[Rcpp-devel] Detecting Singular Matrices in RcppArmadillo

[Zé Vinícius]

Very interesting, Dirk. Thanks!

On Mon, Jan 31, 2022 at 12:18 PM Dirk Eddelbuettel <edd at debian.org> wrote:

>
> On 31 January 2022 at 09:13, Zé Vinícius wrote:
> | Yes, quoting the paper on which ‘solve’ is based on (
> | http://arma.sourceforge.net/armadillo_solver_2020.pdf):
> |
> | “The SVD-based solver uses the xGELSD set of functions, which find a
> | minimum-norm solution to a linear least squares problem.”
>
> Yes. A longer story though on how this is not what may matter. I should
> start
> by saying that I never found really decent documentation describing this
> 'split' in the world view as this problem is, in essence, seen differently
> by
> numerical analysis specialists (as for example the LAPACK authors of the
> *GELSD functions) and the statistical users which differs in what they
> focus
> on. Which is why R uses a modified version of LINPACK (as I recall going
> back
> to by Ross Ihaka) when computing lm(). And not the LAPACK routines.
>
> Doug was always adamant about this when I wrote the different simple
> fastLm()
> approaches (in RcppGSL, RcppArmadillo, ...) which do _not_ properly account
> for rank-deficiency (as R's lm() would) -- Doug also wrote the nicest
> fastLm
> example in RcppEigen.
>
> There is a little bit more in the help pages for the various lmFast()
> versions as well as an explicit example (also due to Doug).
>
> Now, I should add that whenever I tried to construct an example on a more
> real-world-alike regression problem, I could not come anywhere close to
> actually seeing the rank deficiency. But it is unmistakenly there is the
> appropriately created case. So buyer beware.
>
> Dirk
>
> --
> https://dirk.eddelbuettel.com | @eddelbuettel | edd at debian.org
>
-- 
Zé Vinícius
https://mirca.github.io
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