# [R] Fast matrix multiplication

Ista Zahn |@t@z@hn @end|ng |rom gm@||@com
Mon Aug 13 21:17:54 CEST 2018

```On Mon, Aug 13, 2018 at 2:41 PM Ravi Varadhan <ravi.varadhan using jhu.edu> wrote:
>
> 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?

Not sure. If you want an easy way I would use MRO. More info at
https://mran.microsoft.com/rro#intelmkl1

--Ista

> 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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