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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> <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> * An interface to classes that implement an algorithm to calculate the<a name="line.23"></a>
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27 <FONT color="green">024</FONT> * Singular Value Decomposition of a real matrix.<a name="line.24"></a>
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28 <FONT color="green">025</FONT> * <p><a name="line.25"></a>
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29 <FONT color="green">026</FONT> * The Singular Value Decomposition of matrix A is a set of three matrices: U,<a name="line.26"></a>
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30 <FONT color="green">027</FONT> * &Sigma; and V such that A = U &times; &Sigma; &times; V<sup>T</sup>. Let A be<a name="line.27"></a>
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31 <FONT color="green">028</FONT> * a m &times; n matrix, then U is a m &times; p orthogonal matrix, &Sigma; is a<a name="line.28"></a>
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32 <FONT color="green">029</FONT> * p &times; p diagonal matrix with positive or null elements, V is a p &times;<a name="line.29"></a>
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33 <FONT color="green">030</FONT> * n orthogonal matrix (hence V<sup>T</sup> is also orthogonal) where<a name="line.30"></a>
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34 <FONT color="green">031</FONT> * p=min(m,n).<a name="line.31"></a>
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35 <FONT color="green">032</FONT> * </p><a name="line.32"></a>
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36 <FONT color="green">033</FONT> * <p>This interface is similar to the class with similar name from the<a name="line.33"></a>
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37 <FONT color="green">034</FONT> * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the<a name="line.34"></a>
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38 <FONT color="green">035</FONT> * following changes:</p><a name="line.35"></a>
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39 <FONT color="green">036</FONT> * <ul><a name="line.36"></a>
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40 <FONT color="green">037</FONT> * <li>the <code>norm2</code> method which has been renamed as {@link #getNorm()<a name="line.37"></a>
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41 <FONT color="green">038</FONT> * getNorm},</li><a name="line.38"></a>
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42 <FONT color="green">039</FONT> * <li>the <code>cond</code> method which has been renamed as {@link<a name="line.39"></a>
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43 <FONT color="green">040</FONT> * #getConditionNumber() getConditionNumber},</li><a name="line.40"></a>
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44 <FONT color="green">041</FONT> * <li>the <code>rank</code> method which has been renamed as {@link #getRank()<a name="line.41"></a>
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45 <FONT color="green">042</FONT> * getRank},</li><a name="line.42"></a>
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46 <FONT color="green">043</FONT> * <li>a {@link #getUT() getUT} method has been added,</li><a name="line.43"></a>
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47 <FONT color="green">044</FONT> * <li>a {@link #getVT() getVT} method has been added,</li><a name="line.44"></a>
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48 <FONT color="green">045</FONT> * <li>a {@link #getSolver() getSolver} method has been added,</li><a name="line.45"></a>
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49 <FONT color="green">046</FONT> * <li>a {@link #getCovariance(double) getCovariance} method has been added.</li><a name="line.46"></a>
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50 <FONT color="green">047</FONT> * </ul><a name="line.47"></a>
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51 <FONT color="green">048</FONT> * @see <a href="http://mathworld.wolfram.com/SingularValueDecomposition.html">MathWorld</a><a name="line.48"></a>
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52 <FONT color="green">049</FONT> * @see <a href="http://en.wikipedia.org/wiki/Singular_value_decomposition">Wikipedia</a><a name="line.49"></a>
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53 <FONT color="green">050</FONT> * @version $Revision: 928081 $ $Date: 2010-03-26 18:36:38 -0400 (Fri, 26 Mar 2010) $<a name="line.50"></a>
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54 <FONT color="green">051</FONT> * @since 2.0<a name="line.51"></a>
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55 <FONT color="green">052</FONT> */<a name="line.52"></a>
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56 <FONT color="green">053</FONT> public interface SingularValueDecomposition {<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> /**<a name="line.55"></a>
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59 <FONT color="green">056</FONT> * Returns the matrix U of the decomposition.<a name="line.56"></a>
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60 <FONT color="green">057</FONT> * <p>U is an orthogonal matrix, i.e. its transpose is also its inverse.</p><a name="line.57"></a>
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61 <FONT color="green">058</FONT> * @return the U matrix<a name="line.58"></a>
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62 <FONT color="green">059</FONT> * @see #getUT()<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> RealMatrix getU();<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> /**<a name="line.63"></a>
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67 <FONT color="green">064</FONT> * Returns the transpose of the matrix U of the decomposition.<a name="line.64"></a>
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68 <FONT color="green">065</FONT> * <p>U is an orthogonal matrix, i.e. its transpose is also its inverse.</p><a name="line.65"></a>
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69 <FONT color="green">066</FONT> * @return the U matrix (or null if decomposed matrix is singular)<a name="line.66"></a>
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70 <FONT color="green">067</FONT> * @see #getU()<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> RealMatrix getUT();<a name="line.69"></a>
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73 <FONT color="green">070</FONT> <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> * Returns the diagonal matrix &Sigma; of the decomposition.<a name="line.72"></a>
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76 <FONT color="green">073</FONT> * <p>&Sigma; is a diagonal matrix. The singular values are provided in<a name="line.73"></a>
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77 <FONT color="green">074</FONT> * non-increasing order, for compatibility with Jama.</p><a name="line.74"></a>
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78 <FONT color="green">075</FONT> * @return the &Sigma; matrix<a name="line.75"></a>
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79 <FONT color="green">076</FONT> */<a name="line.76"></a>
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80 <FONT color="green">077</FONT> RealMatrix getS();<a name="line.77"></a>
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81 <FONT color="green">078</FONT> <a name="line.78"></a>
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82 <FONT color="green">079</FONT> /**<a name="line.79"></a>
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83 <FONT color="green">080</FONT> * Returns the diagonal elements of the matrix &Sigma; of the decomposition.<a name="line.80"></a>
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84 <FONT color="green">081</FONT> * <p>The singular values are provided in non-increasing order, for<a name="line.81"></a>
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85 <FONT color="green">082</FONT> * compatibility with Jama.</p><a name="line.82"></a>
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86 <FONT color="green">083</FONT> * @return the diagonal elements of the &Sigma; matrix<a name="line.83"></a>
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87 <FONT color="green">084</FONT> */<a name="line.84"></a>
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88 <FONT color="green">085</FONT> double[] getSingularValues();<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> * Returns the matrix V of the decomposition.<a name="line.88"></a>
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92 <FONT color="green">089</FONT> * <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p><a name="line.89"></a>
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93 <FONT color="green">090</FONT> * @return the V matrix (or null if decomposed matrix is singular)<a name="line.90"></a>
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94 <FONT color="green">091</FONT> * @see #getVT()<a name="line.91"></a>
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95 <FONT color="green">092</FONT> */<a name="line.92"></a>
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96 <FONT color="green">093</FONT> RealMatrix getV();<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> /**<a name="line.95"></a>
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99 <FONT color="green">096</FONT> * Returns the transpose of the matrix V of the decomposition.<a name="line.96"></a>
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100 <FONT color="green">097</FONT> * <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p><a name="line.97"></a>
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101 <FONT color="green">098</FONT> * @return the V matrix (or null if decomposed matrix is singular)<a name="line.98"></a>
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102 <FONT color="green">099</FONT> * @see #getV()<a name="line.99"></a>
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103 <FONT color="green">100</FONT> */<a name="line.100"></a>
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104 <FONT color="green">101</FONT> RealMatrix getVT();<a name="line.101"></a>
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105 <FONT color="green">102</FONT> <a name="line.102"></a>
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106 <FONT color="green">103</FONT> /**<a name="line.103"></a>
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107 <FONT color="green">104</FONT> * Returns the n &times; n covariance matrix.<a name="line.104"></a>
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108 <FONT color="green">105</FONT> * <p>The covariance matrix is V &times; J &times; V<sup>T</sup><a name="line.105"></a>
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109 <FONT color="green">106</FONT> * where J is the diagonal matrix of the inverse of the squares of<a name="line.106"></a>
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110 <FONT color="green">107</FONT> * the singular values.</p><a name="line.107"></a>
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111 <FONT color="green">108</FONT> * @param minSingularValue value below which singular values are ignored<a name="line.108"></a>
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112 <FONT color="green">109</FONT> * (a 0 or negative value implies all singular value will be used)<a name="line.109"></a>
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113 <FONT color="green">110</FONT> * @return covariance matrix<a name="line.110"></a>
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114 <FONT color="green">111</FONT> * @exception IllegalArgumentException if minSingularValue is larger than<a name="line.111"></a>
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115 <FONT color="green">112</FONT> * the largest singular value, meaning all singular values are ignored<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> RealMatrix getCovariance(double minSingularValue) throws IllegalArgumentException;<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> * Returns the L<sub>2</sub> norm of the matrix.<a name="line.117"></a>
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121 <FONT color="green">118</FONT> * <p>The L<sub>2</sub> norm is max(|A &times; u|<sub>2</sub> /<a name="line.118"></a>
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122 <FONT color="green">119</FONT> * |u|<sub>2</sub>), where |.|<sub>2</sub> denotes the vectorial 2-norm<a name="line.119"></a>
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123 <FONT color="green">120</FONT> * (i.e. the traditional euclidian norm).</p><a name="line.120"></a>
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124 <FONT color="green">121</FONT> * @return norm<a name="line.121"></a>
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125 <FONT color="green">122</FONT> */<a name="line.122"></a>
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126 <FONT color="green">123</FONT> double getNorm();<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> /**<a name="line.125"></a>
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129 <FONT color="green">126</FONT> * Return the condition number of the matrix.<a name="line.126"></a>
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130 <FONT color="green">127</FONT> * @return condition number of the matrix<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> double getConditionNumber();<a name="line.129"></a>
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133 <FONT color="green">130</FONT> <a name="line.130"></a>
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134 <FONT color="green">131</FONT> /**<a name="line.131"></a>
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135 <FONT color="green">132</FONT> * Return the effective numerical matrix rank.<a name="line.132"></a>
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136 <FONT color="green">133</FONT> * <p>The effective numerical rank is the number of non-negligible<a name="line.133"></a>
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137 <FONT color="green">134</FONT> * singular values. The threshold used to identify non-negligible<a name="line.134"></a>
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138 <FONT color="green">135</FONT> * terms is max(m,n) &times; ulp(s<sub>1</sub>) where ulp(s<sub>1</sub>)<a name="line.135"></a>
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139 <FONT color="green">136</FONT> * is the least significant bit of the largest singular value.</p><a name="line.136"></a>
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140 <FONT color="green">137</FONT> * @return effective numerical matrix rank<a name="line.137"></a>
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141 <FONT color="green">138</FONT> */<a name="line.138"></a>
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142 <FONT color="green">139</FONT> int getRank();<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> * Get a solver for finding the A &times; X = B solution in least square sense.<a name="line.142"></a>
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146 <FONT color="green">143</FONT> * @return a solver<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> DecompositionSolver getSolver();<a name="line.145"></a>
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149 <FONT color="green">146</FONT> <a name="line.146"></a>
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150 <FONT color="green">147</FONT> }<a name="line.147"></a>
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211 </PRE>
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212 </BODY>
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213 </HTML>
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