Scilab: Variance-Covariance Matrix

This is a Scilab-related post that may be of little interest to most of the people who read this blog. I'll try to title any future Scilab posts similarly for easy avoidance. This mostly serves as a personal note, but, hopefully, others might find it useful.

The following code is provided as is with no warranties express or implied or statutory or whatever, standard disclaimers apply, use at your own risk, yatta, yatta, yatta. If you find any problems, please make a comment.

Here's a little Scilab code I wrote to calculate a Variance-Covariance Matrix (MathWorld, NIST).

function [y] = varcovar(m)

   // copy source

   x = m;



   // dimensions

   [nrows,ncols] = size(m);



   // scaling factor

   scale = sqrt(1.0 / (nrows-1));



   // subtract mean from each column

   for i=1:ncols

      x(:,i) = (x(:,i) - mean(x(:,i))) * scale;

   end



   // x'x

   y = x' * x;

endfunction



Example using NIST data


-->x = [4.0 2.0 0.60; 4.2 2.1 0.59; 3.9 2.0 0.58;
 4.3 2.1 0.62; 4.1 2.2 0.63]

 x  =



    4.     2.     0.6

    4.2    2.1    0.59

    3.9    2.     0.58

    4.3    2.1    0.62

    4.1    2.2    0.63



-->varcovar(x)

 ans  =



    0.025      0.0075     0.00175

    0.0075     0.007      0.00135

    0.00175    0.00135    0.00043




Note: If you're concerned with issues of stability and performance, see Knuth, et al.