[Gretl-devel] SVD issues

Herewith some more detail regarding the warning I posted on the users list https://www.mail-archive.com/gretl-users@gretlml.univpm.it/msg14491.html The business with VAR standard errors was due to a crucial difference between the "old" lapack SVD solver, dgelss(), and the "new", faster dgelsd (divide-and-conquer variant) that I failed to notice at first. That is, dgelss leaves the right-hand singular vectors in the input matrix X on successful exit -- which provides a nice quick way of computing (X'X)^{-1} -- while dgelsd leaves nothing but rubble in X. So our (X'X)^{-1} computed after dgelsd was garbage. Solution: revert to dgelss if (X'X)^{-1} is needed. I also found another SVD issue: the tall_SVD() function (SVD via eigen-analysis) is much faster than regular lapack SVD for the case where X has a lot more columns than rows, but as it's not accurate for singular or near-singular input. It's therefore not suitable as a back-end for rank determination or for computation of a generalized inverse. I've therefore ensured that such functions call regular lapack SVD internally. In addition I've added a check on tall_SVD, plus redirection, for other SVD uses: if we find any negative eigenvalues we get out and call regular lapack SVD. Allin