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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> * An interface to classes that implement an algorithm to calculate the<a name="line.22"></a> <FONT color="green">023</FONT> * eigen decomposition of a real matrix.<a name="line.23"></a> <FONT color="green">024</FONT> * <p>The eigen decomposition of matrix A is a set of two matrices:<a name="line.24"></a> <FONT color="green">025</FONT> * V and D such that A = V &times; D &times; V<sup>T</sup>.<a name="line.25"></a> <FONT color="green">026</FONT> * A, V and D are all m &times; m matrices.</p><a name="line.26"></a> <FONT color="green">027</FONT> * <p>This interface is similar in spirit to the <code>EigenvalueDecomposition</code><a name="line.27"></a> <FONT color="green">028</FONT> * class from the <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a><a name="line.28"></a> <FONT color="green">029</FONT> * library, with the following changes:</p><a name="line.29"></a> <FONT color="green">030</FONT> * <ul><a name="line.30"></a> <FONT color="green">031</FONT> * <li>a {@link #getVT() getVt} method has been added,</li><a name="line.31"></a> <FONT color="green">032</FONT> * <li>two {@link #getRealEigenvalue(int) getRealEigenvalue} and {@link #getImagEigenvalue(int)<a name="line.32"></a> <FONT color="green">033</FONT> * getImagEigenvalue} methods to pick up a single eigenvalue have been added,</li><a name="line.33"></a> <FONT color="green">034</FONT> * <li>a {@link #getEigenvector(int) getEigenvector} method to pick up a single<a name="line.34"></a> <FONT color="green">035</FONT> * eigenvector has been added,</li><a name="line.35"></a> <FONT color="green">036</FONT> * <li>a {@link #getDeterminant() getDeterminant} method has been added.</li><a name="line.36"></a> <FONT color="green">037</FONT> * <li>a {@link #getSolver() getSolver} method has been added.</li><a name="line.37"></a> <FONT color="green">038</FONT> * </ul><a name="line.38"></a> <FONT color="green">039</FONT> * @see <a href="http://mathworld.wolfram.com/EigenDecomposition.html">MathWorld</a><a name="line.39"></a> <FONT color="green">040</FONT> * @see <a href="http://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix">Wikipedia</a><a name="line.40"></a> <FONT color="green">041</FONT> * @version $Revision: 826627 $ $Date: 2009-10-19 06:27:47 -0400 (Mon, 19 Oct 2009) $<a name="line.41"></a> <FONT color="green">042</FONT> * @since 2.0<a name="line.42"></a> <FONT color="green">043</FONT> */<a name="line.43"></a> <FONT color="green">044</FONT> public interface EigenDecomposition {<a name="line.44"></a> <FONT color="green">045</FONT> <a name="line.45"></a> <FONT color="green">046</FONT> /**<a name="line.46"></a> <FONT color="green">047</FONT> * Returns the matrix V of the decomposition.<a name="line.47"></a> <FONT color="green">048</FONT> * <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p><a name="line.48"></a> <FONT color="green">049</FONT> * <p>The columns of V are the eigenvectors of the original matrix.</p><a name="line.49"></a> <FONT color="green">050</FONT> * @return the V matrix<a name="line.50"></a> <FONT color="green">051</FONT> */<a name="line.51"></a> <FONT color="green">052</FONT> RealMatrix getV();<a name="line.52"></a> <FONT color="green">053</FONT> <a name="line.53"></a> <FONT color="green">054</FONT> /**<a name="line.54"></a> <FONT color="green">055</FONT> * Returns the block diagonal matrix D of the decomposition.<a name="line.55"></a> <FONT color="green">056</FONT> * <p>D is a block diagonal matrix.</p><a name="line.56"></a> <FONT color="green">057</FONT> * <p>Real eigenvalues are on the diagonal while complex values are on<a name="line.57"></a> <FONT color="green">058</FONT> * 2x2 blocks { {real +imaginary}, {-imaginary, real} }.</p><a name="line.58"></a> <FONT color="green">059</FONT> * @return the D matrix<a name="line.59"></a> <FONT color="green">060</FONT> * @see #getRealEigenvalues()<a name="line.60"></a> <FONT color="green">061</FONT> * @see #getImagEigenvalues()<a name="line.61"></a> <FONT color="green">062</FONT> */<a name="line.62"></a> <FONT color="green">063</FONT> RealMatrix getD();<a name="line.63"></a> <FONT color="green">064</FONT> <a name="line.64"></a> <FONT color="green">065</FONT> /**<a name="line.65"></a> <FONT color="green">066</FONT> * Returns the transpose of the matrix V of the decomposition.<a name="line.66"></a> <FONT color="green">067</FONT> * <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p><a name="line.67"></a> <FONT color="green">068</FONT> * <p>The columns of V are the eigenvectors of the original matrix.</p><a name="line.68"></a> <FONT color="green">069</FONT> * @return the transpose of the V matrix<a name="line.69"></a> <FONT color="green">070</FONT> */<a name="line.70"></a> <FONT color="green">071</FONT> RealMatrix getVT();<a name="line.71"></a> <FONT color="green">072</FONT> <a name="line.72"></a> <FONT color="green">073</FONT> /**<a name="line.73"></a> <FONT color="green">074</FONT> * Returns a copy of the real parts of the eigenvalues of the original matrix.<a name="line.74"></a> <FONT color="green">075</FONT> * @return a copy of the real parts of the eigenvalues of the original matrix<a name="line.75"></a> <FONT color="green">076</FONT> * @see #getD()<a name="line.76"></a> <FONT color="green">077</FONT> * @see #getRealEigenvalue(int)<a name="line.77"></a> <FONT color="green">078</FONT> * @see #getImagEigenvalues()<a name="line.78"></a> <FONT color="green">079</FONT> */<a name="line.79"></a> <FONT color="green">080</FONT> double[] getRealEigenvalues();<a name="line.80"></a> <FONT color="green">081</FONT> <a name="line.81"></a> <FONT color="green">082</FONT> /**<a name="line.82"></a> <FONT color="green">083</FONT> * Returns the real part of the i<sup>th</sup> eigenvalue of the original matrix.<a name="line.83"></a> <FONT color="green">084</FONT> * @param i index of the eigenvalue (counting from 0)<a name="line.84"></a> <FONT color="green">085</FONT> * @return real part of the i<sup>th</sup> eigenvalue of the original matrix<a name="line.85"></a> <FONT color="green">086</FONT> * @see #getD()<a name="line.86"></a> <FONT color="green">087</FONT> * @see #getRealEigenvalues()<a name="line.87"></a> <FONT color="green">088</FONT> * @see #getImagEigenvalue(int)<a name="line.88"></a> <FONT color="green">089</FONT> */<a name="line.89"></a> <FONT color="green">090</FONT> double getRealEigenvalue(int i);<a name="line.90"></a> <FONT color="green">091</FONT> <a name="line.91"></a> <FONT color="green">092</FONT> /**<a name="line.92"></a> <FONT color="green">093</FONT> * Returns a copy of the imaginary parts of the eigenvalues of the original matrix.<a name="line.93"></a> <FONT color="green">094</FONT> * @return a copy of the imaginary parts of the eigenvalues of the original matrix<a name="line.94"></a> <FONT color="green">095</FONT> * @see #getD()<a name="line.95"></a> <FONT color="green">096</FONT> * @see #getImagEigenvalue(int)<a name="line.96"></a> <FONT color="green">097</FONT> * @see #getRealEigenvalues()<a name="line.97"></a> <FONT color="green">098</FONT> */<a name="line.98"></a> <FONT color="green">099</FONT> double[] getImagEigenvalues();<a name="line.99"></a> <FONT color="green">100</FONT> <a name="line.100"></a> <FONT color="green">101</FONT> /**<a name="line.101"></a> <FONT color="green">102</FONT> * Returns the imaginary part of the i<sup>th</sup> eigenvalue of the original matrix.<a name="line.102"></a> <FONT color="green">103</FONT> * @param i index of the eigenvalue (counting from 0)<a name="line.103"></a> <FONT color="green">104</FONT> * @return imaginary part of the i<sup>th</sup> eigenvalue of the original matrix<a name="line.104"></a> <FONT color="green">105</FONT> * @see #getD()<a name="line.105"></a> <FONT color="green">106</FONT> * @see #getImagEigenvalues()<a name="line.106"></a> <FONT color="green">107</FONT> * @see #getRealEigenvalue(int)<a name="line.107"></a> <FONT color="green">108</FONT> */<a name="line.108"></a> <FONT color="green">109</FONT> double getImagEigenvalue(int i);<a name="line.109"></a> <FONT color="green">110</FONT> <a name="line.110"></a> <FONT color="green">111</FONT> /**<a name="line.111"></a> <FONT color="green">112</FONT> * Returns a copy of the i<sup>th</sup> eigenvector of the original matrix.<a name="line.112"></a> <FONT color="green">113</FONT> * @param i index of the eigenvector (counting from 0)<a name="line.113"></a> <FONT color="green">114</FONT> * @return copy of the i<sup>th</sup> eigenvector of the original matrix<a name="line.114"></a> <FONT color="green">115</FONT> * @see #getD()<a name="line.115"></a> <FONT color="green">116</FONT> */<a name="line.116"></a> <FONT color="green">117</FONT> RealVector getEigenvector(int i);<a name="line.117"></a> <FONT color="green">118</FONT> <a name="line.118"></a> <FONT color="green">119</FONT> /**<a name="line.119"></a> <FONT color="green">120</FONT> * Return the determinant of the matrix<a name="line.120"></a> <FONT color="green">121</FONT> * @return determinant of the matrix<a name="line.121"></a> <FONT color="green">122</FONT> */<a name="line.122"></a> <FONT color="green">123</FONT> double getDeterminant();<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> * Get a solver for finding the A &times; X = B solution in exact linear sense.<a name="line.126"></a> <FONT color="green">127</FONT> * @return a solver<a name="line.127"></a> <FONT color="green">128</FONT> */<a name="line.128"></a> <FONT color="green">129</FONT> DecompositionSolver getSolver();<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> </PRE> </BODY> </HTML>