9:09 p.m.
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
10 a.m.
Am 06.02.2020 um 22:09 schrieb Allin Cottrell:
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.
Thanks Allin - I feel partly guilty because I suggested the switch to
the faster versions. What I don't understand, though: Isn't (X'X)^{-1}
always needed? I mean we have the $xtxinv accessor after a VAR which
should always contain valid stuff.
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.
OK, very good. When the dust is settled let's see what the speedups are
between 2019d and 2020a in this linear-algebra area.
cheers
sven
7:48 p.m.
On Fri, 7 Feb 2020, Sven Schreiber wrote:
Am 06.02.2020 um 22:09 schrieb Allin Cottrell:
> 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.
Thanks Allin - I feel partly guilty because I suggested the switch to
the faster versions. What I don't understand, though: Isn't (X'X)^{-1}
always needed? I mean we have the $xtxinv accessor after a VAR which
should always contain valid stuff.
Yes, it's always needed when called on behalf of the "var" command,
but for some internal uses we just need parameter estimates and have
no use for the covariance matrix.
Allin
1780
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Allin Cottrell -
Sven Schreiber