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| <pre><span class="sourceLineNo">001</span>/*-<a name="line.1"></a> |
| <span class="sourceLineNo">002</span> *******************************************************************************<a name="line.2"></a> |
| <span class="sourceLineNo">003</span> * Copyright (c) 2011, 2016 Diamond Light Source Ltd.<a name="line.3"></a> |
| <span class="sourceLineNo">004</span> * All rights reserved. This program and the accompanying materials<a name="line.4"></a> |
| <span class="sourceLineNo">005</span> * are made available under the terms of the Eclipse Public License v1.0<a name="line.5"></a> |
| <span class="sourceLineNo">006</span> * which accompanies this distribution, and is available at<a name="line.6"></a> |
| <span class="sourceLineNo">007</span> * http://www.eclipse.org/legal/epl-v10.html<a name="line.7"></a> |
| <span class="sourceLineNo">008</span> *<a name="line.8"></a> |
| <span class="sourceLineNo">009</span> * Contributors:<a name="line.9"></a> |
| <span class="sourceLineNo">010</span> * Peter Chang - initial API and implementation and/or initial documentation<a name="line.10"></a> |
| <span class="sourceLineNo">011</span> *******************************************************************************/<a name="line.11"></a> |
| <span class="sourceLineNo">012</span><a name="line.12"></a> |
| <span class="sourceLineNo">013</span>package org.eclipse.january.dataset;<a name="line.13"></a> |
| <span class="sourceLineNo">014</span><a name="line.14"></a> |
| <span class="sourceLineNo">015</span>import java.util.Arrays;<a name="line.15"></a> |
| <span class="sourceLineNo">016</span>import java.util.List;<a name="line.16"></a> |
| <span class="sourceLineNo">017</span><a name="line.17"></a> |
| <span class="sourceLineNo">018</span>import org.apache.commons.math3.complex.Complex;<a name="line.18"></a> |
| <span class="sourceLineNo">019</span>import org.apache.commons.math3.linear.Array2DRowRealMatrix;<a name="line.19"></a> |
| <span class="sourceLineNo">020</span>import org.apache.commons.math3.linear.ArrayRealVector;<a name="line.20"></a> |
| <span class="sourceLineNo">021</span>import org.apache.commons.math3.linear.CholeskyDecomposition;<a name="line.21"></a> |
| <span class="sourceLineNo">022</span>import org.apache.commons.math3.linear.ConjugateGradient;<a name="line.22"></a> |
| <span class="sourceLineNo">023</span>import org.apache.commons.math3.linear.EigenDecomposition;<a name="line.23"></a> |
| <span class="sourceLineNo">024</span>import org.apache.commons.math3.linear.LUDecomposition;<a name="line.24"></a> |
| <span class="sourceLineNo">025</span>import org.apache.commons.math3.linear.MatrixUtils;<a name="line.25"></a> |
| <span class="sourceLineNo">026</span>import org.apache.commons.math3.linear.QRDecomposition;<a name="line.26"></a> |
| <span class="sourceLineNo">027</span>import org.apache.commons.math3.linear.RealLinearOperator;<a name="line.27"></a> |
| <span class="sourceLineNo">028</span>import org.apache.commons.math3.linear.RealMatrix;<a name="line.28"></a> |
| <span class="sourceLineNo">029</span>import org.apache.commons.math3.linear.RealVector;<a name="line.29"></a> |
| <span class="sourceLineNo">030</span>import org.apache.commons.math3.linear.SingularValueDecomposition;<a name="line.30"></a> |
| <span class="sourceLineNo">031</span><a name="line.31"></a> |
| <span class="sourceLineNo">032</span><a name="line.32"></a> |
| <span class="sourceLineNo">033</span>public class LinearAlgebra {<a name="line.33"></a> |
| <span class="sourceLineNo">034</span><a name="line.34"></a> |
| <span class="sourceLineNo">035</span> private static final int CROSSOVERPOINT = 16; // point at which using slice iterators for inner loop is faster <a name="line.35"></a> |
| <span class="sourceLineNo">036</span><a name="line.36"></a> |
| <span class="sourceLineNo">037</span> /**<a name="line.37"></a> |
| <span class="sourceLineNo">038</span> * Calculate the tensor dot product over given axes. This is the sum of products of elements selected<a name="line.38"></a> |
| <span class="sourceLineNo">039</span> * from the given axes in each dataset<a name="line.39"></a> |
| <span class="sourceLineNo">040</span> * @param a<a name="line.40"></a> |
| <span class="sourceLineNo">041</span> * @param b<a name="line.41"></a> |
| <span class="sourceLineNo">042</span> * @param axisa axis dimension in a to sum over (can be -ve)<a name="line.42"></a> |
| <span class="sourceLineNo">043</span> * @param axisb axis dimension in b to sum over (can be -ve)<a name="line.43"></a> |
| <span class="sourceLineNo">044</span> * @return tensor dot product<a name="line.44"></a> |
| <span class="sourceLineNo">045</span> */<a name="line.45"></a> |
| <span class="sourceLineNo">046</span> public static Dataset tensorDotProduct(final Dataset a, final Dataset b, final int axisa, final int axisb) {<a name="line.46"></a> |
| <span class="sourceLineNo">047</span> // this is slower for summing lengths < ~15<a name="line.47"></a> |
| <span class="sourceLineNo">048</span> final int[] ashape = a.getShapeRef();<a name="line.48"></a> |
| <span class="sourceLineNo">049</span> final int[] bshape = b.getShapeRef();<a name="line.49"></a> |
| <span class="sourceLineNo">050</span> final int arank = ashape.length;<a name="line.50"></a> |
| <span class="sourceLineNo">051</span> final int brank = bshape.length;<a name="line.51"></a> |
| <span class="sourceLineNo">052</span> int aaxis = ShapeUtils.checkAxis(arank, axisa);<a name="line.52"></a> |
| <span class="sourceLineNo">053</span><a name="line.53"></a> |
| <span class="sourceLineNo">054</span> if (ashape[aaxis] < CROSSOVERPOINT) { // faster to use position iteration<a name="line.54"></a> |
| <span class="sourceLineNo">055</span> return tensorDotProduct(a, b, new int[] {axisa}, new int[] {axisb});<a name="line.55"></a> |
| <span class="sourceLineNo">056</span> }<a name="line.56"></a> |
| <span class="sourceLineNo">057</span> int baxis = ShapeUtils.checkAxis(brank, axisb);<a name="line.57"></a> |
| <span class="sourceLineNo">058</span><a name="line.58"></a> |
| <span class="sourceLineNo">059</span> final boolean[] achoice = new boolean[arank];<a name="line.59"></a> |
| <span class="sourceLineNo">060</span> final boolean[] bchoice = new boolean[brank];<a name="line.60"></a> |
| <span class="sourceLineNo">061</span> Arrays.fill(achoice, true);<a name="line.61"></a> |
| <span class="sourceLineNo">062</span> Arrays.fill(bchoice, true);<a name="line.62"></a> |
| <span class="sourceLineNo">063</span> achoice[aaxis] = false; // flag which axes not to iterate over<a name="line.63"></a> |
| <span class="sourceLineNo">064</span> bchoice[baxis] = false;<a name="line.64"></a> |
| <span class="sourceLineNo">065</span><a name="line.65"></a> |
| <span class="sourceLineNo">066</span> final boolean[] notachoice = new boolean[arank];<a name="line.66"></a> |
| <span class="sourceLineNo">067</span> final boolean[] notbchoice = new boolean[brank];<a name="line.67"></a> |
| <span class="sourceLineNo">068</span> notachoice[aaxis] = true; // flag which axes to iterate over<a name="line.68"></a> |
| <span class="sourceLineNo">069</span> notbchoice[baxis] = true;<a name="line.69"></a> |
| <span class="sourceLineNo">070</span><a name="line.70"></a> |
| <span class="sourceLineNo">071</span> int drank = arank + brank - 2;<a name="line.71"></a> |
| <span class="sourceLineNo">072</span> int[] dshape = new int[drank];<a name="line.72"></a> |
| <span class="sourceLineNo">073</span> int d = 0;<a name="line.73"></a> |
| <span class="sourceLineNo">074</span> for (int i = 0; i < arank; i++) {<a name="line.74"></a> |
| <span class="sourceLineNo">075</span> if (achoice[i])<a name="line.75"></a> |
| <span class="sourceLineNo">076</span> dshape[d++] = ashape[i];<a name="line.76"></a> |
| <span class="sourceLineNo">077</span> }<a name="line.77"></a> |
| <span class="sourceLineNo">078</span> for (int i = 0; i < brank; i++) {<a name="line.78"></a> |
| <span class="sourceLineNo">079</span> if (bchoice[i])<a name="line.79"></a> |
| <span class="sourceLineNo">080</span> dshape[d++] = bshape[i];<a name="line.80"></a> |
| <span class="sourceLineNo">081</span> }<a name="line.81"></a> |
| <span class="sourceLineNo">082</span> Dataset data = DatasetFactory.zeros(InterfaceUtils.getBestInterface(a.getClass(), b.getClass()), dshape);<a name="line.82"></a> |
| <span class="sourceLineNo">083</span><a name="line.83"></a> |
| <span class="sourceLineNo">084</span> SliceIterator ita = a.getSliceIteratorFromAxes(null, achoice);<a name="line.84"></a> |
| <span class="sourceLineNo">085</span> int l = 0;<a name="line.85"></a> |
| <span class="sourceLineNo">086</span> final int[] apos = ita.getPos();<a name="line.86"></a> |
| <span class="sourceLineNo">087</span> while (ita.hasNext()) {<a name="line.87"></a> |
| <span class="sourceLineNo">088</span> SliceIterator itb = b.getSliceIteratorFromAxes(null, bchoice);<a name="line.88"></a> |
| <span class="sourceLineNo">089</span> final int[] bpos = itb.getPos();<a name="line.89"></a> |
| <span class="sourceLineNo">090</span> while (itb.hasNext()) {<a name="line.90"></a> |
| <span class="sourceLineNo">091</span> SliceIterator itaa = a.getSliceIteratorFromAxes(apos, notachoice);<a name="line.91"></a> |
| <span class="sourceLineNo">092</span> SliceIterator itba = b.getSliceIteratorFromAxes(bpos, notbchoice);<a name="line.92"></a> |
| <span class="sourceLineNo">093</span> double sum = 0.0;<a name="line.93"></a> |
| <span class="sourceLineNo">094</span> double com = 0.0;<a name="line.94"></a> |
| <span class="sourceLineNo">095</span> while (itaa.hasNext() && itba.hasNext()) {<a name="line.95"></a> |
| <span class="sourceLineNo">096</span> final double y = a.getElementDoubleAbs(itaa.index) * b.getElementDoubleAbs(itba.index) - com;<a name="line.96"></a> |
| <span class="sourceLineNo">097</span> final double t = sum + y;<a name="line.97"></a> |
| <span class="sourceLineNo">098</span> com = (t - sum) - y;<a name="line.98"></a> |
| <span class="sourceLineNo">099</span> sum = t;<a name="line.99"></a> |
| <span class="sourceLineNo">100</span> }<a name="line.100"></a> |
| <span class="sourceLineNo">101</span> data.setObjectAbs(l++, sum);<a name="line.101"></a> |
| <span class="sourceLineNo">102</span> }<a name="line.102"></a> |
| <span class="sourceLineNo">103</span> }<a name="line.103"></a> |
| <span class="sourceLineNo">104</span><a name="line.104"></a> |
| <span class="sourceLineNo">105</span> return data;<a name="line.105"></a> |
| <span class="sourceLineNo">106</span> }<a name="line.106"></a> |
| <span class="sourceLineNo">107</span><a name="line.107"></a> |
| <span class="sourceLineNo">108</span> /**<a name="line.108"></a> |
| <span class="sourceLineNo">109</span> * Calculate the tensor dot product over given axes. This is the sum of products of elements selected<a name="line.109"></a> |
| <span class="sourceLineNo">110</span> * from the given axes in each dataset<a name="line.110"></a> |
| <span class="sourceLineNo">111</span> * @param a<a name="line.111"></a> |
| <span class="sourceLineNo">112</span> * @param b<a name="line.112"></a> |
| <span class="sourceLineNo">113</span> * @param axisa axis dimensions in a to sum over (can be -ve)<a name="line.113"></a> |
| <span class="sourceLineNo">114</span> * @param axisb axis dimensions in b to sum over (can be -ve)<a name="line.114"></a> |
| <span class="sourceLineNo">115</span> * @return tensor dot product<a name="line.115"></a> |
| <span class="sourceLineNo">116</span> */<a name="line.116"></a> |
| <span class="sourceLineNo">117</span> public static Dataset tensorDotProduct(final Dataset a, final Dataset b, final int[] axisa, final int[] axisb) {<a name="line.117"></a> |
| <span class="sourceLineNo">118</span> if (axisa.length != axisb.length) {<a name="line.118"></a> |
| <span class="sourceLineNo">119</span> throw new IllegalArgumentException("Numbers of summing axes must be same");<a name="line.119"></a> |
| <span class="sourceLineNo">120</span> }<a name="line.120"></a> |
| <span class="sourceLineNo">121</span> final int[] ashape = a.getShapeRef();<a name="line.121"></a> |
| <span class="sourceLineNo">122</span> final int[] bshape = b.getShapeRef();<a name="line.122"></a> |
| <span class="sourceLineNo">123</span> final int arank = ashape.length;<a name="line.123"></a> |
| <span class="sourceLineNo">124</span> final int brank = bshape.length;<a name="line.124"></a> |
| <span class="sourceLineNo">125</span> final int[] aaxes = new int[axisa.length];<a name="line.125"></a> |
| <span class="sourceLineNo">126</span> final int[] baxes = new int[axisa.length];<a name="line.126"></a> |
| <span class="sourceLineNo">127</span> for (int i = 0; i < axisa.length; i++) {<a name="line.127"></a> |
| <span class="sourceLineNo">128</span> aaxes[i] = ShapeUtils.checkAxis(arank, axisa[i]);<a name="line.128"></a> |
| <span class="sourceLineNo">129</span> int n = ShapeUtils.checkAxis(brank, axisb[i]);<a name="line.129"></a> |
| <span class="sourceLineNo">130</span> baxes[i] = n;<a name="line.130"></a> |
| <span class="sourceLineNo">131</span><a name="line.131"></a> |
| <span class="sourceLineNo">132</span> if (ashape[aaxes[i]] != bshape[n]) {<a name="line.132"></a> |
| <span class="sourceLineNo">133</span> throw new IllegalArgumentException("Summing axes do not have matching lengths");<a name="line.133"></a> |
| <span class="sourceLineNo">134</span> }<a name="line.134"></a> |
| <span class="sourceLineNo">135</span> }<a name="line.135"></a> |
| <span class="sourceLineNo">136</span><a name="line.136"></a> |
| <span class="sourceLineNo">137</span> final boolean[] achoice = new boolean[arank];<a name="line.137"></a> |
| <span class="sourceLineNo">138</span> final boolean[] bchoice = new boolean[brank];<a name="line.138"></a> |
| <span class="sourceLineNo">139</span> Arrays.fill(achoice, true);<a name="line.139"></a> |
| <span class="sourceLineNo">140</span> Arrays.fill(bchoice, true);<a name="line.140"></a> |
| <span class="sourceLineNo">141</span> for (int i = 0; i < aaxes.length; i++) { // flag which axes to iterate over<a name="line.141"></a> |
| <span class="sourceLineNo">142</span> achoice[aaxes[i]] = false;<a name="line.142"></a> |
| <span class="sourceLineNo">143</span> bchoice[baxes[i]] = false;<a name="line.143"></a> |
| <span class="sourceLineNo">144</span> }<a name="line.144"></a> |
| <span class="sourceLineNo">145</span><a name="line.145"></a> |
| <span class="sourceLineNo">146</span> int drank = arank + brank - 2*aaxes.length;<a name="line.146"></a> |
| <span class="sourceLineNo">147</span> int[] dshape = new int[drank];<a name="line.147"></a> |
| <span class="sourceLineNo">148</span> int d = 0;<a name="line.148"></a> |
| <span class="sourceLineNo">149</span> for (int i = 0; i < arank; i++) {<a name="line.149"></a> |
| <span class="sourceLineNo">150</span> if (achoice[i])<a name="line.150"></a> |
| <span class="sourceLineNo">151</span> dshape[d++] = ashape[i];<a name="line.151"></a> |
| <span class="sourceLineNo">152</span> }<a name="line.152"></a> |
| <span class="sourceLineNo">153</span> for (int i = 0; i < brank; i++) {<a name="line.153"></a> |
| <span class="sourceLineNo">154</span> if (bchoice[i])<a name="line.154"></a> |
| <span class="sourceLineNo">155</span> dshape[d++] = bshape[i];<a name="line.155"></a> |
| <span class="sourceLineNo">156</span> }<a name="line.156"></a> |
| <span class="sourceLineNo">157</span> Dataset data = DatasetFactory.zeros(InterfaceUtils.getBestInterface(a.getClass(), b.getClass()), dshape);<a name="line.157"></a> |
| <span class="sourceLineNo">158</span><a name="line.158"></a> |
| <span class="sourceLineNo">159</span> SliceIterator ita = a.getSliceIteratorFromAxes(null, achoice);<a name="line.159"></a> |
| <span class="sourceLineNo">160</span> int l = 0;<a name="line.160"></a> |
| <span class="sourceLineNo">161</span> final int[] apos = ita.getPos();<a name="line.161"></a> |
| <span class="sourceLineNo">162</span> while (ita.hasNext()) {<a name="line.162"></a> |
| <span class="sourceLineNo">163</span> SliceIterator itb = b.getSliceIteratorFromAxes(null, bchoice);<a name="line.163"></a> |
| <span class="sourceLineNo">164</span> final int[] bpos = itb.getPos();<a name="line.164"></a> |
| <span class="sourceLineNo">165</span> while (itb.hasNext()) {<a name="line.165"></a> |
| <span class="sourceLineNo">166</span> double sum = 0.0;<a name="line.166"></a> |
| <span class="sourceLineNo">167</span> double com = 0.0;<a name="line.167"></a> |
| <span class="sourceLineNo">168</span> apos[aaxes[aaxes.length - 1]] = -1;<a name="line.168"></a> |
| <span class="sourceLineNo">169</span> bpos[baxes[aaxes.length - 1]] = -1;<a name="line.169"></a> |
| <span class="sourceLineNo">170</span> while (true) { // step through summing axes<a name="line.170"></a> |
| <span class="sourceLineNo">171</span> int e = aaxes.length - 1;<a name="line.171"></a> |
| <span class="sourceLineNo">172</span> for (; e >= 0; e--) {<a name="line.172"></a> |
| <span class="sourceLineNo">173</span> int ai = aaxes[e];<a name="line.173"></a> |
| <span class="sourceLineNo">174</span> int bi = baxes[e];<a name="line.174"></a> |
| <span class="sourceLineNo">175</span><a name="line.175"></a> |
| <span class="sourceLineNo">176</span> apos[ai]++;<a name="line.176"></a> |
| <span class="sourceLineNo">177</span> bpos[bi]++;<a name="line.177"></a> |
| <span class="sourceLineNo">178</span> if (apos[ai] == ashape[ai]) {<a name="line.178"></a> |
| <span class="sourceLineNo">179</span> apos[ai] = 0;<a name="line.179"></a> |
| <span class="sourceLineNo">180</span> bpos[bi] = 0;<a name="line.180"></a> |
| <span class="sourceLineNo">181</span> } else<a name="line.181"></a> |
| <span class="sourceLineNo">182</span> break;<a name="line.182"></a> |
| <span class="sourceLineNo">183</span> }<a name="line.183"></a> |
| <span class="sourceLineNo">184</span> if (e == -1) break;<a name="line.184"></a> |
| <span class="sourceLineNo">185</span> final double y = a.getDouble(apos) * b.getDouble(bpos) - com;<a name="line.185"></a> |
| <span class="sourceLineNo">186</span> final double t = sum + y;<a name="line.186"></a> |
| <span class="sourceLineNo">187</span> com = (t - sum) - y;<a name="line.187"></a> |
| <span class="sourceLineNo">188</span> sum = t;<a name="line.188"></a> |
| <span class="sourceLineNo">189</span> }<a name="line.189"></a> |
| <span class="sourceLineNo">190</span> data.setObjectAbs(l++, sum);<a name="line.190"></a> |
| <span class="sourceLineNo">191</span> }<a name="line.191"></a> |
| <span class="sourceLineNo">192</span> }<a name="line.192"></a> |
| <span class="sourceLineNo">193</span><a name="line.193"></a> |
| <span class="sourceLineNo">194</span> return data;<a name="line.194"></a> |
| <span class="sourceLineNo">195</span> }<a name="line.195"></a> |
| <span class="sourceLineNo">196</span><a name="line.196"></a> |
| <span class="sourceLineNo">197</span> /**<a name="line.197"></a> |
| <span class="sourceLineNo">198</span> * Calculate the dot product of two datasets. When <b>b</b> is a 1D dataset, the sum product over<a name="line.198"></a> |
| <span class="sourceLineNo">199</span> * the last axis of <b>a</b> and <b>b</b> is returned. Where <b>a</b> is also a 1D dataset, a zero-rank dataset<a name="line.199"></a> |
| <span class="sourceLineNo">200</span> * is returned. If <b>b</b> is 2D or higher, its second-to-last axis is used<a name="line.200"></a> |
| <span class="sourceLineNo">201</span> * @param a<a name="line.201"></a> |
| <span class="sourceLineNo">202</span> * @param b<a name="line.202"></a> |
| <span class="sourceLineNo">203</span> * @return dot product<a name="line.203"></a> |
| <span class="sourceLineNo">204</span> */<a name="line.204"></a> |
| <span class="sourceLineNo">205</span> public static Dataset dotProduct(Dataset a, Dataset b) {<a name="line.205"></a> |
| <span class="sourceLineNo">206</span> if (b.getRank() < 2)<a name="line.206"></a> |
| <span class="sourceLineNo">207</span> return tensorDotProduct(a, b, -1, 0);<a name="line.207"></a> |
| <span class="sourceLineNo">208</span> return tensorDotProduct(a, b, -1, -2);<a name="line.208"></a> |
| <span class="sourceLineNo">209</span> }<a name="line.209"></a> |
| <span class="sourceLineNo">210</span><a name="line.210"></a> |
| <span class="sourceLineNo">211</span> /**<a name="line.211"></a> |
| <span class="sourceLineNo">212</span> * Calculate the outer product of two datasets<a name="line.212"></a> |
| <span class="sourceLineNo">213</span> * @param a<a name="line.213"></a> |
| <span class="sourceLineNo">214</span> * @param b<a name="line.214"></a> |
| <span class="sourceLineNo">215</span> * @return outer product<a name="line.215"></a> |
| <span class="sourceLineNo">216</span> */<a name="line.216"></a> |
| <span class="sourceLineNo">217</span> public static Dataset outerProduct(Dataset a, Dataset b) {<a name="line.217"></a> |
| <span class="sourceLineNo">218</span> int[] as = a.getShapeRef();<a name="line.218"></a> |
| <span class="sourceLineNo">219</span> int[] bs = b.getShapeRef();<a name="line.219"></a> |
| <span class="sourceLineNo">220</span> int rank = as.length + bs.length;<a name="line.220"></a> |
| <span class="sourceLineNo">221</span> int[] shape = new int[rank];<a name="line.221"></a> |
| <span class="sourceLineNo">222</span> for (int i = 0; i < as.length; i++) {<a name="line.222"></a> |
| <span class="sourceLineNo">223</span> shape[i] = as[i];<a name="line.223"></a> |
| <span class="sourceLineNo">224</span> }<a name="line.224"></a> |
| <span class="sourceLineNo">225</span> for (int i = 0; i < bs.length; i++) {<a name="line.225"></a> |
| <span class="sourceLineNo">226</span> shape[as.length + i] = bs[i];<a name="line.226"></a> |
| <span class="sourceLineNo">227</span> }<a name="line.227"></a> |
| <span class="sourceLineNo">228</span> int isa = a.getElementsPerItem();<a name="line.228"></a> |
| <span class="sourceLineNo">229</span> int isb = b.getElementsPerItem();<a name="line.229"></a> |
| <span class="sourceLineNo">230</span> if (isa != 1 || isb != 1) {<a name="line.230"></a> |
| <span class="sourceLineNo">231</span> throw new UnsupportedOperationException("Compound datasets not supported");<a name="line.231"></a> |
| <span class="sourceLineNo">232</span> }<a name="line.232"></a> |
| <span class="sourceLineNo">233</span> Dataset o = DatasetFactory.zeros(InterfaceUtils.getBestInterface(a.getClass(), b.getClass()), shape);<a name="line.233"></a> |
| <span class="sourceLineNo">234</span><a name="line.234"></a> |
| <span class="sourceLineNo">235</span> IndexIterator ita = a.getIterator();<a name="line.235"></a> |
| <span class="sourceLineNo">236</span> IndexIterator itb = b.getIterator();<a name="line.236"></a> |
| <span class="sourceLineNo">237</span> int j = 0;<a name="line.237"></a> |
| <span class="sourceLineNo">238</span> while (ita.hasNext()) {<a name="line.238"></a> |
| <span class="sourceLineNo">239</span> double va = a.getElementDoubleAbs(ita.index);<a name="line.239"></a> |
| <span class="sourceLineNo">240</span> while (itb.hasNext()) {<a name="line.240"></a> |
| <span class="sourceLineNo">241</span> o.setObjectAbs(j++, va * b.getElementDoubleAbs(itb.index));<a name="line.241"></a> |
| <span class="sourceLineNo">242</span> }<a name="line.242"></a> |
| <span class="sourceLineNo">243</span> itb.reset();<a name="line.243"></a> |
| <span class="sourceLineNo">244</span> }<a name="line.244"></a> |
| <span class="sourceLineNo">245</span> return o;<a name="line.245"></a> |
| <span class="sourceLineNo">246</span> }<a name="line.246"></a> |
| <span class="sourceLineNo">247</span><a name="line.247"></a> |
| <span class="sourceLineNo">248</span> /**<a name="line.248"></a> |
| <span class="sourceLineNo">249</span> * Calculate the cross product of two datasets. Datasets must be broadcastable and<a name="line.249"></a> |
| <span class="sourceLineNo">250</span> * possess last dimensions of length 2 or 3<a name="line.250"></a> |
| <span class="sourceLineNo">251</span> * @param a<a name="line.251"></a> |
| <span class="sourceLineNo">252</span> * @param b<a name="line.252"></a> |
| <span class="sourceLineNo">253</span> * @return cross product<a name="line.253"></a> |
| <span class="sourceLineNo">254</span> */<a name="line.254"></a> |
| <span class="sourceLineNo">255</span> public static Dataset crossProduct(Dataset a, Dataset b) {<a name="line.255"></a> |
| <span class="sourceLineNo">256</span> return crossProduct(a, b, -1, -1, -1);<a name="line.256"></a> |
| <span class="sourceLineNo">257</span> }<a name="line.257"></a> |
| <span class="sourceLineNo">258</span><a name="line.258"></a> |
| <span class="sourceLineNo">259</span> /**<a name="line.259"></a> |
| <span class="sourceLineNo">260</span> * Calculate the cross product of two datasets. Datasets must be broadcastable and<a name="line.260"></a> |
| <span class="sourceLineNo">261</span> * possess dimensions of length 2 or 3. The axis parameters can be negative to indicate<a name="line.261"></a> |
| <span class="sourceLineNo">262</span> * dimensions from the end of their shapes<a name="line.262"></a> |
| <span class="sourceLineNo">263</span> * @param a<a name="line.263"></a> |
| <span class="sourceLineNo">264</span> * @param b<a name="line.264"></a> |
| <span class="sourceLineNo">265</span> * @param axisA dimension to be used a vector (must have length of 2 or 3)<a name="line.265"></a> |
| <span class="sourceLineNo">266</span> * @param axisB dimension to be used a vector (must have length of 2 or 3)<a name="line.266"></a> |
| <span class="sourceLineNo">267</span> * @param axisC dimension to assign as cross-product<a name="line.267"></a> |
| <span class="sourceLineNo">268</span> * @return cross product<a name="line.268"></a> |
| <span class="sourceLineNo">269</span> */<a name="line.269"></a> |
| <span class="sourceLineNo">270</span> public static Dataset crossProduct(Dataset a, Dataset b, int axisA, int axisB, int axisC) {<a name="line.270"></a> |
| <span class="sourceLineNo">271</span> final int rankA = a.getRank();<a name="line.271"></a> |
| <span class="sourceLineNo">272</span> final int rankB = b.getRank();<a name="line.272"></a> |
| <span class="sourceLineNo">273</span> if (rankA == 0 || rankB == 0) {<a name="line.273"></a> |
| <span class="sourceLineNo">274</span> throw new IllegalArgumentException("Datasets must have one or more dimensions");<a name="line.274"></a> |
| <span class="sourceLineNo">275</span> }<a name="line.275"></a> |
| <span class="sourceLineNo">276</span> axisA = a.checkAxis(axisA);<a name="line.276"></a> |
| <span class="sourceLineNo">277</span> axisB = b.checkAxis(axisB);<a name="line.277"></a> |
| <span class="sourceLineNo">278</span><a name="line.278"></a> |
| <span class="sourceLineNo">279</span> int la = a.getShapeRef()[axisA];<a name="line.279"></a> |
| <span class="sourceLineNo">280</span> int lb = b.getShapeRef()[axisB];<a name="line.280"></a> |
| <span class="sourceLineNo">281</span> if (Math.min(la, lb) < 2 || Math.max(la, lb) > 3) {<a name="line.281"></a> |
| <span class="sourceLineNo">282</span> throw new IllegalArgumentException("Chosen dimension of A & B must be 2 or 3");<a name="line.282"></a> |
| <span class="sourceLineNo">283</span> }<a name="line.283"></a> |
| <span class="sourceLineNo">284</span><a name="line.284"></a> |
| <span class="sourceLineNo">285</span> if (Math.max(la, lb) == 2) {<a name="line.285"></a> |
| <span class="sourceLineNo">286</span> return crossProduct2D(a, b, axisA, axisB);<a name="line.286"></a> |
| <span class="sourceLineNo">287</span> }<a name="line.287"></a> |
| <span class="sourceLineNo">288</span><a name="line.288"></a> |
| <span class="sourceLineNo">289</span> return crossProduct3D(a, b, axisA, axisB, axisC);<a name="line.289"></a> |
| <span class="sourceLineNo">290</span> }<a name="line.290"></a> |
| <span class="sourceLineNo">291</span><a name="line.291"></a> |
| <span class="sourceLineNo">292</span> private static int[] removeAxisFromShape(int[] shape, int axis) {<a name="line.292"></a> |
| <span class="sourceLineNo">293</span> int[] s = new int[shape.length - 1];<a name="line.293"></a> |
| <span class="sourceLineNo">294</span> int i = 0;<a name="line.294"></a> |
| <span class="sourceLineNo">295</span> int j = 0;<a name="line.295"></a> |
| <span class="sourceLineNo">296</span> while (i < axis) {<a name="line.296"></a> |
| <span class="sourceLineNo">297</span> s[j++] = shape[i++];<a name="line.297"></a> |
| <span class="sourceLineNo">298</span> }<a name="line.298"></a> |
| <span class="sourceLineNo">299</span> i++;<a name="line.299"></a> |
| <span class="sourceLineNo">300</span> while (i < shape.length) {<a name="line.300"></a> |
| <span class="sourceLineNo">301</span> s[j++] = shape[i++];<a name="line.301"></a> |
| <span class="sourceLineNo">302</span> }<a name="line.302"></a> |
| <span class="sourceLineNo">303</span> return s;<a name="line.303"></a> |
| <span class="sourceLineNo">304</span> }<a name="line.304"></a> |
| <span class="sourceLineNo">305</span><a name="line.305"></a> |
| <span class="sourceLineNo">306</span> // assume axes is in increasing order<a name="line.306"></a> |
| <span class="sourceLineNo">307</span> private static int[] removeAxesFromShape(int[] shape, int... axes) {<a name="line.307"></a> |
| <span class="sourceLineNo">308</span> int n = axes.length;<a name="line.308"></a> |
| <span class="sourceLineNo">309</span> int[] s = new int[shape.length - n];<a name="line.309"></a> |
| <span class="sourceLineNo">310</span> int i = 0;<a name="line.310"></a> |
| <span class="sourceLineNo">311</span> int j = 0;<a name="line.311"></a> |
| <span class="sourceLineNo">312</span> for (int k = 0; k < n; k++) {<a name="line.312"></a> |
| <span class="sourceLineNo">313</span> int a = axes[k];<a name="line.313"></a> |
| <span class="sourceLineNo">314</span> while (i < a) {<a name="line.314"></a> |
| <span class="sourceLineNo">315</span> s[j++] = shape[i++];<a name="line.315"></a> |
| <span class="sourceLineNo">316</span> }<a name="line.316"></a> |
| <span class="sourceLineNo">317</span> i++;<a name="line.317"></a> |
| <span class="sourceLineNo">318</span> }<a name="line.318"></a> |
| <span class="sourceLineNo">319</span> while (i < shape.length) {<a name="line.319"></a> |
| <span class="sourceLineNo">320</span> s[j++] = shape[i++];<a name="line.320"></a> |
| <span class="sourceLineNo">321</span> }<a name="line.321"></a> |
| <span class="sourceLineNo">322</span> return s;<a name="line.322"></a> |
| <span class="sourceLineNo">323</span> }<a name="line.323"></a> |
| <span class="sourceLineNo">324</span><a name="line.324"></a> |
| <span class="sourceLineNo">325</span> private static int[] addAxisToShape(int[] shape, int axis, int length) {<a name="line.325"></a> |
| <span class="sourceLineNo">326</span> int[] s = new int[shape.length + 1];<a name="line.326"></a> |
| <span class="sourceLineNo">327</span> int i = 0;<a name="line.327"></a> |
| <span class="sourceLineNo">328</span> int j = 0;<a name="line.328"></a> |
| <span class="sourceLineNo">329</span> while (i < axis) {<a name="line.329"></a> |
| <span class="sourceLineNo">330</span> s[j++] = shape[i++];<a name="line.330"></a> |
| <span class="sourceLineNo">331</span> }<a name="line.331"></a> |
| <span class="sourceLineNo">332</span> s[j++] = length;<a name="line.332"></a> |
| <span class="sourceLineNo">333</span> while (i < shape.length) {<a name="line.333"></a> |
| <span class="sourceLineNo">334</span> s[j++] = shape[i++];<a name="line.334"></a> |
| <span class="sourceLineNo">335</span> }<a name="line.335"></a> |
| <span class="sourceLineNo">336</span> return s;<a name="line.336"></a> |
| <span class="sourceLineNo">337</span> }<a name="line.337"></a> |
| <span class="sourceLineNo">338</span><a name="line.338"></a> |
| <span class="sourceLineNo">339</span> private static Dataset crossProduct2D(Dataset a, Dataset b, int axisA, int axisB) {<a name="line.339"></a> |
| <span class="sourceLineNo">340</span> // need to broadcast and omit given axes<a name="line.340"></a> |
| <span class="sourceLineNo">341</span> int[] shapeA = removeAxisFromShape(a.getShapeRef(), axisA);<a name="line.341"></a> |
| <span class="sourceLineNo">342</span> int[] shapeB = removeAxisFromShape(b.getShapeRef(), axisB);<a name="line.342"></a> |
| <span class="sourceLineNo">343</span><a name="line.343"></a> |
| <span class="sourceLineNo">344</span> List<int[]> fullShapes = BroadcastUtils.broadcastShapes(shapeA, shapeB);<a name="line.344"></a> |
| <span class="sourceLineNo">345</span><a name="line.345"></a> |
| <span class="sourceLineNo">346</span> int[] maxShape = fullShapes.get(0);<a name="line.346"></a> |
| <span class="sourceLineNo">347</span> Dataset c = DatasetFactory.zeros(InterfaceUtils.getBestInterface(a.getClass(), b.getClass()), maxShape);<a name="line.347"></a> |
| <span class="sourceLineNo">348</span><a name="line.348"></a> |
| <span class="sourceLineNo">349</span> PositionIterator ita = a.getPositionIterator(axisA);<a name="line.349"></a> |
| <span class="sourceLineNo">350</span> PositionIterator itb = b.getPositionIterator(axisB);<a name="line.350"></a> |
| <span class="sourceLineNo">351</span> IndexIterator itc = c.getIterator();<a name="line.351"></a> |
| <span class="sourceLineNo">352</span><a name="line.352"></a> |
| <span class="sourceLineNo">353</span> final int[] pa = ita.getPos();<a name="line.353"></a> |
| <span class="sourceLineNo">354</span> final int[] pb = itb.getPos();<a name="line.354"></a> |
| <span class="sourceLineNo">355</span> while (itc.hasNext()) {<a name="line.355"></a> |
| <span class="sourceLineNo">356</span> if (!ita.hasNext()) // TODO use broadcasting...<a name="line.356"></a> |
| <span class="sourceLineNo">357</span> ita.reset();<a name="line.357"></a> |
| <span class="sourceLineNo">358</span> if (!itb.hasNext())<a name="line.358"></a> |
| <span class="sourceLineNo">359</span> itb.reset();<a name="line.359"></a> |
| <span class="sourceLineNo">360</span> pa[axisA] = 0;<a name="line.360"></a> |
| <span class="sourceLineNo">361</span> pb[axisB] = 1;<a name="line.361"></a> |
| <span class="sourceLineNo">362</span> double cv = a.getDouble(pa) * b.getDouble(pb);<a name="line.362"></a> |
| <span class="sourceLineNo">363</span> pa[axisA] = 1;<a name="line.363"></a> |
| <span class="sourceLineNo">364</span> pb[axisB] = 0;<a name="line.364"></a> |
| <span class="sourceLineNo">365</span> cv -= a.getDouble(pa) * b.getDouble(pb);<a name="line.365"></a> |
| <span class="sourceLineNo">366</span><a name="line.366"></a> |
| <span class="sourceLineNo">367</span> c.setObjectAbs(itc.index, cv);<a name="line.367"></a> |
| <span class="sourceLineNo">368</span> }<a name="line.368"></a> |
| <span class="sourceLineNo">369</span> return c;<a name="line.369"></a> |
| <span class="sourceLineNo">370</span> }<a name="line.370"></a> |
| <span class="sourceLineNo">371</span><a name="line.371"></a> |
| <span class="sourceLineNo">372</span> private static Dataset crossProduct3D(Dataset a, Dataset b, int axisA, int axisB, int axisC) {<a name="line.372"></a> |
| <span class="sourceLineNo">373</span> int[] shapeA = removeAxisFromShape(a.getShapeRef(), axisA);<a name="line.373"></a> |
| <span class="sourceLineNo">374</span> int[] shapeB = removeAxisFromShape(b.getShapeRef(), axisB);<a name="line.374"></a> |
| <span class="sourceLineNo">375</span><a name="line.375"></a> |
| <span class="sourceLineNo">376</span> List<int[]> fullShapes = BroadcastUtils.broadcastShapes(shapeA, shapeB);<a name="line.376"></a> |
| <span class="sourceLineNo">377</span><a name="line.377"></a> |
| <span class="sourceLineNo">378</span> int[] maxShape = fullShapes.get(0);<a name="line.378"></a> |
| <span class="sourceLineNo">379</span> int rankC = maxShape.length + 1;<a name="line.379"></a> |
| <span class="sourceLineNo">380</span> axisC = ShapeUtils.checkAxis(rankC, axisC);<a name="line.380"></a> |
| <span class="sourceLineNo">381</span> maxShape = addAxisToShape(maxShape, axisC, 3);<a name="line.381"></a> |
| <span class="sourceLineNo">382</span> Dataset c = DatasetFactory.zeros(InterfaceUtils.getBestInterface(a.getClass(), b.getClass()), maxShape);<a name="line.382"></a> |
| <span class="sourceLineNo">383</span><a name="line.383"></a> |
| <span class="sourceLineNo">384</span> PositionIterator ita = a.getPositionIterator(axisA);<a name="line.384"></a> |
| <span class="sourceLineNo">385</span> PositionIterator itb = b.getPositionIterator(axisB);<a name="line.385"></a> |
| <span class="sourceLineNo">386</span> PositionIterator itc = c.getPositionIterator(axisC);<a name="line.386"></a> |
| <span class="sourceLineNo">387</span><a name="line.387"></a> |
| <span class="sourceLineNo">388</span> final int[] pa = ita.getPos();<a name="line.388"></a> |
| <span class="sourceLineNo">389</span> final int[] pb = itb.getPos();<a name="line.389"></a> |
| <span class="sourceLineNo">390</span> final int[] pc = itc.getPos();<a name="line.390"></a> |
| <span class="sourceLineNo">391</span> final int la = a.getShapeRef()[axisA];<a name="line.391"></a> |
| <span class="sourceLineNo">392</span> final int lb = b.getShapeRef()[axisB];<a name="line.392"></a> |
| <span class="sourceLineNo">393</span><a name="line.393"></a> |
| <span class="sourceLineNo">394</span> if (la == 2) {<a name="line.394"></a> |
| <span class="sourceLineNo">395</span> while (itc.hasNext()) {<a name="line.395"></a> |
| <span class="sourceLineNo">396</span> if (!ita.hasNext()) // TODO use broadcasting...<a name="line.396"></a> |
| <span class="sourceLineNo">397</span> ita.reset();<a name="line.397"></a> |
| <span class="sourceLineNo">398</span> if (!itb.hasNext())<a name="line.398"></a> |
| <span class="sourceLineNo">399</span> itb.reset();<a name="line.399"></a> |
| <span class="sourceLineNo">400</span> double cv;<a name="line.400"></a> |
| <span class="sourceLineNo">401</span> pa[axisA] = 1;<a name="line.401"></a> |
| <span class="sourceLineNo">402</span> pb[axisB] = 2;<a name="line.402"></a> |
| <span class="sourceLineNo">403</span> cv = a.getDouble(pa) * b.getDouble(pb);<a name="line.403"></a> |
| <span class="sourceLineNo">404</span> pc[axisC] = 0;<a name="line.404"></a> |
| <span class="sourceLineNo">405</span> c.set(cv, pc);<a name="line.405"></a> |
| <span class="sourceLineNo">406</span><a name="line.406"></a> |
| <span class="sourceLineNo">407</span> pa[axisA] = 0;<a name="line.407"></a> |
| <span class="sourceLineNo">408</span> pb[axisB] = 2;<a name="line.408"></a> |
| <span class="sourceLineNo">409</span> cv = -a.getDouble(pa) * b.getDouble(pb);<a name="line.409"></a> |
| <span class="sourceLineNo">410</span> pc[axisC] = 1;<a name="line.410"></a> |
| <span class="sourceLineNo">411</span> c.set(cv, pc);<a name="line.411"></a> |
| <span class="sourceLineNo">412</span><a name="line.412"></a> |
| <span class="sourceLineNo">413</span> pa[axisA] = 0;<a name="line.413"></a> |
| <span class="sourceLineNo">414</span> pb[axisB] = 1;<a name="line.414"></a> |
| <span class="sourceLineNo">415</span> cv = a.getDouble(pa) * b.getDouble(pb);<a name="line.415"></a> |
| <span class="sourceLineNo">416</span> pa[axisA] = 1;<a name="line.416"></a> |
| <span class="sourceLineNo">417</span> pb[axisB] = 0;<a name="line.417"></a> |
| <span class="sourceLineNo">418</span> cv -= a.getDouble(pa) * b.getDouble(pb);<a name="line.418"></a> |
| <span class="sourceLineNo">419</span> pc[axisC] = 2;<a name="line.419"></a> |
| <span class="sourceLineNo">420</span> c.set(cv, pc);<a name="line.420"></a> |
| <span class="sourceLineNo">421</span> }<a name="line.421"></a> |
| <span class="sourceLineNo">422</span> } else if (lb == 2) {<a name="line.422"></a> |
| <span class="sourceLineNo">423</span> while (itc.hasNext()) {<a name="line.423"></a> |
| <span class="sourceLineNo">424</span> if (!ita.hasNext()) // TODO use broadcasting...<a name="line.424"></a> |
| <span class="sourceLineNo">425</span> ita.reset();<a name="line.425"></a> |
| <span class="sourceLineNo">426</span> if (!itb.hasNext())<a name="line.426"></a> |
| <span class="sourceLineNo">427</span> itb.reset();<a name="line.427"></a> |
| <span class="sourceLineNo">428</span> double cv;<a name="line.428"></a> |
| <span class="sourceLineNo">429</span> pa[axisA] = 2;<a name="line.429"></a> |
| <span class="sourceLineNo">430</span> pb[axisB] = 1;<a name="line.430"></a> |
| <span class="sourceLineNo">431</span> cv = -a.getDouble(pa) * b.getDouble(pb);<a name="line.431"></a> |
| <span class="sourceLineNo">432</span> pc[axisC] = 0;<a name="line.432"></a> |
| <span class="sourceLineNo">433</span> c.set(cv, pc);<a name="line.433"></a> |
| <span class="sourceLineNo">434</span><a name="line.434"></a> |
| <span class="sourceLineNo">435</span> pa[axisA] = 2;<a name="line.435"></a> |
| <span class="sourceLineNo">436</span> pb[axisB] = 0;<a name="line.436"></a> |
| <span class="sourceLineNo">437</span> cv = a.getDouble(pa) * b.getDouble(pb);<a name="line.437"></a> |
| <span class="sourceLineNo">438</span> pc[axisC] = 1;<a name="line.438"></a> |
| <span class="sourceLineNo">439</span> c.set(cv, pc);<a name="line.439"></a> |
| <span class="sourceLineNo">440</span><a name="line.440"></a> |
| <span class="sourceLineNo">441</span> pa[axisA] = 0;<a name="line.441"></a> |
| <span class="sourceLineNo">442</span> pb[axisB] = 1;<a name="line.442"></a> |
| <span class="sourceLineNo">443</span> cv = a.getDouble(pa) * b.getDouble(pb);<a name="line.443"></a> |
| <span class="sourceLineNo">444</span> pa[axisA] = 1;<a name="line.444"></a> |
| <span class="sourceLineNo">445</span> pb[axisB] = 0;<a name="line.445"></a> |
| <span class="sourceLineNo">446</span> cv -= a.getDouble(pa) * b.getDouble(pb);<a name="line.446"></a> |
| <span class="sourceLineNo">447</span> pc[axisC] = 2;<a name="line.447"></a> |
| <span class="sourceLineNo">448</span> c.set(cv, pc);<a name="line.448"></a> |
| <span class="sourceLineNo">449</span> }<a name="line.449"></a> |
| <span class="sourceLineNo">450</span> <a name="line.450"></a> |
| <span class="sourceLineNo">451</span> } else {<a name="line.451"></a> |
| <span class="sourceLineNo">452</span> while (itc.hasNext()) {<a name="line.452"></a> |
| <span class="sourceLineNo">453</span> if (!ita.hasNext()) // TODO use broadcasting...<a name="line.453"></a> |
| <span class="sourceLineNo">454</span> ita.reset();<a name="line.454"></a> |
| <span class="sourceLineNo">455</span> if (!itb.hasNext())<a name="line.455"></a> |
| <span class="sourceLineNo">456</span> itb.reset();<a name="line.456"></a> |
| <span class="sourceLineNo">457</span> double cv;<a name="line.457"></a> |
| <span class="sourceLineNo">458</span> pa[axisA] = 1;<a name="line.458"></a> |
| <span class="sourceLineNo">459</span> pb[axisB] = 2;<a name="line.459"></a> |
| <span class="sourceLineNo">460</span> cv = a.getDouble(pa) * b.getDouble(pb);<a name="line.460"></a> |
| <span class="sourceLineNo">461</span> pa[axisA] = 2;<a name="line.461"></a> |
| <span class="sourceLineNo">462</span> pb[axisB] = 1;<a name="line.462"></a> |
| <span class="sourceLineNo">463</span> cv -= a.getDouble(pa) * b.getDouble(pb);<a name="line.463"></a> |
| <span class="sourceLineNo">464</span> pc[axisC] = 0;<a name="line.464"></a> |
| <span class="sourceLineNo">465</span> c.set(cv, pc);<a name="line.465"></a> |
| <span class="sourceLineNo">466</span><a name="line.466"></a> |
| <span class="sourceLineNo">467</span> pa[axisA] = 2;<a name="line.467"></a> |
| <span class="sourceLineNo">468</span> pb[axisB] = 0;<a name="line.468"></a> |
| <span class="sourceLineNo">469</span> cv = a.getDouble(pa) * b.getDouble(pb);<a name="line.469"></a> |
| <span class="sourceLineNo">470</span> pa[axisA] = 0;<a name="line.470"></a> |
| <span class="sourceLineNo">471</span> pb[axisB] = 2;<a name="line.471"></a> |
| <span class="sourceLineNo">472</span> cv -= a.getDouble(pa) * b.getDouble(pb);<a name="line.472"></a> |
| <span class="sourceLineNo">473</span> pc[axisC] = 1;<a name="line.473"></a> |
| <span class="sourceLineNo">474</span> c.set(cv, pc);<a name="line.474"></a> |
| <span class="sourceLineNo">475</span><a name="line.475"></a> |
| <span class="sourceLineNo">476</span> pa[axisA] = 0;<a name="line.476"></a> |
| <span class="sourceLineNo">477</span> pb[axisB] = 1;<a name="line.477"></a> |
| <span class="sourceLineNo">478</span> cv = a.getDouble(pa) * b.getDouble(pb);<a name="line.478"></a> |
| <span class="sourceLineNo">479</span> pa[axisA] = 1;<a name="line.479"></a> |
| <span class="sourceLineNo">480</span> pb[axisB] = 0;<a name="line.480"></a> |
| <span class="sourceLineNo">481</span> cv -= a.getDouble(pa) * b.getDouble(pb);<a name="line.481"></a> |
| <span class="sourceLineNo">482</span> pc[axisC] = 2;<a name="line.482"></a> |
| <span class="sourceLineNo">483</span> c.set(cv, pc);<a name="line.483"></a> |
| <span class="sourceLineNo">484</span> }<a name="line.484"></a> |
| <span class="sourceLineNo">485</span> }<a name="line.485"></a> |
| <span class="sourceLineNo">486</span> return c;<a name="line.486"></a> |
| <span class="sourceLineNo">487</span> }<a name="line.487"></a> |
| <span class="sourceLineNo">488</span><a name="line.488"></a> |
| <span class="sourceLineNo">489</span> /**<a name="line.489"></a> |
| <span class="sourceLineNo">490</span> * Raise dataset to given power by matrix multiplication<a name="line.490"></a> |
| <span class="sourceLineNo">491</span> * @param a<a name="line.491"></a> |
| <span class="sourceLineNo">492</span> * @param n power<a name="line.492"></a> |
| <span class="sourceLineNo">493</span> * @return {@code a ** n}<a name="line.493"></a> |
| <span class="sourceLineNo">494</span> */<a name="line.494"></a> |
| <span class="sourceLineNo">495</span> public static Dataset power(Dataset a, int n) {<a name="line.495"></a> |
| <span class="sourceLineNo">496</span> if (n < 0) {<a name="line.496"></a> |
| <span class="sourceLineNo">497</span> LUDecomposition lud = new LUDecomposition(createRealMatrix(a));<a name="line.497"></a> |
| <span class="sourceLineNo">498</span> return createDataset(lud.getSolver().getInverse().power(-n));<a name="line.498"></a> |
| <span class="sourceLineNo">499</span> }<a name="line.499"></a> |
| <span class="sourceLineNo">500</span> Dataset p = createDataset(createRealMatrix(a).power(n));<a name="line.500"></a> |
| <span class="sourceLineNo">501</span> if (!a.hasFloatingPointElements()) {<a name="line.501"></a> |
| <span class="sourceLineNo">502</span> return p.cast(a.getClass());<a name="line.502"></a> |
| <span class="sourceLineNo">503</span> }<a name="line.503"></a> |
| <span class="sourceLineNo">504</span> return p;<a name="line.504"></a> |
| <span class="sourceLineNo">505</span> }<a name="line.505"></a> |
| <span class="sourceLineNo">506</span><a name="line.506"></a> |
| <span class="sourceLineNo">507</span> /**<a name="line.507"></a> |
| <span class="sourceLineNo">508</span> * Create the Kronecker product as defined by <a name="line.508"></a> |
| <span class="sourceLineNo">509</span> * {@code kron[k0,...,kN] = a[i0,...,iN] * b[j0,...,jN]}<a name="line.509"></a> |
| <span class="sourceLineNo">510</span> * where {@code kn = sn * in + jn} for {@code n = 0...N} and {@code s} is shape of {@code b}<a name="line.510"></a> |
| <span class="sourceLineNo">511</span> * @param a<a name="line.511"></a> |
| <span class="sourceLineNo">512</span> * @param b<a name="line.512"></a> |
| <span class="sourceLineNo">513</span> * @return Kronecker product of a and b<a name="line.513"></a> |
| <span class="sourceLineNo">514</span> */<a name="line.514"></a> |
| <span class="sourceLineNo">515</span> public static Dataset kroneckerProduct(Dataset a, Dataset b) {<a name="line.515"></a> |
| <span class="sourceLineNo">516</span> if (a.getElementsPerItem() != 1 || b.getElementsPerItem() != 1) {<a name="line.516"></a> |
| <span class="sourceLineNo">517</span> throw new UnsupportedOperationException("Compound datasets (including complex ones) are not currently supported");<a name="line.517"></a> |
| <span class="sourceLineNo">518</span> }<a name="line.518"></a> |
| <span class="sourceLineNo">519</span> int ar = a.getRank();<a name="line.519"></a> |
| <span class="sourceLineNo">520</span> int br = b.getRank();<a name="line.520"></a> |
| <span class="sourceLineNo">521</span> int[] aShape;<a name="line.521"></a> |
| <span class="sourceLineNo">522</span> int[] bShape;<a name="line.522"></a> |
| <span class="sourceLineNo">523</span> aShape = a.getShapeRef();<a name="line.523"></a> |
| <span class="sourceLineNo">524</span> bShape = b.getShapeRef();<a name="line.524"></a> |
| <span class="sourceLineNo">525</span> int r = ar;<a name="line.525"></a> |
| <span class="sourceLineNo">526</span> // pre-pad if ranks are not same<a name="line.526"></a> |
| <span class="sourceLineNo">527</span> if (ar < br) {<a name="line.527"></a> |
| <span class="sourceLineNo">528</span> r = br;<a name="line.528"></a> |
| <span class="sourceLineNo">529</span> int[] shape = new int[br];<a name="line.529"></a> |
| <span class="sourceLineNo">530</span> int j = 0;<a name="line.530"></a> |
| <span class="sourceLineNo">531</span> for (int i = ar; i < br; i++) {<a name="line.531"></a> |
| <span class="sourceLineNo">532</span> shape[j++] = 1;<a name="line.532"></a> |
| <span class="sourceLineNo">533</span> }<a name="line.533"></a> |
| <span class="sourceLineNo">534</span> int i = 0;<a name="line.534"></a> |
| <span class="sourceLineNo">535</span> while (j < br) {<a name="line.535"></a> |
| <span class="sourceLineNo">536</span> shape[j++] = aShape[i++];<a name="line.536"></a> |
| <span class="sourceLineNo">537</span> }<a name="line.537"></a> |
| <span class="sourceLineNo">538</span> a = a.reshape(shape);<a name="line.538"></a> |
| <span class="sourceLineNo">539</span> aShape = shape;<a name="line.539"></a> |
| <span class="sourceLineNo">540</span> } else if (ar > br) {<a name="line.540"></a> |
| <span class="sourceLineNo">541</span> int[] shape = new int[ar];<a name="line.541"></a> |
| <span class="sourceLineNo">542</span> int j = 0;<a name="line.542"></a> |
| <span class="sourceLineNo">543</span> for (int i = br; i < ar; i++) {<a name="line.543"></a> |
| <span class="sourceLineNo">544</span> shape[j++] = 1;<a name="line.544"></a> |
| <span class="sourceLineNo">545</span> }<a name="line.545"></a> |
| <span class="sourceLineNo">546</span> int i = 0;<a name="line.546"></a> |
| <span class="sourceLineNo">547</span> while (j < ar) {<a name="line.547"></a> |
| <span class="sourceLineNo">548</span> shape[j++] = bShape[i++];<a name="line.548"></a> |
| <span class="sourceLineNo">549</span> }<a name="line.549"></a> |
| <span class="sourceLineNo">550</span> b = b.reshape(shape);<a name="line.550"></a> |
| <span class="sourceLineNo">551</span> bShape = shape;<a name="line.551"></a> |
| <span class="sourceLineNo">552</span> }<a name="line.552"></a> |
| <span class="sourceLineNo">553</span><a name="line.553"></a> |
| <span class="sourceLineNo">554</span> int[] nShape = new int[r];<a name="line.554"></a> |
| <span class="sourceLineNo">555</span> for (int i = 0; i < r; i++) {<a name="line.555"></a> |
| <span class="sourceLineNo">556</span> nShape[i] = aShape[i] * bShape[i];<a name="line.556"></a> |
| <span class="sourceLineNo">557</span> }<a name="line.557"></a> |
| <span class="sourceLineNo">558</span> Dataset kron = DatasetFactory.zeros(InterfaceUtils.getBestInterface(a.getClass(), b.getClass()), nShape);<a name="line.558"></a> |
| <span class="sourceLineNo">559</span> IndexIterator ita = a.getIterator(true);<a name="line.559"></a> |
| <span class="sourceLineNo">560</span> IndexIterator itb = b.getIterator(true);<a name="line.560"></a> |
| <span class="sourceLineNo">561</span> int[] pa = ita.getPos();<a name="line.561"></a> |
| <span class="sourceLineNo">562</span> int[] pb = itb.getPos();<a name="line.562"></a> |
| <span class="sourceLineNo">563</span> int[] off = new int[1];<a name="line.563"></a> |
| <span class="sourceLineNo">564</span> int[] stride = AbstractDataset.createStrides(1, nShape, null, 0, off);<a name="line.564"></a> |
| <span class="sourceLineNo">565</span> if (kron instanceof LongDataset) {<a name="line.565"></a> |
| <span class="sourceLineNo">566</span> while (ita.hasNext()) {<a name="line.566"></a> |
| <span class="sourceLineNo">567</span> long av = a.getElementLongAbs(ita.index);<a name="line.567"></a> |
| <span class="sourceLineNo">568</span><a name="line.568"></a> |
| <span class="sourceLineNo">569</span> int ka = 0; <a name="line.569"></a> |
| <span class="sourceLineNo">570</span> for (int i = 0; i < r; i++) {<a name="line.570"></a> |
| <span class="sourceLineNo">571</span> ka += stride[i] * bShape[i] * pa[i];<a name="line.571"></a> |
| <span class="sourceLineNo">572</span> }<a name="line.572"></a> |
| <span class="sourceLineNo">573</span> itb.reset();<a name="line.573"></a> |
| <span class="sourceLineNo">574</span> while (itb.hasNext()) {<a name="line.574"></a> |
| <span class="sourceLineNo">575</span> long bv = b.getElementLongAbs(itb.index);<a name="line.575"></a> |
| <span class="sourceLineNo">576</span> int kb = ka;<a name="line.576"></a> |
| <span class="sourceLineNo">577</span> for (int i = 0; i < r; i++) {<a name="line.577"></a> |
| <span class="sourceLineNo">578</span> kb += stride[i] * pb[i];<a name="line.578"></a> |
| <span class="sourceLineNo">579</span> }<a name="line.579"></a> |
| <span class="sourceLineNo">580</span> kron.setObjectAbs(kb, av * bv);<a name="line.580"></a> |
| <span class="sourceLineNo">581</span> }<a name="line.581"></a> |
| <span class="sourceLineNo">582</span> }<a name="line.582"></a> |
| <span class="sourceLineNo">583</span> } else {<a name="line.583"></a> |
| <span class="sourceLineNo">584</span> while (ita.hasNext()) {<a name="line.584"></a> |
| <span class="sourceLineNo">585</span> double av = a.getElementDoubleAbs(ita.index);<a name="line.585"></a> |
| <span class="sourceLineNo">586</span><a name="line.586"></a> |
| <span class="sourceLineNo">587</span> int ka = 0; <a name="line.587"></a> |
| <span class="sourceLineNo">588</span> for (int i = 0; i < r; i++) {<a name="line.588"></a> |
| <span class="sourceLineNo">589</span> ka += stride[i] * bShape[i] * pa[i];<a name="line.589"></a> |
| <span class="sourceLineNo">590</span> }<a name="line.590"></a> |
| <span class="sourceLineNo">591</span> itb.reset();<a name="line.591"></a> |
| <span class="sourceLineNo">592</span> while (itb.hasNext()) {<a name="line.592"></a> |
| <span class="sourceLineNo">593</span> double bv = b.getElementLongAbs(itb.index);<a name="line.593"></a> |
| <span class="sourceLineNo">594</span> int kb = ka;<a name="line.594"></a> |
| <span class="sourceLineNo">595</span> for (int i = 0; i < r; i++) {<a name="line.595"></a> |
| <span class="sourceLineNo">596</span> kb += stride[i] * pb[i];<a name="line.596"></a> |
| <span class="sourceLineNo">597</span> }<a name="line.597"></a> |
| <span class="sourceLineNo">598</span> kron.setObjectAbs(kb, av * bv);<a name="line.598"></a> |
| <span class="sourceLineNo">599</span> }<a name="line.599"></a> |
| <span class="sourceLineNo">600</span> }<a name="line.600"></a> |
| <span class="sourceLineNo">601</span> }<a name="line.601"></a> |
| <span class="sourceLineNo">602</span><a name="line.602"></a> |
| <span class="sourceLineNo">603</span> return kron;<a name="line.603"></a> |
| <span class="sourceLineNo">604</span> }<a name="line.604"></a> |
| <span class="sourceLineNo">605</span><a name="line.605"></a> |
| <span class="sourceLineNo">606</span> /**<a name="line.606"></a> |
| <span class="sourceLineNo">607</span> * Calculate trace of dataset - sum of values over 1st axis and 2nd axis<a name="line.607"></a> |
| <span class="sourceLineNo">608</span> * @param a<a name="line.608"></a> |
| <span class="sourceLineNo">609</span> * @return trace of dataset<a name="line.609"></a> |
| <span class="sourceLineNo">610</span> */<a name="line.610"></a> |
| <span class="sourceLineNo">611</span> public static Dataset trace(Dataset a) {<a name="line.611"></a> |
| <span class="sourceLineNo">612</span> return trace(a, 0, 0, 1);<a name="line.612"></a> |
| <span class="sourceLineNo">613</span> }<a name="line.613"></a> |
| <span class="sourceLineNo">614</span><a name="line.614"></a> |
| <span class="sourceLineNo">615</span> /**<a name="line.615"></a> |
| <span class="sourceLineNo">616</span> * Calculate trace of dataset - sum of values over axis1 and axis2 where axis2 is offset<a name="line.616"></a> |
| <span class="sourceLineNo">617</span> * @param a<a name="line.617"></a> |
| <span class="sourceLineNo">618</span> * @param offset<a name="line.618"></a> |
| <span class="sourceLineNo">619</span> * @param axis1<a name="line.619"></a> |
| <span class="sourceLineNo">620</span> * @param axis2<a name="line.620"></a> |
| <span class="sourceLineNo">621</span> * @return trace of dataset<a name="line.621"></a> |
| <span class="sourceLineNo">622</span> */<a name="line.622"></a> |
| <span class="sourceLineNo">623</span> public static Dataset trace(Dataset a, int offset, int axis1, int axis2) {<a name="line.623"></a> |
| <span class="sourceLineNo">624</span> int[] shape = a.getShapeRef();<a name="line.624"></a> |
| <span class="sourceLineNo">625</span> int[] axes = new int[] { a.checkAxis(axis1), a.checkAxis(axis2) };<a name="line.625"></a> |
| <span class="sourceLineNo">626</span> Arrays.sort(axes);<a name="line.626"></a> |
| <span class="sourceLineNo">627</span> int is = a.getElementsPerItem();<a name="line.627"></a> |
| <span class="sourceLineNo">628</span> Dataset trace = DatasetFactory.zeros(is, a.getClass(), removeAxesFromShape(shape, axes));<a name="line.628"></a> |
| <span class="sourceLineNo">629</span><a name="line.629"></a> |
| <span class="sourceLineNo">630</span> int am = axes[0];<a name="line.630"></a> |
| <span class="sourceLineNo">631</span> int mmax = shape[am];<a name="line.631"></a> |
| <span class="sourceLineNo">632</span> int an = axes[1];<a name="line.632"></a> |
| <span class="sourceLineNo">633</span> int nmax = shape[an];<a name="line.633"></a> |
| <span class="sourceLineNo">634</span> PositionIterator it = new PositionIterator(shape, axes);<a name="line.634"></a> |
| <span class="sourceLineNo">635</span> int[] pos = it.getPos();<a name="line.635"></a> |
| <span class="sourceLineNo">636</span> int i = 0;<a name="line.636"></a> |
| <span class="sourceLineNo">637</span> int mmin;<a name="line.637"></a> |
| <span class="sourceLineNo">638</span> int nmin;<a name="line.638"></a> |
| <span class="sourceLineNo">639</span> if (offset >= 0) {<a name="line.639"></a> |
| <span class="sourceLineNo">640</span> mmin = 0;<a name="line.640"></a> |
| <span class="sourceLineNo">641</span> nmin = offset;<a name="line.641"></a> |
| <span class="sourceLineNo">642</span> } else {<a name="line.642"></a> |
| <span class="sourceLineNo">643</span> mmin = -offset;<a name="line.643"></a> |
| <span class="sourceLineNo">644</span> nmin = 0;<a name="line.644"></a> |
| <span class="sourceLineNo">645</span> }<a name="line.645"></a> |
| <span class="sourceLineNo">646</span> if (is == 1) {<a name="line.646"></a> |
| <span class="sourceLineNo">647</span> if (a instanceof LongDataset) {<a name="line.647"></a> |
| <span class="sourceLineNo">648</span> while (it.hasNext()) {<a name="line.648"></a> |
| <span class="sourceLineNo">649</span> int m = mmin;<a name="line.649"></a> |
| <span class="sourceLineNo">650</span> int n = nmin;<a name="line.650"></a> |
| <span class="sourceLineNo">651</span> long s = 0;<a name="line.651"></a> |
| <span class="sourceLineNo">652</span> while (m < mmax && n < nmax) {<a name="line.652"></a> |
| <span class="sourceLineNo">653</span> pos[am] = m++;<a name="line.653"></a> |
| <span class="sourceLineNo">654</span> pos[an] = n++;<a name="line.654"></a> |
| <span class="sourceLineNo">655</span> s += a.getLong(pos);<a name="line.655"></a> |
| <span class="sourceLineNo">656</span> }<a name="line.656"></a> |
| <span class="sourceLineNo">657</span> trace.setObjectAbs(i++, s);<a name="line.657"></a> |
| <span class="sourceLineNo">658</span> }<a name="line.658"></a> |
| <span class="sourceLineNo">659</span> } else {<a name="line.659"></a> |
| <span class="sourceLineNo">660</span> while (it.hasNext()) {<a name="line.660"></a> |
| <span class="sourceLineNo">661</span> int m = mmin;<a name="line.661"></a> |
| <span class="sourceLineNo">662</span> int n = nmin;<a name="line.662"></a> |
| <span class="sourceLineNo">663</span> double s = 0;<a name="line.663"></a> |
| <span class="sourceLineNo">664</span> while (m < mmax && n < nmax) {<a name="line.664"></a> |
| <span class="sourceLineNo">665</span> pos[am] = m++;<a name="line.665"></a> |
| <span class="sourceLineNo">666</span> pos[an] = n++;<a name="line.666"></a> |
| <span class="sourceLineNo">667</span> s += a.getDouble(pos);<a name="line.667"></a> |
| <span class="sourceLineNo">668</span> }<a name="line.668"></a> |
| <span class="sourceLineNo">669</span> trace.setObjectAbs(i++, s);<a name="line.669"></a> |
| <span class="sourceLineNo">670</span> }<a name="line.670"></a> |
| <span class="sourceLineNo">671</span> }<a name="line.671"></a> |
| <span class="sourceLineNo">672</span> } else {<a name="line.672"></a> |
| <span class="sourceLineNo">673</span> AbstractCompoundDataset ca = (AbstractCompoundDataset) a;<a name="line.673"></a> |
| <span class="sourceLineNo">674</span> if (ca instanceof CompoundLongDataset) {<a name="line.674"></a> |
| <span class="sourceLineNo">675</span> long[] t = new long[is];<a name="line.675"></a> |
| <span class="sourceLineNo">676</span> long[] s = new long[is];<a name="line.676"></a> |
| <span class="sourceLineNo">677</span> while (it.hasNext()) {<a name="line.677"></a> |
| <span class="sourceLineNo">678</span> int m = mmin;<a name="line.678"></a> |
| <span class="sourceLineNo">679</span> int n = nmin;<a name="line.679"></a> |
| <span class="sourceLineNo">680</span> Arrays.fill(s, 0);<a name="line.680"></a> |
| <span class="sourceLineNo">681</span> while (m < mmax && n < nmax) {<a name="line.681"></a> |
| <span class="sourceLineNo">682</span> pos[am] = m++;<a name="line.682"></a> |
| <span class="sourceLineNo">683</span> pos[an] = n++;<a name="line.683"></a> |
| <span class="sourceLineNo">684</span> ((CompoundLongDataset)ca).getAbs(ca.get1DIndex(pos), t);<a name="line.684"></a> |
| <span class="sourceLineNo">685</span> for (int k = 0; k < is; k++) {<a name="line.685"></a> |
| <span class="sourceLineNo">686</span> s[k] += t[k];<a name="line.686"></a> |
| <span class="sourceLineNo">687</span> }<a name="line.687"></a> |
| <span class="sourceLineNo">688</span> }<a name="line.688"></a> |
| <span class="sourceLineNo">689</span> trace.setObjectAbs(i++, s);<a name="line.689"></a> |
| <span class="sourceLineNo">690</span> }<a name="line.690"></a> |
| <span class="sourceLineNo">691</span> } else {<a name="line.691"></a> |
| <span class="sourceLineNo">692</span> double[] t = new double[is];<a name="line.692"></a> |
| <span class="sourceLineNo">693</span> double[] s = new double[is];<a name="line.693"></a> |
| <span class="sourceLineNo">694</span> while (it.hasNext()) {<a name="line.694"></a> |
| <span class="sourceLineNo">695</span> int m = mmin;<a name="line.695"></a> |
| <span class="sourceLineNo">696</span> int n = nmin;<a name="line.696"></a> |
| <span class="sourceLineNo">697</span> Arrays.fill(s, 0);<a name="line.697"></a> |
| <span class="sourceLineNo">698</span> while (m < mmax && n < nmax) {<a name="line.698"></a> |
| <span class="sourceLineNo">699</span> pos[am] = m++;<a name="line.699"></a> |
| <span class="sourceLineNo">700</span> pos[an] = n++;<a name="line.700"></a> |
| <span class="sourceLineNo">701</span> ca.getDoubleArray(t, pos);<a name="line.701"></a> |
| <span class="sourceLineNo">702</span> for (int k = 0; k < is; k++) {<a name="line.702"></a> |
| <span class="sourceLineNo">703</span> s[k] += t[k];<a name="line.703"></a> |
| <span class="sourceLineNo">704</span> }<a name="line.704"></a> |
| <span class="sourceLineNo">705</span> }<a name="line.705"></a> |
| <span class="sourceLineNo">706</span> trace.setObjectAbs(i++, s);<a name="line.706"></a> |
| <span class="sourceLineNo">707</span> }<a name="line.707"></a> |
| <span class="sourceLineNo">708</span> }<a name="line.708"></a> |
| <span class="sourceLineNo">709</span> }<a name="line.709"></a> |
| <span class="sourceLineNo">710</span><a name="line.710"></a> |
| <span class="sourceLineNo">711</span> return trace;<a name="line.711"></a> |
| <span class="sourceLineNo">712</span> }<a name="line.712"></a> |
| <span class="sourceLineNo">713</span><a name="line.713"></a> |
| <span class="sourceLineNo">714</span> /**<a name="line.714"></a> |
| <span class="sourceLineNo">715</span> * Order value for norm<a name="line.715"></a> |
| <span class="sourceLineNo">716</span> */<a name="line.716"></a> |
| <span class="sourceLineNo">717</span> public enum NormOrder {<a name="line.717"></a> |
| <span class="sourceLineNo">718</span> /**<a name="line.718"></a> |
| <span class="sourceLineNo">719</span> * 2-norm for vectors and Frobenius for matrices<a name="line.719"></a> |
| <span class="sourceLineNo">720</span> */<a name="line.720"></a> |
| <span class="sourceLineNo">721</span> DEFAULT,<a name="line.721"></a> |
| <span class="sourceLineNo">722</span> /**<a name="line.722"></a> |
| <span class="sourceLineNo">723</span> * Frobenius (not allowed for vectors)<a name="line.723"></a> |
| <span class="sourceLineNo">724</span> */<a name="line.724"></a> |
| <span class="sourceLineNo">725</span> FROBENIUS,<a name="line.725"></a> |
| <span class="sourceLineNo">726</span> /**<a name="line.726"></a> |
| <span class="sourceLineNo">727</span> * Zero-order (not allowed for matrices)<a name="line.727"></a> |
| <span class="sourceLineNo">728</span> */<a name="line.728"></a> |
| <span class="sourceLineNo">729</span> ZERO,<a name="line.729"></a> |
| <span class="sourceLineNo">730</span> /**<a name="line.730"></a> |
| <span class="sourceLineNo">731</span> * Positive infinity<a name="line.731"></a> |
| <span class="sourceLineNo">732</span> */<a name="line.732"></a> |
| <span class="sourceLineNo">733</span> POS_INFINITY,<a name="line.733"></a> |
| <span class="sourceLineNo">734</span> /**<a name="line.734"></a> |
| <span class="sourceLineNo">735</span> * Negative infinity<a name="line.735"></a> |
| <span class="sourceLineNo">736</span> */<a name="line.736"></a> |
| <span class="sourceLineNo">737</span> NEG_INFINITY;<a name="line.737"></a> |
| <span class="sourceLineNo">738</span> }<a name="line.738"></a> |
| <span class="sourceLineNo">739</span><a name="line.739"></a> |
| <span class="sourceLineNo">740</span> /**<a name="line.740"></a> |
| <span class="sourceLineNo">741</span> * @param a<a name="line.741"></a> |
| <span class="sourceLineNo">742</span> * @return norm of dataset<a name="line.742"></a> |
| <span class="sourceLineNo">743</span> */<a name="line.743"></a> |
| <span class="sourceLineNo">744</span> public static double norm(Dataset a) {<a name="line.744"></a> |
| <span class="sourceLineNo">745</span> return norm(a, NormOrder.DEFAULT);<a name="line.745"></a> |
| <span class="sourceLineNo">746</span> }<a name="line.746"></a> |
| <span class="sourceLineNo">747</span><a name="line.747"></a> |
| <span class="sourceLineNo">748</span> /**<a name="line.748"></a> |
| <span class="sourceLineNo">749</span> * @param a<a name="line.749"></a> |
| <span class="sourceLineNo">750</span> * @param order<a name="line.750"></a> |
| <span class="sourceLineNo">751</span> * @return norm of dataset<a name="line.751"></a> |
| <span class="sourceLineNo">752</span> */<a name="line.752"></a> |
| <span class="sourceLineNo">753</span> public static double norm(Dataset a, NormOrder order) {<a name="line.753"></a> |
| <span class="sourceLineNo">754</span> int r = a.getRank();<a name="line.754"></a> |
| <span class="sourceLineNo">755</span> if (r == 1) {<a name="line.755"></a> |
| <span class="sourceLineNo">756</span> return vectorNorm(a, order);<a name="line.756"></a> |
| <span class="sourceLineNo">757</span> } else if (r == 2) {<a name="line.757"></a> |
| <span class="sourceLineNo">758</span> return matrixNorm(a, order);<a name="line.758"></a> |
| <span class="sourceLineNo">759</span> }<a name="line.759"></a> |
| <span class="sourceLineNo">760</span> throw new IllegalArgumentException("Rank of dataset must be one or two");<a name="line.760"></a> |
| <span class="sourceLineNo">761</span> }<a name="line.761"></a> |
| <span class="sourceLineNo">762</span><a name="line.762"></a> |
| <span class="sourceLineNo">763</span> private static double vectorNorm(Dataset a, NormOrder order) {<a name="line.763"></a> |
| <span class="sourceLineNo">764</span> double n;<a name="line.764"></a> |
| <span class="sourceLineNo">765</span> IndexIterator it;<a name="line.765"></a> |
| <span class="sourceLineNo">766</span> switch (order) {<a name="line.766"></a> |
| <span class="sourceLineNo">767</span> case FROBENIUS:<a name="line.767"></a> |
| <span class="sourceLineNo">768</span> throw new IllegalArgumentException("Not allowed for vectors");<a name="line.768"></a> |
| <span class="sourceLineNo">769</span> case NEG_INFINITY:<a name="line.769"></a> |
| <span class="sourceLineNo">770</span> case POS_INFINITY:<a name="line.770"></a> |
| <span class="sourceLineNo">771</span> it = a.getIterator();<a name="line.771"></a> |
| <span class="sourceLineNo">772</span> if (order == NormOrder.POS_INFINITY) {<a name="line.772"></a> |
| <span class="sourceLineNo">773</span> n = Double.NEGATIVE_INFINITY;<a name="line.773"></a> |
| <span class="sourceLineNo">774</span> if (a.isComplex()) {<a name="line.774"></a> |
| <span class="sourceLineNo">775</span> while (it.hasNext()) {<a name="line.775"></a> |
| <span class="sourceLineNo">776</span> double v = ((Complex) a.getObjectAbs(it.index)).abs();<a name="line.776"></a> |
| <span class="sourceLineNo">777</span> n = Math.max(n, v);<a name="line.777"></a> |
| <span class="sourceLineNo">778</span> }<a name="line.778"></a> |
| <span class="sourceLineNo">779</span> } else {<a name="line.779"></a> |
| <span class="sourceLineNo">780</span> while (it.hasNext()) {<a name="line.780"></a> |
| <span class="sourceLineNo">781</span> double v = Math.abs(a.getElementDoubleAbs(it.index));<a name="line.781"></a> |
| <span class="sourceLineNo">782</span> n = Math.max(n, v);<a name="line.782"></a> |
| <span class="sourceLineNo">783</span> }<a name="line.783"></a> |
| <span class="sourceLineNo">784</span> }<a name="line.784"></a> |
| <span class="sourceLineNo">785</span> } else {<a name="line.785"></a> |
| <span class="sourceLineNo">786</span> n = Double.POSITIVE_INFINITY;<a name="line.786"></a> |
| <span class="sourceLineNo">787</span> if (a.isComplex()) {<a name="line.787"></a> |
| <span class="sourceLineNo">788</span> while (it.hasNext()) {<a name="line.788"></a> |
| <span class="sourceLineNo">789</span> double v = ((Complex) a.getObjectAbs(it.index)).abs();<a name="line.789"></a> |
| <span class="sourceLineNo">790</span> n = Math.min(n, v);<a name="line.790"></a> |
| <span class="sourceLineNo">791</span> }<a name="line.791"></a> |
| <span class="sourceLineNo">792</span> } else {<a name="line.792"></a> |
| <span class="sourceLineNo">793</span> while (it.hasNext()) {<a name="line.793"></a> |
| <span class="sourceLineNo">794</span> double v = Math.abs(a.getElementDoubleAbs(it.index));<a name="line.794"></a> |
| <span class="sourceLineNo">795</span> n = Math.min(n, v);<a name="line.795"></a> |
| <span class="sourceLineNo">796</span> }<a name="line.796"></a> |
| <span class="sourceLineNo">797</span> }<a name="line.797"></a> |
| <span class="sourceLineNo">798</span> }<a name="line.798"></a> |
| <span class="sourceLineNo">799</span> break;<a name="line.799"></a> |
| <span class="sourceLineNo">800</span> case ZERO:<a name="line.800"></a> |
| <span class="sourceLineNo">801</span> it = a.getIterator();<a name="line.801"></a> |
| <span class="sourceLineNo">802</span> n = 0;<a name="line.802"></a> |
| <span class="sourceLineNo">803</span> if (a.isComplex()) {<a name="line.803"></a> |
| <span class="sourceLineNo">804</span> while (it.hasNext()) {<a name="line.804"></a> |
| <span class="sourceLineNo">805</span> if (!((Complex) a.getObjectAbs(it.index)).equals(Complex.ZERO))<a name="line.805"></a> |
| <span class="sourceLineNo">806</span> n++;<a name="line.806"></a> |
| <span class="sourceLineNo">807</span> }<a name="line.807"></a> |
| <span class="sourceLineNo">808</span> } else {<a name="line.808"></a> |
| <span class="sourceLineNo">809</span> while (it.hasNext()) {<a name="line.809"></a> |
| <span class="sourceLineNo">810</span> if (a.getElementBooleanAbs(it.index))<a name="line.810"></a> |
| <span class="sourceLineNo">811</span> n++;<a name="line.811"></a> |
| <span class="sourceLineNo">812</span> }<a name="line.812"></a> |
| <span class="sourceLineNo">813</span> }<a name="line.813"></a> |
| <span class="sourceLineNo">814</span> <a name="line.814"></a> |
| <span class="sourceLineNo">815</span> break;<a name="line.815"></a> |
| <span class="sourceLineNo">816</span> default:<a name="line.816"></a> |
| <span class="sourceLineNo">817</span> n = vectorNorm(a, 2);<a name="line.817"></a> |
| <span class="sourceLineNo">818</span> break;<a name="line.818"></a> |
| <span class="sourceLineNo">819</span> }<a name="line.819"></a> |
| <span class="sourceLineNo">820</span> return n;<a name="line.820"></a> |
| <span class="sourceLineNo">821</span> }<a name="line.821"></a> |
| <span class="sourceLineNo">822</span><a name="line.822"></a> |
| <span class="sourceLineNo">823</span> private static double matrixNorm(Dataset a, NormOrder order) {<a name="line.823"></a> |
| <span class="sourceLineNo">824</span> double n;<a name="line.824"></a> |
| <span class="sourceLineNo">825</span> IndexIterator it;<a name="line.825"></a> |
| <span class="sourceLineNo">826</span> switch (order) {<a name="line.826"></a> |
| <span class="sourceLineNo">827</span> case NEG_INFINITY:<a name="line.827"></a> |
| <span class="sourceLineNo">828</span> case POS_INFINITY:<a name="line.828"></a> |
| <span class="sourceLineNo">829</span> n = maxMinMatrixNorm(a, 1, order == NormOrder.POS_INFINITY);<a name="line.829"></a> |
| <span class="sourceLineNo">830</span> break;<a name="line.830"></a> |
| <span class="sourceLineNo">831</span> case ZERO:<a name="line.831"></a> |
| <span class="sourceLineNo">832</span> throw new IllegalArgumentException("Not allowed for matrices");<a name="line.832"></a> |
| <span class="sourceLineNo">833</span> default:<a name="line.833"></a> |
| <span class="sourceLineNo">834</span> case FROBENIUS:<a name="line.834"></a> |
| <span class="sourceLineNo">835</span> it = a.getIterator();<a name="line.835"></a> |
| <span class="sourceLineNo">836</span> n = 0;<a name="line.836"></a> |
| <span class="sourceLineNo">837</span> if (a.isComplex()) {<a name="line.837"></a> |
| <span class="sourceLineNo">838</span> while (it.hasNext()) {<a name="line.838"></a> |
| <span class="sourceLineNo">839</span> double v = ((Complex) a.getObjectAbs(it.index)).abs();<a name="line.839"></a> |
| <span class="sourceLineNo">840</span> n += v*v;<a name="line.840"></a> |
| <span class="sourceLineNo">841</span> }<a name="line.841"></a> |
| <span class="sourceLineNo">842</span> } else {<a name="line.842"></a> |
| <span class="sourceLineNo">843</span> while (it.hasNext()) {<a name="line.843"></a> |
| <span class="sourceLineNo">844</span> double v = a.getElementDoubleAbs(it.index);<a name="line.844"></a> |
| <span class="sourceLineNo">845</span> n += v*v;<a name="line.845"></a> |
| <span class="sourceLineNo">846</span> }<a name="line.846"></a> |
| <span class="sourceLineNo">847</span> }<a name="line.847"></a> |
| <span class="sourceLineNo">848</span> n = Math.sqrt(n);<a name="line.848"></a> |
| <span class="sourceLineNo">849</span> break;<a name="line.849"></a> |
| <span class="sourceLineNo">850</span> }<a name="line.850"></a> |
| <span class="sourceLineNo">851</span> return n;<a name="line.851"></a> |
| <span class="sourceLineNo">852</span> }<a name="line.852"></a> |
| <span class="sourceLineNo">853</span><a name="line.853"></a> |
| <span class="sourceLineNo">854</span> /**<a name="line.854"></a> |
| <span class="sourceLineNo">855</span> * @param a<a name="line.855"></a> |
| <span class="sourceLineNo">856</span> * @param p<a name="line.856"></a> |
| <span class="sourceLineNo">857</span> * @return p-norm of dataset<a name="line.857"></a> |
| <span class="sourceLineNo">858</span> */<a name="line.858"></a> |
| <span class="sourceLineNo">859</span> public static double norm(Dataset a, final double p) {<a name="line.859"></a> |
| <span class="sourceLineNo">860</span> if (p == 0) {<a name="line.860"></a> |
| <span class="sourceLineNo">861</span> return norm(a, NormOrder.ZERO);<a name="line.861"></a> |
| <span class="sourceLineNo">862</span> }<a name="line.862"></a> |
| <span class="sourceLineNo">863</span> int r = a.getRank();<a name="line.863"></a> |
| <span class="sourceLineNo">864</span> if (r == 1) {<a name="line.864"></a> |
| <span class="sourceLineNo">865</span> return vectorNorm(a, p);<a name="line.865"></a> |
| <span class="sourceLineNo">866</span> } else if (r == 2) {<a name="line.866"></a> |
| <span class="sourceLineNo">867</span> return matrixNorm(a, p);<a name="line.867"></a> |
| <span class="sourceLineNo">868</span> }<a name="line.868"></a> |
| <span class="sourceLineNo">869</span> throw new IllegalArgumentException("Rank of dataset must be one or two");<a name="line.869"></a> |
| <span class="sourceLineNo">870</span> }<a name="line.870"></a> |
| <span class="sourceLineNo">871</span><a name="line.871"></a> |
| <span class="sourceLineNo">872</span> private static double vectorNorm(Dataset a, final double p) {<a name="line.872"></a> |
| <span class="sourceLineNo">873</span> IndexIterator it = a.getIterator();<a name="line.873"></a> |
| <span class="sourceLineNo">874</span> double n = 0;<a name="line.874"></a> |
| <span class="sourceLineNo">875</span> if (a.isComplex()) {<a name="line.875"></a> |
| <span class="sourceLineNo">876</span> while (it.hasNext()) {<a name="line.876"></a> |
| <span class="sourceLineNo">877</span> double v = ((Complex) a.getObjectAbs(it.index)).abs();<a name="line.877"></a> |
| <span class="sourceLineNo">878</span> if (p == 2) {<a name="line.878"></a> |
| <span class="sourceLineNo">879</span> v *= v;<a name="line.879"></a> |
| <span class="sourceLineNo">880</span> } else if (p != 1) {<a name="line.880"></a> |
| <span class="sourceLineNo">881</span> v = Math.pow(v, p);<a name="line.881"></a> |
| <span class="sourceLineNo">882</span> }<a name="line.882"></a> |
| <span class="sourceLineNo">883</span> n += v;<a name="line.883"></a> |
| <span class="sourceLineNo">884</span> }<a name="line.884"></a> |
| <span class="sourceLineNo">885</span> } else {<a name="line.885"></a> |
| <span class="sourceLineNo">886</span> while (it.hasNext()) {<a name="line.886"></a> |
| <span class="sourceLineNo">887</span> double v = a.getElementDoubleAbs(it.index);<a name="line.887"></a> |
| <span class="sourceLineNo">888</span> if (p == 1) {<a name="line.888"></a> |
| <span class="sourceLineNo">889</span> v = Math.abs(v);<a name="line.889"></a> |
| <span class="sourceLineNo">890</span> } else if (p == 2) {<a name="line.890"></a> |
| <span class="sourceLineNo">891</span> v *= v;<a name="line.891"></a> |
| <span class="sourceLineNo">892</span> } else {<a name="line.892"></a> |
| <span class="sourceLineNo">893</span> v = Math.pow(Math.abs(v), p);<a name="line.893"></a> |
| <span class="sourceLineNo">894</span> }<a name="line.894"></a> |
| <span class="sourceLineNo">895</span> n += v;<a name="line.895"></a> |
| <span class="sourceLineNo">896</span> }<a name="line.896"></a> |
| <span class="sourceLineNo">897</span> }<a name="line.897"></a> |
| <span class="sourceLineNo">898</span> return Math.pow(n, 1./p);<a name="line.898"></a> |
| <span class="sourceLineNo">899</span> }<a name="line.899"></a> |
| <span class="sourceLineNo">900</span><a name="line.900"></a> |
| <span class="sourceLineNo">901</span> private static double matrixNorm(Dataset a, final double p) {<a name="line.901"></a> |
| <span class="sourceLineNo">902</span> double n;<a name="line.902"></a> |
| <span class="sourceLineNo">903</span> if (Math.abs(p) == 1) {<a name="line.903"></a> |
| <span class="sourceLineNo">904</span> n = maxMinMatrixNorm(a, 0, p > 0);<a name="line.904"></a> |
| <span class="sourceLineNo">905</span> } else if (Math.abs(p) == 2) {<a name="line.905"></a> |
| <span class="sourceLineNo">906</span> double[] s = calcSingularValues(a);<a name="line.906"></a> |
| <span class="sourceLineNo">907</span> n = p > 0 ? s[0] : s[s.length - 1];<a name="line.907"></a> |
| <span class="sourceLineNo">908</span> } else {<a name="line.908"></a> |
| <span class="sourceLineNo">909</span> throw new IllegalArgumentException("Order not allowed");<a name="line.909"></a> |
| <span class="sourceLineNo">910</span> }<a name="line.910"></a> |
| <span class="sourceLineNo">911</span><a name="line.911"></a> |
| <span class="sourceLineNo">912</span> return n;<a name="line.912"></a> |
| <span class="sourceLineNo">913</span> }<a name="line.913"></a> |
| <span class="sourceLineNo">914</span><a name="line.914"></a> |
| <span class="sourceLineNo">915</span> private static double maxMinMatrixNorm(Dataset a, int d, boolean max) {<a name="line.915"></a> |
| <span class="sourceLineNo">916</span> double n;<a name="line.916"></a> |
| <span class="sourceLineNo">917</span> IndexIterator it;<a name="line.917"></a> |
| <span class="sourceLineNo">918</span> int[] pos;<a name="line.918"></a> |
| <span class="sourceLineNo">919</span> int l;<a name="line.919"></a> |
| <span class="sourceLineNo">920</span> it = a.getPositionIterator(d);<a name="line.920"></a> |
| <span class="sourceLineNo">921</span> pos = it.getPos();<a name="line.921"></a> |
| <span class="sourceLineNo">922</span> l = a.getShapeRef()[d];<a name="line.922"></a> |
| <span class="sourceLineNo">923</span> if (max) {<a name="line.923"></a> |
| <span class="sourceLineNo">924</span> n = Double.NEGATIVE_INFINITY;<a name="line.924"></a> |
| <span class="sourceLineNo">925</span> if (a.isComplex()) {<a name="line.925"></a> |
| <span class="sourceLineNo">926</span> while (it.hasNext()) {<a name="line.926"></a> |
| <span class="sourceLineNo">927</span> double v = ((Complex) a.getObject(pos)).abs();<a name="line.927"></a> |
| <span class="sourceLineNo">928</span> for (int i = 1; i < l; i++) {<a name="line.928"></a> |
| <span class="sourceLineNo">929</span> pos[d] = i;<a name="line.929"></a> |
| <span class="sourceLineNo">930</span> v += ((Complex) a.getObject(pos)).abs();<a name="line.930"></a> |
| <span class="sourceLineNo">931</span> }<a name="line.931"></a> |
| <span class="sourceLineNo">932</span> pos[d] = 0;<a name="line.932"></a> |
| <span class="sourceLineNo">933</span> n = Math.max(n, v);<a name="line.933"></a> |
| <span class="sourceLineNo">934</span> }<a name="line.934"></a> |
| <span class="sourceLineNo">935</span> } else {<a name="line.935"></a> |
| <span class="sourceLineNo">936</span> while (it.hasNext()) {<a name="line.936"></a> |
| <span class="sourceLineNo">937</span> double v = Math.abs(a.getDouble(pos));<a name="line.937"></a> |
| <span class="sourceLineNo">938</span> for (int i = 1; i < l; i++) {<a name="line.938"></a> |
| <span class="sourceLineNo">939</span> pos[d] = i;<a name="line.939"></a> |
| <span class="sourceLineNo">940</span> v += Math.abs(a.getDouble(pos));<a name="line.940"></a> |
| <span class="sourceLineNo">941</span> }<a name="line.941"></a> |
| <span class="sourceLineNo">942</span> pos[d] = 0;<a name="line.942"></a> |
| <span class="sourceLineNo">943</span> n = Math.max(n, v);<a name="line.943"></a> |
| <span class="sourceLineNo">944</span> }<a name="line.944"></a> |
| <span class="sourceLineNo">945</span> }<a name="line.945"></a> |
| <span class="sourceLineNo">946</span> } else {<a name="line.946"></a> |
| <span class="sourceLineNo">947</span> n = Double.POSITIVE_INFINITY;<a name="line.947"></a> |
| <span class="sourceLineNo">948</span> if (a.isComplex()) {<a name="line.948"></a> |
| <span class="sourceLineNo">949</span> while (it.hasNext()) {<a name="line.949"></a> |
| <span class="sourceLineNo">950</span> double v = ((Complex) a.getObject(pos)).abs();<a name="line.950"></a> |
| <span class="sourceLineNo">951</span> for (int i = 1; i < l; i++) {<a name="line.951"></a> |
| <span class="sourceLineNo">952</span> pos[d] = i;<a name="line.952"></a> |
| <span class="sourceLineNo">953</span> v += ((Complex) a.getObject(pos)).abs();<a name="line.953"></a> |
| <span class="sourceLineNo">954</span> }<a name="line.954"></a> |
| <span class="sourceLineNo">955</span> pos[d] = 0;<a name="line.955"></a> |
| <span class="sourceLineNo">956</span> n = Math.min(n, v);<a name="line.956"></a> |
| <span class="sourceLineNo">957</span> }<a name="line.957"></a> |
| <span class="sourceLineNo">958</span> } else {<a name="line.958"></a> |
| <span class="sourceLineNo">959</span> while (it.hasNext()) {<a name="line.959"></a> |
| <span class="sourceLineNo">960</span> double v = Math.abs(a.getDouble(pos));<a name="line.960"></a> |
| <span class="sourceLineNo">961</span> for (int i = 1; i < l; i++) {<a name="line.961"></a> |
| <span class="sourceLineNo">962</span> pos[d] = i;<a name="line.962"></a> |
| <span class="sourceLineNo">963</span> v += Math.abs(a.getDouble(pos));<a name="line.963"></a> |
| <span class="sourceLineNo">964</span> }<a name="line.964"></a> |
| <span class="sourceLineNo">965</span> pos[d] = 0;<a name="line.965"></a> |
| <span class="sourceLineNo">966</span> n = Math.min(n, v);<a name="line.966"></a> |
| <span class="sourceLineNo">967</span> }<a name="line.967"></a> |
| <span class="sourceLineNo">968</span> }<a name="line.968"></a> |
| <span class="sourceLineNo">969</span> }<a name="line.969"></a> |
| <span class="sourceLineNo">970</span> return n;<a name="line.970"></a> |
| <span class="sourceLineNo">971</span> }<a name="line.971"></a> |
| <span class="sourceLineNo">972</span><a name="line.972"></a> |
| <span class="sourceLineNo">973</span> /**<a name="line.973"></a> |
| <span class="sourceLineNo">974</span> * @param a<a name="line.974"></a> |
| <span class="sourceLineNo">975</span> * @return array of singular values<a name="line.975"></a> |
| <span class="sourceLineNo">976</span> */<a name="line.976"></a> |
| <span class="sourceLineNo">977</span> public static double[] calcSingularValues(Dataset a) {<a name="line.977"></a> |
| <span class="sourceLineNo">978</span> SingularValueDecomposition svd = new SingularValueDecomposition(createRealMatrix(a));<a name="line.978"></a> |
| <span class="sourceLineNo">979</span> return svd.getSingularValues();<a name="line.979"></a> |
| <span class="sourceLineNo">980</span> }<a name="line.980"></a> |
| <span class="sourceLineNo">981</span><a name="line.981"></a> |
| <span class="sourceLineNo">982</span><a name="line.982"></a> |
| <span class="sourceLineNo">983</span> /**<a name="line.983"></a> |
| <span class="sourceLineNo">984</span> * Calculate singular value decomposition {@code A = U S V^T}<a name="line.984"></a> |
| <span class="sourceLineNo">985</span> * @param a<a name="line.985"></a> |
| <span class="sourceLineNo">986</span> * @return array of U - orthogonal matrix, s - singular values vector, V - orthogonal matrix<a name="line.986"></a> |
| <span class="sourceLineNo">987</span> */<a name="line.987"></a> |
| <span class="sourceLineNo">988</span> public static Dataset[] calcSingularValueDecomposition(Dataset a) {<a name="line.988"></a> |
| <span class="sourceLineNo">989</span> SingularValueDecomposition svd = new SingularValueDecomposition(createRealMatrix(a));<a name="line.989"></a> |
| <span class="sourceLineNo">990</span> return new Dataset[] {createDataset(svd.getU()), DatasetFactory.createFromObject(svd.getSingularValues()),<a name="line.990"></a> |
| <span class="sourceLineNo">991</span> createDataset(svd.getV())};<a name="line.991"></a> |
| <span class="sourceLineNo">992</span> }<a name="line.992"></a> |
| <span class="sourceLineNo">993</span><a name="line.993"></a> |
| <span class="sourceLineNo">994</span> /**<a name="line.994"></a> |
| <span class="sourceLineNo">995</span> * Calculate (Moore-Penrose) pseudo-inverse<a name="line.995"></a> |
| <span class="sourceLineNo">996</span> * @param a<a name="line.996"></a> |
| <span class="sourceLineNo">997</span> * @return pseudo-inverse<a name="line.997"></a> |
| <span class="sourceLineNo">998</span> */<a name="line.998"></a> |
| <span class="sourceLineNo">999</span> public static Dataset calcPseudoInverse(Dataset a) {<a name="line.999"></a> |
| <span class="sourceLineNo">1000</span> SingularValueDecomposition svd = new SingularValueDecomposition(createRealMatrix(a));<a name="line.1000"></a> |
| <span class="sourceLineNo">1001</span> return createDataset(svd.getSolver().getInverse());<a name="line.1001"></a> |
| <span class="sourceLineNo">1002</span> }<a name="line.1002"></a> |
| <span class="sourceLineNo">1003</span><a name="line.1003"></a> |
| <span class="sourceLineNo">1004</span> /**<a name="line.1004"></a> |
| <span class="sourceLineNo">1005</span> * Calculate matrix rank by singular value decomposition method<a name="line.1005"></a> |
| <span class="sourceLineNo">1006</span> * @param a<a name="line.1006"></a> |
| <span class="sourceLineNo">1007</span> * @return effective numerical rank of matrix<a name="line.1007"></a> |
| <span class="sourceLineNo">1008</span> */<a name="line.1008"></a> |
| <span class="sourceLineNo">1009</span> public static int calcMatrixRank(Dataset a) {<a name="line.1009"></a> |
| <span class="sourceLineNo">1010</span> SingularValueDecomposition svd = new SingularValueDecomposition(createRealMatrix(a));<a name="line.1010"></a> |
| <span class="sourceLineNo">1011</span> return svd.getRank();<a name="line.1011"></a> |
| <span class="sourceLineNo">1012</span> }<a name="line.1012"></a> |
| <span class="sourceLineNo">1013</span><a name="line.1013"></a> |
| <span class="sourceLineNo">1014</span> /**<a name="line.1014"></a> |
| <span class="sourceLineNo">1015</span> * Calculate condition number of matrix by singular value decomposition method<a name="line.1015"></a> |
| <span class="sourceLineNo">1016</span> * @param a<a name="line.1016"></a> |
| <span class="sourceLineNo">1017</span> * @return condition number<a name="line.1017"></a> |
| <span class="sourceLineNo">1018</span> */<a name="line.1018"></a> |
| <span class="sourceLineNo">1019</span> public static double calcConditionNumber(Dataset a) {<a name="line.1019"></a> |
| <span class="sourceLineNo">1020</span> SingularValueDecomposition svd = new SingularValueDecomposition(createRealMatrix(a));<a name="line.1020"></a> |
| <span class="sourceLineNo">1021</span> return svd.getConditionNumber();<a name="line.1021"></a> |
| <span class="sourceLineNo">1022</span> }<a name="line.1022"></a> |
| <span class="sourceLineNo">1023</span><a name="line.1023"></a> |
| <span class="sourceLineNo">1024</span> /**<a name="line.1024"></a> |
| <span class="sourceLineNo">1025</span> * @param a<a name="line.1025"></a> |
| <span class="sourceLineNo">1026</span> * @return determinant of dataset<a name="line.1026"></a> |
| <span class="sourceLineNo">1027</span> */<a name="line.1027"></a> |
| <span class="sourceLineNo">1028</span> public static double calcDeterminant(Dataset a) {<a name="line.1028"></a> |
| <span class="sourceLineNo">1029</span> EigenDecomposition evd = new EigenDecomposition(createRealMatrix(a));<a name="line.1029"></a> |
| <span class="sourceLineNo">1030</span> return evd.getDeterminant();<a name="line.1030"></a> |
| <span class="sourceLineNo">1031</span> }<a name="line.1031"></a> |
| <span class="sourceLineNo">1032</span><a name="line.1032"></a> |
| <span class="sourceLineNo">1033</span> /**<a name="line.1033"></a> |
| <span class="sourceLineNo">1034</span> * @param a<a name="line.1034"></a> |
| <span class="sourceLineNo">1035</span> * @return dataset of eigenvalues (can be double or complex double)<a name="line.1035"></a> |
| <span class="sourceLineNo">1036</span> */<a name="line.1036"></a> |
| <span class="sourceLineNo">1037</span> public static Dataset calcEigenvalues(Dataset a) {<a name="line.1037"></a> |
| <span class="sourceLineNo">1038</span> EigenDecomposition evd = new EigenDecomposition(createRealMatrix(a));<a name="line.1038"></a> |
| <span class="sourceLineNo">1039</span> double[] rev = evd.getRealEigenvalues();<a name="line.1039"></a> |
| <span class="sourceLineNo">1040</span><a name="line.1040"></a> |
| <span class="sourceLineNo">1041</span> if (evd.hasComplexEigenvalues()) {<a name="line.1041"></a> |
| <span class="sourceLineNo">1042</span> double[] iev = evd.getImagEigenvalues();<a name="line.1042"></a> |
| <span class="sourceLineNo">1043</span> return DatasetFactory.createComplexDataset(ComplexDoubleDataset.class, rev, iev);<a name="line.1043"></a> |
| <span class="sourceLineNo">1044</span> }<a name="line.1044"></a> |
| <span class="sourceLineNo">1045</span> return DatasetFactory.createFromObject(rev);<a name="line.1045"></a> |
| <span class="sourceLineNo">1046</span> }<a name="line.1046"></a> |
| <span class="sourceLineNo">1047</span><a name="line.1047"></a> |
| <span class="sourceLineNo">1048</span> /**<a name="line.1048"></a> |
| <span class="sourceLineNo">1049</span> * Calculate eigen-decomposition {@code A = V D V^T}<a name="line.1049"></a> |
| <span class="sourceLineNo">1050</span> * @param a<a name="line.1050"></a> |
| <span class="sourceLineNo">1051</span> * @return array of D eigenvalues (can be double or complex double) and V eigenvectors<a name="line.1051"></a> |
| <span class="sourceLineNo">1052</span> */<a name="line.1052"></a> |
| <span class="sourceLineNo">1053</span> public static Dataset[] calcEigenDecomposition(Dataset a) {<a name="line.1053"></a> |
| <span class="sourceLineNo">1054</span> EigenDecomposition evd = new EigenDecomposition(createRealMatrix(a));<a name="line.1054"></a> |
| <span class="sourceLineNo">1055</span> Dataset[] results = new Dataset[2];<a name="line.1055"></a> |
| <span class="sourceLineNo">1056</span><a name="line.1056"></a> |
| <span class="sourceLineNo">1057</span> double[] rev = evd.getRealEigenvalues();<a name="line.1057"></a> |
| <span class="sourceLineNo">1058</span> if (evd.hasComplexEigenvalues()) {<a name="line.1058"></a> |
| <span class="sourceLineNo">1059</span> double[] iev = evd.getImagEigenvalues();<a name="line.1059"></a> |
| <span class="sourceLineNo">1060</span> results[0] = DatasetFactory.createComplexDataset(ComplexDoubleDataset.class, rev, iev);<a name="line.1060"></a> |
| <span class="sourceLineNo">1061</span> } else {<a name="line.1061"></a> |
| <span class="sourceLineNo">1062</span> results[0] = DatasetFactory.createFromObject(rev);<a name="line.1062"></a> |
| <span class="sourceLineNo">1063</span> }<a name="line.1063"></a> |
| <span class="sourceLineNo">1064</span> results[1] = createDataset(evd.getV());<a name="line.1064"></a> |
| <span class="sourceLineNo">1065</span> return results;<a name="line.1065"></a> |
| <span class="sourceLineNo">1066</span> }<a name="line.1066"></a> |
| <span class="sourceLineNo">1067</span><a name="line.1067"></a> |
| <span class="sourceLineNo">1068</span> /**<a name="line.1068"></a> |
| <span class="sourceLineNo">1069</span> * Calculate QR decomposition {@code A = Q R}<a name="line.1069"></a> |
| <span class="sourceLineNo">1070</span> * @param a<a name="line.1070"></a> |
| <span class="sourceLineNo">1071</span> * @return array of Q and R<a name="line.1071"></a> |
| <span class="sourceLineNo">1072</span> */<a name="line.1072"></a> |
| <span class="sourceLineNo">1073</span> public static Dataset[] calcQRDecomposition(Dataset a) {<a name="line.1073"></a> |
| <span class="sourceLineNo">1074</span> QRDecomposition qrd = new QRDecomposition(createRealMatrix(a));<a name="line.1074"></a> |
| <span class="sourceLineNo">1075</span> return new Dataset[] {createDataset(qrd.getQT()).getTransposedView(), createDataset(qrd.getR())};<a name="line.1075"></a> |
| <span class="sourceLineNo">1076</span> }<a name="line.1076"></a> |
| <span class="sourceLineNo">1077</span><a name="line.1077"></a> |
| <span class="sourceLineNo">1078</span> /**<a name="line.1078"></a> |
| <span class="sourceLineNo">1079</span> * Calculate LU decomposition {@code A = P^-1 L U}<a name="line.1079"></a> |
| <span class="sourceLineNo">1080</span> * @param a<a name="line.1080"></a> |
| <span class="sourceLineNo">1081</span> * @return array of L, U and P<a name="line.1081"></a> |
| <span class="sourceLineNo">1082</span> */<a name="line.1082"></a> |
| <span class="sourceLineNo">1083</span> public static Dataset[] calcLUDecomposition(Dataset a) {<a name="line.1083"></a> |
| <span class="sourceLineNo">1084</span> LUDecomposition lud = new LUDecomposition(createRealMatrix(a));<a name="line.1084"></a> |
| <span class="sourceLineNo">1085</span> return new Dataset[] {createDataset(lud.getL()), createDataset(lud.getU()),<a name="line.1085"></a> |
| <span class="sourceLineNo">1086</span> createDataset(lud.getP())};<a name="line.1086"></a> |
| <span class="sourceLineNo">1087</span> }<a name="line.1087"></a> |
| <span class="sourceLineNo">1088</span><a name="line.1088"></a> |
| <span class="sourceLineNo">1089</span> /**<a name="line.1089"></a> |
| <span class="sourceLineNo">1090</span> * Calculate inverse of square dataset<a name="line.1090"></a> |
| <span class="sourceLineNo">1091</span> * @param a<a name="line.1091"></a> |
| <span class="sourceLineNo">1092</span> * @return inverse<a name="line.1092"></a> |
| <span class="sourceLineNo">1093</span> */<a name="line.1093"></a> |
| <span class="sourceLineNo">1094</span> public static Dataset calcInverse(Dataset a) {<a name="line.1094"></a> |
| <span class="sourceLineNo">1095</span> LUDecomposition lud = new LUDecomposition(createRealMatrix(a));<a name="line.1095"></a> |
| <span class="sourceLineNo">1096</span> return createDataset(lud.getSolver().getInverse());<a name="line.1096"></a> |
| <span class="sourceLineNo">1097</span> }<a name="line.1097"></a> |
| <span class="sourceLineNo">1098</span><a name="line.1098"></a> |
| <span class="sourceLineNo">1099</span> /**<a name="line.1099"></a> |
| <span class="sourceLineNo">1100</span> * Solve linear matrix equation {@code A x = v}<a name="line.1100"></a> |
| <span class="sourceLineNo">1101</span> * @param a<a name="line.1101"></a> |
| <span class="sourceLineNo">1102</span> * @param v<a name="line.1102"></a> |
| <span class="sourceLineNo">1103</span> * @return x<a name="line.1103"></a> |
| <span class="sourceLineNo">1104</span> */<a name="line.1104"></a> |
| <span class="sourceLineNo">1105</span> public static Dataset solve(Dataset a, Dataset v) {<a name="line.1105"></a> |
| <span class="sourceLineNo">1106</span> LUDecomposition lud = new LUDecomposition(createRealMatrix(a));<a name="line.1106"></a> |
| <span class="sourceLineNo">1107</span> if (v.getRank() == 1) {<a name="line.1107"></a> |
| <span class="sourceLineNo">1108</span> RealVector x = createRealVector(v);<a name="line.1108"></a> |
| <span class="sourceLineNo">1109</span> return createDataset(lud.getSolver().solve(x));<a name="line.1109"></a> |
| <span class="sourceLineNo">1110</span> }<a name="line.1110"></a> |
| <span class="sourceLineNo">1111</span> RealMatrix x = createRealMatrix(v);<a name="line.1111"></a> |
| <span class="sourceLineNo">1112</span> return createDataset(lud.getSolver().solve(x));<a name="line.1112"></a> |
| <span class="sourceLineNo">1113</span> }<a name="line.1113"></a> |
| <span class="sourceLineNo">1114</span><a name="line.1114"></a> |
| <span class="sourceLineNo">1115</span> <a name="line.1115"></a> |
| <span class="sourceLineNo">1116</span> /**<a name="line.1116"></a> |
| <span class="sourceLineNo">1117</span> * Solve least squares matrix equation {@code A x = v} by SVD<a name="line.1117"></a> |
| <span class="sourceLineNo">1118</span> * @param a<a name="line.1118"></a> |
| <span class="sourceLineNo">1119</span> * @param v<a name="line.1119"></a> |
| <span class="sourceLineNo">1120</span> * @return x<a name="line.1120"></a> |
| <span class="sourceLineNo">1121</span> */<a name="line.1121"></a> |
| <span class="sourceLineNo">1122</span> public static Dataset solveSVD(Dataset a, Dataset v) {<a name="line.1122"></a> |
| <span class="sourceLineNo">1123</span> SingularValueDecomposition svd = new SingularValueDecomposition(createRealMatrix(a));<a name="line.1123"></a> |
| <span class="sourceLineNo">1124</span> if (v.getRank() == 1) {<a name="line.1124"></a> |
| <span class="sourceLineNo">1125</span> RealVector x = createRealVector(v);<a name="line.1125"></a> |
| <span class="sourceLineNo">1126</span> return createDataset(svd.getSolver().solve(x));<a name="line.1126"></a> |
| <span class="sourceLineNo">1127</span> }<a name="line.1127"></a> |
| <span class="sourceLineNo">1128</span> RealMatrix x = createRealMatrix(v);<a name="line.1128"></a> |
| <span class="sourceLineNo">1129</span> return createDataset(svd.getSolver().solve(x));<a name="line.1129"></a> |
| <span class="sourceLineNo">1130</span> }<a name="line.1130"></a> |
| <span class="sourceLineNo">1131</span> <a name="line.1131"></a> |
| <span class="sourceLineNo">1132</span> /**<a name="line.1132"></a> |
| <span class="sourceLineNo">1133</span> * Calculate Cholesky decomposition {@code A = L L^T}<a name="line.1133"></a> |
| <span class="sourceLineNo">1134</span> * @param a<a name="line.1134"></a> |
| <span class="sourceLineNo">1135</span> * @return L<a name="line.1135"></a> |
| <span class="sourceLineNo">1136</span> */<a name="line.1136"></a> |
| <span class="sourceLineNo">1137</span> public static Dataset calcCholeskyDecomposition(Dataset a) {<a name="line.1137"></a> |
| <span class="sourceLineNo">1138</span> CholeskyDecomposition cd = new CholeskyDecomposition(createRealMatrix(a));<a name="line.1138"></a> |
| <span class="sourceLineNo">1139</span> return createDataset(cd.getL());<a name="line.1139"></a> |
| <span class="sourceLineNo">1140</span> }<a name="line.1140"></a> |
| <span class="sourceLineNo">1141</span><a name="line.1141"></a> |
| <span class="sourceLineNo">1142</span> /**<a name="line.1142"></a> |
| <span class="sourceLineNo">1143</span> * Calculation {@code A x = v} by conjugate gradient method with the stopping criterion being<a name="line.1143"></a> |
| <span class="sourceLineNo">1144</span> * that the estimated residual {@code r = v - A x} satisfies {@code ||r|| < ||v||} with maximum of 100 iterations<a name="line.1144"></a> |
| <span class="sourceLineNo">1145</span> * @param a<a name="line.1145"></a> |
| <span class="sourceLineNo">1146</span> * @param v<a name="line.1146"></a> |
| <span class="sourceLineNo">1147</span> * @return value of {@code A^-1 v} by conjugate gradient method<a name="line.1147"></a> |
| <span class="sourceLineNo">1148</span> */<a name="line.1148"></a> |
| <span class="sourceLineNo">1149</span> public static Dataset calcConjugateGradient(Dataset a, Dataset v) {<a name="line.1149"></a> |
| <span class="sourceLineNo">1150</span> return calcConjugateGradient(a, v, 100, 1);<a name="line.1150"></a> |
| <span class="sourceLineNo">1151</span> }<a name="line.1151"></a> |
| <span class="sourceLineNo">1152</span><a name="line.1152"></a> |
| <span class="sourceLineNo">1153</span> /**<a name="line.1153"></a> |
| <span class="sourceLineNo">1154</span> * Calculation {@code A x = v} by conjugate gradient method with the stopping criterion being<a name="line.1154"></a> |
| <span class="sourceLineNo">1155</span> * that the estimated residual {@code r = v - A x} satisfies {@code ||r|| < delta ||v||}<a name="line.1155"></a> |
| <span class="sourceLineNo">1156</span> * @param a<a name="line.1156"></a> |
| <span class="sourceLineNo">1157</span> * @param v<a name="line.1157"></a> |
| <span class="sourceLineNo">1158</span> * @param maxIterations<a name="line.1158"></a> |
| <span class="sourceLineNo">1159</span> * @param delta parameter used by stopping criterion<a name="line.1159"></a> |
| <span class="sourceLineNo">1160</span> * @return value of {@code A^-1 v} by conjugate gradient method<a name="line.1160"></a> |
| <span class="sourceLineNo">1161</span> */<a name="line.1161"></a> |
| <span class="sourceLineNo">1162</span> public static Dataset calcConjugateGradient(Dataset a, Dataset v, int maxIterations, double delta) {<a name="line.1162"></a> |
| <span class="sourceLineNo">1163</span> ConjugateGradient cg = new ConjugateGradient(maxIterations, delta, false);<a name="line.1163"></a> |
| <span class="sourceLineNo">1164</span> return createDataset(cg.solve((RealLinearOperator) createRealMatrix(a), createRealVector(v)));<a name="line.1164"></a> |
| <span class="sourceLineNo">1165</span> }<a name="line.1165"></a> |
| <span class="sourceLineNo">1166</span><a name="line.1166"></a> |
| <span class="sourceLineNo">1167</span> private static RealMatrix createRealMatrix(Dataset a) {<a name="line.1167"></a> |
| <span class="sourceLineNo">1168</span> if (a.getRank() != 2) {<a name="line.1168"></a> |
| <span class="sourceLineNo">1169</span> throw new IllegalArgumentException("Dataset must be rank 2");<a name="line.1169"></a> |
| <span class="sourceLineNo">1170</span> }<a name="line.1170"></a> |
| <span class="sourceLineNo">1171</span> int[] shape = a.getShapeRef();<a name="line.1171"></a> |
| <span class="sourceLineNo">1172</span> IndexIterator it = a.getIterator(true);<a name="line.1172"></a> |
| <span class="sourceLineNo">1173</span> int[] pos = it.getPos();<a name="line.1173"></a> |
| <span class="sourceLineNo">1174</span> RealMatrix m = MatrixUtils.createRealMatrix(shape[0], shape[1]);<a name="line.1174"></a> |
| <span class="sourceLineNo">1175</span> while (it.hasNext()) {<a name="line.1175"></a> |
| <span class="sourceLineNo">1176</span> m.setEntry(pos[0], pos[1], a.getElementDoubleAbs(it.index));<a name="line.1176"></a> |
| <span class="sourceLineNo">1177</span> }<a name="line.1177"></a> |
| <span class="sourceLineNo">1178</span> return m;<a name="line.1178"></a> |
| <span class="sourceLineNo">1179</span> }<a name="line.1179"></a> |
| <span class="sourceLineNo">1180</span><a name="line.1180"></a> |
| <span class="sourceLineNo">1181</span> private static RealVector createRealVector(Dataset a) {<a name="line.1181"></a> |
| <span class="sourceLineNo">1182</span> if (a.getRank() != 1) {<a name="line.1182"></a> |
| <span class="sourceLineNo">1183</span> throw new IllegalArgumentException("Dataset must be rank 1");<a name="line.1183"></a> |
| <span class="sourceLineNo">1184</span> }<a name="line.1184"></a> |
| <span class="sourceLineNo">1185</span> int size = a.getSize();<a name="line.1185"></a> |
| <span class="sourceLineNo">1186</span> IndexIterator it = a.getIterator(true);<a name="line.1186"></a> |
| <span class="sourceLineNo">1187</span> int[] pos = it.getPos();<a name="line.1187"></a> |
| <span class="sourceLineNo">1188</span> RealVector m = new ArrayRealVector(size);<a name="line.1188"></a> |
| <span class="sourceLineNo">1189</span> while (it.hasNext()) {<a name="line.1189"></a> |
| <span class="sourceLineNo">1190</span> m.setEntry(pos[0], a.getElementDoubleAbs(it.index));<a name="line.1190"></a> |
| <span class="sourceLineNo">1191</span> }<a name="line.1191"></a> |
| <span class="sourceLineNo">1192</span> return m;<a name="line.1192"></a> |
| <span class="sourceLineNo">1193</span> }<a name="line.1193"></a> |
| <span class="sourceLineNo">1194</span><a name="line.1194"></a> |
| <span class="sourceLineNo">1195</span> private static Dataset createDataset(RealVector v) {<a name="line.1195"></a> |
| <span class="sourceLineNo">1196</span> DoubleDataset r = DatasetFactory.zeros(DoubleDataset.class, v.getDimension());<a name="line.1196"></a> |
| <span class="sourceLineNo">1197</span> int size = r.getSize();<a name="line.1197"></a> |
| <span class="sourceLineNo">1198</span> if (v instanceof ArrayRealVector) {<a name="line.1198"></a> |
| <span class="sourceLineNo">1199</span> double[] data = ((ArrayRealVector) v).getDataRef();<a name="line.1199"></a> |
| <span class="sourceLineNo">1200</span> for (int i = 0; i < size; i++) {<a name="line.1200"></a> |
| <span class="sourceLineNo">1201</span> r.setAbs(i, data[i]);<a name="line.1201"></a> |
| <span class="sourceLineNo">1202</span> }<a name="line.1202"></a> |
| <span class="sourceLineNo">1203</span> } else {<a name="line.1203"></a> |
| <span class="sourceLineNo">1204</span> for (int i = 0; i < size; i++) {<a name="line.1204"></a> |
| <span class="sourceLineNo">1205</span> r.setAbs(i, v.getEntry(i));<a name="line.1205"></a> |
| <span class="sourceLineNo">1206</span> }<a name="line.1206"></a> |
| <span class="sourceLineNo">1207</span> }<a name="line.1207"></a> |
| <span class="sourceLineNo">1208</span> return r;<a name="line.1208"></a> |
| <span class="sourceLineNo">1209</span> }<a name="line.1209"></a> |
| <span class="sourceLineNo">1210</span><a name="line.1210"></a> |
| <span class="sourceLineNo">1211</span> private static Dataset createDataset(RealMatrix m) {<a name="line.1211"></a> |
| <span class="sourceLineNo">1212</span> DoubleDataset r = DatasetFactory.zeros(DoubleDataset.class, m.getRowDimension(), m.getColumnDimension());<a name="line.1212"></a> |
| <span class="sourceLineNo">1213</span> if (m instanceof Array2DRowRealMatrix) {<a name="line.1213"></a> |
| <span class="sourceLineNo">1214</span> double[][] data = ((Array2DRowRealMatrix) m).getDataRef();<a name="line.1214"></a> |
| <span class="sourceLineNo">1215</span> IndexIterator it = r.getIterator(true);<a name="line.1215"></a> |
| <span class="sourceLineNo">1216</span> int[] pos = it.getPos();<a name="line.1216"></a> |
| <span class="sourceLineNo">1217</span> while (it.hasNext()) {<a name="line.1217"></a> |
| <span class="sourceLineNo">1218</span> r.setAbs(it.index, data[pos[0]][pos[1]]);<a name="line.1218"></a> |
| <span class="sourceLineNo">1219</span> }<a name="line.1219"></a> |
| <span class="sourceLineNo">1220</span> } else {<a name="line.1220"></a> |
| <span class="sourceLineNo">1221</span> IndexIterator it = r.getIterator(true);<a name="line.1221"></a> |
| <span class="sourceLineNo">1222</span> int[] pos = it.getPos();<a name="line.1222"></a> |
| <span class="sourceLineNo">1223</span> while (it.hasNext()) {<a name="line.1223"></a> |
| <span class="sourceLineNo">1224</span> r.setAbs(it.index, m.getEntry(pos[0], pos[1]));<a name="line.1224"></a> |
| <span class="sourceLineNo">1225</span> }<a name="line.1225"></a> |
| <span class="sourceLineNo">1226</span> }<a name="line.1226"></a> |
| <span class="sourceLineNo">1227</span> return r;<a name="line.1227"></a> |
| <span class="sourceLineNo">1228</span> }<a name="line.1228"></a> |
| <span class="sourceLineNo">1229</span>}<a name="line.1229"></a> |
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| </pre> |
| </div> |
| </body> |
| </html> |
