# [R] Fast matrix multiplication

Ravi Varadhan r@vi@v@r@dh@n @ending from jhu@edu
Mon Aug 13 20:41:57 CEST 2018

```Hi Ista,
Thank you for the response.  I use Windows.  Is there a pre-compiled version of openBLAS for windows that would make it easy for me to use it?
Thanks,
Ravi

-----Original Message-----
From: Ista Zahn <istazahn using gmail.com>
Sent: Friday, August 10, 2018 12:20 PM
Cc: r-help using r-project.org
Subject: Re: [R] Fast matrix multiplication

Hi Ravi,

You can achieve substantial speed up by using a faster BLAS (e.g., OpenBLAS or MKL), especially on systems with multiple CPUs. On my (6 year old, but 8 core) system your example takes 3.9 seconds with using the reference BLAS and only 0.9 seconds using OpenBLAS.

Best,
Ista
On Fri, Aug 10, 2018 at 11:46 AM Ravi Varadhan <ravi.varadhan using jhu.edu> wrote:
>
> Hi,
>
> I would like to compute:  A %*% B %*% t(A)
>
>
>
> A is a mxn matrix and B is an nxn symmetric, positive-definite matrix, where m is large relative to n (e.g., m=50,000 and n=100).
>
>
>
> Here is a sample code.
>
>
>
> M <- 10000
>
> N <- 100
>
> A <- matrix(rnorm(M*N), M, N)
>
> B <- crossprod(matrix(rnorm(N*N), N, N)) # creating a symmetric
> positive-definite matrix
>
>
>
> # method 1
>
> system.time(D <- A %*% B %*% t(A))
>
>
>
> # I can obtain speedup by using a Cholesky decomposition of B
>
> # method 2
>
> system.time({
>
> C <- t(chol(B))
>
> E <- tcrossprod(A%*%C)
>
> })
>
>
>
> all.equal(D, E)
>
>
>
> I am wondering how to obtain more substantial speedup.  Any suggestions would be greatly appreciated.
>
>
>
> Thanks,
>
> Ravi
>
>
>
>         [[alternative HTML version deleted]]
>
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