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comparison libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/analysis/solvers/RiddersSolver.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> package org.apache.commons.math.analysis.solvers;<a name="line.17"></a>
21 <FONT color="green">018</FONT> <a name="line.18"></a>
22 <FONT color="green">019</FONT> import org.apache.commons.math.ConvergenceException;<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.MaxIterationsExceededException;<a name="line.21"></a>
25 <FONT color="green">022</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.22"></a>
26 <FONT color="green">023</FONT> import org.apache.commons.math.util.MathUtils;<a name="line.23"></a>
27 <FONT color="green">024</FONT> <a name="line.24"></a>
28 <FONT color="green">025</FONT> /**<a name="line.25"></a>
29 <FONT color="green">026</FONT> * Implements the &lt;a href="http://mathworld.wolfram.com/RiddersMethod.html"&gt;<a name="line.26"></a>
30 <FONT color="green">027</FONT> * Ridders' Method&lt;/a&gt; for root finding of real univariate functions. For<a name="line.27"></a>
31 <FONT color="green">028</FONT> * reference, see C. Ridders, &lt;i&gt;A new algorithm for computing a single root<a name="line.28"></a>
32 <FONT color="green">029</FONT> * of a real continuous function &lt;/i&gt;, IEEE Transactions on Circuits and<a name="line.29"></a>
33 <FONT color="green">030</FONT> * Systems, 26 (1979), 979 - 980.<a name="line.30"></a>
34 <FONT color="green">031</FONT> * &lt;p&gt;<a name="line.31"></a>
35 <FONT color="green">032</FONT> * The function should be continuous but not necessarily smooth.&lt;/p&gt;<a name="line.32"></a>
36 <FONT color="green">033</FONT> *<a name="line.33"></a>
37 <FONT color="green">034</FONT> * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $<a name="line.34"></a>
38 <FONT color="green">035</FONT> * @since 1.2<a name="line.35"></a>
39 <FONT color="green">036</FONT> */<a name="line.36"></a>
40 <FONT color="green">037</FONT> public class RiddersSolver extends UnivariateRealSolverImpl {<a name="line.37"></a>
41 <FONT color="green">038</FONT> <a name="line.38"></a>
42 <FONT color="green">039</FONT> /**<a name="line.39"></a>
43 <FONT color="green">040</FONT> * Construct a solver for the given function.<a name="line.40"></a>
44 <FONT color="green">041</FONT> *<a name="line.41"></a>
45 <FONT color="green">042</FONT> * @param f function to solve<a name="line.42"></a>
46 <FONT color="green">043</FONT> * @deprecated as of 2.0 the function to solve is passed as an argument<a name="line.43"></a>
47 <FONT color="green">044</FONT> * to the {@link #solve(UnivariateRealFunction, double, double)} or<a name="line.44"></a>
48 <FONT color="green">045</FONT> * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)}<a name="line.45"></a>
49 <FONT color="green">046</FONT> * method.<a name="line.46"></a>
50 <FONT color="green">047</FONT> */<a name="line.47"></a>
51 <FONT color="green">048</FONT> @Deprecated<a name="line.48"></a>
52 <FONT color="green">049</FONT> public RiddersSolver(UnivariateRealFunction f) {<a name="line.49"></a>
53 <FONT color="green">050</FONT> super(f, 100, 1E-6);<a name="line.50"></a>
54 <FONT color="green">051</FONT> }<a name="line.51"></a>
55 <FONT color="green">052</FONT> <a name="line.52"></a>
56 <FONT color="green">053</FONT> /**<a name="line.53"></a>
57 <FONT color="green">054</FONT> * Construct a solver.<a name="line.54"></a>
58 <FONT color="green">055</FONT> */<a name="line.55"></a>
59 <FONT color="green">056</FONT> public RiddersSolver() {<a name="line.56"></a>
60 <FONT color="green">057</FONT> super(100, 1E-6);<a name="line.57"></a>
61 <FONT color="green">058</FONT> }<a name="line.58"></a>
62 <FONT color="green">059</FONT> <a name="line.59"></a>
63 <FONT color="green">060</FONT> /** {@inheritDoc} */<a name="line.60"></a>
64 <FONT color="green">061</FONT> @Deprecated<a name="line.61"></a>
65 <FONT color="green">062</FONT> public double solve(final double min, final double max)<a name="line.62"></a>
66 <FONT color="green">063</FONT> throws ConvergenceException, FunctionEvaluationException {<a name="line.63"></a>
67 <FONT color="green">064</FONT> return solve(f, min, max);<a name="line.64"></a>
68 <FONT color="green">065</FONT> }<a name="line.65"></a>
69 <FONT color="green">066</FONT> <a name="line.66"></a>
70 <FONT color="green">067</FONT> /** {@inheritDoc} */<a name="line.67"></a>
71 <FONT color="green">068</FONT> @Deprecated<a name="line.68"></a>
72 <FONT color="green">069</FONT> public double solve(final double min, final double max, final double initial)<a name="line.69"></a>
73 <FONT color="green">070</FONT> throws ConvergenceException, FunctionEvaluationException {<a name="line.70"></a>
74 <FONT color="green">071</FONT> return solve(f, min, max, initial);<a name="line.71"></a>
75 <FONT color="green">072</FONT> }<a name="line.72"></a>
76 <FONT color="green">073</FONT> <a name="line.73"></a>
77 <FONT color="green">074</FONT> /**<a name="line.74"></a>
78 <FONT color="green">075</FONT> * Find a root in the given interval with initial value.<a name="line.75"></a>
79 <FONT color="green">076</FONT> * &lt;p&gt;<a name="line.76"></a>
80 <FONT color="green">077</FONT> * Requires bracketing condition.&lt;/p&gt;<a name="line.77"></a>
81 <FONT color="green">078</FONT> *<a name="line.78"></a>
82 <FONT color="green">079</FONT> * @param f the function to solve<a name="line.79"></a>
83 <FONT color="green">080</FONT> * @param min the lower bound for the interval<a name="line.80"></a>
84 <FONT color="green">081</FONT> * @param max the upper bound for the interval<a name="line.81"></a>
85 <FONT color="green">082</FONT> * @param initial the start value to use<a name="line.82"></a>
86 <FONT color="green">083</FONT> * @return the point at which the function value is zero<a name="line.83"></a>
87 <FONT color="green">084</FONT> * @throws MaxIterationsExceededException if the maximum iteration count is exceeded<a name="line.84"></a>
88 <FONT color="green">085</FONT> * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.85"></a>
89 <FONT color="green">086</FONT> * function<a name="line.86"></a>
90 <FONT color="green">087</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.87"></a>
91 <FONT color="green">088</FONT> */<a name="line.88"></a>
92 <FONT color="green">089</FONT> public double solve(final UnivariateRealFunction f,<a name="line.89"></a>
93 <FONT color="green">090</FONT> final double min, final double max, final double initial)<a name="line.90"></a>
94 <FONT color="green">091</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.91"></a>
95 <FONT color="green">092</FONT> <a name="line.92"></a>
96 <FONT color="green">093</FONT> // check for zeros before verifying bracketing<a name="line.93"></a>
97 <FONT color="green">094</FONT> if (f.value(min) == 0.0) { return min; }<a name="line.94"></a>
98 <FONT color="green">095</FONT> if (f.value(max) == 0.0) { return max; }<a name="line.95"></a>
99 <FONT color="green">096</FONT> if (f.value(initial) == 0.0) { return initial; }<a name="line.96"></a>
100 <FONT color="green">097</FONT> <a name="line.97"></a>
101 <FONT color="green">098</FONT> verifyBracketing(min, max, f);<a name="line.98"></a>
102 <FONT color="green">099</FONT> verifySequence(min, initial, max);<a name="line.99"></a>
103 <FONT color="green">100</FONT> if (isBracketing(min, initial, f)) {<a name="line.100"></a>
104 <FONT color="green">101</FONT> return solve(f, min, initial);<a name="line.101"></a>
105 <FONT color="green">102</FONT> } else {<a name="line.102"></a>
106 <FONT color="green">103</FONT> return solve(f, initial, max);<a name="line.103"></a>
107 <FONT color="green">104</FONT> }<a name="line.104"></a>
108 <FONT color="green">105</FONT> }<a name="line.105"></a>
109 <FONT color="green">106</FONT> <a name="line.106"></a>
110 <FONT color="green">107</FONT> /**<a name="line.107"></a>
111 <FONT color="green">108</FONT> * Find a root in the given interval.<a name="line.108"></a>
112 <FONT color="green">109</FONT> * &lt;p&gt;<a name="line.109"></a>
113 <FONT color="green">110</FONT> * Requires bracketing condition.&lt;/p&gt;<a name="line.110"></a>
114 <FONT color="green">111</FONT> *<a name="line.111"></a>
115 <FONT color="green">112</FONT> * @param f the function to solve<a name="line.112"></a>
116 <FONT color="green">113</FONT> * @param min the lower bound for the interval<a name="line.113"></a>
117 <FONT color="green">114</FONT> * @param max the upper bound for the interval<a name="line.114"></a>
118 <FONT color="green">115</FONT> * @return the point at which the function value is zero<a name="line.115"></a>
119 <FONT color="green">116</FONT> * @throws MaxIterationsExceededException if the maximum iteration count is exceeded<a name="line.116"></a>
120 <FONT color="green">117</FONT> * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.117"></a>
121 <FONT color="green">118</FONT> * function<a name="line.118"></a>
122 <FONT color="green">119</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.119"></a>
123 <FONT color="green">120</FONT> */<a name="line.120"></a>
124 <FONT color="green">121</FONT> public double solve(final UnivariateRealFunction f,<a name="line.121"></a>
125 <FONT color="green">122</FONT> final double min, final double max)<a name="line.122"></a>
126 <FONT color="green">123</FONT> throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.123"></a>
127 <FONT color="green">124</FONT> <a name="line.124"></a>
128 <FONT color="green">125</FONT> // [x1, x2] is the bracketing interval in each iteration<a name="line.125"></a>
129 <FONT color="green">126</FONT> // x3 is the midpoint of [x1, x2]<a name="line.126"></a>
130 <FONT color="green">127</FONT> // x is the new root approximation and an endpoint of the new interval<a name="line.127"></a>
131 <FONT color="green">128</FONT> double x1 = min;<a name="line.128"></a>
132 <FONT color="green">129</FONT> double y1 = f.value(x1);<a name="line.129"></a>
133 <FONT color="green">130</FONT> double x2 = max;<a name="line.130"></a>
134 <FONT color="green">131</FONT> double y2 = f.value(x2);<a name="line.131"></a>
135 <FONT color="green">132</FONT> <a name="line.132"></a>
136 <FONT color="green">133</FONT> // check for zeros before verifying bracketing<a name="line.133"></a>
137 <FONT color="green">134</FONT> if (y1 == 0.0) {<a name="line.134"></a>
138 <FONT color="green">135</FONT> return min;<a name="line.135"></a>
139 <FONT color="green">136</FONT> }<a name="line.136"></a>
140 <FONT color="green">137</FONT> if (y2 == 0.0) {<a name="line.137"></a>
141 <FONT color="green">138</FONT> return max;<a name="line.138"></a>
142 <FONT color="green">139</FONT> }<a name="line.139"></a>
143 <FONT color="green">140</FONT> verifyBracketing(min, max, f);<a name="line.140"></a>
144 <FONT color="green">141</FONT> <a name="line.141"></a>
145 <FONT color="green">142</FONT> int i = 1;<a name="line.142"></a>
146 <FONT color="green">143</FONT> double oldx = Double.POSITIVE_INFINITY;<a name="line.143"></a>
147 <FONT color="green">144</FONT> while (i &lt;= maximalIterationCount) {<a name="line.144"></a>
148 <FONT color="green">145</FONT> // calculate the new root approximation<a name="line.145"></a>
149 <FONT color="green">146</FONT> final double x3 = 0.5 * (x1 + x2);<a name="line.146"></a>
150 <FONT color="green">147</FONT> final double y3 = f.value(x3);<a name="line.147"></a>
151 <FONT color="green">148</FONT> if (Math.abs(y3) &lt;= functionValueAccuracy) {<a name="line.148"></a>
152 <FONT color="green">149</FONT> setResult(x3, i);<a name="line.149"></a>
153 <FONT color="green">150</FONT> return result;<a name="line.150"></a>
154 <FONT color="green">151</FONT> }<a name="line.151"></a>
155 <FONT color="green">152</FONT> final double delta = 1 - (y1 * y2) / (y3 * y3); // delta &gt; 1 due to bracketing<a name="line.152"></a>
156 <FONT color="green">153</FONT> final double correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) *<a name="line.153"></a>
157 <FONT color="green">154</FONT> (x3 - x1) / Math.sqrt(delta);<a name="line.154"></a>
158 <FONT color="green">155</FONT> final double x = x3 - correction; // correction != 0<a name="line.155"></a>
159 <FONT color="green">156</FONT> final double y = f.value(x);<a name="line.156"></a>
160 <FONT color="green">157</FONT> <a name="line.157"></a>
161 <FONT color="green">158</FONT> // check for convergence<a name="line.158"></a>
162 <FONT color="green">159</FONT> final double tolerance = Math.max(relativeAccuracy * Math.abs(x), absoluteAccuracy);<a name="line.159"></a>
163 <FONT color="green">160</FONT> if (Math.abs(x - oldx) &lt;= tolerance) {<a name="line.160"></a>
164 <FONT color="green">161</FONT> setResult(x, i);<a name="line.161"></a>
165 <FONT color="green">162</FONT> return result;<a name="line.162"></a>
166 <FONT color="green">163</FONT> }<a name="line.163"></a>
167 <FONT color="green">164</FONT> if (Math.abs(y) &lt;= functionValueAccuracy) {<a name="line.164"></a>
168 <FONT color="green">165</FONT> setResult(x, i);<a name="line.165"></a>
169 <FONT color="green">166</FONT> return result;<a name="line.166"></a>
170 <FONT color="green">167</FONT> }<a name="line.167"></a>
171 <FONT color="green">168</FONT> <a name="line.168"></a>
172 <FONT color="green">169</FONT> // prepare the new interval for next iteration<a name="line.169"></a>
173 <FONT color="green">170</FONT> // Ridders' method guarantees x1 &lt; x &lt; x2<a name="line.170"></a>
174 <FONT color="green">171</FONT> if (correction &gt; 0.0) { // x1 &lt; x &lt; x3<a name="line.171"></a>
175 <FONT color="green">172</FONT> if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) {<a name="line.172"></a>
176 <FONT color="green">173</FONT> x2 = x;<a name="line.173"></a>
177 <FONT color="green">174</FONT> y2 = y;<a name="line.174"></a>
178 <FONT color="green">175</FONT> } else {<a name="line.175"></a>
179 <FONT color="green">176</FONT> x1 = x;<a name="line.176"></a>
180 <FONT color="green">177</FONT> x2 = x3;<a name="line.177"></a>
181 <FONT color="green">178</FONT> y1 = y;<a name="line.178"></a>
182 <FONT color="green">179</FONT> y2 = y3;<a name="line.179"></a>
183 <FONT color="green">180</FONT> }<a name="line.180"></a>
184 <FONT color="green">181</FONT> } else { // x3 &lt; x &lt; x2<a name="line.181"></a>
185 <FONT color="green">182</FONT> if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) {<a name="line.182"></a>
186 <FONT color="green">183</FONT> x1 = x;<a name="line.183"></a>
187 <FONT color="green">184</FONT> y1 = y;<a name="line.184"></a>
188 <FONT color="green">185</FONT> } else {<a name="line.185"></a>
189 <FONT color="green">186</FONT> x1 = x3;<a name="line.186"></a>
190 <FONT color="green">187</FONT> x2 = x;<a name="line.187"></a>
191 <FONT color="green">188</FONT> y1 = y3;<a name="line.188"></a>
192 <FONT color="green">189</FONT> y2 = y;<a name="line.189"></a>
193 <FONT color="green">190</FONT> }<a name="line.190"></a>
194 <FONT color="green">191</FONT> }<a name="line.191"></a>
195 <FONT color="green">192</FONT> oldx = x;<a name="line.192"></a>
196 <FONT color="green">193</FONT> i++;<a name="line.193"></a>
197 <FONT color="green">194</FONT> }<a name="line.194"></a>
198 <FONT color="green">195</FONT> throw new MaxIterationsExceededException(maximalIterationCount);<a name="line.195"></a>
199 <FONT color="green">196</FONT> }<a name="line.196"></a>
200 <FONT color="green">197</FONT> }<a name="line.197"></a>
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261 </PRE>
262 </BODY>
263 </HTML>