[Rd] Numerical accuracy of matrix multiplication

[Martin Maechler]

>>>>> peter dalgaard <pdalgd at gmail.com>
>>>>>     on Fri, 16 Sep 2016 13:33:11 +0200 writes:

    > On 16 Sep 2016, at 12:41 , Alexis Sarda <alexis.sarda at gmail.com> wrote:

    >> Hello,
    >> 
    >> while testing the crossprod() function under Linux, I noticed the following:
    >> 
    >> set.seed(883)
    >> x <- rnorm(100)
    >> x %*% x - sum(x^2) # equal to 1.421085e-14
    >> 
    >> Is this difference normal? It seems to be rather large for double precision.
    >> 

    > It's less than .Machine$double.eps, relative (!) to x  %*% x ~= 100.

indeed!

Still, it gives exactly 0 on my platform(s), where I'm using R's
own version of BLAS / Lapack.

Are you perhaps using an "optimized" BLAS / LAPACK , i.e, one
that is fast but slightly less so accurate ?

Martin Maechler,
ETH Zurich


    > -pd

    >> Regards,
    >> Alexis.
    >> 
    >> [[alternative HTML version deleted]]
    >> 
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