potrf function in lapack updates the lower or upper part of its
argument but leaves the rest "as is".

there was a serious bug in the calculation of the design matrix
(confusion between indices of row and columns), but also in principle
it was incorrect, because it was not full rank. One hot encoding means
the related columns sum to 1, that is the sum is equal to the offset
column.

Finally when computing the degrees of freedom for the F-distribution
there were a few confusions.