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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> <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 org.apache.commons.math.MathRuntimeException;<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> /**<a name="line.22"></a>
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26 <FONT color="green">023</FONT> * Calculates the LUP-decomposition of a square matrix.<a name="line.23"></a>
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27 <FONT color="green">024</FONT> * <p>The LUP-decomposition of a matrix A consists of three matrices<a name="line.24"></a>
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28 <FONT color="green">025</FONT> * L, U and P that satisfy: PA = LU, L is lower triangular, and U is<a name="line.25"></a>
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29 <FONT color="green">026</FONT> * upper triangular and P is a permutation matrix. All matrices are<a name="line.26"></a>
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30 <FONT color="green">027</FONT> * m&times;m.</p><a name="line.27"></a>
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31 <FONT color="green">028</FONT> * <p>As shown by the presence of the P matrix, this decomposition is<a name="line.28"></a>
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32 <FONT color="green">029</FONT> * implemented using partial pivoting.</p><a name="line.29"></a>
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33 <FONT color="green">030</FONT> *<a name="line.30"></a>
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34 <FONT color="green">031</FONT> * @version $Revision: 885278 $ $Date: 2009-11-29 16:47:51 -0500 (Sun, 29 Nov 2009) $<a name="line.31"></a>
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35 <FONT color="green">032</FONT> * @since 2.0<a name="line.32"></a>
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36 <FONT color="green">033</FONT> */<a name="line.33"></a>
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37 <FONT color="green">034</FONT> public class LUDecompositionImpl implements LUDecomposition {<a name="line.34"></a>
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38 <FONT color="green">035</FONT> <a name="line.35"></a>
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39 <FONT color="green">036</FONT> /** Default bound to determine effective singularity in LU decomposition */<a name="line.36"></a>
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40 <FONT color="green">037</FONT> private static final double DEFAULT_TOO_SMALL = 10E-12;<a name="line.37"></a>
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41 <FONT color="green">038</FONT> <a name="line.38"></a>
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42 <FONT color="green">039</FONT> /** Message for vector length mismatch. */<a name="line.39"></a>
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43 <FONT color="green">040</FONT> private static final String VECTOR_LENGTH_MISMATCH_MESSAGE =<a name="line.40"></a>
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44 <FONT color="green">041</FONT> "vector length mismatch: got {0} but expected {1}";<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> /** Entries of LU decomposition. */<a name="line.43"></a>
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47 <FONT color="green">044</FONT> private double lu[][];<a name="line.44"></a>
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48 <FONT color="green">045</FONT> <a name="line.45"></a>
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49 <FONT color="green">046</FONT> /** Pivot permutation associated with LU decomposition */<a name="line.46"></a>
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50 <FONT color="green">047</FONT> private int[] pivot;<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> /** Parity of the permutation associated with the LU decomposition */<a name="line.49"></a>
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53 <FONT color="green">050</FONT> private boolean even;<a name="line.50"></a>
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54 <FONT color="green">051</FONT> <a name="line.51"></a>
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55 <FONT color="green">052</FONT> /** Singularity indicator. */<a name="line.52"></a>
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56 <FONT color="green">053</FONT> private boolean singular;<a name="line.53"></a>
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57 <FONT color="green">054</FONT> <a name="line.54"></a>
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58 <FONT color="green">055</FONT> /** Cached value of L. */<a name="line.55"></a>
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59 <FONT color="green">056</FONT> private RealMatrix cachedL;<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> /** Cached value of U. */<a name="line.58"></a>
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62 <FONT color="green">059</FONT> private RealMatrix cachedU;<a name="line.59"></a>
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63 <FONT color="green">060</FONT> <a name="line.60"></a>
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64 <FONT color="green">061</FONT> /** Cached value of P. */<a name="line.61"></a>
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65 <FONT color="green">062</FONT> private RealMatrix cachedP;<a name="line.62"></a>
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66 <FONT color="green">063</FONT> <a name="line.63"></a>
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67 <FONT color="green">064</FONT> /**<a name="line.64"></a>
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68 <FONT color="green">065</FONT> * Calculates the LU-decomposition of the given matrix.<a name="line.65"></a>
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69 <FONT color="green">066</FONT> * @param matrix The matrix to decompose.<a name="line.66"></a>
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70 <FONT color="green">067</FONT> * @exception InvalidMatrixException if matrix is not square<a name="line.67"></a>
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71 <FONT color="green">068</FONT> */<a name="line.68"></a>
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72 <FONT color="green">069</FONT> public LUDecompositionImpl(RealMatrix matrix)<a name="line.69"></a>
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73 <FONT color="green">070</FONT> throws InvalidMatrixException {<a name="line.70"></a>
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74 <FONT color="green">071</FONT> this(matrix, DEFAULT_TOO_SMALL);<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> <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> * Calculates the LU-decomposition of the given matrix.<a name="line.75"></a>
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79 <FONT color="green">076</FONT> * @param matrix The matrix to decompose.<a name="line.76"></a>
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80 <FONT color="green">077</FONT> * @param singularityThreshold threshold (based on partial row norm)<a name="line.77"></a>
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81 <FONT color="green">078</FONT> * under which a matrix is considered singular<a name="line.78"></a>
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82 <FONT color="green">079</FONT> * @exception NonSquareMatrixException if matrix is not square<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> public LUDecompositionImpl(RealMatrix matrix, double singularityThreshold)<a name="line.81"></a>
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85 <FONT color="green">082</FONT> throws NonSquareMatrixException {<a name="line.82"></a>
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86 <FONT color="green">083</FONT> <a name="line.83"></a>
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87 <FONT color="green">084</FONT> if (!matrix.isSquare()) {<a name="line.84"></a>
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88 <FONT color="green">085</FONT> throw new NonSquareMatrixException(matrix.getRowDimension(), matrix.getColumnDimension());<a name="line.85"></a>
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89 <FONT color="green">086</FONT> }<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 int m = matrix.getColumnDimension();<a name="line.88"></a>
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92 <FONT color="green">089</FONT> lu = matrix.getData();<a name="line.89"></a>
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93 <FONT color="green">090</FONT> pivot = new int[m];<a name="line.90"></a>
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94 <FONT color="green">091</FONT> cachedL = null;<a name="line.91"></a>
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95 <FONT color="green">092</FONT> cachedU = null;<a name="line.92"></a>
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96 <FONT color="green">093</FONT> cachedP = null;<a name="line.93"></a>
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97 <FONT color="green">094</FONT> <a name="line.94"></a>
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98 <FONT color="green">095</FONT> // Initialize permutation array and parity<a name="line.95"></a>
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99 <FONT color="green">096</FONT> for (int row = 0; row < m; row++) {<a name="line.96"></a>
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100 <FONT color="green">097</FONT> pivot[row] = row;<a name="line.97"></a>
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101 <FONT color="green">098</FONT> }<a name="line.98"></a>
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102 <FONT color="green">099</FONT> even = true;<a name="line.99"></a>
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103 <FONT color="green">100</FONT> singular = false;<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> // Loop over columns<a name="line.102"></a>
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106 <FONT color="green">103</FONT> for (int col = 0; col < m; col++) {<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> double sum = 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> // upper<a name="line.107"></a>
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111 <FONT color="green">108</FONT> for (int row = 0; row < col; row++) {<a name="line.108"></a>
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112 <FONT color="green">109</FONT> final double[] luRow = lu[row];<a name="line.109"></a>
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113 <FONT color="green">110</FONT> sum = luRow[col];<a name="line.110"></a>
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114 <FONT color="green">111</FONT> for (int i = 0; i < row; i++) {<a name="line.111"></a>
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115 <FONT color="green">112</FONT> sum -= luRow[i] * lu[i][col];<a name="line.112"></a>
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116 <FONT color="green">113</FONT> }<a name="line.113"></a>
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117 <FONT color="green">114</FONT> luRow[col] = sum;<a name="line.114"></a>
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118 <FONT color="green">115</FONT> }<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> // lower<a name="line.117"></a>
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121 <FONT color="green">118</FONT> int max = col; // permutation row<a name="line.118"></a>
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122 <FONT color="green">119</FONT> double largest = Double.NEGATIVE_INFINITY;<a name="line.119"></a>
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123 <FONT color="green">120</FONT> for (int row = col; row < m; row++) {<a name="line.120"></a>
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124 <FONT color="green">121</FONT> final double[] luRow = lu[row];<a name="line.121"></a>
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125 <FONT color="green">122</FONT> sum = luRow[col];<a name="line.122"></a>
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126 <FONT color="green">123</FONT> for (int i = 0; i < col; i++) {<a name="line.123"></a>
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127 <FONT color="green">124</FONT> sum -= luRow[i] * lu[i][col];<a name="line.124"></a>
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128 <FONT color="green">125</FONT> }<a name="line.125"></a>
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129 <FONT color="green">126</FONT> luRow[col] = sum;<a name="line.126"></a>
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130 <FONT color="green">127</FONT> <a name="line.127"></a>
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131 <FONT color="green">128</FONT> // maintain best permutation choice<a name="line.128"></a>
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132 <FONT color="green">129</FONT> if (Math.abs(sum) > largest) {<a name="line.129"></a>
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133 <FONT color="green">130</FONT> largest = Math.abs(sum);<a name="line.130"></a>
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134 <FONT color="green">131</FONT> max = row;<a name="line.131"></a>
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135 <FONT color="green">132</FONT> }<a name="line.132"></a>
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136 <FONT color="green">133</FONT> }<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> // Singularity check<a name="line.135"></a>
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139 <FONT color="green">136</FONT> if (Math.abs(lu[max][col]) < singularityThreshold) {<a name="line.136"></a>
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140 <FONT color="green">137</FONT> singular = true;<a name="line.137"></a>
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141 <FONT color="green">138</FONT> return;<a name="line.138"></a>
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142 <FONT color="green">139</FONT> }<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> // Pivot if necessary<a name="line.141"></a>
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145 <FONT color="green">142</FONT> if (max != col) {<a name="line.142"></a>
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146 <FONT color="green">143</FONT> double tmp = 0;<a name="line.143"></a>
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147 <FONT color="green">144</FONT> final double[] luMax = lu[max];<a name="line.144"></a>
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148 <FONT color="green">145</FONT> final double[] luCol = lu[col];<a name="line.145"></a>
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149 <FONT color="green">146</FONT> for (int i = 0; i < m; i++) {<a name="line.146"></a>
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150 <FONT color="green">147</FONT> tmp = luMax[i];<a name="line.147"></a>
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151 <FONT color="green">148</FONT> luMax[i] = luCol[i];<a name="line.148"></a>
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152 <FONT color="green">149</FONT> luCol[i] = tmp;<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> int temp = pivot[max];<a name="line.151"></a>
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155 <FONT color="green">152</FONT> pivot[max] = pivot[col];<a name="line.152"></a>
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156 <FONT color="green">153</FONT> pivot[col] = temp;<a name="line.153"></a>
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157 <FONT color="green">154</FONT> even = !even;<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> <a name="line.156"></a>
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160 <FONT color="green">157</FONT> // Divide the lower elements by the "winning" diagonal elt.<a name="line.157"></a>
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161 <FONT color="green">158</FONT> final double luDiag = lu[col][col];<a name="line.158"></a>
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162 <FONT color="green">159</FONT> for (int row = col + 1; row < m; row++) {<a name="line.159"></a>
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163 <FONT color="green">160</FONT> lu[row][col] /= luDiag;<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> /** {@inheritDoc} */<a name="line.166"></a>
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170 <FONT color="green">167</FONT> public RealMatrix getL() {<a name="line.167"></a>
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171 <FONT color="green">168</FONT> if ((cachedL == null) && !singular) {<a name="line.168"></a>
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172 <FONT color="green">169</FONT> final int m = pivot.length;<a name="line.169"></a>
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173 <FONT color="green">170</FONT> cachedL = MatrixUtils.createRealMatrix(m, m);<a name="line.170"></a>
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174 <FONT color="green">171</FONT> for (int i = 0; i < m; ++i) {<a name="line.171"></a>
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175 <FONT color="green">172</FONT> final double[] luI = lu[i];<a name="line.172"></a>
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176 <FONT color="green">173</FONT> for (int j = 0; j < i; ++j) {<a name="line.173"></a>
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177 <FONT color="green">174</FONT> cachedL.setEntry(i, j, luI[j]);<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> cachedL.setEntry(i, i, 1.0);<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> return cachedL;<a name="line.179"></a>
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183 <FONT color="green">180</FONT> }<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> /** {@inheritDoc} */<a name="line.182"></a>
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186 <FONT color="green">183</FONT> public RealMatrix getU() {<a name="line.183"></a>
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187 <FONT color="green">184</FONT> if ((cachedU == null) && !singular) {<a name="line.184"></a>
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188 <FONT color="green">185</FONT> final int m = pivot.length;<a name="line.185"></a>
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189 <FONT color="green">186</FONT> cachedU = MatrixUtils.createRealMatrix(m, m);<a name="line.186"></a>
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190 <FONT color="green">187</FONT> for (int i = 0; i < m; ++i) {<a name="line.187"></a>
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191 <FONT color="green">188</FONT> final double[] luI = lu[i];<a name="line.188"></a>
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192 <FONT color="green">189</FONT> for (int j = i; j < m; ++j) {<a name="line.189"></a>
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193 <FONT color="green">190</FONT> cachedU.setEntry(i, j, luI[j]);<a name="line.190"></a>
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194 <FONT color="green">191</FONT> }<a name="line.191"></a>
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195 <FONT color="green">192</FONT> }<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> return cachedU;<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> /** {@inheritDoc} */<a name="line.197"></a>
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201 <FONT color="green">198</FONT> public RealMatrix getP() {<a name="line.198"></a>
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202 <FONT color="green">199</FONT> if ((cachedP == null) && !singular) {<a name="line.199"></a>
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203 <FONT color="green">200</FONT> final int m = pivot.length;<a name="line.200"></a>
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204 <FONT color="green">201</FONT> cachedP = MatrixUtils.createRealMatrix(m, m);<a name="line.201"></a>
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205 <FONT color="green">202</FONT> for (int i = 0; i < m; ++i) {<a name="line.202"></a>
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206 <FONT color="green">203</FONT> cachedP.setEntry(i, pivot[i], 1.0);<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> }<a name="line.205"></a>
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209 <FONT color="green">206</FONT> return cachedP;<a name="line.206"></a>
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210 <FONT color="green">207</FONT> }<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> /** {@inheritDoc} */<a name="line.209"></a>
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213 <FONT color="green">210</FONT> public int[] getPivot() {<a name="line.210"></a>
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214 <FONT color="green">211</FONT> return pivot.clone();<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> /** {@inheritDoc} */<a name="line.214"></a>
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218 <FONT color="green">215</FONT> public double getDeterminant() {<a name="line.215"></a>
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219 <FONT color="green">216</FONT> if (singular) {<a name="line.216"></a>
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220 <FONT color="green">217</FONT> return 0;<a name="line.217"></a>
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221 <FONT color="green">218</FONT> } else {<a name="line.218"></a>
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222 <FONT color="green">219</FONT> final int m = pivot.length;<a name="line.219"></a>
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223 <FONT color="green">220</FONT> double determinant = even ? 1 : -1;<a name="line.220"></a>
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224 <FONT color="green">221</FONT> for (int i = 0; i < m; i++) {<a name="line.221"></a>
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225 <FONT color="green">222</FONT> determinant *= lu[i][i];<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> return determinant;<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> }<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> /** {@inheritDoc} */<a name="line.228"></a>
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232 <FONT color="green">229</FONT> public DecompositionSolver getSolver() {<a name="line.229"></a>
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233 <FONT color="green">230</FONT> return new Solver(lu, pivot, singular);<a name="line.230"></a>
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234 <FONT color="green">231</FONT> }<a name="line.231"></a>
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235 <FONT color="green">232</FONT> <a name="line.232"></a>
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236 <FONT color="green">233</FONT> /** Specialized solver. */<a name="line.233"></a>
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237 <FONT color="green">234</FONT> private static class Solver implements DecompositionSolver {<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> /** Entries of LU decomposition. */<a name="line.236"></a>
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240 <FONT color="green">237</FONT> private final double lu[][];<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> /** Pivot permutation associated with LU decomposition. */<a name="line.239"></a>
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243 <FONT color="green">240</FONT> private final int[] pivot;<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> /** Singularity indicator. */<a name="line.242"></a>
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246 <FONT color="green">243</FONT> private final boolean singular;<a name="line.243"></a>
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247 <FONT color="green">244</FONT> <a name="line.244"></a>
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248 <FONT color="green">245</FONT> /**<a name="line.245"></a>
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249 <FONT color="green">246</FONT> * Build a solver from decomposed matrix.<a name="line.246"></a>
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250 <FONT color="green">247</FONT> * @param lu entries of LU decomposition<a name="line.247"></a>
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251 <FONT color="green">248</FONT> * @param pivot pivot permutation associated with LU decomposition<a name="line.248"></a>
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252 <FONT color="green">249</FONT> * @param singular singularity indicator<a name="line.249"></a>
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253 <FONT color="green">250</FONT> */<a name="line.250"></a>
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254 <FONT color="green">251</FONT> private Solver(final double[][] lu, final int[] pivot, final boolean singular) {<a name="line.251"></a>
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255 <FONT color="green">252</FONT> this.lu = lu;<a name="line.252"></a>
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256 <FONT color="green">253</FONT> this.pivot = pivot;<a name="line.253"></a>
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257 <FONT color="green">254</FONT> this.singular = singular;<a name="line.254"></a>
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258 <FONT color="green">255</FONT> }<a name="line.255"></a>
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259 <FONT color="green">256</FONT> <a name="line.256"></a>
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260 <FONT color="green">257</FONT> /** {@inheritDoc} */<a name="line.257"></a>
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261 <FONT color="green">258</FONT> public boolean isNonSingular() {<a name="line.258"></a>
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262 <FONT color="green">259</FONT> return !singular;<a name="line.259"></a>
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263 <FONT color="green">260</FONT> }<a name="line.260"></a>
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264 <FONT color="green">261</FONT> <a name="line.261"></a>
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265 <FONT color="green">262</FONT> /** {@inheritDoc} */<a name="line.262"></a>
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266 <FONT color="green">263</FONT> public double[] solve(double[] b)<a name="line.263"></a>
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267 <FONT color="green">264</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.264"></a>
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268 <FONT color="green">265</FONT> <a name="line.265"></a>
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269 <FONT color="green">266</FONT> final int m = pivot.length;<a name="line.266"></a>
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270 <FONT color="green">267</FONT> if (b.length != m) {<a name="line.267"></a>
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271 <FONT color="green">268</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.268"></a>
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272 <FONT color="green">269</FONT> VECTOR_LENGTH_MISMATCH_MESSAGE, b.length, m);<a name="line.269"></a>
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273 <FONT color="green">270</FONT> }<a name="line.270"></a>
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274 <FONT color="green">271</FONT> if (singular) {<a name="line.271"></a>
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275 <FONT color="green">272</FONT> throw new SingularMatrixException();<a name="line.272"></a>
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276 <FONT color="green">273</FONT> }<a name="line.273"></a>
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277 <FONT color="green">274</FONT> <a name="line.274"></a>
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278 <FONT color="green">275</FONT> final double[] bp = new double[m];<a name="line.275"></a>
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279 <FONT color="green">276</FONT> <a name="line.276"></a>
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280 <FONT color="green">277</FONT> // Apply permutations to b<a name="line.277"></a>
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281 <FONT color="green">278</FONT> for (int row = 0; row < m; row++) {<a name="line.278"></a>
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282 <FONT color="green">279</FONT> bp[row] = b[pivot[row]];<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> <a name="line.281"></a>
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285 <FONT color="green">282</FONT> // Solve LY = b<a name="line.282"></a>
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286 <FONT color="green">283</FONT> for (int col = 0; col < m; col++) {<a name="line.283"></a>
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287 <FONT color="green">284</FONT> final double bpCol = bp[col];<a name="line.284"></a>
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288 <FONT color="green">285</FONT> for (int i = col + 1; i < m; i++) {<a name="line.285"></a>
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289 <FONT color="green">286</FONT> bp[i] -= bpCol * lu[i][col];<a name="line.286"></a>
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290 <FONT color="green">287</FONT> }<a name="line.287"></a>
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291 <FONT color="green">288</FONT> }<a name="line.288"></a>
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292 <FONT color="green">289</FONT> <a name="line.289"></a>
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293 <FONT color="green">290</FONT> // Solve UX = Y<a name="line.290"></a>
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|
294 <FONT color="green">291</FONT> for (int col = m - 1; col >= 0; col--) {<a name="line.291"></a>
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295 <FONT color="green">292</FONT> bp[col] /= lu[col][col];<a name="line.292"></a>
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296 <FONT color="green">293</FONT> final double bpCol = bp[col];<a name="line.293"></a>
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297 <FONT color="green">294</FONT> for (int i = 0; i < col; i++) {<a name="line.294"></a>
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298 <FONT color="green">295</FONT> bp[i] -= bpCol * lu[i][col];<a name="line.295"></a>
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299 <FONT color="green">296</FONT> }<a name="line.296"></a>
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|
300 <FONT color="green">297</FONT> }<a name="line.297"></a>
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301 <FONT color="green">298</FONT> <a name="line.298"></a>
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302 <FONT color="green">299</FONT> return bp;<a name="line.299"></a>
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|
303 <FONT color="green">300</FONT> <a name="line.300"></a>
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304 <FONT color="green">301</FONT> }<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> /** {@inheritDoc} */<a name="line.303"></a>
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307 <FONT color="green">304</FONT> public RealVector solve(RealVector b)<a name="line.304"></a>
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|
308 <FONT color="green">305</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.305"></a>
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|
309 <FONT color="green">306</FONT> try {<a name="line.306"></a>
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310 <FONT color="green">307</FONT> return solve((ArrayRealVector) b);<a name="line.307"></a>
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311 <FONT color="green">308</FONT> } catch (ClassCastException cce) {<a name="line.308"></a>
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312 <FONT color="green">309</FONT> <a name="line.309"></a>
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313 <FONT color="green">310</FONT> final int m = pivot.length;<a name="line.310"></a>
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|
314 <FONT color="green">311</FONT> if (b.getDimension() != m) {<a name="line.311"></a>
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|
315 <FONT color="green">312</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.312"></a>
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|
316 <FONT color="green">313</FONT> VECTOR_LENGTH_MISMATCH_MESSAGE, b.getDimension(), m);<a name="line.313"></a>
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317 <FONT color="green">314</FONT> }<a name="line.314"></a>
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318 <FONT color="green">315</FONT> if (singular) {<a name="line.315"></a>
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319 <FONT color="green">316</FONT> throw new SingularMatrixException();<a name="line.316"></a>
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320 <FONT color="green">317</FONT> }<a name="line.317"></a>
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321 <FONT color="green">318</FONT> <a name="line.318"></a>
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322 <FONT color="green">319</FONT> final double[] bp = new double[m];<a name="line.319"></a>
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|
323 <FONT color="green">320</FONT> <a name="line.320"></a>
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|
324 <FONT color="green">321</FONT> // Apply permutations to b<a name="line.321"></a>
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|
325 <FONT color="green">322</FONT> for (int row = 0; row < m; row++) {<a name="line.322"></a>
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|
|
326 <FONT color="green">323</FONT> bp[row] = b.getEntry(pivot[row]);<a name="line.323"></a>
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|
327 <FONT color="green">324</FONT> }<a name="line.324"></a>
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328 <FONT color="green">325</FONT> <a name="line.325"></a>
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329 <FONT color="green">326</FONT> // Solve LY = b<a name="line.326"></a>
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|
330 <FONT color="green">327</FONT> for (int col = 0; col < m; col++) {<a name="line.327"></a>
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331 <FONT color="green">328</FONT> final double bpCol = bp[col];<a name="line.328"></a>
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|
332 <FONT color="green">329</FONT> for (int i = col + 1; i < m; i++) {<a name="line.329"></a>
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|
333 <FONT color="green">330</FONT> bp[i] -= bpCol * lu[i][col];<a name="line.330"></a>
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|
334 <FONT color="green">331</FONT> }<a name="line.331"></a>
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|
335 <FONT color="green">332</FONT> }<a name="line.332"></a>
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|
336 <FONT color="green">333</FONT> <a name="line.333"></a>
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|
337 <FONT color="green">334</FONT> // Solve UX = Y<a name="line.334"></a>
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|
338 <FONT color="green">335</FONT> for (int col = m - 1; col >= 0; col--) {<a name="line.335"></a>
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|
339 <FONT color="green">336</FONT> bp[col] /= lu[col][col];<a name="line.336"></a>
|
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|
340 <FONT color="green">337</FONT> final double bpCol = bp[col];<a name="line.337"></a>
|
|
|
341 <FONT color="green">338</FONT> for (int i = 0; i < col; i++) {<a name="line.338"></a>
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|
|
342 <FONT color="green">339</FONT> bp[i] -= bpCol * lu[i][col];<a name="line.339"></a>
|
|
|
343 <FONT color="green">340</FONT> }<a name="line.340"></a>
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|
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> return new ArrayRealVector(bp, false);<a name="line.343"></a>
|
|
|
347 <FONT color="green">344</FONT> <a name="line.344"></a>
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|
|
348 <FONT color="green">345</FONT> }<a name="line.345"></a>
|
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|
349 <FONT color="green">346</FONT> }<a name="line.346"></a>
|
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|
350 <FONT color="green">347</FONT> <a name="line.347"></a>
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|
351 <FONT color="green">348</FONT> /** Solve the linear equation A &times; X = B.<a name="line.348"></a>
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|
352 <FONT color="green">349</FONT> * <p>The A matrix is implicit here. It is </p><a name="line.349"></a>
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|
353 <FONT color="green">350</FONT> * @param b right-hand side of the equation A &times; X = B<a name="line.350"></a>
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|
354 <FONT color="green">351</FONT> * @return a vector X such that A &times; X = B<a name="line.351"></a>
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|
355 <FONT color="green">352</FONT> * @exception IllegalArgumentException if matrices dimensions don't match<a name="line.352"></a>
|
|
|
356 <FONT color="green">353</FONT> * @exception InvalidMatrixException if decomposed matrix is singular<a name="line.353"></a>
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|
|
357 <FONT color="green">354</FONT> */<a name="line.354"></a>
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|
358 <FONT color="green">355</FONT> public ArrayRealVector solve(ArrayRealVector b)<a name="line.355"></a>
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|
|
359 <FONT color="green">356</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.356"></a>
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|
|
360 <FONT color="green">357</FONT> return new ArrayRealVector(solve(b.getDataRef()), false);<a name="line.357"></a>
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|
|
361 <FONT color="green">358</FONT> }<a name="line.358"></a>
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|
362 <FONT color="green">359</FONT> <a name="line.359"></a>
|
|
|
363 <FONT color="green">360</FONT> /** {@inheritDoc} */<a name="line.360"></a>
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|
|
364 <FONT color="green">361</FONT> public RealMatrix solve(RealMatrix b)<a name="line.361"></a>
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|
|
365 <FONT color="green">362</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.362"></a>
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|
366 <FONT color="green">363</FONT> <a name="line.363"></a>
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|
367 <FONT color="green">364</FONT> final int m = pivot.length;<a name="line.364"></a>
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|
368 <FONT color="green">365</FONT> if (b.getRowDimension() != m) {<a name="line.365"></a>
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|
369 <FONT color="green">366</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.366"></a>
|
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|
370 <FONT color="green">367</FONT> "dimensions mismatch: got {0}x{1} but expected {2}x{3}",<a name="line.367"></a>
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|
371 <FONT color="green">368</FONT> b.getRowDimension(), b.getColumnDimension(), m, "n");<a name="line.368"></a>
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|
372 <FONT color="green">369</FONT> }<a name="line.369"></a>
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|
373 <FONT color="green">370</FONT> if (singular) {<a name="line.370"></a>
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|
374 <FONT color="green">371</FONT> throw new SingularMatrixException();<a name="line.371"></a>
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|
375 <FONT color="green">372</FONT> }<a name="line.372"></a>
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|
376 <FONT color="green">373</FONT> <a name="line.373"></a>
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|
377 <FONT color="green">374</FONT> final int nColB = b.getColumnDimension();<a name="line.374"></a>
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|
378 <FONT color="green">375</FONT> <a name="line.375"></a>
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|
379 <FONT color="green">376</FONT> // Apply permutations to b<a name="line.376"></a>
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|
380 <FONT color="green">377</FONT> final double[][] bp = new double[m][nColB];<a name="line.377"></a>
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|
381 <FONT color="green">378</FONT> for (int row = 0; row < m; row++) {<a name="line.378"></a>
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|
382 <FONT color="green">379</FONT> final double[] bpRow = bp[row];<a name="line.379"></a>
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|
|
383 <FONT color="green">380</FONT> final int pRow = pivot[row];<a name="line.380"></a>
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|
|
384 <FONT color="green">381</FONT> for (int col = 0; col < nColB; col++) {<a name="line.381"></a>
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|
|
385 <FONT color="green">382</FONT> bpRow[col] = b.getEntry(pRow, col);<a name="line.382"></a>
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|
|
386 <FONT color="green">383</FONT> }<a name="line.383"></a>
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|
387 <FONT color="green">384</FONT> }<a name="line.384"></a>
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|
388 <FONT color="green">385</FONT> <a name="line.385"></a>
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|
389 <FONT color="green">386</FONT> // Solve LY = b<a name="line.386"></a>
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|
390 <FONT color="green">387</FONT> for (int col = 0; col < m; col++) {<a name="line.387"></a>
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|
|
391 <FONT color="green">388</FONT> final double[] bpCol = bp[col];<a name="line.388"></a>
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|
|
392 <FONT color="green">389</FONT> for (int i = col + 1; i < m; i++) {<a name="line.389"></a>
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|
|
393 <FONT color="green">390</FONT> final double[] bpI = bp[i];<a name="line.390"></a>
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|
|
394 <FONT color="green">391</FONT> final double luICol = lu[i][col];<a name="line.391"></a>
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|
|
395 <FONT color="green">392</FONT> for (int j = 0; j < nColB; j++) {<a name="line.392"></a>
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|
|
396 <FONT color="green">393</FONT> bpI[j] -= bpCol[j] * luICol;<a name="line.393"></a>
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|
|
397 <FONT color="green">394</FONT> }<a name="line.394"></a>
|
|
|
398 <FONT color="green">395</FONT> }<a name="line.395"></a>
|
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|
399 <FONT color="green">396</FONT> }<a name="line.396"></a>
|
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|
400 <FONT color="green">397</FONT> <a name="line.397"></a>
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|
401 <FONT color="green">398</FONT> // Solve UX = Y<a name="line.398"></a>
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|
|
402 <FONT color="green">399</FONT> for (int col = m - 1; col >= 0; col--) {<a name="line.399"></a>
|
|
|
403 <FONT color="green">400</FONT> final double[] bpCol = bp[col];<a name="line.400"></a>
|
|
|
404 <FONT color="green">401</FONT> final double luDiag = lu[col][col];<a name="line.401"></a>
|
|
|
405 <FONT color="green">402</FONT> for (int j = 0; j < nColB; j++) {<a name="line.402"></a>
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|
|
406 <FONT color="green">403</FONT> bpCol[j] /= luDiag;<a name="line.403"></a>
|
|
|
407 <FONT color="green">404</FONT> }<a name="line.404"></a>
|
|
|
408 <FONT color="green">405</FONT> for (int i = 0; i < col; i++) {<a name="line.405"></a>
|
|
|
409 <FONT color="green">406</FONT> final double[] bpI = bp[i];<a name="line.406"></a>
|
|
|
410 <FONT color="green">407</FONT> final double luICol = lu[i][col];<a name="line.407"></a>
|
|
|
411 <FONT color="green">408</FONT> for (int j = 0; j < nColB; j++) {<a name="line.408"></a>
|
|
|
412 <FONT color="green">409</FONT> bpI[j] -= bpCol[j] * luICol;<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> <a name="line.413"></a>
|
|
|
417 <FONT color="green">414</FONT> return new Array2DRowRealMatrix(bp, false);<a name="line.414"></a>
|
|
|
418 <FONT color="green">415</FONT> <a name="line.415"></a>
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|
419 <FONT color="green">416</FONT> }<a name="line.416"></a>
|
|
|
420 <FONT color="green">417</FONT> <a name="line.417"></a>
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|
|
421 <FONT color="green">418</FONT> /** {@inheritDoc} */<a name="line.418"></a>
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|
|
422 <FONT color="green">419</FONT> public RealMatrix getInverse() throws InvalidMatrixException {<a name="line.419"></a>
|
|
|
423 <FONT color="green">420</FONT> return solve(MatrixUtils.createRealIdentityMatrix(pivot.length));<a name="line.420"></a>
|
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489 </PRE>
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490 </BODY>
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491 </HTML>
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