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comparison libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/analysis/solvers/NewtonSolver.html @ 13:cbf34dd4d7e6

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commons-math-2.1 added
author dwinter
date Tue, 04 Jan 2011 10:02:07 +0100
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12:970d26a94fb7 13:cbf34dd4d7e6
1 <HTML>
2 <BODY BGCOLOR="white">
3 <PRE>
4 <FONT color="green">001</FONT> /*<a name="line.1"></a>
5 <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
6 <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a>
7 <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a>
8 <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
9 <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
10 <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a>
11 <FONT color="green">008</FONT> *<a name="line.8"></a>
12 <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
13 <FONT color="green">010</FONT> *<a name="line.10"></a>
14 <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
15 <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
16 <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
17 <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a>
18 <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a>
19 <FONT color="green">016</FONT> */<a name="line.16"></a>
20 <FONT color="green">017</FONT> <a name="line.17"></a>
21 <FONT color="green">018</FONT> package org.apache.commons.math.analysis.solvers;<a name="line.18"></a>
22 <FONT color="green">019</FONT> <a name="line.19"></a>
23 <FONT color="green">020</FONT> import org.apache.commons.math.FunctionEvaluationException;<a name="line.20"></a>
24 <FONT color="green">021</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.21"></a>
25 <FONT color="green">022</FONT> import org.apache.commons.math.MaxIterationsExceededException;<a name="line.22"></a>
26 <FONT color="green">023</FONT> import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;<a name="line.23"></a>
27 <FONT color="green">024</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.24"></a>
28 <FONT color="green">025</FONT> <a name="line.25"></a>
29 <FONT color="green">026</FONT> /**<a name="line.26"></a>
30 <FONT color="green">027</FONT> * Implements &lt;a href="http://mathworld.wolfram.com/NewtonsMethod.html"&gt;<a name="line.27"></a>
31 <FONT color="green">028</FONT> * Newton's Method&lt;/a&gt; for finding zeros of real univariate functions.<a name="line.28"></a>
32 <FONT color="green">029</FONT> * &lt;p&gt;<a name="line.29"></a>
33 <FONT color="green">030</FONT> * The function should be continuous but not necessarily smooth.&lt;/p&gt;<a name="line.30"></a>
34 <FONT color="green">031</FONT> *<a name="line.31"></a>
35 <FONT color="green">032</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.32"></a>
36 <FONT color="green">033</FONT> */<a name="line.33"></a>
37 <FONT color="green">034</FONT> public class NewtonSolver extends UnivariateRealSolverImpl {<a name="line.34"></a>
38 <FONT color="green">035</FONT> <a name="line.35"></a>
39 <FONT color="green">036</FONT> /**<a name="line.36"></a>
40 <FONT color="green">037</FONT> * Construct a solver for the given function.<a name="line.37"></a>
41 <FONT color="green">038</FONT> * @param f function to solve.<a name="line.38"></a>
42 <FONT color="green">039</FONT> * @deprecated as of 2.0 the function to solve is passed as an argument<a name="line.39"></a>
43 <FONT color="green">040</FONT> * to the {@link #solve(UnivariateRealFunction, double, double)} or<a name="line.40"></a>
44 <FONT color="green">041</FONT> * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)}<a name="line.41"></a>
45 <FONT color="green">042</FONT> * method.<a name="line.42"></a>
46 <FONT color="green">043</FONT> */<a name="line.43"></a>
47 <FONT color="green">044</FONT> @Deprecated<a name="line.44"></a>
48 <FONT color="green">045</FONT> public NewtonSolver(DifferentiableUnivariateRealFunction f) {<a name="line.45"></a>
49 <FONT color="green">046</FONT> super(f, 100, 1E-6);<a name="line.46"></a>
50 <FONT color="green">047</FONT> }<a name="line.47"></a>
51 <FONT color="green">048</FONT> <a name="line.48"></a>
52 <FONT color="green">049</FONT> /**<a name="line.49"></a>
53 <FONT color="green">050</FONT> * Construct a solver.<a name="line.50"></a>
54 <FONT color="green">051</FONT> */<a name="line.51"></a>
55 <FONT color="green">052</FONT> public NewtonSolver() {<a name="line.52"></a>
56 <FONT color="green">053</FONT> super(100, 1E-6);<a name="line.53"></a>
57 <FONT color="green">054</FONT> }<a name="line.54"></a>
58 <FONT color="green">055</FONT> <a name="line.55"></a>
59 <FONT color="green">056</FONT> /** {@inheritDoc} */<a name="line.56"></a>
60 <FONT color="green">057</FONT> @Deprecated<a name="line.57"></a>
61 <FONT color="green">058</FONT> public double solve(final double min, final double max)<a name="line.58"></a>
62 <FONT color="green">059</FONT> throws MaxIterationsExceededException,<a name="line.59"></a>
63 <FONT color="green">060</FONT> FunctionEvaluationException {<a name="line.60"></a>
64 <FONT color="green">061</FONT> return solve(f, min, max);<a name="line.61"></a>
65 <FONT color="green">062</FONT> }<a name="line.62"></a>
66 <FONT color="green">063</FONT> <a name="line.63"></a>
67 <FONT color="green">064</FONT> /** {@inheritDoc} */<a name="line.64"></a>
68 <FONT color="green">065</FONT> @Deprecated<a name="line.65"></a>
69 <FONT color="green">066</FONT> public double solve(final double min, final double max, final double startValue)<a name="line.66"></a>
70 <FONT color="green">067</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.67"></a>
71 <FONT color="green">068</FONT> return solve(f, min, max, startValue);<a name="line.68"></a>
72 <FONT color="green">069</FONT> }<a name="line.69"></a>
73 <FONT color="green">070</FONT> <a name="line.70"></a>
74 <FONT color="green">071</FONT> /**<a name="line.71"></a>
75 <FONT color="green">072</FONT> * Find a zero near the midpoint of &lt;code&gt;min&lt;/code&gt; and &lt;code&gt;max&lt;/code&gt;.<a name="line.72"></a>
76 <FONT color="green">073</FONT> *<a name="line.73"></a>
77 <FONT color="green">074</FONT> * @param f the function to solve<a name="line.74"></a>
78 <FONT color="green">075</FONT> * @param min the lower bound for the interval<a name="line.75"></a>
79 <FONT color="green">076</FONT> * @param max the upper bound for the interval<a name="line.76"></a>
80 <FONT color="green">077</FONT> * @return the value where the function is zero<a name="line.77"></a>
81 <FONT color="green">078</FONT> * @throws MaxIterationsExceededException if the maximum iteration count is exceeded<a name="line.78"></a>
82 <FONT color="green">079</FONT> * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.79"></a>
83 <FONT color="green">080</FONT> * function or derivative<a name="line.80"></a>
84 <FONT color="green">081</FONT> * @throws IllegalArgumentException if min is not less than max<a name="line.81"></a>
85 <FONT color="green">082</FONT> */<a name="line.82"></a>
86 <FONT color="green">083</FONT> public double solve(final UnivariateRealFunction f,<a name="line.83"></a>
87 <FONT color="green">084</FONT> final double min, final double max)<a name="line.84"></a>
88 <FONT color="green">085</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.85"></a>
89 <FONT color="green">086</FONT> return solve(f, min, max, UnivariateRealSolverUtils.midpoint(min, max));<a name="line.86"></a>
90 <FONT color="green">087</FONT> }<a name="line.87"></a>
91 <FONT color="green">088</FONT> <a name="line.88"></a>
92 <FONT color="green">089</FONT> /**<a name="line.89"></a>
93 <FONT color="green">090</FONT> * Find a zero near the value &lt;code&gt;startValue&lt;/code&gt;.<a name="line.90"></a>
94 <FONT color="green">091</FONT> *<a name="line.91"></a>
95 <FONT color="green">092</FONT> * @param f the function to solve<a name="line.92"></a>
96 <FONT color="green">093</FONT> * @param min the lower bound for the interval (ignored).<a name="line.93"></a>
97 <FONT color="green">094</FONT> * @param max the upper bound for the interval (ignored).<a name="line.94"></a>
98 <FONT color="green">095</FONT> * @param startValue the start value to use.<a name="line.95"></a>
99 <FONT color="green">096</FONT> * @return the value where the function is zero<a name="line.96"></a>
100 <FONT color="green">097</FONT> * @throws MaxIterationsExceededException if the maximum iteration count is exceeded<a name="line.97"></a>
101 <FONT color="green">098</FONT> * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.98"></a>
102 <FONT color="green">099</FONT> * function or derivative<a name="line.99"></a>
103 <FONT color="green">100</FONT> * @throws IllegalArgumentException if startValue is not between min and max or<a name="line.100"></a>
104 <FONT color="green">101</FONT> * if function is not a {@link DifferentiableUnivariateRealFunction} instance<a name="line.101"></a>
105 <FONT color="green">102</FONT> */<a name="line.102"></a>
106 <FONT color="green">103</FONT> public double solve(final UnivariateRealFunction f,<a name="line.103"></a>
107 <FONT color="green">104</FONT> final double min, final double max, final double startValue)<a name="line.104"></a>
108 <FONT color="green">105</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.105"></a>
109 <FONT color="green">106</FONT> <a name="line.106"></a>
110 <FONT color="green">107</FONT> try {<a name="line.107"></a>
111 <FONT color="green">108</FONT> <a name="line.108"></a>
112 <FONT color="green">109</FONT> final UnivariateRealFunction derivative =<a name="line.109"></a>
113 <FONT color="green">110</FONT> ((DifferentiableUnivariateRealFunction) f).derivative();<a name="line.110"></a>
114 <FONT color="green">111</FONT> clearResult();<a name="line.111"></a>
115 <FONT color="green">112</FONT> verifySequence(min, startValue, max);<a name="line.112"></a>
116 <FONT color="green">113</FONT> <a name="line.113"></a>
117 <FONT color="green">114</FONT> double x0 = startValue;<a name="line.114"></a>
118 <FONT color="green">115</FONT> double x1;<a name="line.115"></a>
119 <FONT color="green">116</FONT> <a name="line.116"></a>
120 <FONT color="green">117</FONT> int i = 0;<a name="line.117"></a>
121 <FONT color="green">118</FONT> while (i &lt; maximalIterationCount) {<a name="line.118"></a>
122 <FONT color="green">119</FONT> <a name="line.119"></a>
123 <FONT color="green">120</FONT> x1 = x0 - (f.value(x0) / derivative.value(x0));<a name="line.120"></a>
124 <FONT color="green">121</FONT> if (Math.abs(x1 - x0) &lt;= absoluteAccuracy) {<a name="line.121"></a>
125 <FONT color="green">122</FONT> setResult(x1, i);<a name="line.122"></a>
126 <FONT color="green">123</FONT> return x1;<a name="line.123"></a>
127 <FONT color="green">124</FONT> }<a name="line.124"></a>
128 <FONT color="green">125</FONT> <a name="line.125"></a>
129 <FONT color="green">126</FONT> x0 = x1;<a name="line.126"></a>
130 <FONT color="green">127</FONT> ++i;<a name="line.127"></a>
131 <FONT color="green">128</FONT> }<a name="line.128"></a>
132 <FONT color="green">129</FONT> <a name="line.129"></a>
133 <FONT color="green">130</FONT> throw new MaxIterationsExceededException(maximalIterationCount);<a name="line.130"></a>
134 <FONT color="green">131</FONT> } catch (ClassCastException cce) {<a name="line.131"></a>
135 <FONT color="green">132</FONT> throw MathRuntimeException.createIllegalArgumentException("function is not differentiable");<a name="line.132"></a>
136 <FONT color="green">133</FONT> }<a name="line.133"></a>
137 <FONT color="green">134</FONT> }<a name="line.134"></a>
138 <FONT color="green">135</FONT> <a name="line.135"></a>
139 <FONT color="green">136</FONT> }<a name="line.136"></a>
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200 </PRE>
201 </BODY>
202 </HTML>