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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.MathRuntimeException;<a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.linear.RealMatrix;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.linear.BlockRealMatrix;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.stat.descriptive.moment.Mean;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.stat.descriptive.moment.Variance;<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> * Computes covariances for pairs of arrays or columns of a matrix.<a name="line.26"></a> <FONT color="green">027</FONT> *<a name="line.27"></a> <FONT color="green">028</FONT> * <p>The constructors that take <code>RealMatrix</code> or<a name="line.28"></a> <FONT color="green">029</FONT> * <code>double[][]</code> arguments generate covariance matrices. The<a name="line.29"></a> <FONT color="green">030</FONT> * columns of the input matrices are assumed to represent variable values.</p><a name="line.30"></a> <FONT color="green">031</FONT> *<a name="line.31"></a> <FONT color="green">032</FONT> * <p>The constructor argument <code>biasCorrected</code> determines whether or<a name="line.32"></a> <FONT color="green">033</FONT> * not computed covariances are bias-corrected.</p><a name="line.33"></a> <FONT color="green">034</FONT> *<a name="line.34"></a> <FONT color="green">035</FONT> * <p>Unbiased covariances are given by the formula</p><a name="line.35"></a> <FONT color="green">036</FONT> * <code>cov(X, Y) = &Sigma;[(x<sub>i</sub> - E(X))(y<sub>i</sub> - E(Y))] / (n - 1)</code><a name="line.36"></a> <FONT color="green">037</FONT> * where <code>E(X)</code> is the mean of <code>X</code> and <code>E(Y)</code><a name="line.37"></a> <FONT color="green">038</FONT> * is the mean of the <code>Y</code> values.<a name="line.38"></a> <FONT color="green">039</FONT> *<a name="line.39"></a> <FONT color="green">040</FONT> * <p>Non-bias-corrected estimates use <code>n</code> in place of <code>n - 1</code><a name="line.40"></a> <FONT color="green">041</FONT> *<a name="line.41"></a> <FONT color="green">042</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.42"></a> <FONT color="green">043</FONT> * @since 2.0<a name="line.43"></a> <FONT color="green">044</FONT> */<a name="line.44"></a> <FONT color="green">045</FONT> public class Covariance {<a name="line.45"></a> <FONT color="green">046</FONT> <a name="line.46"></a> <FONT color="green">047</FONT> /** covariance matrix */<a name="line.47"></a> <FONT color="green">048</FONT> private final RealMatrix covarianceMatrix;<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 an empty covariance matrix.<a name="line.51"></a> <FONT color="green">052</FONT> */<a name="line.52"></a> <FONT color="green">053</FONT> /** Number of observations (length of covariate vectors) */<a name="line.53"></a> <FONT color="green">054</FONT> private final int n;<a name="line.54"></a> <FONT color="green">055</FONT> <a name="line.55"></a> <FONT color="green">056</FONT> /**<a name="line.56"></a> <FONT color="green">057</FONT> * Create a Covariance with no data<a name="line.57"></a> <FONT color="green">058</FONT> */<a name="line.58"></a> <FONT color="green">059</FONT> public Covariance() {<a name="line.59"></a> <FONT color="green">060</FONT> super();<a name="line.60"></a> <FONT color="green">061</FONT> covarianceMatrix = null;<a name="line.61"></a> <FONT color="green">062</FONT> n = 0;<a name="line.62"></a> <FONT color="green">063</FONT> }<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> * Create a Covariance matrix from a rectangular array<a name="line.66"></a> <FONT color="green">067</FONT> * whose columns represent covariates.<a name="line.67"></a> <FONT color="green">068</FONT> *<a name="line.68"></a> <FONT color="green">069</FONT> * <p>The <code>biasCorrected</code> parameter determines whether or not<a name="line.69"></a> <FONT color="green">070</FONT> * covariance estimates are bias-corrected.</p><a name="line.70"></a> <FONT color="green">071</FONT> *<a name="line.71"></a> <FONT color="green">072</FONT> * <p>The input array must be rectangular with at least two columns<a name="line.72"></a> <FONT color="green">073</FONT> * and two rows.</p><a name="line.73"></a> <FONT color="green">074</FONT> *<a name="line.74"></a> <FONT color="green">075</FONT> * @param data rectangular array with columns representing covariates<a name="line.75"></a> <FONT color="green">076</FONT> * @param biasCorrected true means covariances are bias-corrected<a name="line.76"></a> <FONT color="green">077</FONT> * @throws IllegalArgumentException if the input data array is not<a name="line.77"></a> <FONT color="green">078</FONT> * rectangular with at least two rows and two columns.<a name="line.78"></a> <FONT color="green">079</FONT> */<a name="line.79"></a> <FONT color="green">080</FONT> public Covariance(double[][] data, boolean biasCorrected) {<a name="line.80"></a> <FONT color="green">081</FONT> this(new BlockRealMatrix(data), biasCorrected);<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> /**<a name="line.84"></a> <FONT color="green">085</FONT> * Create a Covariance matrix from a rectangular array<a name="line.85"></a> <FONT color="green">086</FONT> * whose columns represent covariates.<a name="line.86"></a> <FONT color="green">087</FONT> *<a name="line.87"></a> <FONT color="green">088</FONT> * <p>The input array must be rectangular with at least two columns<a name="line.88"></a> <FONT color="green">089</FONT> * and two rows</p><a name="line.89"></a> <FONT color="green">090</FONT> *<a name="line.90"></a> <FONT color="green">091</FONT> * @param data rectangular array with columns representing covariates<a name="line.91"></a> <FONT color="green">092</FONT> * @throws IllegalArgumentException if the input data array is not<a name="line.92"></a> <FONT color="green">093</FONT> * rectangular with at least two rows and two columns.<a name="line.93"></a> <FONT color="green">094</FONT> */<a name="line.94"></a> <FONT color="green">095</FONT> public Covariance(double[][] data) {<a name="line.95"></a> <FONT color="green">096</FONT> this(data, true);<a name="line.96"></a> <FONT color="green">097</FONT> }<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> * Create a covariance matrix from a matrix whose columns<a name="line.100"></a> <FONT color="green">101</FONT> * represent covariates.<a name="line.101"></a> <FONT color="green">102</FONT> *<a name="line.102"></a> <FONT color="green">103</FONT> * <p>The <code>biasCorrected</code> parameter determines whether or not<a name="line.103"></a> <FONT color="green">104</FONT> * covariance estimates are bias-corrected.</p><a name="line.104"></a> <FONT color="green">105</FONT> *<a name="line.105"></a> <FONT color="green">106</FONT> * <p>The matrix must have at least two columns and two rows</p><a name="line.106"></a> <FONT color="green">107</FONT> *<a name="line.107"></a> <FONT color="green">108</FONT> * @param matrix matrix with columns representing covariates<a name="line.108"></a> <FONT color="green">109</FONT> * @param biasCorrected true means covariances are bias-corrected<a name="line.109"></a> <FONT color="green">110</FONT> * @throws IllegalArgumentException if the input matrix does not have<a name="line.110"></a> <FONT color="green">111</FONT> * at least two rows and two columns<a name="line.111"></a> <FONT color="green">112</FONT> */<a name="line.112"></a> <FONT color="green">113</FONT> public Covariance(RealMatrix matrix, boolean biasCorrected) {<a name="line.113"></a> <FONT color="green">114</FONT> checkSufficientData(matrix);<a name="line.114"></a> <FONT color="green">115</FONT> n = matrix.getRowDimension();<a name="line.115"></a> <FONT color="green">116</FONT> covarianceMatrix = computeCovarianceMatrix(matrix, biasCorrected);<a name="line.116"></a> <FONT color="green">117</FONT> }<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> * Create a covariance matrix from a matrix whose columns<a name="line.120"></a> <FONT color="green">121</FONT> * represent covariates.<a name="line.121"></a> <FONT color="green">122</FONT> *<a name="line.122"></a> <FONT color="green">123</FONT> * <p>The matrix must have at least two columns and two rows</p><a name="line.123"></a> <FONT color="green">124</FONT> *<a name="line.124"></a> <FONT color="green">125</FONT> * @param matrix matrix with columns representing covariates<a name="line.125"></a> <FONT color="green">126</FONT> * @throws IllegalArgumentException if the input matrix does not have<a name="line.126"></a> <FONT color="green">127</FONT> * at least two rows and two columns<a name="line.127"></a> <FONT color="green">128</FONT> */<a name="line.128"></a> <FONT color="green">129</FONT> public Covariance(RealMatrix matrix) {<a name="line.129"></a> <FONT color="green">130</FONT> this(matrix, true);<a name="line.130"></a> <FONT color="green">131</FONT> }<a name="line.131"></a> <FONT color="green">132</FONT> <a name="line.132"></a> <FONT color="green">133</FONT> /**<a name="line.133"></a> <FONT color="green">134</FONT> * Returns the covariance matrix<a name="line.134"></a> <FONT color="green">135</FONT> *<a name="line.135"></a> <FONT color="green">136</FONT> * @return covariance matrix<a name="line.136"></a> <FONT color="green">137</FONT> */<a name="line.137"></a> <FONT color="green">138</FONT> public RealMatrix getCovarianceMatrix() {<a name="line.138"></a> <FONT color="green">139</FONT> return covarianceMatrix;<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> /**<a name="line.142"></a> <FONT color="green">143</FONT> * Returns the number of observations (length of covariate vectors)<a name="line.143"></a> <FONT color="green">144</FONT> *<a name="line.144"></a> <FONT color="green">145</FONT> * @return number of observations<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> public int getN() {<a name="line.148"></a> <FONT color="green">149</FONT> return n;<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> * Compute a covariance matrix from a matrix whose columns represent<a name="line.153"></a> <FONT color="green">154</FONT> * covariates.<a name="line.154"></a> <FONT color="green">155</FONT> * @param matrix input matrix (must have at least two columns and two rows)<a name="line.155"></a> <FONT color="green">156</FONT> * @param biasCorrected determines whether or not covariance estimates are bias-corrected<a name="line.156"></a> <FONT color="green">157</FONT> * @return covariance matrix<a name="line.157"></a> <FONT color="green">158</FONT> */<a name="line.158"></a> <FONT color="green">159</FONT> protected RealMatrix computeCovarianceMatrix(RealMatrix matrix, boolean biasCorrected) {<a name="line.159"></a> <FONT color="green">160</FONT> int dimension = matrix.getColumnDimension();<a name="line.160"></a> <FONT color="green">161</FONT> Variance variance = new Variance(biasCorrected);<a name="line.161"></a> <FONT color="green">162</FONT> RealMatrix outMatrix = new BlockRealMatrix(dimension, dimension);<a name="line.162"></a> <FONT color="green">163</FONT> for (int i = 0; i < dimension; i++) {<a name="line.163"></a> <FONT color="green">164</FONT> for (int j = 0; j < i; j++) {<a name="line.164"></a> <FONT color="green">165</FONT> double cov = covariance(matrix.getColumn(i), matrix.getColumn(j), biasCorrected);<a name="line.165"></a> <FONT color="green">166</FONT> outMatrix.setEntry(i, j, cov);<a name="line.166"></a> <FONT color="green">167</FONT> outMatrix.setEntry(j, i, cov);<a name="line.167"></a> <FONT color="green">168</FONT> }<a name="line.168"></a> <FONT color="green">169</FONT> outMatrix.setEntry(i, i, variance.evaluate(matrix.getColumn(i)));<a name="line.169"></a> <FONT color="green">170</FONT> }<a name="line.170"></a> <FONT color="green">171</FONT> return outMatrix;<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> * Create a covariance matrix from a matrix whose columns represent<a name="line.175"></a> <FONT color="green">176</FONT> * covariates. Covariances are computed using the bias-corrected formula.<a name="line.176"></a> <FONT color="green">177</FONT> * @param matrix input matrix (must have at least two columns and two rows)<a name="line.177"></a> <FONT color="green">178</FONT> * @return covariance matrix<a name="line.178"></a> <FONT color="green">179</FONT> * @see #Covariance<a name="line.179"></a> <FONT color="green">180</FONT> */<a name="line.180"></a> <FONT color="green">181</FONT> protected RealMatrix computeCovarianceMatrix(RealMatrix matrix) {<a name="line.181"></a> <FONT color="green">182</FONT> return computeCovarianceMatrix(matrix, true);<a name="line.182"></a> <FONT color="green">183</FONT> }<a name="line.183"></a> <FONT color="green">184</FONT> <a name="line.184"></a> <FONT color="green">185</FONT> /**<a name="line.185"></a> <FONT color="green">186</FONT> * Compute a covariance matrix from a rectangular array whose columns represent<a name="line.186"></a> <FONT color="green">187</FONT> * covariates.<a name="line.187"></a> <FONT color="green">188</FONT> * @param data input array (must have at least two columns and two rows)<a name="line.188"></a> <FONT color="green">189</FONT> * @param biasCorrected determines whether or not covariance estimates are bias-corrected<a name="line.189"></a> <FONT color="green">190</FONT> * @return covariance matrix<a name="line.190"></a> <FONT color="green">191</FONT> */<a name="line.191"></a> <FONT color="green">192</FONT> protected RealMatrix computeCovarianceMatrix(double[][] data, boolean biasCorrected) {<a name="line.192"></a> <FONT color="green">193</FONT> return computeCovarianceMatrix(new BlockRealMatrix(data), biasCorrected);<a name="line.193"></a> <FONT color="green">194</FONT> }<a name="line.194"></a> <FONT color="green">195</FONT> <a name="line.195"></a> <FONT color="green">196</FONT> /**<a name="line.196"></a> <FONT color="green">197</FONT> * Create a covariance matrix from a rectangual array whose columns represent<a name="line.197"></a> <FONT color="green">198</FONT> * covariates. Covariances are computed using the bias-corrected formula.<a name="line.198"></a> <FONT color="green">199</FONT> * @param data input array (must have at least two columns and two rows)<a name="line.199"></a> <FONT color="green">200</FONT> * @return covariance matrix<a name="line.200"></a> <FONT color="green">201</FONT> * @see #Covariance<a name="line.201"></a> <FONT color="green">202</FONT> */<a name="line.202"></a> <FONT color="green">203</FONT> protected RealMatrix computeCovarianceMatrix(double[][] data) {<a name="line.203"></a> <FONT color="green">204</FONT> return computeCovarianceMatrix(data, true);<a name="line.204"></a> <FONT color="green">205</FONT> }<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> * Computes the covariance between the two arrays.<a name="line.208"></a> <FONT color="green">209</FONT> *<a name="line.209"></a> <FONT color="green">210</FONT> * <p>Array lengths must match and the common length must be at least 2.</p><a name="line.210"></a> <FONT color="green">211</FONT> *<a name="line.211"></a> <FONT color="green">212</FONT> * @param xArray first data array<a name="line.212"></a> <FONT color="green">213</FONT> * @param yArray second data array<a name="line.213"></a> <FONT color="green">214</FONT> * @param biasCorrected if true, returned value will be bias-corrected<a name="line.214"></a> <FONT color="green">215</FONT> * @return returns the covariance for the two arrays<a name="line.215"></a> <FONT color="green">216</FONT> * @throws IllegalArgumentException if the arrays lengths do not match or<a name="line.216"></a> <FONT color="green">217</FONT> * there is insufficient data<a name="line.217"></a> <FONT color="green">218</FONT> */<a name="line.218"></a> <FONT color="green">219</FONT> public double covariance(final double[] xArray, final double[] yArray, boolean biasCorrected)<a name="line.219"></a> <FONT color="green">220</FONT> throws IllegalArgumentException {<a name="line.220"></a> <FONT color="green">221</FONT> Mean mean = new Mean();<a name="line.221"></a> <FONT color="green">222</FONT> double result = 0d;<a name="line.222"></a> <FONT color="green">223</FONT> int length = xArray.length;<a name="line.223"></a> <FONT color="green">224</FONT> if(length == yArray.length && length > 1) {<a name="line.224"></a> <FONT color="green">225</FONT> double xMean = mean.evaluate(xArray);<a name="line.225"></a> <FONT color="green">226</FONT> double yMean = mean.evaluate(yArray);<a name="line.226"></a> <FONT color="green">227</FONT> for (int i = 0; i < length; i++) {<a name="line.227"></a> <FONT color="green">228</FONT> double xDev = xArray[i] - xMean;<a name="line.228"></a> <FONT color="green">229</FONT> double yDev = yArray[i] - yMean;<a name="line.229"></a> <FONT color="green">230</FONT> result += (xDev * yDev - result) / (i + 1);<a name="line.230"></a> <FONT color="green">231</FONT> }<a name="line.231"></a> <FONT color="green">232</FONT> }<a name="line.232"></a> <FONT color="green">233</FONT> else {<a name="line.233"></a> <FONT color="green">234</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.234"></a> <FONT color="green">235</FONT> "arrays must have the same length and both must have at " +<a name="line.235"></a> <FONT color="green">236</FONT> "least two elements. xArray has size {0}, yArray has {1} elements",<a name="line.236"></a> <FONT color="green">237</FONT> length, yArray.length);<a name="line.237"></a> <FONT color="green">238</FONT> }<a name="line.238"></a> <FONT color="green">239</FONT> return biasCorrected ? result * ((double) length / (double)(length - 1)) : result;<a name="line.239"></a> <FONT color="green">240</FONT> }<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> * Computes the covariance between the two arrays, using the bias-corrected<a name="line.243"></a> <FONT color="green">244</FONT> * formula.<a name="line.244"></a> <FONT color="green">245</FONT> *<a name="line.245"></a> <FONT color="green">246</FONT> * <p>Array lengths must match and the common length must be at least 2.</p><a name="line.246"></a> <FONT color="green">247</FONT> *<a name="line.247"></a> <FONT color="green">248</FONT> * @param xArray first data array<a name="line.248"></a> <FONT color="green">249</FONT> * @param yArray second data array<a name="line.249"></a> <FONT color="green">250</FONT> * @return returns the covariance for the two arrays<a name="line.250"></a> <FONT color="green">251</FONT> * @throws IllegalArgumentException if the arrays lengths do not match or<a name="line.251"></a> <FONT color="green">252</FONT> * there is insufficient data<a name="line.252"></a> <FONT color="green">253</FONT> */<a name="line.253"></a> <FONT color="green">254</FONT> public double covariance(final double[] xArray, final double[] yArray)<a name="line.254"></a> <FONT color="green">255</FONT> throws IllegalArgumentException {<a name="line.255"></a> <FONT color="green">256</FONT> return covariance(xArray, yArray, true);<a name="line.256"></a> <FONT color="green">257</FONT> }<a name="line.257"></a> <FONT color="green">258</FONT> <a name="line.258"></a> <FONT color="green">259</FONT> /**<a name="line.259"></a> <FONT color="green">260</FONT> * Throws IllegalArgumentException of the matrix does not have at least<a name="line.260"></a> <FONT color="green">261</FONT> * two columns and two rows<a name="line.261"></a> <FONT color="green">262</FONT> * @param matrix matrix to check<a name="line.262"></a> <FONT color="green">263</FONT> */<a name="line.263"></a> <FONT color="green">264</FONT> private void checkSufficientData(final RealMatrix matrix) {<a name="line.264"></a> <FONT color="green">265</FONT> int nRows = matrix.getRowDimension();<a name="line.265"></a> <FONT color="green">266</FONT> int nCols = matrix.getColumnDimension();<a name="line.266"></a> <FONT color="green">267</FONT> if (nRows < 2 || nCols < 2) {<a name="line.267"></a> <FONT color="green">268</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.268"></a> <FONT color="green">269</FONT> "insufficient data: only {0} rows and {1} columns.",<a name="line.269"></a> <FONT color="green">270</FONT> nRows, nCols);<a name="line.270"></a> <FONT color="green">271</FONT> }<a name="line.271"></a> <FONT color="green">272</FONT> }<a name="line.272"></a> <FONT color="green">273</FONT> }<a name="line.273"></a> </PRE> </BODY> </HTML>