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| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.linear;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> <a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> /**<a name="line.22"></a> <FONT color="green">023</FONT> * An interface to classes that implement an algorithm to calculate the<a name="line.23"></a> <FONT color="green">024</FONT> * Singular Value Decomposition of a real matrix.<a name="line.24"></a> <FONT color="green">025</FONT> * <p><a name="line.25"></a> <FONT color="green">026</FONT> * The Singular Value Decomposition of matrix A is a set of three matrices: U,<a name="line.26"></a> <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> <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> <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> <FONT color="green">030</FONT> * n orthogonal matrix (hence V<sup>T</sup> is also orthogonal) where<a name="line.30"></a> <FONT color="green">031</FONT> * p=min(m,n).<a name="line.31"></a> <FONT color="green">032</FONT> * </p><a name="line.32"></a> <FONT color="green">033</FONT> * <p>This interface is similar to the class with similar name from the<a name="line.33"></a> <FONT color="green">034</FONT> * <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the<a name="line.34"></a> <FONT color="green">035</FONT> * following changes:</p><a name="line.35"></a> <FONT color="green">036</FONT> * <ul><a name="line.36"></a> <FONT color="green">037</FONT> * <li>the <code>norm2</code> method which has been renamed as {@link #getNorm()<a name="line.37"></a> <FONT color="green">038</FONT> * getNorm},</li><a name="line.38"></a> <FONT color="green">039</FONT> * <li>the <code>cond</code> method which has been renamed as {@link<a name="line.39"></a> <FONT color="green">040</FONT> * #getConditionNumber() getConditionNumber},</li><a name="line.40"></a> <FONT color="green">041</FONT> * <li>the <code>rank</code> method which has been renamed as {@link #getRank()<a name="line.41"></a> <FONT color="green">042</FONT> * getRank},</li><a name="line.42"></a> <FONT color="green">043</FONT> * <li>a {@link #getUT() getUT} method has been added,</li><a name="line.43"></a> <FONT color="green">044</FONT> * <li>a {@link #getVT() getVT} method has been added,</li><a name="line.44"></a> <FONT color="green">045</FONT> * <li>a {@link #getSolver() getSolver} method has been added,</li><a name="line.45"></a> <FONT color="green">046</FONT> * <li>a {@link #getCovariance(double) getCovariance} method has been added.</li><a name="line.46"></a> <FONT color="green">047</FONT> * </ul><a name="line.47"></a> <FONT color="green">048</FONT> * @see <a href="http://mathworld.wolfram.com/SingularValueDecomposition.html">MathWorld</a><a name="line.48"></a> <FONT color="green">049</FONT> * @see <a href="http://en.wikipedia.org/wiki/Singular_value_decomposition">Wikipedia</a><a name="line.49"></a> <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> <FONT color="green">051</FONT> * @since 2.0<a name="line.51"></a> <FONT color="green">052</FONT> */<a name="line.52"></a> <FONT color="green">053</FONT> public interface SingularValueDecomposition {<a name="line.53"></a> <FONT color="green">054</FONT> <a name="line.54"></a> <FONT color="green">055</FONT> /**<a name="line.55"></a> <FONT color="green">056</FONT> * Returns the matrix U of the decomposition.<a name="line.56"></a> <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> <FONT color="green">058</FONT> * @return the U matrix<a name="line.58"></a> <FONT color="green">059</FONT> * @see #getUT()<a name="line.59"></a> <FONT color="green">060</FONT> */<a name="line.60"></a> <FONT color="green">061</FONT> RealMatrix getU();<a name="line.61"></a> <FONT color="green">062</FONT> <a name="line.62"></a> <FONT color="green">063</FONT> /**<a name="line.63"></a> <FONT color="green">064</FONT> * Returns the transpose of the matrix U of the decomposition.<a name="line.64"></a> <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> <FONT color="green">066</FONT> * @return the U matrix (or null if decomposed matrix is singular)<a name="line.66"></a> <FONT color="green">067</FONT> * @see #getU()<a name="line.67"></a> <FONT color="green">068</FONT> */<a name="line.68"></a> <FONT color="green">069</FONT> RealMatrix getUT();<a name="line.69"></a> <FONT color="green">070</FONT> <a name="line.70"></a> <FONT color="green">071</FONT> /**<a name="line.71"></a> <FONT color="green">072</FONT> * Returns the diagonal matrix &Sigma; of the decomposition.<a name="line.72"></a> <FONT color="green">073</FONT> * <p>&Sigma; is a diagonal matrix. The singular values are provided in<a name="line.73"></a> <FONT color="green">074</FONT> * non-increasing order, for compatibility with Jama.</p><a name="line.74"></a> <FONT color="green">075</FONT> * @return the &Sigma; matrix<a name="line.75"></a> <FONT color="green">076</FONT> */<a name="line.76"></a> <FONT color="green">077</FONT> RealMatrix getS();<a name="line.77"></a> <FONT color="green">078</FONT> <a name="line.78"></a> <FONT color="green">079</FONT> /**<a name="line.79"></a> <FONT color="green">080</FONT> * Returns the diagonal elements of the matrix &Sigma; of the decomposition.<a name="line.80"></a> <FONT color="green">081</FONT> * <p>The singular values are provided in non-increasing order, for<a name="line.81"></a> <FONT color="green">082</FONT> * compatibility with Jama.</p><a name="line.82"></a> <FONT color="green">083</FONT> * @return the diagonal elements of the &Sigma; matrix<a name="line.83"></a> <FONT color="green">084</FONT> */<a name="line.84"></a> <FONT color="green">085</FONT> double[] getSingularValues();<a name="line.85"></a> <FONT color="green">086</FONT> <a name="line.86"></a> <FONT color="green">087</FONT> /**<a name="line.87"></a> <FONT color="green">088</FONT> * Returns the matrix V of the decomposition.<a name="line.88"></a> <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> <FONT color="green">090</FONT> * @return the V matrix (or null if decomposed matrix is singular)<a name="line.90"></a> <FONT color="green">091</FONT> * @see #getVT()<a name="line.91"></a> <FONT color="green">092</FONT> */<a name="line.92"></a> <FONT color="green">093</FONT> RealMatrix getV();<a name="line.93"></a> <FONT color="green">094</FONT> <a name="line.94"></a> <FONT color="green">095</FONT> /**<a name="line.95"></a> <FONT color="green">096</FONT> * Returns the transpose of the matrix V of the decomposition.<a name="line.96"></a> <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> <FONT color="green">098</FONT> * @return the V matrix (or null if decomposed matrix is singular)<a name="line.98"></a> <FONT color="green">099</FONT> * @see #getV()<a name="line.99"></a> <FONT color="green">100</FONT> */<a name="line.100"></a> <FONT color="green">101</FONT> RealMatrix getVT();<a name="line.101"></a> <FONT color="green">102</FONT> <a name="line.102"></a> <FONT color="green">103</FONT> /**<a name="line.103"></a> <FONT color="green">104</FONT> * Returns the n &times; n covariance matrix.<a name="line.104"></a> <FONT color="green">105</FONT> * <p>The covariance matrix is V &times; J &times; V<sup>T</sup><a name="line.105"></a> <FONT color="green">106</FONT> * where J is the diagonal matrix of the inverse of the squares of<a name="line.106"></a> <FONT color="green">107</FONT> * the singular values.</p><a name="line.107"></a> <FONT color="green">108</FONT> * @param minSingularValue value below which singular values are ignored<a name="line.108"></a> <FONT color="green">109</FONT> * (a 0 or negative value implies all singular value will be used)<a name="line.109"></a> <FONT color="green">110</FONT> * @return covariance matrix<a name="line.110"></a> <FONT color="green">111</FONT> * @exception IllegalArgumentException if minSingularValue is larger than<a name="line.111"></a> <FONT color="green">112</FONT> * the largest singular value, meaning all singular values are ignored<a name="line.112"></a> <FONT color="green">113</FONT> */<a name="line.113"></a> <FONT color="green">114</FONT> RealMatrix getCovariance(double minSingularValue) throws IllegalArgumentException;<a name="line.114"></a> <FONT color="green">115</FONT> <a name="line.115"></a> <FONT color="green">116</FONT> /**<a name="line.116"></a> <FONT color="green">117</FONT> * Returns the L<sub>2</sub> norm of the matrix.<a name="line.117"></a> <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> <FONT color="green">119</FONT> * |u|<sub>2</sub>), where |.|<sub>2</sub> denotes the vectorial 2-norm<a name="line.119"></a> <FONT color="green">120</FONT> * (i.e. the traditional euclidian norm).</p><a name="line.120"></a> <FONT color="green">121</FONT> * @return norm<a name="line.121"></a> <FONT color="green">122</FONT> */<a name="line.122"></a> <FONT color="green">123</FONT> double getNorm();<a name="line.123"></a> <FONT color="green">124</FONT> <a name="line.124"></a> <FONT color="green">125</FONT> /**<a name="line.125"></a> <FONT color="green">126</FONT> * Return the condition number of the matrix.<a name="line.126"></a> <FONT color="green">127</FONT> * @return condition number of the matrix<a name="line.127"></a> <FONT color="green">128</FONT> */<a name="line.128"></a> <FONT color="green">129</FONT> double getConditionNumber();<a name="line.129"></a> <FONT color="green">130</FONT> <a name="line.130"></a> <FONT color="green">131</FONT> /**<a name="line.131"></a> <FONT color="green">132</FONT> * Return the effective numerical matrix rank.<a name="line.132"></a> <FONT color="green">133</FONT> * <p>The effective numerical rank is the number of non-negligible<a name="line.133"></a> <FONT color="green">134</FONT> * singular values. The threshold used to identify non-negligible<a name="line.134"></a> <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> <FONT color="green">136</FONT> * is the least significant bit of the largest singular value.</p><a name="line.136"></a> <FONT color="green">137</FONT> * @return effective numerical matrix rank<a name="line.137"></a> <FONT color="green">138</FONT> */<a name="line.138"></a> <FONT color="green">139</FONT> int getRank();<a name="line.139"></a> <FONT color="green">140</FONT> <a name="line.140"></a> <FONT color="green">141</FONT> /**<a name="line.141"></a> <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> <FONT color="green">143</FONT> * @return a solver<a name="line.143"></a> <FONT color="green">144</FONT> */<a name="line.144"></a> <FONT color="green">145</FONT> DecompositionSolver getSolver();<a name="line.145"></a> <FONT color="green">146</FONT> <a name="line.146"></a> <FONT color="green">147</FONT> }<a name="line.147"></a> </PRE> </BODY> </HTML>