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comparison libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/analysis/interpolation/DividedDifferenceInterpolator.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.interpolation;<a name="line.17"></a>
21 <FONT color="green">018</FONT> <a name="line.18"></a>
22 <FONT color="green">019</FONT> import java.io.Serializable;<a name="line.19"></a>
23 <FONT color="green">020</FONT> <a name="line.20"></a>
24 <FONT color="green">021</FONT> import org.apache.commons.math.DuplicateSampleAbscissaException;<a name="line.21"></a>
25 <FONT color="green">022</FONT> import org.apache.commons.math.analysis.polynomials.PolynomialFunctionLagrangeForm;<a name="line.22"></a>
26 <FONT color="green">023</FONT> import org.apache.commons.math.analysis.polynomials.PolynomialFunctionNewtonForm;<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="<a name="line.26"></a>
30 <FONT color="green">027</FONT> * "http://mathworld.wolfram.com/NewtonsDividedDifferenceInterpolationFormula.html"&gt;<a name="line.27"></a>
31 <FONT color="green">028</FONT> * Divided Difference Algorithm&lt;/a&gt; for interpolation of real univariate<a name="line.28"></a>
32 <FONT color="green">029</FONT> * functions. For reference, see &lt;b&gt;Introduction to Numerical Analysis&lt;/b&gt;,<a name="line.29"></a>
33 <FONT color="green">030</FONT> * ISBN 038795452X, chapter 2.<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 actual code of Neville's evaluation is in PolynomialFunctionLagrangeForm,<a name="line.32"></a>
36 <FONT color="green">033</FONT> * this class provides an easy-to-use interface to it.&lt;/p&gt;<a name="line.33"></a>
37 <FONT color="green">034</FONT> *<a name="line.34"></a>
38 <FONT color="green">035</FONT> * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $<a name="line.35"></a>
39 <FONT color="green">036</FONT> * @since 1.2<a name="line.36"></a>
40 <FONT color="green">037</FONT> */<a name="line.37"></a>
41 <FONT color="green">038</FONT> public class DividedDifferenceInterpolator implements UnivariateRealInterpolator,<a name="line.38"></a>
42 <FONT color="green">039</FONT> Serializable {<a name="line.39"></a>
43 <FONT color="green">040</FONT> <a name="line.40"></a>
44 <FONT color="green">041</FONT> /** serializable version identifier */<a name="line.41"></a>
45 <FONT color="green">042</FONT> private static final long serialVersionUID = 107049519551235069L;<a name="line.42"></a>
46 <FONT color="green">043</FONT> <a name="line.43"></a>
47 <FONT color="green">044</FONT> /**<a name="line.44"></a>
48 <FONT color="green">045</FONT> * Computes an interpolating function for the data set.<a name="line.45"></a>
49 <FONT color="green">046</FONT> *<a name="line.46"></a>
50 <FONT color="green">047</FONT> * @param x the interpolating points array<a name="line.47"></a>
51 <FONT color="green">048</FONT> * @param y the interpolating values array<a name="line.48"></a>
52 <FONT color="green">049</FONT> * @return a function which interpolates the data set<a name="line.49"></a>
53 <FONT color="green">050</FONT> * @throws DuplicateSampleAbscissaException if arguments are invalid<a name="line.50"></a>
54 <FONT color="green">051</FONT> */<a name="line.51"></a>
55 <FONT color="green">052</FONT> public PolynomialFunctionNewtonForm interpolate(double x[], double y[]) throws<a name="line.52"></a>
56 <FONT color="green">053</FONT> DuplicateSampleAbscissaException {<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> * a[] and c[] are defined in the general formula of Newton form:<a name="line.56"></a>
60 <FONT color="green">057</FONT> * p(x) = a[0] + a[1](x-c[0]) + a[2](x-c[0])(x-c[1]) + ... +<a name="line.57"></a>
61 <FONT color="green">058</FONT> * a[n](x-c[0])(x-c[1])...(x-c[n-1])<a name="line.58"></a>
62 <FONT color="green">059</FONT> */<a name="line.59"></a>
63 <FONT color="green">060</FONT> PolynomialFunctionLagrangeForm.verifyInterpolationArray(x, y);<a name="line.60"></a>
64 <FONT color="green">061</FONT> <a name="line.61"></a>
65 <FONT color="green">062</FONT> /**<a name="line.62"></a>
66 <FONT color="green">063</FONT> * When used for interpolation, the Newton form formula becomes<a name="line.63"></a>
67 <FONT color="green">064</FONT> * p(x) = f[x0] + f[x0,x1](x-x0) + f[x0,x1,x2](x-x0)(x-x1) + ... +<a name="line.64"></a>
68 <FONT color="green">065</FONT> * f[x0,x1,...,x[n-1]](x-x0)(x-x1)...(x-x[n-2])<a name="line.65"></a>
69 <FONT color="green">066</FONT> * Therefore, a[k] = f[x0,x1,...,xk], c[k] = x[k].<a name="line.66"></a>
70 <FONT color="green">067</FONT> * &lt;p&gt;<a name="line.67"></a>
71 <FONT color="green">068</FONT> * Note x[], y[], a[] have the same length but c[]'s size is one less.&lt;/p&gt;<a name="line.68"></a>
72 <FONT color="green">069</FONT> */<a name="line.69"></a>
73 <FONT color="green">070</FONT> final double[] c = new double[x.length-1];<a name="line.70"></a>
74 <FONT color="green">071</FONT> System.arraycopy(x, 0, c, 0, c.length);<a name="line.71"></a>
75 <FONT color="green">072</FONT> <a name="line.72"></a>
76 <FONT color="green">073</FONT> final double[] a = computeDividedDifference(x, y);<a name="line.73"></a>
77 <FONT color="green">074</FONT> return new PolynomialFunctionNewtonForm(a, c);<a name="line.74"></a>
78 <FONT color="green">075</FONT> <a name="line.75"></a>
79 <FONT color="green">076</FONT> }<a name="line.76"></a>
80 <FONT color="green">077</FONT> <a name="line.77"></a>
81 <FONT color="green">078</FONT> /**<a name="line.78"></a>
82 <FONT color="green">079</FONT> * Returns a copy of the divided difference array.<a name="line.79"></a>
83 <FONT color="green">080</FONT> * &lt;p&gt;<a name="line.80"></a>
84 <FONT color="green">081</FONT> * The divided difference array is defined recursively by &lt;pre&gt;<a name="line.81"></a>
85 <FONT color="green">082</FONT> * f[x0] = f(x0)<a name="line.82"></a>
86 <FONT color="green">083</FONT> * f[x0,x1,...,xk] = (f(x1,...,xk) - f(x0,...,x[k-1])) / (xk - x0)<a name="line.83"></a>
87 <FONT color="green">084</FONT> * &lt;/pre&gt;&lt;/p&gt;<a name="line.84"></a>
88 <FONT color="green">085</FONT> * &lt;p&gt;<a name="line.85"></a>
89 <FONT color="green">086</FONT> * The computational complexity is O(N^2).&lt;/p&gt;<a name="line.86"></a>
90 <FONT color="green">087</FONT> *<a name="line.87"></a>
91 <FONT color="green">088</FONT> * @param x the interpolating points array<a name="line.88"></a>
92 <FONT color="green">089</FONT> * @param y the interpolating values array<a name="line.89"></a>
93 <FONT color="green">090</FONT> * @return a fresh copy of the divided difference array<a name="line.90"></a>
94 <FONT color="green">091</FONT> * @throws DuplicateSampleAbscissaException if any abscissas coincide<a name="line.91"></a>
95 <FONT color="green">092</FONT> */<a name="line.92"></a>
96 <FONT color="green">093</FONT> protected static double[] computeDividedDifference(final double x[], final double y[])<a name="line.93"></a>
97 <FONT color="green">094</FONT> throws DuplicateSampleAbscissaException {<a name="line.94"></a>
98 <FONT color="green">095</FONT> <a name="line.95"></a>
99 <FONT color="green">096</FONT> PolynomialFunctionLagrangeForm.verifyInterpolationArray(x, y);<a name="line.96"></a>
100 <FONT color="green">097</FONT> <a name="line.97"></a>
101 <FONT color="green">098</FONT> final double[] divdiff = y.clone(); // initialization<a name="line.98"></a>
102 <FONT color="green">099</FONT> <a name="line.99"></a>
103 <FONT color="green">100</FONT> final int n = x.length;<a name="line.100"></a>
104 <FONT color="green">101</FONT> final double[] a = new double [n];<a name="line.101"></a>
105 <FONT color="green">102</FONT> a[0] = divdiff[0];<a name="line.102"></a>
106 <FONT color="green">103</FONT> for (int i = 1; i &lt; n; i++) {<a name="line.103"></a>
107 <FONT color="green">104</FONT> for (int j = 0; j &lt; n-i; j++) {<a name="line.104"></a>
108 <FONT color="green">105</FONT> final double denominator = x[j+i] - x[j];<a name="line.105"></a>
109 <FONT color="green">106</FONT> if (denominator == 0.0) {<a name="line.106"></a>
110 <FONT color="green">107</FONT> // This happens only when two abscissas are identical.<a name="line.107"></a>
111 <FONT color="green">108</FONT> throw new DuplicateSampleAbscissaException(x[j], j, j+i);<a name="line.108"></a>
112 <FONT color="green">109</FONT> }<a name="line.109"></a>
113 <FONT color="green">110</FONT> divdiff[j] = (divdiff[j+1] - divdiff[j]) / denominator;<a name="line.110"></a>
114 <FONT color="green">111</FONT> }<a name="line.111"></a>
115 <FONT color="green">112</FONT> a[i] = divdiff[0];<a name="line.112"></a>
116 <FONT color="green">113</FONT> }<a name="line.113"></a>
117 <FONT color="green">114</FONT> <a name="line.114"></a>
118 <FONT color="green">115</FONT> return a;<a name="line.115"></a>
119 <FONT color="green">116</FONT> }<a name="line.116"></a>
120 <FONT color="green">117</FONT> }<a name="line.117"></a>
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181 </PRE>
182 </BODY>
183 </HTML>