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| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.linear;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import java.util.Arrays;<a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.22"></a> <FONT color="green">023</FONT> <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> * Calculates the QR-decomposition of a matrix.<a name="line.26"></a> <FONT color="green">027</FONT> * <p>The QR-decomposition of a matrix A consists of two matrices Q and R<a name="line.27"></a> <FONT color="green">028</FONT> * that satisfy: A = QR, Q is orthogonal (Q<sup>T</sup>Q = I), and R is<a name="line.28"></a> <FONT color="green">029</FONT> * upper triangular. If A is m&times;n, Q is m&times;m and R m&times;n.</p><a name="line.29"></a> <FONT color="green">030</FONT> * <p>This class compute the decomposition using Householder reflectors.</p><a name="line.30"></a> <FONT color="green">031</FONT> * <p>For efficiency purposes, the decomposition in packed form is transposed.<a name="line.31"></a> <FONT color="green">032</FONT> * This allows inner loop to iterate inside rows, which is much more cache-efficient<a name="line.32"></a> <FONT color="green">033</FONT> * in Java.</p><a name="line.33"></a> <FONT color="green">034</FONT> *<a name="line.34"></a> <FONT color="green">035</FONT> * @see <a href="http://mathworld.wolfram.com/QRDecomposition.html">MathWorld</a><a name="line.35"></a> <FONT color="green">036</FONT> * @see <a href="http://en.wikipedia.org/wiki/QR_decomposition">Wikipedia</a><a name="line.36"></a> <FONT color="green">037</FONT> *<a name="line.37"></a> <FONT color="green">038</FONT> * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $<a name="line.38"></a> <FONT color="green">039</FONT> * @since 1.2<a name="line.39"></a> <FONT color="green">040</FONT> */<a name="line.40"></a> <FONT color="green">041</FONT> public class QRDecompositionImpl implements QRDecomposition {<a name="line.41"></a> <FONT color="green">042</FONT> <a name="line.42"></a> <FONT color="green">043</FONT> /**<a name="line.43"></a> <FONT color="green">044</FONT> * A packed TRANSPOSED representation of the QR decomposition.<a name="line.44"></a> <FONT color="green">045</FONT> * <p>The elements BELOW the diagonal are the elements of the UPPER triangular<a name="line.45"></a> <FONT color="green">046</FONT> * matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors<a name="line.46"></a> <FONT color="green">047</FONT> * from which an explicit form of Q can be recomputed if desired.</p><a name="line.47"></a> <FONT color="green">048</FONT> */<a name="line.48"></a> <FONT color="green">049</FONT> private double[][] qrt;<a name="line.49"></a> <FONT color="green">050</FONT> <a name="line.50"></a> <FONT color="green">051</FONT> /** The diagonal elements of R. */<a name="line.51"></a> <FONT color="green">052</FONT> private double[] rDiag;<a name="line.52"></a> <FONT color="green">053</FONT> <a name="line.53"></a> <FONT color="green">054</FONT> /** Cached value of Q. */<a name="line.54"></a> <FONT color="green">055</FONT> private RealMatrix cachedQ;<a name="line.55"></a> <FONT color="green">056</FONT> <a name="line.56"></a> <FONT color="green">057</FONT> /** Cached value of QT. */<a name="line.57"></a> <FONT color="green">058</FONT> private RealMatrix cachedQT;<a name="line.58"></a> <FONT color="green">059</FONT> <a name="line.59"></a> <FONT color="green">060</FONT> /** Cached value of R. */<a name="line.60"></a> <FONT color="green">061</FONT> private RealMatrix cachedR;<a name="line.61"></a> <FONT color="green">062</FONT> <a name="line.62"></a> <FONT color="green">063</FONT> /** Cached value of H. */<a name="line.63"></a> <FONT color="green">064</FONT> private RealMatrix cachedH;<a name="line.64"></a> <FONT color="green">065</FONT> <a name="line.65"></a> <FONT color="green">066</FONT> /**<a name="line.66"></a> <FONT color="green">067</FONT> * Calculates the QR-decomposition of the given matrix.<a name="line.67"></a> <FONT color="green">068</FONT> * @param matrix The matrix to decompose.<a name="line.68"></a> <FONT color="green">069</FONT> */<a name="line.69"></a> <FONT color="green">070</FONT> public QRDecompositionImpl(RealMatrix matrix) {<a name="line.70"></a> <FONT color="green">071</FONT> <a name="line.71"></a> <FONT color="green">072</FONT> final int m = matrix.getRowDimension();<a name="line.72"></a> <FONT color="green">073</FONT> final int n = matrix.getColumnDimension();<a name="line.73"></a> <FONT color="green">074</FONT> qrt = matrix.transpose().getData();<a name="line.74"></a> <FONT color="green">075</FONT> rDiag = new double[Math.min(m, n)];<a name="line.75"></a> <FONT color="green">076</FONT> cachedQ = null;<a name="line.76"></a> <FONT color="green">077</FONT> cachedQT = null;<a name="line.77"></a> <FONT color="green">078</FONT> cachedR = null;<a name="line.78"></a> <FONT color="green">079</FONT> cachedH = null;<a name="line.79"></a> <FONT color="green">080</FONT> <a name="line.80"></a> <FONT color="green">081</FONT> /*<a name="line.81"></a> <FONT color="green">082</FONT> * The QR decomposition of a matrix A is calculated using Householder<a name="line.82"></a> <FONT color="green">083</FONT> * reflectors by repeating the following operations to each minor<a name="line.83"></a> <FONT color="green">084</FONT> * A(minor,minor) of A:<a name="line.84"></a> <FONT color="green">085</FONT> */<a name="line.85"></a> <FONT color="green">086</FONT> for (int minor = 0; minor < Math.min(m, n); minor++) {<a name="line.86"></a> <FONT color="green">087</FONT> <a name="line.87"></a> <FONT color="green">088</FONT> final double[] qrtMinor = qrt[minor];<a name="line.88"></a> <FONT color="green">089</FONT> <a name="line.89"></a> <FONT color="green">090</FONT> /*<a name="line.90"></a> <FONT color="green">091</FONT> * Let x be the first column of the minor, and a^2 = |x|^2.<a name="line.91"></a> <FONT color="green">092</FONT> * x will be in the positions qr[minor][minor] through qr[m][minor].<a name="line.92"></a> <FONT color="green">093</FONT> * The first column of the transformed minor will be (a,0,0,..)'<a name="line.93"></a> <FONT color="green">094</FONT> * The sign of a is chosen to be opposite to the sign of the first<a name="line.94"></a> <FONT color="green">095</FONT> * component of x. Let's find a:<a name="line.95"></a> <FONT color="green">096</FONT> */<a name="line.96"></a> <FONT color="green">097</FONT> double xNormSqr = 0;<a name="line.97"></a> <FONT color="green">098</FONT> for (int row = minor; row < m; row++) {<a name="line.98"></a> <FONT color="green">099</FONT> final double c = qrtMinor[row];<a name="line.99"></a> <FONT color="green">100</FONT> xNormSqr += c * c;<a name="line.100"></a> <FONT color="green">101</FONT> }<a name="line.101"></a> <FONT color="green">102</FONT> final double a = (qrtMinor[minor] > 0) ? -Math.sqrt(xNormSqr) : Math.sqrt(xNormSqr);<a name="line.102"></a> <FONT color="green">103</FONT> rDiag[minor] = a;<a name="line.103"></a> <FONT color="green">104</FONT> <a name="line.104"></a> <FONT color="green">105</FONT> if (a != 0.0) {<a name="line.105"></a> <FONT color="green">106</FONT> <a name="line.106"></a> <FONT color="green">107</FONT> /*<a name="line.107"></a> <FONT color="green">108</FONT> * Calculate the normalized reflection vector v and transform<a name="line.108"></a> <FONT color="green">109</FONT> * the first column. We know the norm of v beforehand: v = x-ae<a name="line.109"></a> <FONT color="green">110</FONT> * so |v|^2 = <x-ae,x-ae> = <x,x>-2a<x,e>+a^2<e,e> =<a name="line.110"></a> <FONT color="green">111</FONT> * a^2+a^2-2a<x,e> = 2a*(a - <x,e>).<a name="line.111"></a> <FONT color="green">112</FONT> * Here <x, e> is now qr[minor][minor].<a name="line.112"></a> <FONT color="green">113</FONT> * v = x-ae is stored in the column at qr:<a name="line.113"></a> <FONT color="green">114</FONT> */<a name="line.114"></a> <FONT color="green">115</FONT> qrtMinor[minor] -= a; // now |v|^2 = -2a*(qr[minor][minor])<a name="line.115"></a> <FONT color="green">116</FONT> <a name="line.116"></a> <FONT color="green">117</FONT> /*<a name="line.117"></a> <FONT color="green">118</FONT> * Transform the rest of the columns of the minor:<a name="line.118"></a> <FONT color="green">119</FONT> * They will be transformed by the matrix H = I-2vv'/|v|^2.<a name="line.119"></a> <FONT color="green">120</FONT> * If x is a column vector of the minor, then<a name="line.120"></a> <FONT color="green">121</FONT> * Hx = (I-2vv'/|v|^2)x = x-2vv'x/|v|^2 = x - 2<x,v>/|v|^2 v.<a name="line.121"></a> <FONT color="green">122</FONT> * Therefore the transformation is easily calculated by<a name="line.122"></a> <FONT color="green">123</FONT> * subtracting the column vector (2<x,v>/|v|^2)v from x.<a name="line.123"></a> <FONT color="green">124</FONT> *<a name="line.124"></a> <FONT color="green">125</FONT> * Let 2<x,v>/|v|^2 = alpha. From above we have<a name="line.125"></a> <FONT color="green">126</FONT> * |v|^2 = -2a*(qr[minor][minor]), so<a name="line.126"></a> <FONT color="green">127</FONT> * alpha = -<x,v>/(a*qr[minor][minor])<a name="line.127"></a> <FONT color="green">128</FONT> */<a name="line.128"></a> <FONT color="green">129</FONT> for (int col = minor+1; col < n; col++) {<a name="line.129"></a> <FONT color="green">130</FONT> final double[] qrtCol = qrt[col];<a name="line.130"></a> <FONT color="green">131</FONT> double alpha = 0;<a name="line.131"></a> <FONT color="green">132</FONT> for (int row = minor; row < m; row++) {<a name="line.132"></a> <FONT color="green">133</FONT> alpha -= qrtCol[row] * qrtMinor[row];<a name="line.133"></a> <FONT color="green">134</FONT> }<a name="line.134"></a> <FONT color="green">135</FONT> alpha /= a * qrtMinor[minor];<a name="line.135"></a> <FONT color="green">136</FONT> <a name="line.136"></a> <FONT color="green">137</FONT> // Subtract the column vector alpha*v from x.<a name="line.137"></a> <FONT color="green">138</FONT> for (int row = minor; row < m; row++) {<a name="line.138"></a> <FONT color="green">139</FONT> qrtCol[row] -= alpha * qrtMinor[row];<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> }<a name="line.143"></a> <FONT color="green">144</FONT> }<a name="line.144"></a> <FONT color="green">145</FONT> <a name="line.145"></a> <FONT color="green">146</FONT> /** {@inheritDoc} */<a name="line.146"></a> <FONT color="green">147</FONT> public RealMatrix getR() {<a name="line.147"></a> <FONT color="green">148</FONT> <a name="line.148"></a> <FONT color="green">149</FONT> if (cachedR == null) {<a name="line.149"></a> <FONT color="green">150</FONT> <a name="line.150"></a> <FONT color="green">151</FONT> // R is supposed to be m x n<a name="line.151"></a> <FONT color="green">152</FONT> final int n = qrt.length;<a name="line.152"></a> <FONT color="green">153</FONT> final int m = qrt[0].length;<a name="line.153"></a> <FONT color="green">154</FONT> cachedR = MatrixUtils.createRealMatrix(m, n);<a name="line.154"></a> <FONT color="green">155</FONT> <a name="line.155"></a> <FONT color="green">156</FONT> // copy the diagonal from rDiag and the upper triangle of qr<a name="line.156"></a> <FONT color="green">157</FONT> for (int row = Math.min(m, n) - 1; row >= 0; row--) {<a name="line.157"></a> <FONT color="green">158</FONT> cachedR.setEntry(row, row, rDiag[row]);<a name="line.158"></a> <FONT color="green">159</FONT> for (int col = row + 1; col < n; col++) {<a name="line.159"></a> <FONT color="green">160</FONT> cachedR.setEntry(row, col, qrt[col][row]);<a name="line.160"></a> <FONT color="green">161</FONT> }<a name="line.161"></a> <FONT color="green">162</FONT> }<a name="line.162"></a> <FONT color="green">163</FONT> <a name="line.163"></a> <FONT color="green">164</FONT> }<a name="line.164"></a> <FONT color="green">165</FONT> <a name="line.165"></a> <FONT color="green">166</FONT> // return the cached matrix<a name="line.166"></a> <FONT color="green">167</FONT> return cachedR;<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> <a name="line.170"></a> <FONT color="green">171</FONT> /** {@inheritDoc} */<a name="line.171"></a> <FONT color="green">172</FONT> public RealMatrix getQ() {<a name="line.172"></a> <FONT color="green">173</FONT> if (cachedQ == null) {<a name="line.173"></a> <FONT color="green">174</FONT> cachedQ = getQT().transpose();<a name="line.174"></a> <FONT color="green">175</FONT> }<a name="line.175"></a> <FONT color="green">176</FONT> return cachedQ;<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> /** {@inheritDoc} */<a name="line.179"></a> <FONT color="green">180</FONT> public RealMatrix getQT() {<a name="line.180"></a> <FONT color="green">181</FONT> <a name="line.181"></a> <FONT color="green">182</FONT> if (cachedQT == null) {<a name="line.182"></a> <FONT color="green">183</FONT> <a name="line.183"></a> <FONT color="green">184</FONT> // QT is supposed to be m x m<a name="line.184"></a> <FONT color="green">185</FONT> final int n = qrt.length;<a name="line.185"></a> <FONT color="green">186</FONT> final int m = qrt[0].length;<a name="line.186"></a> <FONT color="green">187</FONT> cachedQT = MatrixUtils.createRealMatrix(m, m);<a name="line.187"></a> <FONT color="green">188</FONT> <a name="line.188"></a> <FONT color="green">189</FONT> /*<a name="line.189"></a> <FONT color="green">190</FONT> * Q = Q1 Q2 ... Q_m, so Q is formed by first constructing Q_m and then<a name="line.190"></a> <FONT color="green">191</FONT> * applying the Householder transformations Q_(m-1),Q_(m-2),...,Q1 in<a name="line.191"></a> <FONT color="green">192</FONT> * succession to the result<a name="line.192"></a> <FONT color="green">193</FONT> */<a name="line.193"></a> <FONT color="green">194</FONT> for (int minor = m - 1; minor >= Math.min(m, n); minor--) {<a name="line.194"></a> <FONT color="green">195</FONT> cachedQT.setEntry(minor, minor, 1.0);<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> for (int minor = Math.min(m, n)-1; minor >= 0; minor--){<a name="line.198"></a> <FONT color="green">199</FONT> final double[] qrtMinor = qrt[minor];<a name="line.199"></a> <FONT color="green">200</FONT> cachedQT.setEntry(minor, minor, 1.0);<a name="line.200"></a> <FONT color="green">201</FONT> if (qrtMinor[minor] != 0.0) {<a name="line.201"></a> <FONT color="green">202</FONT> for (int col = minor; col < m; col++) {<a name="line.202"></a> <FONT color="green">203</FONT> double alpha = 0;<a name="line.203"></a> <FONT color="green">204</FONT> for (int row = minor; row < m; row++) {<a name="line.204"></a> <FONT color="green">205</FONT> alpha -= cachedQT.getEntry(col, row) * qrtMinor[row];<a name="line.205"></a> <FONT color="green">206</FONT> }<a name="line.206"></a> <FONT color="green">207</FONT> alpha /= rDiag[minor] * qrtMinor[minor];<a name="line.207"></a> <FONT color="green">208</FONT> <a name="line.208"></a> <FONT color="green">209</FONT> for (int row = minor; row < m; row++) {<a name="line.209"></a> <FONT color="green">210</FONT> cachedQT.addToEntry(col, row, -alpha * qrtMinor[row]);<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> }<a name="line.214"></a> <FONT color="green">215</FONT> <a name="line.215"></a> <FONT color="green">216</FONT> }<a name="line.216"></a> <FONT color="green">217</FONT> <a name="line.217"></a> <FONT color="green">218</FONT> // return the cached matrix<a name="line.218"></a> <FONT color="green">219</FONT> return cachedQT;<a name="line.219"></a> <FONT color="green">220</FONT> <a name="line.220"></a> <FONT color="green">221</FONT> }<a name="line.221"></a> <FONT color="green">222</FONT> <a name="line.222"></a> <FONT color="green">223</FONT> /** {@inheritDoc} */<a name="line.223"></a> <FONT color="green">224</FONT> public RealMatrix getH() {<a name="line.224"></a> <FONT color="green">225</FONT> <a name="line.225"></a> <FONT color="green">226</FONT> if (cachedH == null) {<a name="line.226"></a> <FONT color="green">227</FONT> <a name="line.227"></a> <FONT color="green">228</FONT> final int n = qrt.length;<a name="line.228"></a> <FONT color="green">229</FONT> final int m = qrt[0].length;<a name="line.229"></a> <FONT color="green">230</FONT> cachedH = MatrixUtils.createRealMatrix(m, n);<a name="line.230"></a> <FONT color="green">231</FONT> for (int i = 0; i < m; ++i) {<a name="line.231"></a> <FONT color="green">232</FONT> for (int j = 0; j < Math.min(i + 1, n); ++j) {<a name="line.232"></a> <FONT color="green">233</FONT> cachedH.setEntry(i, j, qrt[j][i] / -rDiag[j]);<a name="line.233"></a> <FONT color="green">234</FONT> }<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> <a name="line.238"></a> <FONT color="green">239</FONT> // return the cached matrix<a name="line.239"></a> <FONT color="green">240</FONT> return cachedH;<a name="line.240"></a> <FONT color="green">241</FONT> <a name="line.241"></a> <FONT color="green">242</FONT> }<a name="line.242"></a> <FONT color="green">243</FONT> <a name="line.243"></a> <FONT color="green">244</FONT> /** {@inheritDoc} */<a name="line.244"></a> <FONT color="green">245</FONT> public DecompositionSolver getSolver() {<a name="line.245"></a> <FONT color="green">246</FONT> return new Solver(qrt, rDiag);<a name="line.246"></a> <FONT color="green">247</FONT> }<a name="line.247"></a> <FONT color="green">248</FONT> <a name="line.248"></a> <FONT color="green">249</FONT> /** Specialized solver. */<a name="line.249"></a> <FONT color="green">250</FONT> private static class Solver implements DecompositionSolver {<a name="line.250"></a> <FONT color="green">251</FONT> <a name="line.251"></a> <FONT color="green">252</FONT> /**<a name="line.252"></a> <FONT color="green">253</FONT> * A packed TRANSPOSED representation of the QR decomposition.<a name="line.253"></a> <FONT color="green">254</FONT> * <p>The elements BELOW the diagonal are the elements of the UPPER triangular<a name="line.254"></a> <FONT color="green">255</FONT> * matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors<a name="line.255"></a> <FONT color="green">256</FONT> * from which an explicit form of Q can be recomputed if desired.</p><a name="line.256"></a> <FONT color="green">257</FONT> */<a name="line.257"></a> <FONT color="green">258</FONT> private final double[][] qrt;<a name="line.258"></a> <FONT color="green">259</FONT> <a name="line.259"></a> <FONT color="green">260</FONT> /** The diagonal elements of R. */<a name="line.260"></a> <FONT color="green">261</FONT> private final double[] rDiag;<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> * Build a solver from decomposed matrix.<a name="line.264"></a> <FONT color="green">265</FONT> * @param qrt packed TRANSPOSED representation of the QR decomposition<a name="line.265"></a> <FONT color="green">266</FONT> * @param rDiag diagonal elements of R<a name="line.266"></a> <FONT color="green">267</FONT> */<a name="line.267"></a> <FONT color="green">268</FONT> private Solver(final double[][] qrt, final double[] rDiag) {<a name="line.268"></a> <FONT color="green">269</FONT> this.qrt = qrt;<a name="line.269"></a> <FONT color="green">270</FONT> this.rDiag = rDiag;<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> /** {@inheritDoc} */<a name="line.273"></a> <FONT color="green">274</FONT> public boolean isNonSingular() {<a name="line.274"></a> <FONT color="green">275</FONT> <a name="line.275"></a> <FONT color="green">276</FONT> for (double diag : rDiag) {<a name="line.276"></a> <FONT color="green">277</FONT> if (diag == 0) {<a name="line.277"></a> <FONT color="green">278</FONT> return false;<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> return true;<a name="line.281"></a> <FONT color="green">282</FONT> <a name="line.282"></a> <FONT color="green">283</FONT> }<a name="line.283"></a> <FONT color="green">284</FONT> <a name="line.284"></a> <FONT color="green">285</FONT> /** {@inheritDoc} */<a name="line.285"></a> <FONT color="green">286</FONT> public double[] solve(double[] b)<a name="line.286"></a> <FONT color="green">287</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.287"></a> <FONT color="green">288</FONT> <a name="line.288"></a> <FONT color="green">289</FONT> final int n = qrt.length;<a name="line.289"></a> <FONT color="green">290</FONT> final int m = qrt[0].length;<a name="line.290"></a> <FONT color="green">291</FONT> if (b.length != m) {<a name="line.291"></a> <FONT color="green">292</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.292"></a> <FONT color="green">293</FONT> "vector length mismatch: got {0} but expected {1}",<a name="line.293"></a> <FONT color="green">294</FONT> b.length, m);<a name="line.294"></a> <FONT color="green">295</FONT> }<a name="line.295"></a> <FONT color="green">296</FONT> if (!isNonSingular()) {<a name="line.296"></a> <FONT color="green">297</FONT> throw new SingularMatrixException();<a name="line.297"></a> <FONT color="green">298</FONT> }<a name="line.298"></a> <FONT color="green">299</FONT> <a name="line.299"></a> <FONT color="green">300</FONT> final double[] x = new double[n];<a name="line.300"></a> <FONT color="green">301</FONT> final double[] y = b.clone();<a name="line.301"></a> <FONT color="green">302</FONT> <a name="line.302"></a> <FONT color="green">303</FONT> // apply Householder transforms to solve Q.y = b<a name="line.303"></a> <FONT color="green">304</FONT> for (int minor = 0; minor < Math.min(m, n); minor++) {<a name="line.304"></a> <FONT color="green">305</FONT> <a name="line.305"></a> <FONT color="green">306</FONT> final double[] qrtMinor = qrt[minor];<a name="line.306"></a> <FONT color="green">307</FONT> double dotProduct = 0;<a name="line.307"></a> <FONT color="green">308</FONT> for (int row = minor; row < m; row++) {<a name="line.308"></a> <FONT color="green">309</FONT> dotProduct += y[row] * qrtMinor[row];<a name="line.309"></a> <FONT color="green">310</FONT> }<a name="line.310"></a> <FONT color="green">311</FONT> dotProduct /= rDiag[minor] * qrtMinor[minor];<a name="line.311"></a> <FONT color="green">312</FONT> <a name="line.312"></a> <FONT color="green">313</FONT> for (int row = minor; row < m; row++) {<a name="line.313"></a> <FONT color="green">314</FONT> y[row] += dotProduct * qrtMinor[row];<a name="line.314"></a> <FONT color="green">315</FONT> }<a name="line.315"></a> <FONT color="green">316</FONT> <a name="line.316"></a> <FONT color="green">317</FONT> }<a name="line.317"></a> <FONT color="green">318</FONT> <a name="line.318"></a> <FONT color="green">319</FONT> // solve triangular system R.x = y<a name="line.319"></a> <FONT color="green">320</FONT> for (int row = rDiag.length - 1; row >= 0; --row) {<a name="line.320"></a> <FONT color="green">321</FONT> y[row] /= rDiag[row];<a name="line.321"></a> <FONT color="green">322</FONT> final double yRow = y[row];<a name="line.322"></a> <FONT color="green">323</FONT> final double[] qrtRow = qrt[row];<a name="line.323"></a> <FONT color="green">324</FONT> x[row] = yRow;<a name="line.324"></a> <FONT color="green">325</FONT> for (int i = 0; i < row; i++) {<a name="line.325"></a> <FONT color="green">326</FONT> y[i] -= yRow * qrtRow[i];<a name="line.326"></a> <FONT color="green">327</FONT> }<a name="line.327"></a> <FONT color="green">328</FONT> }<a name="line.328"></a> <FONT color="green">329</FONT> <a name="line.329"></a> <FONT color="green">330</FONT> return x;<a name="line.330"></a> <FONT color="green">331</FONT> <a name="line.331"></a> <FONT color="green">332</FONT> }<a name="line.332"></a> <FONT color="green">333</FONT> <a name="line.333"></a> <FONT color="green">334</FONT> /** {@inheritDoc} */<a name="line.334"></a> <FONT color="green">335</FONT> public RealVector solve(RealVector b)<a name="line.335"></a> <FONT color="green">336</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.336"></a> <FONT color="green">337</FONT> try {<a name="line.337"></a> <FONT color="green">338</FONT> return solve((ArrayRealVector) b);<a name="line.338"></a> <FONT color="green">339</FONT> } catch (ClassCastException cce) {<a name="line.339"></a> <FONT color="green">340</FONT> return new ArrayRealVector(solve(b.getData()), false);<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.<a name="line.344"></a> <FONT color="green">345</FONT> * <p>The A matrix is implicit here. It is </p><a name="line.345"></a> <FONT color="green">346</FONT> * @param b right-hand side of the equation A &times; X = B<a name="line.346"></a> <FONT color="green">347</FONT> * @return a vector X that minimizes the two norm of A &times; X - B<a name="line.347"></a> <FONT color="green">348</FONT> * @throws IllegalArgumentException if matrices dimensions don't match<a name="line.348"></a> <FONT color="green">349</FONT> * @throws InvalidMatrixException if decomposed matrix is singular<a name="line.349"></a> <FONT color="green">350</FONT> */<a name="line.350"></a> <FONT color="green">351</FONT> public ArrayRealVector solve(ArrayRealVector b)<a name="line.351"></a> <FONT color="green">352</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.352"></a> <FONT color="green">353</FONT> return new ArrayRealVector(solve(b.getDataRef()), false);<a name="line.353"></a> <FONT color="green">354</FONT> }<a name="line.354"></a> <FONT color="green">355</FONT> <a name="line.355"></a> <FONT color="green">356</FONT> /** {@inheritDoc} */<a name="line.356"></a> <FONT color="green">357</FONT> public RealMatrix solve(RealMatrix b)<a name="line.357"></a> <FONT color="green">358</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.358"></a> <FONT color="green">359</FONT> <a name="line.359"></a> <FONT color="green">360</FONT> final int n = qrt.length;<a name="line.360"></a> <FONT color="green">361</FONT> final int m = qrt[0].length;<a name="line.361"></a> <FONT color="green">362</FONT> if (b.getRowDimension() != m) {<a name="line.362"></a> <FONT color="green">363</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.363"></a> <FONT color="green">364</FONT> "dimensions mismatch: got {0}x{1} but expected {2}x{3}",<a name="line.364"></a> <FONT color="green">365</FONT> b.getRowDimension(), b.getColumnDimension(), m, "n");<a name="line.365"></a> <FONT color="green">366</FONT> }<a name="line.366"></a> <FONT color="green">367</FONT> if (!isNonSingular()) {<a name="line.367"></a> <FONT color="green">368</FONT> throw new SingularMatrixException();<a name="line.368"></a> <FONT color="green">369</FONT> }<a name="line.369"></a> <FONT color="green">370</FONT> <a name="line.370"></a> <FONT color="green">371</FONT> final int columns = b.getColumnDimension();<a name="line.371"></a> <FONT color="green">372</FONT> final int blockSize = BlockRealMatrix.BLOCK_SIZE;<a name="line.372"></a> <FONT color="green">373</FONT> final int cBlocks = (columns + blockSize - 1) / blockSize;<a name="line.373"></a> <FONT color="green">374</FONT> final double[][] xBlocks = BlockRealMatrix.createBlocksLayout(n, columns);<a name="line.374"></a> <FONT color="green">375</FONT> final double[][] y = new double[b.getRowDimension()][blockSize];<a name="line.375"></a> <FONT color="green">376</FONT> final double[] alpha = new double[blockSize];<a name="line.376"></a> <FONT color="green">377</FONT> <a name="line.377"></a> <FONT color="green">378</FONT> for (int kBlock = 0; kBlock < cBlocks; ++kBlock) {<a name="line.378"></a> <FONT color="green">379</FONT> final int kStart = kBlock * blockSize;<a name="line.379"></a> <FONT color="green">380</FONT> final int kEnd = Math.min(kStart + blockSize, columns);<a name="line.380"></a> <FONT color="green">381</FONT> final int kWidth = kEnd - kStart;<a name="line.381"></a> <FONT color="green">382</FONT> <a name="line.382"></a> <FONT color="green">383</FONT> // get the right hand side vector<a name="line.383"></a> <FONT color="green">384</FONT> b.copySubMatrix(0, m - 1, kStart, kEnd - 1, y);<a name="line.384"></a> <FONT color="green">385</FONT> <a name="line.385"></a> <FONT color="green">386</FONT> // apply Householder transforms to solve Q.y = b<a name="line.386"></a> <FONT color="green">387</FONT> for (int minor = 0; minor < Math.min(m, n); minor++) {<a name="line.387"></a> <FONT color="green">388</FONT> final double[] qrtMinor = qrt[minor];<a name="line.388"></a> <FONT color="green">389</FONT> final double factor = 1.0 / (rDiag[minor] * qrtMinor[minor]);<a name="line.389"></a> <FONT color="green">390</FONT> <a name="line.390"></a> <FONT color="green">391</FONT> Arrays.fill(alpha, 0, kWidth, 0.0);<a name="line.391"></a> <FONT color="green">392</FONT> for (int row = minor; row < m; ++row) {<a name="line.392"></a> <FONT color="green">393</FONT> final double d = qrtMinor[row];<a name="line.393"></a> <FONT color="green">394</FONT> final double[] yRow = y[row];<a name="line.394"></a> <FONT color="green">395</FONT> for (int k = 0; k < kWidth; ++k) {<a name="line.395"></a> <FONT color="green">396</FONT> alpha[k] += d * yRow[k];<a name="line.396"></a> <FONT color="green">397</FONT> }<a name="line.397"></a> <FONT color="green">398</FONT> }<a name="line.398"></a> <FONT color="green">399</FONT> for (int k = 0; k < kWidth; ++k) {<a name="line.399"></a> <FONT color="green">400</FONT> alpha[k] *= factor;<a name="line.400"></a> <FONT color="green">401</FONT> }<a name="line.401"></a> <FONT color="green">402</FONT> <a name="line.402"></a> <FONT color="green">403</FONT> for (int row = minor; row < m; ++row) {<a name="line.403"></a> <FONT color="green">404</FONT> final double d = qrtMinor[row];<a name="line.404"></a> <FONT color="green">405</FONT> final double[] yRow = y[row];<a name="line.405"></a> <FONT color="green">406</FONT> for (int k = 0; k < kWidth; ++k) {<a name="line.406"></a> <FONT color="green">407</FONT> yRow[k] += alpha[k] * d;<a name="line.407"></a> <FONT color="green">408</FONT> }<a name="line.408"></a> <FONT color="green">409</FONT> }<a name="line.409"></a> <FONT color="green">410</FONT> <a name="line.410"></a> <FONT color="green">411</FONT> }<a name="line.411"></a> <FONT color="green">412</FONT> <a name="line.412"></a> <FONT color="green">413</FONT> // solve triangular system R.x = y<a name="line.413"></a> <FONT color="green">414</FONT> for (int j = rDiag.length - 1; j >= 0; --j) {<a name="line.414"></a> <FONT color="green">415</FONT> final int jBlock = j / blockSize;<a name="line.415"></a> <FONT color="green">416</FONT> final int jStart = jBlock * blockSize;<a name="line.416"></a> <FONT color="green">417</FONT> final double factor = 1.0 / rDiag[j];<a name="line.417"></a> <FONT color="green">418</FONT> final double[] yJ = y[j];<a name="line.418"></a> <FONT color="green">419</FONT> final double[] xBlock = xBlocks[jBlock * cBlocks + kBlock];<a name="line.419"></a> <FONT color="green">420</FONT> int index = (j - jStart) * kWidth;<a name="line.420"></a> <FONT color="green">421</FONT> for (int k = 0; k < kWidth; ++k) {<a name="line.421"></a> <FONT color="green">422</FONT> yJ[k] *= factor;<a name="line.422"></a> <FONT color="green">423</FONT> xBlock[index++] = yJ[k];<a name="line.423"></a> <FONT color="green">424</FONT> }<a name="line.424"></a> <FONT color="green">425</FONT> <a name="line.425"></a> <FONT color="green">426</FONT> final double[] qrtJ = qrt[j];<a name="line.426"></a> <FONT color="green">427</FONT> for (int i = 0; i < j; ++i) {<a name="line.427"></a> <FONT color="green">428</FONT> final double rIJ = qrtJ[i];<a name="line.428"></a> <FONT color="green">429</FONT> final double[] yI = y[i];<a name="line.429"></a> <FONT color="green">430</FONT> for (int k = 0; k < kWidth; ++k) {<a name="line.430"></a> <FONT color="green">431</FONT> yI[k] -= yJ[k] * rIJ;<a name="line.431"></a> <FONT color="green">432</FONT> }<a name="line.432"></a> <FONT color="green">433</FONT> }<a name="line.433"></a> <FONT color="green">434</FONT> <a name="line.434"></a> <FONT color="green">435</FONT> }<a name="line.435"></a> <FONT color="green">436</FONT> <a name="line.436"></a> <FONT color="green">437</FONT> }<a name="line.437"></a> <FONT color="green">438</FONT> <a name="line.438"></a> <FONT color="green">439</FONT> return new BlockRealMatrix(n, columns, xBlocks, false);<a name="line.439"></a> <FONT color="green">440</FONT> <a name="line.440"></a> <FONT color="green">441</FONT> }<a name="line.441"></a> <FONT color="green">442</FONT> <a name="line.442"></a> <FONT color="green">443</FONT> /** {@inheritDoc} */<a name="line.443"></a> <FONT color="green">444</FONT> public RealMatrix getInverse()<a name="line.444"></a> <FONT color="green">445</FONT> throws InvalidMatrixException {<a name="line.445"></a> <FONT color="green">446</FONT> return solve(MatrixUtils.createRealIdentityMatrix(rDiag.length));<a name="line.446"></a> <FONT color="green">447</FONT> }<a name="line.447"></a> <FONT color="green">448</FONT> <a name="line.448"></a> <FONT color="green">449</FONT> }<a name="line.449"></a> <FONT color="green">450</FONT> <a name="line.450"></a> <FONT color="green">451</FONT> }<a name="line.451"></a> </PRE> </BODY> </HTML>