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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.polynomials;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import java.util.Arrays;<a name="line.19"></a> <FONT color="green">020</FONT> <a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.ArgumentOutsideDomainException;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.24"></a> <FONT color="green">025</FONT> <a name="line.25"></a> <FONT color="green">026</FONT> /**<a name="line.26"></a> <FONT color="green">027</FONT> * Represents a polynomial spline function.<a name="line.27"></a> <FONT color="green">028</FONT> * <p><a name="line.28"></a> <FONT color="green">029</FONT> * A <strong>polynomial spline function</strong> consists of a set of<a name="line.29"></a> <FONT color="green">030</FONT> * <i>interpolating polynomials</i> and an ascending array of domain<a name="line.30"></a> <FONT color="green">031</FONT> * <i>knot points</i>, determining the intervals over which the spline function<a name="line.31"></a> <FONT color="green">032</FONT> * is defined by the constituent polynomials. The polynomials are assumed to<a name="line.32"></a> <FONT color="green">033</FONT> * have been computed to match the values of another function at the knot<a name="line.33"></a> <FONT color="green">034</FONT> * points. The value consistency constraints are not currently enforced by<a name="line.34"></a> <FONT color="green">035</FONT> * <code>PolynomialSplineFunction</code> itself, but are assumed to hold among<a name="line.35"></a> <FONT color="green">036</FONT> * the polynomials and knot points passed to the constructor.</p><a name="line.36"></a> <FONT color="green">037</FONT> * <p><a name="line.37"></a> <FONT color="green">038</FONT> * N.B.: The polynomials in the <code>polynomials</code> property must be<a name="line.38"></a> <FONT color="green">039</FONT> * centered on the knot points to compute the spline function values.<a name="line.39"></a> <FONT color="green">040</FONT> * See below.</p><a name="line.40"></a> <FONT color="green">041</FONT> * <p><a name="line.41"></a> <FONT color="green">042</FONT> * The domain of the polynomial spline function is<a name="line.42"></a> <FONT color="green">043</FONT> * <code>[smallest knot, largest knot]</code>. Attempts to evaluate the<a name="line.43"></a> <FONT color="green">044</FONT> * function at values outside of this range generate IllegalArgumentExceptions.<a name="line.44"></a> <FONT color="green">045</FONT> * </p><a name="line.45"></a> <FONT color="green">046</FONT> * <p><a name="line.46"></a> <FONT color="green">047</FONT> * The value of the polynomial spline function for an argument <code>x</code><a name="line.47"></a> <FONT color="green">048</FONT> * is computed as follows:<a name="line.48"></a> <FONT color="green">049</FONT> * <ol><a name="line.49"></a> <FONT color="green">050</FONT> * <li>The knot array is searched to find the segment to which <code>x</code><a name="line.50"></a> <FONT color="green">051</FONT> * belongs. If <code>x</code> is less than the smallest knot point or greater<a name="line.51"></a> <FONT color="green">052</FONT> * than the largest one, an <code>IllegalArgumentException</code><a name="line.52"></a> <FONT color="green">053</FONT> * is thrown.</li><a name="line.53"></a> <FONT color="green">054</FONT> * <li> Let <code>j</code> be the index of the largest knot point that is less<a name="line.54"></a> <FONT color="green">055</FONT> * than or equal to <code>x</code>. The value returned is <br><a name="line.55"></a> <FONT color="green">056</FONT> * <code>polynomials[j](x - knot[j])</code></li></ol></p><a name="line.56"></a> <FONT color="green">057</FONT> *<a name="line.57"></a> <FONT color="green">058</FONT> * @version $Revision: 922708 $ $Date: 2010-03-13 20:15:47 -0500 (Sat, 13 Mar 2010) $<a name="line.58"></a> <FONT color="green">059</FONT> */<a name="line.59"></a> <FONT color="green">060</FONT> public class PolynomialSplineFunction<a name="line.60"></a> <FONT color="green">061</FONT> implements DifferentiableUnivariateRealFunction {<a name="line.61"></a> <FONT color="green">062</FONT> <a name="line.62"></a> <FONT color="green">063</FONT> /** Spline segment interval delimiters (knots). Size is n+1 for n segments. */<a name="line.63"></a> <FONT color="green">064</FONT> private final double knots[];<a name="line.64"></a> <FONT color="green">065</FONT> <a name="line.65"></a> <FONT color="green">066</FONT> /**<a name="line.66"></a> <FONT color="green">067</FONT> * The polynomial functions that make up the spline. The first element<a name="line.67"></a> <FONT color="green">068</FONT> * determines the value of the spline over the first subinterval, the<a name="line.68"></a> <FONT color="green">069</FONT> * second over the second, etc. Spline function values are determined by<a name="line.69"></a> <FONT color="green">070</FONT> * evaluating these functions at <code>(x - knot[i])</code> where i is the<a name="line.70"></a> <FONT color="green">071</FONT> * knot segment to which x belongs.<a name="line.71"></a> <FONT color="green">072</FONT> */<a name="line.72"></a> <FONT color="green">073</FONT> private final PolynomialFunction polynomials[];<a name="line.73"></a> <FONT color="green">074</FONT> <a name="line.74"></a> <FONT color="green">075</FONT> /**<a name="line.75"></a> <FONT color="green">076</FONT> * Number of spline segments = number of polynomials<a name="line.76"></a> <FONT color="green">077</FONT> * = number of partition points - 1<a name="line.77"></a> <FONT color="green">078</FONT> */<a name="line.78"></a> <FONT color="green">079</FONT> private final int n;<a name="line.79"></a> <FONT color="green">080</FONT> <a name="line.80"></a> <FONT color="green">081</FONT> <a name="line.81"></a> <FONT color="green">082</FONT> /**<a name="line.82"></a> <FONT color="green">083</FONT> * Construct a polynomial spline function with the given segment delimiters<a name="line.83"></a> <FONT color="green">084</FONT> * and interpolating polynomials.<a name="line.84"></a> <FONT color="green">085</FONT> * <p><a name="line.85"></a> <FONT color="green">086</FONT> * The constructor copies both arrays and assigns the copies to the knots<a name="line.86"></a> <FONT color="green">087</FONT> * and polynomials properties, respectively.</p><a name="line.87"></a> <FONT color="green">088</FONT> *<a name="line.88"></a> <FONT color="green">089</FONT> * @param knots spline segment interval delimiters<a name="line.89"></a> <FONT color="green">090</FONT> * @param polynomials polynomial functions that make up the spline<a name="line.90"></a> <FONT color="green">091</FONT> * @throws NullPointerException if either of the input arrays is null<a name="line.91"></a> <FONT color="green">092</FONT> * @throws IllegalArgumentException if knots has length less than 2,<a name="line.92"></a> <FONT color="green">093</FONT> * <code>polynomials.length != knots.length - 1 </code>, or the knots array<a name="line.93"></a> <FONT color="green">094</FONT> * is not strictly increasing.<a name="line.94"></a> <FONT color="green">095</FONT> *<a name="line.95"></a> <FONT color="green">096</FONT> */<a name="line.96"></a> <FONT color="green">097</FONT> public PolynomialSplineFunction(double knots[], PolynomialFunction polynomials[]) {<a name="line.97"></a> <FONT color="green">098</FONT> if (knots.length < 2) {<a name="line.98"></a> <FONT color="green">099</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.99"></a> <FONT color="green">100</FONT> "spline partition must have at least {0} points, got {1}",<a name="line.100"></a> <FONT color="green">101</FONT> 2, knots.length);<a name="line.101"></a> <FONT color="green">102</FONT> }<a name="line.102"></a> <FONT color="green">103</FONT> if (knots.length - 1 != polynomials.length) {<a name="line.103"></a> <FONT color="green">104</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.104"></a> <FONT color="green">105</FONT> "number of polynomial interpolants must match the number of segments ({0} != {1} - 1)",<a name="line.105"></a> <FONT color="green">106</FONT> polynomials.length, knots.length);<a name="line.106"></a> <FONT color="green">107</FONT> }<a name="line.107"></a> <FONT color="green">108</FONT> if (!isStrictlyIncreasing(knots)) {<a name="line.108"></a> <FONT color="green">109</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.109"></a> <FONT color="green">110</FONT> "knot values must be strictly increasing");<a name="line.110"></a> <FONT color="green">111</FONT> }<a name="line.111"></a> <FONT color="green">112</FONT> <a name="line.112"></a> <FONT color="green">113</FONT> this.n = knots.length -1;<a name="line.113"></a> <FONT color="green">114</FONT> this.knots = new double[n + 1];<a name="line.114"></a> <FONT color="green">115</FONT> System.arraycopy(knots, 0, this.knots, 0, n + 1);<a name="line.115"></a> <FONT color="green">116</FONT> this.polynomials = new PolynomialFunction[n];<a name="line.116"></a> <FONT color="green">117</FONT> System.arraycopy(polynomials, 0, this.polynomials, 0, n);<a name="line.117"></a> <FONT color="green">118</FONT> }<a name="line.118"></a> <FONT color="green">119</FONT> <a name="line.119"></a> <FONT color="green">120</FONT> /**<a name="line.120"></a> <FONT color="green">121</FONT> * Compute the value for the function.<a name="line.121"></a> <FONT color="green">122</FONT> * <p><a name="line.122"></a> <FONT color="green">123</FONT> * Throws FunctionEvaluationException if v is outside of the domain of the<a name="line.123"></a> <FONT color="green">124</FONT> * function. The domain is [smallest knot, largest knot].</p><a name="line.124"></a> <FONT color="green">125</FONT> * <p><a name="line.125"></a> <FONT color="green">126</FONT> * See {@link PolynomialSplineFunction} for details on the algorithm for<a name="line.126"></a> <FONT color="green">127</FONT> * computing the value of the function.</p><a name="line.127"></a> <FONT color="green">128</FONT> *<a name="line.128"></a> <FONT color="green">129</FONT> * @param v the point for which the function value should be computed<a name="line.129"></a> <FONT color="green">130</FONT> * @return the value<a name="line.130"></a> <FONT color="green">131</FONT> * @throws ArgumentOutsideDomainException if v is outside of the domain of<a name="line.131"></a> <FONT color="green">132</FONT> * of the spline function (less than the smallest knot point or greater<a name="line.132"></a> <FONT color="green">133</FONT> * than the largest knot point)<a name="line.133"></a> <FONT color="green">134</FONT> */<a name="line.134"></a> <FONT color="green">135</FONT> public double value(double v) throws ArgumentOutsideDomainException {<a name="line.135"></a> <FONT color="green">136</FONT> if (v < knots[0] || v > knots[n]) {<a name="line.136"></a> <FONT color="green">137</FONT> throw new ArgumentOutsideDomainException(v, knots[0], knots[n]);<a name="line.137"></a> <FONT color="green">138</FONT> }<a name="line.138"></a> <FONT color="green">139</FONT> int i = Arrays.binarySearch(knots, v);<a name="line.139"></a> <FONT color="green">140</FONT> if (i < 0) {<a name="line.140"></a> <FONT color="green">141</FONT> i = -i - 2;<a name="line.141"></a> <FONT color="green">142</FONT> }<a name="line.142"></a> <FONT color="green">143</FONT> //This will handle the case where v is the last knot value<a name="line.143"></a> <FONT color="green">144</FONT> //There are only n-1 polynomials, so if v is the last knot<a name="line.144"></a> <FONT color="green">145</FONT> //then we will use the last polynomial to calculate the value.<a name="line.145"></a> <FONT color="green">146</FONT> if ( i >= polynomials.length ) {<a name="line.146"></a> <FONT color="green">147</FONT> i--;<a name="line.147"></a> <FONT color="green">148</FONT> }<a name="line.148"></a> <FONT color="green">149</FONT> return polynomials[i].value(v - knots[i]);<a name="line.149"></a> <FONT color="green">150</FONT> }<a name="line.150"></a> <FONT color="green">151</FONT> <a name="line.151"></a> <FONT color="green">152</FONT> /**<a name="line.152"></a> <FONT color="green">153</FONT> * Returns the derivative of the polynomial spline function as a UnivariateRealFunction<a name="line.153"></a> <FONT color="green">154</FONT> * @return the derivative function<a name="line.154"></a> <FONT color="green">155</FONT> */<a name="line.155"></a> <FONT color="green">156</FONT> public UnivariateRealFunction derivative() {<a name="line.156"></a> <FONT color="green">157</FONT> return polynomialSplineDerivative();<a name="line.157"></a> <FONT color="green">158</FONT> }<a name="line.158"></a> <FONT color="green">159</FONT> <a name="line.159"></a> <FONT color="green">160</FONT> /**<a name="line.160"></a> <FONT color="green">161</FONT> * Returns the derivative of the polynomial spline function as a PolynomialSplineFunction<a name="line.161"></a> <FONT color="green">162</FONT> *<a name="line.162"></a> <FONT color="green">163</FONT> * @return the derivative function<a name="line.163"></a> <FONT color="green">164</FONT> */<a name="line.164"></a> <FONT color="green">165</FONT> public PolynomialSplineFunction polynomialSplineDerivative() {<a name="line.165"></a> <FONT color="green">166</FONT> PolynomialFunction derivativePolynomials[] = new PolynomialFunction[n];<a name="line.166"></a> <FONT color="green">167</FONT> for (int i = 0; i < n; i++) {<a name="line.167"></a> <FONT color="green">168</FONT> derivativePolynomials[i] = polynomials[i].polynomialDerivative();<a name="line.168"></a> <FONT color="green">169</FONT> }<a name="line.169"></a> <FONT color="green">170</FONT> return new PolynomialSplineFunction(knots, derivativePolynomials);<a name="line.170"></a> <FONT color="green">171</FONT> }<a name="line.171"></a> <FONT color="green">172</FONT> <a name="line.172"></a> <FONT color="green">173</FONT> /**<a name="line.173"></a> <FONT color="green">174</FONT> * Returns the number of spline segments = the number of polynomials<a name="line.174"></a> <FONT color="green">175</FONT> * = the number of knot points - 1.<a name="line.175"></a> <FONT color="green">176</FONT> *<a name="line.176"></a> <FONT color="green">177</FONT> * @return the number of spline segments<a name="line.177"></a> <FONT color="green">178</FONT> */<a name="line.178"></a> <FONT color="green">179</FONT> public int getN() {<a name="line.179"></a> <FONT color="green">180</FONT> return n;<a name="line.180"></a> <FONT color="green">181</FONT> }<a name="line.181"></a> <FONT color="green">182</FONT> <a name="line.182"></a> <FONT color="green">183</FONT> /**<a name="line.183"></a> <FONT color="green">184</FONT> * Returns a copy of the interpolating polynomials array.<a name="line.184"></a> <FONT color="green">185</FONT> * <p><a name="line.185"></a> <FONT color="green">186</FONT> * Returns a fresh copy of the array. Changes made to the copy will<a name="line.186"></a> <FONT color="green">187</FONT> * not affect the polynomials property.</p><a name="line.187"></a> <FONT color="green">188</FONT> *<a name="line.188"></a> <FONT color="green">189</FONT> * @return the interpolating polynomials<a name="line.189"></a> <FONT color="green">190</FONT> */<a name="line.190"></a> <FONT color="green">191</FONT> public PolynomialFunction[] getPolynomials() {<a name="line.191"></a> <FONT color="green">192</FONT> PolynomialFunction p[] = new PolynomialFunction[n];<a name="line.192"></a> <FONT color="green">193</FONT> System.arraycopy(polynomials, 0, p, 0, n);<a name="line.193"></a> <FONT color="green">194</FONT> return p;<a name="line.194"></a> <FONT color="green">195</FONT> }<a name="line.195"></a> <FONT color="green">196</FONT> <a name="line.196"></a> <FONT color="green">197</FONT> /**<a name="line.197"></a> <FONT color="green">198</FONT> * Returns an array copy of the knot points.<a name="line.198"></a> <FONT color="green">199</FONT> * <p><a name="line.199"></a> <FONT color="green">200</FONT> * Returns a fresh copy of the array. Changes made to the copy<a name="line.200"></a> <FONT color="green">201</FONT> * will not affect the knots property.</p><a name="line.201"></a> <FONT color="green">202</FONT> *<a name="line.202"></a> <FONT color="green">203</FONT> * @return the knot points<a name="line.203"></a> <FONT color="green">204</FONT> */<a name="line.204"></a> <FONT color="green">205</FONT> public double[] getKnots() {<a name="line.205"></a> <FONT color="green">206</FONT> double out[] = new double[n + 1];<a name="line.206"></a> <FONT color="green">207</FONT> System.arraycopy(knots, 0, out, 0, n + 1);<a name="line.207"></a> <FONT color="green">208</FONT> return out;<a name="line.208"></a> <FONT color="green">209</FONT> }<a name="line.209"></a> <FONT color="green">210</FONT> <a name="line.210"></a> <FONT color="green">211</FONT> /**<a name="line.211"></a> <FONT color="green">212</FONT> * Determines if the given array is ordered in a strictly increasing<a name="line.212"></a> <FONT color="green">213</FONT> * fashion.<a name="line.213"></a> <FONT color="green">214</FONT> *<a name="line.214"></a> <FONT color="green">215</FONT> * @param x the array to examine.<a name="line.215"></a> <FONT color="green">216</FONT> * @return <code>true</code> if the elements in <code>x</code> are ordered<a name="line.216"></a> <FONT color="green">217</FONT> * in a stricly increasing manner. <code>false</code>, otherwise.<a name="line.217"></a> <FONT color="green">218</FONT> */<a name="line.218"></a> <FONT color="green">219</FONT> private static boolean isStrictlyIncreasing(double[] x) {<a name="line.219"></a> <FONT color="green">220</FONT> for (int i = 1; i < x.length; ++i) {<a name="line.220"></a> <FONT color="green">221</FONT> if (x[i - 1] >= x[i]) {<a name="line.221"></a> <FONT color="green">222</FONT> return false;<a name="line.222"></a> <FONT color="green">223</FONT> }<a name="line.223"></a> <FONT color="green">224</FONT> }<a name="line.224"></a> <FONT color="green">225</FONT> return true;<a name="line.225"></a> <FONT color="green">226</FONT> }<a name="line.226"></a> <FONT color="green">227</FONT> }<a name="line.227"></a> </PRE> </BODY> </HTML>