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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.analysis.interpolation;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.analysis.polynomials.PolynomialFunction;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.analysis.polynomials.PolynomialSplineFunction;<a name="line.21"></a> <FONT color="green">022</FONT> <a name="line.22"></a> <FONT color="green">023</FONT> /**<a name="line.23"></a> <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> <FONT color="green">025</FONT> * <p><a name="line.25"></a> <FONT color="green">026</FONT> * The {@link #interpolate(double[], double[])} method returns a {@link PolynomialSplineFunction}<a name="line.26"></a> <FONT color="green">027</FONT> * consisting of n cubic polynomials, defined over the subintervals determined by the x values,<a name="line.27"></a> <FONT color="green">028</FONT> * x[0] < x[i] ... < x[n]. The x values are referred to as "knot points."</p><a name="line.28"></a> <FONT color="green">029</FONT> * <p><a name="line.29"></a> <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> <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> <FONT color="green">032</FONT> * x belongs and computing the value of the corresponding polynomial at <code>x - x[i] </code> where<a name="line.32"></a> <FONT color="green">033</FONT> * <code>i</code> is the index of the subinterval. See {@link PolynomialSplineFunction} for more details.<a name="line.33"></a> <FONT color="green">034</FONT> * </p><a name="line.34"></a> <FONT color="green">035</FONT> * <p><a name="line.35"></a> <FONT color="green">036</FONT> * The interpolating polynomials satisfy: <ol><a name="line.36"></a> <FONT color="green">037</FONT> * <li>The value of the PolynomialSplineFunction at each of the input x values equals the<a name="line.37"></a> <FONT color="green">038</FONT> * corresponding y value.</li><a name="line.38"></a> <FONT color="green">039</FONT> * <li>Adjacent polynomials are equal through two derivatives at the knot points (i.e., adjacent polynomials<a name="line.39"></a> <FONT color="green">040</FONT> * "match up" at the knot points, as do their first and second derivatives).</li><a name="line.40"></a> <FONT color="green">041</FONT> * </ol></p><a name="line.41"></a> <FONT color="green">042</FONT> * <p><a name="line.42"></a> <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> <FONT color="green">044</FONT> * <u>Numerical Analysis</u>, 4th Ed., 1989, PWS-Kent, ISBN 0-53491-585-X, pp 126-131.<a name="line.44"></a> <FONT color="green">045</FONT> * </p><a name="line.45"></a> <FONT color="green">046</FONT> *<a name="line.46"></a> <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> <FONT color="green">048</FONT> *<a name="line.48"></a> <FONT color="green">049</FONT> */<a name="line.49"></a> <FONT color="green">050</FONT> public class SplineInterpolator implements UnivariateRealInterpolator {<a name="line.50"></a> <FONT color="green">051</FONT> <a name="line.51"></a> <FONT color="green">052</FONT> /**<a name="line.52"></a> <FONT color="green">053</FONT> * Computes an interpolating function for the data set.<a name="line.53"></a> <FONT color="green">054</FONT> * @param x the arguments for the interpolation points<a name="line.54"></a> <FONT color="green">055</FONT> * @param y the values for the interpolation points<a name="line.55"></a> <FONT color="green">056</FONT> * @return a function which interpolates the data set<a name="line.56"></a> <FONT color="green">057</FONT> */<a name="line.57"></a> <FONT color="green">058</FONT> public PolynomialSplineFunction interpolate(double x[], double y[]) {<a name="line.58"></a> <FONT color="green">059</FONT> if (x.length != y.length) {<a name="line.59"></a> <FONT color="green">060</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.60"></a> <FONT color="green">061</FONT> "dimension mismatch {0} != {1}", x.length, y.length);<a name="line.61"></a> <FONT color="green">062</FONT> }<a name="line.62"></a> <FONT color="green">063</FONT> <a name="line.63"></a> <FONT color="green">064</FONT> if (x.length < 3) {<a name="line.64"></a> <FONT color="green">065</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.65"></a> <FONT color="green">066</FONT> "{0} points are required, got only {1}", 3, x.length);<a name="line.66"></a> <FONT color="green">067</FONT> }<a name="line.67"></a> <FONT color="green">068</FONT> <a name="line.68"></a> <FONT color="green">069</FONT> // Number of intervals. The number of data points is n + 1.<a name="line.69"></a> <FONT color="green">070</FONT> int n = x.length - 1;<a name="line.70"></a> <FONT color="green">071</FONT> <a name="line.71"></a> <FONT color="green">072</FONT> for (int i = 0; i < n; i++) {<a name="line.72"></a> <FONT color="green">073</FONT> if (x[i] >= x[i + 1]) {<a name="line.73"></a> <FONT color="green">074</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.74"></a> <FONT color="green">075</FONT> "points {0} and {1} are not strictly increasing ({2} >= {3})",<a name="line.75"></a> <FONT color="green">076</FONT> i, i+1, x[i], x[i+1]);<a name="line.76"></a> <FONT color="green">077</FONT> }<a name="line.77"></a> <FONT color="green">078</FONT> }<a name="line.78"></a> <FONT color="green">079</FONT> <a name="line.79"></a> <FONT color="green">080</FONT> // Differences between knot points<a name="line.80"></a> <FONT color="green">081</FONT> double h[] = new double[n];<a name="line.81"></a> <FONT color="green">082</FONT> for (int i = 0; i < n; i++) {<a name="line.82"></a> <FONT color="green">083</FONT> h[i] = x[i + 1] - x[i];<a name="line.83"></a> <FONT color="green">084</FONT> }<a name="line.84"></a> <FONT color="green">085</FONT> <a name="line.85"></a> <FONT color="green">086</FONT> double mu[] = new double[n];<a name="line.86"></a> <FONT color="green">087</FONT> double z[] = new double[n + 1];<a name="line.87"></a> <FONT color="green">088</FONT> mu[0] = 0d;<a name="line.88"></a> <FONT color="green">089</FONT> z[0] = 0d;<a name="line.89"></a> <FONT color="green">090</FONT> double g = 0;<a name="line.90"></a> <FONT color="green">091</FONT> for (int i = 1; i < n; i++) {<a name="line.91"></a> <FONT color="green">092</FONT> g = 2d * (x[i+1] - x[i - 1]) - h[i - 1] * mu[i -1];<a name="line.92"></a> <FONT color="green">093</FONT> mu[i] = h[i] / g;<a name="line.93"></a> <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> <FONT color="green">095</FONT> (h[i - 1] * h[i]) - h[i - 1] * z[i - 1]) / g;<a name="line.95"></a> <FONT color="green">096</FONT> }<a name="line.96"></a> <FONT color="green">097</FONT> <a name="line.97"></a> <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> <FONT color="green">099</FONT> double b[] = new double[n];<a name="line.99"></a> <FONT color="green">100</FONT> double c[] = new double[n + 1];<a name="line.100"></a> <FONT color="green">101</FONT> double d[] = new double[n];<a name="line.101"></a> <FONT color="green">102</FONT> <a name="line.102"></a> <FONT color="green">103</FONT> z[n] = 0d;<a name="line.103"></a> <FONT color="green">104</FONT> c[n] = 0d;<a name="line.104"></a> <FONT color="green">105</FONT> <a name="line.105"></a> <FONT color="green">106</FONT> for (int j = n -1; j >=0; j--) {<a name="line.106"></a> <FONT color="green">107</FONT> c[j] = z[j] - mu[j] * c[j + 1];<a name="line.107"></a> <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> <FONT color="green">109</FONT> d[j] = (c[j + 1] - c[j]) / (3d * h[j]);<a name="line.109"></a> <FONT color="green">110</FONT> }<a name="line.110"></a> <FONT color="green">111</FONT> <a name="line.111"></a> <FONT color="green">112</FONT> PolynomialFunction polynomials[] = new PolynomialFunction[n];<a name="line.112"></a> <FONT color="green">113</FONT> double coefficients[] = new double[4];<a name="line.113"></a> <FONT color="green">114</FONT> for (int i = 0; i < n; i++) {<a name="line.114"></a> <FONT color="green">115</FONT> coefficients[0] = y[i];<a name="line.115"></a> <FONT color="green">116</FONT> coefficients[1] = b[i];<a name="line.116"></a> <FONT color="green">117</FONT> coefficients[2] = c[i];<a name="line.117"></a> <FONT color="green">118</FONT> coefficients[3] = d[i];<a name="line.118"></a> <FONT color="green">119</FONT> polynomials[i] = new PolynomialFunction(coefficients);<a name="line.119"></a> <FONT color="green">120</FONT> }<a name="line.120"></a> <FONT color="green">121</FONT> <a name="line.121"></a> <FONT color="green">122</FONT> return new PolynomialSplineFunction(x, polynomials);<a name="line.122"></a> <FONT color="green">123</FONT> }<a name="line.123"></a> <FONT color="green">124</FONT> <a name="line.124"></a> <FONT color="green">125</FONT> }<a name="line.125"></a> </PRE> </BODY> </HTML>