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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.optimization.fitting;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.optimization.OptimizationException;<a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> /** This class guesses harmonic coefficients from a sample.<a name="line.22"></a> <FONT color="green">023</FONT> <a name="line.23"></a> <FONT color="green">024</FONT> * <p>The algorithm used to guess the coefficients is as follows:</p><a name="line.24"></a> <FONT color="green">025</FONT> <a name="line.25"></a> <FONT color="green">026</FONT> * <p>We know f (t) at some sampling points t<sub>i</sub> and want to find a,<a name="line.26"></a> <FONT color="green">027</FONT> * &omega; and &phi; such that f (t) = a cos (&omega; t + &phi;).<a name="line.27"></a> <FONT color="green">028</FONT> * </p><a name="line.28"></a> <FONT color="green">029</FONT> *<a name="line.29"></a> <FONT color="green">030</FONT> * <p>From the analytical expression, we can compute two primitives :<a name="line.30"></a> <FONT color="green">031</FONT> * <pre><a name="line.31"></a> <FONT color="green">032</FONT> * If2 (t) = &int; f<sup>2</sup> = a<sup>2</sup> &times; [t + S (t)] / 2<a name="line.32"></a> <FONT color="green">033</FONT> * If'2 (t) = &int; f'<sup>2</sup> = a<sup>2</sup> &omega;<sup>2</sup> &times; [t - S (t)] / 2<a name="line.33"></a> <FONT color="green">034</FONT> * where S (t) = sin (2 (&omega; t + &phi;)) / (2 &omega;)<a name="line.34"></a> <FONT color="green">035</FONT> * </pre><a name="line.35"></a> <FONT color="green">036</FONT> * </p><a name="line.36"></a> <FONT color="green">037</FONT> *<a name="line.37"></a> <FONT color="green">038</FONT> * <p>We can remove S between these expressions :<a name="line.38"></a> <FONT color="green">039</FONT> * <pre><a name="line.39"></a> <FONT color="green">040</FONT> * If'2 (t) = a<sup>2</sup> &omega;<sup>2</sup> t - &omega;<sup>2</sup> If2 (t)<a name="line.40"></a> <FONT color="green">041</FONT> * </pre><a name="line.41"></a> <FONT color="green">042</FONT> * </p><a name="line.42"></a> <FONT color="green">043</FONT> *<a name="line.43"></a> <FONT color="green">044</FONT> * <p>The preceding expression shows that If'2 (t) is a linear<a name="line.44"></a> <FONT color="green">045</FONT> * combination of both t and If2 (t): If'2 (t) = A &times; t + B &times; If2 (t)<a name="line.45"></a> <FONT color="green">046</FONT> * </p><a name="line.46"></a> <FONT color="green">047</FONT> *<a name="line.47"></a> <FONT color="green">048</FONT> * <p>From the primitive, we can deduce the same form for definite<a name="line.48"></a> <FONT color="green">049</FONT> * integrals between t<sub>1</sub> and t<sub>i</sub> for each t<sub>i</sub> :<a name="line.49"></a> <FONT color="green">050</FONT> * <pre><a name="line.50"></a> <FONT color="green">051</FONT> * If2 (t<sub>i</sub>) - If2 (t<sub>1</sub>) = A &times; (t<sub>i</sub> - t<sub>1</sub>) + B &times; (If2 (t<sub>i</sub>) - If2 (t<sub>1</sub>))<a name="line.51"></a> <FONT color="green">052</FONT> * </pre><a name="line.52"></a> <FONT color="green">053</FONT> * </p><a name="line.53"></a> <FONT color="green">054</FONT> *<a name="line.54"></a> <FONT color="green">055</FONT> * <p>We can find the coefficients A and B that best fit the sample<a name="line.55"></a> <FONT color="green">056</FONT> * to this linear expression by computing the definite integrals for<a name="line.56"></a> <FONT color="green">057</FONT> * each sample points.<a name="line.57"></a> <FONT color="green">058</FONT> * </p><a name="line.58"></a> <FONT color="green">059</FONT> *<a name="line.59"></a> <FONT color="green">060</FONT> * <p>For a bilinear expression z (x<sub>i</sub>, y<sub>i</sub>) = A &times; x<sub>i</sub> + B &times; y<sub>i</sub>, the<a name="line.60"></a> <FONT color="green">061</FONT> * coefficients A and B that minimize a least square criterion<a name="line.61"></a> <FONT color="green">062</FONT> * &sum; (z<sub>i</sub> - z (x<sub>i</sub>, y<sub>i</sub>))<sup>2</sup> are given by these expressions:</p><a name="line.62"></a> <FONT color="green">063</FONT> * <pre><a name="line.63"></a> <FONT color="green">064</FONT> *<a name="line.64"></a> <FONT color="green">065</FONT> * &sum;y<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>z<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;y<sub>i</sub>z<sub>i</sub><a name="line.65"></a> <FONT color="green">066</FONT> * A = ------------------------<a name="line.66"></a> <FONT color="green">067</FONT> * &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>y<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>y<sub>i</sub><a name="line.67"></a> <FONT color="green">068</FONT> *<a name="line.68"></a> <FONT color="green">069</FONT> * &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>z<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>z<sub>i</sub><a name="line.69"></a> <FONT color="green">070</FONT> * B = ------------------------<a name="line.70"></a> <FONT color="green">071</FONT> * &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>y<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>y<sub>i</sub><a name="line.71"></a> <FONT color="green">072</FONT> * </pre><a name="line.72"></a> <FONT color="green">073</FONT> * </p><a name="line.73"></a> <FONT color="green">074</FONT> *<a name="line.74"></a> <FONT color="green">075</FONT> *<a name="line.75"></a> <FONT color="green">076</FONT> * <p>In fact, we can assume both a and &omega; are positive and<a name="line.76"></a> <FONT color="green">077</FONT> * compute them directly, knowing that A = a<sup>2</sup> &omega;<sup>2</sup> and that<a name="line.77"></a> <FONT color="green">078</FONT> * B = - &omega;<sup>2</sup>. The complete algorithm is therefore:</p><a name="line.78"></a> <FONT color="green">079</FONT> * <pre><a name="line.79"></a> <FONT color="green">080</FONT> *<a name="line.80"></a> <FONT color="green">081</FONT> * for each t<sub>i</sub> from t<sub>1</sub> to t<sub>n-1</sub>, compute:<a name="line.81"></a> <FONT color="green">082</FONT> * f (t<sub>i</sub>)<a name="line.82"></a> <FONT color="green">083</FONT> * f' (t<sub>i</sub>) = (f (t<sub>i+1</sub>) - f(t<sub>i-1</sub>)) / (t<sub>i+1</sub> - t<sub>i-1</sub>)<a name="line.83"></a> <FONT color="green">084</FONT> * x<sub>i</sub> = t<sub>i</sub> - t<sub>1</sub><a name="line.84"></a> <FONT color="green">085</FONT> * y<sub>i</sub> = &int; f<sup>2</sup> from t<sub>1</sub> to t<sub>i</sub><a name="line.85"></a> <FONT color="green">086</FONT> * z<sub>i</sub> = &int; f'<sup>2</sup> from t<sub>1</sub> to t<sub>i</sub><a name="line.86"></a> <FONT color="green">087</FONT> * update the sums &sum;x<sub>i</sub>x<sub>i</sub>, &sum;y<sub>i</sub>y<sub>i</sub>, &sum;x<sub>i</sub>y<sub>i</sub>, &sum;x<sub>i</sub>z<sub>i</sub> and &sum;y<sub>i</sub>z<sub>i</sub><a name="line.87"></a> <FONT color="green">088</FONT> * end for<a name="line.88"></a> <FONT color="green">089</FONT> *<a name="line.89"></a> <FONT color="green">090</FONT> * |--------------------------<a name="line.90"></a> <FONT color="green">091</FONT> * \ | &sum;y<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>z<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;y<sub>i</sub>z<sub>i</sub><a name="line.91"></a> <FONT color="green">092</FONT> * a = \ | ------------------------<a name="line.92"></a> <FONT color="green">093</FONT> * \| &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>z<sub>i</sub> - &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>z<sub>i</sub><a name="line.93"></a> <FONT color="green">094</FONT> *<a name="line.94"></a> <FONT color="green">095</FONT> *<a name="line.95"></a> <FONT color="green">096</FONT> * |--------------------------<a name="line.96"></a> <FONT color="green">097</FONT> * \ | &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>z<sub>i</sub> - &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>z<sub>i</sub><a name="line.97"></a> <FONT color="green">098</FONT> * &omega; = \ | ------------------------<a name="line.98"></a> <FONT color="green">099</FONT> * \| &sum;x<sub>i</sub>x<sub>i</sub> &sum;y<sub>i</sub>y<sub>i</sub> - &sum;x<sub>i</sub>y<sub>i</sub> &sum;x<sub>i</sub>y<sub>i</sub><a name="line.99"></a> <FONT color="green">100</FONT> *<a name="line.100"></a> <FONT color="green">101</FONT> * </pre><a name="line.101"></a> <FONT color="green">102</FONT> * </p><a name="line.102"></a> <FONT color="green">103</FONT> <a name="line.103"></a> <FONT color="green">104</FONT> * <p>Once we know &omega;, we can compute:<a name="line.104"></a> <FONT color="green">105</FONT> * <pre><a name="line.105"></a> <FONT color="green">106</FONT> * fc = &omega; f (t) cos (&omega; t) - f' (t) sin (&omega; t)<a name="line.106"></a> <FONT color="green">107</FONT> * fs = &omega; f (t) sin (&omega; t) + f' (t) cos (&omega; t)<a name="line.107"></a> <FONT color="green">108</FONT> * </pre><a name="line.108"></a> <FONT color="green">109</FONT> * </p><a name="line.109"></a> <FONT color="green">110</FONT> <a name="line.110"></a> <FONT color="green">111</FONT> * <p>It appears that <code>fc = a &omega; cos (&phi;)</code> and<a name="line.111"></a> <FONT color="green">112</FONT> * <code>fs = -a &omega; sin (&phi;)</code>, so we can use these<a name="line.112"></a> <FONT color="green">113</FONT> * expressions to compute &phi;. The best estimate over the sample is<a name="line.113"></a> <FONT color="green">114</FONT> * given by averaging these expressions.<a name="line.114"></a> <FONT color="green">115</FONT> * </p><a name="line.115"></a> <FONT color="green">116</FONT> <a name="line.116"></a> <FONT color="green">117</FONT> * <p>Since integrals and means are involved in the preceding<a name="line.117"></a> <FONT color="green">118</FONT> * estimations, these operations run in O(n) time, where n is the<a name="line.118"></a> <FONT color="green">119</FONT> * number of measurements.</p><a name="line.119"></a> <FONT color="green">120</FONT> <a name="line.120"></a> <FONT color="green">121</FONT> * @version $Revision: 786479 $ $Date: 2009-06-19 08:36:16 -0400 (Fri, 19 Jun 2009) $<a name="line.121"></a> <FONT color="green">122</FONT> * @since 2.0<a name="line.122"></a> <FONT color="green">123</FONT> <a name="line.123"></a> <FONT color="green">124</FONT> */<a name="line.124"></a> <FONT color="green">125</FONT> public class HarmonicCoefficientsGuesser {<a name="line.125"></a> <FONT color="green">126</FONT> <a name="line.126"></a> <FONT color="green">127</FONT> /** Sampled observations. */<a name="line.127"></a> <FONT color="green">128</FONT> private final WeightedObservedPoint[] observations;<a name="line.128"></a> <FONT color="green">129</FONT> <a name="line.129"></a> <FONT color="green">130</FONT> /** Guessed amplitude. */<a name="line.130"></a> <FONT color="green">131</FONT> private double a;<a name="line.131"></a> <FONT color="green">132</FONT> <a name="line.132"></a> <FONT color="green">133</FONT> /** Guessed pulsation &omega;. */<a name="line.133"></a> <FONT color="green">134</FONT> private double omega;<a name="line.134"></a> <FONT color="green">135</FONT> <a name="line.135"></a> <FONT color="green">136</FONT> /** Guessed phase &phi;. */<a name="line.136"></a> <FONT color="green">137</FONT> private double phi;<a name="line.137"></a> <FONT color="green">138</FONT> <a name="line.138"></a> <FONT color="green">139</FONT> /** Simple constructor.<a name="line.139"></a> <FONT color="green">140</FONT> * @param observations sampled observations<a name="line.140"></a> <FONT color="green">141</FONT> */<a name="line.141"></a> <FONT color="green">142</FONT> public HarmonicCoefficientsGuesser(WeightedObservedPoint[] observations) {<a name="line.142"></a> <FONT color="green">143</FONT> this.observations = observations.clone();<a name="line.143"></a> <FONT color="green">144</FONT> a = Double.NaN;<a name="line.144"></a> <FONT color="green">145</FONT> omega = Double.NaN;<a name="line.145"></a> <FONT color="green">146</FONT> }<a name="line.146"></a> <FONT color="green">147</FONT> <a name="line.147"></a> <FONT color="green">148</FONT> /** Estimate a first guess of the coefficients.<a name="line.148"></a> <FONT color="green">149</FONT> * @exception OptimizationException if the sample is too short or if<a name="line.149"></a> <FONT color="green">150</FONT> * the first guess cannot be computed (when the elements under the<a name="line.150"></a> <FONT color="green">151</FONT> * square roots are negative).<a name="line.151"></a> <FONT color="green">152</FONT> * */<a name="line.152"></a> <FONT color="green">153</FONT> public void guess() throws OptimizationException {<a name="line.153"></a> <FONT color="green">154</FONT> sortObservations();<a name="line.154"></a> <FONT color="green">155</FONT> guessAOmega();<a name="line.155"></a> <FONT color="green">156</FONT> guessPhi();<a name="line.156"></a> <FONT color="green">157</FONT> }<a name="line.157"></a> <FONT color="green">158</FONT> <a name="line.158"></a> <FONT color="green">159</FONT> /** Sort the observations with respect to the abscissa.<a name="line.159"></a> <FONT color="green">160</FONT> */<a name="line.160"></a> <FONT color="green">161</FONT> private void sortObservations() {<a name="line.161"></a> <FONT color="green">162</FONT> <a name="line.162"></a> <FONT color="green">163</FONT> // Since the samples are almost always already sorted, this<a name="line.163"></a> <FONT color="green">164</FONT> // method is implemented as an insertion sort that reorders the<a name="line.164"></a> <FONT color="green">165</FONT> // elements in place. Insertion sort is very efficient in this case.<a name="line.165"></a> <FONT color="green">166</FONT> WeightedObservedPoint curr = observations[0];<a name="line.166"></a> <FONT color="green">167</FONT> for (int j = 1; j < observations.length; ++j) {<a name="line.167"></a> <FONT color="green">168</FONT> WeightedObservedPoint prec = curr;<a name="line.168"></a> <FONT color="green">169</FONT> curr = observations[j];<a name="line.169"></a> <FONT color="green">170</FONT> if (curr.getX() < prec.getX()) {<a name="line.170"></a> <FONT color="green">171</FONT> // the current element should be inserted closer to the beginning<a name="line.171"></a> <FONT color="green">172</FONT> int i = j - 1;<a name="line.172"></a> <FONT color="green">173</FONT> WeightedObservedPoint mI = observations[i];<a name="line.173"></a> <FONT color="green">174</FONT> while ((i >= 0) && (curr.getX() < mI.getX())) {<a name="line.174"></a> <FONT color="green">175</FONT> observations[i + 1] = mI;<a name="line.175"></a> <FONT color="green">176</FONT> if (i-- != 0) {<a name="line.176"></a> <FONT color="green">177</FONT> mI = observations[i];<a name="line.177"></a> <FONT color="green">178</FONT> } else {<a name="line.178"></a> <FONT color="green">179</FONT> mI = null;<a name="line.179"></a> <FONT color="green">180</FONT> }<a name="line.180"></a> <FONT color="green">181</FONT> }<a name="line.181"></a> <FONT color="green">182</FONT> observations[i + 1] = curr;<a name="line.182"></a> <FONT color="green">183</FONT> curr = observations[j];<a name="line.183"></a> <FONT color="green">184</FONT> }<a name="line.184"></a> <FONT color="green">185</FONT> }<a name="line.185"></a> <FONT color="green">186</FONT> <a name="line.186"></a> <FONT color="green">187</FONT> }<a name="line.187"></a> <FONT color="green">188</FONT> <a name="line.188"></a> <FONT color="green">189</FONT> /** Estimate a first guess of the a and &omega; coefficients.<a name="line.189"></a> <FONT color="green">190</FONT> * @exception OptimizationException if the sample is too short or if<a name="line.190"></a> <FONT color="green">191</FONT> * the first guess cannot be computed (when the elements under the<a name="line.191"></a> <FONT color="green">192</FONT> * square roots are negative).<a name="line.192"></a> <FONT color="green">193</FONT> */<a name="line.193"></a> <FONT color="green">194</FONT> private void guessAOmega() throws OptimizationException {<a name="line.194"></a> <FONT color="green">195</FONT> <a name="line.195"></a> <FONT color="green">196</FONT> // initialize the sums for the linear model between the two integrals<a name="line.196"></a> <FONT color="green">197</FONT> double sx2 = 0.0;<a name="line.197"></a> <FONT color="green">198</FONT> double sy2 = 0.0;<a name="line.198"></a> <FONT color="green">199</FONT> double sxy = 0.0;<a name="line.199"></a> <FONT color="green">200</FONT> double sxz = 0.0;<a name="line.200"></a> <FONT color="green">201</FONT> double syz = 0.0;<a name="line.201"></a> <FONT color="green">202</FONT> <a name="line.202"></a> <FONT color="green">203</FONT> double currentX = observations[0].getX();<a name="line.203"></a> <FONT color="green">204</FONT> double currentY = observations[0].getY();<a name="line.204"></a> <FONT color="green">205</FONT> double f2Integral = 0;<a name="line.205"></a> <FONT color="green">206</FONT> double fPrime2Integral = 0;<a name="line.206"></a> <FONT color="green">207</FONT> final double startX = currentX;<a name="line.207"></a> <FONT color="green">208</FONT> for (int i = 1; i < observations.length; ++i) {<a name="line.208"></a> <FONT color="green">209</FONT> <a name="line.209"></a> <FONT color="green">210</FONT> // one step forward<a name="line.210"></a> <FONT color="green">211</FONT> final double previousX = currentX;<a name="line.211"></a> <FONT color="green">212</FONT> final double previousY = currentY;<a name="line.212"></a> <FONT color="green">213</FONT> currentX = observations[i].getX();<a name="line.213"></a> <FONT color="green">214</FONT> currentY = observations[i].getY();<a name="line.214"></a> <FONT color="green">215</FONT> <a name="line.215"></a> <FONT color="green">216</FONT> // update the integrals of f<sup>2</sup> and f'<sup>2</sup><a name="line.216"></a> <FONT color="green">217</FONT> // considering a linear model for f (and therefore constant f')<a name="line.217"></a> <FONT color="green">218</FONT> final double dx = currentX - previousX;<a name="line.218"></a> <FONT color="green">219</FONT> final double dy = currentY - previousY;<a name="line.219"></a> <FONT color="green">220</FONT> final double f2StepIntegral =<a name="line.220"></a> <FONT color="green">221</FONT> dx * (previousY * previousY + previousY * currentY + currentY * currentY) / 3;<a name="line.221"></a> <FONT color="green">222</FONT> final double fPrime2StepIntegral = dy * dy / dx;<a name="line.222"></a> <FONT color="green">223</FONT> <a name="line.223"></a> <FONT color="green">224</FONT> final double x = currentX - startX;<a name="line.224"></a> <FONT color="green">225</FONT> f2Integral += f2StepIntegral;<a name="line.225"></a> <FONT color="green">226</FONT> fPrime2Integral += fPrime2StepIntegral;<a name="line.226"></a> <FONT color="green">227</FONT> <a name="line.227"></a> <FONT color="green">228</FONT> sx2 += x * x;<a name="line.228"></a> <FONT color="green">229</FONT> sy2 += f2Integral * f2Integral;<a name="line.229"></a> <FONT color="green">230</FONT> sxy += x * f2Integral;<a name="line.230"></a> <FONT color="green">231</FONT> sxz += x * fPrime2Integral;<a name="line.231"></a> <FONT color="green">232</FONT> syz += f2Integral * fPrime2Integral;<a name="line.232"></a> <FONT color="green">233</FONT> <a name="line.233"></a> <FONT color="green">234</FONT> }<a name="line.234"></a> <FONT color="green">235</FONT> <a name="line.235"></a> <FONT color="green">236</FONT> // compute the amplitude and pulsation coefficients<a name="line.236"></a> <FONT color="green">237</FONT> double c1 = sy2 * sxz - sxy * syz;<a name="line.237"></a> <FONT color="green">238</FONT> double c2 = sxy * sxz - sx2 * syz;<a name="line.238"></a> <FONT color="green">239</FONT> double c3 = sx2 * sy2 - sxy * sxy;<a name="line.239"></a> <FONT color="green">240</FONT> if ((c1 / c2 < 0.0) || (c2 / c3 < 0.0)) {<a name="line.240"></a> <FONT color="green">241</FONT> throw new OptimizationException("unable to first guess the harmonic coefficients");<a name="line.241"></a> <FONT color="green">242</FONT> }<a name="line.242"></a> <FONT color="green">243</FONT> a = Math.sqrt(c1 / c2);<a name="line.243"></a> <FONT color="green">244</FONT> omega = Math.sqrt(c2 / c3);<a name="line.244"></a> <FONT color="green">245</FONT> <a name="line.245"></a> <FONT color="green">246</FONT> }<a name="line.246"></a> <FONT color="green">247</FONT> <a name="line.247"></a> <FONT color="green">248</FONT> /** Estimate a first guess of the &phi; coefficient.<a name="line.248"></a> <FONT color="green">249</FONT> */<a name="line.249"></a> <FONT color="green">250</FONT> private void guessPhi() {<a name="line.250"></a> <FONT color="green">251</FONT> <a name="line.251"></a> <FONT color="green">252</FONT> // initialize the means<a name="line.252"></a> <FONT color="green">253</FONT> double fcMean = 0.0;<a name="line.253"></a> <FONT color="green">254</FONT> double fsMean = 0.0;<a name="line.254"></a> <FONT color="green">255</FONT> <a name="line.255"></a> <FONT color="green">256</FONT> double currentX = observations[0].getX();<a name="line.256"></a> <FONT color="green">257</FONT> double currentY = observations[0].getY();<a name="line.257"></a> <FONT color="green">258</FONT> for (int i = 1; i < observations.length; ++i) {<a name="line.258"></a> <FONT color="green">259</FONT> <a name="line.259"></a> <FONT color="green">260</FONT> // one step forward<a name="line.260"></a> <FONT color="green">261</FONT> final double previousX = currentX;<a name="line.261"></a> <FONT color="green">262</FONT> final double previousY = currentY;<a name="line.262"></a> <FONT color="green">263</FONT> currentX = observations[i].getX();<a name="line.263"></a> <FONT color="green">264</FONT> currentY = observations[i].getY();<a name="line.264"></a> <FONT color="green">265</FONT> final double currentYPrime = (currentY - previousY) / (currentX - previousX);<a name="line.265"></a> <FONT color="green">266</FONT> <a name="line.266"></a> <FONT color="green">267</FONT> double omegaX = omega * currentX;<a name="line.267"></a> <FONT color="green">268</FONT> double cosine = Math.cos(omegaX);<a name="line.268"></a> <FONT color="green">269</FONT> double sine = Math.sin(omegaX);<a name="line.269"></a> <FONT color="green">270</FONT> fcMean += omega * currentY * cosine - currentYPrime * sine;<a name="line.270"></a> <FONT color="green">271</FONT> fsMean += omega * currentY * sine + currentYPrime * cosine;<a name="line.271"></a> <FONT color="green">272</FONT> <a name="line.272"></a> <FONT color="green">273</FONT> }<a name="line.273"></a> <FONT color="green">274</FONT> <a name="line.274"></a> <FONT color="green">275</FONT> phi = Math.atan2(-fsMean, fcMean);<a name="line.275"></a> <FONT color="green">276</FONT> <a name="line.276"></a> <FONT color="green">277</FONT> }<a name="line.277"></a> <FONT color="green">278</FONT> <a name="line.278"></a> <FONT color="green">279</FONT> /** Get the guessed amplitude a.<a name="line.279"></a> <FONT color="green">280</FONT> * @return guessed amplitude a;<a name="line.280"></a> <FONT color="green">281</FONT> */<a name="line.281"></a> <FONT color="green">282</FONT> public double getGuessedAmplitude() {<a name="line.282"></a> <FONT color="green">283</FONT> return a;<a name="line.283"></a> <FONT color="green">284</FONT> }<a name="line.284"></a> <FONT color="green">285</FONT> <a name="line.285"></a> <FONT color="green">286</FONT> /** Get the guessed pulsation &omega;.<a name="line.286"></a> <FONT color="green">287</FONT> * @return guessed pulsation &omega;<a name="line.287"></a> <FONT color="green">288</FONT> */<a name="line.288"></a> <FONT color="green">289</FONT> public double getGuessedPulsation() {<a name="line.289"></a> <FONT color="green">290</FONT> return omega;<a name="line.290"></a> <FONT color="green">291</FONT> }<a name="line.291"></a> <FONT color="green">292</FONT> <a name="line.292"></a> <FONT color="green">293</FONT> /** Get the guessed phase &phi;.<a name="line.293"></a> <FONT color="green">294</FONT> * @return guessed phase &phi;<a name="line.294"></a> <FONT color="green">295</FONT> */<a name="line.295"></a> <FONT color="green">296</FONT> public double getGuessedPhase() {<a name="line.296"></a> <FONT color="green">297</FONT> return phi;<a name="line.297"></a> <FONT color="green">298</FONT> }<a name="line.298"></a> <FONT color="green">299</FONT> <a name="line.299"></a> <FONT color="green">300</FONT> }<a name="line.300"></a> </PRE> </BODY> </HTML>