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<html><head><title>Gaussian kernel correlation integral</title></head><body bgcolor="#ffffff"><h3><a name="c2g"></a>Gaussian kernel correlation integral</h3><font color=blue><tt>c2g [-o </tt><em>outfile</em><tt> -V# -h] </tt><em> file</em></font><blockquote> <br> <font color=blue><tt> -o </tt></font><a href=../general.html#outfile>output file name</a>, just <font color=blue><tt> -o </tt></font>means <font color=blue><em>file</em></font><font color=blue><tt>_g</tt></font> <br> <font color=blue><tt> -V </tt></font><a href=../general.html#verbosity>verbosity level</a> (0 = only fatal errors) <br> <font color=blue><tt> -h </tt></font>show this message</blockquote>Reads two columns, r, c(r) from <font color=blue><em>file</em></font> (correlation integral output of <a href="c2naive.html">c2naive</a> or<a href="../docs_c/d2.html">d2</a> (extension <b>.c2</b>)and computes the <a href="../chaospaper/node32.html">Gaussian kernel</a> correlation integral<pre> /00 2 1 | / x \ C (r) = --- | dx exp |- ----- | x C(x) G 2 | \ 2 / r /0 2r </pre>As well as its logarithmic derivative with respect to r:<pre> d D (r) = ------- log C (r) G d log r G</pre><b><font color=red>Note:</font></b> The length scale has been shifted by2<sup>1/2</sup> with respect to the manual: r<sup>2</sup>=2<IMG WIDTH=6 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline6495" SRC="epsilon.gif"><sup>2</sup>.<p>Between the given values of r, C(r) is interpolated by an exact power law andthe integral is evaluated numerically. Above the largest given value of r,C(r)=1 is assumed and the corresponding integral is evaluated analytically.The derivative is carried out analytically on the above expression and theresulting integral is evaluated in the same manner as described.<p>Output is to <font color=blue><tt>stdout</tt></font>, or to file <font color=blue><em>file</em><tt>_g</tt></font> if <font color=blue><tt> -o</tt></font> is given. The first column containsr, the second the Gaussian kernel correlation integral C<sub>G</sub>(r) and the third itslogarithmic derivative D<sub>G</sub>(r).<p><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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