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1 <HTML>
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2 <BODY BGCOLOR="white">
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3 <PRE>
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4 <FONT color="green">001</FONT> /*<a name="line.1"></a>
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5 <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
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6 <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a>
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7 <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a>
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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>
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9 <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
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10 <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a>
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11 <FONT color="green">008</FONT> *<a name="line.8"></a>
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12 <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
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13 <FONT color="green">010</FONT> *<a name="line.10"></a>
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14 <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
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15 <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
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16 <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
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17 <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a>
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18 <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a>
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19 <FONT color="green">016</FONT> */<a name="line.16"></a>
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20 <FONT color="green">017</FONT> package org.apache.commons.math.transform;<a name="line.17"></a>
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21 <FONT color="green">018</FONT> <a name="line.18"></a>
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22 <FONT color="green">019</FONT> import java.io.Serializable;<a name="line.19"></a>
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23 <FONT color="green">020</FONT> import java.lang.reflect.Array;<a name="line.20"></a>
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24 <FONT color="green">021</FONT> <a name="line.21"></a>
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25 <FONT color="green">022</FONT> import org.apache.commons.math.FunctionEvaluationException;<a name="line.22"></a>
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26 <FONT color="green">023</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.23"></a>
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27 <FONT color="green">024</FONT> import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.24"></a>
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28 <FONT color="green">025</FONT> import org.apache.commons.math.complex.Complex;<a name="line.25"></a>
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29 <FONT color="green">026</FONT> <a name="line.26"></a>
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30 <FONT color="green">027</FONT> /**<a name="line.27"></a>
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31 <FONT color="green">028</FONT> * Implements the <a href="http://mathworld.wolfram.com/FastFourierTransform.html"><a name="line.28"></a>
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32 <FONT color="green">029</FONT> * Fast Fourier Transform</a> for transformation of one-dimensional data sets.<a name="line.29"></a>
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33 <FONT color="green">030</FONT> * For reference, see <b>Applied Numerical Linear Algebra</b>, ISBN 0898713897,<a name="line.30"></a>
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34 <FONT color="green">031</FONT> * chapter 6.<a name="line.31"></a>
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35 <FONT color="green">032</FONT> * <p><a name="line.32"></a>
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36 <FONT color="green">033</FONT> * There are several conventions for the definition of FFT and inverse FFT,<a name="line.33"></a>
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37 <FONT color="green">034</FONT> * mainly on different coefficient and exponent. Here the equations are listed<a name="line.34"></a>
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38 <FONT color="green">035</FONT> * in the comments of the corresponding methods.</p><a name="line.35"></a>
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39 <FONT color="green">036</FONT> * <p><a name="line.36"></a>
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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>
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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>
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42 <FONT color="green">039</FONT> * requirement. There are other flavors of FFT, for reference, see S. Winograd,<a name="line.39"></a>
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43 <FONT color="green">040</FONT> * <i>On computing the discrete Fourier transform</i>, Mathematics of Computation,<a name="line.40"></a>
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44 <FONT color="green">041</FONT> * 32 (1978), 175 - 199.</p><a name="line.41"></a>
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45 <FONT color="green">042</FONT> *<a name="line.42"></a>
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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>
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47 <FONT color="green">044</FONT> * @since 1.2<a name="line.44"></a>
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48 <FONT color="green">045</FONT> */<a name="line.45"></a>
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49 <FONT color="green">046</FONT> public class FastFourierTransformer implements Serializable {<a name="line.46"></a>
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50 <FONT color="green">047</FONT> <a name="line.47"></a>
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51 <FONT color="green">048</FONT> /** Serializable version identifier. */<a name="line.48"></a>
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52 <FONT color="green">049</FONT> static final long serialVersionUID = 5138259215438106000L;<a name="line.49"></a>
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53 <FONT color="green">050</FONT> <a name="line.50"></a>
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54 <FONT color="green">051</FONT> /** Message for not power of 2. */<a name="line.51"></a>
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55 <FONT color="green">052</FONT> private static final String NOT_POWER_OF_TWO_MESSAGE =<a name="line.52"></a>
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56 <FONT color="green">053</FONT> "{0} is not a power of 2, consider padding for fix";<a name="line.53"></a>
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57 <FONT color="green">054</FONT> <a name="line.54"></a>
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58 <FONT color="green">055</FONT> /** Message for dimension mismatch. */<a name="line.55"></a>
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59 <FONT color="green">056</FONT> private static final String DIMENSION_MISMATCH_MESSAGE =<a name="line.56"></a>
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60 <FONT color="green">057</FONT> "some dimensions don't match: {0} != {1}";<a name="line.57"></a>
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61 <FONT color="green">058</FONT> <a name="line.58"></a>
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62 <FONT color="green">059</FONT> /** Message for not computed roots of unity. */<a name="line.59"></a>
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63 <FONT color="green">060</FONT> private static final String MISSING_ROOTS_OF_UNITY_MESSAGE =<a name="line.60"></a>
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64 <FONT color="green">061</FONT> "roots of unity have not been computed yet";<a name="line.61"></a>
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65 <FONT color="green">062</FONT> <a name="line.62"></a>
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66 <FONT color="green">063</FONT> /** Message for out of range root index. */<a name="line.63"></a>
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67 <FONT color="green">064</FONT> private static final String OUT_OF_RANGE_ROOT_INDEX_MESSAGE =<a name="line.64"></a>
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68 <FONT color="green">065</FONT> "out of range root of unity index {0} (must be in [{1};{2}])";<a name="line.65"></a>
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69 <FONT color="green">066</FONT> <a name="line.66"></a>
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70 <FONT color="green">067</FONT> /** roots of unity */<a name="line.67"></a>
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71 <FONT color="green">068</FONT> private RootsOfUnity roots = new RootsOfUnity();<a name="line.68"></a>
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72 <FONT color="green">069</FONT> <a name="line.69"></a>
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73 <FONT color="green">070</FONT> /**<a name="line.70"></a>
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74 <FONT color="green">071</FONT> * Construct a default transformer.<a name="line.71"></a>
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75 <FONT color="green">072</FONT> */<a name="line.72"></a>
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76 <FONT color="green">073</FONT> public FastFourierTransformer() {<a name="line.73"></a>
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77 <FONT color="green">074</FONT> super();<a name="line.74"></a>
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78 <FONT color="green">075</FONT> }<a name="line.75"></a>
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79 <FONT color="green">076</FONT> <a name="line.76"></a>
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80 <FONT color="green">077</FONT> /**<a name="line.77"></a>
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81 <FONT color="green">078</FONT> * Transform the given real data set.<a name="line.78"></a>
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82 <FONT color="green">079</FONT> * <p><a name="line.79"></a>
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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>
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84 <FONT color="green">081</FONT> * </p><a name="line.81"></a>
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85 <FONT color="green">082</FONT> *<a name="line.82"></a>
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86 <FONT color="green">083</FONT> * @param f the real data array to be transformed<a name="line.83"></a>
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87 <FONT color="green">084</FONT> * @return the complex transformed array<a name="line.84"></a>
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88 <FONT color="green">085</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.85"></a>
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89 <FONT color="green">086</FONT> */<a name="line.86"></a>
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90 <FONT color="green">087</FONT> public Complex[] transform(double f[])<a name="line.87"></a>
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91 <FONT color="green">088</FONT> throws IllegalArgumentException {<a name="line.88"></a>
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92 <FONT color="green">089</FONT> return fft(f, false);<a name="line.89"></a>
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93 <FONT color="green">090</FONT> }<a name="line.90"></a>
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94 <FONT color="green">091</FONT> <a name="line.91"></a>
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95 <FONT color="green">092</FONT> /**<a name="line.92"></a>
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96 <FONT color="green">093</FONT> * Transform the given real function, sampled on the given interval.<a name="line.93"></a>
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97 <FONT color="green">094</FONT> * <p><a name="line.94"></a>
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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>
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99 <FONT color="green">096</FONT> * </p><a name="line.96"></a>
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100 <FONT color="green">097</FONT> *<a name="line.97"></a>
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101 <FONT color="green">098</FONT> * @param f the function to be sampled and transformed<a name="line.98"></a>
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102 <FONT color="green">099</FONT> * @param min the lower bound for the interval<a name="line.99"></a>
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103 <FONT color="green">100</FONT> * @param max the upper bound for the interval<a name="line.100"></a>
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104 <FONT color="green">101</FONT> * @param n the number of sample points<a name="line.101"></a>
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105 <FONT color="green">102</FONT> * @return the complex transformed array<a name="line.102"></a>
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106 <FONT color="green">103</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.103"></a>
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107 <FONT color="green">104</FONT> * at some point<a name="line.104"></a>
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108 <FONT color="green">105</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.105"></a>
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109 <FONT color="green">106</FONT> */<a name="line.106"></a>
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110 <FONT color="green">107</FONT> public Complex[] transform(UnivariateRealFunction f,<a name="line.107"></a>
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111 <FONT color="green">108</FONT> double min, double max, int n)<a name="line.108"></a>
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112 <FONT color="green">109</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.109"></a>
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113 <FONT color="green">110</FONT> double data[] = sample(f, min, max, n);<a name="line.110"></a>
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114 <FONT color="green">111</FONT> return fft(data, false);<a name="line.111"></a>
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115 <FONT color="green">112</FONT> }<a name="line.112"></a>
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116 <FONT color="green">113</FONT> <a name="line.113"></a>
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117 <FONT color="green">114</FONT> /**<a name="line.114"></a>
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118 <FONT color="green">115</FONT> * Transform the given complex data set.<a name="line.115"></a>
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119 <FONT color="green">116</FONT> * <p><a name="line.116"></a>
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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>
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121 <FONT color="green">118</FONT> * </p><a name="line.118"></a>
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122 <FONT color="green">119</FONT> *<a name="line.119"></a>
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123 <FONT color="green">120</FONT> * @param f the complex data array to be transformed<a name="line.120"></a>
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124 <FONT color="green">121</FONT> * @return the complex transformed array<a name="line.121"></a>
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125 <FONT color="green">122</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.122"></a>
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126 <FONT color="green">123</FONT> */<a name="line.123"></a>
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127 <FONT color="green">124</FONT> public Complex[] transform(Complex f[])<a name="line.124"></a>
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128 <FONT color="green">125</FONT> throws IllegalArgumentException {<a name="line.125"></a>
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129 <FONT color="green">126</FONT> roots.computeOmega(f.length);<a name="line.126"></a>
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130 <FONT color="green">127</FONT> return fft(f);<a name="line.127"></a>
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131 <FONT color="green">128</FONT> }<a name="line.128"></a>
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132 <FONT color="green">129</FONT> <a name="line.129"></a>
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133 <FONT color="green">130</FONT> /**<a name="line.130"></a>
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134 <FONT color="green">131</FONT> * Transform the given real data set.<a name="line.131"></a>
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135 <FONT color="green">132</FONT> * <p><a name="line.132"></a>
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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>
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137 <FONT color="green">134</FONT> * </p><a name="line.134"></a>
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138 <FONT color="green">135</FONT> *<a name="line.135"></a>
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139 <FONT color="green">136</FONT> * @param f the real data array to be transformed<a name="line.136"></a>
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140 <FONT color="green">137</FONT> * @return the complex transformed array<a name="line.137"></a>
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141 <FONT color="green">138</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.138"></a>
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142 <FONT color="green">139</FONT> */<a name="line.139"></a>
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143 <FONT color="green">140</FONT> public Complex[] transform2(double f[])<a name="line.140"></a>
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144 <FONT color="green">141</FONT> throws IllegalArgumentException {<a name="line.141"></a>
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145 <FONT color="green">142</FONT> <a name="line.142"></a>
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146 <FONT color="green">143</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.143"></a>
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147 <FONT color="green">144</FONT> return scaleArray(fft(f, false), scaling_coefficient);<a name="line.144"></a>
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148 <FONT color="green">145</FONT> }<a name="line.145"></a>
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149 <FONT color="green">146</FONT> <a name="line.146"></a>
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150 <FONT color="green">147</FONT> /**<a name="line.147"></a>
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151 <FONT color="green">148</FONT> * Transform the given real function, sampled on the given interval.<a name="line.148"></a>
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152 <FONT color="green">149</FONT> * <p><a name="line.149"></a>
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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>
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154 <FONT color="green">151</FONT> * </p><a name="line.151"></a>
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155 <FONT color="green">152</FONT> *<a name="line.152"></a>
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156 <FONT color="green">153</FONT> * @param f the function to be sampled and transformed<a name="line.153"></a>
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157 <FONT color="green">154</FONT> * @param min the lower bound for the interval<a name="line.154"></a>
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158 <FONT color="green">155</FONT> * @param max the upper bound for the interval<a name="line.155"></a>
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159 <FONT color="green">156</FONT> * @param n the number of sample points<a name="line.156"></a>
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160 <FONT color="green">157</FONT> * @return the complex transformed array<a name="line.157"></a>
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161 <FONT color="green">158</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.158"></a>
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162 <FONT color="green">159</FONT> * at some point<a name="line.159"></a>
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163 <FONT color="green">160</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.160"></a>
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164 <FONT color="green">161</FONT> */<a name="line.161"></a>
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165 <FONT color="green">162</FONT> public Complex[] transform2(UnivariateRealFunction f,<a name="line.162"></a>
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166 <FONT color="green">163</FONT> double min, double max, int n)<a name="line.163"></a>
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167 <FONT color="green">164</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.164"></a>
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168 <FONT color="green">165</FONT> <a name="line.165"></a>
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169 <FONT color="green">166</FONT> double data[] = sample(f, min, max, n);<a name="line.166"></a>
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170 <FONT color="green">167</FONT> double scaling_coefficient = 1.0 / Math.sqrt(n);<a name="line.167"></a>
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171 <FONT color="green">168</FONT> return scaleArray(fft(data, false), scaling_coefficient);<a name="line.168"></a>
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172 <FONT color="green">169</FONT> }<a name="line.169"></a>
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173 <FONT color="green">170</FONT> <a name="line.170"></a>
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174 <FONT color="green">171</FONT> /**<a name="line.171"></a>
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175 <FONT color="green">172</FONT> * Transform the given complex data set.<a name="line.172"></a>
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176 <FONT color="green">173</FONT> * <p><a name="line.173"></a>
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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>
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178 <FONT color="green">175</FONT> * </p><a name="line.175"></a>
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179 <FONT color="green">176</FONT> *<a name="line.176"></a>
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180 <FONT color="green">177</FONT> * @param f the complex data array to be transformed<a name="line.177"></a>
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181 <FONT color="green">178</FONT> * @return the complex transformed array<a name="line.178"></a>
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182 <FONT color="green">179</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.179"></a>
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183 <FONT color="green">180</FONT> */<a name="line.180"></a>
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184 <FONT color="green">181</FONT> public Complex[] transform2(Complex f[])<a name="line.181"></a>
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185 <FONT color="green">182</FONT> throws IllegalArgumentException {<a name="line.182"></a>
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186 <FONT color="green">183</FONT> <a name="line.183"></a>
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187 <FONT color="green">184</FONT> roots.computeOmega(f.length);<a name="line.184"></a>
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188 <FONT color="green">185</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.185"></a>
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189 <FONT color="green">186</FONT> return scaleArray(fft(f), scaling_coefficient);<a name="line.186"></a>
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190 <FONT color="green">187</FONT> }<a name="line.187"></a>
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191 <FONT color="green">188</FONT> <a name="line.188"></a>
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192 <FONT color="green">189</FONT> /**<a name="line.189"></a>
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193 <FONT color="green">190</FONT> * Inversely transform the given real data set.<a name="line.190"></a>
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194 <FONT color="green">191</FONT> * <p><a name="line.191"></a>
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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>
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196 <FONT color="green">193</FONT> * </p><a name="line.193"></a>
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197 <FONT color="green">194</FONT> *<a name="line.194"></a>
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198 <FONT color="green">195</FONT> * @param f the real data array to be inversely transformed<a name="line.195"></a>
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199 <FONT color="green">196</FONT> * @return the complex inversely transformed array<a name="line.196"></a>
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200 <FONT color="green">197</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.197"></a>
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201 <FONT color="green">198</FONT> */<a name="line.198"></a>
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202 <FONT color="green">199</FONT> public Complex[] inversetransform(double f[])<a name="line.199"></a>
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203 <FONT color="green">200</FONT> throws IllegalArgumentException {<a name="line.200"></a>
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204 <FONT color="green">201</FONT> <a name="line.201"></a>
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205 <FONT color="green">202</FONT> double scaling_coefficient = 1.0 / f.length;<a name="line.202"></a>
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206 <FONT color="green">203</FONT> return scaleArray(fft(f, true), scaling_coefficient);<a name="line.203"></a>
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207 <FONT color="green">204</FONT> }<a name="line.204"></a>
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208 <FONT color="green">205</FONT> <a name="line.205"></a>
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209 <FONT color="green">206</FONT> /**<a name="line.206"></a>
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210 <FONT color="green">207</FONT> * Inversely transform the given real function, sampled on the given interval.<a name="line.207"></a>
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211 <FONT color="green">208</FONT> * <p><a name="line.208"></a>
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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>
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213 <FONT color="green">210</FONT> * </p><a name="line.210"></a>
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214 <FONT color="green">211</FONT> *<a name="line.211"></a>
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215 <FONT color="green">212</FONT> * @param f the function to be sampled and inversely transformed<a name="line.212"></a>
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216 <FONT color="green">213</FONT> * @param min the lower bound for the interval<a name="line.213"></a>
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217 <FONT color="green">214</FONT> * @param max the upper bound for the interval<a name="line.214"></a>
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218 <FONT color="green">215</FONT> * @param n the number of sample points<a name="line.215"></a>
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219 <FONT color="green">216</FONT> * @return the complex inversely transformed array<a name="line.216"></a>
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220 <FONT color="green">217</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.217"></a>
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221 <FONT color="green">218</FONT> * at some point<a name="line.218"></a>
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222 <FONT color="green">219</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.219"></a>
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223 <FONT color="green">220</FONT> */<a name="line.220"></a>
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224 <FONT color="green">221</FONT> public Complex[] inversetransform(UnivariateRealFunction f,<a name="line.221"></a>
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225 <FONT color="green">222</FONT> double min, double max, int n)<a name="line.222"></a>
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226 <FONT color="green">223</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.223"></a>
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227 <FONT color="green">224</FONT> <a name="line.224"></a>
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228 <FONT color="green">225</FONT> double data[] = sample(f, min, max, n);<a name="line.225"></a>
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229 <FONT color="green">226</FONT> double scaling_coefficient = 1.0 / n;<a name="line.226"></a>
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230 <FONT color="green">227</FONT> return scaleArray(fft(data, true), scaling_coefficient);<a name="line.227"></a>
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231 <FONT color="green">228</FONT> }<a name="line.228"></a>
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232 <FONT color="green">229</FONT> <a name="line.229"></a>
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233 <FONT color="green">230</FONT> /**<a name="line.230"></a>
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234 <FONT color="green">231</FONT> * Inversely transform the given complex data set.<a name="line.231"></a>
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235 <FONT color="green">232</FONT> * <p><a name="line.232"></a>
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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>
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237 <FONT color="green">234</FONT> * </p><a name="line.234"></a>
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238 <FONT color="green">235</FONT> *<a name="line.235"></a>
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239 <FONT color="green">236</FONT> * @param f the complex data array to be inversely transformed<a name="line.236"></a>
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240 <FONT color="green">237</FONT> * @return the complex inversely transformed array<a name="line.237"></a>
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241 <FONT color="green">238</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.238"></a>
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242 <FONT color="green">239</FONT> */<a name="line.239"></a>
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243 <FONT color="green">240</FONT> public Complex[] inversetransform(Complex f[])<a name="line.240"></a>
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244 <FONT color="green">241</FONT> throws IllegalArgumentException {<a name="line.241"></a>
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245 <FONT color="green">242</FONT> <a name="line.242"></a>
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246 <FONT color="green">243</FONT> roots.computeOmega(-f.length); // pass negative argument<a name="line.243"></a>
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247 <FONT color="green">244</FONT> double scaling_coefficient = 1.0 / f.length;<a name="line.244"></a>
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248 <FONT color="green">245</FONT> return scaleArray(fft(f), scaling_coefficient);<a name="line.245"></a>
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249 <FONT color="green">246</FONT> }<a name="line.246"></a>
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250 <FONT color="green">247</FONT> <a name="line.247"></a>
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251 <FONT color="green">248</FONT> /**<a name="line.248"></a>
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252 <FONT color="green">249</FONT> * Inversely transform the given real data set.<a name="line.249"></a>
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253 <FONT color="green">250</FONT> * <p><a name="line.250"></a>
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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>
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255 <FONT color="green">252</FONT> * </p><a name="line.252"></a>
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256 <FONT color="green">253</FONT> *<a name="line.253"></a>
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257 <FONT color="green">254</FONT> * @param f the real data array to be inversely transformed<a name="line.254"></a>
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258 <FONT color="green">255</FONT> * @return the complex inversely transformed array<a name="line.255"></a>
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259 <FONT color="green">256</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.256"></a>
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260 <FONT color="green">257</FONT> */<a name="line.257"></a>
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261 <FONT color="green">258</FONT> public Complex[] inversetransform2(double f[])<a name="line.258"></a>
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262 <FONT color="green">259</FONT> throws IllegalArgumentException {<a name="line.259"></a>
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263 <FONT color="green">260</FONT> <a name="line.260"></a>
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264 <FONT color="green">261</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.261"></a>
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265 <FONT color="green">262</FONT> return scaleArray(fft(f, true), scaling_coefficient);<a name="line.262"></a>
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266 <FONT color="green">263</FONT> }<a name="line.263"></a>
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267 <FONT color="green">264</FONT> <a name="line.264"></a>
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268 <FONT color="green">265</FONT> /**<a name="line.265"></a>
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269 <FONT color="green">266</FONT> * Inversely transform the given real function, sampled on the given interval.<a name="line.266"></a>
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270 <FONT color="green">267</FONT> * <p><a name="line.267"></a>
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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>
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272 <FONT color="green">269</FONT> * </p><a name="line.269"></a>
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273 <FONT color="green">270</FONT> *<a name="line.270"></a>
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274 <FONT color="green">271</FONT> * @param f the function to be sampled and inversely transformed<a name="line.271"></a>
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275 <FONT color="green">272</FONT> * @param min the lower bound for the interval<a name="line.272"></a>
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276 <FONT color="green">273</FONT> * @param max the upper bound for the interval<a name="line.273"></a>
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277 <FONT color="green">274</FONT> * @param n the number of sample points<a name="line.274"></a>
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278 <FONT color="green">275</FONT> * @return the complex inversely transformed array<a name="line.275"></a>
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279 <FONT color="green">276</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.276"></a>
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280 <FONT color="green">277</FONT> * at some point<a name="line.277"></a>
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281 <FONT color="green">278</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.278"></a>
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282 <FONT color="green">279</FONT> */<a name="line.279"></a>
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283 <FONT color="green">280</FONT> public Complex[] inversetransform2(UnivariateRealFunction f,<a name="line.280"></a>
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284 <FONT color="green">281</FONT> double min, double max, int n)<a name="line.281"></a>
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285 <FONT color="green">282</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.282"></a>
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286 <FONT color="green">283</FONT> <a name="line.283"></a>
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287 <FONT color="green">284</FONT> double data[] = sample(f, min, max, n);<a name="line.284"></a>
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288 <FONT color="green">285</FONT> double scaling_coefficient = 1.0 / Math.sqrt(n);<a name="line.285"></a>
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289 <FONT color="green">286</FONT> return scaleArray(fft(data, true), scaling_coefficient);<a name="line.286"></a>
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290 <FONT color="green">287</FONT> }<a name="line.287"></a>
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291 <FONT color="green">288</FONT> <a name="line.288"></a>
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292 <FONT color="green">289</FONT> /**<a name="line.289"></a>
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293 <FONT color="green">290</FONT> * Inversely transform the given complex data set.<a name="line.290"></a>
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294 <FONT color="green">291</FONT> * <p><a name="line.291"></a>
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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>
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296 <FONT color="green">293</FONT> * </p><a name="line.293"></a>
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297 <FONT color="green">294</FONT> *<a name="line.294"></a>
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298 <FONT color="green">295</FONT> * @param f the complex data array to be inversely transformed<a name="line.295"></a>
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299 <FONT color="green">296</FONT> * @return the complex inversely transformed array<a name="line.296"></a>
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300 <FONT color="green">297</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.297"></a>
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301 <FONT color="green">298</FONT> */<a name="line.298"></a>
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302 <FONT color="green">299</FONT> public Complex[] inversetransform2(Complex f[])<a name="line.299"></a>
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303 <FONT color="green">300</FONT> throws IllegalArgumentException {<a name="line.300"></a>
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304 <FONT color="green">301</FONT> <a name="line.301"></a>
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305 <FONT color="green">302</FONT> roots.computeOmega(-f.length); // pass negative argument<a name="line.302"></a>
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306 <FONT color="green">303</FONT> double scaling_coefficient = 1.0 / Math.sqrt(f.length);<a name="line.303"></a>
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307 <FONT color="green">304</FONT> return scaleArray(fft(f), scaling_coefficient);<a name="line.304"></a>
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308 <FONT color="green">305</FONT> }<a name="line.305"></a>
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309 <FONT color="green">306</FONT> <a name="line.306"></a>
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310 <FONT color="green">307</FONT> /**<a name="line.307"></a>
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311 <FONT color="green">308</FONT> * Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).<a name="line.308"></a>
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312 <FONT color="green">309</FONT> *<a name="line.309"></a>
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313 <FONT color="green">310</FONT> * @param f the real data array to be transformed<a name="line.310"></a>
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314 <FONT color="green">311</FONT> * @param isInverse the indicator of forward or inverse transform<a name="line.311"></a>
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315 <FONT color="green">312</FONT> * @return the complex transformed array<a name="line.312"></a>
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316 <FONT color="green">313</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.313"></a>
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317 <FONT color="green">314</FONT> */<a name="line.314"></a>
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318 <FONT color="green">315</FONT> protected Complex[] fft(double f[], boolean isInverse)<a name="line.315"></a>
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319 <FONT color="green">316</FONT> throws IllegalArgumentException {<a name="line.316"></a>
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320 <FONT color="green">317</FONT> <a name="line.317"></a>
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321 <FONT color="green">318</FONT> verifyDataSet(f);<a name="line.318"></a>
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322 <FONT color="green">319</FONT> Complex F[] = new Complex[f.length];<a name="line.319"></a>
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323 <FONT color="green">320</FONT> if (f.length == 1) {<a name="line.320"></a>
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324 <FONT color="green">321</FONT> F[0] = new Complex(f[0], 0.0);<a name="line.321"></a>
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325 <FONT color="green">322</FONT> return F;<a name="line.322"></a>
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326 <FONT color="green">323</FONT> }<a name="line.323"></a>
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327 <FONT color="green">324</FONT> <a name="line.324"></a>
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328 <FONT color="green">325</FONT> // Rather than the naive real to complex conversion, pack 2N<a name="line.325"></a>
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329 <FONT color="green">326</FONT> // real numbers into N complex numbers for better performance.<a name="line.326"></a>
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330 <FONT color="green">327</FONT> int N = f.length >> 1;<a name="line.327"></a>
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331 <FONT color="green">328</FONT> Complex c[] = new Complex[N];<a name="line.328"></a>
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332 <FONT color="green">329</FONT> for (int i = 0; i < N; i++) {<a name="line.329"></a>
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333 <FONT color="green">330</FONT> c[i] = new Complex(f[2*i], f[2*i+1]);<a name="line.330"></a>
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334 <FONT color="green">331</FONT> }<a name="line.331"></a>
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335 <FONT color="green">332</FONT> roots.computeOmega(isInverse ? -N : N);<a name="line.332"></a>
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336 <FONT color="green">333</FONT> Complex z[] = fft(c);<a name="line.333"></a>
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337 <FONT color="green">334</FONT> <a name="line.334"></a>
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338 <FONT color="green">335</FONT> // reconstruct the FFT result for the original array<a name="line.335"></a>
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339 <FONT color="green">336</FONT> roots.computeOmega(isInverse ? -2*N : 2*N);<a name="line.336"></a>
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340 <FONT color="green">337</FONT> F[0] = new Complex(2 * (z[0].getReal() + z[0].getImaginary()), 0.0);<a name="line.337"></a>
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341 <FONT color="green">338</FONT> F[N] = new Complex(2 * (z[0].getReal() - z[0].getImaginary()), 0.0);<a name="line.338"></a>
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342 <FONT color="green">339</FONT> for (int i = 1; i < N; i++) {<a name="line.339"></a>
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343 <FONT color="green">340</FONT> Complex A = z[N-i].conjugate();<a name="line.340"></a>
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344 <FONT color="green">341</FONT> Complex B = z[i].add(A);<a name="line.341"></a>
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345 <FONT color="green">342</FONT> Complex C = z[i].subtract(A);<a name="line.342"></a>
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346 <FONT color="green">343</FONT> //Complex D = roots.getOmega(i).multiply(Complex.I);<a name="line.343"></a>
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347 <FONT color="green">344</FONT> Complex D = new Complex(-roots.getOmegaImaginary(i),<a name="line.344"></a>
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348 <FONT color="green">345</FONT> roots.getOmegaReal(i));<a name="line.345"></a>
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349 <FONT color="green">346</FONT> F[i] = B.subtract(C.multiply(D));<a name="line.346"></a>
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350 <FONT color="green">347</FONT> F[2*N-i] = F[i].conjugate();<a name="line.347"></a>
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351 <FONT color="green">348</FONT> }<a name="line.348"></a>
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352 <FONT color="green">349</FONT> <a name="line.349"></a>
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353 <FONT color="green">350</FONT> return scaleArray(F, 0.5);<a name="line.350"></a>
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354 <FONT color="green">351</FONT> }<a name="line.351"></a>
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355 <FONT color="green">352</FONT> <a name="line.352"></a>
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356 <FONT color="green">353</FONT> /**<a name="line.353"></a>
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357 <FONT color="green">354</FONT> * Perform the base-4 Cooley-Tukey FFT algorithm (including inverse).<a name="line.354"></a>
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|
358 <FONT color="green">355</FONT> *<a name="line.355"></a>
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|
359 <FONT color="green">356</FONT> * @param data the complex data array to be transformed<a name="line.356"></a>
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360 <FONT color="green">357</FONT> * @return the complex transformed array<a name="line.357"></a>
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|
361 <FONT color="green">358</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.358"></a>
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|
362 <FONT color="green">359</FONT> */<a name="line.359"></a>
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|
363 <FONT color="green">360</FONT> protected Complex[] fft(Complex data[])<a name="line.360"></a>
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364 <FONT color="green">361</FONT> throws IllegalArgumentException {<a name="line.361"></a>
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365 <FONT color="green">362</FONT> <a name="line.362"></a>
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366 <FONT color="green">363</FONT> final int n = data.length;<a name="line.363"></a>
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367 <FONT color="green">364</FONT> final Complex f[] = new Complex[n];<a name="line.364"></a>
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368 <FONT color="green">365</FONT> <a name="line.365"></a>
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369 <FONT color="green">366</FONT> // initial simple cases<a name="line.366"></a>
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370 <FONT color="green">367</FONT> verifyDataSet(data);<a name="line.367"></a>
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371 <FONT color="green">368</FONT> if (n == 1) {<a name="line.368"></a>
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372 <FONT color="green">369</FONT> f[0] = data[0];<a name="line.369"></a>
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|
373 <FONT color="green">370</FONT> return f;<a name="line.370"></a>
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374 <FONT color="green">371</FONT> }<a name="line.371"></a>
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375 <FONT color="green">372</FONT> if (n == 2) {<a name="line.372"></a>
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|
376 <FONT color="green">373</FONT> f[0] = data[0].add(data[1]);<a name="line.373"></a>
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377 <FONT color="green">374</FONT> f[1] = data[0].subtract(data[1]);<a name="line.374"></a>
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|
378 <FONT color="green">375</FONT> return f;<a name="line.375"></a>
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379 <FONT color="green">376</FONT> }<a name="line.376"></a>
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380 <FONT color="green">377</FONT> <a name="line.377"></a>
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|
381 <FONT color="green">378</FONT> // permute original data array in bit-reversal order<a name="line.378"></a>
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|
382 <FONT color="green">379</FONT> int ii = 0;<a name="line.379"></a>
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383 <FONT color="green">380</FONT> for (int i = 0; i < n; i++) {<a name="line.380"></a>
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|
384 <FONT color="green">381</FONT> f[i] = data[ii];<a name="line.381"></a>
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|
385 <FONT color="green">382</FONT> int k = n >> 1;<a name="line.382"></a>
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386 <FONT color="green">383</FONT> while (ii >= k && k > 0) {<a name="line.383"></a>
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387 <FONT color="green">384</FONT> ii -= k; k >>= 1;<a name="line.384"></a>
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388 <FONT color="green">385</FONT> }<a name="line.385"></a>
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|
389 <FONT color="green">386</FONT> ii += k;<a name="line.386"></a>
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390 <FONT color="green">387</FONT> }<a name="line.387"></a>
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|
391 <FONT color="green">388</FONT> <a name="line.388"></a>
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|
392 <FONT color="green">389</FONT> // the bottom base-4 round<a name="line.389"></a>
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|
393 <FONT color="green">390</FONT> for (int i = 0; i < n; i += 4) {<a name="line.390"></a>
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|
394 <FONT color="green">391</FONT> final Complex a = f[i].add(f[i+1]);<a name="line.391"></a>
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|
395 <FONT color="green">392</FONT> final Complex b = f[i+2].add(f[i+3]);<a name="line.392"></a>
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|
396 <FONT color="green">393</FONT> final Complex c = f[i].subtract(f[i+1]);<a name="line.393"></a>
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|
397 <FONT color="green">394</FONT> final Complex d = f[i+2].subtract(f[i+3]);<a name="line.394"></a>
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|
398 <FONT color="green">395</FONT> final Complex e1 = c.add(d.multiply(Complex.I));<a name="line.395"></a>
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|
|
399 <FONT color="green">396</FONT> final Complex e2 = c.subtract(d.multiply(Complex.I));<a name="line.396"></a>
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|
400 <FONT color="green">397</FONT> f[i] = a.add(b);<a name="line.397"></a>
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|
|
401 <FONT color="green">398</FONT> f[i+2] = a.subtract(b);<a name="line.398"></a>
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|
402 <FONT color="green">399</FONT> // omegaCount indicates forward or inverse transform<a name="line.399"></a>
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|
|
403 <FONT color="green">400</FONT> f[i+1] = roots.isForward() ? e2 : e1;<a name="line.400"></a>
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|
404 <FONT color="green">401</FONT> f[i+3] = roots.isForward() ? e1 : e2;<a name="line.401"></a>
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405 <FONT color="green">402</FONT> }<a name="line.402"></a>
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406 <FONT color="green">403</FONT> <a name="line.403"></a>
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407 <FONT color="green">404</FONT> // iterations from bottom to top take O(N*logN) time<a name="line.404"></a>
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408 <FONT color="green">405</FONT> for (int i = 4; i < n; i <<= 1) {<a name="line.405"></a>
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409 <FONT color="green">406</FONT> final int m = n / (i<<1);<a name="line.406"></a>
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410 <FONT color="green">407</FONT> for (int j = 0; j < n; j += i<<1) {<a name="line.407"></a>
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411 <FONT color="green">408</FONT> for (int k = 0; k < i; k++) {<a name="line.408"></a>
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412 <FONT color="green">409</FONT> //z = f[i+j+k].multiply(roots.getOmega(k*m));<a name="line.409"></a>
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413 <FONT color="green">410</FONT> final int k_times_m = k*m;<a name="line.410"></a>
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414 <FONT color="green">411</FONT> final double omega_k_times_m_real = roots.getOmegaReal(k_times_m);<a name="line.411"></a>
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415 <FONT color="green">412</FONT> final double omega_k_times_m_imaginary = roots.getOmegaImaginary(k_times_m);<a name="line.412"></a>
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416 <FONT color="green">413</FONT> //z = f[i+j+k].multiply(omega[k*m]);<a name="line.413"></a>
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417 <FONT color="green">414</FONT> final Complex z = new Complex(<a name="line.414"></a>
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418 <FONT color="green">415</FONT> f[i+j+k].getReal() * omega_k_times_m_real -<a name="line.415"></a>
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419 <FONT color="green">416</FONT> f[i+j+k].getImaginary() * omega_k_times_m_imaginary,<a name="line.416"></a>
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420 <FONT color="green">417</FONT> f[i+j+k].getReal() * omega_k_times_m_imaginary +<a name="line.417"></a>
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421 <FONT color="green">418</FONT> f[i+j+k].getImaginary() * omega_k_times_m_real);<a name="line.418"></a>
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422 <FONT color="green">419</FONT> <a name="line.419"></a>
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423 <FONT color="green">420</FONT> f[i+j+k] = f[j+k].subtract(z);<a name="line.420"></a>
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424 <FONT color="green">421</FONT> f[j+k] = f[j+k].add(z);<a name="line.421"></a>
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425 <FONT color="green">422</FONT> }<a name="line.422"></a>
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426 <FONT color="green">423</FONT> }<a name="line.423"></a>
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427 <FONT color="green">424</FONT> }<a name="line.424"></a>
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428 <FONT color="green">425</FONT> return f;<a name="line.425"></a>
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429 <FONT color="green">426</FONT> }<a name="line.426"></a>
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430 <FONT color="green">427</FONT> <a name="line.427"></a>
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431 <FONT color="green">428</FONT> /**<a name="line.428"></a>
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432 <FONT color="green">429</FONT> * Sample the given univariate real function on the given interval.<a name="line.429"></a>
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433 <FONT color="green">430</FONT> * <p><a name="line.430"></a>
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434 <FONT color="green">431</FONT> * The interval is divided equally into N sections and sample points<a name="line.431"></a>
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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>
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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>
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437 <FONT color="green">434</FONT> * require that.</p><a name="line.434"></a>
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438 <FONT color="green">435</FONT> *<a name="line.435"></a>
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439 <FONT color="green">436</FONT> * @param f the function to be sampled<a name="line.436"></a>
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440 <FONT color="green">437</FONT> * @param min the lower bound for the interval<a name="line.437"></a>
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441 <FONT color="green">438</FONT> * @param max the upper bound for the interval<a name="line.438"></a>
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442 <FONT color="green">439</FONT> * @param n the number of sample points<a name="line.439"></a>
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443 <FONT color="green">440</FONT> * @return the samples array<a name="line.440"></a>
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444 <FONT color="green">441</FONT> * @throws FunctionEvaluationException if function cannot be evaluated<a name="line.441"></a>
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445 <FONT color="green">442</FONT> * at some point<a name="line.442"></a>
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446 <FONT color="green">443</FONT> * @throws IllegalArgumentException if any parameters are invalid<a name="line.443"></a>
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447 <FONT color="green">444</FONT> */<a name="line.444"></a>
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|
448 <FONT color="green">445</FONT> public static double[] sample(UnivariateRealFunction f,<a name="line.445"></a>
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449 <FONT color="green">446</FONT> double min, double max, int n)<a name="line.446"></a>
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450 <FONT color="green">447</FONT> throws FunctionEvaluationException, IllegalArgumentException {<a name="line.447"></a>
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|
451 <FONT color="green">448</FONT> <a name="line.448"></a>
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452 <FONT color="green">449</FONT> if (n <= 0) {<a name="line.449"></a>
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453 <FONT color="green">450</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.450"></a>
|
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|
454 <FONT color="green">451</FONT> "number of sample is not positive: {0}",<a name="line.451"></a>
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|
455 <FONT color="green">452</FONT> n);<a name="line.452"></a>
|
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456 <FONT color="green">453</FONT> }<a name="line.453"></a>
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|
457 <FONT color="green">454</FONT> verifyInterval(min, max);<a name="line.454"></a>
|
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|
458 <FONT color="green">455</FONT> <a name="line.455"></a>
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|
459 <FONT color="green">456</FONT> double s[] = new double[n];<a name="line.456"></a>
|
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|
460 <FONT color="green">457</FONT> double h = (max - min) / n;<a name="line.457"></a>
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|
|
461 <FONT color="green">458</FONT> for (int i = 0; i < n; i++) {<a name="line.458"></a>
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|
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462 <FONT color="green">459</FONT> s[i] = f.value(min + i * h);<a name="line.459"></a>
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463 <FONT color="green">460</FONT> }<a name="line.460"></a>
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464 <FONT color="green">461</FONT> return s;<a name="line.461"></a>
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|
465 <FONT color="green">462</FONT> }<a name="line.462"></a>
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|
466 <FONT color="green">463</FONT> <a name="line.463"></a>
|
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|
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>
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|
|
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>
|
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|
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>
|
|
|
935
|
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936
|
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937
|
|
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938
|
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939
|
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940
|
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941
|
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942
|
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943
|
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944
|
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945
|
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946
|
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947
|
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948
|
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949
|
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950
|
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951
|
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952
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953
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954
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955
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956
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957
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958
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959
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960
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961
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962
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963
|
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964
|
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965
|
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966
|
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967
|
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968
|
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969
|
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970
|
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971
|
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972
|
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973
|
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974
|
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975
|
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976
|
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977
|
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978
|
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979
|
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980
|
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981
|
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982
|
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983
|
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984
|
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|
985
|
|
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986
|
|
|
987
|
|
|
988
|
|
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989
|
|
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990
|
|
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991
|
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992
|
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993
|
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994
|
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995 </PRE>
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996 </BODY>
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997 </HTML>
|
