Mercurial > hg > de.mpg.mpiwg.itgroup.digilib.plugin
view libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/linear/SingularValueDecompositionImpl.html @ 13:cbf34dd4d7e6
commons-math-2.1 added
| author | dwinter |
|---|---|
| date | Tue, 04 Jan 2011 10:02:07 +0100 |
| parents | |
| children |
line wrap: on
line source
<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> * Calculates the compact Singular Value Decomposition of a matrix.<a name="line.23"></a> <FONT color="green">024</FONT> * <p><a name="line.24"></a> <FONT color="green">025</FONT> * The Singular Value Decomposition of matrix A is a set of three matrices: U,<a name="line.25"></a> <FONT color="green">026</FONT> * &Sigma; and V such that A = U &times; &Sigma; &times; V<sup>T</sup>. Let A be<a name="line.26"></a> <FONT color="green">027</FONT> * a m &times; n matrix, then U is a m &times; p orthogonal matrix, &Sigma; is a<a name="line.27"></a> <FONT color="green">028</FONT> * p &times; p diagonal matrix with positive or null elements, V is a p &times;<a name="line.28"></a> <FONT color="green">029</FONT> * n orthogonal matrix (hence V<sup>T</sup> is also orthogonal) where<a name="line.29"></a> <FONT color="green">030</FONT> * p=min(m,n).<a name="line.30"></a> <FONT color="green">031</FONT> * </p><a name="line.31"></a> <FONT color="green">032</FONT> * @version $Revision: 912413 $ $Date: 2010-02-21 16:46:12 -0500 (Sun, 21 Feb 2010) $<a name="line.32"></a> <FONT color="green">033</FONT> * @since 2.0<a name="line.33"></a> <FONT color="green">034</FONT> */<a name="line.34"></a> <FONT color="green">035</FONT> public class SingularValueDecompositionImpl implements<a name="line.35"></a> <FONT color="green">036</FONT> SingularValueDecomposition {<a name="line.36"></a> <FONT color="green">037</FONT> <a name="line.37"></a> <FONT color="green">038</FONT> /** Number of rows of the initial matrix. */<a name="line.38"></a> <FONT color="green">039</FONT> private int m;<a name="line.39"></a> <FONT color="green">040</FONT> <a name="line.40"></a> <FONT color="green">041</FONT> /** Number of columns of the initial matrix. */<a name="line.41"></a> <FONT color="green">042</FONT> private int n;<a name="line.42"></a> <FONT color="green">043</FONT> <a name="line.43"></a> <FONT color="green">044</FONT> /** Eigen decomposition of the tridiagonal matrix. */<a name="line.44"></a> <FONT color="green">045</FONT> private EigenDecomposition eigenDecomposition;<a name="line.45"></a> <FONT color="green">046</FONT> <a name="line.46"></a> <FONT color="green">047</FONT> /** Singular values. */<a name="line.47"></a> <FONT color="green">048</FONT> private double[] singularValues;<a name="line.48"></a> <FONT color="green">049</FONT> <a name="line.49"></a> <FONT color="green">050</FONT> /** Cached value of U. */<a name="line.50"></a> <FONT color="green">051</FONT> private RealMatrix cachedU;<a name="line.51"></a> <FONT color="green">052</FONT> <a name="line.52"></a> <FONT color="green">053</FONT> /** Cached value of U<sup>T</sup>. */<a name="line.53"></a> <FONT color="green">054</FONT> private RealMatrix cachedUt;<a name="line.54"></a> <FONT color="green">055</FONT> <a name="line.55"></a> <FONT color="green">056</FONT> /** Cached value of S. */<a name="line.56"></a> <FONT color="green">057</FONT> private RealMatrix cachedS;<a name="line.57"></a> <FONT color="green">058</FONT> <a name="line.58"></a> <FONT color="green">059</FONT> /** Cached value of V. */<a name="line.59"></a> <FONT color="green">060</FONT> private RealMatrix cachedV;<a name="line.60"></a> <FONT color="green">061</FONT> <a name="line.61"></a> <FONT color="green">062</FONT> /** Cached value of V<sup>T</sup>. */<a name="line.62"></a> <FONT color="green">063</FONT> private RealMatrix cachedVt;<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> * Calculates the compact Singular Value Decomposition of the given matrix.<a name="line.66"></a> <FONT color="green">067</FONT> * @param matrix<a name="line.67"></a> <FONT color="green">068</FONT> * The matrix to decompose.<a name="line.68"></a> <FONT color="green">069</FONT> * @exception InvalidMatrixException<a name="line.69"></a> <FONT color="green">070</FONT> * (wrapping a<a name="line.70"></a> <FONT color="green">071</FONT> * {@link org.apache.commons.math.ConvergenceException} if<a name="line.71"></a> <FONT color="green">072</FONT> * algorithm fails to converge<a name="line.72"></a> <FONT color="green">073</FONT> */<a name="line.73"></a> <FONT color="green">074</FONT> public SingularValueDecompositionImpl(final RealMatrix matrix)<a name="line.74"></a> <FONT color="green">075</FONT> throws InvalidMatrixException {<a name="line.75"></a> <FONT color="green">076</FONT> <a name="line.76"></a> <FONT color="green">077</FONT> m = matrix.getRowDimension();<a name="line.77"></a> <FONT color="green">078</FONT> n = matrix.getColumnDimension();<a name="line.78"></a> <FONT color="green">079</FONT> <a name="line.79"></a> <FONT color="green">080</FONT> cachedU = null;<a name="line.80"></a> <FONT color="green">081</FONT> cachedS = null;<a name="line.81"></a> <FONT color="green">082</FONT> cachedV = null;<a name="line.82"></a> <FONT color="green">083</FONT> cachedVt = null;<a name="line.83"></a> <FONT color="green">084</FONT> <a name="line.84"></a> <FONT color="green">085</FONT> double[][] localcopy = matrix.getData();<a name="line.85"></a> <FONT color="green">086</FONT> double[][] matATA = new double[n][n];<a name="line.86"></a> <FONT color="green">087</FONT> //<a name="line.87"></a> <FONT color="green">088</FONT> // create A^T*A<a name="line.88"></a> <FONT color="green">089</FONT> //<a name="line.89"></a> <FONT color="green">090</FONT> for (int i = 0; i < n; i++) {<a name="line.90"></a> <FONT color="green">091</FONT> for (int j = i; j < n; j++) {<a name="line.91"></a> <FONT color="green">092</FONT> matATA[i][j] = 0.0;<a name="line.92"></a> <FONT color="green">093</FONT> for (int k = 0; k < m; k++) {<a name="line.93"></a> <FONT color="green">094</FONT> matATA[i][j] += localcopy[k][i] * localcopy[k][j];<a name="line.94"></a> <FONT color="green">095</FONT> }<a name="line.95"></a> <FONT color="green">096</FONT> matATA[j][i]=matATA[i][j];<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> double[][] matAAT = new double[m][m];<a name="line.100"></a> <FONT color="green">101</FONT> //<a name="line.101"></a> <FONT color="green">102</FONT> // create A*A^T<a name="line.102"></a> <FONT color="green">103</FONT> //<a name="line.103"></a> <FONT color="green">104</FONT> for (int i = 0; i < m; i++) {<a name="line.104"></a> <FONT color="green">105</FONT> for (int j = i; j < m; j++) {<a name="line.105"></a> <FONT color="green">106</FONT> matAAT[i][j] = 0.0;<a name="line.106"></a> <FONT color="green">107</FONT> for (int k = 0; k < n; k++) {<a name="line.107"></a> <FONT color="green">108</FONT> matAAT[i][j] += localcopy[i][k] * localcopy[j][k];<a name="line.108"></a> <FONT color="green">109</FONT> }<a name="line.109"></a> <FONT color="green">110</FONT> matAAT[j][i]=matAAT[i][j];<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> int p;<a name="line.113"></a> <FONT color="green">114</FONT> if (m>=n) {<a name="line.114"></a> <FONT color="green">115</FONT> p=n;<a name="line.115"></a> <FONT color="green">116</FONT> // compute eigen decomposition of A^T*A<a name="line.116"></a> <FONT color="green">117</FONT> eigenDecomposition = new EigenDecompositionImpl(<a name="line.117"></a> <FONT color="green">118</FONT> new Array2DRowRealMatrix(matATA),1.0);<a name="line.118"></a> <FONT color="green">119</FONT> singularValues = eigenDecomposition.getRealEigenvalues();<a name="line.119"></a> <FONT color="green">120</FONT> cachedV = eigenDecomposition.getV();<a name="line.120"></a> <FONT color="green">121</FONT> <a name="line.121"></a> <FONT color="green">122</FONT> // compute eigen decomposition of A*A^T<a name="line.122"></a> <FONT color="green">123</FONT> eigenDecomposition = new EigenDecompositionImpl(<a name="line.123"></a> <FONT color="green">124</FONT> new Array2DRowRealMatrix(matAAT),1.0);<a name="line.124"></a> <FONT color="green">125</FONT> cachedU = eigenDecomposition.getV().getSubMatrix(0, m - 1, 0, p - 1);<a name="line.125"></a> <FONT color="green">126</FONT> } else {<a name="line.126"></a> <FONT color="green">127</FONT> p=m;<a name="line.127"></a> <FONT color="green">128</FONT> // compute eigen decomposition of A*A^T<a name="line.128"></a> <FONT color="green">129</FONT> eigenDecomposition = new EigenDecompositionImpl(<a name="line.129"></a> <FONT color="green">130</FONT> new Array2DRowRealMatrix(matAAT),1.0);<a name="line.130"></a> <FONT color="green">131</FONT> singularValues = eigenDecomposition.getRealEigenvalues();<a name="line.131"></a> <FONT color="green">132</FONT> cachedU = eigenDecomposition.getV();<a name="line.132"></a> <FONT color="green">133</FONT> <a name="line.133"></a> <FONT color="green">134</FONT> // compute eigen decomposition of A^T*A<a name="line.134"></a> <FONT color="green">135</FONT> eigenDecomposition = new EigenDecompositionImpl(<a name="line.135"></a> <FONT color="green">136</FONT> new Array2DRowRealMatrix(matATA),1.0);<a name="line.136"></a> <FONT color="green">137</FONT> cachedV = eigenDecomposition.getV().getSubMatrix(0,n-1,0,p-1);<a name="line.137"></a> <FONT color="green">138</FONT> }<a name="line.138"></a> <FONT color="green">139</FONT> for (int i = 0; i < p; i++) {<a name="line.139"></a> <FONT color="green">140</FONT> singularValues[i] = Math.sqrt(Math.abs(singularValues[i]));<a name="line.140"></a> <FONT color="green">141</FONT> }<a name="line.141"></a> <FONT color="green">142</FONT> // Up to this point, U and V are computed independently of each other.<a name="line.142"></a> <FONT color="green">143</FONT> // There still an sign indetermination of each column of, say, U.<a name="line.143"></a> <FONT color="green">144</FONT> // The sign is set such that A.V_i=sigma_i.U_i (i<=p)<a name="line.144"></a> <FONT color="green">145</FONT> // The right sign corresponds to a positive dot product of A.V_i and U_i<a name="line.145"></a> <FONT color="green">146</FONT> for (int i = 0; i < p; i++) {<a name="line.146"></a> <FONT color="green">147</FONT> RealVector tmp = cachedU.getColumnVector(i);<a name="line.147"></a> <FONT color="green">148</FONT> double product=matrix.operate(cachedV.getColumnVector(i)).dotProduct(tmp);<a name="line.148"></a> <FONT color="green">149</FONT> if (product<0) {<a name="line.149"></a> <FONT color="green">150</FONT> cachedU.setColumnVector(i, tmp.mapMultiply(-1.0));<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> }<a name="line.153"></a> <FONT color="green">154</FONT> <a name="line.154"></a> <FONT color="green">155</FONT> /** {@inheritDoc} */<a name="line.155"></a> <FONT color="green">156</FONT> public RealMatrix getU() throws InvalidMatrixException {<a name="line.156"></a> <FONT color="green">157</FONT> // return the cached matrix<a name="line.157"></a> <FONT color="green">158</FONT> return cachedU;<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> <a name="line.161"></a> <FONT color="green">162</FONT> /** {@inheritDoc} */<a name="line.162"></a> <FONT color="green">163</FONT> public RealMatrix getUT() throws InvalidMatrixException {<a name="line.163"></a> <FONT color="green">164</FONT> <a name="line.164"></a> <FONT color="green">165</FONT> if (cachedUt == null) {<a name="line.165"></a> <FONT color="green">166</FONT> cachedUt = getU().transpose();<a name="line.166"></a> <FONT color="green">167</FONT> }<a name="line.167"></a> <FONT color="green">168</FONT> <a name="line.168"></a> <FONT color="green">169</FONT> // return the cached matrix<a name="line.169"></a> <FONT color="green">170</FONT> return cachedUt;<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> <a name="line.173"></a> <FONT color="green">174</FONT> /** {@inheritDoc} */<a name="line.174"></a> <FONT color="green">175</FONT> public RealMatrix getS() throws InvalidMatrixException {<a name="line.175"></a> <FONT color="green">176</FONT> <a name="line.176"></a> <FONT color="green">177</FONT> if (cachedS == null) {<a name="line.177"></a> <FONT color="green">178</FONT> <a name="line.178"></a> <FONT color="green">179</FONT> // cache the matrix for subsequent calls<a name="line.179"></a> <FONT color="green">180</FONT> cachedS = MatrixUtils.createRealDiagonalMatrix(singularValues);<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> return cachedS;<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> /** {@inheritDoc} */<a name="line.186"></a> <FONT color="green">187</FONT> public double[] getSingularValues() throws InvalidMatrixException {<a name="line.187"></a> <FONT color="green">188</FONT> return singularValues.clone();<a name="line.188"></a> <FONT color="green">189</FONT> }<a name="line.189"></a> <FONT color="green">190</FONT> <a name="line.190"></a> <FONT color="green">191</FONT> /** {@inheritDoc} */<a name="line.191"></a> <FONT color="green">192</FONT> public RealMatrix getV() throws InvalidMatrixException {<a name="line.192"></a> <FONT color="green">193</FONT> // return the cached matrix<a name="line.193"></a> <FONT color="green">194</FONT> return cachedV;<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> <a name="line.197"></a> <FONT color="green">198</FONT> /** {@inheritDoc} */<a name="line.198"></a> <FONT color="green">199</FONT> public RealMatrix getVT() throws InvalidMatrixException {<a name="line.199"></a> <FONT color="green">200</FONT> <a name="line.200"></a> <FONT color="green">201</FONT> if (cachedVt == null) {<a name="line.201"></a> <FONT color="green">202</FONT> cachedVt = getV().transpose();<a name="line.202"></a> <FONT color="green">203</FONT> }<a name="line.203"></a> <FONT color="green">204</FONT> <a name="line.204"></a> <FONT color="green">205</FONT> // return the cached matrix<a name="line.205"></a> <FONT color="green">206</FONT> return cachedVt;<a name="line.206"></a> <FONT color="green">207</FONT> <a name="line.207"></a> <FONT color="green">208</FONT> }<a name="line.208"></a> <FONT color="green">209</FONT> <a name="line.209"></a> <FONT color="green">210</FONT> /** {@inheritDoc} */<a name="line.210"></a> <FONT color="green">211</FONT> public RealMatrix getCovariance(final double minSingularValue) {<a name="line.211"></a> <FONT color="green">212</FONT> <a name="line.212"></a> <FONT color="green">213</FONT> // get the number of singular values to consider<a name="line.213"></a> <FONT color="green">214</FONT> final int p = singularValues.length;<a name="line.214"></a> <FONT color="green">215</FONT> int dimension = 0;<a name="line.215"></a> <FONT color="green">216</FONT> while ((dimension < p) && (singularValues[dimension] >= minSingularValue)) {<a name="line.216"></a> <FONT color="green">217</FONT> ++dimension;<a name="line.217"></a> <FONT color="green">218</FONT> }<a name="line.218"></a> <FONT color="green">219</FONT> <a name="line.219"></a> <FONT color="green">220</FONT> if (dimension == 0) {<a name="line.220"></a> <FONT color="green">221</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.221"></a> <FONT color="green">222</FONT> "cutoff singular value is {0}, should be at most {1}",<a name="line.222"></a> <FONT color="green">223</FONT> minSingularValue, singularValues[0]);<a name="line.223"></a> <FONT color="green">224</FONT> }<a name="line.224"></a> <FONT color="green">225</FONT> <a name="line.225"></a> <FONT color="green">226</FONT> final double[][] data = new double[dimension][p];<a name="line.226"></a> <FONT color="green">227</FONT> getVT().walkInOptimizedOrder(new DefaultRealMatrixPreservingVisitor() {<a name="line.227"></a> <FONT color="green">228</FONT> /** {@inheritDoc} */<a name="line.228"></a> <FONT color="green">229</FONT> @Override<a name="line.229"></a> <FONT color="green">230</FONT> public void visit(final int row, final int column,<a name="line.230"></a> <FONT color="green">231</FONT> final double value) {<a name="line.231"></a> <FONT color="green">232</FONT> data[row][column] = value / singularValues[row];<a name="line.232"></a> <FONT color="green">233</FONT> }<a name="line.233"></a> <FONT color="green">234</FONT> }, 0, dimension - 1, 0, p - 1);<a name="line.234"></a> <FONT color="green">235</FONT> <a name="line.235"></a> <FONT color="green">236</FONT> RealMatrix jv = new Array2DRowRealMatrix(data, false);<a name="line.236"></a> <FONT color="green">237</FONT> return jv.transpose().multiply(jv);<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> <a name="line.240"></a> <FONT color="green">241</FONT> /** {@inheritDoc} */<a name="line.241"></a> <FONT color="green">242</FONT> public double getNorm() throws InvalidMatrixException {<a name="line.242"></a> <FONT color="green">243</FONT> return singularValues[0];<a name="line.243"></a> <FONT color="green">244</FONT> }<a name="line.244"></a> <FONT color="green">245</FONT> <a name="line.245"></a> <FONT color="green">246</FONT> /** {@inheritDoc} */<a name="line.246"></a> <FONT color="green">247</FONT> public double getConditionNumber() throws InvalidMatrixException {<a name="line.247"></a> <FONT color="green">248</FONT> return singularValues[0] / singularValues[singularValues.length - 1];<a name="line.248"></a> <FONT color="green">249</FONT> }<a name="line.249"></a> <FONT color="green">250</FONT> <a name="line.250"></a> <FONT color="green">251</FONT> /** {@inheritDoc} */<a name="line.251"></a> <FONT color="green">252</FONT> public int getRank() throws IllegalStateException {<a name="line.252"></a> <FONT color="green">253</FONT> <a name="line.253"></a> <FONT color="green">254</FONT> final double threshold = Math.max(m, n) * Math.ulp(singularValues[0]);<a name="line.254"></a> <FONT color="green">255</FONT> <a name="line.255"></a> <FONT color="green">256</FONT> for (int i = singularValues.length - 1; i >= 0; --i) {<a name="line.256"></a> <FONT color="green">257</FONT> if (singularValues[i] > threshold) {<a name="line.257"></a> <FONT color="green">258</FONT> return i + 1;<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> return 0;<a name="line.261"></a> <FONT color="green">262</FONT> <a name="line.262"></a> <FONT color="green">263</FONT> }<a name="line.263"></a> <FONT color="green">264</FONT> <a name="line.264"></a> <FONT color="green">265</FONT> /** {@inheritDoc} */<a name="line.265"></a> <FONT color="green">266</FONT> public DecompositionSolver getSolver() {<a name="line.266"></a> <FONT color="green">267</FONT> return new Solver(singularValues, getUT(), getV(), getRank() == Math<a name="line.267"></a> <FONT color="green">268</FONT> .max(m, n));<a name="line.268"></a> <FONT color="green">269</FONT> }<a name="line.269"></a> <FONT color="green">270</FONT> <a name="line.270"></a> <FONT color="green">271</FONT> /** Specialized solver. */<a name="line.271"></a> <FONT color="green">272</FONT> private static class Solver implements DecompositionSolver {<a name="line.272"></a> <FONT color="green">273</FONT> <a name="line.273"></a> <FONT color="green">274</FONT> /** Pseudo-inverse of the initial matrix. */<a name="line.274"></a> <FONT color="green">275</FONT> private final RealMatrix pseudoInverse;<a name="line.275"></a> <FONT color="green">276</FONT> <a name="line.276"></a> <FONT color="green">277</FONT> /** Singularity indicator. */<a name="line.277"></a> <FONT color="green">278</FONT> private boolean nonSingular;<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> * Build a solver from decomposed matrix.<a name="line.281"></a> <FONT color="green">282</FONT> * @param singularValues<a name="line.282"></a> <FONT color="green">283</FONT> * singularValues<a name="line.283"></a> <FONT color="green">284</FONT> * @param uT<a name="line.284"></a> <FONT color="green">285</FONT> * U<sup>T</sup> matrix of the decomposition<a name="line.285"></a> <FONT color="green">286</FONT> * @param v<a name="line.286"></a> <FONT color="green">287</FONT> * V matrix of the decomposition<a name="line.287"></a> <FONT color="green">288</FONT> * @param nonSingular<a name="line.288"></a> <FONT color="green">289</FONT> * singularity indicator<a name="line.289"></a> <FONT color="green">290</FONT> */<a name="line.290"></a> <FONT color="green">291</FONT> private Solver(final double[] singularValues, final RealMatrix uT,<a name="line.291"></a> <FONT color="green">292</FONT> final RealMatrix v, final boolean nonSingular) {<a name="line.292"></a> <FONT color="green">293</FONT> double[][] suT = uT.getData();<a name="line.293"></a> <FONT color="green">294</FONT> for (int i = 0; i < singularValues.length; ++i) {<a name="line.294"></a> <FONT color="green">295</FONT> final double a;<a name="line.295"></a> <FONT color="green">296</FONT> if (singularValues[i]>0) {<a name="line.296"></a> <FONT color="green">297</FONT> a=1.0 / singularValues[i];<a name="line.297"></a> <FONT color="green">298</FONT> } else {<a name="line.298"></a> <FONT color="green">299</FONT> a=0.0;<a name="line.299"></a> <FONT color="green">300</FONT> }<a name="line.300"></a> <FONT color="green">301</FONT> final double[] suTi = suT[i];<a name="line.301"></a> <FONT color="green">302</FONT> for (int j = 0; j < suTi.length; ++j) {<a name="line.302"></a> <FONT color="green">303</FONT> suTi[j] *= a;<a name="line.303"></a> <FONT color="green">304</FONT> }<a name="line.304"></a> <FONT color="green">305</FONT> }<a name="line.305"></a> <FONT color="green">306</FONT> pseudoInverse = v.multiply(new Array2DRowRealMatrix(suT, false));<a name="line.306"></a> <FONT color="green">307</FONT> this.nonSingular = nonSingular;<a name="line.307"></a> <FONT color="green">308</FONT> }<a name="line.308"></a> <FONT color="green">309</FONT> <a name="line.309"></a> <FONT color="green">310</FONT> /**<a name="line.310"></a> <FONT color="green">311</FONT> * Solve the linear equation A &times; X = B in least square sense.<a name="line.311"></a> <FONT color="green">312</FONT> * <p><a name="line.312"></a> <FONT color="green">313</FONT> * The m&times;n matrix A may not be square, the solution X is such that<a name="line.313"></a> <FONT color="green">314</FONT> * ||A &times; X - B|| is minimal.<a name="line.314"></a> <FONT color="green">315</FONT> * </p><a name="line.315"></a> <FONT color="green">316</FONT> * @param b<a name="line.316"></a> <FONT color="green">317</FONT> * right-hand side of the equation A &times; X = B<a name="line.317"></a> <FONT color="green">318</FONT> * @return a vector X that minimizes the two norm of A &times; X - B<a name="line.318"></a> <FONT color="green">319</FONT> * @exception IllegalArgumentException<a name="line.319"></a> <FONT color="green">320</FONT> * if matrices dimensions don't match<a name="line.320"></a> <FONT color="green">321</FONT> */<a name="line.321"></a> <FONT color="green">322</FONT> public double[] solve(final double[] b) throws IllegalArgumentException {<a name="line.322"></a> <FONT color="green">323</FONT> return pseudoInverse.operate(b);<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 the linear equation A &times; X = B in least square sense.<a name="line.327"></a> <FONT color="green">328</FONT> * <p><a name="line.328"></a> <FONT color="green">329</FONT> * The m&times;n matrix A may not be square, the solution X is such that<a name="line.329"></a> <FONT color="green">330</FONT> * ||A &times; X - B|| is minimal.<a name="line.330"></a> <FONT color="green">331</FONT> * </p><a name="line.331"></a> <FONT color="green">332</FONT> * @param b<a name="line.332"></a> <FONT color="green">333</FONT> * right-hand side of the equation A &times; X = B<a name="line.333"></a> <FONT color="green">334</FONT> * @return a vector X that minimizes the two norm of A &times; X - B<a name="line.334"></a> <FONT color="green">335</FONT> * @exception IllegalArgumentException<a name="line.335"></a> <FONT color="green">336</FONT> * if matrices dimensions don't match<a name="line.336"></a> <FONT color="green">337</FONT> */<a name="line.337"></a> <FONT color="green">338</FONT> public RealVector solve(final RealVector b)<a name="line.338"></a> <FONT color="green">339</FONT> throws IllegalArgumentException {<a name="line.339"></a> <FONT color="green">340</FONT> return pseudoInverse.operate(b);<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> /**<a name="line.343"></a> <FONT color="green">344</FONT> * Solve the linear equation A &times; X = B in least square sense.<a name="line.344"></a> <FONT color="green">345</FONT> * <p><a name="line.345"></a> <FONT color="green">346</FONT> * The m&times;n matrix A may not be square, the solution X is such that<a name="line.346"></a> <FONT color="green">347</FONT> * ||A &times; X - B|| is minimal.<a name="line.347"></a> <FONT color="green">348</FONT> * </p><a name="line.348"></a> <FONT color="green">349</FONT> * @param b<a name="line.349"></a> <FONT color="green">350</FONT> * right-hand side of the equation A &times; X = B<a name="line.350"></a> <FONT color="green">351</FONT> * @return a matrix X that minimizes the two norm of A &times; X - B<a name="line.351"></a> <FONT color="green">352</FONT> * @exception IllegalArgumentException<a name="line.352"></a> <FONT color="green">353</FONT> * if matrices dimensions don't match<a name="line.353"></a> <FONT color="green">354</FONT> */<a name="line.354"></a> <FONT color="green">355</FONT> public RealMatrix solve(final RealMatrix b)<a name="line.355"></a> <FONT color="green">356</FONT> throws IllegalArgumentException {<a name="line.356"></a> <FONT color="green">357</FONT> return pseudoInverse.multiply(b);<a name="line.357"></a> <FONT color="green">358</FONT> }<a name="line.358"></a> <FONT color="green">359</FONT> <a name="line.359"></a> <FONT color="green">360</FONT> /**<a name="line.360"></a> <FONT color="green">361</FONT> * Check if the decomposed matrix is non-singular.<a name="line.361"></a> <FONT color="green">362</FONT> * @return true if the decomposed matrix is non-singular<a name="line.362"></a> <FONT color="green">363</FONT> */<a name="line.363"></a> <FONT color="green">364</FONT> public boolean isNonSingular() {<a name="line.364"></a> <FONT color="green">365</FONT> return nonSingular;<a name="line.365"></a> <FONT color="green">366</FONT> }<a name="line.366"></a> <FONT color="green">367</FONT> <a name="line.367"></a> <FONT color="green">368</FONT> /**<a name="line.368"></a> <FONT color="green">369</FONT> * Get the pseudo-inverse of the decomposed matrix.<a name="line.369"></a> <FONT color="green">370</FONT> * @return inverse matrix<a name="line.370"></a> <FONT color="green">371</FONT> */<a name="line.371"></a> <FONT color="green">372</FONT> public RealMatrix getInverse() {<a name="line.372"></a> <FONT color="green">373</FONT> return pseudoInverse;<a name="line.373"></a> <FONT color="green">374</FONT> }<a name="line.374"></a> <FONT color="green">375</FONT> <a name="line.375"></a> <FONT color="green">376</FONT> }<a name="line.376"></a> <FONT color="green">377</FONT> <a name="line.377"></a> <FONT color="green">378</FONT> }<a name="line.378"></a> </PRE> </BODY> </HTML>