[Rd] external BLAS library triggering erroneous ill-condtionned matrices

Fri Oct 30 19:08:41 CET 2026

Dear Martin, dear Dirk,

Thank you both. The matrix, a reproduction script and Martin's kappasX()

check are now at

https://gist.github.com/bastienchassagnol/2236f6d95ae4485e2e7ed6b8fa421675

The matrix is far from singular. With reference BLAS and LAPACK 3.10.0,

and identically with OpenBLAS under the SkylakeX or Haswell kernels:

kappa(A) 8.003

kappa(A, exact = TRUE) 14.339 (= 0.2050 / 0.0143)

rcond(A) 0.01091

kappasX(A): M 2.922 2 14.339 1 91.62 F 263.81

eigen(A, symmetric = TRUE, only.values = TRUE) succeeds everywhere; only

the call with eigenvectors (JOBZ = 'V') returns INFO = 2, under both the

default kernel (OpenBLAS selects Cooperlake on this Granite Rapids CPU)

and SkylakeX. Under the default kernel, solve() is also wrong, so rcond()

and the 1- and F-norm values of kappasX() change (1-norm 149.0 instead of

91.6) without any error.

I agree a newer Ubuntu is the real fix: Noble has

0.3.26, 26.04 0.3.32. The Jammy backport of the upstream CPU-detection

fix (Launchpad #2040027) was rejected as an abandoned SRU in August 2025,

so Jammy users, including the rocker/r-ver 4.2.2 to 4.4.1 images (rocker

issue #836), will keep this behaviour. I have not yet tested releases

after 0.3.20. I used LD_PRELOAD only because update-alternatives needs

root on this machine; it selects the same libraries. Thanks for the

pointer to gcbd.

The wrong results under the Cooperlake kernel are the known part. What I

have not found reported is the dsyevr failure that remains under the

SkylakeX kernel, with either OpenBLAS's LAPACK or reference LAPACK 3.10.0.

Best regards,
‌

‌‌Bastien CHASSAGNOL, Post-Doc student, supervised by Pr. Anais Baudot

Affiliation: MMG, Marseille Medical Genetics

U 1251, Faculté de Médecine de La Timone,

27 Bd Jean Moulin

13005 Marseille – France

Tél: 07 88 09 09 47

Site : https://www.marseille-medical-genetics.org/a-baudot/
   ͏‌ 

Scientific Communication and Volunteer Activity: 

Vice-Treasury, JeBiF - RSG France.

Website: https://jebif.fr/

Website:   https://github.com/bastienchassagnol.
LinkedIn:  www.linkedin.com/in/bastien-chassagnol-677b67140.͏‌ 

Mails: bastien_chassagnol using laposte.net // chassagnolbastien using gmail.com // bastien.chassagnol using univ-amu.fr 

De : "Martin Maechler" <maechler using stat.math.ethz.ch>
A : "Dirk Eddelbuettel" <edd using debian.org>,bastien_chassagnol using laposte.net,r-devel using r-project.org
Envoyé: vendredi 30 Octobre 2026 17:08
Objet : Re: [Rd] external BLAS library triggering erroneous ill-condtionned matrices

>>>>> Dirk Eddelbuettel
>>>>> on Thu, 29 Oct 2026 07:41:19 -0500 writes:

> On 29 October 2026 at 10:02, bastien_chassagnol--- via R-devel wrote:
> | Set-up: R 4.6.1 (Ubuntu 22.04 build), linked to the system OpenBLAS

> That's dated / a mismatch. Why current R but older BLAS/LAPACK? I recommend
> Ubuntu 26.04 or 26.10 if you want to engage with upstream.

> It's also ... sort-of well known.

Well, yes - as e.g., I knew about such problems and I think have
written here ("R-devel mailing list" or "R-devel" or "R-help")
probably more than once.

Still most useRs do *not* know about such problems.

Also, I'm glad for Bastien's example
-- yes, please make it available electronically! --
because what he describes is much more severe than I'd have
expected, the matrix so far away from singular {judged from the eigen values}.
More (or 'much more') revealing should be to see the condition number(s):
Bastien, can you please also report

kappa()

and/or

rcond()

maybe kappa(*, exact=TRUE, norm="")
or use {what I have added to the base/man/kappa.Rd examples now in R-devel}

kappasX <- function(x, inv = solve(x))
vapply(c("M","2","1","F"), # NB: 'O' = 'I' = '1'
\(nrm) kappa(x, exact=TRUE, norm=nrm, inv_z=inv), 1.2)

to apply to your matrix?

Best regards,
Martin

> Just rotate through the available BLAS /
> LAPACK combinations. On a Debian / Ubuntu system is so easy that many (many)
> years ago I wrote a package doing just that to compare and time with GPUs,
> see https://cran.r-project.org/package=gcbd -- could use some love and an
> update to current packages.

> There is also flexiblas, already in Fedora and last I checked 'being
> packaged' for Debian.

> | The reference libraries were loaded with `LD_PRELOAD`; the kernel was set

> You don't need to do that. `gcbd` just uninstall / reinstalls. If you check
> the manual page, you can see how the `update-alternatives` command (a Debian
> / Ubuntu special) allows you to switch. The number of available BLAS /
> LAPACK varies from year to year but there are way more than just reference
> BLAS and OpenBLAS. On my (26.04) machine just now

> $ apt-cache search libblas | wc -l
> 33
> $
> $ apt-cache search libblas | grep -- -dev | wc -l
> 16
> $

> It's big topic, and if you check source (of e.g. R itself) you will often
> find comments about precision varying. "Practical" numerical analysis has
> challenges that more theoretical approaches may gloss over.

> Dirk

> --
> dirk.eddelbuettel.com | @eddelbuettel | edd using debian.org

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