Mercurial > hg > de.mpg.mpiwg.itgroup.digilib.plugin
comparison libs/commons-math-2.1/docs/apidocs/src-html/org/apache/commons/math/transform/FastFourierTransformer.html @ 13:cbf34dd4d7e6
commons-math-2.1 added
| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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| 12:970d26a94fb7 | 13:cbf34dd4d7e6 |
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| 1 <HTML> | |
| 2 <BODY BGCOLOR="white"> | |
| 3 <PRE> | |
| 4 <FONT color="green">001</FONT> /*<a name="line.1"></a> | |
| 5 <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> | |
| 6 <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> | |
| 7 <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> | |
| 8 <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> | |
| 9 <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> | |
| 10 <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> | |
| 11 <FONT color="green">008</FONT> *<a name="line.8"></a> | |
| 12 <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> | |
| 13 <FONT color="green">010</FONT> *<a name="line.10"></a> | |
| 14 <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> | |
| 15 <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> | |
| 16 <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> | |
| 17 <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> | |
| 18 <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> | |
| 19 <FONT color="green">016</FONT> */<a name="line.16"></a> | |
| 20 <FONT color="green">017</FONT> package org.apache.commons.math.transform;<a name="line.17"></a> | |
| 21 <FONT color="green">018</FONT> <a name="line.18"></a> | |
| 22 <FONT color="green">019</FONT> import java.io.Serializable;<a name="line.19"></a> | |
| 23 <FONT color="green">020</FONT> import java.lang.reflect.Array;<a name="line.20"></a> | |
| 24 <FONT color="green">021</FONT> <a name="line.21"></a> | |
| 25 <FONT color="green">022</FONT> import org.apache.commons.math.FunctionEvaluationException;<a name="line.22"></a> | |
| 26 <FONT color="green">023</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.23"></a> | |
| 27 <FONT color="green">024</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.24"></a> | |
| 28 <FONT color="green">025</FONT> import org.apache.commons.math.complex.Complex;<a name="line.25"></a> | |
| 29 <FONT color="green">026</FONT> <a name="line.26"></a> | |
| 30 <FONT color="green">027</FONT> /**<a name="line.27"></a> | |
| 31 <FONT color="green">028</FONT> * Implements the <a href="http://mathworld.wolfram.com/FastFourierTransform.html"><a name="line.28"></a> | |
| 32 <FONT color="green">029</FONT> * Fast Fourier Transform</a> for transformation of one-dimensional data sets.<a name="line.29"></a> | |
| 33 <FONT color="green">030</FONT> * For reference, see <b>Applied Numerical Linear Algebra</b>, ISBN 0898713897,<a name="line.30"></a> | |
| 34 <FONT color="green">031</FONT> * chapter 6.<a name="line.31"></a> | |
| 35 <FONT color="green">032</FONT> * <p><a name="line.32"></a> | |
| 36 <FONT color="green">033</FONT> * There are several conventions for the definition of FFT and inverse FFT,<a name="line.33"></a> | |
| 37 <FONT color="green">034</FONT> * mainly on different coefficient and exponent. Here the equations are listed<a name="line.34"></a> | |
| 38 <FONT color="green">035</FONT> * in the comments of the corresponding methods.</p><a name="line.35"></a> | |
| 39 <FONT color="green">036</FONT> * <p><a name="line.36"></a> | |
| 40 <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> | |
| 41 <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> | |
| 42 <FONT color="green">039</FONT> * requirement. There are other flavors of FFT, for reference, see S. Winograd,<a name="line.39"></a> | |
| 43 <FONT color="green">040</FONT> * <i>On computing the discrete Fourier transform</i>, Mathematics of Computation,<a name="line.40"></a> | |
| 44 <FONT color="green">041</FONT> * 32 (1978), 175 - 199.</p><a name="line.41"></a> | |
| 45 <FONT color="green">042</FONT> *<a name="line.42"></a> | |
| 46 <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> | |
| 47 <FONT color="green">044</FONT> * @since 1.2<a name="line.44"></a> | |
| 48 <FONT color="green">045</FONT> */<a name="line.45"></a> | |
| 49 <FONT color="green">046</FONT> public class FastFourierTransformer implements Serializable {<a name="line.46"></a> | |
| 50 <FONT color="green">047</FONT> <a name="line.47"></a> | |
| 51 <FONT color="green">048</FONT> /** Serializable version identifier. */<a name="line.48"></a> | |
| 52 <FONT color="green">049</FONT> static final long serialVersionUID = 5138259215438106000L;<a name="line.49"></a> | |
| 53 <FONT color="green">050</FONT> <a name="line.50"></a> | |
| 54 <FONT color="green">051</FONT> /** Message for not power of 2. */<a name="line.51"></a> | |
| 55 <FONT color="green">052</FONT> private static final String NOT_POWER_OF_TWO_MESSAGE =<a name="line.52"></a> | |
| 56 <FONT color="green">053</FONT> "{0} is not a power of 2, consider padding for fix";<a name="line.53"></a> | |
| 57 <FONT color="green">054</FONT> <a name="line.54"></a> | |
| 58 <FONT color="green">055</FONT> /** Message for dimension mismatch. */<a name="line.55"></a> | |
| 59 <FONT color="green">056</FONT> private static final String DIMENSION_MISMATCH_MESSAGE =<a name="line.56"></a> | |
| 60 <FONT color="green">057</FONT> "some dimensions don't match: {0} != {1}";<a name="line.57"></a> | |
| 61 <FONT color="green">058</FONT> <a name="line.58"></a> | |
| 62 <FONT color="green">059</FONT> /** Message for not computed roots of unity. */<a name="line.59"></a> | |
| 63 <FONT color="green">060</FONT> private static final String MISSING_ROOTS_OF_UNITY_MESSAGE =<a name="line.60"></a> | |
| 64 <FONT color="green">061</FONT> "roots of unity have not been computed yet";<a name="line.61"></a> | |
| 65 <FONT color="green">062</FONT> <a name="line.62"></a> | |
| 66 <FONT color="green">063</FONT> /** Message for out of range root index. */<a name="line.63"></a> | |
| 67 <FONT color="green">064</FONT> private static final String OUT_OF_RANGE_ROOT_INDEX_MESSAGE =<a name="line.64"></a> | |
| 68 <FONT color="green">065</FONT> "out of range root of unity index {0} (must be in [{1};{2}])";<a name="line.65"></a> | |
| 69 <FONT color="green">066</FONT> <a name="line.66"></a> | |
| 70 <FONT color="green">067</FONT> /** roots of unity */<a name="line.67"></a> | |
| 71 <FONT color="green">068</FONT> private RootsOfUnity roots = new RootsOfUnity();<a name="line.68"></a> | |
| 72 <FONT color="green">069</FONT> <a name="line.69"></a> | |
| 73 <FONT color="green">070</FONT> /**<a name="line.70"></a> | |
| 74 <FONT color="green">071</FONT> * Construct a default transformer.<a name="line.71"></a> | |
| 75 <FONT color="green">072</FONT> */<a name="line.72"></a> | |
| 76 <FONT color="green">073</FONT> public FastFourierTransformer() {<a name="line.73"></a> | |
| 77 <FONT color="green">074</FONT> super();<a name="line.74"></a> | |
| 78 <FONT color="green">075</FONT> }<a name="line.75"></a> | |
| 79 <FONT color="green">076</FONT> <a name="line.76"></a> | |
| 80 <FONT color="green">077</FONT> /**<a name="line.77"></a> | |
| 81 <FONT color="green">078</FONT> * Transform the given real data set.<a name="line.78"></a> | |
| 82 <FONT color="green">079</FONT> * <p><a name="line.79"></a> | |
| 83 <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> | |
| 84 <FONT color="green">081</FONT> * </p><a name="line.81"></a> | |
| 85 <FONT color="green">082</FONT> *<a name="line.82"></a> | |
| 86 <FONT color="green">083</FONT> * @param f the real data array to be transformed<a name="line.83"></a> | |
| 87 <FONT color="green">084</FONT> * @return the complex transformed array<a name="line.84"></a> | |
| 88 <FONT color="green">085</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.85"></a> | |
| 89 <FONT color="green">086</FONT> */<a name="line.86"></a> | |
| 90 <FONT color="green">087</FONT> public Complex[] transform(double f[])<a name="line.87"></a> | |
| 91 <FONT color="green">088</FONT> throws IllegalArgumentException {<a name="line.88"></a> | |
| 92 <FONT color="green">089</FONT> return fft(f, false);<a name="line.89"></a> | |
| 93 <FONT color="green">090</FONT> }<a name="line.90"></a> | |
| 94 <FONT color="green">091</FONT> <a name="line.91"></a> | |
| 95 <FONT color="green">092</FONT> /**<a name="line.92"></a> | |
| 96 <FONT color="green">093</FONT> * Transform the given real function, sampled on the given interval.<a name="line.93"></a> | |
| 97 <FONT color="green">094</FONT> * <p><a name="line.94"></a> | |
| 98 <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> | |
| 99 <FONT color="green">096</FONT> * </p><a name="line.96"></a> | |
| 100 <FONT color="green">097</FONT> *<a name="line.97"></a> | |
| 101 <FONT color="green">098</FONT> * @param f the function to be sampled and transformed<a name="line.98"></a> | |
| 102 <FONT color="green">099</FONT> * @param min the lower bound for the interval<a name="line.99"></a> | |
| 103 <FONT color="green">100</FONT> * @param max the upper bound for the interval<a name="line.100"></a> | |
| 104 <FONT color="green">101</FONT> * @param n the number of sample points<a name="line.101"></a> | |
| 105 <FONT color="green">102</FONT> * @return the complex transformed array<a name="line.102"></a> | |
| 106 <FONT color="green">103</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.103"></a> | |
| 107 <FONT color="green">104</FONT> * at some point<a name="line.104"></a> | |
| 108 <FONT color="green">105</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.105"></a> | |
| 109 <FONT color="green">106</FONT> */<a name="line.106"></a> | |
| 110 <FONT color="green">107</FONT> public Complex[] transform(UnivariateRealFunction f,<a name="line.107"></a> | |
| 111 <FONT color="green">108</FONT> double min, double max, int n)<a name="line.108"></a> | |
| 112 <FONT color="green">109</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.109"></a> | |
| 113 <FONT color="green">110</FONT> double data[] = sample(f, min, max, n);<a name="line.110"></a> | |
| 114 <FONT color="green">111</FONT> return fft(data, false);<a name="line.111"></a> | |
| 115 <FONT color="green">112</FONT> }<a name="line.112"></a> | |
| 116 <FONT color="green">113</FONT> <a name="line.113"></a> | |
| 117 <FONT color="green">114</FONT> /**<a name="line.114"></a> | |
| 118 <FONT color="green">115</FONT> * Transform the given complex data set.<a name="line.115"></a> | |
| 119 <FONT color="green">116</FONT> * <p><a name="line.116"></a> | |
| 120 <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> | |
| 121 <FONT color="green">118</FONT> * </p><a name="line.118"></a> | |
| 122 <FONT color="green">119</FONT> *<a name="line.119"></a> | |
| 123 <FONT color="green">120</FONT> * @param f the complex data array to be transformed<a name="line.120"></a> | |
| 124 <FONT color="green">121</FONT> * @return the complex transformed array<a name="line.121"></a> | |
| 125 <FONT color="green">122</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.122"></a> | |
| 126 <FONT color="green">123</FONT> */<a name="line.123"></a> | |
| 127 <FONT color="green">124</FONT> public Complex[] transform(Complex f[])<a name="line.124"></a> | |
| 128 <FONT color="green">125</FONT> throws IllegalArgumentException {<a name="line.125"></a> | |
| 129 <FONT color="green">126</FONT> roots.computeOmega(f.length);<a name="line.126"></a> | |
| 130 <FONT color="green">127</FONT> return fft(f);<a name="line.127"></a> | |
| 131 <FONT color="green">128</FONT> }<a name="line.128"></a> | |
| 132 <FONT color="green">129</FONT> <a name="line.129"></a> | |
| 133 <FONT color="green">130</FONT> /**<a name="line.130"></a> | |
| 134 <FONT color="green">131</FONT> * Transform the given real data set.<a name="line.131"></a> | |
| 135 <FONT color="green">132</FONT> * <p><a name="line.132"></a> | |
| 136 <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> | |
| 137 <FONT color="green">134</FONT> * </p><a name="line.134"></a> | |
| 138 <FONT color="green">135</FONT> *<a name="line.135"></a> | |
| 139 <FONT color="green">136</FONT> * @param f the real data array to be transformed<a name="line.136"></a> | |
| 140 <FONT color="green">137</FONT> * @return the complex transformed array<a name="line.137"></a> | |
| 141 <FONT color="green">138</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.138"></a> | |
| 142 <FONT color="green">139</FONT> */<a name="line.139"></a> | |
| 143 <FONT color="green">140</FONT> public Complex[] transform2(double f[])<a name="line.140"></a> | |
| 144 <FONT color="green">141</FONT> throws IllegalArgumentException {<a name="line.141"></a> | |
| 145 <FONT color="green">142</FONT> <a name="line.142"></a> | |
| 146 <FONT color="green">143</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.143"></a> | |
| 147 <FONT color="green">144</FONT> return scaleArray(fft(f, false), scaling_coefficient);<a name="line.144"></a> | |
| 148 <FONT color="green">145</FONT> }<a name="line.145"></a> | |
| 149 <FONT color="green">146</FONT> <a name="line.146"></a> | |
| 150 <FONT color="green">147</FONT> /**<a name="line.147"></a> | |
| 151 <FONT color="green">148</FONT> * Transform the given real function, sampled on the given interval.<a name="line.148"></a> | |
| 152 <FONT color="green">149</FONT> * <p><a name="line.149"></a> | |
| 153 <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> | |
| 154 <FONT color="green">151</FONT> * </p><a name="line.151"></a> | |
| 155 <FONT color="green">152</FONT> *<a name="line.152"></a> | |
| 156 <FONT color="green">153</FONT> * @param f the function to be sampled and transformed<a name="line.153"></a> | |
| 157 <FONT color="green">154</FONT> * @param min the lower bound for the interval<a name="line.154"></a> | |
| 158 <FONT color="green">155</FONT> * @param max the upper bound for the interval<a name="line.155"></a> | |
| 159 <FONT color="green">156</FONT> * @param n the number of sample points<a name="line.156"></a> | |
| 160 <FONT color="green">157</FONT> * @return the complex transformed array<a name="line.157"></a> | |
| 161 <FONT color="green">158</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.158"></a> | |
| 162 <FONT color="green">159</FONT> * at some point<a name="line.159"></a> | |
| 163 <FONT color="green">160</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.160"></a> | |
| 164 <FONT color="green">161</FONT> */<a name="line.161"></a> | |
| 165 <FONT color="green">162</FONT> public Complex[] transform2(UnivariateRealFunction f,<a name="line.162"></a> | |
| 166 <FONT color="green">163</FONT> double min, double max, int n)<a name="line.163"></a> | |
| 167 <FONT color="green">164</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.164"></a> | |
| 168 <FONT color="green">165</FONT> <a name="line.165"></a> | |
| 169 <FONT color="green">166</FONT> double data[] = sample(f, min, max, n);<a name="line.166"></a> | |
| 170 <FONT color="green">167</FONT> double scaling_coefficient = 1.0 / Math.sqrt(n);<a name="line.167"></a> | |
| 171 <FONT color="green">168</FONT> return scaleArray(fft(data, false), scaling_coefficient);<a name="line.168"></a> | |
| 172 <FONT color="green">169</FONT> }<a name="line.169"></a> | |
| 173 <FONT color="green">170</FONT> <a name="line.170"></a> | |
| 174 <FONT color="green">171</FONT> /**<a name="line.171"></a> | |
| 175 <FONT color="green">172</FONT> * Transform the given complex data set.<a name="line.172"></a> | |
| 176 <FONT color="green">173</FONT> * <p><a name="line.173"></a> | |
| 177 <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> | |
| 178 <FONT color="green">175</FONT> * </p><a name="line.175"></a> | |
| 179 <FONT color="green">176</FONT> *<a name="line.176"></a> | |
| 180 <FONT color="green">177</FONT> * @param f the complex data array to be transformed<a name="line.177"></a> | |
| 181 <FONT color="green">178</FONT> * @return the complex transformed array<a name="line.178"></a> | |
| 182 <FONT color="green">179</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.179"></a> | |
| 183 <FONT color="green">180</FONT> */<a name="line.180"></a> | |
| 184 <FONT color="green">181</FONT> public Complex[] transform2(Complex f[])<a name="line.181"></a> | |
| 185 <FONT color="green">182</FONT> throws IllegalArgumentException {<a name="line.182"></a> | |
| 186 <FONT color="green">183</FONT> <a name="line.183"></a> | |
| 187 <FONT color="green">184</FONT> roots.computeOmega(f.length);<a name="line.184"></a> | |
| 188 <FONT color="green">185</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.185"></a> | |
| 189 <FONT color="green">186</FONT> return scaleArray(fft(f), scaling_coefficient);<a name="line.186"></a> | |
| 190 <FONT color="green">187</FONT> }<a name="line.187"></a> | |
| 191 <FONT color="green">188</FONT> <a name="line.188"></a> | |
| 192 <FONT color="green">189</FONT> /**<a name="line.189"></a> | |
| 193 <FONT color="green">190</FONT> * Inversely transform the given real data set.<a name="line.190"></a> | |
| 194 <FONT color="green">191</FONT> * <p><a name="line.191"></a> | |
| 195 <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> | |
| 196 <FONT color="green">193</FONT> * </p><a name="line.193"></a> | |
| 197 <FONT color="green">194</FONT> *<a name="line.194"></a> | |
| 198 <FONT color="green">195</FONT> * @param f the real data array to be inversely transformed<a name="line.195"></a> | |
| 199 <FONT color="green">196</FONT> * @return the complex inversely transformed array<a name="line.196"></a> | |
| 200 <FONT color="green">197</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.197"></a> | |
| 201 <FONT color="green">198</FONT> */<a name="line.198"></a> | |
| 202 <FONT color="green">199</FONT> public Complex[] inversetransform(double f[])<a name="line.199"></a> | |
| 203 <FONT color="green">200</FONT> throws IllegalArgumentException {<a name="line.200"></a> | |
| 204 <FONT color="green">201</FONT> <a name="line.201"></a> | |
| 205 <FONT color="green">202</FONT> double scaling_coefficient = 1.0 / f.length;<a name="line.202"></a> | |
| 206 <FONT color="green">203</FONT> return scaleArray(fft(f, true), scaling_coefficient);<a name="line.203"></a> | |
| 207 <FONT color="green">204</FONT> }<a name="line.204"></a> | |
| 208 <FONT color="green">205</FONT> <a name="line.205"></a> | |
| 209 <FONT color="green">206</FONT> /**<a name="line.206"></a> | |
| 210 <FONT color="green">207</FONT> * Inversely transform the given real function, sampled on the given interval.<a name="line.207"></a> | |
| 211 <FONT color="green">208</FONT> * <p><a name="line.208"></a> | |
| 212 <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> | |
| 213 <FONT color="green">210</FONT> * </p><a name="line.210"></a> | |
| 214 <FONT color="green">211</FONT> *<a name="line.211"></a> | |
| 215 <FONT color="green">212</FONT> * @param f the function to be sampled and inversely transformed<a name="line.212"></a> | |
| 216 <FONT color="green">213</FONT> * @param min the lower bound for the interval<a name="line.213"></a> | |
| 217 <FONT color="green">214</FONT> * @param max the upper bound for the interval<a name="line.214"></a> | |
| 218 <FONT color="green">215</FONT> * @param n the number of sample points<a name="line.215"></a> | |
| 219 <FONT color="green">216</FONT> * @return the complex inversely transformed array<a name="line.216"></a> | |
| 220 <FONT color="green">217</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.217"></a> | |
| 221 <FONT color="green">218</FONT> * at some point<a name="line.218"></a> | |
| 222 <FONT color="green">219</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.219"></a> | |
| 223 <FONT color="green">220</FONT> */<a name="line.220"></a> | |
| 224 <FONT color="green">221</FONT> public Complex[] inversetransform(UnivariateRealFunction f,<a name="line.221"></a> | |
| 225 <FONT color="green">222</FONT> double min, double max, int n)<a name="line.222"></a> | |
| 226 <FONT color="green">223</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.223"></a> | |
| 227 <FONT color="green">224</FONT> <a name="line.224"></a> | |
| 228 <FONT color="green">225</FONT> double data[] = sample(f, min, max, n);<a name="line.225"></a> | |
| 229 <FONT color="green">226</FONT> double scaling_coefficient = 1.0 / n;<a name="line.226"></a> | |
| 230 <FONT color="green">227</FONT> return scaleArray(fft(data, true), scaling_coefficient);<a name="line.227"></a> | |
| 231 <FONT color="green">228</FONT> }<a name="line.228"></a> | |
| 232 <FONT color="green">229</FONT> <a name="line.229"></a> | |
| 233 <FONT color="green">230</FONT> /**<a name="line.230"></a> | |
| 234 <FONT color="green">231</FONT> * Inversely transform the given complex data set.<a name="line.231"></a> | |
| 235 <FONT color="green">232</FONT> * <p><a name="line.232"></a> | |
| 236 <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> | |
| 237 <FONT color="green">234</FONT> * </p><a name="line.234"></a> | |
| 238 <FONT color="green">235</FONT> *<a name="line.235"></a> | |
| 239 <FONT color="green">236</FONT> * @param f the complex data array to be inversely transformed<a name="line.236"></a> | |
| 240 <FONT color="green">237</FONT> * @return the complex inversely transformed array<a name="line.237"></a> | |
| 241 <FONT color="green">238</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.238"></a> | |
| 242 <FONT color="green">239</FONT> */<a name="line.239"></a> | |
| 243 <FONT color="green">240</FONT> public Complex[] inversetransform(Complex f[])<a name="line.240"></a> | |
| 244 <FONT color="green">241</FONT> throws IllegalArgumentException {<a name="line.241"></a> | |
| 245 <FONT color="green">242</FONT> <a name="line.242"></a> | |
| 246 <FONT color="green">243</FONT> roots.computeOmega(-f.length); // pass negative argument<a name="line.243"></a> | |
| 247 <FONT color="green">244</FONT> double scaling_coefficient = 1.0 / f.length;<a name="line.244"></a> | |
| 248 <FONT color="green">245</FONT> return scaleArray(fft(f), scaling_coefficient);<a name="line.245"></a> | |
| 249 <FONT color="green">246</FONT> }<a name="line.246"></a> | |
| 250 <FONT color="green">247</FONT> <a name="line.247"></a> | |
| 251 <FONT color="green">248</FONT> /**<a name="line.248"></a> | |
| 252 <FONT color="green">249</FONT> * Inversely transform the given real data set.<a name="line.249"></a> | |
| 253 <FONT color="green">250</FONT> * <p><a name="line.250"></a> | |
| 254 <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> | |
| 255 <FONT color="green">252</FONT> * </p><a name="line.252"></a> | |
| 256 <FONT color="green">253</FONT> *<a name="line.253"></a> | |
| 257 <FONT color="green">254</FONT> * @param f the real data array to be inversely transformed<a name="line.254"></a> | |
| 258 <FONT color="green">255</FONT> * @return the complex inversely transformed array<a name="line.255"></a> | |
| 259 <FONT color="green">256</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.256"></a> | |
| 260 <FONT color="green">257</FONT> */<a name="line.257"></a> | |
| 261 <FONT color="green">258</FONT> public Complex[] inversetransform2(double f[])<a name="line.258"></a> | |
| 262 <FONT color="green">259</FONT> throws IllegalArgumentException {<a name="line.259"></a> | |
| 263 <FONT color="green">260</FONT> <a name="line.260"></a> | |
| 264 <FONT color="green">261</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.261"></a> | |
| 265 <FONT color="green">262</FONT> return scaleArray(fft(f, true), scaling_coefficient);<a name="line.262"></a> | |
| 266 <FONT color="green">263</FONT> }<a name="line.263"></a> | |
| 267 <FONT color="green">264</FONT> <a name="line.264"></a> | |
| 268 <FONT color="green">265</FONT> /**<a name="line.265"></a> | |
| 269 <FONT color="green">266</FONT> * Inversely transform the given real function, sampled on the given interval.<a name="line.266"></a> | |
| 270 <FONT color="green">267</FONT> * <p><a name="line.267"></a> | |
| 271 <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> | |
| 272 <FONT color="green">269</FONT> * </p><a name="line.269"></a> | |
| 273 <FONT color="green">270</FONT> *<a name="line.270"></a> | |
| 274 <FONT color="green">271</FONT> * @param f the function to be sampled and inversely transformed<a name="line.271"></a> | |
| 275 <FONT color="green">272</FONT> * @param min the lower bound for the interval<a name="line.272"></a> | |
| 276 <FONT color="green">273</FONT> * @param max the upper bound for the interval<a name="line.273"></a> | |
| 277 <FONT color="green">274</FONT> * @param n the number of sample points<a name="line.274"></a> | |
| 278 <FONT color="green">275</FONT> * @return the complex inversely transformed array<a name="line.275"></a> | |
| 279 <FONT color="green">276</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.276"></a> | |
| 280 <FONT color="green">277</FONT> * at some point<a name="line.277"></a> | |
| 281 <FONT color="green">278</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.278"></a> | |
| 282 <FONT color="green">279</FONT> */<a name="line.279"></a> | |
| 283 <FONT color="green">280</FONT> public Complex[] inversetransform2(UnivariateRealFunction f,<a name="line.280"></a> | |
| 284 <FONT color="green">281</FONT> double min, double max, int n)<a name="line.281"></a> | |
| 285 <FONT color="green">282</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.282"></a> | |
| 286 <FONT color="green">283</FONT> <a name="line.283"></a> | |
| 287 <FONT color="green">284</FONT> double data[] = sample(f, min, max, n);<a name="line.284"></a> | |
| 288 <FONT color="green">285</FONT> double scaling_coefficient = 1.0 / Math.sqrt(n);<a name="line.285"></a> | |
| 289 <FONT color="green">286</FONT> return scaleArray(fft(data, true), scaling_coefficient);<a name="line.286"></a> | |
| 290 <FONT color="green">287</FONT> }<a name="line.287"></a> | |
| 291 <FONT color="green">288</FONT> <a name="line.288"></a> | |
| 292 <FONT color="green">289</FONT> /**<a name="line.289"></a> | |
| 293 <FONT color="green">290</FONT> * Inversely transform the given complex data set.<a name="line.290"></a> | |
| 294 <FONT color="green">291</FONT> * <p><a name="line.291"></a> | |
| 295 <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> | |
| 296 <FONT color="green">293</FONT> * </p><a name="line.293"></a> | |
| 297 <FONT color="green">294</FONT> *<a name="line.294"></a> | |
| 298 <FONT color="green">295</FONT> * @param f the complex data array to be inversely transformed<a name="line.295"></a> | |
| 299 <FONT color="green">296</FONT> * @return the complex inversely transformed array<a name="line.296"></a> | |
| 300 <FONT color="green">297</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.297"></a> | |
| 301 <FONT color="green">298</FONT> */<a name="line.298"></a> | |
| 302 <FONT color="green">299</FONT> public Complex[] inversetransform2(Complex f[])<a name="line.299"></a> | |
| 303 <FONT color="green">300</FONT> throws IllegalArgumentException {<a name="line.300"></a> | |
| 304 <FONT color="green">301</FONT> <a name="line.301"></a> | |
| 305 <FONT color="green">302</FONT> roots.computeOmega(-f.length); // pass negative argument<a name="line.302"></a> | |
| 306 <FONT color="green">303</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.303"></a> | |
| 307 <FONT color="green">304</FONT> return scaleArray(fft(f), scaling_coefficient);<a name="line.304"></a> | |
| 308 <FONT color="green">305</FONT> }<a name="line.305"></a> | |
| 309 <FONT color="green">306</FONT> <a name="line.306"></a> | |
| 310 <FONT color="green">307</FONT> /**<a name="line.307"></a> | |
| 311 <FONT color="green">308</FONT> * Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).<a name="line.308"></a> | |
| 312 <FONT color="green">309</FONT> *<a name="line.309"></a> | |
| 313 <FONT color="green">310</FONT> * @param f the real data array to be transformed<a name="line.310"></a> | |
| 314 <FONT color="green">311</FONT> * @param isInverse the indicator of forward or inverse transform<a name="line.311"></a> | |
| 315 <FONT color="green">312</FONT> * @return the complex transformed array<a name="line.312"></a> | |
| 316 <FONT color="green">313</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.313"></a> | |
| 317 <FONT color="green">314</FONT> */<a name="line.314"></a> | |
| 318 <FONT color="green">315</FONT> protected Complex[] fft(double f[], boolean isInverse)<a name="line.315"></a> | |
| 319 <FONT color="green">316</FONT> throws IllegalArgumentException {<a name="line.316"></a> | |
| 320 <FONT color="green">317</FONT> <a name="line.317"></a> | |
| 321 <FONT color="green">318</FONT> verifyDataSet(f);<a name="line.318"></a> | |
| 322 <FONT color="green">319</FONT> Complex F[] = new Complex[f.length];<a name="line.319"></a> | |
| 323 <FONT color="green">320</FONT> if (f.length == 1) {<a name="line.320"></a> | |
| 324 <FONT color="green">321</FONT> F[0] = new Complex(f[0], 0.0);<a name="line.321"></a> | |
| 325 <FONT color="green">322</FONT> return F;<a name="line.322"></a> | |
| 326 <FONT color="green">323</FONT> }<a name="line.323"></a> | |
| 327 <FONT color="green">324</FONT> <a name="line.324"></a> | |
| 328 <FONT color="green">325</FONT> // Rather than the naive real to complex conversion, pack 2N<a name="line.325"></a> | |
| 329 <FONT color="green">326</FONT> // real numbers into N complex numbers for better performance.<a name="line.326"></a> | |
| 330 <FONT color="green">327</FONT> int N = f.length >> 1;<a name="line.327"></a> | |
| 331 <FONT color="green">328</FONT> Complex c[] = new Complex[N];<a name="line.328"></a> | |
| 332 <FONT color="green">329</FONT> for (int i = 0; i < N; i++) {<a name="line.329"></a> | |
| 333 <FONT color="green">330</FONT> c[i] = new Complex(f[2*i], f[2*i+1]);<a name="line.330"></a> | |
| 334 <FONT color="green">331</FONT> }<a name="line.331"></a> | |
| 335 <FONT color="green">332</FONT> roots.computeOmega(isInverse ? -N : N);<a name="line.332"></a> | |
| 336 <FONT color="green">333</FONT> Complex z[] = fft(c);<a name="line.333"></a> | |
| 337 <FONT color="green">334</FONT> <a name="line.334"></a> | |
| 338 <FONT color="green">335</FONT> // reconstruct the FFT result for the original array<a name="line.335"></a> | |
| 339 <FONT color="green">336</FONT> roots.computeOmega(isInverse ? -2*N : 2*N);<a name="line.336"></a> | |
| 340 <FONT color="green">337</FONT> F[0] = new Complex(2 * (z[0].getReal() + z[0].getImaginary()), 0.0);<a name="line.337"></a> | |
| 341 <FONT color="green">338</FONT> F[N] = new Complex(2 * (z[0].getReal() - z[0].getImaginary()), 0.0);<a name="line.338"></a> | |
| 342 <FONT color="green">339</FONT> for (int i = 1; i < N; i++) {<a name="line.339"></a> | |
| 343 <FONT color="green">340</FONT> Complex A = z[N-i].conjugate();<a name="line.340"></a> | |
| 344 <FONT color="green">341</FONT> Complex B = z[i].add(A);<a name="line.341"></a> | |
| 345 <FONT color="green">342</FONT> Complex C = z[i].subtract(A);<a name="line.342"></a> | |
| 346 <FONT color="green">343</FONT> //Complex D = roots.getOmega(i).multiply(Complex.I);<a name="line.343"></a> | |
| 347 <FONT color="green">344</FONT> Complex D = new Complex(-roots.getOmegaImaginary(i),<a name="line.344"></a> | |
| 348 <FONT color="green">345</FONT> roots.getOmegaReal(i));<a name="line.345"></a> | |
| 349 <FONT color="green">346</FONT> F[i] = B.subtract(C.multiply(D));<a name="line.346"></a> | |
| 350 <FONT color="green">347</FONT> F[2*N-i] = F[i].conjugate();<a name="line.347"></a> | |
| 351 <FONT color="green">348</FONT> }<a name="line.348"></a> | |
| 352 <FONT color="green">349</FONT> <a name="line.349"></a> | |
| 353 <FONT color="green">350</FONT> return scaleArray(F, 0.5);<a name="line.350"></a> | |
| 354 <FONT color="green">351</FONT> }<a name="line.351"></a> | |
| 355 <FONT color="green">352</FONT> <a name="line.352"></a> | |
| 356 <FONT color="green">353</FONT> /**<a name="line.353"></a> | |
| 357 <FONT color="green">354</FONT> * Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).<a name="line.354"></a> | |
| 358 <FONT color="green">355</FONT> *<a name="line.355"></a> | |
| 359 <FONT color="green">356</FONT> * @param data the complex data array to be transformed<a name="line.356"></a> | |
| 360 <FONT color="green">357</FONT> * @return the complex transformed array<a name="line.357"></a> | |
| 361 <FONT color="green">358</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.358"></a> | |
| 362 <FONT color="green">359</FONT> */<a name="line.359"></a> | |
| 363 <FONT color="green">360</FONT> protected Complex[] fft(Complex data[])<a name="line.360"></a> | |
| 364 <FONT color="green">361</FONT> throws IllegalArgumentException {<a name="line.361"></a> | |
| 365 <FONT color="green">362</FONT> <a name="line.362"></a> | |
| 366 <FONT color="green">363</FONT> final int n = data.length;<a name="line.363"></a> | |
| 367 <FONT color="green">364</FONT> final Complex f[] = new Complex[n];<a name="line.364"></a> | |
| 368 <FONT color="green">365</FONT> <a name="line.365"></a> | |
| 369 <FONT color="green">366</FONT> // initial simple cases<a name="line.366"></a> | |
| 370 <FONT color="green">367</FONT> verifyDataSet(data);<a name="line.367"></a> | |
| 371 <FONT color="green">368</FONT> if (n == 1) {<a name="line.368"></a> | |
| 372 <FONT color="green">369</FONT> f[0] = data[0];<a name="line.369"></a> | |
| 373 <FONT color="green">370</FONT> return f;<a name="line.370"></a> | |
| 374 <FONT color="green">371</FONT> }<a name="line.371"></a> | |
| 375 <FONT color="green">372</FONT> if (n == 2) {<a name="line.372"></a> | |
| 376 <FONT color="green">373</FONT> f[0] = data[0].add(data[1]);<a name="line.373"></a> | |
| 377 <FONT color="green">374</FONT> f[1] = data[0].subtract(data[1]);<a name="line.374"></a> | |
| 378 <FONT color="green">375</FONT> return f;<a name="line.375"></a> | |
| 379 <FONT color="green">376</FONT> }<a name="line.376"></a> | |
| 380 <FONT color="green">377</FONT> <a name="line.377"></a> | |
| 381 <FONT color="green">378</FONT> // permute original data array in bit-reversal order<a name="line.378"></a> | |
| 382 <FONT color="green">379</FONT> int ii = 0;<a name="line.379"></a> | |
| 383 <FONT color="green">380</FONT> for (int i = 0; i < n; i++) {<a name="line.380"></a> | |
| 384 <FONT color="green">381</FONT> f[i] = data[ii];<a name="line.381"></a> | |
| 385 <FONT color="green">382</FONT> int k = n >> 1;<a name="line.382"></a> | |
| 386 <FONT color="green">383</FONT> while (ii >= k && k > 0) {<a name="line.383"></a> | |
| 387 <FONT color="green">384</FONT> ii -= k; k >>= 1;<a name="line.384"></a> | |
| 388 <FONT color="green">385</FONT> }<a name="line.385"></a> | |
| 389 <FONT color="green">386</FONT> ii += k;<a name="line.386"></a> | |
| 390 <FONT color="green">387</FONT> }<a name="line.387"></a> | |
| 391 <FONT color="green">388</FONT> <a name="line.388"></a> | |
| 392 <FONT color="green">389</FONT> // the bottom base-4 round<a name="line.389"></a> | |
| 393 <FONT color="green">390</FONT> for (int i = 0; i < n; i += 4) {<a name="line.390"></a> | |
| 394 <FONT color="green">391</FONT> final Complex a = f[i].add(f[i+1]);<a name="line.391"></a> | |
| 395 <FONT color="green">392</FONT> final Complex b = f[i+2].add(f[i+3]);<a name="line.392"></a> | |
| 396 <FONT color="green">393</FONT> final Complex c = f[i].subtract(f[i+1]);<a name="line.393"></a> | |
| 397 <FONT color="green">394</FONT> final Complex d = f[i+2].subtract(f[i+3]);<a name="line.394"></a> | |
| 398 <FONT color="green">395</FONT> final Complex e1 = c.add(d.multiply(Complex.I));<a name="line.395"></a> | |
| 399 <FONT color="green">396</FONT> final Complex e2 = c.subtract(d.multiply(Complex.I));<a name="line.396"></a> | |
| 400 <FONT color="green">397</FONT> f[i] = a.add(b);<a name="line.397"></a> | |
| 401 <FONT color="green">398</FONT> f[i+2] = a.subtract(b);<a name="line.398"></a> | |
| 402 <FONT color="green">399</FONT> // omegaCount indicates forward or inverse transform<a name="line.399"></a> | |
| 403 <FONT color="green">400</FONT> f[i+1] = roots.isForward() ? e2 : e1;<a name="line.400"></a> | |
| 404 <FONT color="green">401</FONT> f[i+3] = roots.isForward() ? e1 : e2;<a name="line.401"></a> | |
| 405 <FONT color="green">402</FONT> }<a name="line.402"></a> | |
| 406 <FONT color="green">403</FONT> <a name="line.403"></a> | |
| 407 <FONT color="green">404</FONT> // iterations from bottom to top take O(N*logN) time<a name="line.404"></a> | |
| 408 <FONT color="green">405</FONT> for (int i = 4; i < n; i <<= 1) {<a name="line.405"></a> | |
| 409 <FONT color="green">406</FONT> final int m = n / (i<<1);<a name="line.406"></a> | |
| 410 <FONT color="green">407</FONT> for (int j = 0; j < n; j += i<<1) {<a name="line.407"></a> | |
| 411 <FONT color="green">408</FONT> for (int k = 0; k < i; k++) {<a name="line.408"></a> | |
| 412 <FONT color="green">409</FONT> //z = f[i+j+k].multiply(roots.getOmega(k*m));<a name="line.409"></a> | |
| 413 <FONT color="green">410</FONT> final int k_times_m = k*m;<a name="line.410"></a> | |
| 414 <FONT color="green">411</FONT> final double omega_k_times_m_real = roots.getOmegaReal(k_times_m);<a name="line.411"></a> | |
| 415 <FONT color="green">412</FONT> final double omega_k_times_m_imaginary = roots.getOmegaImaginary(k_times_m);<a name="line.412"></a> | |
| 416 <FONT color="green">413</FONT> //z = f[i+j+k].multiply(omega[k*m]);<a name="line.413"></a> | |
| 417 <FONT color="green">414</FONT> final Complex z = new Complex(<a name="line.414"></a> | |
| 418 <FONT color="green">415</FONT> f[i+j+k].getReal() * omega_k_times_m_real -<a name="line.415"></a> | |
| 419 <FONT color="green">416</FONT> f[i+j+k].getImaginary() * omega_k_times_m_imaginary,<a name="line.416"></a> | |
| 420 <FONT color="green">417</FONT> f[i+j+k].getReal() * omega_k_times_m_imaginary +<a name="line.417"></a> | |
| 421 <FONT color="green">418</FONT> f[i+j+k].getImaginary() * omega_k_times_m_real);<a name="line.418"></a> | |
| 422 <FONT color="green">419</FONT> <a name="line.419"></a> | |
| 423 <FONT color="green">420</FONT> f[i+j+k] = f[j+k].subtract(z);<a name="line.420"></a> | |
| 424 <FONT color="green">421</FONT> f[j+k] = f[j+k].add(z);<a name="line.421"></a> | |
| 425 <FONT color="green">422</FONT> }<a name="line.422"></a> | |
| 426 <FONT color="green">423</FONT> }<a name="line.423"></a> | |
| 427 <FONT color="green">424</FONT> }<a name="line.424"></a> | |
| 428 <FONT color="green">425</FONT> return f;<a name="line.425"></a> | |
| 429 <FONT color="green">426</FONT> }<a name="line.426"></a> | |
| 430 <FONT color="green">427</FONT> <a name="line.427"></a> | |
| 431 <FONT color="green">428</FONT> /**<a name="line.428"></a> | |
| 432 <FONT color="green">429</FONT> * Sample the given univariate real function on the given interval.<a name="line.429"></a> | |
| 433 <FONT color="green">430</FONT> * <p><a name="line.430"></a> | |
| 434 <FONT color="green">431</FONT> * The interval is divided equally into N sections and sample points<a name="line.431"></a> | |
| 435 <FONT color="green">432</FONT> * are taken from min to max-(max-min)/N. Usually f(x) is periodic<a name="line.432"></a> | |
| 436 <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> | |
| 437 <FONT color="green">434</FONT> * require that.</p><a name="line.434"></a> | |
| 438 <FONT color="green">435</FONT> *<a name="line.435"></a> | |
| 439 <FONT color="green">436</FONT> * @param f the function to be sampled<a name="line.436"></a> | |
| 440 <FONT color="green">437</FONT> * @param min the lower bound for the interval<a name="line.437"></a> | |
| 441 <FONT color="green">438</FONT> * @param max the upper bound for the interval<a name="line.438"></a> | |
| 442 <FONT color="green">439</FONT> * @param n the number of sample points<a name="line.439"></a> | |
| 443 <FONT color="green">440</FONT> * @return the samples array<a name="line.440"></a> | |
| 444 <FONT color="green">441</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.441"></a> | |
| 445 <FONT color="green">442</FONT> * at some point<a name="line.442"></a> | |
| 446 <FONT color="green">443</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.443"></a> | |
| 447 <FONT color="green">444</FONT> */<a name="line.444"></a> | |
| 448 <FONT color="green">445</FONT> public static double[] sample(UnivariateRealFunction f,<a name="line.445"></a> | |
| 449 <FONT color="green">446</FONT> double min, double max, int n)<a name="line.446"></a> | |
| 450 <FONT color="green">447</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.447"></a> | |
| 451 <FONT color="green">448</FONT> <a name="line.448"></a> | |
| 452 <FONT color="green">449</FONT> if (n <= 0) {<a name="line.449"></a> | |
| 453 <FONT color="green">450</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.450"></a> | |
| 454 <FONT color="green">451</FONT> "number of sample is not positive: {0}",<a name="line.451"></a> | |
| 455 <FONT color="green">452</FONT> n);<a name="line.452"></a> | |
| 456 <FONT color="green">453</FONT> }<a name="line.453"></a> | |
| 457 <FONT color="green">454</FONT> verifyInterval(min, max);<a name="line.454"></a> | |
| 458 <FONT color="green">455</FONT> <a name="line.455"></a> | |
| 459 <FONT color="green">456</FONT> double s[] = new double[n];<a name="line.456"></a> | |
| 460 <FONT color="green">457</FONT> double h = (max - min) / n;<a name="line.457"></a> | |
| 461 <FONT color="green">458</FONT> for (int i = 0; i < n; i++) {<a name="line.458"></a> | |
| 462 <FONT color="green">459</FONT> s[i] = f.value(min + i * h);<a name="line.459"></a> | |
| 463 <FONT color="green">460</FONT> }<a name="line.460"></a> | |
| 464 <FONT color="green">461</FONT> return s;<a name="line.461"></a> | |
| 465 <FONT color="green">462</FONT> }<a name="line.462"></a> | |
| 466 <FONT color="green">463</FONT> <a name="line.463"></a> | |
| 467 <FONT color="green">464</FONT> /**<a name="line.464"></a> | |
| 468 <FONT color="green">465</FONT> * Multiply every component in the given real array by the<a name="line.465"></a> | |
| 469 <FONT color="green">466</FONT> * given real number. The change is made in place.<a name="line.466"></a> | |
| 470 <FONT color="green">467</FONT> *<a name="line.467"></a> | |
| 471 <FONT color="green">468</FONT> * @param f the real array to be scaled<a name="line.468"></a> | |
| 472 <FONT color="green">469</FONT> * @param d the real scaling coefficient<a name="line.469"></a> | |
| 473 <FONT color="green">470</FONT> * @return a reference to the scaled array<a name="line.470"></a> | |
| 474 <FONT color="green">471</FONT> */<a name="line.471"></a> | |
| 475 <FONT color="green">472</FONT> public static double[] scaleArray(double f[], double d) {<a name="line.472"></a> | |
| 476 <FONT color="green">473</FONT> for (int i = 0; i < f.length; i++) {<a name="line.473"></a> | |
| 477 <FONT color="green">474</FONT> f[i] *= d;<a name="line.474"></a> | |
| 478 <FONT color="green">475</FONT> }<a name="line.475"></a> | |
| 479 <FONT color="green">476</FONT> return f;<a name="line.476"></a> | |
| 480 <FONT color="green">477</FONT> }<a name="line.477"></a> | |
| 481 <FONT color="green">478</FONT> <a name="line.478"></a> | |
| 482 <FONT color="green">479</FONT> /**<a name="line.479"></a> | |
| 483 <FONT color="green">480</FONT> * Multiply every component in the given complex array by the<a name="line.480"></a> | |
| 484 <FONT color="green">481</FONT> * given real number. The change is made in place.<a name="line.481"></a> | |
| 485 <FONT color="green">482</FONT> *<a name="line.482"></a> | |
| 486 <FONT color="green">483</FONT> * @param f the complex array to be scaled<a name="line.483"></a> | |
| 487 <FONT color="green">484</FONT> * @param d the real scaling coefficient<a name="line.484"></a> | |
| 488 <FONT color="green">485</FONT> * @return a reference to the scaled array<a name="line.485"></a> | |
| 489 <FONT color="green">486</FONT> */<a name="line.486"></a> | |
| 490 <FONT color="green">487</FONT> public static Complex[] scaleArray(Complex f[], double d) {<a name="line.487"></a> | |
| 491 <FONT color="green">488</FONT> for (int i = 0; i < f.length; i++) {<a name="line.488"></a> | |
| 492 <FONT color="green">489</FONT> f[i] = new Complex(d * f[i].getReal(), d * f[i].getImaginary());<a name="line.489"></a> | |
| 493 <FONT color="green">490</FONT> }<a name="line.490"></a> | |
| 494 <FONT color="green">491</FONT> return f;<a name="line.491"></a> | |
| 495 <FONT color="green">492</FONT> }<a name="line.492"></a> | |
| 496 <FONT color="green">493</FONT> <a name="line.493"></a> | |
| 497 <FONT color="green">494</FONT> /**<a name="line.494"></a> | |
| 498 <FONT color="green">495</FONT> * Returns true if the argument is power of 2.<a name="line.495"></a> | |
| 499 <FONT color="green">496</FONT> *<a name="line.496"></a> | |
| 500 <FONT color="green">497</FONT> * @param n the number to test<a name="line.497"></a> | |
| 501 <FONT color="green">498</FONT> * @return true if the argument is power of 2<a name="line.498"></a> | |
| 502 <FONT color="green">499</FONT> */<a name="line.499"></a> | |
| 503 <FONT color="green">500</FONT> public static boolean isPowerOf2(long n) {<a name="line.500"></a> | |
| 504 <FONT color="green">501</FONT> return (n > 0) && ((n & (n - 1)) == 0);<a name="line.501"></a> | |
| 505 <FONT color="green">502</FONT> }<a name="line.502"></a> | |
| 506 <FONT color="green">503</FONT> <a name="line.503"></a> | |
| 507 <FONT color="green">504</FONT> /**<a name="line.504"></a> | |
| 508 <FONT color="green">505</FONT> * Verifies that the data set has length of power of 2.<a name="line.505"></a> | |
| 509 <FONT color="green">506</FONT> *<a name="line.506"></a> | |
| 510 <FONT color="green">507</FONT> * @param d the data array<a name="line.507"></a> | |
| 511 <FONT color="green">508</FONT> * @throws IllegalArgumentException if array length is not power of 2<a name="line.508"></a> | |
| 512 <FONT color="green">509</FONT> */<a name="line.509"></a> | |
| 513 <FONT color="green">510</FONT> public static void verifyDataSet(double d[]) throws IllegalArgumentException {<a name="line.510"></a> | |
| 514 <FONT color="green">511</FONT> if (!isPowerOf2(d.length)) {<a name="line.511"></a> | |
| 515 <FONT color="green">512</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.512"></a> | |
| 516 <FONT color="green">513</FONT> NOT_POWER_OF_TWO_MESSAGE, d.length);<a name="line.513"></a> | |
| 517 <FONT color="green">514</FONT> }<a name="line.514"></a> | |
| 518 <FONT color="green">515</FONT> }<a name="line.515"></a> | |
| 519 <FONT color="green">516</FONT> <a name="line.516"></a> | |
| 520 <FONT color="green">517</FONT> /**<a name="line.517"></a> | |
| 521 <FONT color="green">518</FONT> * Verifies that the data set has length of power of 2.<a name="line.518"></a> | |
| 522 <FONT color="green">519</FONT> *<a name="line.519"></a> | |
| 523 <FONT color="green">520</FONT> * @param o the data array<a name="line.520"></a> | |
| 524 <FONT color="green">521</FONT> * @throws IllegalArgumentException if array length is not power of 2<a name="line.521"></a> | |
| 525 <FONT color="green">522</FONT> */<a name="line.522"></a> | |
| 526 <FONT color="green">523</FONT> public static void verifyDataSet(Object o[]) throws IllegalArgumentException {<a name="line.523"></a> | |
| 527 <FONT color="green">524</FONT> if (!isPowerOf2(o.length)) {<a name="line.524"></a> | |
| 528 <FONT color="green">525</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.525"></a> | |
| 529 <FONT color="green">526</FONT> NOT_POWER_OF_TWO_MESSAGE, o.length);<a name="line.526"></a> | |
| 530 <FONT color="green">527</FONT> }<a name="line.527"></a> | |
| 531 <FONT color="green">528</FONT> }<a name="line.528"></a> | |
| 532 <FONT color="green">529</FONT> <a name="line.529"></a> | |
| 533 <FONT color="green">530</FONT> /**<a name="line.530"></a> | |
| 534 <FONT color="green">531</FONT> * Verifies that the endpoints specify an interval.<a name="line.531"></a> | |
| 535 <FONT color="green">532</FONT> *<a name="line.532"></a> | |
| 536 <FONT color="green">533</FONT> * @param lower lower endpoint<a name="line.533"></a> | |
| 537 <FONT color="green">534</FONT> * @param upper upper endpoint<a name="line.534"></a> | |
| 538 <FONT color="green">535</FONT> * @throws IllegalArgumentException if not interval<a name="line.535"></a> | |
| 539 <FONT color="green">536</FONT> */<a name="line.536"></a> | |
| 540 <FONT color="green">537</FONT> public static void verifyInterval(double lower, double upper)<a name="line.537"></a> | |
| 541 <FONT color="green">538</FONT> throws IllegalArgumentException {<a name="line.538"></a> | |
| 542 <FONT color="green">539</FONT> <a name="line.539"></a> | |
| 543 <FONT color="green">540</FONT> if (lower >= upper) {<a name="line.540"></a> | |
| 544 <FONT color="green">541</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.541"></a> | |
| 545 <FONT color="green">542</FONT> "endpoints do not specify an interval: [{0}, {1}]",<a name="line.542"></a> | |
| 546 <FONT color="green">543</FONT> lower, upper);<a name="line.543"></a> | |
| 547 <FONT color="green">544</FONT> }<a name="line.544"></a> | |
| 548 <FONT color="green">545</FONT> }<a name="line.545"></a> | |
| 549 <FONT color="green">546</FONT> <a name="line.546"></a> | |
| 550 <FONT color="green">547</FONT> /**<a name="line.547"></a> | |
| 551 <FONT color="green">548</FONT> * Performs a multi-dimensional Fourier transform on a given array.<a name="line.548"></a> | |
| 552 <FONT color="green">549</FONT> * Use {@link #inversetransform2(Complex[])} and<a name="line.549"></a> | |
| 553 <FONT color="green">550</FONT> * {@link #transform2(Complex[])} in a row-column implementation<a name="line.550"></a> | |
| 554 <FONT color="green">551</FONT> * in any number of dimensions with O(N&times;log(N)) complexity with<a name="line.551"></a> | |
| 555 <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> | |
| 556 <FONT color="green">553</FONT> * n<sub>x</sub>=number of elements in dimension x,<a name="line.553"></a> | |
| 557 <FONT color="green">554</FONT> * and d=total number of dimensions.<a name="line.554"></a> | |
| 558 <FONT color="green">555</FONT> *<a name="line.555"></a> | |
| 559 <FONT color="green">556</FONT> * @param mdca Multi-Dimensional Complex Array id est Complex[][][][]<a name="line.556"></a> | |
| 560 <FONT color="green">557</FONT> * @param forward inverseTransform2 is preformed if this is false<a name="line.557"></a> | |
| 561 <FONT color="green">558</FONT> * @return transform of mdca as a Multi-Dimensional Complex Array id est Complex[][][][]<a name="line.558"></a> | |
| 562 <FONT color="green">559</FONT> * @throws IllegalArgumentException if any dimension is not a power of two<a name="line.559"></a> | |
| 563 <FONT color="green">560</FONT> */<a name="line.560"></a> | |
| 564 <FONT color="green">561</FONT> public Object mdfft(Object mdca, boolean forward)<a name="line.561"></a> | |
| 565 <FONT color="green">562</FONT> throws IllegalArgumentException {<a name="line.562"></a> | |
| 566 <FONT color="green">563</FONT> MultiDimensionalComplexMatrix mdcm = (MultiDimensionalComplexMatrix)<a name="line.563"></a> | |
| 567 <FONT color="green">564</FONT> new MultiDimensionalComplexMatrix(mdca).clone();<a name="line.564"></a> | |
| 568 <FONT color="green">565</FONT> int[] dimensionSize = mdcm.getDimensionSizes();<a name="line.565"></a> | |
| 569 <FONT color="green">566</FONT> //cycle through each dimension<a name="line.566"></a> | |
| 570 <FONT color="green">567</FONT> for (int i = 0; i < dimensionSize.length; i++) {<a name="line.567"></a> | |
| 571 <FONT color="green">568</FONT> mdfft(mdcm, forward, i, new int[0]);<a name="line.568"></a> | |
| 572 <FONT color="green">569</FONT> }<a name="line.569"></a> | |
| 573 <FONT color="green">570</FONT> return mdcm.getArray();<a name="line.570"></a> | |
| 574 <FONT color="green">571</FONT> }<a name="line.571"></a> | |
| 575 <FONT color="green">572</FONT> <a name="line.572"></a> | |
| 576 <FONT color="green">573</FONT> /**<a name="line.573"></a> | |
| 577 <FONT color="green">574</FONT> * Performs one dimension of a multi-dimensional Fourier transform.<a name="line.574"></a> | |
| 578 <FONT color="green">575</FONT> *<a name="line.575"></a> | |
| 579 <FONT color="green">576</FONT> * @param mdcm input matrix<a name="line.576"></a> | |
| 580 <FONT color="green">577</FONT> * @param forward inverseTransform2 is preformed if this is false<a name="line.577"></a> | |
| 581 <FONT color="green">578</FONT> * @param d index of the dimension to process<a name="line.578"></a> | |
| 582 <FONT color="green">579</FONT> * @param subVector recursion subvector<a name="line.579"></a> | |
| 583 <FONT color="green">580</FONT> * @throws IllegalArgumentException if any dimension is not a power of two<a name="line.580"></a> | |
| 584 <FONT color="green">581</FONT> */<a name="line.581"></a> | |
| 585 <FONT color="green">582</FONT> private void mdfft(MultiDimensionalComplexMatrix mdcm, boolean forward,<a name="line.582"></a> | |
| 586 <FONT color="green">583</FONT> int d, int[] subVector)<a name="line.583"></a> | |
| 587 <FONT color="green">584</FONT> throws IllegalArgumentException {<a name="line.584"></a> | |
| 588 <FONT color="green">585</FONT> int[] dimensionSize = mdcm.getDimensionSizes();<a name="line.585"></a> | |
| 589 <FONT color="green">586</FONT> //if done<a name="line.586"></a> | |
| 590 <FONT color="green">587</FONT> if (subVector.length == dimensionSize.length) {<a name="line.587"></a> | |
| 591 <FONT color="green">588</FONT> Complex[] temp = new Complex[dimensionSize[d]];<a name="line.588"></a> | |
| 592 <FONT color="green">589</FONT> for (int i = 0; i < dimensionSize[d]; i++) {<a name="line.589"></a> | |
| 593 <FONT color="green">590</FONT> //fft along dimension d<a name="line.590"></a> | |
| 594 <FONT color="green">591</FONT> subVector[d] = i;<a name="line.591"></a> | |
| 595 <FONT color="green">592</FONT> temp[i] = mdcm.get(subVector);<a name="line.592"></a> | |
| 596 <FONT color="green">593</FONT> }<a name="line.593"></a> | |
| 597 <FONT color="green">594</FONT> <a name="line.594"></a> | |
| 598 <FONT color="green">595</FONT> if (forward)<a name="line.595"></a> | |
| 599 <FONT color="green">596</FONT> temp = transform2(temp);<a name="line.596"></a> | |
| 600 <FONT color="green">597</FONT> else<a name="line.597"></a> | |
| 601 <FONT color="green">598</FONT> temp = inversetransform2(temp);<a name="line.598"></a> | |
| 602 <FONT color="green">599</FONT> <a name="line.599"></a> | |
| 603 <FONT color="green">600</FONT> for (int i = 0; i < dimensionSize[d]; i++) {<a name="line.600"></a> | |
| 604 <FONT color="green">601</FONT> subVector[d] = i;<a name="line.601"></a> | |
| 605 <FONT color="green">602</FONT> mdcm.set(temp[i], subVector);<a name="line.602"></a> | |
| 606 <FONT color="green">603</FONT> }<a name="line.603"></a> | |
| 607 <FONT color="green">604</FONT> } else {<a name="line.604"></a> | |
| 608 <FONT color="green">605</FONT> int[] vector = new int[subVector.length + 1];<a name="line.605"></a> | |
| 609 <FONT color="green">606</FONT> System.arraycopy(subVector, 0, vector, 0, subVector.length);<a name="line.606"></a> | |
| 610 <FONT color="green">607</FONT> if (subVector.length == d) {<a name="line.607"></a> | |
| 611 <FONT color="green">608</FONT> //value is not important once the recursion is done.<a name="line.608"></a> | |
| 612 <FONT color="green">609</FONT> //then an fft will be applied along the dimension d.<a name="line.609"></a> | |
| 613 <FONT color="green">610</FONT> vector[d] = 0;<a name="line.610"></a> | |
| 614 <FONT color="green">611</FONT> mdfft(mdcm, forward, d, vector);<a name="line.611"></a> | |
| 615 <FONT color="green">612</FONT> } else {<a name="line.612"></a> | |
| 616 <FONT color="green">613</FONT> for (int i = 0; i < dimensionSize[subVector.length]; i++) {<a name="line.613"></a> | |
| 617 <FONT color="green">614</FONT> vector[subVector.length] = i;<a name="line.614"></a> | |
| 618 <FONT color="green">615</FONT> //further split along the next dimension<a name="line.615"></a> | |
| 619 <FONT color="green">616</FONT> mdfft(mdcm, forward, d, vector);<a name="line.616"></a> | |
| 620 <FONT color="green">617</FONT> }<a name="line.617"></a> | |
| 621 <FONT color="green">618</FONT> }<a name="line.618"></a> | |
| 622 <FONT color="green">619</FONT> }<a name="line.619"></a> | |
| 623 <FONT color="green">620</FONT> return;<a name="line.620"></a> | |
| 624 <FONT color="green">621</FONT> }<a name="line.621"></a> | |
| 625 <FONT color="green">622</FONT> <a name="line.622"></a> | |
| 626 <FONT color="green">623</FONT> /**<a name="line.623"></a> | |
| 627 <FONT color="green">624</FONT> * Complex matrix implementation.<a name="line.624"></a> | |
| 628 <FONT color="green">625</FONT> * Not designed for synchronized access<a name="line.625"></a> | |
| 629 <FONT color="green">626</FONT> * may eventually be replaced by jsr-83 of the java community process<a name="line.626"></a> | |
| 630 <FONT color="green">627</FONT> * http://jcp.org/en/jsr/detail?id=83<a name="line.627"></a> | |
| 631 <FONT color="green">628</FONT> * may require additional exception throws for other basic requirements.<a name="line.628"></a> | |
| 632 <FONT color="green">629</FONT> */<a name="line.629"></a> | |
| 633 <FONT color="green">630</FONT> private static class MultiDimensionalComplexMatrix<a name="line.630"></a> | |
| 634 <FONT color="green">631</FONT> implements Cloneable {<a name="line.631"></a> | |
| 635 <FONT color="green">632</FONT> <a name="line.632"></a> | |
| 636 <FONT color="green">633</FONT> /** Size in all dimensions. */<a name="line.633"></a> | |
| 637 <FONT color="green">634</FONT> protected int[] dimensionSize;<a name="line.634"></a> | |
| 638 <FONT color="green">635</FONT> <a name="line.635"></a> | |
| 639 <FONT color="green">636</FONT> /** Storage array. */<a name="line.636"></a> | |
| 640 <FONT color="green">637</FONT> protected Object multiDimensionalComplexArray;<a name="line.637"></a> | |
| 641 <FONT color="green">638</FONT> <a name="line.638"></a> | |
| 642 <FONT color="green">639</FONT> /** Simple constructor.<a name="line.639"></a> | |
| 643 <FONT color="green">640</FONT> * @param multiDimensionalComplexArray array containing the matrix elements<a name="line.640"></a> | |
| 644 <FONT color="green">641</FONT> */<a name="line.641"></a> | |
| 645 <FONT color="green">642</FONT> public MultiDimensionalComplexMatrix(Object multiDimensionalComplexArray) {<a name="line.642"></a> | |
| 646 <FONT color="green">643</FONT> <a name="line.643"></a> | |
| 647 <FONT color="green">644</FONT> this.multiDimensionalComplexArray = multiDimensionalComplexArray;<a name="line.644"></a> | |
| 648 <FONT color="green">645</FONT> <a name="line.645"></a> | |
| 649 <FONT color="green">646</FONT> // count dimensions<a name="line.646"></a> | |
| 650 <FONT color="green">647</FONT> int numOfDimensions = 0;<a name="line.647"></a> | |
| 651 <FONT color="green">648</FONT> for (Object lastDimension = multiDimensionalComplexArray;<a name="line.648"></a> | |
| 652 <FONT color="green">649</FONT> lastDimension instanceof Object[];) {<a name="line.649"></a> | |
| 653 <FONT color="green">650</FONT> final Object[] array = (Object[]) lastDimension;<a name="line.650"></a> | |
| 654 <FONT color="green">651</FONT> numOfDimensions++;<a name="line.651"></a> | |
| 655 <FONT color="green">652</FONT> lastDimension = array[0];<a name="line.652"></a> | |
| 656 <FONT color="green">653</FONT> }<a name="line.653"></a> | |
| 657 <FONT color="green">654</FONT> <a name="line.654"></a> | |
| 658 <FONT color="green">655</FONT> // allocate array with exact count<a name="line.655"></a> | |
| 659 <FONT color="green">656</FONT> dimensionSize = new int[numOfDimensions];<a name="line.656"></a> | |
| 660 <FONT color="green">657</FONT> <a name="line.657"></a> | |
| 661 <FONT color="green">658</FONT> // fill array<a name="line.658"></a> | |
| 662 <FONT color="green">659</FONT> numOfDimensions = 0;<a name="line.659"></a> | |
| 663 <FONT color="green">660</FONT> for (Object lastDimension = multiDimensionalComplexArray;<a name="line.660"></a> | |
| 664 <FONT color="green">661</FONT> lastDimension instanceof Object[];) {<a name="line.661"></a> | |
| 665 <FONT color="green">662</FONT> final Object[] array = (Object[]) lastDimension;<a name="line.662"></a> | |
| 666 <FONT color="green">663</FONT> dimensionSize[numOfDimensions++] = array.length;<a name="line.663"></a> | |
| 667 <FONT color="green">664</FONT> lastDimension = array[0];<a name="line.664"></a> | |
| 668 <FONT color="green">665</FONT> }<a name="line.665"></a> | |
| 669 <FONT color="green">666</FONT> <a name="line.666"></a> | |
| 670 <FONT color="green">667</FONT> }<a name="line.667"></a> | |
| 671 <FONT color="green">668</FONT> <a name="line.668"></a> | |
| 672 <FONT color="green">669</FONT> /**<a name="line.669"></a> | |
| 673 <FONT color="green">670</FONT> * Get a matrix element.<a name="line.670"></a> | |
| 674 <FONT color="green">671</FONT> * @param vector indices of the element<a name="line.671"></a> | |
| 675 <FONT color="green">672</FONT> * @return matrix element<a name="line.672"></a> | |
| 676 <FONT color="green">673</FONT> * @exception IllegalArgumentException if dimensions do not match<a name="line.673"></a> | |
| 677 <FONT color="green">674</FONT> */<a name="line.674"></a> | |
| 678 <FONT color="green">675</FONT> public Complex get(int... vector)<a name="line.675"></a> | |
| 679 <FONT color="green">676</FONT> throws IllegalArgumentException {<a name="line.676"></a> | |
| 680 <FONT color="green">677</FONT> if (vector == null) {<a name="line.677"></a> | |
| 681 <FONT color="green">678</FONT> if (dimensionSize.length > 0) {<a name="line.678"></a> | |
| 682 <FONT color="green">679</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.679"></a> | |
| 683 <FONT color="green">680</FONT> DIMENSION_MISMATCH_MESSAGE, 0, dimensionSize.length);<a name="line.680"></a> | |
| 684 <FONT color="green">681</FONT> }<a name="line.681"></a> | |
| 685 <FONT color="green">682</FONT> return null;<a name="line.682"></a> | |
| 686 <FONT color="green">683</FONT> }<a name="line.683"></a> | |
| 687 <FONT color="green">684</FONT> if (vector.length != dimensionSize.length) {<a name="line.684"></a> | |
| 688 <FONT color="green">685</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.685"></a> | |
| 689 <FONT color="green">686</FONT> DIMENSION_MISMATCH_MESSAGE, vector.length, dimensionSize.length);<a name="line.686"></a> | |
| 690 <FONT color="green">687</FONT> }<a name="line.687"></a> | |
| 691 <FONT color="green">688</FONT> <a name="line.688"></a> | |
| 692 <FONT color="green">689</FONT> Object lastDimension = multiDimensionalComplexArray;<a name="line.689"></a> | |
| 693 <FONT color="green">690</FONT> <a name="line.690"></a> | |
| 694 <FONT color="green">691</FONT> for (int i = 0; i < dimensionSize.length; i++) {<a name="line.691"></a> | |
| 695 <FONT color="green">692</FONT> lastDimension = ((Object[]) lastDimension)[vector[i]];<a name="line.692"></a> | |
| 696 <FONT color="green">693</FONT> }<a name="line.693"></a> | |
| 697 <FONT color="green">694</FONT> return (Complex) lastDimension;<a name="line.694"></a> | |
| 698 <FONT color="green">695</FONT> }<a name="line.695"></a> | |
| 699 <FONT color="green">696</FONT> <a name="line.696"></a> | |
| 700 <FONT color="green">697</FONT> /**<a name="line.697"></a> | |
| 701 <FONT color="green">698</FONT> * Set a matrix element.<a name="line.698"></a> | |
| 702 <FONT color="green">699</FONT> * @param magnitude magnitude of the element<a name="line.699"></a> | |
| 703 <FONT color="green">700</FONT> * @param vector indices of the element<a name="line.700"></a> | |
| 704 <FONT color="green">701</FONT> * @return the previous value<a name="line.701"></a> | |
| 705 <FONT color="green">702</FONT> * @exception IllegalArgumentException if dimensions do not match<a name="line.702"></a> | |
| 706 <FONT color="green">703</FONT> */<a name="line.703"></a> | |
| 707 <FONT color="green">704</FONT> public Complex set(Complex magnitude, int... vector)<a name="line.704"></a> | |
| 708 <FONT color="green">705</FONT> throws IllegalArgumentException {<a name="line.705"></a> | |
| 709 <FONT color="green">706</FONT> if (vector == null) {<a name="line.706"></a> | |
| 710 <FONT color="green">707</FONT> if (dimensionSize.length > 0) {<a name="line.707"></a> | |
| 711 <FONT color="green">708</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.708"></a> | |
| 712 <FONT color="green">709</FONT> DIMENSION_MISMATCH_MESSAGE, 0, dimensionSize.length);<a name="line.709"></a> | |
| 713 <FONT color="green">710</FONT> }<a name="line.710"></a> | |
| 714 <FONT color="green">711</FONT> return null;<a name="line.711"></a> | |
| 715 <FONT color="green">712</FONT> }<a name="line.712"></a> | |
| 716 <FONT color="green">713</FONT> if (vector.length != dimensionSize.length) {<a name="line.713"></a> | |
| 717 <FONT color="green">714</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.714"></a> | |
| 718 <FONT color="green">715</FONT> DIMENSION_MISMATCH_MESSAGE, vector.length,dimensionSize.length);<a name="line.715"></a> | |
| 719 <FONT color="green">716</FONT> }<a name="line.716"></a> | |
| 720 <FONT color="green">717</FONT> <a name="line.717"></a> | |
| 721 <FONT color="green">718</FONT> Object[] lastDimension = (Object[]) multiDimensionalComplexArray;<a name="line.718"></a> | |
| 722 <FONT color="green">719</FONT> for (int i = 0; i < dimensionSize.length - 1; i++) {<a name="line.719"></a> | |
| 723 <FONT color="green">720</FONT> lastDimension = (Object[]) lastDimension[vector[i]];<a name="line.720"></a> | |
| 724 <FONT color="green">721</FONT> }<a name="line.721"></a> | |
| 725 <FONT color="green">722</FONT> <a name="line.722"></a> | |
| 726 <FONT color="green">723</FONT> Complex lastValue = (Complex) lastDimension[vector[dimensionSize.length - 1]];<a name="line.723"></a> | |
| 727 <FONT color="green">724</FONT> lastDimension[vector[dimensionSize.length - 1]] = magnitude;<a name="line.724"></a> | |
| 728 <FONT color="green">725</FONT> <a name="line.725"></a> | |
| 729 <FONT color="green">726</FONT> return lastValue;<a name="line.726"></a> | |
| 730 <FONT color="green">727</FONT> }<a name="line.727"></a> | |
| 731 <FONT color="green">728</FONT> <a name="line.728"></a> | |
| 732 <FONT color="green">729</FONT> /**<a name="line.729"></a> | |
| 733 <FONT color="green">730</FONT> * Get the size in all dimensions.<a name="line.730"></a> | |
| 734 <FONT color="green">731</FONT> * @return size in all dimensions<a name="line.731"></a> | |
| 735 <FONT color="green">732</FONT> */<a name="line.732"></a> | |
| 736 <FONT color="green">733</FONT> public int[] getDimensionSizes() {<a name="line.733"></a> | |
| 737 <FONT color="green">734</FONT> return dimensionSize.clone();<a name="line.734"></a> | |
| 738 <FONT color="green">735</FONT> }<a name="line.735"></a> | |
| 739 <FONT color="green">736</FONT> <a name="line.736"></a> | |
| 740 <FONT color="green">737</FONT> /**<a name="line.737"></a> | |
| 741 <FONT color="green">738</FONT> * Get the underlying storage array<a name="line.738"></a> | |
| 742 <FONT color="green">739</FONT> * @return underlying storage array<a name="line.739"></a> | |
| 743 <FONT color="green">740</FONT> */<a name="line.740"></a> | |
| 744 <FONT color="green">741</FONT> public Object getArray() {<a name="line.741"></a> | |
| 745 <FONT color="green">742</FONT> return multiDimensionalComplexArray;<a name="line.742"></a> | |
| 746 <FONT color="green">743</FONT> }<a name="line.743"></a> | |
| 747 <FONT color="green">744</FONT> <a name="line.744"></a> | |
| 748 <FONT color="green">745</FONT> /** {@inheritDoc} */<a name="line.745"></a> | |
| 749 <FONT color="green">746</FONT> @Override<a name="line.746"></a> | |
| 750 <FONT color="green">747</FONT> public Object clone() {<a name="line.747"></a> | |
| 751 <FONT color="green">748</FONT> MultiDimensionalComplexMatrix mdcm =<a name="line.748"></a> | |
| 752 <FONT color="green">749</FONT> new MultiDimensionalComplexMatrix(Array.newInstance(<a name="line.749"></a> | |
| 753 <FONT color="green">750</FONT> Complex.class, dimensionSize));<a name="line.750"></a> | |
| 754 <FONT color="green">751</FONT> clone(mdcm);<a name="line.751"></a> | |
| 755 <FONT color="green">752</FONT> return mdcm;<a name="line.752"></a> | |
| 756 <FONT color="green">753</FONT> }<a name="line.753"></a> | |
| 757 <FONT color="green">754</FONT> <a name="line.754"></a> | |
| 758 <FONT color="green">755</FONT> /**<a name="line.755"></a> | |
| 759 <FONT color="green">756</FONT> * Copy contents of current array into mdcm.<a name="line.756"></a> | |
| 760 <FONT color="green">757</FONT> * @param mdcm array where to copy data<a name="line.757"></a> | |
| 761 <FONT color="green">758</FONT> */<a name="line.758"></a> | |
| 762 <FONT color="green">759</FONT> private void clone(MultiDimensionalComplexMatrix mdcm) {<a name="line.759"></a> | |
| 763 <FONT color="green">760</FONT> int[] vector = new int[dimensionSize.length];<a name="line.760"></a> | |
| 764 <FONT color="green">761</FONT> int size = 1;<a name="line.761"></a> | |
| 765 <FONT color="green">762</FONT> for (int i = 0; i < dimensionSize.length; i++) {<a name="line.762"></a> | |
| 766 <FONT color="green">763</FONT> size *= dimensionSize[i];<a name="line.763"></a> | |
| 767 <FONT color="green">764</FONT> }<a name="line.764"></a> | |
| 768 <FONT color="green">765</FONT> int[][] vectorList = new int[size][dimensionSize.length];<a name="line.765"></a> | |
| 769 <FONT color="green">766</FONT> for (int[] nextVector: vectorList) {<a name="line.766"></a> | |
| 770 <FONT color="green">767</FONT> System.arraycopy(vector, 0, nextVector, 0,<a name="line.767"></a> | |
| 771 <FONT color="green">768</FONT> dimensionSize.length);<a name="line.768"></a> | |
| 772 <FONT color="green">769</FONT> for (int i = 0; i < dimensionSize.length; i++) {<a name="line.769"></a> | |
| 773 <FONT color="green">770</FONT> vector[i]++;<a name="line.770"></a> | |
| 774 <FONT color="green">771</FONT> if (vector[i] < dimensionSize[i]) {<a name="line.771"></a> | |
| 775 <FONT color="green">772</FONT> break;<a name="line.772"></a> | |
| 776 <FONT color="green">773</FONT> } else {<a name="line.773"></a> | |
| 777 <FONT color="green">774</FONT> vector[i] = 0;<a name="line.774"></a> | |
| 778 <FONT color="green">775</FONT> }<a name="line.775"></a> | |
| 779 <FONT color="green">776</FONT> }<a name="line.776"></a> | |
| 780 <FONT color="green">777</FONT> }<a name="line.777"></a> | |
| 781 <FONT color="green">778</FONT> <a name="line.778"></a> | |
| 782 <FONT color="green">779</FONT> for (int[] nextVector: vectorList) {<a name="line.779"></a> | |
| 783 <FONT color="green">780</FONT> mdcm.set(get(nextVector), nextVector);<a name="line.780"></a> | |
| 784 <FONT color="green">781</FONT> }<a name="line.781"></a> | |
| 785 <FONT color="green">782</FONT> }<a name="line.782"></a> | |
| 786 <FONT color="green">783</FONT> }<a name="line.783"></a> | |
| 787 <FONT color="green">784</FONT> <a name="line.784"></a> | |
| 788 <FONT color="green">785</FONT> <a name="line.785"></a> | |
| 789 <FONT color="green">786</FONT> /** Computes the n<sup>th</sup> roots of unity.<a name="line.786"></a> | |
| 790 <FONT color="green">787</FONT> * A cache of already computed values is maintained.<a name="line.787"></a> | |
| 791 <FONT color="green">788</FONT> */<a name="line.788"></a> | |
| 792 <FONT color="green">789</FONT> private static class RootsOfUnity implements Serializable {<a name="line.789"></a> | |
| 793 <FONT color="green">790</FONT> <a name="line.790"></a> | |
| 794 <FONT color="green">791</FONT> /** Serializable version id. */<a name="line.791"></a> | |
| 795 <FONT color="green">792</FONT> private static final long serialVersionUID = 6404784357747329667L;<a name="line.792"></a> | |
| 796 <FONT color="green">793</FONT> <a name="line.793"></a> | |
| 797 <FONT color="green">794</FONT> /** Number of roots of unity. */<a name="line.794"></a> | |
| 798 <FONT color="green">795</FONT> private int omegaCount;<a name="line.795"></a> | |
| 799 <FONT color="green">796</FONT> <a name="line.796"></a> | |
| 800 <FONT color="green">797</FONT> /** Real part of the roots. */<a name="line.797"></a> | |
| 801 <FONT color="green">798</FONT> private double[] omegaReal;<a name="line.798"></a> | |
| 802 <FONT color="green">799</FONT> <a name="line.799"></a> | |
| 803 <FONT color="green">800</FONT> /** Imaginary part of the roots for forward transform. */<a name="line.800"></a> | |
| 804 <FONT color="green">801</FONT> private double[] omegaImaginaryForward;<a name="line.801"></a> | |
| 805 <FONT color="green">802</FONT> <a name="line.802"></a> | |
| 806 <FONT color="green">803</FONT> /** Imaginary part of the roots for reverse transform. */<a name="line.803"></a> | |
| 807 <FONT color="green">804</FONT> private double[] omegaImaginaryInverse;<a name="line.804"></a> | |
| 808 <FONT color="green">805</FONT> <a name="line.805"></a> | |
| 809 <FONT color="green">806</FONT> /** Forward/reverse indicator. */<a name="line.806"></a> | |
| 810 <FONT color="green">807</FONT> private boolean isForward;<a name="line.807"></a> | |
| 811 <FONT color="green">808</FONT> <a name="line.808"></a> | |
| 812 <FONT color="green">809</FONT> /**<a name="line.809"></a> | |
| 813 <FONT color="green">810</FONT> * Build an engine for computing then <sup>th</sup> roots of unity<a name="line.810"></a> | |
| 814 <FONT color="green">811</FONT> */<a name="line.811"></a> | |
| 815 <FONT color="green">812</FONT> public RootsOfUnity() {<a name="line.812"></a> | |
| 816 <FONT color="green">813</FONT> <a name="line.813"></a> | |
| 817 <FONT color="green">814</FONT> omegaCount = 0;<a name="line.814"></a> | |
| 818 <FONT color="green">815</FONT> omegaReal = null;<a name="line.815"></a> | |
| 819 <FONT color="green">816</FONT> omegaImaginaryForward = null;<a name="line.816"></a> | |
| 820 <FONT color="green">817</FONT> omegaImaginaryInverse = null;<a name="line.817"></a> | |
| 821 <FONT color="green">818</FONT> isForward = true;<a name="line.818"></a> | |
| 822 <FONT color="green">819</FONT> <a name="line.819"></a> | |
| 823 <FONT color="green">820</FONT> }<a name="line.820"></a> | |
| 824 <FONT color="green">821</FONT> <a name="line.821"></a> | |
| 825 <FONT color="green">822</FONT> /**<a name="line.822"></a> | |
| 826 <FONT color="green">823</FONT> * Check if computation has been done for forward or reverse transform.<a name="line.823"></a> | |
| 827 <FONT color="green">824</FONT> * @return true if computation has been done for forward transform<a name="line.824"></a> | |
| 828 <FONT color="green">825</FONT> * @throws IllegalStateException if no roots of unity have been computed yet<a name="line.825"></a> | |
| 829 <FONT color="green">826</FONT> */<a name="line.826"></a> | |
| 830 <FONT color="green">827</FONT> public synchronized boolean isForward() throws IllegalStateException {<a name="line.827"></a> | |
| 831 <FONT color="green">828</FONT> <a name="line.828"></a> | |
| 832 <FONT color="green">829</FONT> if (omegaCount == 0) {<a name="line.829"></a> | |
| 833 <FONT color="green">830</FONT> throw MathRuntimeException.createIllegalStateException(<a name="line.830"></a> | |
| 834 <FONT color="green">831</FONT> MISSING_ROOTS_OF_UNITY_MESSAGE);<a name="line.831"></a> | |
| 835 <FONT color="green">832</FONT> }<a name="line.832"></a> | |
| 836 <FONT color="green">833</FONT> return isForward;<a name="line.833"></a> | |
| 837 <FONT color="green">834</FONT> <a name="line.834"></a> | |
| 838 <FONT color="green">835</FONT> }<a name="line.835"></a> | |
| 839 <FONT color="green">836</FONT> <a name="line.836"></a> | |
| 840 <FONT color="green">837</FONT> /** Computes the n<sup>th</sup> roots of unity.<a name="line.837"></a> | |
| 841 <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> | |
| 842 <FONT color="green">839</FONT> * w = exp(-2 &pi; i / n), i = &sqrt;(-1).</p><a name="line.839"></a> | |
| 843 <FONT color="green">840</FONT> * <p>Note that n is positive for<a name="line.840"></a> | |
| 844 <FONT color="green">841</FONT> * forward transform and negative for inverse transform.</p><a name="line.841"></a> | |
| 845 <FONT color="green">842</FONT> * @param n number of roots of unity to compute,<a name="line.842"></a> | |
| 846 <FONT color="green">843</FONT> * positive for forward transform, negative for inverse transform<a name="line.843"></a> | |
| 847 <FONT color="green">844</FONT> * @throws IllegalArgumentException if n = 0<a name="line.844"></a> | |
| 848 <FONT color="green">845</FONT> */<a name="line.845"></a> | |
| 849 <FONT color="green">846</FONT> public synchronized void computeOmega(int n) throws IllegalArgumentException {<a name="line.846"></a> | |
| 850 <FONT color="green">847</FONT> <a name="line.847"></a> | |
| 851 <FONT color="green">848</FONT> if (n == 0) {<a name="line.848"></a> | |
| 852 <FONT color="green">849</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.849"></a> | |
| 853 <FONT color="green">850</FONT> "cannot compute 0-th root of unity, indefinite result");<a name="line.850"></a> | |
| 854 <FONT color="green">851</FONT> }<a name="line.851"></a> | |
| 855 <FONT color="green">852</FONT> <a name="line.852"></a> | |
| 856 <FONT color="green">853</FONT> isForward = n > 0;<a name="line.853"></a> | |
| 857 <FONT color="green">854</FONT> <a name="line.854"></a> | |
| 858 <FONT color="green">855</FONT> // avoid repetitive calculations<a name="line.855"></a> | |
| 859 <FONT color="green">856</FONT> final int absN = Math.abs(n);<a name="line.856"></a> | |
| 860 <FONT color="green">857</FONT> <a name="line.857"></a> | |
| 861 <FONT color="green">858</FONT> if (absN == omegaCount) {<a name="line.858"></a> | |
| 862 <FONT color="green">859</FONT> return;<a name="line.859"></a> | |
| 863 <FONT color="green">860</FONT> }<a name="line.860"></a> | |
| 864 <FONT color="green">861</FONT> <a name="line.861"></a> | |
| 865 <FONT color="green">862</FONT> // calculate everything from scratch, for both forward and inverse versions<a name="line.862"></a> | |
| 866 <FONT color="green">863</FONT> final double t = 2.0 * Math.PI / absN;<a name="line.863"></a> | |
| 867 <FONT color="green">864</FONT> final double cosT = Math.cos(t);<a name="line.864"></a> | |
| 868 <FONT color="green">865</FONT> final double sinT = Math.sin(t);<a name="line.865"></a> | |
| 869 <FONT color="green">866</FONT> omegaReal = new double[absN];<a name="line.866"></a> | |
| 870 <FONT color="green">867</FONT> omegaImaginaryForward = new double[absN];<a name="line.867"></a> | |
| 871 <FONT color="green">868</FONT> omegaImaginaryInverse = new double[absN];<a name="line.868"></a> | |
| 872 <FONT color="green">869</FONT> omegaReal[0] = 1.0;<a name="line.869"></a> | |
| 873 <FONT color="green">870</FONT> omegaImaginaryForward[0] = 0.0;<a name="line.870"></a> | |
| 874 <FONT color="green">871</FONT> omegaImaginaryInverse[0] = 0.0;<a name="line.871"></a> | |
| 875 <FONT color="green">872</FONT> for (int i = 1; i < absN; i++) {<a name="line.872"></a> | |
| 876 <FONT color="green">873</FONT> omegaReal[i] =<a name="line.873"></a> | |
| 877 <FONT color="green">874</FONT> omegaReal[i-1] * cosT + omegaImaginaryForward[i-1] * sinT;<a name="line.874"></a> | |
| 878 <FONT color="green">875</FONT> omegaImaginaryForward[i] =<a name="line.875"></a> | |
| 879 <FONT color="green">876</FONT> omegaImaginaryForward[i-1] * cosT - omegaReal[i-1] * sinT;<a name="line.876"></a> | |
| 880 <FONT color="green">877</FONT> omegaImaginaryInverse[i] = -omegaImaginaryForward[i];<a name="line.877"></a> | |
| 881 <FONT color="green">878</FONT> }<a name="line.878"></a> | |
| 882 <FONT color="green">879</FONT> omegaCount = absN;<a name="line.879"></a> | |
| 883 <FONT color="green">880</FONT> <a name="line.880"></a> | |
| 884 <FONT color="green">881</FONT> }<a name="line.881"></a> | |
| 885 <FONT color="green">882</FONT> <a name="line.882"></a> | |
| 886 <FONT color="green">883</FONT> /**<a name="line.883"></a> | |
| 887 <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> | |
| 888 <FONT color="green">885</FONT> * @param k index of the n<sup>th</sup> root of unity<a name="line.885"></a> | |
| 889 <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> | |
| 890 <FONT color="green">887</FONT> * @throws IllegalStateException if no roots of unity have been computed yet<a name="line.887"></a> | |
| 891 <FONT color="green">888</FONT> * @throws IllegalArgumentException if k is out of range<a name="line.888"></a> | |
| 892 <FONT color="green">889</FONT> */<a name="line.889"></a> | |
| 893 <FONT color="green">890</FONT> public synchronized double getOmegaReal(int k)<a name="line.890"></a> | |
| 894 <FONT color="green">891</FONT> throws IllegalStateException, IllegalArgumentException {<a name="line.891"></a> | |
| 895 <FONT color="green">892</FONT> <a name="line.892"></a> | |
| 896 <FONT color="green">893</FONT> if (omegaCount == 0) {<a name="line.893"></a> | |
| 897 <FONT color="green">894</FONT> throw MathRuntimeException.createIllegalStateException(<a name="line.894"></a> | |
| 898 <FONT color="green">895</FONT> MISSING_ROOTS_OF_UNITY_MESSAGE);<a name="line.895"></a> | |
| 899 <FONT color="green">896</FONT> }<a name="line.896"></a> | |
| 900 <FONT color="green">897</FONT> if ((k < 0) || (k >= omegaCount)) {<a name="line.897"></a> | |
| 901 <FONT color="green">898</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.898"></a> | |
| 902 <FONT color="green">899</FONT> OUT_OF_RANGE_ROOT_INDEX_MESSAGE, k, 0, omegaCount - 1);<a name="line.899"></a> | |
| 903 <FONT color="green">900</FONT> }<a name="line.900"></a> | |
| 904 <FONT color="green">901</FONT> <a name="line.901"></a> | |
| 905 <FONT color="green">902</FONT> return omegaReal[k];<a name="line.902"></a> | |
| 906 <FONT color="green">903</FONT> <a name="line.903"></a> | |
| 907 <FONT color="green">904</FONT> }<a name="line.904"></a> | |
| 908 <FONT color="green">905</FONT> <a name="line.905"></a> | |
| 909 <FONT color="green">906</FONT> /**<a name="line.906"></a> | |
| 910 <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> | |
| 911 <FONT color="green">908</FONT> * @param k index of the n<sup>th</sup> root of unity<a name="line.908"></a> | |
| 912 <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> | |
| 913 <FONT color="green">910</FONT> * @throws IllegalStateException if no roots of unity have been computed yet<a name="line.910"></a> | |
| 914 <FONT color="green">911</FONT> * @throws IllegalArgumentException if k is out of range<a name="line.911"></a> | |
| 915 <FONT color="green">912</FONT> */<a name="line.912"></a> | |
| 916 <FONT color="green">913</FONT> public synchronized double getOmegaImaginary(int k)<a name="line.913"></a> | |
| 917 <FONT color="green">914</FONT> throws IllegalStateException, IllegalArgumentException {<a name="line.914"></a> | |
| 918 <FONT color="green">915</FONT> <a name="line.915"></a> | |
| 919 <FONT color="green">916</FONT> if (omegaCount == 0) {<a name="line.916"></a> | |
| 920 <FONT color="green">917</FONT> throw MathRuntimeException.createIllegalStateException(<a name="line.917"></a> | |
| 921 <FONT color="green">918</FONT> MISSING_ROOTS_OF_UNITY_MESSAGE);<a name="line.918"></a> | |
| 922 <FONT color="green">919</FONT> }<a name="line.919"></a> | |
| 923 <FONT color="green">920</FONT> if ((k < 0) || (k >= omegaCount)) {<a name="line.920"></a> | |
| 924 <FONT color="green">921</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.921"></a> | |
| 925 <FONT color="green">922</FONT> OUT_OF_RANGE_ROOT_INDEX_MESSAGE, k, 0, omegaCount - 1);<a name="line.922"></a> | |
| 926 <FONT color="green">923</FONT> }<a name="line.923"></a> | |
| 927 <FONT color="green">924</FONT> <a name="line.924"></a> | |
| 928 <FONT color="green">925</FONT> return isForward ? omegaImaginaryForward[k] : omegaImaginaryInverse[k];<a name="line.925"></a> | |
| 929 <FONT color="green">926</FONT> <a name="line.926"></a> | |
| 930 <FONT color="green">927</FONT> }<a name="line.927"></a> | |
| 931 <FONT color="green">928</FONT> <a name="line.928"></a> | |
| 932 <FONT color="green">929</FONT> }<a name="line.929"></a> | |
| 933 <FONT color="green">930</FONT> <a name="line.930"></a> | |
| 934 <FONT color="green">931</FONT> }<a name="line.931"></a> | |
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| 950 | |
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| 952 | |
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| 956 | |
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| 995 </PRE> | |
| 996 </BODY> | |
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