[Gretl-users] Re: efficient duplication matrix?
Am 03.01.2021 um 10:05 schrieb Riccardo (Jack) Lucchetti:
On Sat, 2 Jan 2021, Sven Schreiber wrote:
> However, there's also a use case for an efficient
multiplication with
> the _transpose_ of the duplication matrix (so applied to a matrix with
> n^2 rows).
Hm, do you have a use case for that? In most cases, what is needed is
premultimplication by its generalised inverse $D_n^+$, which we could
also write a function for, by and easy adaptation of your code.
Well the ported code I'm working with does premulti with D_n^\prime all
the time. Of course by using transposition this could also be reframed
as postmulti with D_n, but ATM we don't have that in a non-naive way,
either (AFAIK). Maybe that's another extension.
I admit I don't have a very clear understanding yet about the properties
and equivalences of the various duplication variants - pre and post,
transpose or not and so on, and how one can be efficiently reformulated
as the other.
cheers
sven