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 <jvmi...@gmail.com> wrote: > Very interesting, Dirk. Thanks! > > On Mon, Jan 31, 2022 at 12:18 PM Dirk Eddelbuettel <e...@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 | e...@debian.org >> > -- > Zé Vinícius > https://mirca.github.io >
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