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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> import org.apache.commons.math.MathRuntimeException;<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> /**<a name="line.23"></a> <FONT color="green">024</FONT> * Calculates the Cholesky decomposition of a matrix.<a name="line.24"></a> <FONT color="green">025</FONT> * <p>The Cholesky decomposition of a real symmetric positive-definite<a name="line.25"></a> <FONT color="green">026</FONT> * matrix A consists of a lower triangular matrix L with same size that<a name="line.26"></a> <FONT color="green">027</FONT> * satisfy: A = LL<sup>T</sup>Q = I). In a sense, this is the square root of A.</p><a name="line.27"></a> <FONT color="green">028</FONT> *<a name="line.28"></a> <FONT color="green">029</FONT> * @see <a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a><a name="line.29"></a> <FONT color="green">030</FONT> * @see <a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a><a name="line.30"></a> <FONT color="green">031</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.31"></a> <FONT color="green">032</FONT> * @since 2.0<a name="line.32"></a> <FONT color="green">033</FONT> */<a name="line.33"></a> <FONT color="green">034</FONT> public class CholeskyDecompositionImpl implements CholeskyDecomposition {<a name="line.34"></a> <FONT color="green">035</FONT> <a name="line.35"></a> <FONT color="green">036</FONT> /** Default threshold above which off-diagonal elements are considered too different<a name="line.36"></a> <FONT color="green">037</FONT> * and matrix not symmetric. */<a name="line.37"></a> <FONT color="green">038</FONT> public static final double DEFAULT_RELATIVE_SYMMETRY_THRESHOLD = 1.0e-15;<a name="line.38"></a> <FONT color="green">039</FONT> <a name="line.39"></a> <FONT color="green">040</FONT> /** Default threshold below which diagonal elements are considered null<a name="line.40"></a> <FONT color="green">041</FONT> * and matrix not positive definite. */<a name="line.41"></a> <FONT color="green">042</FONT> public static final double DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD = 1.0e-10;<a name="line.42"></a> <FONT color="green">043</FONT> <a name="line.43"></a> <FONT color="green">044</FONT> /** Row-oriented storage for L<sup>T</sup> matrix data. */<a name="line.44"></a> <FONT color="green">045</FONT> private double[][] lTData;<a name="line.45"></a> <FONT color="green">046</FONT> <a name="line.46"></a> <FONT color="green">047</FONT> /** Cached value of L. */<a name="line.47"></a> <FONT color="green">048</FONT> private RealMatrix cachedL;<a name="line.48"></a> <FONT color="green">049</FONT> <a name="line.49"></a> <FONT color="green">050</FONT> /** Cached value of LT. */<a name="line.50"></a> <FONT color="green">051</FONT> private RealMatrix cachedLT;<a name="line.51"></a> <FONT color="green">052</FONT> <a name="line.52"></a> <FONT color="green">053</FONT> /**<a name="line.53"></a> <FONT color="green">054</FONT> * Calculates the Cholesky decomposition of the given matrix.<a name="line.54"></a> <FONT color="green">055</FONT> * <p><a name="line.55"></a> <FONT color="green">056</FONT> * Calling this constructor is equivalent to call {@link<a name="line.56"></a> <FONT color="green">057</FONT> * #CholeskyDecompositionImpl(RealMatrix, double, double)} with the<a name="line.57"></a> <FONT color="green">058</FONT> * thresholds set to the default values {@link<a name="line.58"></a> <FONT color="green">059</FONT> * #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD} and {@link<a name="line.59"></a> <FONT color="green">060</FONT> * #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD}<a name="line.60"></a> <FONT color="green">061</FONT> * </p><a name="line.61"></a> <FONT color="green">062</FONT> * @param matrix the matrix to decompose<a name="line.62"></a> <FONT color="green">063</FONT> * @exception NonSquareMatrixException if matrix is not square<a name="line.63"></a> <FONT color="green">064</FONT> * @exception NotSymmetricMatrixException if matrix is not symmetric<a name="line.64"></a> <FONT color="green">065</FONT> * @exception NotPositiveDefiniteMatrixException if the matrix is not<a name="line.65"></a> <FONT color="green">066</FONT> * strictly positive definite<a name="line.66"></a> <FONT color="green">067</FONT> * @see #CholeskyDecompositionImpl(RealMatrix, double, double)<a name="line.67"></a> <FONT color="green">068</FONT> * @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD<a name="line.68"></a> <FONT color="green">069</FONT> * @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD<a name="line.69"></a> <FONT color="green">070</FONT> */<a name="line.70"></a> <FONT color="green">071</FONT> public CholeskyDecompositionImpl(final RealMatrix matrix)<a name="line.71"></a> <FONT color="green">072</FONT> throws NonSquareMatrixException,<a name="line.72"></a> <FONT color="green">073</FONT> NotSymmetricMatrixException, NotPositiveDefiniteMatrixException {<a name="line.73"></a> <FONT color="green">074</FONT> this(matrix, DEFAULT_RELATIVE_SYMMETRY_THRESHOLD,<a name="line.74"></a> <FONT color="green">075</FONT> DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD);<a name="line.75"></a> <FONT color="green">076</FONT> }<a name="line.76"></a> <FONT color="green">077</FONT> <a name="line.77"></a> <FONT color="green">078</FONT> /**<a name="line.78"></a> <FONT color="green">079</FONT> * Calculates the Cholesky decomposition of the given matrix.<a name="line.79"></a> <FONT color="green">080</FONT> * @param matrix the matrix to decompose<a name="line.80"></a> <FONT color="green">081</FONT> * @param relativeSymmetryThreshold threshold above which off-diagonal<a name="line.81"></a> <FONT color="green">082</FONT> * elements are considered too different and matrix not symmetric<a name="line.82"></a> <FONT color="green">083</FONT> * @param absolutePositivityThreshold threshold below which diagonal<a name="line.83"></a> <FONT color="green">084</FONT> * elements are considered null and matrix not positive definite<a name="line.84"></a> <FONT color="green">085</FONT> * @exception NonSquareMatrixException if matrix is not square<a name="line.85"></a> <FONT color="green">086</FONT> * @exception NotSymmetricMatrixException if matrix is not symmetric<a name="line.86"></a> <FONT color="green">087</FONT> * @exception NotPositiveDefiniteMatrixException if the matrix is not<a name="line.87"></a> <FONT color="green">088</FONT> * strictly positive definite<a name="line.88"></a> <FONT color="green">089</FONT> * @see #CholeskyDecompositionImpl(RealMatrix)<a name="line.89"></a> <FONT color="green">090</FONT> * @see #DEFAULT_RELATIVE_SYMMETRY_THRESHOLD<a name="line.90"></a> <FONT color="green">091</FONT> * @see #DEFAULT_ABSOLUTE_POSITIVITY_THRESHOLD<a name="line.91"></a> <FONT color="green">092</FONT> */<a name="line.92"></a> <FONT color="green">093</FONT> public CholeskyDecompositionImpl(final RealMatrix matrix,<a name="line.93"></a> <FONT color="green">094</FONT> final double relativeSymmetryThreshold,<a name="line.94"></a> <FONT color="green">095</FONT> final double absolutePositivityThreshold)<a name="line.95"></a> <FONT color="green">096</FONT> throws NonSquareMatrixException,<a name="line.96"></a> <FONT color="green">097</FONT> NotSymmetricMatrixException, NotPositiveDefiniteMatrixException {<a name="line.97"></a> <FONT color="green">098</FONT> <a name="line.98"></a> <FONT color="green">099</FONT> if (!matrix.isSquare()) {<a name="line.99"></a> <FONT color="green">100</FONT> throw new NonSquareMatrixException(matrix.getRowDimension(),<a name="line.100"></a> <FONT color="green">101</FONT> matrix.getColumnDimension());<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> final int order = matrix.getRowDimension();<a name="line.104"></a> <FONT color="green">105</FONT> lTData = matrix.getData();<a name="line.105"></a> <FONT color="green">106</FONT> cachedL = null;<a name="line.106"></a> <FONT color="green">107</FONT> cachedLT = null;<a name="line.107"></a> <FONT color="green">108</FONT> <a name="line.108"></a> <FONT color="green">109</FONT> // check the matrix before transformation<a name="line.109"></a> <FONT color="green">110</FONT> for (int i = 0; i < order; ++i) {<a name="line.110"></a> <FONT color="green">111</FONT> <a name="line.111"></a> <FONT color="green">112</FONT> final double[] lI = lTData[i];<a name="line.112"></a> <FONT color="green">113</FONT> <a name="line.113"></a> <FONT color="green">114</FONT> // check off-diagonal elements (and reset them to 0)<a name="line.114"></a> <FONT color="green">115</FONT> for (int j = i + 1; j < order; ++j) {<a name="line.115"></a> <FONT color="green">116</FONT> final double[] lJ = lTData[j];<a name="line.116"></a> <FONT color="green">117</FONT> final double lIJ = lI[j];<a name="line.117"></a> <FONT color="green">118</FONT> final double lJI = lJ[i];<a name="line.118"></a> <FONT color="green">119</FONT> final double maxDelta =<a name="line.119"></a> <FONT color="green">120</FONT> relativeSymmetryThreshold * Math.max(Math.abs(lIJ), Math.abs(lJI));<a name="line.120"></a> <FONT color="green">121</FONT> if (Math.abs(lIJ - lJI) > maxDelta) {<a name="line.121"></a> <FONT color="green">122</FONT> throw new NotSymmetricMatrixException();<a name="line.122"></a> <FONT color="green">123</FONT> }<a name="line.123"></a> <FONT color="green">124</FONT> lJ[i] = 0;<a name="line.124"></a> <FONT color="green">125</FONT> }<a name="line.125"></a> <FONT color="green">126</FONT> }<a name="line.126"></a> <FONT color="green">127</FONT> <a name="line.127"></a> <FONT color="green">128</FONT> // transform the matrix<a name="line.128"></a> <FONT color="green">129</FONT> for (int i = 0; i < order; ++i) {<a name="line.129"></a> <FONT color="green">130</FONT> <a name="line.130"></a> <FONT color="green">131</FONT> final double[] ltI = lTData[i];<a name="line.131"></a> <FONT color="green">132</FONT> <a name="line.132"></a> <FONT color="green">133</FONT> // check diagonal element<a name="line.133"></a> <FONT color="green">134</FONT> if (ltI[i] < absolutePositivityThreshold) {<a name="line.134"></a> <FONT color="green">135</FONT> throw new NotPositiveDefiniteMatrixException();<a name="line.135"></a> <FONT color="green">136</FONT> }<a name="line.136"></a> <FONT color="green">137</FONT> <a name="line.137"></a> <FONT color="green">138</FONT> ltI[i] = Math.sqrt(ltI[i]);<a name="line.138"></a> <FONT color="green">139</FONT> final double inverse = 1.0 / ltI[i];<a name="line.139"></a> <FONT color="green">140</FONT> <a name="line.140"></a> <FONT color="green">141</FONT> for (int q = order - 1; q > i; --q) {<a name="line.141"></a> <FONT color="green">142</FONT> ltI[q] *= inverse;<a name="line.142"></a> <FONT color="green">143</FONT> final double[] ltQ = lTData[q];<a name="line.143"></a> <FONT color="green">144</FONT> for (int p = q; p < order; ++p) {<a name="line.144"></a> <FONT color="green">145</FONT> ltQ[p] -= ltI[q] * ltI[p];<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> <FONT color="green">148</FONT> <a name="line.148"></a> <FONT color="green">149</FONT> }<a name="line.149"></a> <FONT color="green">150</FONT> <a name="line.150"></a> <FONT color="green">151</FONT> }<a name="line.151"></a> <FONT color="green">152</FONT> <a name="line.152"></a> <FONT color="green">153</FONT> /** {@inheritDoc} */<a name="line.153"></a> <FONT color="green">154</FONT> public RealMatrix getL() {<a name="line.154"></a> <FONT color="green">155</FONT> if (cachedL == null) {<a name="line.155"></a> <FONT color="green">156</FONT> cachedL = getLT().transpose();<a name="line.156"></a> <FONT color="green">157</FONT> }<a name="line.157"></a> <FONT color="green">158</FONT> return cachedL;<a name="line.158"></a> <FONT color="green">159</FONT> }<a name="line.159"></a> <FONT color="green">160</FONT> <a name="line.160"></a> <FONT color="green">161</FONT> /** {@inheritDoc} */<a name="line.161"></a> <FONT color="green">162</FONT> public RealMatrix getLT() {<a name="line.162"></a> <FONT color="green">163</FONT> <a name="line.163"></a> <FONT color="green">164</FONT> if (cachedLT == null) {<a name="line.164"></a> <FONT color="green">165</FONT> cachedLT = MatrixUtils.createRealMatrix(lTData);<a name="line.165"></a> <FONT color="green">166</FONT> }<a name="line.166"></a> <FONT color="green">167</FONT> <a name="line.167"></a> <FONT color="green">168</FONT> // return the cached matrix<a name="line.168"></a> <FONT color="green">169</FONT> return cachedLT;<a name="line.169"></a> <FONT color="green">170</FONT> <a name="line.170"></a> <FONT color="green">171</FONT> }<a name="line.171"></a> <FONT color="green">172</FONT> <a name="line.172"></a> <FONT color="green">173</FONT> /** {@inheritDoc} */<a name="line.173"></a> <FONT color="green">174</FONT> public double getDeterminant() {<a name="line.174"></a> <FONT color="green">175</FONT> double determinant = 1.0;<a name="line.175"></a> <FONT color="green">176</FONT> for (int i = 0; i < lTData.length; ++i) {<a name="line.176"></a> <FONT color="green">177</FONT> double lTii = lTData[i][i];<a name="line.177"></a> <FONT color="green">178</FONT> determinant *= lTii * lTii;<a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> <FONT color="green">180</FONT> return determinant;<a name="line.180"></a> <FONT color="green">181</FONT> }<a name="line.181"></a> <FONT color="green">182</FONT> <a name="line.182"></a> <FONT color="green">183</FONT> /** {@inheritDoc} */<a name="line.183"></a> <FONT color="green">184</FONT> public DecompositionSolver getSolver() {<a name="line.184"></a> <FONT color="green">185</FONT> return new Solver(lTData);<a name="line.185"></a> <FONT color="green">186</FONT> }<a name="line.186"></a> <FONT color="green">187</FONT> <a name="line.187"></a> <FONT color="green">188</FONT> /** Specialized solver. */<a name="line.188"></a> <FONT color="green">189</FONT> private static class Solver implements DecompositionSolver {<a name="line.189"></a> <FONT color="green">190</FONT> <a name="line.190"></a> <FONT color="green">191</FONT> /** Row-oriented storage for L<sup>T</sup> matrix data. */<a name="line.191"></a> <FONT color="green">192</FONT> private final double[][] lTData;<a name="line.192"></a> <FONT color="green">193</FONT> <a name="line.193"></a> <FONT color="green">194</FONT> /**<a name="line.194"></a> <FONT color="green">195</FONT> * Build a solver from decomposed matrix.<a name="line.195"></a> <FONT color="green">196</FONT> * @param lTData row-oriented storage for L<sup>T</sup> matrix data<a name="line.196"></a> <FONT color="green">197</FONT> */<a name="line.197"></a> <FONT color="green">198</FONT> private Solver(final double[][] lTData) {<a name="line.198"></a> <FONT color="green">199</FONT> this.lTData = lTData;<a name="line.199"></a> <FONT color="green">200</FONT> }<a name="line.200"></a> <FONT color="green">201</FONT> <a name="line.201"></a> <FONT color="green">202</FONT> /** {@inheritDoc} */<a name="line.202"></a> <FONT color="green">203</FONT> public boolean isNonSingular() {<a name="line.203"></a> <FONT color="green">204</FONT> // if we get this far, the matrix was positive definite, hence non-singular<a name="line.204"></a> <FONT color="green">205</FONT> return true;<a name="line.205"></a> <FONT color="green">206</FONT> }<a name="line.206"></a> <FONT color="green">207</FONT> <a name="line.207"></a> <FONT color="green">208</FONT> /** {@inheritDoc} */<a name="line.208"></a> <FONT color="green">209</FONT> public double[] solve(double[] b)<a name="line.209"></a> <FONT color="green">210</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.210"></a> <FONT color="green">211</FONT> <a name="line.211"></a> <FONT color="green">212</FONT> final int m = lTData.length;<a name="line.212"></a> <FONT color="green">213</FONT> if (b.length != m) {<a name="line.213"></a> <FONT color="green">214</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.214"></a> <FONT color="green">215</FONT> "vector length mismatch: got {0} but expected {1}",<a name="line.215"></a> <FONT color="green">216</FONT> b.length, m);<a name="line.216"></a> <FONT color="green">217</FONT> }<a name="line.217"></a> <FONT color="green">218</FONT> <a name="line.218"></a> <FONT color="green">219</FONT> final double[] x = b.clone();<a name="line.219"></a> <FONT color="green">220</FONT> <a name="line.220"></a> <FONT color="green">221</FONT> // Solve LY = b<a name="line.221"></a> <FONT color="green">222</FONT> for (int j = 0; j < m; j++) {<a name="line.222"></a> <FONT color="green">223</FONT> final double[] lJ = lTData[j];<a name="line.223"></a> <FONT color="green">224</FONT> x[j] /= lJ[j];<a name="line.224"></a> <FONT color="green">225</FONT> final double xJ = x[j];<a name="line.225"></a> <FONT color="green">226</FONT> for (int i = j + 1; i < m; i++) {<a name="line.226"></a> <FONT color="green">227</FONT> x[i] -= xJ * lJ[i];<a name="line.227"></a> <FONT color="green">228</FONT> }<a name="line.228"></a> <FONT color="green">229</FONT> }<a name="line.229"></a> <FONT color="green">230</FONT> <a name="line.230"></a> <FONT color="green">231</FONT> // Solve LTX = Y<a name="line.231"></a> <FONT color="green">232</FONT> for (int j = m - 1; j >= 0; j--) {<a name="line.232"></a> <FONT color="green">233</FONT> x[j] /= lTData[j][j];<a name="line.233"></a> <FONT color="green">234</FONT> final double xJ = x[j];<a name="line.234"></a> <FONT color="green">235</FONT> for (int i = 0; i < j; i++) {<a name="line.235"></a> <FONT color="green">236</FONT> x[i] -= xJ * lTData[i][j];<a name="line.236"></a> <FONT color="green">237</FONT> }<a name="line.237"></a> <FONT color="green">238</FONT> }<a name="line.238"></a> <FONT color="green">239</FONT> <a name="line.239"></a> <FONT color="green">240</FONT> return x;<a name="line.240"></a> <FONT color="green">241</FONT> <a name="line.241"></a> <FONT color="green">242</FONT> }<a name="line.242"></a> <FONT color="green">243</FONT> <a name="line.243"></a> <FONT color="green">244</FONT> /** {@inheritDoc} */<a name="line.244"></a> <FONT color="green">245</FONT> public RealVector solve(RealVector b)<a name="line.245"></a> <FONT color="green">246</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.246"></a> <FONT color="green">247</FONT> try {<a name="line.247"></a> <FONT color="green">248</FONT> return solve((ArrayRealVector) b);<a name="line.248"></a> <FONT color="green">249</FONT> } catch (ClassCastException cce) {<a name="line.249"></a> <FONT color="green">250</FONT> <a name="line.250"></a> <FONT color="green">251</FONT> final int m = lTData.length;<a name="line.251"></a> <FONT color="green">252</FONT> if (b.getDimension() != m) {<a name="line.252"></a> <FONT color="green">253</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.253"></a> <FONT color="green">254</FONT> "vector length mismatch: got {0} but expected {1}",<a name="line.254"></a> <FONT color="green">255</FONT> b.getDimension(), m);<a name="line.255"></a> <FONT color="green">256</FONT> }<a name="line.256"></a> <FONT color="green">257</FONT> <a name="line.257"></a> <FONT color="green">258</FONT> final double[] x = b.getData();<a name="line.258"></a> <FONT color="green">259</FONT> <a name="line.259"></a> <FONT color="green">260</FONT> // Solve LY = b<a name="line.260"></a> <FONT color="green">261</FONT> for (int j = 0; j < m; j++) {<a name="line.261"></a> <FONT color="green">262</FONT> final double[] lJ = lTData[j];<a name="line.262"></a> <FONT color="green">263</FONT> x[j] /= lJ[j];<a name="line.263"></a> <FONT color="green">264</FONT> final double xJ = x[j];<a name="line.264"></a> <FONT color="green">265</FONT> for (int i = j + 1; i < m; i++) {<a name="line.265"></a> <FONT color="green">266</FONT> x[i] -= xJ * lJ[i];<a name="line.266"></a> <FONT color="green">267</FONT> }<a name="line.267"></a> <FONT color="green">268</FONT> }<a name="line.268"></a> <FONT color="green">269</FONT> <a name="line.269"></a> <FONT color="green">270</FONT> // Solve LTX = Y<a name="line.270"></a> <FONT color="green">271</FONT> for (int j = m - 1; j >= 0; j--) {<a name="line.271"></a> <FONT color="green">272</FONT> x[j] /= lTData[j][j];<a name="line.272"></a> <FONT color="green">273</FONT> final double xJ = x[j];<a name="line.273"></a> <FONT color="green">274</FONT> for (int i = 0; i < j; i++) {<a name="line.274"></a> <FONT color="green">275</FONT> x[i] -= xJ * lTData[i][j];<a name="line.275"></a> <FONT color="green">276</FONT> }<a name="line.276"></a> <FONT color="green">277</FONT> }<a name="line.277"></a> <FONT color="green">278</FONT> <a name="line.278"></a> <FONT color="green">279</FONT> return new ArrayRealVector(x, false);<a name="line.279"></a> <FONT color="green">280</FONT> <a name="line.280"></a> <FONT color="green">281</FONT> }<a name="line.281"></a> <FONT color="green">282</FONT> }<a name="line.282"></a> <FONT color="green">283</FONT> <a name="line.283"></a> <FONT color="green">284</FONT> /** Solve the linear equation A &times; X = B.<a name="line.284"></a> <FONT color="green">285</FONT> * <p>The A matrix is implicit here. It is </p><a name="line.285"></a> <FONT color="green">286</FONT> * @param b right-hand side of the equation A &times; X = B<a name="line.286"></a> <FONT color="green">287</FONT> * @return a vector X such that A &times; X = B<a name="line.287"></a> <FONT color="green">288</FONT> * @exception IllegalArgumentException if matrices dimensions don't match<a name="line.288"></a> <FONT color="green">289</FONT> * @exception InvalidMatrixException if decomposed matrix is singular<a name="line.289"></a> <FONT color="green">290</FONT> */<a name="line.290"></a> <FONT color="green">291</FONT> public ArrayRealVector solve(ArrayRealVector b)<a name="line.291"></a> <FONT color="green">292</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.292"></a> <FONT color="green">293</FONT> return new ArrayRealVector(solve(b.getDataRef()), false);<a name="line.293"></a> <FONT color="green">294</FONT> }<a name="line.294"></a> <FONT color="green">295</FONT> <a name="line.295"></a> <FONT color="green">296</FONT> /** {@inheritDoc} */<a name="line.296"></a> <FONT color="green">297</FONT> public RealMatrix solve(RealMatrix b)<a name="line.297"></a> <FONT color="green">298</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.298"></a> <FONT color="green">299</FONT> <a name="line.299"></a> <FONT color="green">300</FONT> final int m = lTData.length;<a name="line.300"></a> <FONT color="green">301</FONT> if (b.getRowDimension() != m) {<a name="line.301"></a> <FONT color="green">302</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.302"></a> <FONT color="green">303</FONT> "dimensions mismatch: got {0}x{1} but expected {2}x{3}",<a name="line.303"></a> <FONT color="green">304</FONT> b.getRowDimension(), b.getColumnDimension(), m, "n");<a name="line.304"></a> <FONT color="green">305</FONT> }<a name="line.305"></a> <FONT color="green">306</FONT> <a name="line.306"></a> <FONT color="green">307</FONT> final int nColB = b.getColumnDimension();<a name="line.307"></a> <FONT color="green">308</FONT> double[][] x = b.getData();<a name="line.308"></a> <FONT color="green">309</FONT> <a name="line.309"></a> <FONT color="green">310</FONT> // Solve LY = b<a name="line.310"></a> <FONT color="green">311</FONT> for (int j = 0; j < m; j++) {<a name="line.311"></a> <FONT color="green">312</FONT> final double[] lJ = lTData[j];<a name="line.312"></a> <FONT color="green">313</FONT> final double lJJ = lJ[j];<a name="line.313"></a> <FONT color="green">314</FONT> final double[] xJ = x[j];<a name="line.314"></a> <FONT color="green">315</FONT> for (int k = 0; k < nColB; ++k) {<a name="line.315"></a> <FONT color="green">316</FONT> xJ[k] /= lJJ;<a name="line.316"></a> <FONT color="green">317</FONT> }<a name="line.317"></a> <FONT color="green">318</FONT> for (int i = j + 1; i < m; i++) {<a name="line.318"></a> <FONT color="green">319</FONT> final double[] xI = x[i];<a name="line.319"></a> <FONT color="green">320</FONT> final double lJI = lJ[i];<a name="line.320"></a> <FONT color="green">321</FONT> for (int k = 0; k < nColB; ++k) {<a name="line.321"></a> <FONT color="green">322</FONT> xI[k] -= xJ[k] * lJI;<a name="line.322"></a> <FONT color="green">323</FONT> }<a name="line.323"></a> <FONT color="green">324</FONT> }<a name="line.324"></a> <FONT color="green">325</FONT> }<a name="line.325"></a> <FONT color="green">326</FONT> <a name="line.326"></a> <FONT color="green">327</FONT> // Solve LTX = Y<a name="line.327"></a> <FONT color="green">328</FONT> for (int j = m - 1; j >= 0; j--) {<a name="line.328"></a> <FONT color="green">329</FONT> final double lJJ = lTData[j][j];<a name="line.329"></a> <FONT color="green">330</FONT> final double[] xJ = x[j];<a name="line.330"></a> <FONT color="green">331</FONT> for (int k = 0; k < nColB; ++k) {<a name="line.331"></a> <FONT color="green">332</FONT> xJ[k] /= lJJ;<a name="line.332"></a> <FONT color="green">333</FONT> }<a name="line.333"></a> <FONT color="green">334</FONT> for (int i = 0; i < j; i++) {<a name="line.334"></a> <FONT color="green">335</FONT> final double[] xI = x[i];<a name="line.335"></a> <FONT color="green">336</FONT> final double lIJ = lTData[i][j];<a name="line.336"></a> <FONT color="green">337</FONT> for (int k = 0; k < nColB; ++k) {<a name="line.337"></a> <FONT color="green">338</FONT> xI[k] -= xJ[k] * lIJ;<a name="line.338"></a> <FONT color="green">339</FONT> }<a name="line.339"></a> <FONT color="green">340</FONT> }<a name="line.340"></a> <FONT color="green">341</FONT> }<a name="line.341"></a> <FONT color="green">342</FONT> <a name="line.342"></a> <FONT color="green">343</FONT> return new Array2DRowRealMatrix(x, false);<a name="line.343"></a> <FONT color="green">344</FONT> <a name="line.344"></a> <FONT color="green">345</FONT> }<a name="line.345"></a> <FONT color="green">346</FONT> <a name="line.346"></a> <FONT color="green">347</FONT> /** {@inheritDoc} */<a name="line.347"></a> <FONT color="green">348</FONT> public RealMatrix getInverse() throws InvalidMatrixException {<a name="line.348"></a> <FONT color="green">349</FONT> return solve(MatrixUtils.createRealIdentityMatrix(lTData.length));<a name="line.349"></a> <FONT color="green">350</FONT> }<a name="line.350"></a> <FONT color="green">351</FONT> <a name="line.351"></a> <FONT color="green">352</FONT> }<a name="line.352"></a> <FONT color="green">353</FONT> <a name="line.353"></a> <FONT color="green">354</FONT> }<a name="line.354"></a> </PRE> </BODY> </HTML>