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1 <HTML>
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2 <BODY BGCOLOR="white">
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3 <PRE>
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4 <FONT color="green">001</FONT> /*<a name="line.1"></a>
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5 <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
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6 <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a>
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7 <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a>
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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>
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9 <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
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10 <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a>
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11 <FONT color="green">008</FONT> *<a name="line.8"></a>
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12 <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
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13 <FONT color="green">010</FONT> *<a name="line.10"></a>
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14 <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
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15 <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
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16 <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
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17 <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a>
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18 <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a>
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19 <FONT color="green">016</FONT> */<a name="line.16"></a>
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20 <FONT color="green">017</FONT> package org.apache.commons.math.analysis.polynomials;<a name="line.17"></a>
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21 <FONT color="green">018</FONT> <a name="line.18"></a>
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22 <FONT color="green">019</FONT> import java.util.Arrays;<a name="line.19"></a>
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23 <FONT color="green">020</FONT> <a name="line.20"></a>
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24 <FONT color="green">021</FONT> import org.apache.commons.math.ArgumentOutsideDomainException;<a name="line.21"></a>
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25 <FONT color="green">022</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.22"></a>
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26 <FONT color="green">023</FONT> import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;<a name="line.23"></a>
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27 <FONT color="green">024</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.24"></a>
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28 <FONT color="green">025</FONT> <a name="line.25"></a>
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29 <FONT color="green">026</FONT> /**<a name="line.26"></a>
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30 <FONT color="green">027</FONT> * Represents a polynomial spline function.<a name="line.27"></a>
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31 <FONT color="green">028</FONT> * <p><a name="line.28"></a>
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32 <FONT color="green">029</FONT> * A <strong>polynomial spline function</strong> consists of a set of<a name="line.29"></a>
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33 <FONT color="green">030</FONT> * <i>interpolating polynomials</i> and an ascending array of domain<a name="line.30"></a>
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34 <FONT color="green">031</FONT> * <i>knot points</i>, determining the intervals over which the spline function<a name="line.31"></a>
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35 <FONT color="green">032</FONT> * is defined by the constituent polynomials. The polynomials are assumed to<a name="line.32"></a>
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36 <FONT color="green">033</FONT> * have been computed to match the values of another function at the knot<a name="line.33"></a>
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37 <FONT color="green">034</FONT> * points. The value consistency constraints are not currently enforced by<a name="line.34"></a>
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38 <FONT color="green">035</FONT> * <code>PolynomialSplineFunction</code> itself, but are assumed to hold among<a name="line.35"></a>
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39 <FONT color="green">036</FONT> * the polynomials and knot points passed to the constructor.</p><a name="line.36"></a>
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40 <FONT color="green">037</FONT> * <p><a name="line.37"></a>
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41 <FONT color="green">038</FONT> * N.B.: The polynomials in the <code>polynomials</code> property must be<a name="line.38"></a>
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42 <FONT color="green">039</FONT> * centered on the knot points to compute the spline function values.<a name="line.39"></a>
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43 <FONT color="green">040</FONT> * See below.</p><a name="line.40"></a>
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44 <FONT color="green">041</FONT> * <p><a name="line.41"></a>
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45 <FONT color="green">042</FONT> * The domain of the polynomial spline function is<a name="line.42"></a>
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46 <FONT color="green">043</FONT> * <code>[smallest knot, largest knot]</code>. Attempts to evaluate the<a name="line.43"></a>
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47 <FONT color="green">044</FONT> * function at values outside of this range generate IllegalArgumentExceptions.<a name="line.44"></a>
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48 <FONT color="green">045</FONT> * </p><a name="line.45"></a>
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49 <FONT color="green">046</FONT> * <p><a name="line.46"></a>
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50 <FONT color="green">047</FONT> * The value of the polynomial spline function for an argument <code>x</code><a name="line.47"></a>
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51 <FONT color="green">048</FONT> * is computed as follows:<a name="line.48"></a>
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52 <FONT color="green">049</FONT> * <ol><a name="line.49"></a>
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53 <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>
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54 <FONT color="green">051</FONT> * belongs. If <code>x</code> is less than the smallest knot point or greater<a name="line.51"></a>
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55 <FONT color="green">052</FONT> * than the largest one, an <code>IllegalArgumentException</code><a name="line.52"></a>
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56 <FONT color="green">053</FONT> * is thrown.</li><a name="line.53"></a>
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57 <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>
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58 <FONT color="green">055</FONT> * than or equal to <code>x</code>. The value returned is <br><a name="line.55"></a>
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59 <FONT color="green">056</FONT> * <code>polynomials[j](x - knot[j])</code></li></ol></p><a name="line.56"></a>
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60 <FONT color="green">057</FONT> *<a name="line.57"></a>
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61 <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>
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62 <FONT color="green">059</FONT> */<a name="line.59"></a>
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63 <FONT color="green">060</FONT> public class PolynomialSplineFunction<a name="line.60"></a>
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64 <FONT color="green">061</FONT> implements DifferentiableUnivariateRealFunction {<a name="line.61"></a>
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65 <FONT color="green">062</FONT> <a name="line.62"></a>
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66 <FONT color="green">063</FONT> /** Spline segment interval delimiters (knots). Size is n+1 for n segments. */<a name="line.63"></a>
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67 <FONT color="green">064</FONT> private final double knots[];<a name="line.64"></a>
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68 <FONT color="green">065</FONT> <a name="line.65"></a>
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69 <FONT color="green">066</FONT> /**<a name="line.66"></a>
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70 <FONT color="green">067</FONT> * The polynomial functions that make up the spline. The first element<a name="line.67"></a>
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71 <FONT color="green">068</FONT> * determines the value of the spline over the first subinterval, the<a name="line.68"></a>
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72 <FONT color="green">069</FONT> * second over the second, etc. Spline function values are determined by<a name="line.69"></a>
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73 <FONT color="green">070</FONT> * evaluating these functions at <code>(x - knot[i])</code> where i is the<a name="line.70"></a>
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74 <FONT color="green">071</FONT> * knot segment to which x belongs.<a name="line.71"></a>
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75 <FONT color="green">072</FONT> */<a name="line.72"></a>
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76 <FONT color="green">073</FONT> private final PolynomialFunction polynomials[];<a name="line.73"></a>
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77 <FONT color="green">074</FONT> <a name="line.74"></a>
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78 <FONT color="green">075</FONT> /**<a name="line.75"></a>
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79 <FONT color="green">076</FONT> * Number of spline segments = number of polynomials<a name="line.76"></a>
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80 <FONT color="green">077</FONT> * = number of partition points - 1<a name="line.77"></a>
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81 <FONT color="green">078</FONT> */<a name="line.78"></a>
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82 <FONT color="green">079</FONT> private final int n;<a name="line.79"></a>
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83 <FONT color="green">080</FONT> <a name="line.80"></a>
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84 <FONT color="green">081</FONT> <a name="line.81"></a>
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85 <FONT color="green">082</FONT> /**<a name="line.82"></a>
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86 <FONT color="green">083</FONT> * Construct a polynomial spline function with the given segment delimiters<a name="line.83"></a>
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87 <FONT color="green">084</FONT> * and interpolating polynomials.<a name="line.84"></a>
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88 <FONT color="green">085</FONT> * <p><a name="line.85"></a>
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89 <FONT color="green">086</FONT> * The constructor copies both arrays and assigns the copies to the knots<a name="line.86"></a>
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90 <FONT color="green">087</FONT> * and polynomials properties, respectively.</p><a name="line.87"></a>
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91 <FONT color="green">088</FONT> *<a name="line.88"></a>
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92 <FONT color="green">089</FONT> * @param knots spline segment interval delimiters<a name="line.89"></a>
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93 <FONT color="green">090</FONT> * @param polynomials polynomial functions that make up the spline<a name="line.90"></a>
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94 <FONT color="green">091</FONT> * @throws NullPointerException if either of the input arrays is null<a name="line.91"></a>
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95 <FONT color="green">092</FONT> * @throws IllegalArgumentException if knots has length less than 2,<a name="line.92"></a>
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96 <FONT color="green">093</FONT> * <code>polynomials.length != knots.length - 1 </code>, or the knots array<a name="line.93"></a>
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97 <FONT color="green">094</FONT> * is not strictly increasing.<a name="line.94"></a>
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98 <FONT color="green">095</FONT> *<a name="line.95"></a>
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99 <FONT color="green">096</FONT> */<a name="line.96"></a>
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100 <FONT color="green">097</FONT> public PolynomialSplineFunction(double knots[], PolynomialFunction polynomials[]) {<a name="line.97"></a>
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101 <FONT color="green">098</FONT> if (knots.length < 2) {<a name="line.98"></a>
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102 <FONT color="green">099</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.99"></a>
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103 <FONT color="green">100</FONT> "spline partition must have at least {0} points, got {1}",<a name="line.100"></a>
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104 <FONT color="green">101</FONT> 2, knots.length);<a name="line.101"></a>
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105 <FONT color="green">102</FONT> }<a name="line.102"></a>
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106 <FONT color="green">103</FONT> if (knots.length - 1 != polynomials.length) {<a name="line.103"></a>
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107 <FONT color="green">104</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.104"></a>
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108 <FONT color="green">105</FONT> "number of polynomial interpolants must match the number of segments ({0} != {1} - 1)",<a name="line.105"></a>
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109 <FONT color="green">106</FONT> polynomials.length, knots.length);<a name="line.106"></a>
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110 <FONT color="green">107</FONT> }<a name="line.107"></a>
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111 <FONT color="green">108</FONT> if (!isStrictlyIncreasing(knots)) {<a name="line.108"></a>
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112 <FONT color="green">109</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.109"></a>
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113 <FONT color="green">110</FONT> "knot values must be strictly increasing");<a name="line.110"></a>
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114 <FONT color="green">111</FONT> }<a name="line.111"></a>
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115 <FONT color="green">112</FONT> <a name="line.112"></a>
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116 <FONT color="green">113</FONT> this.n = knots.length -1;<a name="line.113"></a>
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117 <FONT color="green">114</FONT> this.knots = new double[n + 1];<a name="line.114"></a>
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118 <FONT color="green">115</FONT> System.arraycopy(knots, 0, this.knots, 0, n + 1);<a name="line.115"></a>
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119 <FONT color="green">116</FONT> this.polynomials = new PolynomialFunction[n];<a name="line.116"></a>
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120 <FONT color="green">117</FONT> System.arraycopy(polynomials, 0, this.polynomials, 0, n);<a name="line.117"></a>
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121 <FONT color="green">118</FONT> }<a name="line.118"></a>
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122 <FONT color="green">119</FONT> <a name="line.119"></a>
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123 <FONT color="green">120</FONT> /**<a name="line.120"></a>
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124 <FONT color="green">121</FONT> * Compute the value for the function.<a name="line.121"></a>
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125 <FONT color="green">122</FONT> * <p><a name="line.122"></a>
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126 <FONT color="green">123</FONT> * Throws FunctionEvaluationException if v is outside of the domain of the<a name="line.123"></a>
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127 <FONT color="green">124</FONT> * function. The domain is [smallest knot, largest knot].</p><a name="line.124"></a>
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128 <FONT color="green">125</FONT> * <p><a name="line.125"></a>
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129 <FONT color="green">126</FONT> * See {@link PolynomialSplineFunction} for details on the algorithm for<a name="line.126"></a>
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130 <FONT color="green">127</FONT> * computing the value of the function.</p><a name="line.127"></a>
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131 <FONT color="green">128</FONT> *<a name="line.128"></a>
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132 <FONT color="green">129</FONT> * @param v the point for which the function value should be computed<a name="line.129"></a>
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133 <FONT color="green">130</FONT> * @return the value<a name="line.130"></a>
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134 <FONT color="green">131</FONT> * @throws ArgumentOutsideDomainException if v is outside of the domain of<a name="line.131"></a>
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135 <FONT color="green">132</FONT> * of the spline function (less than the smallest knot point or greater<a name="line.132"></a>
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136 <FONT color="green">133</FONT> * than the largest knot point)<a name="line.133"></a>
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137 <FONT color="green">134</FONT> */<a name="line.134"></a>
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138 <FONT color="green">135</FONT> public double value(double v) throws ArgumentOutsideDomainException {<a name="line.135"></a>
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139 <FONT color="green">136</FONT> if (v < knots[0] || v > knots[n]) {<a name="line.136"></a>
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140 <FONT color="green">137</FONT> throw new ArgumentOutsideDomainException(v, knots[0], knots[n]);<a name="line.137"></a>
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141 <FONT color="green">138</FONT> }<a name="line.138"></a>
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142 <FONT color="green">139</FONT> int i = Arrays.binarySearch(knots, v);<a name="line.139"></a>
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143 <FONT color="green">140</FONT> if (i < 0) {<a name="line.140"></a>
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144 <FONT color="green">141</FONT> i = -i - 2;<a name="line.141"></a>
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145 <FONT color="green">142</FONT> }<a name="line.142"></a>
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146 <FONT color="green">143</FONT> //This will handle the case where v is the last knot value<a name="line.143"></a>
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147 <FONT color="green">144</FONT> //There are only n-1 polynomials, so if v is the last knot<a name="line.144"></a>
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148 <FONT color="green">145</FONT> //then we will use the last polynomial to calculate the value.<a name="line.145"></a>
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149 <FONT color="green">146</FONT> if ( i >= polynomials.length ) {<a name="line.146"></a>
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150 <FONT color="green">147</FONT> i--;<a name="line.147"></a>
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151 <FONT color="green">148</FONT> }<a name="line.148"></a>
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152 <FONT color="green">149</FONT> return polynomials[i].value(v - knots[i]);<a name="line.149"></a>
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153 <FONT color="green">150</FONT> }<a name="line.150"></a>
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154 <FONT color="green">151</FONT> <a name="line.151"></a>
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155 <FONT color="green">152</FONT> /**<a name="line.152"></a>
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156 <FONT color="green">153</FONT> * Returns the derivative of the polynomial spline function as a UnivariateRealFunction<a name="line.153"></a>
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157 <FONT color="green">154</FONT> * @return the derivative function<a name="line.154"></a>
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158 <FONT color="green">155</FONT> */<a name="line.155"></a>
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159 <FONT color="green">156</FONT> public UnivariateRealFunction derivative() {<a name="line.156"></a>
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160 <FONT color="green">157</FONT> return polynomialSplineDerivative();<a name="line.157"></a>
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161 <FONT color="green">158</FONT> }<a name="line.158"></a>
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162 <FONT color="green">159</FONT> <a name="line.159"></a>
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163 <FONT color="green">160</FONT> /**<a name="line.160"></a>
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164 <FONT color="green">161</FONT> * Returns the derivative of the polynomial spline function as a PolynomialSplineFunction<a name="line.161"></a>
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165 <FONT color="green">162</FONT> *<a name="line.162"></a>
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166 <FONT color="green">163</FONT> * @return the derivative function<a name="line.163"></a>
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167 <FONT color="green">164</FONT> */<a name="line.164"></a>
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168 <FONT color="green">165</FONT> public PolynomialSplineFunction polynomialSplineDerivative() {<a name="line.165"></a>
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169 <FONT color="green">166</FONT> PolynomialFunction derivativePolynomials[] = new PolynomialFunction[n];<a name="line.166"></a>
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170 <FONT color="green">167</FONT> for (int i = 0; i < n; i++) {<a name="line.167"></a>
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171 <FONT color="green">168</FONT> derivativePolynomials[i] = polynomials[i].polynomialDerivative();<a name="line.168"></a>
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172 <FONT color="green">169</FONT> }<a name="line.169"></a>
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173 <FONT color="green">170</FONT> return new PolynomialSplineFunction(knots, derivativePolynomials);<a name="line.170"></a>
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174 <FONT color="green">171</FONT> }<a name="line.171"></a>
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175 <FONT color="green">172</FONT> <a name="line.172"></a>
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176 <FONT color="green">173</FONT> /**<a name="line.173"></a>
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177 <FONT color="green">174</FONT> * Returns the number of spline segments = the number of polynomials<a name="line.174"></a>
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178 <FONT color="green">175</FONT> * = the number of knot points - 1.<a name="line.175"></a>
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179 <FONT color="green">176</FONT> *<a name="line.176"></a>
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180 <FONT color="green">177</FONT> * @return the number of spline segments<a name="line.177"></a>
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181 <FONT color="green">178</FONT> */<a name="line.178"></a>
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182 <FONT color="green">179</FONT> public int getN() {<a name="line.179"></a>
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183 <FONT color="green">180</FONT> return n;<a name="line.180"></a>
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184 <FONT color="green">181</FONT> }<a name="line.181"></a>
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185 <FONT color="green">182</FONT> <a name="line.182"></a>
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186 <FONT color="green">183</FONT> /**<a name="line.183"></a>
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187 <FONT color="green">184</FONT> * Returns a copy of the interpolating polynomials array.<a name="line.184"></a>
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188 <FONT color="green">185</FONT> * <p><a name="line.185"></a>
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189 <FONT color="green">186</FONT> * Returns a fresh copy of the array. Changes made to the copy will<a name="line.186"></a>
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190 <FONT color="green">187</FONT> * not affect the polynomials property.</p><a name="line.187"></a>
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191 <FONT color="green">188</FONT> *<a name="line.188"></a>
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192 <FONT color="green">189</FONT> * @return the interpolating polynomials<a name="line.189"></a>
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193 <FONT color="green">190</FONT> */<a name="line.190"></a>
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194 <FONT color="green">191</FONT> public PolynomialFunction[] getPolynomials() {<a name="line.191"></a>
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195 <FONT color="green">192</FONT> PolynomialFunction p[] = new PolynomialFunction[n];<a name="line.192"></a>
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196 <FONT color="green">193</FONT> System.arraycopy(polynomials, 0, p, 0, n);<a name="line.193"></a>
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197 <FONT color="green">194</FONT> return p;<a name="line.194"></a>
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198 <FONT color="green">195</FONT> }<a name="line.195"></a>
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199 <FONT color="green">196</FONT> <a name="line.196"></a>
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200 <FONT color="green">197</FONT> /**<a name="line.197"></a>
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201 <FONT color="green">198</FONT> * Returns an array copy of the knot points.<a name="line.198"></a>
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202 <FONT color="green">199</FONT> * <p><a name="line.199"></a>
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203 <FONT color="green">200</FONT> * Returns a fresh copy of the array. Changes made to the copy<a name="line.200"></a>
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204 <FONT color="green">201</FONT> * will not affect the knots property.</p><a name="line.201"></a>
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205 <FONT color="green">202</FONT> *<a name="line.202"></a>
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206 <FONT color="green">203</FONT> * @return the knot points<a name="line.203"></a>
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207 <FONT color="green">204</FONT> */<a name="line.204"></a>
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208 <FONT color="green">205</FONT> public double[] getKnots() {<a name="line.205"></a>
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209 <FONT color="green">206</FONT> double out[] = new double[n + 1];<a name="line.206"></a>
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210 <FONT color="green">207</FONT> System.arraycopy(knots, 0, out, 0, n + 1);<a name="line.207"></a>
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211 <FONT color="green">208</FONT> return out;<a name="line.208"></a>
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212 <FONT color="green">209</FONT> }<a name="line.209"></a>
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213 <FONT color="green">210</FONT> <a name="line.210"></a>
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214 <FONT color="green">211</FONT> /**<a name="line.211"></a>
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215 <FONT color="green">212</FONT> * Determines if the given array is ordered in a strictly increasing<a name="line.212"></a>
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216 <FONT color="green">213</FONT> * fashion.<a name="line.213"></a>
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217 <FONT color="green">214</FONT> *<a name="line.214"></a>
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218 <FONT color="green">215</FONT> * @param x the array to examine.<a name="line.215"></a>
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219 <FONT color="green">216</FONT> * @return <code>true</code> if the elements in <code>x</code> are ordered<a name="line.216"></a>
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220 <FONT color="green">217</FONT> * in a stricly increasing manner. <code>false</code>, otherwise.<a name="line.217"></a>
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221 <FONT color="green">218</FONT> */<a name="line.218"></a>
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222 <FONT color="green">219</FONT> private static boolean isStrictlyIncreasing(double[] x) {<a name="line.219"></a>
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223 <FONT color="green">220</FONT> for (int i = 1; i < x.length; ++i) {<a name="line.220"></a>
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224 <FONT color="green">221</FONT> if (x[i - 1] >= x[i]) {<a name="line.221"></a>
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225 <FONT color="green">222</FONT> return false;<a name="line.222"></a>
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226 <FONT color="green">223</FONT> }<a name="line.223"></a>
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227 <FONT color="green">224</FONT> }<a name="line.224"></a>
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228 <FONT color="green">225</FONT> return true;<a name="line.225"></a>
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229 <FONT color="green">226</FONT> }<a name="line.226"></a>
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230 <FONT color="green">227</FONT> }<a name="line.227"></a>
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291 </PRE>
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292 </BODY>
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293 </HTML>
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