Covariance matrices in kdb+

A covariance matrix is at the heart of many data analysis and time series models - as it is a measure of how two data sets change together. In Q, the natural data structure is a vector, which can be nested to represent a matrix. A covariance function is already provided that takes two vectors and computes its covariance, but as a scalar and not as a matrix.

Here is a function I wrote that creates a covariance matrix given a set of vectors. It will create a nxn matrix:

q) covar:{{x[y] cov/: x}[x;] each til (x#:)}

Here is how to use it:

q) a:1+til 10
q) b:10-til 10
q) c:2*1+til 10
q) d:2*1-til 10
q) e:4*1+til 10
q) f:4*1-til 10
q) covar (a;b;c;d;e;f)

8.25 -8.25 16.5 -16.5 33 -33
-8.25 8.25 -16.5 16.5 -33 33
16.5 -16.5 33 -33 66 -66
-16.5 16.5 -33 33 -66 66
33 -33 66 -66 132 -132
-33 33 -66 66 -132 132

Next blog post will be how to compute its eigenvectors and eigenvalue.