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<html> <head><title>Cost functions</title></head><body bgcolor="#ffffff"><h3>Cost functions</h3>The <a href="randomize_extend.html">extendable</a> family of routines for thegeneration of annealed surrogate data can accomodate a variety of costfunctions, needed to implement different constraints. In this version,the following modules are available.<h4>Autocorrelation function</h4><p><font color=blue><tt>randomize_</tt><font color=red><tt>auto</tt></font><tt>_</tt><em>cool</em><tt>_</tt><em>perm</em><tt>-D# [-W#] [</tt><em>general options</em><tt>] [</tt><em>cooling options</em><tt>] [</tt><em>permutation options</em><tt>] </tt><em>file</em></font><blockquote> <br><font color=blue><tt> -D </tt></font>number of lags for autocorrelation <br><font color=blue><tt> -W </tt></font>type of average: 0=max(c), 1=|c|/lag, 2=(c/lag)**2, 3=max(c)/lag (default 0)</blockquote>The specified number of shortest lags of the autocorrelation function withoutperiodic continuation is matched with the data. The cost is given by themaximum deviation in any lag, weighted by 1/lag.<p><h4>Periodic autocorrelation function</h4><p><font color=blue><tt>randomize_</tt><font color=red><tt>autop</tt></font><tt>_</tt><em>cool</em><tt>_</tt><em>perm</em><tt>-D# [-W#] [</tt><em>general options</em><tt>] [</tt><em>cooling options</em><tt>] [</tt><em>permutation options</em><tt>] </tt><em>file</em></font><blockquote><br><font color=blue><tt> -D </tt></font>number of lags for autocorrelation <br><font color=blue><tt> -W </tt></font>type of average: 0=max(c), 1=|c|/lag, 2=(c/lag)**2, 3=max(c)/lag (default 0)</blockquote>The specified number of shortest lags of the periodically continuedautocorrelation function is matched with the data. The cost is given by themaximum deviation in any lag, weighted by 1/lag.<p><h4>Generic constraints</h4><p><font color=blue><tt>randomize_</tt><font color=red><tt>generic</tt></font><tt>_</tt><em>cool</em><tt>_</tt><em>perm</em><tt>[</tt><em>general options</em><tt>] [</tt><em>cooling options</em><tt>][</tt><em>permutation options</em><tt>] </tt><em>file</em></font><p>The generic module is provided as the easiest starting point of individualextensions. Virtually anything can be specified as part of the cost functionby editing the source and <a href="randomize_extend.html">recompiling</a> (recommended: rename the module).In the distribution, as an example the maximal deviation in either one of<pre> < x x >, < x x >, n-1 n n-2 n 2 2 2 < x x >, < x x >, < x x >, < x x x >, n-1 n n-1 n n-2 n n-2 n-1 n 2 2 3 3 < x x >, < x x >, < x x > n-1 n n-1 n n-1 n</pre>is minimised. After thorough annealing, this can be used to make randomlyshuffled Hénon attractors - whatever that is good for.<p><h4>Spectrum of spike trains</h4><p><font color=blue><tt>randomize_</tt><font color=red><tt>spikespec</tt></font><tt>_</tt><em>cool</em><tt>_event[-F# -## -i][</tt><em>general options</em><tt>] [</tt><em>cooling options</em><tt>][</tt><em>permutation options</em><tt>] </tt><em>file</em></font><blockquote> <br><font color=blue><tt> -F </tt></font>maximal frequency (2*l / total time) <br><font color=blue><tt> -# </tt></font>number of frequencies (F* total time /2) <br><font color=blue><tt> -i </tt></font>expect intervals rather than times</blockquote>For an explanation of the inter-event spectrum see <a href="spikespec.html">spikespec</a>. S(f) is computed for <font color=blue><tt>#</tt></font> frequencies between 0 and <font color=blue><tt> -F </tt></font> (no binning).By default, a sequence of event timesis expected. If the flag <font color=blue><tt> -i </tt></font> is set,the data is taken to be inter-event intervals.<p><h4>Plans for future releases</h4>I am working on <ul><li>crosscorrelations with a reference signal <li>running mean/variance for nonstationary data<li>Lomb periodogram for unevenly spaced data</ul>Please <a href="mailto:schreibe@theorie.physik.uni-wuppertal.de">tell me</a>if you have implemented any other interesting constraints.<p> <a href="randomize.html"><em>constrained randomization</em></a> *<a href="../contents.html">Table of Contents</a> * <a href="../../index.html" target="_top">TISEAN home</a></body></html>⌨️ 快捷键说明
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