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| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.transform;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import java.io.Serializable;<a name="line.19"></a> <FONT color="green">020</FONT> import java.lang.reflect.Array;<a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.FunctionEvaluationException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.complex.Complex;<a name="line.25"></a> <FONT color="green">026</FONT> <a name="line.26"></a> <FONT color="green">027</FONT> /**<a name="line.27"></a> <FONT color="green">028</FONT> * Implements the <a href="http://mathworld.wolfram.com/FastFourierTransform.html"><a name="line.28"></a> <FONT color="green">029</FONT> * Fast Fourier Transform</a> for transformation of one-dimensional data sets.<a name="line.29"></a> <FONT color="green">030</FONT> * For reference, see <b>Applied Numerical Linear Algebra</b>, ISBN 0898713897,<a name="line.30"></a> <FONT color="green">031</FONT> * chapter 6.<a name="line.31"></a> <FONT color="green">032</FONT> * <p><a name="line.32"></a> <FONT color="green">033</FONT> * There are several conventions for the definition of FFT and inverse FFT,<a name="line.33"></a> <FONT color="green">034</FONT> * mainly on different coefficient and exponent. Here the equations are listed<a name="line.34"></a> <FONT color="green">035</FONT> * in the comments of the corresponding methods.</p><a name="line.35"></a> <FONT color="green">036</FONT> * <p><a name="line.36"></a> <FONT color="green">037</FONT> * We require the length of data set to be power of 2, this greatly simplifies<a name="line.37"></a> <FONT color="green">038</FONT> * and speeds up the code. Users can pad the data with zeros to meet this<a name="line.38"></a> <FONT color="green">039</FONT> * requirement. There are other flavors of FFT, for reference, see S. Winograd,<a name="line.39"></a> <FONT color="green">040</FONT> * <i>On computing the discrete Fourier transform</i>, Mathematics of Computation,<a name="line.40"></a> <FONT color="green">041</FONT> * 32 (1978), 175 - 199.</p><a name="line.41"></a> <FONT color="green">042</FONT> *<a name="line.42"></a> <FONT color="green">043</FONT> * @version $Revision: 885278 $ $Date: 2009-11-29 16:47:51 -0500 (Sun, 29 Nov 2009) $<a name="line.43"></a> <FONT color="green">044</FONT> * @since 1.2<a name="line.44"></a> <FONT color="green">045</FONT> */<a name="line.45"></a> <FONT color="green">046</FONT> public class FastFourierTransformer implements Serializable {<a name="line.46"></a> <FONT color="green">047</FONT> <a name="line.47"></a> <FONT color="green">048</FONT> /** Serializable version identifier. */<a name="line.48"></a> <FONT color="green">049</FONT> static final long serialVersionUID = 5138259215438106000L;<a name="line.49"></a> <FONT color="green">050</FONT> <a name="line.50"></a> <FONT color="green">051</FONT> /** Message for not power of 2. */<a name="line.51"></a> <FONT color="green">052</FONT> private static final String NOT_POWER_OF_TWO_MESSAGE =<a name="line.52"></a> <FONT color="green">053</FONT> "{0} is not a power of 2, consider padding for fix";<a name="line.53"></a> <FONT color="green">054</FONT> <a name="line.54"></a> <FONT color="green">055</FONT> /** Message for dimension mismatch. */<a name="line.55"></a> <FONT color="green">056</FONT> private static final String DIMENSION_MISMATCH_MESSAGE =<a name="line.56"></a> <FONT color="green">057</FONT> "some dimensions don't match: {0} != {1}";<a name="line.57"></a> <FONT color="green">058</FONT> <a name="line.58"></a> <FONT color="green">059</FONT> /** Message for not computed roots of unity. */<a name="line.59"></a> <FONT color="green">060</FONT> private static final String MISSING_ROOTS_OF_UNITY_MESSAGE =<a name="line.60"></a> <FONT color="green">061</FONT> "roots of unity have not been computed yet";<a name="line.61"></a> <FONT color="green">062</FONT> <a name="line.62"></a> <FONT color="green">063</FONT> /** Message for out of range root index. */<a name="line.63"></a> <FONT color="green">064</FONT> private static final String OUT_OF_RANGE_ROOT_INDEX_MESSAGE =<a name="line.64"></a> <FONT color="green">065</FONT> "out of range root of unity index {0} (must be in [{1};{2}])";<a name="line.65"></a> <FONT color="green">066</FONT> <a name="line.66"></a> <FONT color="green">067</FONT> /** roots of unity */<a name="line.67"></a> <FONT color="green">068</FONT> private RootsOfUnity roots = new RootsOfUnity();<a name="line.68"></a> <FONT color="green">069</FONT> <a name="line.69"></a> <FONT color="green">070</FONT> /**<a name="line.70"></a> <FONT color="green">071</FONT> * Construct a default transformer.<a name="line.71"></a> <FONT color="green">072</FONT> */<a name="line.72"></a> <FONT color="green">073</FONT> public FastFourierTransformer() {<a name="line.73"></a> <FONT color="green">074</FONT> super();<a name="line.74"></a> <FONT color="green">075</FONT> }<a name="line.75"></a> <FONT color="green">076</FONT> <a name="line.76"></a> <FONT color="green">077</FONT> /**<a name="line.77"></a> <FONT color="green">078</FONT> * Transform the given real data set.<a name="line.78"></a> <FONT color="green">079</FONT> * <p><a name="line.79"></a> <FONT color="green">080</FONT> * The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $<a name="line.80"></a> <FONT color="green">081</FONT> * </p><a name="line.81"></a> <FONT color="green">082</FONT> *<a name="line.82"></a> <FONT color="green">083</FONT> * @param f the real data array to be transformed<a name="line.83"></a> <FONT color="green">084</FONT> * @return the complex transformed array<a name="line.84"></a> <FONT color="green">085</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.85"></a> <FONT color="green">086</FONT> */<a name="line.86"></a> <FONT color="green">087</FONT> public Complex[] transform(double f[])<a name="line.87"></a> <FONT color="green">088</FONT> throws IllegalArgumentException {<a name="line.88"></a> <FONT color="green">089</FONT> return fft(f, false);<a name="line.89"></a> <FONT color="green">090</FONT> }<a name="line.90"></a> <FONT color="green">091</FONT> <a name="line.91"></a> <FONT color="green">092</FONT> /**<a name="line.92"></a> <FONT color="green">093</FONT> * Transform the given real function, sampled on the given interval.<a name="line.93"></a> <FONT color="green">094</FONT> * <p><a name="line.94"></a> <FONT color="green">095</FONT> * The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $<a name="line.95"></a> <FONT color="green">096</FONT> * </p><a name="line.96"></a> <FONT color="green">097</FONT> *<a name="line.97"></a> <FONT color="green">098</FONT> * @param f the function to be sampled and transformed<a name="line.98"></a> <FONT color="green">099</FONT> * @param min the lower bound for the interval<a name="line.99"></a> <FONT color="green">100</FONT> * @param max the upper bound for the interval<a name="line.100"></a> <FONT color="green">101</FONT> * @param n the number of sample points<a name="line.101"></a> <FONT color="green">102</FONT> * @return the complex transformed array<a name="line.102"></a> <FONT color="green">103</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.103"></a> <FONT color="green">104</FONT> * at some point<a name="line.104"></a> <FONT color="green">105</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.105"></a> <FONT color="green">106</FONT> */<a name="line.106"></a> <FONT color="green">107</FONT> public Complex[] transform(UnivariateRealFunction f,<a name="line.107"></a> <FONT color="green">108</FONT> double min, double max, int n)<a name="line.108"></a> <FONT color="green">109</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.109"></a> <FONT color="green">110</FONT> double data[] = sample(f, min, max, n);<a name="line.110"></a> <FONT color="green">111</FONT> return fft(data, false);<a name="line.111"></a> <FONT color="green">112</FONT> }<a name="line.112"></a> <FONT color="green">113</FONT> <a name="line.113"></a> <FONT color="green">114</FONT> /**<a name="line.114"></a> <FONT color="green">115</FONT> * Transform the given complex data set.<a name="line.115"></a> <FONT color="green">116</FONT> * <p><a name="line.116"></a> <FONT color="green">117</FONT> * The formula is $ y_n = \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k $<a name="line.117"></a> <FONT color="green">118</FONT> * </p><a name="line.118"></a> <FONT color="green">119</FONT> *<a name="line.119"></a> <FONT color="green">120</FONT> * @param f the complex data array to be transformed<a name="line.120"></a> <FONT color="green">121</FONT> * @return the complex transformed array<a name="line.121"></a> <FONT color="green">122</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.122"></a> <FONT color="green">123</FONT> */<a name="line.123"></a> <FONT color="green">124</FONT> public Complex[] transform(Complex f[])<a name="line.124"></a> <FONT color="green">125</FONT> throws IllegalArgumentException {<a name="line.125"></a> <FONT color="green">126</FONT> roots.computeOmega(f.length);<a name="line.126"></a> <FONT color="green">127</FONT> return fft(f);<a name="line.127"></a> <FONT color="green">128</FONT> }<a name="line.128"></a> <FONT color="green">129</FONT> <a name="line.129"></a> <FONT color="green">130</FONT> /**<a name="line.130"></a> <FONT color="green">131</FONT> * Transform the given real data set.<a name="line.131"></a> <FONT color="green">132</FONT> * <p><a name="line.132"></a> <FONT color="green">133</FONT> * The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$<a name="line.133"></a> <FONT color="green">134</FONT> * </p><a name="line.134"></a> <FONT color="green">135</FONT> *<a name="line.135"></a> <FONT color="green">136</FONT> * @param f the real data array to be transformed<a name="line.136"></a> <FONT color="green">137</FONT> * @return the complex transformed array<a name="line.137"></a> <FONT color="green">138</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.138"></a> <FONT color="green">139</FONT> */<a name="line.139"></a> <FONT color="green">140</FONT> public Complex[] transform2(double f[])<a name="line.140"></a> <FONT color="green">141</FONT> throws IllegalArgumentException {<a name="line.141"></a> <FONT color="green">142</FONT> <a name="line.142"></a> <FONT color="green">143</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.143"></a> <FONT color="green">144</FONT> return scaleArray(fft(f, false), scaling_coefficient);<a name="line.144"></a> <FONT color="green">145</FONT> }<a name="line.145"></a> <FONT color="green">146</FONT> <a name="line.146"></a> <FONT color="green">147</FONT> /**<a name="line.147"></a> <FONT color="green">148</FONT> * Transform the given real function, sampled on the given interval.<a name="line.148"></a> <FONT color="green">149</FONT> * <p><a name="line.149"></a> <FONT color="green">150</FONT> * The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$<a name="line.150"></a> <FONT color="green">151</FONT> * </p><a name="line.151"></a> <FONT color="green">152</FONT> *<a name="line.152"></a> <FONT color="green">153</FONT> * @param f the function to be sampled and transformed<a name="line.153"></a> <FONT color="green">154</FONT> * @param min the lower bound for the interval<a name="line.154"></a> <FONT color="green">155</FONT> * @param max the upper bound for the interval<a name="line.155"></a> <FONT color="green">156</FONT> * @param n the number of sample points<a name="line.156"></a> <FONT color="green">157</FONT> * @return the complex transformed array<a name="line.157"></a> <FONT color="green">158</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.158"></a> <FONT color="green">159</FONT> * at some point<a name="line.159"></a> <FONT color="green">160</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.160"></a> <FONT color="green">161</FONT> */<a name="line.161"></a> <FONT color="green">162</FONT> public Complex[] transform2(UnivariateRealFunction f,<a name="line.162"></a> <FONT color="green">163</FONT> double min, double max, int n)<a name="line.163"></a> <FONT color="green">164</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.164"></a> <FONT color="green">165</FONT> <a name="line.165"></a> <FONT color="green">166</FONT> double data[] = sample(f, min, max, n);<a name="line.166"></a> <FONT color="green">167</FONT> double scaling_coefficient = 1.0 / Math.sqrt(n);<a name="line.167"></a> <FONT color="green">168</FONT> return scaleArray(fft(data, false), scaling_coefficient);<a name="line.168"></a> <FONT color="green">169</FONT> }<a name="line.169"></a> <FONT color="green">170</FONT> <a name="line.170"></a> <FONT color="green">171</FONT> /**<a name="line.171"></a> <FONT color="green">172</FONT> * Transform the given complex data set.<a name="line.172"></a> <FONT color="green">173</FONT> * <p><a name="line.173"></a> <FONT color="green">174</FONT> * The formula is $y_n = (1/\sqrt{N}) \Sigma_{k=0}^{N-1} e^{-2 \pi i nk/N} x_k$<a name="line.174"></a> <FONT color="green">175</FONT> * </p><a name="line.175"></a> <FONT color="green">176</FONT> *<a name="line.176"></a> <FONT color="green">177</FONT> * @param f the complex data array to be transformed<a name="line.177"></a> <FONT color="green">178</FONT> * @return the complex transformed array<a name="line.178"></a> <FONT color="green">179</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.179"></a> <FONT color="green">180</FONT> */<a name="line.180"></a> <FONT color="green">181</FONT> public Complex[] transform2(Complex f[])<a name="line.181"></a> <FONT color="green">182</FONT> throws IllegalArgumentException {<a name="line.182"></a> <FONT color="green">183</FONT> <a name="line.183"></a> <FONT color="green">184</FONT> roots.computeOmega(f.length);<a name="line.184"></a> <FONT color="green">185</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.185"></a> <FONT color="green">186</FONT> return scaleArray(fft(f), scaling_coefficient);<a name="line.186"></a> <FONT color="green">187</FONT> }<a name="line.187"></a> <FONT color="green">188</FONT> <a name="line.188"></a> <FONT color="green">189</FONT> /**<a name="line.189"></a> <FONT color="green">190</FONT> * Inversely transform the given real data set.<a name="line.190"></a> <FONT color="green">191</FONT> * <p><a name="line.191"></a> <FONT color="green">192</FONT> * The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $<a name="line.192"></a> <FONT color="green">193</FONT> * </p><a name="line.193"></a> <FONT color="green">194</FONT> *<a name="line.194"></a> <FONT color="green">195</FONT> * @param f the real data array to be inversely transformed<a name="line.195"></a> <FONT color="green">196</FONT> * @return the complex inversely transformed array<a name="line.196"></a> <FONT color="green">197</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.197"></a> <FONT color="green">198</FONT> */<a name="line.198"></a> <FONT color="green">199</FONT> public Complex[] inversetransform(double f[])<a name="line.199"></a> <FONT color="green">200</FONT> throws IllegalArgumentException {<a name="line.200"></a> <FONT color="green">201</FONT> <a name="line.201"></a> <FONT color="green">202</FONT> double scaling_coefficient = 1.0 / f.length;<a name="line.202"></a> <FONT color="green">203</FONT> return scaleArray(fft(f, true), scaling_coefficient);<a name="line.203"></a> <FONT color="green">204</FONT> }<a name="line.204"></a> <FONT color="green">205</FONT> <a name="line.205"></a> <FONT color="green">206</FONT> /**<a name="line.206"></a> <FONT color="green">207</FONT> * Inversely transform the given real function, sampled on the given interval.<a name="line.207"></a> <FONT color="green">208</FONT> * <p><a name="line.208"></a> <FONT color="green">209</FONT> * The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $<a name="line.209"></a> <FONT color="green">210</FONT> * </p><a name="line.210"></a> <FONT color="green">211</FONT> *<a name="line.211"></a> <FONT color="green">212</FONT> * @param f the function to be sampled and inversely transformed<a name="line.212"></a> <FONT color="green">213</FONT> * @param min the lower bound for the interval<a name="line.213"></a> <FONT color="green">214</FONT> * @param max the upper bound for the interval<a name="line.214"></a> <FONT color="green">215</FONT> * @param n the number of sample points<a name="line.215"></a> <FONT color="green">216</FONT> * @return the complex inversely transformed array<a name="line.216"></a> <FONT color="green">217</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.217"></a> <FONT color="green">218</FONT> * at some point<a name="line.218"></a> <FONT color="green">219</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.219"></a> <FONT color="green">220</FONT> */<a name="line.220"></a> <FONT color="green">221</FONT> public Complex[] inversetransform(UnivariateRealFunction f,<a name="line.221"></a> <FONT color="green">222</FONT> double min, double max, int n)<a name="line.222"></a> <FONT color="green">223</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.223"></a> <FONT color="green">224</FONT> <a name="line.224"></a> <FONT color="green">225</FONT> double data[] = sample(f, min, max, n);<a name="line.225"></a> <FONT color="green">226</FONT> double scaling_coefficient = 1.0 / n;<a name="line.226"></a> <FONT color="green">227</FONT> return scaleArray(fft(data, true), scaling_coefficient);<a name="line.227"></a> <FONT color="green">228</FONT> }<a name="line.228"></a> <FONT color="green">229</FONT> <a name="line.229"></a> <FONT color="green">230</FONT> /**<a name="line.230"></a> <FONT color="green">231</FONT> * Inversely transform the given complex data set.<a name="line.231"></a> <FONT color="green">232</FONT> * <p><a name="line.232"></a> <FONT color="green">233</FONT> * The formula is $ x_k = (1/N) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n $<a name="line.233"></a> <FONT color="green">234</FONT> * </p><a name="line.234"></a> <FONT color="green">235</FONT> *<a name="line.235"></a> <FONT color="green">236</FONT> * @param f the complex data array to be inversely transformed<a name="line.236"></a> <FONT color="green">237</FONT> * @return the complex inversely transformed array<a name="line.237"></a> <FONT color="green">238</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.238"></a> <FONT color="green">239</FONT> */<a name="line.239"></a> <FONT color="green">240</FONT> public Complex[] inversetransform(Complex f[])<a name="line.240"></a> <FONT color="green">241</FONT> throws IllegalArgumentException {<a name="line.241"></a> <FONT color="green">242</FONT> <a name="line.242"></a> <FONT color="green">243</FONT> roots.computeOmega(-f.length); // pass negative argument<a name="line.243"></a> <FONT color="green">244</FONT> double scaling_coefficient = 1.0 / f.length;<a name="line.244"></a> <FONT color="green">245</FONT> return scaleArray(fft(f), scaling_coefficient);<a name="line.245"></a> <FONT color="green">246</FONT> }<a name="line.246"></a> <FONT color="green">247</FONT> <a name="line.247"></a> <FONT color="green">248</FONT> /**<a name="line.248"></a> <FONT color="green">249</FONT> * Inversely transform the given real data set.<a name="line.249"></a> <FONT color="green">250</FONT> * <p><a name="line.250"></a> <FONT color="green">251</FONT> * The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$<a name="line.251"></a> <FONT color="green">252</FONT> * </p><a name="line.252"></a> <FONT color="green">253</FONT> *<a name="line.253"></a> <FONT color="green">254</FONT> * @param f the real data array to be inversely transformed<a name="line.254"></a> <FONT color="green">255</FONT> * @return the complex inversely transformed array<a name="line.255"></a> <FONT color="green">256</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.256"></a> <FONT color="green">257</FONT> */<a name="line.257"></a> <FONT color="green">258</FONT> public Complex[] inversetransform2(double f[])<a name="line.258"></a> <FONT color="green">259</FONT> throws IllegalArgumentException {<a name="line.259"></a> <FONT color="green">260</FONT> <a name="line.260"></a> <FONT color="green">261</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.261"></a> <FONT color="green">262</FONT> return scaleArray(fft(f, true), scaling_coefficient);<a name="line.262"></a> <FONT color="green">263</FONT> }<a name="line.263"></a> <FONT color="green">264</FONT> <a name="line.264"></a> <FONT color="green">265</FONT> /**<a name="line.265"></a> <FONT color="green">266</FONT> * Inversely transform the given real function, sampled on the given interval.<a name="line.266"></a> <FONT color="green">267</FONT> * <p><a name="line.267"></a> <FONT color="green">268</FONT> * The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$<a name="line.268"></a> <FONT color="green">269</FONT> * </p><a name="line.269"></a> <FONT color="green">270</FONT> *<a name="line.270"></a> <FONT color="green">271</FONT> * @param f the function to be sampled and inversely transformed<a name="line.271"></a> <FONT color="green">272</FONT> * @param min the lower bound for the interval<a name="line.272"></a> <FONT color="green">273</FONT> * @param max the upper bound for the interval<a name="line.273"></a> <FONT color="green">274</FONT> * @param n the number of sample points<a name="line.274"></a> <FONT color="green">275</FONT> * @return the complex inversely transformed array<a name="line.275"></a> <FONT color="green">276</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.276"></a> <FONT color="green">277</FONT> * at some point<a name="line.277"></a> <FONT color="green">278</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.278"></a> <FONT color="green">279</FONT> */<a name="line.279"></a> <FONT color="green">280</FONT> public Complex[] inversetransform2(UnivariateRealFunction f,<a name="line.280"></a> <FONT color="green">281</FONT> double min, double max, int n)<a name="line.281"></a> <FONT color="green">282</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.282"></a> <FONT color="green">283</FONT> <a name="line.283"></a> <FONT color="green">284</FONT> double data[] = sample(f, min, max, n);<a name="line.284"></a> <FONT color="green">285</FONT> double scaling_coefficient = 1.0 / Math.sqrt(n);<a name="line.285"></a> <FONT color="green">286</FONT> return scaleArray(fft(data, true), scaling_coefficient);<a name="line.286"></a> <FONT color="green">287</FONT> }<a name="line.287"></a> <FONT color="green">288</FONT> <a name="line.288"></a> <FONT color="green">289</FONT> /**<a name="line.289"></a> <FONT color="green">290</FONT> * Inversely transform the given complex data set.<a name="line.290"></a> <FONT color="green">291</FONT> * <p><a name="line.291"></a> <FONT color="green">292</FONT> * The formula is $x_k = (1/\sqrt{N}) \Sigma_{n=0}^{N-1} e^{2 \pi i nk/N} y_n$<a name="line.292"></a> <FONT color="green">293</FONT> * </p><a name="line.293"></a> <FONT color="green">294</FONT> *<a name="line.294"></a> <FONT color="green">295</FONT> * @param f the complex data array to be inversely transformed<a name="line.295"></a> <FONT color="green">296</FONT> * @return the complex inversely transformed array<a name="line.296"></a> <FONT color="green">297</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.297"></a> <FONT color="green">298</FONT> */<a name="line.298"></a> <FONT color="green">299</FONT> public Complex[] inversetransform2(Complex f[])<a name="line.299"></a> <FONT color="green">300</FONT> throws IllegalArgumentException {<a name="line.300"></a> <FONT color="green">301</FONT> <a name="line.301"></a> <FONT color="green">302</FONT> roots.computeOmega(-f.length); // pass negative argument<a name="line.302"></a> <FONT color="green">303</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.303"></a> <FONT color="green">304</FONT> return scaleArray(fft(f), scaling_coefficient);<a name="line.304"></a> <FONT color="green">305</FONT> }<a name="line.305"></a> <FONT color="green">306</FONT> <a name="line.306"></a> <FONT color="green">307</FONT> /**<a name="line.307"></a> <FONT color="green">308</FONT> * Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).<a name="line.308"></a> <FONT color="green">309</FONT> *<a name="line.309"></a> <FONT color="green">310</FONT> * @param f the real data array to be transformed<a name="line.310"></a> <FONT color="green">311</FONT> * @param isInverse the indicator of forward or inverse transform<a name="line.311"></a> <FONT color="green">312</FONT> * @return the complex transformed array<a name="line.312"></a> <FONT color="green">313</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.313"></a> <FONT color="green">314</FONT> */<a name="line.314"></a> <FONT color="green">315</FONT> protected Complex[] fft(double f[], boolean isInverse)<a name="line.315"></a> <FONT color="green">316</FONT> throws IllegalArgumentException {<a name="line.316"></a> <FONT color="green">317</FONT> <a name="line.317"></a> <FONT color="green">318</FONT> verifyDataSet(f);<a name="line.318"></a> <FONT color="green">319</FONT> Complex F[] = new Complex[f.length];<a name="line.319"></a> <FONT color="green">320</FONT> if (f.length == 1) {<a name="line.320"></a> <FONT color="green">321</FONT> F[0] = new Complex(f[0], 0.0);<a name="line.321"></a> <FONT color="green">322</FONT> return F;<a name="line.322"></a> <FONT color="green">323</FONT> }<a name="line.323"></a> <FONT color="green">324</FONT> <a name="line.324"></a> <FONT color="green">325</FONT> // Rather than the naive real to complex conversion, pack 2N<a name="line.325"></a> <FONT color="green">326</FONT> // real numbers into N complex numbers for better performance.<a name="line.326"></a> <FONT color="green">327</FONT> int N = f.length >> 1;<a name="line.327"></a> <FONT color="green">328</FONT> Complex c[] = new Complex[N];<a name="line.328"></a> <FONT color="green">329</FONT> for (int i = 0; i < N; i++) {<a name="line.329"></a> <FONT color="green">330</FONT> c[i] = new Complex(f[2*i], f[2*i+1]);<a name="line.330"></a> <FONT color="green">331</FONT> }<a name="line.331"></a> <FONT color="green">332</FONT> roots.computeOmega(isInverse ? -N : N);<a name="line.332"></a> <FONT color="green">333</FONT> Complex z[] = fft(c);<a name="line.333"></a> <FONT color="green">334</FONT> <a name="line.334"></a> <FONT color="green">335</FONT> // reconstruct the FFT result for the original array<a name="line.335"></a> <FONT color="green">336</FONT> roots.computeOmega(isInverse ? -2*N : 2*N);<a name="line.336"></a> <FONT color="green">337</FONT> F[0] = new Complex(2 * (z[0].getReal() + z[0].getImaginary()), 0.0);<a name="line.337"></a> <FONT color="green">338</FONT> F[N] = new Complex(2 * (z[0].getReal() - z[0].getImaginary()), 0.0);<a name="line.338"></a> <FONT color="green">339</FONT> for (int i = 1; i < N; i++) {<a name="line.339"></a> <FONT color="green">340</FONT> Complex A = z[N-i].conjugate();<a name="line.340"></a> <FONT color="green">341</FONT> Complex B = z[i].add(A);<a name="line.341"></a> <FONT color="green">342</FONT> Complex C = z[i].subtract(A);<a name="line.342"></a> <FONT color="green">343</FONT> //Complex D = roots.getOmega(i).multiply(Complex.I);<a name="line.343"></a> <FONT color="green">344</FONT> Complex D = new Complex(-roots.getOmegaImaginary(i),<a name="line.344"></a> <FONT color="green">345</FONT> roots.getOmegaReal(i));<a name="line.345"></a> <FONT color="green">346</FONT> F[i] = B.subtract(C.multiply(D));<a name="line.346"></a> <FONT color="green">347</FONT> F[2*N-i] = F[i].conjugate();<a name="line.347"></a> <FONT color="green">348</FONT> }<a name="line.348"></a> <FONT color="green">349</FONT> <a name="line.349"></a> <FONT color="green">350</FONT> return scaleArray(F, 0.5);<a name="line.350"></a> <FONT color="green">351</FONT> }<a name="line.351"></a> <FONT color="green">352</FONT> <a name="line.352"></a> <FONT color="green">353</FONT> /**<a name="line.353"></a> <FONT color="green">354</FONT> * Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).<a name="line.354"></a> <FONT color="green">355</FONT> *<a name="line.355"></a> <FONT color="green">356</FONT> * @param data the complex data array to be transformed<a name="line.356"></a> <FONT color="green">357</FONT> * @return the complex transformed array<a name="line.357"></a> <FONT color="green">358</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.358"></a> <FONT color="green">359</FONT> */<a name="line.359"></a> <FONT color="green">360</FONT> protected Complex[] fft(Complex data[])<a name="line.360"></a> <FONT color="green">361</FONT> throws IllegalArgumentException {<a name="line.361"></a> <FONT color="green">362</FONT> <a name="line.362"></a> <FONT color="green">363</FONT> final int n = data.length;<a name="line.363"></a> <FONT color="green">364</FONT> final Complex f[] = new Complex[n];<a name="line.364"></a> <FONT color="green">365</FONT> <a name="line.365"></a> <FONT color="green">366</FONT> // initial simple cases<a name="line.366"></a> <FONT color="green">367</FONT> verifyDataSet(data);<a name="line.367"></a> <FONT color="green">368</FONT> if (n == 1) {<a name="line.368"></a> <FONT color="green">369</FONT> f[0] = data[0];<a name="line.369"></a> <FONT color="green">370</FONT> return f;<a name="line.370"></a> <FONT color="green">371</FONT> }<a name="line.371"></a> <FONT color="green">372</FONT> if (n == 2) {<a name="line.372"></a> <FONT color="green">373</FONT> f[0] = data[0].add(data[1]);<a name="line.373"></a> <FONT color="green">374</FONT> f[1] = data[0].subtract(data[1]);<a name="line.374"></a> <FONT color="green">375</FONT> return f;<a name="line.375"></a> <FONT color="green">376</FONT> }<a name="line.376"></a> <FONT color="green">377</FONT> <a name="line.377"></a> <FONT color="green">378</FONT> // permute original data array in bit-reversal order<a name="line.378"></a> <FONT color="green">379</FONT> int ii = 0;<a name="line.379"></a> <FONT color="green">380</FONT> for (int i = 0; i < n; i++) {<a name="line.380"></a> <FONT color="green">381</FONT> f[i] = data[ii];<a name="line.381"></a> <FONT color="green">382</FONT> int k = n >> 1;<a name="line.382"></a> <FONT color="green">383</FONT> while (ii >= k && k > 0) {<a name="line.383"></a> <FONT color="green">384</FONT> ii -= k; k >>= 1;<a name="line.384"></a> <FONT color="green">385</FONT> }<a name="line.385"></a> <FONT color="green">386</FONT> ii += k;<a name="line.386"></a> <FONT color="green">387</FONT> }<a name="line.387"></a> <FONT color="green">388</FONT> <a name="line.388"></a> <FONT color="green">389</FONT> // the bottom base-4 round<a name="line.389"></a> <FONT color="green">390</FONT> for (int i = 0; i < n; i += 4) {<a name="line.390"></a> <FONT color="green">391</FONT> final Complex a = f[i].add(f[i+1]);<a name="line.391"></a> <FONT color="green">392</FONT> final Complex b = f[i+2].add(f[i+3]);<a name="line.392"></a> <FONT color="green">393</FONT> final Complex c = f[i].subtract(f[i+1]);<a name="line.393"></a> <FONT color="green">394</FONT> final Complex d = f[i+2].subtract(f[i+3]);<a name="line.394"></a> <FONT color="green">395</FONT> final Complex e1 = c.add(d.multiply(Complex.I));<a name="line.395"></a> <FONT color="green">396</FONT> final Complex e2 = c.subtract(d.multiply(Complex.I));<a name="line.396"></a> <FONT color="green">397</FONT> f[i] = a.add(b);<a name="line.397"></a> <FONT color="green">398</FONT> f[i+2] = a.subtract(b);<a name="line.398"></a> <FONT color="green">399</FONT> // omegaCount indicates forward or inverse transform<a name="line.399"></a> <FONT color="green">400</FONT> f[i+1] = roots.isForward() ? e2 : e1;<a name="line.400"></a> <FONT color="green">401</FONT> f[i+3] = roots.isForward() ? e1 : e2;<a name="line.401"></a> <FONT color="green">402</FONT> }<a name="line.402"></a> <FONT color="green">403</FONT> <a name="line.403"></a> <FONT color="green">404</FONT> // iterations from bottom to top take O(N*logN) time<a name="line.404"></a> <FONT color="green">405</FONT> for (int i = 4; i < n; i <<= 1) {<a name="line.405"></a> <FONT color="green">406</FONT> final int m = n / (i<<1);<a name="line.406"></a> <FONT color="green">407</FONT> for (int j = 0; j < n; j += i<<1) {<a name="line.407"></a> <FONT color="green">408</FONT> for (int k = 0; k < i; k++) {<a name="line.408"></a> <FONT color="green">409</FONT> //z = f[i+j+k].multiply(roots.getOmega(k*m));<a name="line.409"></a> <FONT color="green">410</FONT> final int k_times_m = k*m;<a name="line.410"></a> <FONT color="green">411</FONT> final double omega_k_times_m_real = roots.getOmegaReal(k_times_m);<a name="line.411"></a> <FONT color="green">412</FONT> final double omega_k_times_m_imaginary = roots.getOmegaImaginary(k_times_m);<a name="line.412"></a> <FONT color="green">413</FONT> //z = f[i+j+k].multiply(omega[k*m]);<a name="line.413"></a> <FONT color="green">414</FONT> final Complex z = new Complex(<a name="line.414"></a> <FONT color="green">415</FONT> f[i+j+k].getReal() * omega_k_times_m_real -<a name="line.415"></a> <FONT color="green">416</FONT> f[i+j+k].getImaginary() * omega_k_times_m_imaginary,<a name="line.416"></a> <FONT color="green">417</FONT> f[i+j+k].getReal() * omega_k_times_m_imaginary +<a name="line.417"></a> <FONT color="green">418</FONT> f[i+j+k].getImaginary() * omega_k_times_m_real);<a name="line.418"></a> <FONT color="green">419</FONT> <a name="line.419"></a> <FONT color="green">420</FONT> f[i+j+k] = f[j+k].subtract(z);<a name="line.420"></a> <FONT color="green">421</FONT> f[j+k] = f[j+k].add(z);<a name="line.421"></a> <FONT color="green">422</FONT> }<a name="line.422"></a> <FONT color="green">423</FONT> }<a name="line.423"></a> <FONT color="green">424</FONT> }<a name="line.424"></a> <FONT color="green">425</FONT> return f;<a name="line.425"></a> <FONT color="green">426</FONT> }<a name="line.426"></a> <FONT color="green">427</FONT> <a name="line.427"></a> <FONT color="green">428</FONT> /**<a name="line.428"></a> <FONT color="green">429</FONT> * Sample the given univariate real function on the given interval.<a name="line.429"></a> <FONT color="green">430</FONT> * <p><a name="line.430"></a> <FONT color="green">431</FONT> * The interval is divided equally into N sections and sample points<a name="line.431"></a> <FONT color="green">432</FONT> * are taken from min to max-(max-min)/N. Usually f(x) is periodic<a name="line.432"></a> <FONT color="green">433</FONT> * such that f(min) = f(max) (note max is not sampled), but we don't<a name="line.433"></a> <FONT color="green">434</FONT> * require that.</p><a name="line.434"></a> <FONT color="green">435</FONT> *<a name="line.435"></a> <FONT color="green">436</FONT> * @param f the function to be sampled<a name="line.436"></a> <FONT color="green">437</FONT> * @param min the lower bound for the interval<a name="line.437"></a> <FONT color="green">438</FONT> * @param max the upper bound for the interval<a name="line.438"></a> <FONT color="green">439</FONT> * @param n the number of sample points<a name="line.439"></a> <FONT color="green">440</FONT> * @return the samples array<a name="line.440"></a> <FONT color="green">441</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.441"></a> <FONT color="green">442</FONT> * at some point<a name="line.442"></a> <FONT color="green">443</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.443"></a> <FONT color="green">444</FONT> */<a name="line.444"></a> <FONT color="green">445</FONT> public static double[] sample(UnivariateRealFunction f,<a name="line.445"></a> <FONT color="green">446</FONT> double min, double max, int n)<a name="line.446"></a> <FONT color="green">447</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.447"></a> <FONT color="green">448</FONT> <a name="line.448"></a> <FONT color="green">449</FONT> if (n <= 0) {<a name="line.449"></a> <FONT color="green">450</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.450"></a> <FONT color="green">451</FONT> "number of sample is not positive: {0}",<a name="line.451"></a> <FONT color="green">452</FONT> n);<a name="line.452"></a> <FONT color="green">453</FONT> }<a name="line.453"></a> <FONT color="green">454</FONT> verifyInterval(min, max);<a name="line.454"></a> <FONT color="green">455</FONT> <a name="line.455"></a> <FONT color="green">456</FONT> double s[] = new double[n];<a name="line.456"></a> <FONT color="green">457</FONT> double h = (max - min) / n;<a name="line.457"></a> <FONT color="green">458</FONT> for (int i = 0; i < n; i++) {<a name="line.458"></a> <FONT color="green">459</FONT> s[i] = f.value(min + i * h);<a name="line.459"></a> <FONT color="green">460</FONT> }<a name="line.460"></a> <FONT color="green">461</FONT> return s;<a name="line.461"></a> <FONT color="green">462</FONT> }<a name="line.462"></a> <FONT color="green">463</FONT> <a name="line.463"></a> <FONT color="green">464</FONT> /**<a name="line.464"></a> <FONT color="green">465</FONT> * Multiply every component in the given real array by the<a name="line.465"></a> <FONT color="green">466</FONT> * given real number. The change is made in place.<a name="line.466"></a> <FONT color="green">467</FONT> *<a name="line.467"></a> <FONT color="green">468</FONT> * @param f the real array to be scaled<a name="line.468"></a> <FONT color="green">469</FONT> * @param d the real scaling coefficient<a name="line.469"></a> <FONT color="green">470</FONT> * @return a reference to the scaled array<a name="line.470"></a> <FONT color="green">471</FONT> */<a name="line.471"></a> <FONT color="green">472</FONT> public static double[] scaleArray(double f[], double d) {<a name="line.472"></a> <FONT color="green">473</FONT> for (int i = 0; i < f.length; i++) {<a name="line.473"></a> <FONT color="green">474</FONT> f[i] *= d;<a name="line.474"></a> <FONT color="green">475</FONT> }<a name="line.475"></a> <FONT color="green">476</FONT> return f;<a name="line.476"></a> <FONT color="green">477</FONT> }<a name="line.477"></a> <FONT color="green">478</FONT> <a name="line.478"></a> <FONT color="green">479</FONT> /**<a name="line.479"></a> <FONT color="green">480</FONT> * Multiply every component in the given complex array by the<a name="line.480"></a> <FONT color="green">481</FONT> * given real number. The change is made in place.<a name="line.481"></a> <FONT color="green">482</FONT> *<a name="line.482"></a> <FONT color="green">483</FONT> * @param f the complex array to be scaled<a name="line.483"></a> <FONT color="green">484</FONT> * @param d the real scaling coefficient<a name="line.484"></a> <FONT color="green">485</FONT> * @return a reference to the scaled array<a name="line.485"></a> <FONT color="green">486</FONT> */<a name="line.486"></a> <FONT color="green">487</FONT> public static Complex[] scaleArray(Complex f[], double d) {<a name="line.487"></a> <FONT color="green">488</FONT> for (int i = 0; i < f.length; i++) {<a name="line.488"></a> <FONT color="green">489</FONT> f[i] = new Complex(d * f[i].getReal(), d * f[i].getImaginary());<a name="line.489"></a> <FONT color="green">490</FONT> }<a name="line.490"></a> <FONT color="green">491</FONT> return f;<a name="line.491"></a> <FONT color="green">492</FONT> }<a name="line.492"></a> <FONT color="green">493</FONT> <a name="line.493"></a> <FONT color="green">494</FONT> /**<a name="line.494"></a> <FONT color="green">495</FONT> * Returns true if the argument is power of 2.<a name="line.495"></a> <FONT color="green">496</FONT> *<a name="line.496"></a> <FONT color="green">497</FONT> * @param n the number to test<a name="line.497"></a> <FONT color="green">498</FONT> * @return true if the argument is power of 2<a name="line.498"></a> <FONT color="green">499</FONT> */<a name="line.499"></a> <FONT color="green">500</FONT> public static boolean isPowerOf2(long n) {<a name="line.500"></a> <FONT color="green">501</FONT> return (n > 0) && ((n & (n - 1)) == 0);<a name="line.501"></a> <FONT color="green">502</FONT> }<a name="line.502"></a> <FONT color="green">503</FONT> <a name="line.503"></a> <FONT color="green">504</FONT> /**<a name="line.504"></a> <FONT color="green">505</FONT> * Verifies that the data set has length of power of 2.<a name="line.505"></a> <FONT color="green">506</FONT> *<a name="line.506"></a> <FONT color="green">507</FONT> * @param d the data array<a name="line.507"></a> <FONT color="green">508</FONT> * @throws IllegalArgumentException if array length is not power of 2<a name="line.508"></a> <FONT color="green">509</FONT> */<a name="line.509"></a> <FONT color="green">510</FONT> public static void verifyDataSet(double d[]) throws IllegalArgumentException {<a name="line.510"></a> <FONT color="green">511</FONT> if (!isPowerOf2(d.length)) {<a name="line.511"></a> <FONT color="green">512</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.512"></a> <FONT color="green">513</FONT> NOT_POWER_OF_TWO_MESSAGE, d.length);<a name="line.513"></a> <FONT color="green">514</FONT> }<a name="line.514"></a> <FONT color="green">515</FONT> }<a name="line.515"></a> <FONT color="green">516</FONT> <a name="line.516"></a> <FONT color="green">517</FONT> /**<a name="line.517"></a> <FONT color="green">518</FONT> * Verifies that the data set has length of power of 2.<a name="line.518"></a> <FONT color="green">519</FONT> *<a name="line.519"></a> <FONT color="green">520</FONT> * @param o the data array<a name="line.520"></a> <FONT color="green">521</FONT> * @throws IllegalArgumentException if array length is not power of 2<a name="line.521"></a> <FONT color="green">522</FONT> */<a name="line.522"></a> <FONT color="green">523</FONT> public static void verifyDataSet(Object o[]) throws IllegalArgumentException {<a name="line.523"></a> <FONT color="green">524</FONT> if (!isPowerOf2(o.length)) {<a name="line.524"></a> <FONT color="green">525</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.525"></a> <FONT color="green">526</FONT> NOT_POWER_OF_TWO_MESSAGE, o.length);<a name="line.526"></a> <FONT color="green">527</FONT> }<a name="line.527"></a> <FONT color="green">528</FONT> }<a name="line.528"></a> <FONT color="green">529</FONT> <a name="line.529"></a> <FONT color="green">530</FONT> /**<a name="line.530"></a> <FONT color="green">531</FONT> * Verifies that the endpoints specify an interval.<a name="line.531"></a> <FONT color="green">532</FONT> *<a name="line.532"></a> <FONT color="green">533</FONT> * @param lower lower endpoint<a name="line.533"></a> <FONT color="green">534</FONT> * @param upper upper endpoint<a name="line.534"></a> <FONT color="green">535</FONT> * @throws IllegalArgumentException if not interval<a name="line.535"></a> <FONT color="green">536</FONT> */<a name="line.536"></a> <FONT color="green">537</FONT> public static void verifyInterval(double lower, double upper)<a name="line.537"></a> <FONT color="green">538</FONT> throws IllegalArgumentException {<a name="line.538"></a> <FONT color="green">539</FONT> <a name="line.539"></a> <FONT color="green">540</FONT> if (lower >= upper) {<a name="line.540"></a> <FONT color="green">541</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.541"></a> <FONT color="green">542</FONT> "endpoints do not specify an interval: [{0}, {1}]",<a name="line.542"></a> <FONT color="green">543</FONT> lower, upper);<a name="line.543"></a> <FONT color="green">544</FONT> }<a name="line.544"></a> <FONT color="green">545</FONT> }<a name="line.545"></a> <FONT color="green">546</FONT> <a name="line.546"></a> <FONT color="green">547</FONT> /**<a name="line.547"></a> <FONT color="green">548</FONT> * Performs a multi-dimensional Fourier transform on a given array.<a name="line.548"></a> <FONT color="green">549</FONT> * Use {@link #inversetransform2(Complex[])} and<a name="line.549"></a> <FONT color="green">550</FONT> * {@link #transform2(Complex[])} in a row-column implementation<a name="line.550"></a> <FONT color="green">551</FONT> * in any number of dimensions with O(N&times;log(N)) complexity with<a name="line.551"></a> <FONT color="green">552</FONT> * N=n<sub>1</sub>&times;n<sub>2</sub>&times;n<sub>3</sub>&times;...&times;n<sub>d</sub>,<a name="line.552"></a> <FONT color="green">553</FONT> * n<sub>x</sub>=number of elements in dimension x,<a name="line.553"></a> <FONT color="green">554</FONT> * and d=total number of dimensions.<a name="line.554"></a> <FONT color="green">555</FONT> *<a name="line.555"></a> <FONT color="green">556</FONT> * @param mdca Multi-Dimensional Complex Array id est Complex[][][][]<a name="line.556"></a> <FONT color="green">557</FONT> * @param forward inverseTransform2 is preformed if this is false<a name="line.557"></a> <FONT color="green">558</FONT> * @return transform of mdca as a Multi-Dimensional Complex Array id est Complex[][][][]<a name="line.558"></a> <FONT color="green">559</FONT> * @throws IllegalArgumentException if any dimension is not a power of two<a name="line.559"></a> <FONT color="green">560</FONT> */<a name="line.560"></a> <FONT color="green">561</FONT> public Object mdfft(Object mdca, boolean forward)<a name="line.561"></a> <FONT color="green">562</FONT> throws IllegalArgumentException {<a name="line.562"></a> <FONT color="green">563</FONT> MultiDimensionalComplexMatrix mdcm = (MultiDimensionalComplexMatrix)<a name="line.563"></a> <FONT color="green">564</FONT> new MultiDimensionalComplexMatrix(mdca).clone();<a name="line.564"></a> <FONT color="green">565</FONT> int[] dimensionSize = mdcm.getDimensionSizes();<a name="line.565"></a> <FONT color="green">566</FONT> //cycle through each dimension<a name="line.566"></a> <FONT color="green">567</FONT> for (int i = 0; i < dimensionSize.length; i++) {<a name="line.567"></a> <FONT color="green">568</FONT> mdfft(mdcm, forward, i, new int[0]);<a name="line.568"></a> <FONT color="green">569</FONT> }<a name="line.569"></a> <FONT color="green">570</FONT> return mdcm.getArray();<a name="line.570"></a> <FONT color="green">571</FONT> }<a name="line.571"></a> <FONT color="green">572</FONT> <a name="line.572"></a> <FONT color="green">573</FONT> /**<a name="line.573"></a> <FONT color="green">574</FONT> * Performs one dimension of a multi-dimensional Fourier transform.<a name="line.574"></a> <FONT color="green">575</FONT> *<a name="line.575"></a> <FONT color="green">576</FONT> * @param mdcm input matrix<a name="line.576"></a> <FONT color="green">577</FONT> * @param forward inverseTransform2 is preformed if this is false<a name="line.577"></a> <FONT color="green">578</FONT> * @param d index of the dimension to process<a name="line.578"></a> <FONT color="green">579</FONT> * @param subVector recursion subvector<a name="line.579"></a> <FONT color="green">580</FONT> * @throws IllegalArgumentException if any dimension is not a power of two<a name="line.580"></a> <FONT color="green">581</FONT> */<a name="line.581"></a> <FONT color="green">582</FONT> private void mdfft(MultiDimensionalComplexMatrix mdcm, boolean forward,<a name="line.582"></a> <FONT color="green">583</FONT> int d, int[] subVector)<a name="line.583"></a> <FONT color="green">584</FONT> throws IllegalArgumentException {<a name="line.584"></a> <FONT color="green">585</FONT> int[] dimensionSize = mdcm.getDimensionSizes();<a name="line.585"></a> <FONT color="green">586</FONT> //if done<a name="line.586"></a> <FONT color="green">587</FONT> if (subVector.length == dimensionSize.length) {<a name="line.587"></a> <FONT color="green">588</FONT> Complex[] temp = new Complex[dimensionSize[d]];<a name="line.588"></a> <FONT color="green">589</FONT> for (int i = 0; i < dimensionSize[d]; i++) {<a name="line.589"></a> <FONT color="green">590</FONT> //fft along dimension d<a name="line.590"></a> <FONT color="green">591</FONT> subVector[d] = i;<a name="line.591"></a> <FONT color="green">592</FONT> temp[i] = mdcm.get(subVector);<a name="line.592"></a> <FONT color="green">593</FONT> }<a name="line.593"></a> <FONT color="green">594</FONT> <a name="line.594"></a> <FONT color="green">595</FONT> if (forward)<a name="line.595"></a> <FONT color="green">596</FONT> temp = transform2(temp);<a name="line.596"></a> <FONT color="green">597</FONT> else<a name="line.597"></a> <FONT color="green">598</FONT> temp = inversetransform2(temp);<a name="line.598"></a> <FONT color="green">599</FONT> <a name="line.599"></a> <FONT color="green">600</FONT> for (int i = 0; i < dimensionSize[d]; i++) {<a name="line.600"></a> <FONT color="green">601</FONT> subVector[d] = i;<a name="line.601"></a> <FONT color="green">602</FONT> mdcm.set(temp[i], subVector);<a name="line.602"></a> <FONT color="green">603</FONT> }<a name="line.603"></a> <FONT color="green">604</FONT> } else {<a name="line.604"></a> <FONT color="green">605</FONT> int[] vector = new int[subVector.length + 1];<a name="line.605"></a> <FONT color="green">606</FONT> System.arraycopy(subVector, 0, vector, 0, subVector.length);<a name="line.606"></a> <FONT color="green">607</FONT> if (subVector.length == d) {<a name="line.607"></a> <FONT color="green">608</FONT> //value is not important once the recursion is done.<a name="line.608"></a> <FONT color="green">609</FONT> //then an fft will be applied along the dimension d.<a name="line.609"></a> <FONT color="green">610</FONT> vector[d] = 0;<a name="line.610"></a> <FONT color="green">611</FONT> mdfft(mdcm, forward, d, vector);<a name="line.611"></a> <FONT color="green">612</FONT> } else {<a name="line.612"></a> <FONT color="green">613</FONT> for (int i = 0; i < dimensionSize[subVector.length]; i++) {<a name="line.613"></a> <FONT color="green">614</FONT> vector[subVector.length] = i;<a name="line.614"></a> <FONT color="green">615</FONT> //further split along the next dimension<a name="line.615"></a> <FONT color="green">616</FONT> mdfft(mdcm, forward, d, vector);<a name="line.616"></a> <FONT color="green">617</FONT> }<a name="line.617"></a> <FONT color="green">618</FONT> }<a name="line.618"></a> <FONT color="green">619</FONT> }<a name="line.619"></a> <FONT color="green">620</FONT> return;<a name="line.620"></a> <FONT color="green">621</FONT> }<a name="line.621"></a> <FONT color="green">622</FONT> <a name="line.622"></a> <FONT color="green">623</FONT> /**<a name="line.623"></a> <FONT color="green">624</FONT> * Complex matrix implementation.<a name="line.624"></a> <FONT color="green">625</FONT> * Not designed for synchronized access<a name="line.625"></a> <FONT color="green">626</FONT> * may eventually be replaced by jsr-83 of the java community process<a name="line.626"></a> <FONT color="green">627</FONT> * http://jcp.org/en/jsr/detail?id=83<a name="line.627"></a> <FONT color="green">628</FONT> * may require additional exception throws for other basic requirements.<a name="line.628"></a> <FONT color="green">629</FONT> */<a name="line.629"></a> <FONT color="green">630</FONT> private static class MultiDimensionalComplexMatrix<a name="line.630"></a> <FONT color="green">631</FONT> implements Cloneable {<a name="line.631"></a> <FONT color="green">632</FONT> <a name="line.632"></a> <FONT color="green">633</FONT> /** Size in all dimensions. */<a name="line.633"></a> <FONT color="green">634</FONT> protected int[] dimensionSize;<a name="line.634"></a> <FONT color="green">635</FONT> <a name="line.635"></a> <FONT color="green">636</FONT> /** Storage array. */<a name="line.636"></a> <FONT color="green">637</FONT> protected Object multiDimensionalComplexArray;<a name="line.637"></a> <FONT color="green">638</FONT> <a name="line.638"></a> <FONT color="green">639</FONT> /** Simple constructor.<a name="line.639"></a> <FONT color="green">640</FONT> * @param multiDimensionalComplexArray array containing the matrix elements<a name="line.640"></a> <FONT color="green">641</FONT> */<a name="line.641"></a> <FONT color="green">642</FONT> public MultiDimensionalComplexMatrix(Object multiDimensionalComplexArray) {<a name="line.642"></a> <FONT color="green">643</FONT> <a name="line.643"></a> <FONT color="green">644</FONT> this.multiDimensionalComplexArray = multiDimensionalComplexArray;<a name="line.644"></a> <FONT color="green">645</FONT> <a name="line.645"></a> <FONT color="green">646</FONT> // count dimensions<a name="line.646"></a> <FONT color="green">647</FONT> int numOfDimensions = 0;<a name="line.647"></a> <FONT color="green">648</FONT> for (Object lastDimension = multiDimensionalComplexArray;<a name="line.648"></a> <FONT color="green">649</FONT> lastDimension instanceof Object[];) {<a name="line.649"></a> <FONT color="green">650</FONT> final Object[] array = (Object[]) lastDimension;<a name="line.650"></a> <FONT color="green">651</FONT> numOfDimensions++;<a name="line.651"></a> <FONT color="green">652</FONT> lastDimension = array[0];<a name="line.652"></a> <FONT color="green">653</FONT> }<a name="line.653"></a> <FONT color="green">654</FONT> <a name="line.654"></a> <FONT color="green">655</FONT> // allocate array with exact count<a name="line.655"></a> <FONT color="green">656</FONT> dimensionSize = new int[numOfDimensions];<a name="line.656"></a> <FONT color="green">657</FONT> <a name="line.657"></a> <FONT color="green">658</FONT> // fill array<a name="line.658"></a> <FONT color="green">659</FONT> numOfDimensions = 0;<a name="line.659"></a> <FONT color="green">660</FONT> for (Object lastDimension = multiDimensionalComplexArray;<a name="line.660"></a> <FONT color="green">661</FONT> lastDimension instanceof Object[];) {<a name="line.661"></a> <FONT color="green">662</FONT> final Object[] array = (Object[]) lastDimension;<a name="line.662"></a> <FONT color="green">663</FONT> dimensionSize[numOfDimensions++] = array.length;<a name="line.663"></a> <FONT color="green">664</FONT> lastDimension = array[0];<a name="line.664"></a> <FONT color="green">665</FONT> }<a name="line.665"></a> <FONT color="green">666</FONT> <a name="line.666"></a> <FONT color="green">667</FONT> }<a name="line.667"></a> <FONT color="green">668</FONT> <a name="line.668"></a> <FONT color="green">669</FONT> /**<a name="line.669"></a> <FONT color="green">670</FONT> * Get a matrix element.<a name="line.670"></a> <FONT color="green">671</FONT> * @param vector indices of the element<a name="line.671"></a> <FONT color="green">672</FONT> * @return matrix element<a name="line.672"></a> <FONT color="green">673</FONT> * @exception IllegalArgumentException if dimensions do not match<a name="line.673"></a> <FONT color="green">674</FONT> */<a name="line.674"></a> <FONT color="green">675</FONT> public Complex get(int... vector)<a name="line.675"></a> <FONT color="green">676</FONT> throws IllegalArgumentException {<a name="line.676"></a> <FONT color="green">677</FONT> if (vector == null) {<a name="line.677"></a> <FONT color="green">678</FONT> if (dimensionSize.length > 0) {<a name="line.678"></a> <FONT color="green">679</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.679"></a> <FONT color="green">680</FONT> DIMENSION_MISMATCH_MESSAGE, 0, dimensionSize.length);<a name="line.680"></a> <FONT color="green">681</FONT> }<a name="line.681"></a> <FONT color="green">682</FONT> return null;<a name="line.682"></a> <FONT color="green">683</FONT> }<a name="line.683"></a> <FONT color="green">684</FONT> if (vector.length != dimensionSize.length) {<a name="line.684"></a> <FONT color="green">685</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.685"></a> <FONT color="green">686</FONT> DIMENSION_MISMATCH_MESSAGE, vector.length, dimensionSize.length);<a name="line.686"></a> <FONT color="green">687</FONT> }<a name="line.687"></a> <FONT color="green">688</FONT> <a name="line.688"></a> <FONT color="green">689</FONT> Object lastDimension = multiDimensionalComplexArray;<a name="line.689"></a> <FONT color="green">690</FONT> <a name="line.690"></a> <FONT color="green">691</FONT> for (int i = 0; i < dimensionSize.length; i++) {<a name="line.691"></a> <FONT color="green">692</FONT> lastDimension = ((Object[]) lastDimension)[vector[i]];<a name="line.692"></a> <FONT color="green">693</FONT> }<a name="line.693"></a> <FONT color="green">694</FONT> return (Complex) lastDimension;<a name="line.694"></a> <FONT color="green">695</FONT> }<a name="line.695"></a> <FONT color="green">696</FONT> <a name="line.696"></a> <FONT color="green">697</FONT> /**<a name="line.697"></a> <FONT color="green">698</FONT> * Set a matrix element.<a name="line.698"></a> <FONT color="green">699</FONT> * @param magnitude magnitude of the element<a name="line.699"></a> <FONT color="green">700</FONT> * @param vector indices of the element<a name="line.700"></a> <FONT color="green">701</FONT> * @return the previous value<a name="line.701"></a> <FONT color="green">702</FONT> * @exception IllegalArgumentException if dimensions do not match<a name="line.702"></a> <FONT color="green">703</FONT> */<a name="line.703"></a> <FONT color="green">704</FONT> public Complex set(Complex magnitude, int... vector)<a name="line.704"></a> <FONT color="green">705</FONT> throws IllegalArgumentException {<a name="line.705"></a> <FONT color="green">706</FONT> if (vector == null) {<a name="line.706"></a> <FONT color="green">707</FONT> if (dimensionSize.length > 0) {<a name="line.707"></a> <FONT color="green">708</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.708"></a> <FONT color="green">709</FONT> DIMENSION_MISMATCH_MESSAGE, 0, dimensionSize.length);<a name="line.709"></a> <FONT color="green">710</FONT> }<a name="line.710"></a> <FONT color="green">711</FONT> return null;<a name="line.711"></a> <FONT color="green">712</FONT> }<a name="line.712"></a> <FONT color="green">713</FONT> if (vector.length != dimensionSize.length) {<a name="line.713"></a> <FONT color="green">714</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.714"></a> <FONT color="green">715</FONT> DIMENSION_MISMATCH_MESSAGE, vector.length,dimensionSize.length);<a name="line.715"></a> <FONT color="green">716</FONT> }<a name="line.716"></a> <FONT color="green">717</FONT> <a name="line.717"></a> <FONT color="green">718</FONT> Object[] lastDimension = (Object[]) multiDimensionalComplexArray;<a name="line.718"></a> <FONT color="green">719</FONT> for (int i = 0; i < dimensionSize.length - 1; i++) {<a name="line.719"></a> <FONT color="green">720</FONT> lastDimension = (Object[]) lastDimension[vector[i]];<a name="line.720"></a> <FONT color="green">721</FONT> }<a name="line.721"></a> <FONT color="green">722</FONT> <a name="line.722"></a> <FONT color="green">723</FONT> Complex lastValue = (Complex) lastDimension[vector[dimensionSize.length - 1]];<a name="line.723"></a> <FONT color="green">724</FONT> lastDimension[vector[dimensionSize.length - 1]] = magnitude;<a name="line.724"></a> <FONT color="green">725</FONT> <a name="line.725"></a> <FONT color="green">726</FONT> return lastValue;<a name="line.726"></a> <FONT color="green">727</FONT> }<a name="line.727"></a> <FONT color="green">728</FONT> <a name="line.728"></a> <FONT color="green">729</FONT> /**<a name="line.729"></a> <FONT color="green">730</FONT> * Get the size in all dimensions.<a name="line.730"></a> <FONT color="green">731</FONT> * @return size in all dimensions<a name="line.731"></a> <FONT color="green">732</FONT> */<a name="line.732"></a> <FONT color="green">733</FONT> public int[] getDimensionSizes() {<a name="line.733"></a> <FONT color="green">734</FONT> return dimensionSize.clone();<a name="line.734"></a> <FONT color="green">735</FONT> }<a name="line.735"></a> <FONT color="green">736</FONT> <a name="line.736"></a> <FONT color="green">737</FONT> /**<a name="line.737"></a> <FONT color="green">738</FONT> * Get the underlying storage array<a name="line.738"></a> <FONT color="green">739</FONT> * @return underlying storage array<a name="line.739"></a> <FONT color="green">740</FONT> */<a name="line.740"></a> <FONT color="green">741</FONT> public Object getArray() {<a name="line.741"></a> <FONT color="green">742</FONT> return multiDimensionalComplexArray;<a name="line.742"></a> <FONT color="green">743</FONT> }<a name="line.743"></a> <FONT color="green">744</FONT> <a name="line.744"></a> <FONT color="green">745</FONT> /** {@inheritDoc} */<a name="line.745"></a> <FONT color="green">746</FONT> @Override<a name="line.746"></a> <FONT color="green">747</FONT> public Object clone() {<a name="line.747"></a> <FONT color="green">748</FONT> MultiDimensionalComplexMatrix mdcm =<a name="line.748"></a> <FONT color="green">749</FONT> new MultiDimensionalComplexMatrix(Array.newInstance(<a name="line.749"></a> <FONT color="green">750</FONT> Complex.class, dimensionSize));<a name="line.750"></a> <FONT color="green">751</FONT> clone(mdcm);<a name="line.751"></a> <FONT color="green">752</FONT> return mdcm;<a name="line.752"></a> <FONT color="green">753</FONT> }<a name="line.753"></a> <FONT color="green">754</FONT> <a name="line.754"></a> <FONT color="green">755</FONT> /**<a name="line.755"></a> <FONT color="green">756</FONT> * Copy contents of current array into mdcm.<a name="line.756"></a> <FONT color="green">757</FONT> * @param mdcm array where to copy data<a name="line.757"></a> <FONT color="green">758</FONT> */<a name="line.758"></a> <FONT color="green">759</FONT> private void clone(MultiDimensionalComplexMatrix mdcm) {<a name="line.759"></a> <FONT color="green">760</FONT> int[] vector = new int[dimensionSize.length];<a name="line.760"></a> <FONT color="green">761</FONT> int size = 1;<a name="line.761"></a> <FONT color="green">762</FONT> for (int i = 0; i < dimensionSize.length; i++) {<a name="line.762"></a> <FONT color="green">763</FONT> size *= dimensionSize[i];<a name="line.763"></a> <FONT color="green">764</FONT> }<a name="line.764"></a> <FONT color="green">765</FONT> int[][] vectorList = new int[size][dimensionSize.length];<a name="line.765"></a> <FONT color="green">766</FONT> for (int[] nextVector: vectorList) {<a name="line.766"></a> <FONT color="green">767</FONT> System.arraycopy(vector, 0, nextVector, 0,<a name="line.767"></a> <FONT color="green">768</FONT> dimensionSize.length);<a name="line.768"></a> <FONT color="green">769</FONT> for (int i = 0; i < dimensionSize.length; i++) {<a name="line.769"></a> <FONT color="green">770</FONT> vector[i]++;<a name="line.770"></a> <FONT color="green">771</FONT> if (vector[i] < dimensionSize[i]) {<a name="line.771"></a> <FONT color="green">772</FONT> break;<a name="line.772"></a> <FONT color="green">773</FONT> } else {<a name="line.773"></a> <FONT color="green">774</FONT> vector[i] = 0;<a name="line.774"></a> <FONT color="green">775</FONT> }<a name="line.775"></a> <FONT color="green">776</FONT> }<a name="line.776"></a> <FONT color="green">777</FONT> }<a name="line.777"></a> <FONT color="green">778</FONT> <a name="line.778"></a> <FONT color="green">779</FONT> for (int[] nextVector: vectorList) {<a name="line.779"></a> <FONT color="green">780</FONT> mdcm.set(get(nextVector), nextVector);<a name="line.780"></a> <FONT color="green">781</FONT> }<a name="line.781"></a> <FONT color="green">782</FONT> }<a name="line.782"></a> <FONT color="green">783</FONT> }<a name="line.783"></a> <FONT color="green">784</FONT> <a name="line.784"></a> <FONT color="green">785</FONT> <a name="line.785"></a> <FONT color="green">786</FONT> /** Computes the n<sup>th</sup> roots of unity.<a name="line.786"></a> <FONT color="green">787</FONT> * A cache of already computed values is maintained.<a name="line.787"></a> <FONT color="green">788</FONT> */<a name="line.788"></a> <FONT color="green">789</FONT> private static class RootsOfUnity implements Serializable {<a name="line.789"></a> <FONT color="green">790</FONT> <a name="line.790"></a> <FONT color="green">791</FONT> /** Serializable version id. */<a name="line.791"></a> <FONT color="green">792</FONT> private static final long serialVersionUID = 6404784357747329667L;<a name="line.792"></a> <FONT color="green">793</FONT> <a name="line.793"></a> <FONT color="green">794</FONT> /** Number of roots of unity. */<a name="line.794"></a> <FONT color="green">795</FONT> private int omegaCount;<a name="line.795"></a> <FONT color="green">796</FONT> <a name="line.796"></a> <FONT color="green">797</FONT> /** Real part of the roots. */<a name="line.797"></a> <FONT color="green">798</FONT> private double[] omegaReal;<a name="line.798"></a> <FONT color="green">799</FONT> <a name="line.799"></a> <FONT color="green">800</FONT> /** Imaginary part of the roots for forward transform. */<a name="line.800"></a> <FONT color="green">801</FONT> private double[] omegaImaginaryForward;<a name="line.801"></a> <FONT color="green">802</FONT> <a name="line.802"></a> <FONT color="green">803</FONT> /** Imaginary part of the roots for reverse transform. */<a name="line.803"></a> <FONT color="green">804</FONT> private double[] omegaImaginaryInverse;<a name="line.804"></a> <FONT color="green">805</FONT> <a name="line.805"></a> <FONT color="green">806</FONT> /** Forward/reverse indicator. */<a name="line.806"></a> <FONT color="green">807</FONT> private boolean isForward;<a name="line.807"></a> <FONT color="green">808</FONT> <a name="line.808"></a> <FONT color="green">809</FONT> /**<a name="line.809"></a> <FONT color="green">810</FONT> * Build an engine for computing then <sup>th</sup> roots of unity<a name="line.810"></a> <FONT color="green">811</FONT> */<a name="line.811"></a> <FONT color="green">812</FONT> public RootsOfUnity() {<a name="line.812"></a> <FONT color="green">813</FONT> <a name="line.813"></a> <FONT color="green">814</FONT> omegaCount = 0;<a name="line.814"></a> <FONT color="green">815</FONT> omegaReal = null;<a name="line.815"></a> <FONT color="green">816</FONT> omegaImaginaryForward = null;<a name="line.816"></a> <FONT color="green">817</FONT> omegaImaginaryInverse = null;<a name="line.817"></a> <FONT color="green">818</FONT> isForward = true;<a name="line.818"></a> <FONT color="green">819</FONT> <a name="line.819"></a> <FONT color="green">820</FONT> }<a name="line.820"></a> <FONT color="green">821</FONT> <a name="line.821"></a> <FONT color="green">822</FONT> /**<a name="line.822"></a> <FONT color="green">823</FONT> * Check if computation has been done for forward or reverse transform.<a name="line.823"></a> <FONT color="green">824</FONT> * @return true if computation has been done for forward transform<a name="line.824"></a> <FONT color="green">825</FONT> * @throws IllegalStateException if no roots of unity have been computed yet<a name="line.825"></a> <FONT color="green">826</FONT> */<a name="line.826"></a> <FONT color="green">827</FONT> public synchronized boolean isForward() throws IllegalStateException {<a name="line.827"></a> <FONT color="green">828</FONT> <a name="line.828"></a> <FONT color="green">829</FONT> if (omegaCount == 0) {<a name="line.829"></a> <FONT color="green">830</FONT> throw MathRuntimeException.createIllegalStateException(<a name="line.830"></a> <FONT color="green">831</FONT> MISSING_ROOTS_OF_UNITY_MESSAGE);<a name="line.831"></a> <FONT color="green">832</FONT> }<a name="line.832"></a> <FONT color="green">833</FONT> return isForward;<a name="line.833"></a> <FONT color="green">834</FONT> <a name="line.834"></a> <FONT color="green">835</FONT> }<a name="line.835"></a> <FONT color="green">836</FONT> <a name="line.836"></a> <FONT color="green">837</FONT> /** Computes the n<sup>th</sup> roots of unity.<a name="line.837"></a> <FONT color="green">838</FONT> * <p>The computed omega[] = { 1, w, w<sup>2</sup>, ... w<sup>(n-1)</sup> } where<a name="line.838"></a> <FONT color="green">839</FONT> * w = exp(-2 &pi; i / n), i = &sqrt;(-1).</p><a name="line.839"></a> <FONT color="green">840</FONT> * <p>Note that n is positive for<a name="line.840"></a> <FONT color="green">841</FONT> * forward transform and negative for inverse transform.</p><a name="line.841"></a> <FONT color="green">842</FONT> * @param n number of roots of unity to compute,<a name="line.842"></a> <FONT color="green">843</FONT> * positive for forward transform, negative for inverse transform<a name="line.843"></a> <FONT color="green">844</FONT> * @throws IllegalArgumentException if n = 0<a name="line.844"></a> <FONT color="green">845</FONT> */<a name="line.845"></a> <FONT color="green">846</FONT> public synchronized void computeOmega(int n) throws IllegalArgumentException {<a name="line.846"></a> <FONT color="green">847</FONT> <a name="line.847"></a> <FONT color="green">848</FONT> if (n == 0) {<a name="line.848"></a> <FONT color="green">849</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.849"></a> <FONT color="green">850</FONT> "cannot compute 0-th root of unity, indefinite result");<a name="line.850"></a> <FONT color="green">851</FONT> }<a name="line.851"></a> <FONT color="green">852</FONT> <a name="line.852"></a> <FONT color="green">853</FONT> isForward = n > 0;<a name="line.853"></a> <FONT color="green">854</FONT> <a name="line.854"></a> <FONT color="green">855</FONT> // avoid repetitive calculations<a name="line.855"></a> <FONT color="green">856</FONT> final int absN = Math.abs(n);<a name="line.856"></a> <FONT color="green">857</FONT> <a name="line.857"></a> <FONT color="green">858</FONT> if (absN == omegaCount) {<a name="line.858"></a> <FONT color="green">859</FONT> return;<a name="line.859"></a> <FONT color="green">860</FONT> }<a name="line.860"></a> <FONT color="green">861</FONT> <a name="line.861"></a> <FONT color="green">862</FONT> // calculate everything from scratch, for both forward and inverse versions<a name="line.862"></a> <FONT color="green">863</FONT> final double t = 2.0 * Math.PI / absN;<a name="line.863"></a> <FONT color="green">864</FONT> final double cosT = Math.cos(t);<a name="line.864"></a> <FONT color="green">865</FONT> final double sinT = Math.sin(t);<a name="line.865"></a> <FONT color="green">866</FONT> omegaReal = new double[absN];<a name="line.866"></a> <FONT color="green">867</FONT> omegaImaginaryForward = new double[absN];<a name="line.867"></a> <FONT color="green">868</FONT> omegaImaginaryInverse = new double[absN];<a name="line.868"></a> <FONT color="green">869</FONT> omegaReal[0] = 1.0;<a name="line.869"></a> <FONT color="green">870</FONT> omegaImaginaryForward[0] = 0.0;<a name="line.870"></a> <FONT color="green">871</FONT> omegaImaginaryInverse[0] = 0.0;<a name="line.871"></a> <FONT color="green">872</FONT> for (int i = 1; i < absN; i++) {<a name="line.872"></a> <FONT color="green">873</FONT> omegaReal[i] =<a name="line.873"></a> <FONT color="green">874</FONT> omegaReal[i-1] * cosT + omegaImaginaryForward[i-1] * sinT;<a name="line.874"></a> <FONT color="green">875</FONT> omegaImaginaryForward[i] =<a name="line.875"></a> <FONT color="green">876</FONT> omegaImaginaryForward[i-1] * cosT - omegaReal[i-1] * sinT;<a name="line.876"></a> <FONT color="green">877</FONT> omegaImaginaryInverse[i] = -omegaImaginaryForward[i];<a name="line.877"></a> <FONT color="green">878</FONT> }<a name="line.878"></a> <FONT color="green">879</FONT> omegaCount = absN;<a name="line.879"></a> <FONT color="green">880</FONT> <a name="line.880"></a> <FONT color="green">881</FONT> }<a name="line.881"></a> <FONT color="green">882</FONT> <a name="line.882"></a> <FONT color="green">883</FONT> /**<a name="line.883"></a> <FONT color="green">884</FONT> * Get the real part of the k<sup>th</sup> n<sup>th</sup> root of unity<a name="line.884"></a> <FONT color="green">885</FONT> * @param k index of the n<sup>th</sup> root of unity<a name="line.885"></a> <FONT color="green">886</FONT> * @return real part of the k<sup>th</sup> n<sup>th</sup> root of unity<a name="line.886"></a> <FONT color="green">887</FONT> * @throws IllegalStateException if no roots of unity have been computed yet<a name="line.887"></a> <FONT color="green">888</FONT> * @throws IllegalArgumentException if k is out of range<a name="line.888"></a> <FONT color="green">889</FONT> */<a name="line.889"></a> <FONT color="green">890</FONT> public synchronized double getOmegaReal(int k)<a name="line.890"></a> <FONT color="green">891</FONT> throws IllegalStateException, IllegalArgumentException {<a name="line.891"></a> <FONT color="green">892</FONT> <a name="line.892"></a> <FONT color="green">893</FONT> if (omegaCount == 0) {<a name="line.893"></a> <FONT color="green">894</FONT> throw MathRuntimeException.createIllegalStateException(<a name="line.894"></a> <FONT color="green">895</FONT> MISSING_ROOTS_OF_UNITY_MESSAGE);<a name="line.895"></a> <FONT color="green">896</FONT> }<a name="line.896"></a> <FONT color="green">897</FONT> if ((k < 0) || (k >= omegaCount)) {<a name="line.897"></a> <FONT color="green">898</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.898"></a> <FONT color="green">899</FONT> OUT_OF_RANGE_ROOT_INDEX_MESSAGE, k, 0, omegaCount - 1);<a name="line.899"></a> <FONT color="green">900</FONT> }<a name="line.900"></a> <FONT color="green">901</FONT> <a name="line.901"></a> <FONT color="green">902</FONT> return omegaReal[k];<a name="line.902"></a> <FONT color="green">903</FONT> <a name="line.903"></a> <FONT color="green">904</FONT> }<a name="line.904"></a> <FONT color="green">905</FONT> <a name="line.905"></a> <FONT color="green">906</FONT> /**<a name="line.906"></a> <FONT color="green">907</FONT> * Get the imaginary part of the k<sup>th</sup> n<sup>th</sup> root of unity<a name="line.907"></a> <FONT color="green">908</FONT> * @param k index of the n<sup>th</sup> root of unity<a name="line.908"></a> <FONT color="green">909</FONT> * @return imaginary part of the k<sup>th</sup> n<sup>th</sup> root of unity<a name="line.909"></a> <FONT color="green">910</FONT> * @throws IllegalStateException if no roots of unity have been computed yet<a name="line.910"></a> <FONT color="green">911</FONT> * @throws IllegalArgumentException if k is out of range<a name="line.911"></a> <FONT color="green">912</FONT> */<a name="line.912"></a> <FONT color="green">913</FONT> public synchronized double getOmegaImaginary(int k)<a name="line.913"></a> <FONT color="green">914</FONT> throws IllegalStateException, IllegalArgumentException {<a name="line.914"></a> <FONT color="green">915</FONT> <a name="line.915"></a> <FONT color="green">916</FONT> if (omegaCount == 0) {<a name="line.916"></a> <FONT color="green">917</FONT> throw MathRuntimeException.createIllegalStateException(<a name="line.917"></a> <FONT color="green">918</FONT> MISSING_ROOTS_OF_UNITY_MESSAGE);<a name="line.918"></a> <FONT color="green">919</FONT> }<a name="line.919"></a> <FONT color="green">920</FONT> if ((k < 0) || (k >= omegaCount)) {<a name="line.920"></a> <FONT color="green">921</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.921"></a> <FONT color="green">922</FONT> OUT_OF_RANGE_ROOT_INDEX_MESSAGE, k, 0, omegaCount - 1);<a name="line.922"></a> <FONT color="green">923</FONT> }<a name="line.923"></a> <FONT color="green">924</FONT> <a name="line.924"></a> <FONT color="green">925</FONT> return isForward ? omegaImaginaryForward[k] : omegaImaginaryInverse[k];<a name="line.925"></a> <FONT color="green">926</FONT> <a name="line.926"></a> <FONT color="green">927</FONT> }<a name="line.927"></a> <FONT color="green">928</FONT> <a name="line.928"></a> <FONT color="green">929</FONT> }<a name="line.929"></a> <FONT color="green">930</FONT> <a name="line.930"></a> <FONT color="green">931</FONT> }<a name="line.931"></a> </PRE> </BODY> </HTML>