From berger @end|ng |rom mp||b-ber||n@mpg@de  Wed Nov 20 09:56:43 2019
From: berger @end|ng |rom mp||b-ber||n@mpg@de (Hilmar Berger)
Date: Wed, 20 Nov 2019 09:56:43 +0100
Subject: [Rd] Why is matrix product slower when matrix has very small
 values?
In-Reply-To: <CA+6uv10Ok4o-2NRTBjqj_A3K6+_HG++3ss1k942eO279LixxHA@mail.gmail.com>
References: <CA+6uv10Ok4o-2NRTBjqj_A3K6+_HG++3ss1k942eO279LixxHA@mail.gmail.com>
Message-ID: <b4f9ff64-be86-13df-4f98-d3b179d1bae3@mpiib-berlin.mpg.de>

Hi Florian,

just a guess, but couldn't it be that the multiplication of very small 
values leads to FP underflow exceptions which have to be handled by BLAS 
in a less efficient way than "normal" multiplications handled by SIMD 
instructions ?

Best regards,
Hilmar

On 19/11/2019 15:09, Florian Gerber wrote:
> Hi,
>
> I experience surprisingly large timing differences for the
> multiplication of matrices of the same dimension. An example is given
> below. How can this be explained?
> I posted the question on Stackoverflow:
> https://stackoverflow.com/questions/58886111/r-why-is-matrix-product-slower-when-matrix-has-very-small-values
> Somebody could reproduce the behavior but I did not get any useful
> explanations yet.
>
> Many thanks for hints!
> Florian
>
> ## disable openMP
> library(RhpcBLASctl); blas_set_num_threads(1); omp_set_num_threads(1)
>
> A <- exp(-as.matrix(dist(expand.grid(1:60, 1:60))))
> summary(c(A))
> #     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
> # 0.000000 0.000000 0.000000 0.001738 0.000000 1.000000
>
> B <- exp(-as.matrix(dist(expand.grid(1:60, 1:60)))*10)
> summary(c(B))
> #      Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
> # 0.0000000 0.0000000 0.0000000 0.0002778 0.0000000 1.0000000
>
> identical(dim(A), dim(B))
> ## [1] TRUE
>
> system.time(A %*% A)
> #    user  system elapsed
> #   2.387   0.001   2.389
> system.time(B %*% B)
> #    user  system elapsed
> #  21.285   0.020  21.310
>
> sessionInfo()
> # R version 3.6.1 (2019-07-05)
> # Platform: x86_64-pc-linux-gnu (64-bit)
> # Running under: Linux Mint 19.2
>
> # Matrix products: default
> # BLAS:   /usr/lib/x86_64-linux-gnu/openblas/libblas.so.3
> # LAPACK: /usr/lib/x86_64-linux-gnu/libopenblasp-r0.2.20.so
>
> ______________________________________________
> R-devel at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel

-- 
Dr. Hilmar Berger, MD
Max Planck Institute for Infection Biology
Charit?platz 1
D-10117 Berlin
GERMANY

Phone:  + 49 30 28460 430
Fax:    + 49 30 28460 401
  
E-Mail: berger at mpiib-berlin.mpg.de
Web   : www.mpiib-berlin.mpg.de



[Rd] Why is matrix product slower when matrix has very small values?
Hilmar Berger