FONT color="green">042</FONT> * @param f function to integrate<a name="line.42"></a> <FONT color="green">043</FONT> * @deprecated as of 2.0 the integrand function is passed as an argument<a name="line.43"></a> <FONT color="green">044</FONT> * to the {@link #integrate(UnivariateRealFunction, double, double)}method.<a name="line.44"></a> <FONT color="green">045</FONT> */<a name="line.45"></a> <FONT color="green">046</FONT> @Deprecated<a name="line.46"></a> <FONT color="green">047</FONT> public RombergIntegrator(UnivariateRealFunction f) {<a name="line.47"></a> <FONT color="green">048</FONT> super(f, 32);<a name="line.48"></a> <FONT color="green">049</FONT> }<a name="line.49"></a> <FONT color="green">050</FONT> <a name="line.50"></a> <FONT color="green">051</FONT> /**<a name="line.51"></a> <FONT color="green">052</FONT> * Construct an integrator.<a name="line.52"></a> <FONT color="green">053</FONT> */<a name="line.53"></a> <FONT color="green">054</FONT> public RombergIntegrator() {<a name="line.54"></a> <FONT color="green">055</FONT> super(32);<a name="line.55"></a> <FONT color="green">056</FONT> }<a name="line.56"></a> <FONT color="green">057</FONT> <a name="line.57"></a> <FONT color="green">058</FONT> /** {@inheritDoc} */<a name="line.58"></a> <FONT color="green">059</FONT> @Deprecated<a name="line.59"></a> <FONT color="green">060</FONT> public double integrate(final double min, final double max)<a name="line.60"></a> <FONT color="green">061</FONT> throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {<a name="line.61"></a> <FONT color="green">062</FONT> return integrate(f, min, max);<a name="line.62"></a> <FONT color="green">063</FONT> }<a name="line.63"></a> <FONT color="green">064</FONT> <a name="line.64"></a> <FONT color="green">065</FONT> /** {@inheritDoc} */<a name="line.65"></a> <FONT color="green">066</FONT> public double integrate(final UnivariateRealFunction f,<a name="line.66"></a> <FONT color="green">067</FONT> final double min, final double max)<a name="line.67"></a> <FONT color="green">068</FONT> throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {<a name="line.68"></a> <FONT color="green">069</FONT> <a name="line.69"></a> <FONT color="green">070</FONT> final int m = maximalIterationCount + 1;<a name="line.70"></a> <FONT color="green">071</FONT> double previousRow[] = new double[m];<a name="line.71"></a> <FONT color="green">072</FONT> double currentRow[] = new double[m];<a name="line.72"></a> <FONT color="green">073</FONT> <a name="line.73"></a> <FONT color="green">074</FONT> clearResult();<a name="line.74"></a> <FONT color="green">075</FONT> verifyInterval(min, max);<a name="line.75"></a> <FONT color="green">076</FONT> verifyIterationCount();<a name="line.76"></a> <FONT color="green">077</FONT> <a name="line.77"></a> <FONT color="green">078</FONT> TrapezoidIntegrator qtrap = new TrapezoidIntegrator();<a name="line.78"></a> <FONT color="green">079</FONT> currentRow[0] = qtrap.stage(f, min, max, 0);<a name="line.79"></a> <FONT color="green">080</FONT> double olds = currentRow[0];<a name="line.80"></a> <FONT color="green">081</FONT> for (int i = 1; i <= maximalIterationCount; ++i) {<a name="line.81"></a> <FONT color="green">082</FONT> <a name="line.82"></a> <FONT color="green">083</FONT> // switch rows<a name="line.83"></a> <FONT color="green">084</FONT> final double[] tmpRow = previousRow;<a name="line.84"></a> <FONT color="green">085</FONT> previousRow = currentRow;<a name="line.85"></a> <FONT color="green">086</FONT> currentRow = tmpRow;<a name="line.86"></a> <FONT color="green">087</FONT> <a name="line.87"></a> <FONT color="green">088</FONT> currentRow[0] = qtrap.stage(f, min, max, i);<a name="line.88"></a> <FONT color="green">089</FONT> for (int j = 1; j <= i; j++) {<a name="line.89"></a> <FONT color="green">090</FONT> // Richardson extrapolation coefficient<a name="line.90"></a> <FONT color="green">091</FONT> final double r = (1L << (2 * j)) - 1;<a name="line.91"></a> <FONT color="green">092</FONT> final double tIJm1 = currentRow[j - 1];<a name="line.92"></a> <FONT color="green">093</FONT> currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;<a name="line.93"></a> <FONT color="green">094</FONT> }<a name="line.94"></a> <FONT color="green">095</FONT> final double s = currentRow[i];<a name="line.95"></a> <FONT color="green">096</FONT> if (i >= minimalIterationCount) {<a name="line.96"></a> <FONT color="green">097</FONT> final double delta = Math.abs(s - olds);<a name="line.97"></a> <FONT color="green">098</FONT> final double rLimit = relativeAccuracy * (Math.abs(olds) + Math.abs(s)) * 0.5;<a name="line.98"></a> <FONT color="green">099</FONT> if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {<a name="line.99"></a> <FONT color="green">100</FONT> setResult(s, i);<a name="line.100"></a> <FONT color="green">101</FONT> return result;<a name="line.101"></a> <FONT color="green">102</FONT> }<a name="line.102"></a> <FONT color="green">103</FONT> }<a name="line.103"></a> <FONT color="green">104</FONT> olds = s;<a name="line.104"></a> <FONT color="green">105</FONT> }<a name="line.105"></a> <FONT color="green">106</FONT> throw new MaxIterationsExceededException(maximalIterationCount);<a name="line.106"></a> <FONT color="green">107</FONT> }<a name="line.107"></a> <FONT color="green">108</FONT> <a name="line.108"></a> <FONT color="green">109</FONT> /** {@inheritDoc} */<a name="line.109"></a> <FONT color="green">110</FONT> @Override<a name="line.110"></a> <FONT color="green">111</FONT> protected void verifyIterationCount() throws IllegalArgumentException {<a name="line.111"></a> <FONT color="green">112</FONT> super.verifyIterationCount();<a name="line.112"></a> <FONT color="green">113</FONT> // at most 32 bisection refinements due to higher order divider<a name="line.113"></a> <FONT color="green">114</FONT> if (maximalIterationCount > 32) {<a name="line.114"></a> <FONT color="green">115</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.115"></a> <FONT color="green">116</FONT> "invalid iteration limits: min={0}, max={1}",<a name="line.116"></a> <FONT color="green">117</FONT> 0, 32);<a name="line.117"></a> <FONT color="green">118</FONT> }<a name="line.118"></a> <FONT color="green">119</FONT> }<a name="line.119"></a> <FONT color="green">120</FONT> }<a name="line.120"></a> </PRE> </BODY> </HTML>