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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.lang.reflect.Array;<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.Field;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.FieldElement;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.24"></a> <FONT color="green">025</FONT> <a name="line.25"></a> <FONT color="green">026</FONT> /**<a name="line.26"></a> <FONT color="green">027</FONT> * Calculates the LUP-decomposition of a square matrix.<a name="line.27"></a> <FONT color="green">028</FONT> * <p>The LUP-decomposition of a matrix A consists of three matrices<a name="line.28"></a> <FONT color="green">029</FONT> * L, U and P that satisfy: PA = LU, L is lower triangular, and U is<a name="line.29"></a> <FONT color="green">030</FONT> * upper triangular and P is a permutation matrix. All matrices are<a name="line.30"></a> <FONT color="green">031</FONT> * m&times;m.</p><a name="line.31"></a> <FONT color="green">032</FONT> * <p>Since {@link FieldElement field elements} do not provide an ordering<a name="line.32"></a> <FONT color="green">033</FONT> * operator, the permutation matrix is computed here only in order to avoid<a name="line.33"></a> <FONT color="green">034</FONT> * a zero pivot element, no attempt is done to get the largest pivot element.</p><a name="line.34"></a> <FONT color="green">035</FONT> *<a name="line.35"></a> <FONT color="green">036</FONT> * @param <T> the type of the field elements<a name="line.36"></a> <FONT color="green">037</FONT> * @version $Revision: 903046 $ $Date: 2010-01-25 21:07:26 -0500 (Mon, 25 Jan 2010) $<a name="line.37"></a> <FONT color="green">038</FONT> * @since 2.0<a name="line.38"></a> <FONT color="green">039</FONT> */<a name="line.39"></a> <FONT color="green">040</FONT> public class FieldLUDecompositionImpl<T extends FieldElement<T>> implements FieldLUDecomposition<T> {<a name="line.40"></a> <FONT color="green">041</FONT> <a name="line.41"></a> <FONT color="green">042</FONT> /** Field to which the elements belong. */<a name="line.42"></a> <FONT color="green">043</FONT> private final Field<T> field;<a name="line.43"></a> <FONT color="green">044</FONT> <a name="line.44"></a> <FONT color="green">045</FONT> /** Entries of LU decomposition. */<a name="line.45"></a> <FONT color="green">046</FONT> private T lu[][];<a name="line.46"></a> <FONT color="green">047</FONT> <a name="line.47"></a> <FONT color="green">048</FONT> /** Pivot permutation associated with LU decomposition */<a name="line.48"></a> <FONT color="green">049</FONT> private int[] pivot;<a name="line.49"></a> <FONT color="green">050</FONT> <a name="line.50"></a> <FONT color="green">051</FONT> /** Parity of the permutation associated with the LU decomposition */<a name="line.51"></a> <FONT color="green">052</FONT> private boolean even;<a name="line.52"></a> <FONT color="green">053</FONT> <a name="line.53"></a> <FONT color="green">054</FONT> /** Singularity indicator. */<a name="line.54"></a> <FONT color="green">055</FONT> private boolean singular;<a name="line.55"></a> <FONT color="green">056</FONT> <a name="line.56"></a> <FONT color="green">057</FONT> /** Cached value of L. */<a name="line.57"></a> <FONT color="green">058</FONT> private FieldMatrix<T> cachedL;<a name="line.58"></a> <FONT color="green">059</FONT> <a name="line.59"></a> <FONT color="green">060</FONT> /** Cached value of U. */<a name="line.60"></a> <FONT color="green">061</FONT> private FieldMatrix<T> cachedU;<a name="line.61"></a> <FONT color="green">062</FONT> <a name="line.62"></a> <FONT color="green">063</FONT> /** Cached value of P. */<a name="line.63"></a> <FONT color="green">064</FONT> private FieldMatrix<T> cachedP;<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 LU-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> * @exception NonSquareMatrixException if matrix is not square<a name="line.69"></a> <FONT color="green">070</FONT> */<a name="line.70"></a> <FONT color="green">071</FONT> public FieldLUDecompositionImpl(FieldMatrix<T> matrix)<a name="line.71"></a> <FONT color="green">072</FONT> throws NonSquareMatrixException {<a name="line.72"></a> <FONT color="green">073</FONT> <a name="line.73"></a> <FONT color="green">074</FONT> if (!matrix.isSquare()) {<a name="line.74"></a> <FONT color="green">075</FONT> throw new NonSquareMatrixException(matrix.getRowDimension(), matrix.getColumnDimension());<a name="line.75"></a> <FONT color="green">076</FONT> }<a name="line.76"></a> <FONT color="green">077</FONT> <a name="line.77"></a> <FONT color="green">078</FONT> final int m = matrix.getColumnDimension();<a name="line.78"></a> <FONT color="green">079</FONT> field = matrix.getField();<a name="line.79"></a> <FONT color="green">080</FONT> lu = matrix.getData();<a name="line.80"></a> <FONT color="green">081</FONT> pivot = new int[m];<a name="line.81"></a> <FONT color="green">082</FONT> cachedL = null;<a name="line.82"></a> <FONT color="green">083</FONT> cachedU = null;<a name="line.83"></a> <FONT color="green">084</FONT> cachedP = null;<a name="line.84"></a> <FONT color="green">085</FONT> <a name="line.85"></a> <FONT color="green">086</FONT> // Initialize permutation array and parity<a name="line.86"></a> <FONT color="green">087</FONT> for (int row = 0; row < m; row++) {<a name="line.87"></a> <FONT color="green">088</FONT> pivot[row] = row;<a name="line.88"></a> <FONT color="green">089</FONT> }<a name="line.89"></a> <FONT color="green">090</FONT> even = true;<a name="line.90"></a> <FONT color="green">091</FONT> singular = false;<a name="line.91"></a> <FONT color="green">092</FONT> <a name="line.92"></a> <FONT color="green">093</FONT> // Loop over columns<a name="line.93"></a> <FONT color="green">094</FONT> for (int col = 0; col < m; col++) {<a name="line.94"></a> <FONT color="green">095</FONT> <a name="line.95"></a> <FONT color="green">096</FONT> T sum = field.getZero();<a name="line.96"></a> <FONT color="green">097</FONT> <a name="line.97"></a> <FONT color="green">098</FONT> // upper<a name="line.98"></a> <FONT color="green">099</FONT> for (int row = 0; row < col; row++) {<a name="line.99"></a> <FONT color="green">100</FONT> final T[] luRow = lu[row];<a name="line.100"></a> <FONT color="green">101</FONT> sum = luRow[col];<a name="line.101"></a> <FONT color="green">102</FONT> for (int i = 0; i < row; i++) {<a name="line.102"></a> <FONT color="green">103</FONT> sum = sum.subtract(luRow[i].multiply(lu[i][col]));<a name="line.103"></a> <FONT color="green">104</FONT> }<a name="line.104"></a> <FONT color="green">105</FONT> luRow[col] = sum;<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> // lower<a name="line.108"></a> <FONT color="green">109</FONT> int nonZero = col; // permutation row<a name="line.109"></a> <FONT color="green">110</FONT> for (int row = col; row < m; row++) {<a name="line.110"></a> <FONT color="green">111</FONT> final T[] luRow = lu[row];<a name="line.111"></a> <FONT color="green">112</FONT> sum = luRow[col];<a name="line.112"></a> <FONT color="green">113</FONT> for (int i = 0; i < col; i++) {<a name="line.113"></a> <FONT color="green">114</FONT> sum = sum.subtract(luRow[i].multiply(lu[i][col]));<a name="line.114"></a> <FONT color="green">115</FONT> }<a name="line.115"></a> <FONT color="green">116</FONT> luRow[col] = sum;<a name="line.116"></a> <FONT color="green">117</FONT> <a name="line.117"></a> <FONT color="green">118</FONT> if (lu[nonZero][col].equals(field.getZero())) {<a name="line.118"></a> <FONT color="green">119</FONT> // try to select a better permutation choice<a name="line.119"></a> <FONT color="green">120</FONT> ++nonZero;<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> // Singularity check<a name="line.124"></a> <FONT color="green">125</FONT> if (nonZero >= m) {<a name="line.125"></a> <FONT color="green">126</FONT> singular = true;<a name="line.126"></a> <FONT color="green">127</FONT> return;<a name="line.127"></a> <FONT color="green">128</FONT> }<a name="line.128"></a> <FONT color="green">129</FONT> <a name="line.129"></a> <FONT color="green">130</FONT> // Pivot if necessary<a name="line.130"></a> <FONT color="green">131</FONT> if (nonZero != col) {<a name="line.131"></a> <FONT color="green">132</FONT> T tmp = field.getZero();<a name="line.132"></a> <FONT color="green">133</FONT> for (int i = 0; i < m; i++) {<a name="line.133"></a> <FONT color="green">134</FONT> tmp = lu[nonZero][i];<a name="line.134"></a> <FONT color="green">135</FONT> lu[nonZero][i] = lu[col][i];<a name="line.135"></a> <FONT color="green">136</FONT> lu[col][i] = tmp;<a name="line.136"></a> <FONT color="green">137</FONT> }<a name="line.137"></a> <FONT color="green">138</FONT> int temp = pivot[nonZero];<a name="line.138"></a> <FONT color="green">139</FONT> pivot[nonZero] = pivot[col];<a name="line.139"></a> <FONT color="green">140</FONT> pivot[col] = temp;<a name="line.140"></a> <FONT color="green">141</FONT> even = !even;<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> // Divide the lower elements by the "winning" diagonal elt.<a name="line.144"></a> <FONT color="green">145</FONT> final T luDiag = lu[col][col];<a name="line.145"></a> <FONT color="green">146</FONT> for (int row = col + 1; row < m; row++) {<a name="line.146"></a> <FONT color="green">147</FONT> final T[] luRow = lu[row];<a name="line.147"></a> <FONT color="green">148</FONT> luRow[col] = luRow[col].divide(luDiag);<a name="line.148"></a> <FONT color="green">149</FONT> }<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> <a name="line.153"></a> <FONT color="green">154</FONT> /** {@inheritDoc} */<a name="line.154"></a> <FONT color="green">155</FONT> public FieldMatrix<T> getL() {<a name="line.155"></a> <FONT color="green">156</FONT> if ((cachedL == null) && !singular) {<a name="line.156"></a> <FONT color="green">157</FONT> final int m = pivot.length;<a name="line.157"></a> <FONT color="green">158</FONT> cachedL = new Array2DRowFieldMatrix<T>(field, m, m);<a name="line.158"></a> <FONT color="green">159</FONT> for (int i = 0; i < m; ++i) {<a name="line.159"></a> <FONT color="green">160</FONT> final T[] luI = lu[i];<a name="line.160"></a> <FONT color="green">161</FONT> for (int j = 0; j < i; ++j) {<a name="line.161"></a> <FONT color="green">162</FONT> cachedL.setEntry(i, j, luI[j]);<a name="line.162"></a> <FONT color="green">163</FONT> }<a name="line.163"></a> <FONT color="green">164</FONT> cachedL.setEntry(i, i, field.getOne());<a name="line.164"></a> <FONT color="green">165</FONT> }<a name="line.165"></a> <FONT color="green">166</FONT> }<a name="line.166"></a> <FONT color="green">167</FONT> return cachedL;<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> /** {@inheritDoc} */<a name="line.170"></a> <FONT color="green">171</FONT> public FieldMatrix<T> getU() {<a name="line.171"></a> <FONT color="green">172</FONT> if ((cachedU == null) && !singular) {<a name="line.172"></a> <FONT color="green">173</FONT> final int m = pivot.length;<a name="line.173"></a> <FONT color="green">174</FONT> cachedU = new Array2DRowFieldMatrix<T>(field, m, m);<a name="line.174"></a> <FONT color="green">175</FONT> for (int i = 0; i < m; ++i) {<a name="line.175"></a> <FONT color="green">176</FONT> final T[] luI = lu[i];<a name="line.176"></a> <FONT color="green">177</FONT> for (int j = i; j < m; ++j) {<a name="line.177"></a> <FONT color="green">178</FONT> cachedU.setEntry(i, j, luI[j]);<a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> <FONT color="green">180</FONT> }<a name="line.180"></a> <FONT color="green">181</FONT> }<a name="line.181"></a> <FONT color="green">182</FONT> return cachedU;<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> /** {@inheritDoc} */<a name="line.185"></a> <FONT color="green">186</FONT> public FieldMatrix<T> getP() {<a name="line.186"></a> <FONT color="green">187</FONT> if ((cachedP == null) && !singular) {<a name="line.187"></a> <FONT color="green">188</FONT> final int m = pivot.length;<a name="line.188"></a> <FONT color="green">189</FONT> cachedP = new Array2DRowFieldMatrix<T>(field, m, m);<a name="line.189"></a> <FONT color="green">190</FONT> for (int i = 0; i < m; ++i) {<a name="line.190"></a> <FONT color="green">191</FONT> cachedP.setEntry(i, pivot[i], field.getOne());<a name="line.191"></a> <FONT color="green">192</FONT> }<a name="line.192"></a> <FONT color="green">193</FONT> }<a name="line.193"></a> <FONT color="green">194</FONT> return cachedP;<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> /** {@inheritDoc} */<a name="line.197"></a> <FONT color="green">198</FONT> public int[] getPivot() {<a name="line.198"></a> <FONT color="green">199</FONT> return pivot.clone();<a name="line.199"></a> <FONT color="green">200</FONT> }<a name="line.200"></a> <FONT color="green">201</FONT> <a name="line.201"></a> <FONT color="green">202</FONT> /** {@inheritDoc} */<a name="line.202"></a> <FONT color="green">203</FONT> public T getDeterminant() {<a name="line.203"></a> <FONT color="green">204</FONT> if (singular) {<a name="line.204"></a> <FONT color="green">205</FONT> return field.getZero();<a name="line.205"></a> <FONT color="green">206</FONT> } else {<a name="line.206"></a> <FONT color="green">207</FONT> final int m = pivot.length;<a name="line.207"></a> <FONT color="green">208</FONT> T determinant = even ? field.getOne() : field.getZero().subtract(field.getOne());<a name="line.208"></a> <FONT color="green">209</FONT> for (int i = 0; i < m; i++) {<a name="line.209"></a> <FONT color="green">210</FONT> determinant = determinant.multiply(lu[i][i]);<a name="line.210"></a> <FONT color="green">211</FONT> }<a name="line.211"></a> <FONT color="green">212</FONT> return determinant;<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> /** {@inheritDoc} */<a name="line.216"></a> <FONT color="green">217</FONT> public FieldDecompositionSolver<T> getSolver() {<a name="line.217"></a> <FONT color="green">218</FONT> return new Solver<T>(field, lu, pivot, singular);<a name="line.218"></a> <FONT color="green">219</FONT> }<a name="line.219"></a> <FONT color="green">220</FONT> <a name="line.220"></a> <FONT color="green">221</FONT> /** Specialized solver. */<a name="line.221"></a> <FONT color="green">222</FONT> private static class Solver<T extends FieldElement<T>> implements FieldDecompositionSolver<T> {<a name="line.222"></a> <FONT color="green">223</FONT> <a name="line.223"></a> <FONT color="green">224</FONT> /** Serializable version identifier. */<a name="line.224"></a> <FONT color="green">225</FONT> private static final long serialVersionUID = -6353105415121373022L;<a name="line.225"></a> <FONT color="green">226</FONT> <a name="line.226"></a> <FONT color="green">227</FONT> /** Field to which the elements belong. */<a name="line.227"></a> <FONT color="green">228</FONT> private final Field<T> field;<a name="line.228"></a> <FONT color="green">229</FONT> <a name="line.229"></a> <FONT color="green">230</FONT> /** Entries of LU decomposition. */<a name="line.230"></a> <FONT color="green">231</FONT> private final T lu[][];<a name="line.231"></a> <FONT color="green">232</FONT> <a name="line.232"></a> <FONT color="green">233</FONT> /** Pivot permutation associated with LU decomposition. */<a name="line.233"></a> <FONT color="green">234</FONT> private final int[] pivot;<a name="line.234"></a> <FONT color="green">235</FONT> <a name="line.235"></a> <FONT color="green">236</FONT> /** Singularity indicator. */<a name="line.236"></a> <FONT color="green">237</FONT> private final boolean singular;<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> * Build a solver from decomposed matrix.<a name="line.240"></a> <FONT color="green">241</FONT> * @param field field to which the matrix elements belong<a name="line.241"></a> <FONT color="green">242</FONT> * @param lu entries of LU decomposition<a name="line.242"></a> <FONT color="green">243</FONT> * @param pivot pivot permutation associated with LU decomposition<a name="line.243"></a> <FONT color="green">244</FONT> * @param singular singularity indicator<a name="line.244"></a> <FONT color="green">245</FONT> */<a name="line.245"></a> <FONT color="green">246</FONT> private Solver(final Field<T> field, final T[][] lu,<a name="line.246"></a> <FONT color="green">247</FONT> final int[] pivot, final boolean singular) {<a name="line.247"></a> <FONT color="green">248</FONT> this.field = field;<a name="line.248"></a> <FONT color="green">249</FONT> this.lu = lu;<a name="line.249"></a> <FONT color="green">250</FONT> this.pivot = pivot;<a name="line.250"></a> <FONT color="green">251</FONT> this.singular = singular;<a name="line.251"></a> <FONT color="green">252</FONT> }<a name="line.252"></a> <FONT color="green">253</FONT> <a name="line.253"></a> <FONT color="green">254</FONT> /** {@inheritDoc} */<a name="line.254"></a> <FONT color="green">255</FONT> public boolean isNonSingular() {<a name="line.255"></a> <FONT color="green">256</FONT> return !singular;<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> /** {@inheritDoc} */<a name="line.259"></a> <FONT color="green">260</FONT> public T[] solve(T[] b)<a name="line.260"></a> <FONT color="green">261</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.261"></a> <FONT color="green">262</FONT> <a name="line.262"></a> <FONT color="green">263</FONT> final int m = pivot.length;<a name="line.263"></a> <FONT color="green">264</FONT> if (b.length != m) {<a name="line.264"></a> <FONT color="green">265</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.265"></a> <FONT color="green">266</FONT> "vector length mismatch: got {0} but expected {1}",<a name="line.266"></a> <FONT color="green">267</FONT> b.length, m);<a name="line.267"></a> <FONT color="green">268</FONT> }<a name="line.268"></a> <FONT color="green">269</FONT> if (singular) {<a name="line.269"></a> <FONT color="green">270</FONT> throw new SingularMatrixException();<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> @SuppressWarnings("unchecked") // field is of type T<a name="line.273"></a> <FONT color="green">274</FONT> final T[] bp = (T[]) Array.newInstance(field.getZero().getClass(), m);<a name="line.274"></a> <FONT color="green">275</FONT> <a name="line.275"></a> <FONT color="green">276</FONT> // Apply permutations to b<a name="line.276"></a> <FONT color="green">277</FONT> for (int row = 0; row < m; row++) {<a name="line.277"></a> <FONT color="green">278</FONT> bp[row] = b[pivot[row]];<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> // Solve LY = b<a name="line.281"></a> <FONT color="green">282</FONT> for (int col = 0; col < m; col++) {<a name="line.282"></a> <FONT color="green">283</FONT> final T bpCol = bp[col];<a name="line.283"></a> <FONT color="green">284</FONT> for (int i = col + 1; i < m; i++) {<a name="line.284"></a> <FONT color="green">285</FONT> bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));<a name="line.285"></a> <FONT color="green">286</FONT> }<a name="line.286"></a> <FONT color="green">287</FONT> }<a name="line.287"></a> <FONT color="green">288</FONT> <a name="line.288"></a> <FONT color="green">289</FONT> // Solve UX = Y<a name="line.289"></a> <FONT color="green">290</FONT> for (int col = m - 1; col >= 0; col--) {<a name="line.290"></a> <FONT color="green">291</FONT> bp[col] = bp[col].divide(lu[col][col]);<a name="line.291"></a> <FONT color="green">292</FONT> final T bpCol = bp[col];<a name="line.292"></a> <FONT color="green">293</FONT> for (int i = 0; i < col; i++) {<a name="line.293"></a> <FONT color="green">294</FONT> bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));<a name="line.294"></a> <FONT color="green">295</FONT> }<a name="line.295"></a> <FONT color="green">296</FONT> }<a name="line.296"></a> <FONT color="green">297</FONT> <a name="line.297"></a> <FONT color="green">298</FONT> return bp;<a name="line.298"></a> <FONT color="green">299</FONT> <a name="line.299"></a> <FONT color="green">300</FONT> }<a name="line.300"></a> <FONT color="green">301</FONT> <a name="line.301"></a> <FONT color="green">302</FONT> /** {@inheritDoc} */<a name="line.302"></a> <FONT color="green">303</FONT> public FieldVector<T> solve(FieldVector<T> b)<a name="line.303"></a> <FONT color="green">304</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.304"></a> <FONT color="green">305</FONT> try {<a name="line.305"></a> <FONT color="green">306</FONT> return solve((ArrayFieldVector<T>) b);<a name="line.306"></a> <FONT color="green">307</FONT> } catch (ClassCastException cce) {<a name="line.307"></a> <FONT color="green">308</FONT> <a name="line.308"></a> <FONT color="green">309</FONT> final int m = pivot.length;<a name="line.309"></a> <FONT color="green">310</FONT> if (b.getDimension() != m) {<a name="line.310"></a> <FONT color="green">311</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.311"></a> <FONT color="green">312</FONT> "vector length mismatch: got {0} but expected {1}",<a name="line.312"></a> <FONT color="green">313</FONT> b.getDimension(), m);<a name="line.313"></a> <FONT color="green">314</FONT> }<a name="line.314"></a> <FONT color="green">315</FONT> if (singular) {<a name="line.315"></a> <FONT color="green">316</FONT> throw new SingularMatrixException();<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> @SuppressWarnings("unchecked") // field is of type T<a name="line.319"></a> <FONT color="green">320</FONT> final T[] bp = (T[]) Array.newInstance(field.getZero().getClass(), m);<a name="line.320"></a> <FONT color="green">321</FONT> <a name="line.321"></a> <FONT color="green">322</FONT> // Apply permutations to b<a name="line.322"></a> <FONT color="green">323</FONT> for (int row = 0; row < m; row++) {<a name="line.323"></a> <FONT color="green">324</FONT> bp[row] = b.getEntry(pivot[row]);<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 LY = b<a name="line.327"></a> <FONT color="green">328</FONT> for (int col = 0; col < m; col++) {<a name="line.328"></a> <FONT color="green">329</FONT> final T bpCol = bp[col];<a name="line.329"></a> <FONT color="green">330</FONT> for (int i = col + 1; i < m; i++) {<a name="line.330"></a> <FONT color="green">331</FONT> bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));<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> <a name="line.334"></a> <FONT color="green">335</FONT> // Solve UX = Y<a name="line.335"></a> <FONT color="green">336</FONT> for (int col = m - 1; col >= 0; col--) {<a name="line.336"></a> <FONT color="green">337</FONT> bp[col] = bp[col].divide(lu[col][col]);<a name="line.337"></a> <FONT color="green">338</FONT> final T bpCol = bp[col];<a name="line.338"></a> <FONT color="green">339</FONT> for (int i = 0; i < col; i++) {<a name="line.339"></a> <FONT color="green">340</FONT> bp[i] = bp[i].subtract(bpCol.multiply(lu[i][col]));<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> return new ArrayFieldVector<T>(bp, false);<a name="line.344"></a> <FONT color="green">345</FONT> <a name="line.345"></a> <FONT color="green">346</FONT> }<a name="line.346"></a> <FONT color="green">347</FONT> }<a name="line.347"></a> <FONT color="green">348</FONT> <a name="line.348"></a> <FONT color="green">349</FONT> /** Solve the linear equation A &times; X = B.<a name="line.349"></a> <FONT color="green">350</FONT> * <p>The A matrix is implicit here. It is </p><a name="line.350"></a> <FONT color="green">351</FONT> * @param b right-hand side of the equation A &times; X = B<a name="line.351"></a> <FONT color="green">352</FONT> * @return a vector X such that A &times; X = B<a name="line.352"></a> <FONT color="green">353</FONT> * @exception IllegalArgumentException if matrices dimensions don't match<a name="line.353"></a> <FONT color="green">354</FONT> * @exception InvalidMatrixException if decomposed matrix is singular<a name="line.354"></a> <FONT color="green">355</FONT> */<a name="line.355"></a> <FONT color="green">356</FONT> public ArrayFieldVector<T> solve(ArrayFieldVector<T> b)<a name="line.356"></a> <FONT color="green">357</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.357"></a> <FONT color="green">358</FONT> return new ArrayFieldVector<T>(solve(b.getDataRef()), false);<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> /** {@inheritDoc} */<a name="line.361"></a> <FONT color="green">362</FONT> public FieldMatrix<T> solve(FieldMatrix<T> b)<a name="line.362"></a> <FONT color="green">363</FONT> throws IllegalArgumentException, InvalidMatrixException {<a name="line.363"></a> <FONT color="green">364</FONT> <a name="line.364"></a> <FONT color="green">365</FONT> final int m = pivot.length;<a name="line.365"></a> <FONT color="green">366</FONT> if (b.getRowDimension() != m) {<a name="line.366"></a> <FONT color="green">367</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.367"></a> <FONT color="green">368</FONT> "dimensions mismatch: got {0}x{1} but expected {2}x{3}",<a name="line.368"></a> <FONT color="green">369</FONT> b.getRowDimension(), b.getColumnDimension(), m, "n");<a name="line.369"></a> <FONT color="green">370</FONT> }<a name="line.370"></a> <FONT color="green">371</FONT> if (singular) {<a name="line.371"></a> <FONT color="green">372</FONT> throw new SingularMatrixException();<a name="line.372"></a> <FONT color="green">373</FONT> }<a name="line.373"></a> <FONT color="green">374</FONT> <a name="line.374"></a> <FONT color="green">375</FONT> final int nColB = b.getColumnDimension();<a name="line.375"></a> <FONT color="green">376</FONT> <a name="line.376"></a> <FONT color="green">377</FONT> // Apply permutations to b<a name="line.377"></a> <FONT color="green">378</FONT> @SuppressWarnings("unchecked") // field is of type T<a name="line.378"></a> <FONT color="green">379</FONT> final T[][] bp = (T[][]) Array.newInstance(field.getZero().getClass(), new int[] { m, nColB });<a name="line.379"></a> <FONT color="green">380</FONT> for (int row = 0; row < m; row++) {<a name="line.380"></a> <FONT color="green">381</FONT> final T[] bpRow = bp[row];<a name="line.381"></a> <FONT color="green">382</FONT> final int pRow = pivot[row];<a name="line.382"></a> <FONT color="green">383</FONT> for (int col = 0; col < nColB; col++) {<a name="line.383"></a> <FONT color="green">384</FONT> bpRow[col] = b.getEntry(pRow, col);<a name="line.384"></a> <FONT color="green">385</FONT> }<a name="line.385"></a> <FONT color="green">386</FONT> }<a name="line.386"></a> <FONT color="green">387</FONT> <a name="line.387"></a> <FONT color="green">388</FONT> // Solve LY = b<a name="line.388"></a> <FONT color="green">389</FONT> for (int col = 0; col < m; col++) {<a name="line.389"></a> <FONT color="green">390</FONT> final T[] bpCol = bp[col];<a name="line.390"></a> <FONT color="green">391</FONT> for (int i = col + 1; i < m; i++) {<a name="line.391"></a> <FONT color="green">392</FONT> final T[] bpI = bp[i];<a name="line.392"></a> <FONT color="green">393</FONT> final T luICol = lu[i][col];<a name="line.393"></a> <FONT color="green">394</FONT> for (int j = 0; j < nColB; j++) {<a name="line.394"></a> <FONT color="green">395</FONT> bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol));<a name="line.395"></a> <FONT color="green">396</FONT> }<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> <a name="line.399"></a> <FONT color="green">400</FONT> // Solve UX = Y<a name="line.400"></a> <FONT color="green">401</FONT> for (int col = m - 1; col >= 0; col--) {<a name="line.401"></a> <FONT color="green">402</FONT> final T[] bpCol = bp[col];<a name="line.402"></a> <FONT color="green">403</FONT> final T luDiag = lu[col][col];<a name="line.403"></a> <FONT color="green">404</FONT> for (int j = 0; j < nColB; j++) {<a name="line.404"></a> <FONT color="green">405</FONT> bpCol[j] = bpCol[j].divide(luDiag);<a name="line.405"></a> <FONT color="green">406</FONT> }<a name="line.406"></a> <FONT color="green">407</FONT> for (int i = 0; i < col; i++) {<a name="line.407"></a> <FONT color="green">408</FONT> final T[] bpI = bp[i];<a name="line.408"></a> <FONT color="green">409</FONT> final T luICol = lu[i][col];<a name="line.409"></a> <FONT color="green">410</FONT> for (int j = 0; j < nColB; j++) {<a name="line.410"></a> <FONT color="green">411</FONT> bpI[j] = bpI[j].subtract(bpCol[j].multiply(luICol));<a name="line.411"></a> <FONT color="green">412</FONT> }<a name="line.412"></a> <FONT color="green">413</FONT> }<a name="line.413"></a> <FONT color="green">414</FONT> }<a name="line.414"></a> <FONT color="green">415</FONT> <a name="line.415"></a> <FONT color="green">416</FONT> return new Array2DRowFieldMatrix<T>(bp, false);<a name="line.416"></a> <FONT color="green">417</FONT> <a name="line.417"></a> <FONT color="green">418</FONT> }<a name="line.418"></a> <FONT color="green">419</FONT> <a name="line.419"></a> <FONT color="green">420</FONT> /** {@inheritDoc} */<a name="line.420"></a> <FONT color="green">421</FONT> public FieldMatrix<T> getInverse() throws InvalidMatrixException {<a name="line.421"></a> <FONT color="green">422</FONT> final int m = pivot.length;<a name="line.422"></a> <FONT color="green">423</FONT> final T one = field.getOne();<a name="line.423"></a> <FONT color="green">424</FONT> FieldMatrix<T> identity = new Array2DRowFieldMatrix<T>(field, m, m);<a name="line.424"></a> <FONT color="green">425</FONT> for (int i = 0; i < m; ++i) {<a name="line.425"></a> <FONT color="green">426</FONT> identity.setEntry(i, i, one);<a name="line.426"></a> <FONT color="green">427</FONT> }<a name="line.427"></a> <FONT color="green">428</FONT> return solve(identity);<a name="line.428"></a> <FONT color="green">429</FONT> }<a name="line.429"></a> <FONT color="green">430</FONT> <a name="line.430"></a> <FONT color="green">431</FONT> }<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> </PRE> </BODY> </HTML>