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comparison libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/analysis/interpolation/SmoothingBicubicSplineInterpolator.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 org.apache.commons.math.DimensionMismatchException;<a name="line.19"></a>
23 <FONT color="green">020</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.20"></a>
24 <FONT color="green">021</FONT> import org.apache.commons.math.MathException;<a name="line.21"></a>
25 <FONT color="green">022</FONT> import org.apache.commons.math.util.MathUtils;<a name="line.22"></a>
26 <FONT color="green">023</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.23"></a>
27 <FONT color="green">024</FONT> import org.apache.commons.math.analysis.BivariateRealFunction;<a name="line.24"></a>
28 <FONT color="green">025</FONT> import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;<a name="line.25"></a>
29 <FONT color="green">026</FONT> <a name="line.26"></a>
30 <FONT color="green">027</FONT> /**<a name="line.27"></a>
31 <FONT color="green">028</FONT> * Generates a bicubic interpolation function.<a name="line.28"></a>
32 <FONT color="green">029</FONT> * Before interpolating, smoothing of the input data is performed using<a name="line.29"></a>
33 <FONT color="green">030</FONT> * splines.<a name="line.30"></a>
34 <FONT color="green">031</FONT> * See &lt;b&gt;Handbook on splines for the user&lt;/b&gt;, ISBN 084939404X,<a name="line.31"></a>
35 <FONT color="green">032</FONT> * chapter 2.<a name="line.32"></a>
36 <FONT color="green">033</FONT> *<a name="line.33"></a>
37 <FONT color="green">034</FONT> * @version $Revision$ $Date$<a name="line.34"></a>
38 <FONT color="green">035</FONT> * @since 2.1<a name="line.35"></a>
39 <FONT color="green">036</FONT> */<a name="line.36"></a>
40 <FONT color="green">037</FONT> public class SmoothingBicubicSplineInterpolator<a name="line.37"></a>
41 <FONT color="green">038</FONT> implements BivariateRealGridInterpolator {<a name="line.38"></a>
42 <FONT color="green">039</FONT> /**<a name="line.39"></a>
43 <FONT color="green">040</FONT> * {@inheritDoc}<a name="line.40"></a>
44 <FONT color="green">041</FONT> */<a name="line.41"></a>
45 <FONT color="green">042</FONT> public BivariateRealFunction interpolate(final double[] xval,<a name="line.42"></a>
46 <FONT color="green">043</FONT> final double[] yval,<a name="line.43"></a>
47 <FONT color="green">044</FONT> final double[][] zval)<a name="line.44"></a>
48 <FONT color="green">045</FONT> throws MathException, IllegalArgumentException {<a name="line.45"></a>
49 <FONT color="green">046</FONT> if (xval.length == 0 || yval.length == 0 || zval.length == 0) {<a name="line.46"></a>
50 <FONT color="green">047</FONT> throw MathRuntimeException.createIllegalArgumentException("no data");<a name="line.47"></a>
51 <FONT color="green">048</FONT> }<a name="line.48"></a>
52 <FONT color="green">049</FONT> if (xval.length != zval.length) {<a name="line.49"></a>
53 <FONT color="green">050</FONT> throw new DimensionMismatchException(xval.length, zval.length);<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> MathUtils.checkOrder(xval, 1, true);<a name="line.53"></a>
57 <FONT color="green">054</FONT> MathUtils.checkOrder(yval, 1, true);<a name="line.54"></a>
58 <FONT color="green">055</FONT> <a name="line.55"></a>
59 <FONT color="green">056</FONT> final int xLen = xval.length;<a name="line.56"></a>
60 <FONT color="green">057</FONT> final int yLen = yval.length;<a name="line.57"></a>
61 <FONT color="green">058</FONT> <a name="line.58"></a>
62 <FONT color="green">059</FONT> // Samples (first index is y-coordinate, i.e. subarray variable is x)<a name="line.59"></a>
63 <FONT color="green">060</FONT> // 0 &lt;= i &lt; xval.length<a name="line.60"></a>
64 <FONT color="green">061</FONT> // 0 &lt;= j &lt; yval.length<a name="line.61"></a>
65 <FONT color="green">062</FONT> // zX[j][i] = f(xval[i], yval[j])<a name="line.62"></a>
66 <FONT color="green">063</FONT> final double[][] zX = new double[yLen][xLen];<a name="line.63"></a>
67 <FONT color="green">064</FONT> for (int i = 0; i &lt; xLen; i++) {<a name="line.64"></a>
68 <FONT color="green">065</FONT> if (zval[i].length != yLen) {<a name="line.65"></a>
69 <FONT color="green">066</FONT> throw new DimensionMismatchException(zval[i].length, yLen);<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> for (int j = 0; j &lt; yLen; j++) {<a name="line.69"></a>
73 <FONT color="green">070</FONT> zX[j][i] = zval[i][j];<a name="line.70"></a>
74 <FONT color="green">071</FONT> }<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> final SplineInterpolator spInterpolator = new SplineInterpolator();<a name="line.74"></a>
78 <FONT color="green">075</FONT> <a name="line.75"></a>
79 <FONT color="green">076</FONT> // For each line y[j] (0 &lt;= j &lt; yLen), construct a 1D spline with<a name="line.76"></a>
80 <FONT color="green">077</FONT> // respect to variable x<a name="line.77"></a>
81 <FONT color="green">078</FONT> final PolynomialSplineFunction[] ySplineX = new PolynomialSplineFunction[yLen];<a name="line.78"></a>
82 <FONT color="green">079</FONT> for (int j = 0; j &lt; yLen; j++) {<a name="line.79"></a>
83 <FONT color="green">080</FONT> ySplineX[j] = spInterpolator.interpolate(xval, zX[j]);<a name="line.80"></a>
84 <FONT color="green">081</FONT> }<a name="line.81"></a>
85 <FONT color="green">082</FONT> <a name="line.82"></a>
86 <FONT color="green">083</FONT> // For every knot (xval[i], yval[j]) of the grid, calculate corrected<a name="line.83"></a>
87 <FONT color="green">084</FONT> // values zY_1<a name="line.84"></a>
88 <FONT color="green">085</FONT> final double[][] zY_1 = new double[xLen][yLen];<a name="line.85"></a>
89 <FONT color="green">086</FONT> for (int j = 0; j &lt; yLen; j++) {<a name="line.86"></a>
90 <FONT color="green">087</FONT> final PolynomialSplineFunction f = ySplineX[j];<a name="line.87"></a>
91 <FONT color="green">088</FONT> for (int i = 0; i &lt; xLen; i++) {<a name="line.88"></a>
92 <FONT color="green">089</FONT> zY_1[i][j] = f.value(xval[i]);<a name="line.89"></a>
93 <FONT color="green">090</FONT> }<a name="line.90"></a>
94 <FONT color="green">091</FONT> }<a name="line.91"></a>
95 <FONT color="green">092</FONT> <a name="line.92"></a>
96 <FONT color="green">093</FONT> // For each line x[i] (0 &lt;= i &lt; xLen), construct a 1D spline with<a name="line.93"></a>
97 <FONT color="green">094</FONT> // respect to variable y generated by array zY_1[i]<a name="line.94"></a>
98 <FONT color="green">095</FONT> final PolynomialSplineFunction[] xSplineY = new PolynomialSplineFunction[xLen];<a name="line.95"></a>
99 <FONT color="green">096</FONT> for (int i = 0; i &lt; xLen; i++) {<a name="line.96"></a>
100 <FONT color="green">097</FONT> xSplineY[i] = spInterpolator.interpolate(yval, zY_1[i]);<a name="line.97"></a>
101 <FONT color="green">098</FONT> }<a name="line.98"></a>
102 <FONT color="green">099</FONT> <a name="line.99"></a>
103 <FONT color="green">100</FONT> // For every knot (xval[i], yval[j]) of the grid, calculate corrected<a name="line.100"></a>
104 <FONT color="green">101</FONT> // values zY_2<a name="line.101"></a>
105 <FONT color="green">102</FONT> final double[][] zY_2 = new double[xLen][yLen];<a name="line.102"></a>
106 <FONT color="green">103</FONT> for (int i = 0; i &lt; xLen; i++) {<a name="line.103"></a>
107 <FONT color="green">104</FONT> final PolynomialSplineFunction f = xSplineY[i];<a name="line.104"></a>
108 <FONT color="green">105</FONT> for (int j = 0; j &lt; yLen; j++) {<a name="line.105"></a>
109 <FONT color="green">106</FONT> zY_2[i][j] = f.value(yval[j]);<a name="line.106"></a>
110 <FONT color="green">107</FONT> }<a name="line.107"></a>
111 <FONT color="green">108</FONT> }<a name="line.108"></a>
112 <FONT color="green">109</FONT> <a name="line.109"></a>
113 <FONT color="green">110</FONT> // Partial derivatives with respect to x at the grid knots<a name="line.110"></a>
114 <FONT color="green">111</FONT> final double[][] dZdX = new double[xLen][yLen];<a name="line.111"></a>
115 <FONT color="green">112</FONT> for (int j = 0; j &lt; yLen; j++) {<a name="line.112"></a>
116 <FONT color="green">113</FONT> final UnivariateRealFunction f = ySplineX[j].derivative();<a name="line.113"></a>
117 <FONT color="green">114</FONT> for (int i = 0; i &lt; xLen; i++) {<a name="line.114"></a>
118 <FONT color="green">115</FONT> dZdX[i][j] = f.value(xval[i]);<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>
121 <FONT color="green">118</FONT> <a name="line.118"></a>
122 <FONT color="green">119</FONT> // Partial derivatives with respect to y at the grid knots<a name="line.119"></a>
123 <FONT color="green">120</FONT> final double[][] dZdY = new double[xLen][yLen];<a name="line.120"></a>
124 <FONT color="green">121</FONT> for (int i = 0; i &lt; xLen; i++) {<a name="line.121"></a>
125 <FONT color="green">122</FONT> final UnivariateRealFunction f = xSplineY[i].derivative();<a name="line.122"></a>
126 <FONT color="green">123</FONT> for (int j = 0; j &lt; yLen; j++) {<a name="line.123"></a>
127 <FONT color="green">124</FONT> dZdY[i][j] = f.value(yval[j]);<a name="line.124"></a>
128 <FONT color="green">125</FONT> }<a name="line.125"></a>
129 <FONT color="green">126</FONT> }<a name="line.126"></a>
130 <FONT color="green">127</FONT> <a name="line.127"></a>
131 <FONT color="green">128</FONT> // Cross partial derivatives<a name="line.128"></a>
132 <FONT color="green">129</FONT> final double[][] dZdXdY = new double[xLen][yLen];<a name="line.129"></a>
133 <FONT color="green">130</FONT> for (int i = 0; i &lt; xLen ; i++) {<a name="line.130"></a>
134 <FONT color="green">131</FONT> final int nI = nextIndex(i, xLen);<a name="line.131"></a>
135 <FONT color="green">132</FONT> final int pI = previousIndex(i);<a name="line.132"></a>
136 <FONT color="green">133</FONT> for (int j = 0; j &lt; yLen; j++) {<a name="line.133"></a>
137 <FONT color="green">134</FONT> final int nJ = nextIndex(j, yLen);<a name="line.134"></a>
138 <FONT color="green">135</FONT> final int pJ = previousIndex(j);<a name="line.135"></a>
139 <FONT color="green">136</FONT> dZdXdY[i][j] = (zY_2[nI][nJ] - zY_2[nI][pJ] -<a name="line.136"></a>
140 <FONT color="green">137</FONT> zY_2[pI][nJ] + zY_2[pI][pJ]) /<a name="line.137"></a>
141 <FONT color="green">138</FONT> ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ])) ;<a name="line.138"></a>
142 <FONT color="green">139</FONT> }<a name="line.139"></a>
143 <FONT color="green">140</FONT> }<a name="line.140"></a>
144 <FONT color="green">141</FONT> <a name="line.141"></a>
145 <FONT color="green">142</FONT> // Create the interpolating splines<a name="line.142"></a>
146 <FONT color="green">143</FONT> return new BicubicSplineInterpolatingFunction(xval, yval, zY_2,<a name="line.143"></a>
147 <FONT color="green">144</FONT> dZdX, dZdY, dZdXdY);<a name="line.144"></a>
148 <FONT color="green">145</FONT> }<a name="line.145"></a>
149 <FONT color="green">146</FONT> <a name="line.146"></a>
150 <FONT color="green">147</FONT> /**<a name="line.147"></a>
151 <FONT color="green">148</FONT> * Compute the next index of an array, clipping if necessary.<a name="line.148"></a>
152 <FONT color="green">149</FONT> * It is assumed (but not checked) that {@code i} is larger than or equal to 0}.<a name="line.149"></a>
153 <FONT color="green">150</FONT> *<a name="line.150"></a>
154 <FONT color="green">151</FONT> * @param i Index<a name="line.151"></a>
155 <FONT color="green">152</FONT> * @param max Upper limit of the array<a name="line.152"></a>
156 <FONT color="green">153</FONT> * @return the next index<a name="line.153"></a>
157 <FONT color="green">154</FONT> */<a name="line.154"></a>
158 <FONT color="green">155</FONT> private int nextIndex(int i, int max) {<a name="line.155"></a>
159 <FONT color="green">156</FONT> final int index = i + 1;<a name="line.156"></a>
160 <FONT color="green">157</FONT> return index &lt; max ? index : index - 1;<a name="line.157"></a>
161 <FONT color="green">158</FONT> }<a name="line.158"></a>
162 <FONT color="green">159</FONT> /**<a name="line.159"></a>
163 <FONT color="green">160</FONT> * Compute the previous index of an array, clipping if necessary.<a name="line.160"></a>
164 <FONT color="green">161</FONT> * It is assumed (but not checked) that {@code i} is smaller than the size of the array.<a name="line.161"></a>
165 <FONT color="green">162</FONT> *<a name="line.162"></a>
166 <FONT color="green">163</FONT> * @param i Index<a name="line.163"></a>
167 <FONT color="green">164</FONT> * @return the previous index<a name="line.164"></a>
168 <FONT color="green">165</FONT> */<a name="line.165"></a>
169 <FONT color="green">166</FONT> private int previousIndex(int i) {<a name="line.166"></a>
170 <FONT color="green">167</FONT> final int index = i - 1;<a name="line.167"></a>
171 <FONT color="green">168</FONT> return index &gt;= 0 ? index : 0;<a name="line.168"></a>
172 <FONT color="green">169</FONT> }<a name="line.169"></a>
173 <FONT color="green">170</FONT> }<a name="line.170"></a>
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234 </PRE>
235 </BODY>
236 </HTML>