R devel - Sep 2016 - Numerical accuracy of matrix multiplication

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.

Regards,
Alexis.

	[[alternative HTML version deleted]]

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.

-pd
> Regards,
> Alexis.
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-devel at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

>>>>> 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]]
    >> 
    >> ______________________________________________
    >> R-devel at r-project.org mailing list
    >> https://stat.ethz.ch/mailman/listinfo/r-devel

    > -- 
    > Peter Dalgaard, Professor,
    > Center for Statistics, Copenhagen Business School
    > Solbjerg Plads 3, 2000 Frederiksberg, Denmark
    > Phone: (+45)38153501
    > Office: A 4.23
    > Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

    > ______________________________________________
    > R-devel at r-project.org mailing list
    > https://stat.ethz.ch/mailman/listinfo/r-devel