Mercurial > hg > de.mpg.mpiwg.itgroup.digilib.plugin

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

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
commons-math-2.1 added
author dwinter
date Tue, 04 Jan 2011 10:02:07 +0100
parents
children
comparison
equal deleted inserted replaced
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 org.apache.commons.math.MathRuntimeException;<a name="line.19"></a>
23 <FONT color="green">020</FONT> import org.apache.commons.math.analysis.polynomials.PolynomialFunction;<a name="line.20"></a>
24 <FONT color="green">021</FONT> import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;<a name="line.21"></a>
25 <FONT color="green">022</FONT> <a name="line.22"></a>
26 <FONT color="green">023</FONT> /**<a name="line.23"></a>
27 <FONT color="green">024</FONT> * Computes a natural (also known as "free", "unclamped") cubic spline interpolation for the data set.<a name="line.24"></a>
28 <FONT color="green">025</FONT> * &lt;p&gt;<a name="line.25"></a>
29 <FONT color="green">026</FONT> * The {@link #interpolate(double[], double[])} method returns a {@link PolynomialSplineFunction}<a name="line.26"></a>
30 <FONT color="green">027</FONT> * consisting of n cubic polynomials, defined over the subintervals determined by the x values,<a name="line.27"></a>
31 <FONT color="green">028</FONT> * x[0] &lt; x[i] ... &lt; x[n]. The x values are referred to as "knot points."&lt;/p&gt;<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 value of the PolynomialSplineFunction at a point x that is greater than or equal to the smallest<a name="line.30"></a>
34 <FONT color="green">031</FONT> * knot point and strictly less than the largest knot point is computed by finding the subinterval to which<a name="line.31"></a>
35 <FONT color="green">032</FONT> * x belongs and computing the value of the corresponding polynomial at &lt;code&gt;x - x[i] &lt;/code&gt; where<a name="line.32"></a>
36 <FONT color="green">033</FONT> * &lt;code&gt;i&lt;/code&gt; is the index of the subinterval. See {@link PolynomialSplineFunction} for more details.<a name="line.33"></a>
37 <FONT color="green">034</FONT> * &lt;/p&gt;<a name="line.34"></a>
38 <FONT color="green">035</FONT> * &lt;p&gt;<a name="line.35"></a>
39 <FONT color="green">036</FONT> * The interpolating polynomials satisfy: &lt;ol&gt;<a name="line.36"></a>
40 <FONT color="green">037</FONT> * &lt;li&gt;The value of the PolynomialSplineFunction at each of the input x values equals the<a name="line.37"></a>
41 <FONT color="green">038</FONT> * corresponding y value.&lt;/li&gt;<a name="line.38"></a>
42 <FONT color="green">039</FONT> * &lt;li&gt;Adjacent polynomials are equal through two derivatives at the knot points (i.e., adjacent polynomials<a name="line.39"></a>
43 <FONT color="green">040</FONT> * "match up" at the knot points, as do their first and second derivatives).&lt;/li&gt;<a name="line.40"></a>
44 <FONT color="green">041</FONT> * &lt;/ol&gt;&lt;/p&gt;<a name="line.41"></a>
45 <FONT color="green">042</FONT> * &lt;p&gt;<a name="line.42"></a>
46 <FONT color="green">043</FONT> * The cubic spline interpolation algorithm implemented is as described in R.L. Burden, J.D. Faires,<a name="line.43"></a>
47 <FONT color="green">044</FONT> * &lt;u&gt;Numerical Analysis&lt;/u&gt;, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131.<a name="line.44"></a>
48 <FONT color="green">045</FONT> * &lt;/p&gt;<a name="line.45"></a>
49 <FONT color="green">046</FONT> *<a name="line.46"></a>
50 <FONT color="green">047</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<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> public class SplineInterpolator implements UnivariateRealInterpolator {<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> * Computes an interpolating function for the data set.<a name="line.53"></a>
57 <FONT color="green">054</FONT> * @param x the arguments for the interpolation points<a name="line.54"></a>
58 <FONT color="green">055</FONT> * @param y the values for the interpolation points<a name="line.55"></a>
59 <FONT color="green">056</FONT> * @return a function which interpolates the data set<a name="line.56"></a>
60 <FONT color="green">057</FONT> */<a name="line.57"></a>
61 <FONT color="green">058</FONT> public PolynomialSplineFunction interpolate(double x[], double y[]) {<a name="line.58"></a>
62 <FONT color="green">059</FONT> if (x.length != y.length) {<a name="line.59"></a>
63 <FONT color="green">060</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.60"></a>
64 <FONT color="green">061</FONT> "dimension mismatch {0} != {1}", x.length, y.length);<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> if (x.length &lt; 3) {<a name="line.64"></a>
68 <FONT color="green">065</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.65"></a>
69 <FONT color="green">066</FONT> "{0} points are required, got only {1}", 3, x.length);<a name="line.66"></a>
70 <FONT color="green">067</FONT> }<a name="line.67"></a>
71 <FONT color="green">068</FONT> <a name="line.68"></a>
72 <FONT color="green">069</FONT> // Number of intervals. The number of data points is n + 1.<a name="line.69"></a>
73 <FONT color="green">070</FONT> int n = x.length - 1;<a name="line.70"></a>
74 <FONT color="green">071</FONT> <a name="line.71"></a>
75 <FONT color="green">072</FONT> for (int i = 0; i &lt; n; i++) {<a name="line.72"></a>
76 <FONT color="green">073</FONT> if (x[i] &gt;= x[i + 1]) {<a name="line.73"></a>
77 <FONT color="green">074</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.74"></a>
78 <FONT color="green">075</FONT> "points {0} and {1} are not strictly increasing ({2} &gt;= {3})",<a name="line.75"></a>
79 <FONT color="green">076</FONT> i, i+1, x[i], x[i+1]);<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> <a name="line.79"></a>
83 <FONT color="green">080</FONT> // Differences between knot points<a name="line.80"></a>
84 <FONT color="green">081</FONT> double h[] = new double[n];<a name="line.81"></a>
85 <FONT color="green">082</FONT> for (int i = 0; i &lt; n; i++) {<a name="line.82"></a>
86 <FONT color="green">083</FONT> h[i] = x[i + 1] - x[i];<a name="line.83"></a>
87 <FONT color="green">084</FONT> }<a name="line.84"></a>
88 <FONT color="green">085</FONT> <a name="line.85"></a>
89 <FONT color="green">086</FONT> double mu[] = new double[n];<a name="line.86"></a>
90 <FONT color="green">087</FONT> double z[] = new double[n + 1];<a name="line.87"></a>
91 <FONT color="green">088</FONT> mu[0] = 0d;<a name="line.88"></a>
92 <FONT color="green">089</FONT> z[0] = 0d;<a name="line.89"></a>
93 <FONT color="green">090</FONT> double g = 0;<a name="line.90"></a>
94 <FONT color="green">091</FONT> for (int i = 1; i &lt; n; i++) {<a name="line.91"></a>
95 <FONT color="green">092</FONT> g = 2d * (x[i+1] - x[i - 1]) - h[i - 1] * mu[i -1];<a name="line.92"></a>
96 <FONT color="green">093</FONT> mu[i] = h[i] / g;<a name="line.93"></a>
97 <FONT color="green">094</FONT> z[i] = (3d * (y[i + 1] * h[i - 1] - y[i] * (x[i + 1] - x[i - 1])+ y[i - 1] * h[i]) /<a name="line.94"></a>
98 <FONT color="green">095</FONT> (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;<a name="line.95"></a>
99 <FONT color="green">096</FONT> }<a name="line.96"></a>
100 <FONT color="green">097</FONT> <a name="line.97"></a>
101 <FONT color="green">098</FONT> // cubic spline coefficients -- b is linear, c quadratic, d is cubic (original y's are constants)<a name="line.98"></a>
102 <FONT color="green">099</FONT> double b[] = new double[n];<a name="line.99"></a>
103 <FONT color="green">100</FONT> double c[] = new double[n + 1];<a name="line.100"></a>
104 <FONT color="green">101</FONT> double d[] = new double[n];<a name="line.101"></a>
105 <FONT color="green">102</FONT> <a name="line.102"></a>
106 <FONT color="green">103</FONT> z[n] = 0d;<a name="line.103"></a>
107 <FONT color="green">104</FONT> c[n] = 0d;<a name="line.104"></a>
108 <FONT color="green">105</FONT> <a name="line.105"></a>
109 <FONT color="green">106</FONT> for (int j = n -1; j &gt;=0; j--) {<a name="line.106"></a>
110 <FONT color="green">107</FONT> c[j] = z[j] - mu[j] * c[j + 1];<a name="line.107"></a>
111 <FONT color="green">108</FONT> b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2d * c[j]) / 3d;<a name="line.108"></a>
112 <FONT color="green">109</FONT> d[j] = (c[j + 1] - c[j]) / (3d * h[j]);<a name="line.109"></a>
113 <FONT color="green">110</FONT> }<a name="line.110"></a>
114 <FONT color="green">111</FONT> <a name="line.111"></a>
115 <FONT color="green">112</FONT> PolynomialFunction polynomials[] = new PolynomialFunction[n];<a name="line.112"></a>
116 <FONT color="green">113</FONT> double coefficients[] = new double[4];<a name="line.113"></a>
117 <FONT color="green">114</FONT> for (int i = 0; i &lt; n; i++) {<a name="line.114"></a>
118 <FONT color="green">115</FONT> coefficients[0] = y[i];<a name="line.115"></a>
119 <FONT color="green">116</FONT> coefficients[1] = b[i];<a name="line.116"></a>
120 <FONT color="green">117</FONT> coefficients[2] = c[i];<a name="line.117"></a>
121 <FONT color="green">118</FONT> coefficients[3] = d[i];<a name="line.118"></a>
122 <FONT color="green">119</FONT> polynomials[i] = new PolynomialFunction(coefficients);<a name="line.119"></a>
123 <FONT color="green">120</FONT> }<a name="line.120"></a>
124 <FONT color="green">121</FONT> <a name="line.121"></a>
125 <FONT color="green">122</FONT> return new PolynomialSplineFunction(x, polynomials);<a name="line.122"></a>
126 <FONT color="green">123</FONT> }<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
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189 </PRE>
190 </BODY>
191 </HTML>