[Rcpp-devel] Detecting Singular Matrices in RcppArmadillo

[Alex Ilich]

Thank you Zé and Dirk! That helped clarify exactly what solve is doing
which I was having trouble tracking down in just the standard docs page.

On Sun, Jan 30, 2022 at 11:26 PM Zé Vinícius <jvmirca at gmail.com> wrote:

> 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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