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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.random;<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.DimensionMismatchException;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.linear.MatrixUtils;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.linear.NotPositiveDefiniteMatrixException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.linear.RealMatrix;<a name="line.23"></a> <FONT color="green">024</FONT> <a name="line.24"></a> <FONT color="green">025</FONT> /**<a name="line.25"></a> <FONT color="green">026</FONT> * A {@link RandomVectorGenerator} that generates vectors with with<a name="line.26"></a> <FONT color="green">027</FONT> * correlated components.<a name="line.27"></a> <FONT color="green">028</FONT> * <p>Random vectors with correlated components are built by combining<a name="line.28"></a> <FONT color="green">029</FONT> * the uncorrelated components of another random vector in such a way that<a name="line.29"></a> <FONT color="green">030</FONT> * the resulting correlations are the ones specified by a positive<a name="line.30"></a> <FONT color="green">031</FONT> * definite covariance matrix.</p><a name="line.31"></a> <FONT color="green">032</FONT> * <p>The main use for correlated random vector generation is for Monte-Carlo<a name="line.32"></a> <FONT color="green">033</FONT> * simulation of physical problems with several variables, for example to<a name="line.33"></a> <FONT color="green">034</FONT> * generate error vectors to be added to a nominal vector. A particularly<a name="line.34"></a> <FONT color="green">035</FONT> * interesting case is when the generated vector should be drawn from a <a<a name="line.35"></a> <FONT color="green">036</FONT> * href="http://en.wikipedia.org/wiki/Multivariate_normal_distribution"><a name="line.36"></a> <FONT color="green">037</FONT> * Multivariate Normal Distribution</a>. The approach using a Cholesky<a name="line.37"></a> <FONT color="green">038</FONT> * decomposition is quite usual in this case. However, it cas be extended<a name="line.38"></a> <FONT color="green">039</FONT> * to other cases as long as the underlying random generator provides<a name="line.39"></a> <FONT color="green">040</FONT> * {@link NormalizedRandomGenerator normalized values} like {@link<a name="line.40"></a> <FONT color="green">041</FONT> * GaussianRandomGenerator} or {@link UniformRandomGenerator}.</p><a name="line.41"></a> <FONT color="green">042</FONT> * <p>Sometimes, the covariance matrix for a given simulation is not<a name="line.42"></a> <FONT color="green">043</FONT> * strictly positive definite. This means that the correlations are<a name="line.43"></a> <FONT color="green">044</FONT> * not all independent from each other. In this case, however, the non<a name="line.44"></a> <FONT color="green">045</FONT> * strictly positive elements found during the Cholesky decomposition<a name="line.45"></a> <FONT color="green">046</FONT> * of the covariance matrix should not be negative either, they<a name="line.46"></a> <FONT color="green">047</FONT> * should be null. Another non-conventional extension handling this case<a name="line.47"></a> <FONT color="green">048</FONT> * is used here. Rather than computing <code>C = U<sup>T</sup>.U</code><a name="line.48"></a> <FONT color="green">049</FONT> * where <code>C</code> is the covariance matrix and <code>U</code><a name="line.49"></a> <FONT color="green">050</FONT> * is an uppertriangular matrix, we compute <code>C = B.B<sup>T</sup></code><a name="line.50"></a> <FONT color="green">051</FONT> * where <code>B</code> is a rectangular matrix having<a name="line.51"></a> <FONT color="green">052</FONT> * more rows than columns. The number of columns of <code>B</code> is<a name="line.52"></a> <FONT color="green">053</FONT> * the rank of the covariance matrix, and it is the dimension of the<a name="line.53"></a> <FONT color="green">054</FONT> * uncorrelated random vector that is needed to compute the component<a name="line.54"></a> <FONT color="green">055</FONT> * of the correlated vector. This class handles this situation<a name="line.55"></a> <FONT color="green">056</FONT> * automatically.</p><a name="line.56"></a> <FONT color="green">057</FONT> *<a name="line.57"></a> <FONT color="green">058</FONT> * @version $Revision: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $<a name="line.58"></a> <FONT color="green">059</FONT> * @since 1.2<a name="line.59"></a> <FONT color="green">060</FONT> */<a name="line.60"></a> <FONT color="green">061</FONT> <a name="line.61"></a> <FONT color="green">062</FONT> public class CorrelatedRandomVectorGenerator<a name="line.62"></a> <FONT color="green">063</FONT> implements RandomVectorGenerator {<a name="line.63"></a> <FONT color="green">064</FONT> <a name="line.64"></a> <FONT color="green">065</FONT> /** Mean vector. */<a name="line.65"></a> <FONT color="green">066</FONT> private final double[] mean;<a name="line.66"></a> <FONT color="green">067</FONT> <a name="line.67"></a> <FONT color="green">068</FONT> /** Underlying generator. */<a name="line.68"></a> <FONT color="green">069</FONT> private final NormalizedRandomGenerator generator;<a name="line.69"></a> <FONT color="green">070</FONT> <a name="line.70"></a> <FONT color="green">071</FONT> /** Storage for the normalized vector. */<a name="line.71"></a> <FONT color="green">072</FONT> private final double[] normalized;<a name="line.72"></a> <FONT color="green">073</FONT> <a name="line.73"></a> <FONT color="green">074</FONT> /** Permutated Cholesky root of the covariance matrix. */<a name="line.74"></a> <FONT color="green">075</FONT> private RealMatrix root;<a name="line.75"></a> <FONT color="green">076</FONT> <a name="line.76"></a> <FONT color="green">077</FONT> /** Rank of the covariance matrix. */<a name="line.77"></a> <FONT color="green">078</FONT> private int rank;<a name="line.78"></a> <FONT color="green">079</FONT> <a name="line.79"></a> <FONT color="green">080</FONT> /** Simple constructor.<a name="line.80"></a> <FONT color="green">081</FONT> * <p>Build a correlated random vector generator from its mean<a name="line.81"></a> <FONT color="green">082</FONT> * vector and covariance matrix.</p><a name="line.82"></a> <FONT color="green">083</FONT> * @param mean expected mean values for all components<a name="line.83"></a> <FONT color="green">084</FONT> * @param covariance covariance matrix<a name="line.84"></a> <FONT color="green">085</FONT> * @param small diagonal elements threshold under which column are<a name="line.85"></a> <FONT color="green">086</FONT> * considered to be dependent on previous ones and are discarded<a name="line.86"></a> <FONT color="green">087</FONT> * @param generator underlying generator for uncorrelated normalized<a name="line.87"></a> <FONT color="green">088</FONT> * components<a name="line.88"></a> <FONT color="green">089</FONT> * @exception IllegalArgumentException if there is a dimension<a name="line.89"></a> <FONT color="green">090</FONT> * mismatch between the mean vector and the covariance matrix<a name="line.90"></a> <FONT color="green">091</FONT> * @exception NotPositiveDefiniteMatrixException if the<a name="line.91"></a> <FONT color="green">092</FONT> * covariance matrix is not strictly positive definite<a name="line.92"></a> <FONT color="green">093</FONT> * @exception DimensionMismatchException if the mean and covariance<a name="line.93"></a> <FONT color="green">094</FONT> * arrays dimensions don't match<a name="line.94"></a> <FONT color="green">095</FONT> */<a name="line.95"></a> <FONT color="green">096</FONT> public CorrelatedRandomVectorGenerator(double[] mean,<a name="line.96"></a> <FONT color="green">097</FONT> RealMatrix covariance, double small,<a name="line.97"></a> <FONT color="green">098</FONT> NormalizedRandomGenerator generator)<a name="line.98"></a> <FONT color="green">099</FONT> throws NotPositiveDefiniteMatrixException, DimensionMismatchException {<a name="line.99"></a> <FONT color="green">100</FONT> <a name="line.100"></a> <FONT color="green">101</FONT> int order = covariance.getRowDimension();<a name="line.101"></a> <FONT color="green">102</FONT> if (mean.length != order) {<a name="line.102"></a> <FONT color="green">103</FONT> throw new DimensionMismatchException(mean.length, order);<a name="line.103"></a> <FONT color="green">104</FONT> }<a name="line.104"></a> <FONT color="green">105</FONT> this.mean = mean.clone();<a name="line.105"></a> <FONT color="green">106</FONT> <a name="line.106"></a> <FONT color="green">107</FONT> decompose(covariance, small);<a name="line.107"></a> <FONT color="green">108</FONT> <a name="line.108"></a> <FONT color="green">109</FONT> this.generator = generator;<a name="line.109"></a> <FONT color="green">110</FONT> normalized = new double[rank];<a name="line.110"></a> <FONT color="green">111</FONT> <a name="line.111"></a> <FONT color="green">112</FONT> }<a name="line.112"></a> <FONT color="green">113</FONT> <a name="line.113"></a> <FONT color="green">114</FONT> /** Simple constructor.<a name="line.114"></a> <FONT color="green">115</FONT> * <p>Build a null mean random correlated vector generator from its<a name="line.115"></a> <FONT color="green">116</FONT> * covariance matrix.</p><a name="line.116"></a> <FONT color="green">117</FONT> * @param covariance covariance matrix<a name="line.117"></a> <FONT color="green">118</FONT> * @param small diagonal elements threshold under which column are<a name="line.118"></a> <FONT color="green">119</FONT> * considered to be dependent on previous ones and are discarded<a name="line.119"></a> <FONT color="green">120</FONT> * @param generator underlying generator for uncorrelated normalized<a name="line.120"></a> <FONT color="green">121</FONT> * components<a name="line.121"></a> <FONT color="green">122</FONT> * @exception NotPositiveDefiniteMatrixException if the<a name="line.122"></a> <FONT color="green">123</FONT> * covariance matrix is not strictly positive definite<a name="line.123"></a> <FONT color="green">124</FONT> */<a name="line.124"></a> <FONT color="green">125</FONT> public CorrelatedRandomVectorGenerator(RealMatrix covariance, double small,<a name="line.125"></a> <FONT color="green">126</FONT> NormalizedRandomGenerator generator)<a name="line.126"></a> <FONT color="green">127</FONT> throws NotPositiveDefiniteMatrixException {<a name="line.127"></a> <FONT color="green">128</FONT> <a name="line.128"></a> <FONT color="green">129</FONT> int order = covariance.getRowDimension();<a name="line.129"></a> <FONT color="green">130</FONT> mean = new double[order];<a name="line.130"></a> <FONT color="green">131</FONT> for (int i = 0; i < order; ++i) {<a name="line.131"></a> <FONT color="green">132</FONT> mean[i] = 0;<a name="line.132"></a> <FONT color="green">133</FONT> }<a name="line.133"></a> <FONT color="green">134</FONT> <a name="line.134"></a> <FONT color="green">135</FONT> decompose(covariance, small);<a name="line.135"></a> <FONT color="green">136</FONT> <a name="line.136"></a> <FONT color="green">137</FONT> this.generator = generator;<a name="line.137"></a> <FONT color="green">138</FONT> normalized = new double[rank];<a name="line.138"></a> <FONT color="green">139</FONT> <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 the underlying normalized components generator.<a name="line.142"></a> <FONT color="green">143</FONT> * @return underlying uncorrelated components generator<a name="line.143"></a> <FONT color="green">144</FONT> */<a name="line.144"></a> <FONT color="green">145</FONT> public NormalizedRandomGenerator getGenerator() {<a name="line.145"></a> <FONT color="green">146</FONT> return generator;<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> /** Get the root of the covariance matrix.<a name="line.149"></a> <FONT color="green">150</FONT> * The root is the rectangular matrix <code>B</code> such that<a name="line.150"></a> <FONT color="green">151</FONT> * the covariance matrix is equal to <code>B.B<sup>T</sup></code><a name="line.151"></a> <FONT color="green">152</FONT> * @return root of the square matrix<a name="line.152"></a> <FONT color="green">153</FONT> * @see #getRank()<a name="line.153"></a> <FONT color="green">154</FONT> */<a name="line.154"></a> <FONT color="green">155</FONT> public RealMatrix getRootMatrix() {<a name="line.155"></a> <FONT color="green">156</FONT> return root;<a name="line.156"></a> <FONT color="green">157</FONT> }<a name="line.157"></a> <FONT color="green">158</FONT> <a name="line.158"></a> <FONT color="green">159</FONT> /** Get the rank of the covariance matrix.<a name="line.159"></a> <FONT color="green">160</FONT> * The rank is the number of independent rows in the covariance<a name="line.160"></a> <FONT color="green">161</FONT> * matrix, it is also the number of columns of the rectangular<a name="line.161"></a> <FONT color="green">162</FONT> * matrix of the decomposition.<a name="line.162"></a> <FONT color="green">163</FONT> * @return rank of the square matrix.<a name="line.163"></a> <FONT color="green">164</FONT> * @see #getRootMatrix()<a name="line.164"></a> <FONT color="green">165</FONT> */<a name="line.165"></a> <FONT color="green">166</FONT> public int getRank() {<a name="line.166"></a> <FONT color="green">167</FONT> return rank;<a name="line.167"></a> <FONT color="green">168</FONT> }<a name="line.168"></a> <FONT color="green">169</FONT> <a name="line.169"></a> <FONT color="green">170</FONT> /** Decompose the original square matrix.<a name="line.170"></a> <FONT color="green">171</FONT> * <p>The decomposition is based on a Choleski decomposition<a name="line.171"></a> <FONT color="green">172</FONT> * where additional transforms are performed:<a name="line.172"></a> <FONT color="green">173</FONT> * <ul><a name="line.173"></a> <FONT color="green">174</FONT> * <li>the rows of the decomposed matrix are permuted</li><a name="line.174"></a> <FONT color="green">175</FONT> * <li>columns with the too small diagonal element are discarded</li><a name="line.175"></a> <FONT color="green">176</FONT> * <li>the matrix is permuted</li><a name="line.176"></a> <FONT color="green">177</FONT> * </ul><a name="line.177"></a> <FONT color="green">178</FONT> * This means that rather than computing M = U<sup>T</sup>.U where U<a name="line.178"></a> <FONT color="green">179</FONT> * is an upper triangular matrix, this method computed M=B.B<sup>T</sup><a name="line.179"></a> <FONT color="green">180</FONT> * where B is a rectangular matrix.<a name="line.180"></a> <FONT color="green">181</FONT> * @param covariance covariance matrix<a name="line.181"></a> <FONT color="green">182</FONT> * @param small diagonal elements threshold under which column are<a name="line.182"></a> <FONT color="green">183</FONT> * considered to be dependent on previous ones and are discarded<a name="line.183"></a> <FONT color="green">184</FONT> * @exception NotPositiveDefiniteMatrixException if the<a name="line.184"></a> <FONT color="green">185</FONT> * covariance matrix is not strictly positive definite<a name="line.185"></a> <FONT color="green">186</FONT> */<a name="line.186"></a> <FONT color="green">187</FONT> private void decompose(RealMatrix covariance, double small)<a name="line.187"></a> <FONT color="green">188</FONT> throws NotPositiveDefiniteMatrixException {<a name="line.188"></a> <FONT color="green">189</FONT> <a name="line.189"></a> <FONT color="green">190</FONT> int order = covariance.getRowDimension();<a name="line.190"></a> <FONT color="green">191</FONT> double[][] c = covariance.getData();<a name="line.191"></a> <FONT color="green">192</FONT> double[][] b = new double[order][order];<a name="line.192"></a> <FONT color="green">193</FONT> <a name="line.193"></a> <FONT color="green">194</FONT> int[] swap = new int[order];<a name="line.194"></a> <FONT color="green">195</FONT> int[] index = new int[order];<a name="line.195"></a> <FONT color="green">196</FONT> for (int i = 0; i < order; ++i) {<a name="line.196"></a> <FONT color="green">197</FONT> index[i] = i;<a name="line.197"></a> <FONT color="green">198</FONT> }<a name="line.198"></a> <FONT color="green">199</FONT> <a name="line.199"></a> <FONT color="green">200</FONT> rank = 0;<a name="line.200"></a> <FONT color="green">201</FONT> for (boolean loop = true; loop;) {<a name="line.201"></a> <FONT color="green">202</FONT> <a name="line.202"></a> <FONT color="green">203</FONT> // find maximal diagonal element<a name="line.203"></a> <FONT color="green">204</FONT> swap[rank] = rank;<a name="line.204"></a> <FONT color="green">205</FONT> for (int i = rank + 1; i < order; ++i) {<a name="line.205"></a> <FONT color="green">206</FONT> int ii = index[i];<a name="line.206"></a> <FONT color="green">207</FONT> int isi = index[swap[i]];<a name="line.207"></a> <FONT color="green">208</FONT> if (c[ii][ii] > c[isi][isi]) {<a name="line.208"></a> <FONT color="green">209</FONT> swap[rank] = i;<a name="line.209"></a> <FONT color="green">210</FONT> }<a name="line.210"></a> <FONT color="green">211</FONT> }<a name="line.211"></a> <FONT color="green">212</FONT> <a name="line.212"></a> <FONT color="green">213</FONT> <a name="line.213"></a> <FONT color="green">214</FONT> // swap elements<a name="line.214"></a> <FONT color="green">215</FONT> if (swap[rank] != rank) {<a name="line.215"></a> <FONT color="green">216</FONT> int tmp = index[rank];<a name="line.216"></a> <FONT color="green">217</FONT> index[rank] = index[swap[rank]];<a name="line.217"></a> <FONT color="green">218</FONT> index[swap[rank]] = tmp;<a name="line.218"></a> <FONT color="green">219</FONT> }<a name="line.219"></a> <FONT color="green">220</FONT> <a name="line.220"></a> <FONT color="green">221</FONT> // check diagonal element<a name="line.221"></a> <FONT color="green">222</FONT> int ir = index[rank];<a name="line.222"></a> <FONT color="green">223</FONT> if (c[ir][ir] < small) {<a name="line.223"></a> <FONT color="green">224</FONT> <a name="line.224"></a> <FONT color="green">225</FONT> if (rank == 0) {<a name="line.225"></a> <FONT color="green">226</FONT> throw new NotPositiveDefiniteMatrixException();<a name="line.226"></a> <FONT color="green">227</FONT> }<a name="line.227"></a> <FONT color="green">228</FONT> <a name="line.228"></a> <FONT color="green">229</FONT> // check remaining diagonal elements<a name="line.229"></a> <FONT color="green">230</FONT> for (int i = rank; i < order; ++i) {<a name="line.230"></a> <FONT color="green">231</FONT> if (c[index[i]][index[i]] < -small) {<a name="line.231"></a> <FONT color="green">232</FONT> // there is at least one sufficiently negative diagonal element,<a name="line.232"></a> <FONT color="green">233</FONT> // the covariance matrix is wrong<a name="line.233"></a> <FONT color="green">234</FONT> throw new NotPositiveDefiniteMatrixException();<a name="line.234"></a> <FONT color="green">235</FONT> }<a name="line.235"></a> <FONT color="green">236</FONT> }<a name="line.236"></a> <FONT color="green">237</FONT> <a name="line.237"></a> <FONT color="green">238</FONT> // all remaining diagonal elements are close to zero,<a name="line.238"></a> <FONT color="green">239</FONT> // we consider we have found the rank of the covariance matrix<a name="line.239"></a> <FONT color="green">240</FONT> ++rank;<a name="line.240"></a> <FONT color="green">241</FONT> loop = false;<a name="line.241"></a> <FONT color="green">242</FONT> <a name="line.242"></a> <FONT color="green">243</FONT> } else {<a name="line.243"></a> <FONT color="green">244</FONT> <a name="line.244"></a> <FONT color="green">245</FONT> // transform the matrix<a name="line.245"></a> <FONT color="green">246</FONT> double sqrt = Math.sqrt(c[ir][ir]);<a name="line.246"></a> <FONT color="green">247</FONT> b[rank][rank] = sqrt;<a name="line.247"></a> <FONT color="green">248</FONT> double inverse = 1 / sqrt;<a name="line.248"></a> <FONT color="green">249</FONT> for (int i = rank + 1; i < order; ++i) {<a name="line.249"></a> <FONT color="green">250</FONT> int ii = index[i];<a name="line.250"></a> <FONT color="green">251</FONT> double e = inverse * c[ii][ir];<a name="line.251"></a> <FONT color="green">252</FONT> b[i][rank] = e;<a name="line.252"></a> <FONT color="green">253</FONT> c[ii][ii] -= e * e;<a name="line.253"></a> <FONT color="green">254</FONT> for (int j = rank + 1; j < i; ++j) {<a name="line.254"></a> <FONT color="green">255</FONT> int ij = index[j];<a name="line.255"></a> <FONT color="green">256</FONT> double f = c[ii][ij] - e * b[j][rank];<a name="line.256"></a> <FONT color="green">257</FONT> c[ii][ij] = f;<a name="line.257"></a> <FONT color="green">258</FONT> c[ij][ii] = f;<a name="line.258"></a> <FONT color="green">259</FONT> }<a name="line.259"></a> <FONT color="green">260</FONT> }<a name="line.260"></a> <FONT color="green">261</FONT> <a name="line.261"></a> <FONT color="green">262</FONT> // prepare next iteration<a name="line.262"></a> <FONT color="green">263</FONT> loop = ++rank < order;<a name="line.263"></a> <FONT color="green">264</FONT> <a name="line.264"></a> <FONT color="green">265</FONT> }<a name="line.265"></a> <FONT color="green">266</FONT> <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> // build the root matrix<a name="line.269"></a> <FONT color="green">270</FONT> root = MatrixUtils.createRealMatrix(order, rank);<a name="line.270"></a> <FONT color="green">271</FONT> for (int i = 0; i < order; ++i) {<a name="line.271"></a> <FONT color="green">272</FONT> for (int j = 0; j < rank; ++j) {<a name="line.272"></a> <FONT color="green">273</FONT> root.setEntry(index[i], j, b[i][j]);<a name="line.273"></a> <FONT color="green">274</FONT> }<a name="line.274"></a> <FONT color="green">275</FONT> }<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> /** Generate a correlated random vector.<a name="line.279"></a> <FONT color="green">280</FONT> * @return a random vector as an array of double. The returned array<a name="line.280"></a> <FONT color="green">281</FONT> * is created at each call, the caller can do what it wants with it.<a name="line.281"></a> <FONT color="green">282</FONT> */<a name="line.282"></a> <FONT color="green">283</FONT> public double[] nextVector() {<a name="line.283"></a> <FONT color="green">284</FONT> <a name="line.284"></a> <FONT color="green">285</FONT> // generate uncorrelated vector<a name="line.285"></a> <FONT color="green">286</FONT> for (int i = 0; i < rank; ++i) {<a name="line.286"></a> <FONT color="green">287</FONT> normalized[i] = generator.nextNormalizedDouble();<a name="line.287"></a> <FONT color="green">288</FONT> }<a name="line.288"></a> <FONT color="green">289</FONT> <a name="line.289"></a> <FONT color="green">290</FONT> // compute correlated vector<a name="line.290"></a> <FONT color="green">291</FONT> double[] correlated = new double[mean.length];<a name="line.291"></a> <FONT color="green">292</FONT> for (int i = 0; i < correlated.length; ++i) {<a name="line.292"></a> <FONT color="green">293</FONT> correlated[i] = mean[i];<a name="line.293"></a> <FONT color="green">294</FONT> for (int j = 0; j < rank; ++j) {<a name="line.294"></a> <FONT color="green">295</FONT> correlated[i] += root.getEntry(i, j) * normalized[j];<a name="line.295"></a> <FONT color="green">296</FONT> }<a name="line.296"></a> <FONT color="green">297</FONT> }<a name="line.297"></a> <FONT color="green">298</FONT> <a name="line.298"></a> <FONT color="green">299</FONT> return correlated;<a name="line.299"></a> <FONT color="green">300</FONT> <a name="line.300"></a> <FONT color="green">301</FONT> }<a name="line.301"></a> <FONT color="green">302</FONT> <a name="line.302"></a> <FONT color="green">303</FONT> }<a name="line.303"></a> </PRE> </BODY> </HTML>