research:howto:calculation_of_a_principal_component_s_cosine_content [Norma]

Calculation of cosine content from principal components

The equation to calculate cosine content from pricipal components as it appears in several papers (for example Proteins, 2007, 67, 569) contains a typographical error. The correct version looks like this:

$\begin{displaymath} cont = \frac{2}{T} \frac{ ( \int_0^T \cos(i \pi t / T) q_i(t) dt )^2 }{ \int_0^T q^2_i(t) dt } \end{displaymath}$

To apply this: copy & paste the perl script that follows in a suitably named file, make the file executable, and put it somewhere in your path.

Perl script to calculate cosine content from principal components

#!/usr/bin/perl -w
 
use constant PI => 4 * atan2(1, 1);
 
(@ARGV==2) or die "Usage: cos_content.pl filename component\n";
open ( FILE, $ARGV[0] ) or die "Can not open $ARGV[0]\n";
 
$i = $ARGV[1];
 
$T = 0;
while ( $line = <FILE> )
  {
    $T++;
  }
 
close ( FILE );
 
open ( FILE, $ARGV[0] ) or die "Can not open $ARGV[0]\n";
 
$t     = 0;
$sum_1 = 0.0;
$sum_2 = 0.0;
while ( $line = <FILE> )
   {
     @q = split(' ', $line);
     $sum_1 += cos( $i * PI * $t / $T ) * $q[$i];
     $sum_2 += $q[$i] * $q[$i];
     $t++;
   }
 
printf ("Cosine content for component $i is %6.4f\n", (2.0 * $sum_1 * $sum_1) / ( $T * $sum_2 ) );
 
close ( FILE );

To use the script, you need the principal components as produced by carma (file carma.fluctuations.dat). Run the script with something like

cos_content.pl carma.fluctuations.dat 1

where '1' is the principal component for which you want to calculate the cosine content (numbering starts from 1, not from zero).