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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> package org.apache.commons.math.stat.correlation;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import org.apache.commons.math.MathException;<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> import org.apache.commons.math.distribution.TDistribution;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.distribution.TDistributionImpl;<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> import org.apache.commons.math.linear.BlockRealMatrix;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.stat.regression.SimpleRegression;<a name="line.25"></a> <FONT color="green">026</FONT> <a name="line.26"></a> <FONT color="green">027</FONT> /**<a name="line.27"></a> <FONT color="green">028</FONT> * Computes Pearson's product-moment correlation coefficients for pairs of arrays<a name="line.28"></a> <FONT color="green">029</FONT> * or columns of a matrix.<a name="line.29"></a> <FONT color="green">030</FONT> *<a name="line.30"></a> <FONT color="green">031</FONT> * <p>The constructors that take <code>RealMatrix</code> or<a name="line.31"></a> <FONT color="green">032</FONT> * <code>double[][]</code> arguments generate correlation matrices. The<a name="line.32"></a> <FONT color="green">033</FONT> * columns of the input matrices are assumed to represent variable values.<a name="line.33"></a> <FONT color="green">034</FONT> * Correlations are given by the formula</p><a name="line.34"></a> <FONT color="green">035</FONT> * <code>cor(X, Y) = &Sigma;[(x<sub>i</sub> - E(X))(y<sub>i</sub> - E(Y))] / [(n - 1)s(X)s(Y)]</code><a name="line.35"></a> <FONT color="green">036</FONT> * where <code>E(X)</code> is the mean of <code>X</code>, <code>E(Y)</code><a name="line.36"></a> <FONT color="green">037</FONT> * is the mean of the <code>Y</code> values and s(X), s(Y) are standard deviations.<a name="line.37"></a> <FONT color="green">038</FONT> *<a name="line.38"></a> <FONT color="green">039</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.39"></a> <FONT color="green">040</FONT> * @since 2.0<a name="line.40"></a> <FONT color="green">041</FONT> */<a name="line.41"></a> <FONT color="green">042</FONT> public class PearsonsCorrelation {<a name="line.42"></a> <FONT color="green">043</FONT> <a name="line.43"></a> <FONT color="green">044</FONT> /** correlation matrix */<a name="line.44"></a> <FONT color="green">045</FONT> private final RealMatrix correlationMatrix;<a name="line.45"></a> <FONT color="green">046</FONT> <a name="line.46"></a> <FONT color="green">047</FONT> /** number of observations */<a name="line.47"></a> <FONT color="green">048</FONT> private final int nObs;<a name="line.48"></a> <FONT color="green">049</FONT> <a name="line.49"></a> <FONT color="green">050</FONT> /**<a name="line.50"></a> <FONT color="green">051</FONT> * Create a PearsonsCorrelation instance without data<a name="line.51"></a> <FONT color="green">052</FONT> */<a name="line.52"></a> <FONT color="green">053</FONT> public PearsonsCorrelation() {<a name="line.53"></a> <FONT color="green">054</FONT> super();<a name="line.54"></a> <FONT color="green">055</FONT> correlationMatrix = null;<a name="line.55"></a> <FONT color="green">056</FONT> nObs = 0;<a name="line.56"></a> <FONT color="green">057</FONT> }<a name="line.57"></a> <FONT color="green">058</FONT> <a name="line.58"></a> <FONT color="green">059</FONT> /**<a name="line.59"></a> <FONT color="green">060</FONT> * Create a PearsonsCorrelation from a rectangular array<a name="line.60"></a> <FONT color="green">061</FONT> * whose columns represent values of variables to be correlated.<a name="line.61"></a> <FONT color="green">062</FONT> *<a name="line.62"></a> <FONT color="green">063</FONT> * @param data rectangular array with columns representing variables<a name="line.63"></a> <FONT color="green">064</FONT> * @throws IllegalArgumentException if the input data array is not<a name="line.64"></a> <FONT color="green">065</FONT> * rectangular with at least two rows and two columns.<a name="line.65"></a> <FONT color="green">066</FONT> */<a name="line.66"></a> <FONT color="green">067</FONT> public PearsonsCorrelation(double[][] data) {<a name="line.67"></a> <FONT color="green">068</FONT> this(new BlockRealMatrix(data));<a name="line.68"></a> <FONT color="green">069</FONT> }<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> * Create a PearsonsCorrelation from a RealMatrix whose columns<a name="line.72"></a> <FONT color="green">073</FONT> * represent variables to be correlated.<a name="line.73"></a> <FONT color="green">074</FONT> *<a name="line.74"></a> <FONT color="green">075</FONT> * @param matrix matrix with columns representing variables to correlate<a name="line.75"></a> <FONT color="green">076</FONT> */<a name="line.76"></a> <FONT color="green">077</FONT> public PearsonsCorrelation(RealMatrix matrix) {<a name="line.77"></a> <FONT color="green">078</FONT> checkSufficientData(matrix);<a name="line.78"></a> <FONT color="green">079</FONT> nObs = matrix.getRowDimension();<a name="line.79"></a> <FONT color="green">080</FONT> correlationMatrix = computeCorrelationMatrix(matrix);<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> /**<a name="line.83"></a> <FONT color="green">084</FONT> * Create a PearsonsCorrelation from a {@link Covariance}. The correlation<a name="line.84"></a> <FONT color="green">085</FONT> * matrix is computed by scaling the Covariance's covariance matrix.<a name="line.85"></a> <FONT color="green">086</FONT> * The Covariance instance must have been created from a data matrix with<a name="line.86"></a> <FONT color="green">087</FONT> * columns representing variable values.<a name="line.87"></a> <FONT color="green">088</FONT> *<a name="line.88"></a> <FONT color="green">089</FONT> * @param covariance Covariance instance<a name="line.89"></a> <FONT color="green">090</FONT> */<a name="line.90"></a> <FONT color="green">091</FONT> public PearsonsCorrelation(Covariance covariance) {<a name="line.91"></a> <FONT color="green">092</FONT> RealMatrix covarianceMatrix = covariance.getCovarianceMatrix();<a name="line.92"></a> <FONT color="green">093</FONT> if (covarianceMatrix == null) {<a name="line.93"></a> <FONT color="green">094</FONT> throw MathRuntimeException.createIllegalArgumentException("covariance matrix is null");<a name="line.94"></a> <FONT color="green">095</FONT> }<a name="line.95"></a> <FONT color="green">096</FONT> nObs = covariance.getN();<a name="line.96"></a> <FONT color="green">097</FONT> correlationMatrix = covarianceToCorrelation(covarianceMatrix);<a name="line.97"></a> <FONT color="green">098</FONT> }<a name="line.98"></a> <FONT color="green">099</FONT> <a name="line.99"></a> <FONT color="green">100</FONT> /**<a name="line.100"></a> <FONT color="green">101</FONT> * Create a PearsonsCorrelation from a covariance matrix. The correlation<a name="line.101"></a> <FONT color="green">102</FONT> * matrix is computed by scaling the covariance matrix.<a name="line.102"></a> <FONT color="green">103</FONT> *<a name="line.103"></a> <FONT color="green">104</FONT> * @param covarianceMatrix covariance matrix<a name="line.104"></a> <FONT color="green">105</FONT> * @param numberOfObservations the number of observations in the dataset used to compute<a name="line.105"></a> <FONT color="green">106</FONT> * the covariance matrix<a name="line.106"></a> <FONT color="green">107</FONT> */<a name="line.107"></a> <FONT color="green">108</FONT> public PearsonsCorrelation(RealMatrix covarianceMatrix, int numberOfObservations) {<a name="line.108"></a> <FONT color="green">109</FONT> nObs = numberOfObservations;<a name="line.109"></a> <FONT color="green">110</FONT> correlationMatrix = covarianceToCorrelation(covarianceMatrix);<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> /**<a name="line.114"></a> <FONT color="green">115</FONT> * Returns the correlation matrix<a name="line.115"></a> <FONT color="green">116</FONT> *<a name="line.116"></a> <FONT color="green">117</FONT> * @return correlation matrix<a name="line.117"></a> <FONT color="green">118</FONT> */<a name="line.118"></a> <FONT color="green">119</FONT> public RealMatrix getCorrelationMatrix() {<a name="line.119"></a> <FONT color="green">120</FONT> return correlationMatrix;<a name="line.120"></a> <FONT color="green">121</FONT> }<a name="line.121"></a> <FONT color="green">122</FONT> <a name="line.122"></a> <FONT color="green">123</FONT> /**<a name="line.123"></a> <FONT color="green">124</FONT> * Returns a matrix of standard errors associated with the estimates<a name="line.124"></a> <FONT color="green">125</FONT> * in the correlation matrix.<br/><a name="line.125"></a> <FONT color="green">126</FONT> * <code>getCorrelationStandardErrors().getEntry(i,j)</code> is the standard<a name="line.126"></a> <FONT color="green">127</FONT> * error associated with <code>getCorrelationMatrix.getEntry(i,j)</code><a name="line.127"></a> <FONT color="green">128</FONT> * <p>The formula used to compute the standard error is <br/><a name="line.128"></a> <FONT color="green">129</FONT> * <code>SE<sub>r</sub> = ((1 - r<sup>2</sup>) / (n - 2))<sup>1/2</sup></code><a name="line.129"></a> <FONT color="green">130</FONT> * where <code>r</code> is the estimated correlation coefficient and<a name="line.130"></a> <FONT color="green">131</FONT> * <code>n</code> is the number of observations in the source dataset.</p><a name="line.131"></a> <FONT color="green">132</FONT> *<a name="line.132"></a> <FONT color="green">133</FONT> * @return matrix of correlation standard errors<a name="line.133"></a> <FONT color="green">134</FONT> */<a name="line.134"></a> <FONT color="green">135</FONT> public RealMatrix getCorrelationStandardErrors() {<a name="line.135"></a> <FONT color="green">136</FONT> int nVars = correlationMatrix.getColumnDimension();<a name="line.136"></a> <FONT color="green">137</FONT> double[][] out = new double[nVars][nVars];<a name="line.137"></a> <FONT color="green">138</FONT> for (int i = 0; i < nVars; i++) {<a name="line.138"></a> <FONT color="green">139</FONT> for (int j = 0; j < nVars; j++) {<a name="line.139"></a> <FONT color="green">140</FONT> double r = correlationMatrix.getEntry(i, j);<a name="line.140"></a> <FONT color="green">141</FONT> out[i][j] = Math.sqrt((1 - r * r) /(nObs - 2));<a name="line.141"></a> <FONT color="green">142</FONT> }<a name="line.142"></a> <FONT color="green">143</FONT> }<a name="line.143"></a> <FONT color="green">144</FONT> return new BlockRealMatrix(out);<a name="line.144"></a> <FONT color="green">145</FONT> }<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> * Returns a matrix of p-values associated with the (two-sided) null<a name="line.148"></a> <FONT color="green">149</FONT> * hypothesis that the corresponding correlation coefficient is zero.<a name="line.149"></a> <FONT color="green">150</FONT> * <p><code>getCorrelationPValues().getEntry(i,j)</code> is the probability<a name="line.150"></a> <FONT color="green">151</FONT> * that a random variable distributed as <code>t<sub>n-2</sub></code> takes<a name="line.151"></a> <FONT color="green">152</FONT> * a value with absolute value greater than or equal to <br><a name="line.152"></a> <FONT color="green">153</FONT> * <code>|r|((n - 2) / (1 - r<sup>2</sup>))<sup>1/2</sup></code></p><a name="line.153"></a> <FONT color="green">154</FONT> * <p>The values in the matrix are sometimes referred to as the<a name="line.154"></a> <FONT color="green">155</FONT> * <i>significance</i> of the corresponding correlation coefficients.</p><a name="line.155"></a> <FONT color="green">156</FONT> *<a name="line.156"></a> <FONT color="green">157</FONT> * @return matrix of p-values<a name="line.157"></a> <FONT color="green">158</FONT> * @throws MathException if an error occurs estimating probabilities<a name="line.158"></a> <FONT color="green">159</FONT> */<a name="line.159"></a> <FONT color="green">160</FONT> public RealMatrix getCorrelationPValues() throws MathException {<a name="line.160"></a> <FONT color="green">161</FONT> TDistribution tDistribution = new TDistributionImpl(nObs - 2);<a name="line.161"></a> <FONT color="green">162</FONT> int nVars = correlationMatrix.getColumnDimension();<a name="line.162"></a> <FONT color="green">163</FONT> double[][] out = new double[nVars][nVars];<a name="line.163"></a> <FONT color="green">164</FONT> for (int i = 0; i < nVars; i++) {<a name="line.164"></a> <FONT color="green">165</FONT> for (int j = 0; j < nVars; j++) {<a name="line.165"></a> <FONT color="green">166</FONT> if (i == j) {<a name="line.166"></a> <FONT color="green">167</FONT> out[i][j] = 0d;<a name="line.167"></a> <FONT color="green">168</FONT> } else {<a name="line.168"></a> <FONT color="green">169</FONT> double r = correlationMatrix.getEntry(i, j);<a name="line.169"></a> <FONT color="green">170</FONT> double t = Math.abs(r * Math.sqrt((nObs - 2)/(1 - r * r)));<a name="line.170"></a> <FONT color="green">171</FONT> out[i][j] = 2 * (1 - tDistribution.cumulativeProbability(t));<a name="line.171"></a> <FONT color="green">172</FONT> }<a name="line.172"></a> <FONT color="green">173</FONT> }<a name="line.173"></a> <FONT color="green">174</FONT> }<a name="line.174"></a> <FONT color="green">175</FONT> return new BlockRealMatrix(out);<a name="line.175"></a> <FONT color="green">176</FONT> }<a name="line.176"></a> <FONT color="green">177</FONT> <a name="line.177"></a> <FONT color="green">178</FONT> <a name="line.178"></a> <FONT color="green">179</FONT> /**<a name="line.179"></a> <FONT color="green">180</FONT> * Computes the correlation matrix for the columns of the<a name="line.180"></a> <FONT color="green">181</FONT> * input matrix.<a name="line.181"></a> <FONT color="green">182</FONT> *<a name="line.182"></a> <FONT color="green">183</FONT> * @param matrix matrix with columns representing variables to correlate<a name="line.183"></a> <FONT color="green">184</FONT> * @return correlation matrix<a name="line.184"></a> <FONT color="green">185</FONT> */<a name="line.185"></a> <FONT color="green">186</FONT> public RealMatrix computeCorrelationMatrix(RealMatrix matrix) {<a name="line.186"></a> <FONT color="green">187</FONT> int nVars = matrix.getColumnDimension();<a name="line.187"></a> <FONT color="green">188</FONT> RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);<a name="line.188"></a> <FONT color="green">189</FONT> for (int i = 0; i < nVars; i++) {<a name="line.189"></a> <FONT color="green">190</FONT> for (int j = 0; j < i; j++) {<a name="line.190"></a> <FONT color="green">191</FONT> double corr = correlation(matrix.getColumn(i), matrix.getColumn(j));<a name="line.191"></a> <FONT color="green">192</FONT> outMatrix.setEntry(i, j, corr);<a name="line.192"></a> <FONT color="green">193</FONT> outMatrix.setEntry(j, i, corr);<a name="line.193"></a> <FONT color="green">194</FONT> }<a name="line.194"></a> <FONT color="green">195</FONT> outMatrix.setEntry(i, i, 1d);<a name="line.195"></a> <FONT color="green">196</FONT> }<a name="line.196"></a> <FONT color="green">197</FONT> return outMatrix;<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> /**<a name="line.200"></a> <FONT color="green">201</FONT> * Computes the correlation matrix for the columns of the<a name="line.201"></a> <FONT color="green">202</FONT> * input rectangular array. The colums of the array represent values<a name="line.202"></a> <FONT color="green">203</FONT> * of variables to be correlated.<a name="line.203"></a> <FONT color="green">204</FONT> *<a name="line.204"></a> <FONT color="green">205</FONT> * @param data matrix with columns representing variables to correlate<a name="line.205"></a> <FONT color="green">206</FONT> * @return correlation matrix<a name="line.206"></a> <FONT color="green">207</FONT> */<a name="line.207"></a> <FONT color="green">208</FONT> public RealMatrix computeCorrelationMatrix(double[][] data) {<a name="line.208"></a> <FONT color="green">209</FONT> return computeCorrelationMatrix(new BlockRealMatrix(data));<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> * Computes the Pearson's product-moment correlation coefficient between the two arrays.<a name="line.213"></a> <FONT color="green">214</FONT> *<a name="line.214"></a> <FONT color="green">215</FONT> * </p>Throws IllegalArgumentException if the arrays do not have the same length<a name="line.215"></a> <FONT color="green">216</FONT> * or their common length is less than 2</p><a name="line.216"></a> <FONT color="green">217</FONT> *<a name="line.217"></a> <FONT color="green">218</FONT> * @param xArray first data array<a name="line.218"></a> <FONT color="green">219</FONT> * @param yArray second data array<a name="line.219"></a> <FONT color="green">220</FONT> * @return Returns Pearson's correlation coefficient for the two arrays<a name="line.220"></a> <FONT color="green">221</FONT> * @throws IllegalArgumentException if the arrays lengths do not match or<a name="line.221"></a> <FONT color="green">222</FONT> * there is insufficient data<a name="line.222"></a> <FONT color="green">223</FONT> */<a name="line.223"></a> <FONT color="green">224</FONT> public double correlation(final double[] xArray, final double[] yArray) throws IllegalArgumentException {<a name="line.224"></a> <FONT color="green">225</FONT> SimpleRegression regression = new SimpleRegression();<a name="line.225"></a> <FONT color="green">226</FONT> if(xArray.length == yArray.length && xArray.length > 1) {<a name="line.226"></a> <FONT color="green">227</FONT> for(int i=0; i<xArray.length; i++) {<a name="line.227"></a> <FONT color="green">228</FONT> regression.addData(xArray[i], yArray[i]);<a name="line.228"></a> <FONT color="green">229</FONT> }<a name="line.229"></a> <FONT color="green">230</FONT> return regression.getR();<a name="line.230"></a> <FONT color="green">231</FONT> }<a name="line.231"></a> <FONT color="green">232</FONT> else {<a name="line.232"></a> <FONT color="green">233</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.233"></a> <FONT color="green">234</FONT> "invalid array dimensions. xArray has size {0}; yArray has {1} elements",<a name="line.234"></a> <FONT color="green">235</FONT> xArray.length, yArray.length);<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> <a name="line.238"></a> <FONT color="green">239</FONT> /**<a name="line.239"></a> <FONT color="green">240</FONT> * Derives a correlation matrix from a covariance matrix.<a name="line.240"></a> <FONT color="green">241</FONT> *<a name="line.241"></a> <FONT color="green">242</FONT> * <p>Uses the formula <br/><a name="line.242"></a> <FONT color="green">243</FONT> * <code>r(X,Y) = cov(X,Y)/s(X)s(Y)</code> where<a name="line.243"></a> <FONT color="green">244</FONT> * <code>r(&middot,&middot;)</code> is the correlation coefficient and<a name="line.244"></a> <FONT color="green">245</FONT> * <code>s(&middot;)</code> means standard deviation.</p><a name="line.245"></a> <FONT color="green">246</FONT> *<a name="line.246"></a> <FONT color="green">247</FONT> * @param covarianceMatrix the covariance matrix<a name="line.247"></a> <FONT color="green">248</FONT> * @return correlation matrix<a name="line.248"></a> <FONT color="green">249</FONT> */<a name="line.249"></a> <FONT color="green">250</FONT> public RealMatrix covarianceToCorrelation(RealMatrix covarianceMatrix) {<a name="line.250"></a> <FONT color="green">251</FONT> int nVars = covarianceMatrix.getColumnDimension();<a name="line.251"></a> <FONT color="green">252</FONT> RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);<a name="line.252"></a> <FONT color="green">253</FONT> for (int i = 0; i < nVars; i++) {<a name="line.253"></a> <FONT color="green">254</FONT> double sigma = Math.sqrt(covarianceMatrix.getEntry(i, i));<a name="line.254"></a> <FONT color="green">255</FONT> outMatrix.setEntry(i, i, 1d);<a name="line.255"></a> <FONT color="green">256</FONT> for (int j = 0; j < i; j++) {<a name="line.256"></a> <FONT color="green">257</FONT> double entry = covarianceMatrix.getEntry(i, j) /<a name="line.257"></a> <FONT color="green">258</FONT> (sigma * Math.sqrt(covarianceMatrix.getEntry(j, j)));<a name="line.258"></a> <FONT color="green">259</FONT> outMatrix.setEntry(i, j, entry);<a name="line.259"></a> <FONT color="green">260</FONT> outMatrix.setEntry(j, i, entry);<a name="line.260"></a> <FONT color="green">261</FONT> }<a name="line.261"></a> <FONT color="green">262</FONT> }<a name="line.262"></a> <FONT color="green">263</FONT> return outMatrix;<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> * Throws IllegalArgumentException of the matrix does not have at least<a name="line.267"></a> <FONT color="green">268</FONT> * two columns and two rows<a name="line.268"></a> <FONT color="green">269</FONT> *<a name="line.269"></a> <FONT color="green">270</FONT> * @param matrix matrix to check for sufficiency<a name="line.270"></a> <FONT color="green">271</FONT> */<a name="line.271"></a> <FONT color="green">272</FONT> private void checkSufficientData(final RealMatrix matrix) {<a name="line.272"></a> <FONT color="green">273</FONT> int nRows = matrix.getRowDimension();<a name="line.273"></a> <FONT color="green">274</FONT> int nCols = matrix.getColumnDimension();<a name="line.274"></a> <FONT color="green">275</FONT> if (nRows < 2 || nCols < 2) {<a name="line.275"></a> <FONT color="green">276</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.276"></a> <FONT color="green">277</FONT> "insufficient data: only {0} rows and {1} columns.",<a name="line.277"></a> <FONT color="green">278</FONT> nRows, nCols);<a name="line.278"></a> <FONT color="green">279</FONT> }<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> </PRE> </BODY> </HTML>