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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> <a name="line.17"></a>
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21 <FONT color="green">018</FONT> package org.apache.commons.math.linear;<a name="line.18"></a>
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22 <FONT color="green">019</FONT> <a name="line.19"></a>
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23 <FONT color="green">020</FONT> import java.util.Arrays;<a name="line.20"></a>
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24 <FONT color="green">021</FONT> <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> <a name="line.23"></a>
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27 <FONT color="green">024</FONT> <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> * Calculates the QR-decomposition of a matrix.<a name="line.26"></a>
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30 <FONT color="green">027</FONT> * <p>The QR-decomposition of a matrix A consists of two matrices Q and R<a name="line.27"></a>
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31 <FONT color="green">028</FONT> * that satisfy: A = QR, Q is orthogonal (Q<sup>T</sup>Q = I), and R is<a name="line.28"></a>
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32 <FONT color="green">029</FONT> * upper triangular. If A is m&times;n, Q is m&times;m and R m&times;n.</p><a name="line.29"></a>
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33 <FONT color="green">030</FONT> * <p>This class compute the decomposition using Householder reflectors.</p><a name="line.30"></a>
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34 <FONT color="green">031</FONT> * <p>For efficiency purposes, the decomposition in packed form is transposed.<a name="line.31"></a>
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35 <FONT color="green">032</FONT> * This allows inner loop to iterate inside rows, which is much more cache-efficient<a name="line.32"></a>
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36 <FONT color="green">033</FONT> * in Java.</p><a name="line.33"></a>
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37 <FONT color="green">034</FONT> *<a name="line.34"></a>
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38 <FONT color="green">035</FONT> * @see <a href="http://mathworld.wolfram.com/QRDecomposition.html">MathWorld</a><a name="line.35"></a>
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39 <FONT color="green">036</FONT> * @see <a href="http://en.wikipedia.org/wiki/QR_decomposition">Wikipedia</a><a name="line.36"></a>
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40 <FONT color="green">037</FONT> *<a name="line.37"></a>
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41 <FONT color="green">038</FONT> * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $<a name="line.38"></a>
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42 <FONT color="green">039</FONT> * @since 1.2<a name="line.39"></a>
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43 <FONT color="green">040</FONT> */<a name="line.40"></a>
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44 <FONT color="green">041</FONT> public class QRDecompositionImpl implements QRDecomposition {<a name="line.41"></a>
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45 <FONT color="green">042</FONT> <a name="line.42"></a>
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46 <FONT color="green">043</FONT> /**<a name="line.43"></a>
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47 <FONT color="green">044</FONT> * A packed TRANSPOSED representation of the QR decomposition.<a name="line.44"></a>
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48 <FONT color="green">045</FONT> * <p>The elements BELOW the diagonal are the elements of the UPPER triangular<a name="line.45"></a>
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49 <FONT color="green">046</FONT> * matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors<a name="line.46"></a>
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50 <FONT color="green">047</FONT> * from which an explicit form of Q can be recomputed if desired.</p><a name="line.47"></a>
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51 <FONT color="green">048</FONT> */<a name="line.48"></a>
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52 <FONT color="green">049</FONT> private double[][] qrt;<a name="line.49"></a>
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53 <FONT color="green">050</FONT> <a name="line.50"></a>
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54 <FONT color="green">051</FONT> /** The diagonal elements of R. */<a name="line.51"></a>
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55 <FONT color="green">052</FONT> private double[] rDiag;<a name="line.52"></a>
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56 <FONT color="green">053</FONT> <a name="line.53"></a>
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57 <FONT color="green">054</FONT> /** Cached value of Q. */<a name="line.54"></a>
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58 <FONT color="green">055</FONT> private RealMatrix cachedQ;<a name="line.55"></a>
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59 <FONT color="green">056</FONT> <a name="line.56"></a>
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60 <FONT color="green">057</FONT> /** Cached value of QT. */<a name="line.57"></a>
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61 <FONT color="green">058</FONT> private RealMatrix cachedQT;<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> /** Cached value of R. */<a name="line.60"></a>
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64 <FONT color="green">061</FONT> private RealMatrix cachedR;<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> /** Cached value of H. */<a name="line.63"></a>
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67 <FONT color="green">064</FONT> private RealMatrix cachedH;<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> * Calculates the QR-decomposition of the given matrix.<a name="line.67"></a>
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71 <FONT color="green">068</FONT> * @param matrix The matrix to decompose.<a name="line.68"></a>
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72 <FONT color="green">069</FONT> */<a name="line.69"></a>
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73 <FONT color="green">070</FONT> public QRDecompositionImpl(RealMatrix matrix) {<a name="line.70"></a>
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74 <FONT color="green">071</FONT> <a name="line.71"></a>
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75 <FONT color="green">072</FONT> final int m = matrix.getRowDimension();<a name="line.72"></a>
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76 <FONT color="green">073</FONT> final int n = matrix.getColumnDimension();<a name="line.73"></a>
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77 <FONT color="green">074</FONT> qrt = matrix.transpose().getData();<a name="line.74"></a>
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78 <FONT color="green">075</FONT> rDiag = new double[Math.min(m, n)];<a name="line.75"></a>
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79 <FONT color="green">076</FONT> cachedQ = null;<a name="line.76"></a>
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80 <FONT color="green">077</FONT> cachedQT = null;<a name="line.77"></a>
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81 <FONT color="green">078</FONT> cachedR = null;<a name="line.78"></a>
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82 <FONT color="green">079</FONT> cachedH = null;<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> * The QR decomposition of a matrix A is calculated using Householder<a name="line.82"></a>
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86 <FONT color="green">083</FONT> * reflectors by repeating the following operations to each minor<a name="line.83"></a>
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87 <FONT color="green">084</FONT> * A(minor,minor) of A:<a name="line.84"></a>
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88 <FONT color="green">085</FONT> */<a name="line.85"></a>
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89 <FONT color="green">086</FONT> for (int minor = 0; minor < Math.min(m, n); minor++) {<a name="line.86"></a>
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90 <FONT color="green">087</FONT> <a name="line.87"></a>
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91 <FONT color="green">088</FONT> final double[] qrtMinor = qrt[minor];<a name="line.88"></a>
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92 <FONT color="green">089</FONT> <a name="line.89"></a>
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93 <FONT color="green">090</FONT> /*<a name="line.90"></a>
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94 <FONT color="green">091</FONT> * Let x be the first column of the minor, and a^2 = |x|^2.<a name="line.91"></a>
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95 <FONT color="green">092</FONT> * x will be in the positions qr[minor][minor] through qr[m][minor].<a name="line.92"></a>
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96 <FONT color="green">093</FONT> * The first column of the transformed minor will be (a,0,0,..)'<a name="line.93"></a>
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97 <FONT color="green">094</FONT> * The sign of a is chosen to be opposite to the sign of the first<a name="line.94"></a>
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98 <FONT color="green">095</FONT> * component of x. Let's find a:<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> double xNormSqr = 0;<a name="line.97"></a>
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101 <FONT color="green">098</FONT> for (int row = minor; row < m; row++) {<a name="line.98"></a>
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102 <FONT color="green">099</FONT> final double c = qrtMinor[row];<a name="line.99"></a>
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103 <FONT color="green">100</FONT> xNormSqr += c * c;<a name="line.100"></a>
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104 <FONT color="green">101</FONT> }<a name="line.101"></a>
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105 <FONT color="green">102</FONT> final double a = (qrtMinor[minor] > 0) ? -Math.sqrt(xNormSqr) : Math.sqrt(xNormSqr);<a name="line.102"></a>
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106 <FONT color="green">103</FONT> rDiag[minor] = a;<a name="line.103"></a>
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107 <FONT color="green">104</FONT> <a name="line.104"></a>
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108 <FONT color="green">105</FONT> if (a != 0.0) {<a name="line.105"></a>
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109 <FONT color="green">106</FONT> <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> * Calculate the normalized reflection vector v and transform<a name="line.108"></a>
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112 <FONT color="green">109</FONT> * the first column. We know the norm of v beforehand: v = x-ae<a name="line.109"></a>
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113 <FONT color="green">110</FONT> * so |v|^2 = <x-ae,x-ae> = <x,x>-2a<x,e>+a^2<e,e> =<a name="line.110"></a>
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114 <FONT color="green">111</FONT> * a^2+a^2-2a<x,e> = 2a*(a - <x,e>).<a name="line.111"></a>
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115 <FONT color="green">112</FONT> * Here <x, e> is now qr[minor][minor].<a name="line.112"></a>
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116 <FONT color="green">113</FONT> * v = x-ae is stored in the column at qr:<a name="line.113"></a>
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117 <FONT color="green">114</FONT> */<a name="line.114"></a>
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118 <FONT color="green">115</FONT> qrtMinor[minor] -= a; // now |v|^2 = -2a*(qr[minor][minor])<a name="line.115"></a>
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119 <FONT color="green">116</FONT> <a name="line.116"></a>
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120 <FONT color="green">117</FONT> /*<a name="line.117"></a>
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121 <FONT color="green">118</FONT> * Transform the rest of the columns of the minor:<a name="line.118"></a>
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122 <FONT color="green">119</FONT> * They will be transformed by the matrix H = I-2vv'/|v|^2.<a name="line.119"></a>
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123 <FONT color="green">120</FONT> * If x is a column vector of the minor, then<a name="line.120"></a>
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124 <FONT color="green">121</FONT> * Hx = (I-2vv'/|v|^2)x = x-2vv'x/|v|^2 = x - 2<x,v>/|v|^2 v.<a name="line.121"></a>
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125 <FONT color="green">122</FONT> * Therefore the transformation is easily calculated by<a name="line.122"></a>
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126 <FONT color="green">123</FONT> * subtracting the column vector (2<x,v>/|v|^2)v from x.<a name="line.123"></a>
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127 <FONT color="green">124</FONT> *<a name="line.124"></a>
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128 <FONT color="green">125</FONT> * Let 2<x,v>/|v|^2 = alpha. From above we have<a name="line.125"></a>
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129 <FONT color="green">126</FONT> * |v|^2 = -2a*(qr[minor][minor]), so<a name="line.126"></a>
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130 <FONT color="green">127</FONT> * alpha = -<x,v>/(a*qr[minor][minor])<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> for (int col = minor+1; col < n; col++) {<a name="line.129"></a>
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133 <FONT color="green">130</FONT> final double[] qrtCol = qrt[col];<a name="line.130"></a>
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134 <FONT color="green">131</FONT> double alpha = 0;<a name="line.131"></a>
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135 <FONT color="green">132</FONT> for (int row = minor; row < m; row++) {<a name="line.132"></a>
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136 <FONT color="green">133</FONT> alpha -= qrtCol[row] * qrtMinor[row];<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> alpha /= a * qrtMinor[minor];<a name="line.135"></a>
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139 <FONT color="green">136</FONT> <a name="line.136"></a>
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140 <FONT color="green">137</FONT> // Subtract the column vector alpha*v from x.<a name="line.137"></a>
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141 <FONT color="green">138</FONT> for (int row = minor; row < m; row++) {<a name="line.138"></a>
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142 <FONT color="green">139</FONT> qrtCol[row] -= alpha * qrtMinor[row];<a name="line.139"></a>
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143 <FONT color="green">140</FONT> }<a name="line.140"></a>
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144 <FONT color="green">141</FONT> }<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> }<a name="line.143"></a>
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147 <FONT color="green">144</FONT> }<a name="line.144"></a>
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148 <FONT color="green">145</FONT> <a name="line.145"></a>
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149 <FONT color="green">146</FONT> /** {@inheritDoc} */<a name="line.146"></a>
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150 <FONT color="green">147</FONT> public RealMatrix getR() {<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> if (cachedR == null) {<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> // R is supposed to be m x n<a name="line.151"></a>
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155 <FONT color="green">152</FONT> final int n = qrt.length;<a name="line.152"></a>
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156 <FONT color="green">153</FONT> final int m = qrt[0].length;<a name="line.153"></a>
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157 <FONT color="green">154</FONT> cachedR = MatrixUtils.createRealMatrix(m, n);<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> // copy the diagonal from rDiag and the upper triangle of qr<a name="line.156"></a>
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160 <FONT color="green">157</FONT> for (int row = Math.min(m, n) - 1; row >= 0; row--) {<a name="line.157"></a>
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161 <FONT color="green">158</FONT> cachedR.setEntry(row, row, rDiag[row]);<a name="line.158"></a>
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162 <FONT color="green">159</FONT> for (int col = row + 1; col < n; col++) {<a name="line.159"></a>
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163 <FONT color="green">160</FONT> cachedR.setEntry(row, col, qrt[col][row]);<a name="line.160"></a>
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164 <FONT color="green">161</FONT> }<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> <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> <a name="line.165"></a>
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169 <FONT color="green">166</FONT> // return the cached matrix<a name="line.166"></a>
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170 <FONT color="green">167</FONT> return cachedR;<a name="line.167"></a>
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171 <FONT color="green">168</FONT> <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> <a name="line.170"></a>
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174 <FONT color="green">171</FONT> /** {@inheritDoc} */<a name="line.171"></a>
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175 <FONT color="green">172</FONT> public RealMatrix getQ() {<a name="line.172"></a>
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176 <FONT color="green">173</FONT> if (cachedQ == null) {<a name="line.173"></a>
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177 <FONT color="green">174</FONT> cachedQ = getQT().transpose();<a name="line.174"></a>
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178 <FONT color="green">175</FONT> }<a name="line.175"></a>
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179 <FONT color="green">176</FONT> return cachedQ;<a name="line.176"></a>
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180 <FONT color="green">177</FONT> }<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> /** {@inheritDoc} */<a name="line.179"></a>
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183 <FONT color="green">180</FONT> public RealMatrix getQT() {<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> if (cachedQT == null) {<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> // QT is supposed to be m x m<a name="line.184"></a>
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188 <FONT color="green">185</FONT> final int n = qrt.length;<a name="line.185"></a>
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189 <FONT color="green">186</FONT> final int m = qrt[0].length;<a name="line.186"></a>
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190 <FONT color="green">187</FONT> cachedQT = MatrixUtils.createRealMatrix(m, m);<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> /*<a name="line.189"></a>
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193 <FONT color="green">190</FONT> * Q = Q1 Q2 ... Q_m, so Q is formed by first constructing Q_m and then<a name="line.190"></a>
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194 <FONT color="green">191</FONT> * applying the Householder transformations Q_(m-1),Q_(m-2),...,Q1 in<a name="line.191"></a>
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195 <FONT color="green">192</FONT> * succession to the result<a name="line.192"></a>
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196 <FONT color="green">193</FONT> */<a name="line.193"></a>
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197 <FONT color="green">194</FONT> for (int minor = m - 1; minor >= Math.min(m, n); minor--) {<a name="line.194"></a>
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198 <FONT color="green">195</FONT> cachedQT.setEntry(minor, minor, 1.0);<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> for (int minor = Math.min(m, n)-1; minor >= 0; minor--){<a name="line.198"></a>
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202 <FONT color="green">199</FONT> final double[] qrtMinor = qrt[minor];<a name="line.199"></a>
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203 <FONT color="green">200</FONT> cachedQT.setEntry(minor, minor, 1.0);<a name="line.200"></a>
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204 <FONT color="green">201</FONT> if (qrtMinor[minor] != 0.0) {<a name="line.201"></a>
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205 <FONT color="green">202</FONT> for (int col = minor; col < m; col++) {<a name="line.202"></a>
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206 <FONT color="green">203</FONT> double alpha = 0;<a name="line.203"></a>
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207 <FONT color="green">204</FONT> for (int row = minor; row < m; row++) {<a name="line.204"></a>
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208 <FONT color="green">205</FONT> alpha -= cachedQT.getEntry(col, row) * qrtMinor[row];<a name="line.205"></a>
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209 <FONT color="green">206</FONT> }<a name="line.206"></a>
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210 <FONT color="green">207</FONT> alpha /= rDiag[minor] * qrtMinor[minor];<a name="line.207"></a>
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211 <FONT color="green">208</FONT> <a name="line.208"></a>
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212 <FONT color="green">209</FONT> for (int row = minor; row < m; row++) {<a name="line.209"></a>
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213 <FONT color="green">210</FONT> cachedQT.addToEntry(col, row, -alpha * qrtMinor[row]);<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> }<a name="line.212"></a>
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216 <FONT color="green">213</FONT> }<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> <a name="line.215"></a>
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219 <FONT color="green">216</FONT> }<a name="line.216"></a>
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220 <FONT color="green">217</FONT> <a name="line.217"></a>
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221 <FONT color="green">218</FONT> // return the cached matrix<a name="line.218"></a>
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222 <FONT color="green">219</FONT> return cachedQT;<a name="line.219"></a>
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223 <FONT color="green">220</FONT> <a name="line.220"></a>
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224 <FONT color="green">221</FONT> }<a name="line.221"></a>
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225 <FONT color="green">222</FONT> <a name="line.222"></a>
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226 <FONT color="green">223</FONT> /** {@inheritDoc} */<a name="line.223"></a>
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227 <FONT color="green">224</FONT> public RealMatrix getH() {<a name="line.224"></a>
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228 <FONT color="green">225</FONT> <a name="line.225"></a>
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229 <FONT color="green">226</FONT> if (cachedH == null) {<a name="line.226"></a>
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230 <FONT color="green">227</FONT> <a name="line.227"></a>
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231 <FONT color="green">228</FONT> final int n = qrt.length;<a name="line.228"></a>
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232 <FONT color="green">229</FONT> final int m = qrt[0].length;<a name="line.229"></a>
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233 <FONT color="green">230</FONT> cachedH = MatrixUtils.createRealMatrix(m, n);<a name="line.230"></a>
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234 <FONT color="green">231</FONT> for (int i = 0; i < m; ++i) {<a name="line.231"></a>
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235 <FONT color="green">232</FONT> for (int j = 0; j < Math.min(i + 1, n); ++j) {<a name="line.232"></a>
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236 <FONT color="green">233</FONT> cachedH.setEntry(i, j, qrt[j][i] / -rDiag[j]);<a name="line.233"></a>
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237 <FONT color="green">234</FONT> }<a name="line.234"></a>
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238 <FONT color="green">235</FONT> }<a name="line.235"></a>
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239 <FONT color="green">236</FONT> <a name="line.236"></a>
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240 <FONT color="green">237</FONT> }<a name="line.237"></a>
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241 <FONT color="green">238</FONT> <a name="line.238"></a>
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242 <FONT color="green">239</FONT> // return the cached matrix<a name="line.239"></a>
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243 <FONT color="green">240</FONT> return cachedH;<a name="line.240"></a>
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244 <FONT color="green">241</FONT> <a name="line.241"></a>
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245 <FONT color="green">242</FONT> }<a name="line.242"></a>
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246 <FONT color="green">243</FONT> <a name="line.243"></a>
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247 <FONT color="green">244</FONT> /** {@inheritDoc} */<a name="line.244"></a>
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248 <FONT color="green">245</FONT> public DecompositionSolver getSolver() {<a name="line.245"></a>
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249 <FONT color="green">246</FONT> return new Solver(qrt, rDiag);<a name="line.246"></a>
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250 <FONT color="green">247</FONT> }<a name="line.247"></a>
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251 <FONT color="green">248</FONT> <a name="line.248"></a>
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252 <FONT color="green">249</FONT> /** Specialized solver. */<a name="line.249"></a>
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253 <FONT color="green">250</FONT> private static class Solver implements DecompositionSolver {<a name="line.250"></a>
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254 <FONT color="green">251</FONT> <a name="line.251"></a>
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255 <FONT color="green">252</FONT> /**<a name="line.252"></a>
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256 <FONT color="green">253</FONT> * A packed TRANSPOSED representation of the QR decomposition.<a name="line.253"></a>
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257 <FONT color="green">254</FONT> * <p>The elements BELOW the diagonal are the elements of the UPPER triangular<a name="line.254"></a>
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258 <FONT color="green">255</FONT> * matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors<a name="line.255"></a>
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259 <FONT color="green">256</FONT> * from which an explicit form of Q can be recomputed if desired.</p><a name="line.256"></a>
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260 <FONT color="green">257</FONT> */<a name="line.257"></a>
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261 <FONT color="green">258</FONT> private final double[][] qrt;<a name="line.258"></a>
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262 <FONT color="green">259</FONT> <a name="line.259"></a>
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263 <FONT color="green">260</FONT> /** The diagonal elements of R. */<a name="line.260"></a>
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264 <FONT color="green">261</FONT> private final double[] rDiag;<a name="line.261"></a>
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265 <FONT color="green">262</FONT> <a name="line.262"></a>
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266 <FONT color="green">263</FONT> /**<a name="line.263"></a>
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267 <FONT color="green">264</FONT> * Build a solver from decomposed matrix.<a name="line.264"></a>
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268 <FONT color="green">265</FONT> * @param qrt packed TRANSPOSED representation of the QR decomposition<a name="line.265"></a>
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269 <FONT color="green">266</FONT> * @param rDiag diagonal elements of R<a name="line.266"></a>
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270 <FONT color="green">267</FONT> */<a name="line.267"></a>
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271 <FONT color="green">268</FONT> private Solver(final double[][] qrt, final double[] rDiag) {<a name="line.268"></a>
|
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272 <FONT color="green">269</FONT> this.qrt = qrt;<a name="line.269"></a>
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273 <FONT color="green">270</FONT> this.rDiag = rDiag;<a name="line.270"></a>
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274 <FONT color="green">271</FONT> }<a name="line.271"></a>
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275 <FONT color="green">272</FONT> <a name="line.272"></a>
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276 <FONT color="green">273</FONT> /** {@inheritDoc} */<a name="line.273"></a>
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277 <FONT color="green">274</FONT> public boolean isNonSingular() {<a name="line.274"></a>
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278 <FONT color="green">275</FONT> <a name="line.275"></a>
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279 <FONT color="green">276</FONT> for (double diag : rDiag) {<a name="line.276"></a>
|
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280 <FONT color="green">277</FONT> if (diag == 0) {<a name="line.277"></a>
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281 <FONT color="green">278</FONT> return false;<a name="line.278"></a>
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282 <FONT color="green">279</FONT> }<a name="line.279"></a>
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283 <FONT color="green">280</FONT> }<a name="line.280"></a>
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284 <FONT color="green">281</FONT> return true;<a name="line.281"></a>
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285 <FONT color="green">282</FONT> <a name="line.282"></a>
|
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286 <FONT color="green">283</FONT> }<a name="line.283"></a>
|
|
287 <FONT color="green">284</FONT> <a name="line.284"></a>
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288 <FONT color="green">285</FONT> /** {@inheritDoc} */<a name="line.285"></a>
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289 <FONT color="green">286</FONT> public double[] solve(double[] b)<a name="line.286"></a>
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290 <FONT color="green">287</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.287"></a>
|
|
291 <FONT color="green">288</FONT> <a name="line.288"></a>
|
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292 <FONT color="green">289</FONT> final int n = qrt.length;<a name="line.289"></a>
|
|
293 <FONT color="green">290</FONT> final int m = qrt[0].length;<a name="line.290"></a>
|
|
294 <FONT color="green">291</FONT> if (b.length != m) {<a name="line.291"></a>
|
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295 <FONT color="green">292</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.292"></a>
|
|
296 <FONT color="green">293</FONT> "vector length mismatch: got {0} but expected {1}",<a name="line.293"></a>
|
|
297 <FONT color="green">294</FONT> b.length, m);<a name="line.294"></a>
|
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298 <FONT color="green">295</FONT> }<a name="line.295"></a>
|
|
299 <FONT color="green">296</FONT> if (!isNonSingular()) {<a name="line.296"></a>
|
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300 <FONT color="green">297</FONT> throw new SingularMatrixException();<a name="line.297"></a>
|
|
301 <FONT color="green">298</FONT> }<a name="line.298"></a>
|
|
302 <FONT color="green">299</FONT> <a name="line.299"></a>
|
|
303 <FONT color="green">300</FONT> final double[] x = new double[n];<a name="line.300"></a>
|
|
304 <FONT color="green">301</FONT> final double[] y = b.clone();<a name="line.301"></a>
|
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305 <FONT color="green">302</FONT> <a name="line.302"></a>
|
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306 <FONT color="green">303</FONT> // apply Householder transforms to solve Q.y = b<a name="line.303"></a>
|
|
307 <FONT color="green">304</FONT> for (int minor = 0; minor < Math.min(m, n); minor++) {<a name="line.304"></a>
|
|
308 <FONT color="green">305</FONT> <a name="line.305"></a>
|
|
309 <FONT color="green">306</FONT> final double[] qrtMinor = qrt[minor];<a name="line.306"></a>
|
|
310 <FONT color="green">307</FONT> double dotProduct = 0;<a name="line.307"></a>
|
|
311 <FONT color="green">308</FONT> for (int row = minor; row < m; row++) {<a name="line.308"></a>
|
|
312 <FONT color="green">309</FONT> dotProduct += y[row] * qrtMinor[row];<a name="line.309"></a>
|
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313 <FONT color="green">310</FONT> }<a name="line.310"></a>
|
|
314 <FONT color="green">311</FONT> dotProduct /= rDiag[minor] * qrtMinor[minor];<a name="line.311"></a>
|
|
315 <FONT color="green">312</FONT> <a name="line.312"></a>
|
|
316 <FONT color="green">313</FONT> for (int row = minor; row < m; row++) {<a name="line.313"></a>
|
|
317 <FONT color="green">314</FONT> y[row] += dotProduct * qrtMinor[row];<a name="line.314"></a>
|
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318 <FONT color="green">315</FONT> }<a name="line.315"></a>
|
|
319 <FONT color="green">316</FONT> <a name="line.316"></a>
|
|
320 <FONT color="green">317</FONT> }<a name="line.317"></a>
|
|
321 <FONT color="green">318</FONT> <a name="line.318"></a>
|
|
322 <FONT color="green">319</FONT> // solve triangular system R.x = y<a name="line.319"></a>
|
|
323 <FONT color="green">320</FONT> for (int row = rDiag.length - 1; row >= 0; --row) {<a name="line.320"></a>
|
|
324 <FONT color="green">321</FONT> y[row] /= rDiag[row];<a name="line.321"></a>
|
|
325 <FONT color="green">322</FONT> final double yRow = y[row];<a name="line.322"></a>
|
|
326 <FONT color="green">323</FONT> final double[] qrtRow = qrt[row];<a name="line.323"></a>
|
|
327 <FONT color="green">324</FONT> x[row] = yRow;<a name="line.324"></a>
|
|
328 <FONT color="green">325</FONT> for (int i = 0; i < row; i++) {<a name="line.325"></a>
|
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329 <FONT color="green">326</FONT> y[i] -= yRow * qrtRow[i];<a name="line.326"></a>
|
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330 <FONT color="green">327</FONT> }<a name="line.327"></a>
|
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331 <FONT color="green">328</FONT> }<a name="line.328"></a>
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332 <FONT color="green">329</FONT> <a name="line.329"></a>
|
|
333 <FONT color="green">330</FONT> return x;<a name="line.330"></a>
|
|
334 <FONT color="green">331</FONT> <a name="line.331"></a>
|
|
335 <FONT color="green">332</FONT> }<a name="line.332"></a>
|
|
336 <FONT color="green">333</FONT> <a name="line.333"></a>
|
|
337 <FONT color="green">334</FONT> /** {@inheritDoc} */<a name="line.334"></a>
|
|
338 <FONT color="green">335</FONT> public RealVector solve(RealVector b)<a name="line.335"></a>
|
|
339 <FONT color="green">336</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.336"></a>
|
|
340 <FONT color="green">337</FONT> try {<a name="line.337"></a>
|
|
341 <FONT color="green">338</FONT> return solve((ArrayRealVector) b);<a name="line.338"></a>
|
|
342 <FONT color="green">339</FONT> } catch (ClassCastException cce) {<a name="line.339"></a>
|
|
343 <FONT color="green">340</FONT> return new ArrayRealVector(solve(b.getData()), false);<a name="line.340"></a>
|
|
344 <FONT color="green">341</FONT> }<a name="line.341"></a>
|
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345 <FONT color="green">342</FONT> }<a name="line.342"></a>
|
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346 <FONT color="green">343</FONT> <a name="line.343"></a>
|
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347 <FONT color="green">344</FONT> /** Solve the linear equation A &times; X = B.<a name="line.344"></a>
|
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348 <FONT color="green">345</FONT> * <p>The A matrix is implicit here. It is </p><a name="line.345"></a>
|
|
349 <FONT color="green">346</FONT> * @param b right-hand side of the equation A &times; X = B<a name="line.346"></a>
|
|
350 <FONT color="green">347</FONT> * @return a vector X that minimizes the two norm of A &times; X - B<a name="line.347"></a>
|
|
351 <FONT color="green">348</FONT> * @throws IllegalArgumentException if matrices dimensions don't match<a name="line.348"></a>
|
|
352 <FONT color="green">349</FONT> * @throws InvalidMatrixException if decomposed matrix is singular<a name="line.349"></a>
|
|
353 <FONT color="green">350</FONT> */<a name="line.350"></a>
|
|
354 <FONT color="green">351</FONT> public ArrayRealVector solve(ArrayRealVector b)<a name="line.351"></a>
|
|
355 <FONT color="green">352</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.352"></a>
|
|
356 <FONT color="green">353</FONT> return new ArrayRealVector(solve(b.getDataRef()), false);<a name="line.353"></a>
|
|
357 <FONT color="green">354</FONT> }<a name="line.354"></a>
|
|
358 <FONT color="green">355</FONT> <a name="line.355"></a>
|
|
359 <FONT color="green">356</FONT> /** {@inheritDoc} */<a name="line.356"></a>
|
|
360 <FONT color="green">357</FONT> public RealMatrix solve(RealMatrix b)<a name="line.357"></a>
|
|
361 <FONT color="green">358</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.358"></a>
|
|
362 <FONT color="green">359</FONT> <a name="line.359"></a>
|
|
363 <FONT color="green">360</FONT> final int n = qrt.length;<a name="line.360"></a>
|
|
364 <FONT color="green">361</FONT> final int m = qrt[0].length;<a name="line.361"></a>
|
|
365 <FONT color="green">362</FONT> if (b.getRowDimension() != m) {<a name="line.362"></a>
|
|
366 <FONT color="green">363</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.363"></a>
|
|
367 <FONT color="green">364</FONT> "dimensions mismatch: got {0}x{1} but expected {2}x{3}",<a name="line.364"></a>
|
|
368 <FONT color="green">365</FONT> b.getRowDimension(), b.getColumnDimension(), m, "n");<a name="line.365"></a>
|
|
369 <FONT color="green">366</FONT> }<a name="line.366"></a>
|
|
370 <FONT color="green">367</FONT> if (!isNonSingular()) {<a name="line.367"></a>
|
|
371 <FONT color="green">368</FONT> throw new SingularMatrixException();<a name="line.368"></a>
|
|
372 <FONT color="green">369</FONT> }<a name="line.369"></a>
|
|
373 <FONT color="green">370</FONT> <a name="line.370"></a>
|
|
374 <FONT color="green">371</FONT> final int columns = b.getColumnDimension();<a name="line.371"></a>
|
|
375 <FONT color="green">372</FONT> final int blockSize = BlockRealMatrix.BLOCK_SIZE;<a name="line.372"></a>
|
|
376 <FONT color="green">373</FONT> final int cBlocks = (columns + blockSize - 1) / blockSize;<a name="line.373"></a>
|
|
377 <FONT color="green">374</FONT> final double[][] xBlocks = BlockRealMatrix.createBlocksLayout(n, columns);<a name="line.374"></a>
|
|
378 <FONT color="green">375</FONT> final double[][] y = new double[b.getRowDimension()][blockSize];<a name="line.375"></a>
|
|
379 <FONT color="green">376</FONT> final double[] alpha = new double[blockSize];<a name="line.376"></a>
|
|
380 <FONT color="green">377</FONT> <a name="line.377"></a>
|
|
381 <FONT color="green">378</FONT> for (int kBlock = 0; kBlock < cBlocks; ++kBlock) {<a name="line.378"></a>
|
|
382 <FONT color="green">379</FONT> final int kStart = kBlock * blockSize;<a name="line.379"></a>
|
|
383 <FONT color="green">380</FONT> final int kEnd = Math.min(kStart + blockSize, columns);<a name="line.380"></a>
|
|
384 <FONT color="green">381</FONT> final int kWidth = kEnd - kStart;<a name="line.381"></a>
|
|
385 <FONT color="green">382</FONT> <a name="line.382"></a>
|
|
386 <FONT color="green">383</FONT> // get the right hand side vector<a name="line.383"></a>
|
|
387 <FONT color="green">384</FONT> b.copySubMatrix(0, m - 1, kStart, kEnd - 1, y);<a name="line.384"></a>
|
|
388 <FONT color="green">385</FONT> <a name="line.385"></a>
|
|
389 <FONT color="green">386</FONT> // apply Householder transforms to solve Q.y = b<a name="line.386"></a>
|
|
390 <FONT color="green">387</FONT> for (int minor = 0; minor < Math.min(m, n); minor++) {<a name="line.387"></a>
|
|
391 <FONT color="green">388</FONT> final double[] qrtMinor = qrt[minor];<a name="line.388"></a>
|
|
392 <FONT color="green">389</FONT> final double factor = 1.0 / (rDiag[minor] * qrtMinor[minor]);<a name="line.389"></a>
|
|
393 <FONT color="green">390</FONT> <a name="line.390"></a>
|
|
394 <FONT color="green">391</FONT> Arrays.fill(alpha, 0, kWidth, 0.0);<a name="line.391"></a>
|
|
395 <FONT color="green">392</FONT> for (int row = minor; row < m; ++row) {<a name="line.392"></a>
|
|
396 <FONT color="green">393</FONT> final double d = qrtMinor[row];<a name="line.393"></a>
|
|
397 <FONT color="green">394</FONT> final double[] yRow = y[row];<a name="line.394"></a>
|
|
398 <FONT color="green">395</FONT> for (int k = 0; k < kWidth; ++k) {<a name="line.395"></a>
|
|
399 <FONT color="green">396</FONT> alpha[k] += d * yRow[k];<a name="line.396"></a>
|
|
400 <FONT color="green">397</FONT> }<a name="line.397"></a>
|
|
401 <FONT color="green">398</FONT> }<a name="line.398"></a>
|
|
402 <FONT color="green">399</FONT> for (int k = 0; k < kWidth; ++k) {<a name="line.399"></a>
|
|
403 <FONT color="green">400</FONT> alpha[k] *= factor;<a name="line.400"></a>
|
|
404 <FONT color="green">401</FONT> }<a name="line.401"></a>
|
|
405 <FONT color="green">402</FONT> <a name="line.402"></a>
|
|
406 <FONT color="green">403</FONT> for (int row = minor; row < m; ++row) {<a name="line.403"></a>
|
|
407 <FONT color="green">404</FONT> final double d = qrtMinor[row];<a name="line.404"></a>
|
|
408 <FONT color="green">405</FONT> final double[] yRow = y[row];<a name="line.405"></a>
|
|
409 <FONT color="green">406</FONT> for (int k = 0; k < kWidth; ++k) {<a name="line.406"></a>
|
|
410 <FONT color="green">407</FONT> yRow[k] += alpha[k] * d;<a name="line.407"></a>
|
|
411 <FONT color="green">408</FONT> }<a name="line.408"></a>
|
|
412 <FONT color="green">409</FONT> }<a name="line.409"></a>
|
|
413 <FONT color="green">410</FONT> <a name="line.410"></a>
|
|
414 <FONT color="green">411</FONT> }<a name="line.411"></a>
|
|
415 <FONT color="green">412</FONT> <a name="line.412"></a>
|
|
416 <FONT color="green">413</FONT> // solve triangular system R.x = y<a name="line.413"></a>
|
|
417 <FONT color="green">414</FONT> for (int j = rDiag.length - 1; j >= 0; --j) {<a name="line.414"></a>
|
|
418 <FONT color="green">415</FONT> final int jBlock = j / blockSize;<a name="line.415"></a>
|
|
419 <FONT color="green">416</FONT> final int jStart = jBlock * blockSize;<a name="line.416"></a>
|
|
420 <FONT color="green">417</FONT> final double factor = 1.0 / rDiag[j];<a name="line.417"></a>
|
|
421 <FONT color="green">418</FONT> final double[] yJ = y[j];<a name="line.418"></a>
|
|
422 <FONT color="green">419</FONT> final double[] xBlock = xBlocks[jBlock * cBlocks + kBlock];<a name="line.419"></a>
|
|
423 <FONT color="green">420</FONT> int index = (j - jStart) * kWidth;<a name="line.420"></a>
|
|
424 <FONT color="green">421</FONT> for (int k = 0; k < kWidth; ++k) {<a name="line.421"></a>
|
|
425 <FONT color="green">422</FONT> yJ[k] *= factor;<a name="line.422"></a>
|
|
426 <FONT color="green">423</FONT> xBlock[index++] = yJ[k];<a name="line.423"></a>
|
|
427 <FONT color="green">424</FONT> }<a name="line.424"></a>
|
|
428 <FONT color="green">425</FONT> <a name="line.425"></a>
|
|
429 <FONT color="green">426</FONT> final double[] qrtJ = qrt[j];<a name="line.426"></a>
|
|
430 <FONT color="green">427</FONT> for (int i = 0; i < j; ++i) {<a name="line.427"></a>
|
|
431 <FONT color="green">428</FONT> final double rIJ = qrtJ[i];<a name="line.428"></a>
|
|
432 <FONT color="green">429</FONT> final double[] yI = y[i];<a name="line.429"></a>
|
|
433 <FONT color="green">430</FONT> for (int k = 0; k < kWidth; ++k) {<a name="line.430"></a>
|
|
434 <FONT color="green">431</FONT> yI[k] -= yJ[k] * rIJ;<a name="line.431"></a>
|
|
435 <FONT color="green">432</FONT> }<a name="line.432"></a>
|
|
436 <FONT color="green">433</FONT> }<a name="line.433"></a>
|
|
437 <FONT color="green">434</FONT> <a name="line.434"></a>
|
|
438 <FONT color="green">435</FONT> }<a name="line.435"></a>
|
|
439 <FONT color="green">436</FONT> <a name="line.436"></a>
|
|
440 <FONT color="green">437</FONT> }<a name="line.437"></a>
|
|
441 <FONT color="green">438</FONT> <a name="line.438"></a>
|
|
442 <FONT color="green">439</FONT> return new BlockRealMatrix(n, columns, xBlocks, false);<a name="line.439"></a>
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443 <FONT color="green">440</FONT> <a name="line.440"></a>
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444 <FONT color="green">441</FONT> }<a name="line.441"></a>
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445 <FONT color="green">442</FONT> <a name="line.442"></a>
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446 <FONT color="green">443</FONT> /** {@inheritDoc} */<a name="line.443"></a>
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447 <FONT color="green">444</FONT> public RealMatrix getInverse()<a name="line.444"></a>
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448 <FONT color="green">445</FONT> throws InvalidMatrixException {<a name="line.445"></a>
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449 <FONT color="green">446</FONT> return solve(MatrixUtils.createRealIdentityMatrix(rDiag.length));<a name="line.446"></a>
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450 <FONT color="green">447</FONT> }<a name="line.447"></a>
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451 <FONT color="green">448</FONT> <a name="line.448"></a>
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452 <FONT color="green">449</FONT> }<a name="line.449"></a>
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453 <FONT color="green">450</FONT> <a name="line.450"></a>
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454 <FONT color="green">451</FONT> }<a name="line.451"></a>
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515 </PRE>
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516 </BODY>
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517 </HTML>
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