Gaussian kernel correlation integral

c2g [-o outfile -V# -h] file

-o output file name, just -o means file_g
-V verbosity level (0 = only fatal errors)
-h show this message
Reads two columns, r, c(r) from file (correlation integral output of c2naive or d2 (extension .c2) and computes the Gaussian kernel correlation integral 
               
              /00            2
          1   |        /    x   \
 C (r) = ---  | dx exp |- ----- | x C(x)
  G        2  |        \     2  /
          r   /0           2r
As well as its logarithmic derivative with respect to r: 

            d
 D (r) = ------- log C (r)
  G      d log r      G
Note: The length scale has been shifted by 21/2 with respect to the manual: r2=2tex2html_wrap_inline64952.

Between the given values of r, C(r) is interpolated by an exact power law and the 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 the resulting integral is evaluated in the same manner as described.

Output is to stdout, or to file file_g if -o is given. The first column contains r, the second the Gaussian kernel correlation integral CG(r) and the third its logarithmic derivative DG(r).

Table of Contents * TISEAN home