I’m working on a new chapter for my R Programming book and the topic is parallel computation. So, I was happy to see this tweet from David Robinson (@drob) yesterday:

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How fast is this #rstats code? x <- replicate(5e3, rnorm(5e3)) x %*% t(x) For me, w/Microsoft R Open, 2.5sec. Wow. https://t.co/0SbijNxxVa

— David Robinson (@drob) January 20, 2016

What does this have to do with parallel computation? Briefly, the code generates 5,000 standard normal random variates, repeats this 5,000 times and stores them in a 5,000 x 5,000 matrix (`x’). Then it computes x x’. The second part is key, because it involves a matrix multiplication.

Matrix multiplication in R is handled, at a very low level, by the library that implements the Basic Linear Algebra Subroutines, or BLAS. The stock R that you download from CRAN comes with what’s known as a reference implementation of BLAS. It works, it produces what everyone agrees are the right answers, but it is in no way optimized. Here’s what I get when I run this code on my Mac using Studio and the CRAN version of R for Mac OS X:

system.time({ x <- replicate(5e3, rnorm(5e3)); tcrossprod(x) }) user system elapsed 59.622 0.314 59.927

Note that the “user” time and the “elapsed” time are roughly the same. Note also that I use the tcrossprod() function instead of the otherwise equivalent expression x %*% t(x). Both crossprod() and tcrossprod() are generally faster than using the %*% operator.

Now, when I run the same code on my built-from-source version of R (version 3.2.3), here’s what I get:

system.time({ x <- replicate(5e3, rnorm(5e3)); tcrossprod(x) }) user system elapsed 14.378 0.276 3.344

Overall, it’s faster when I don’t run the code through RStudio (14s vs. 59s). Also on this version the elapsed time is about ^{1}⁄_{4} the user time. Why is that?

The build-from-source version of R is linked to Apple’s Accelerate framework, which is a large library that includes an optimized BLAS library for Intel chips. This optimized BLAS, in addition to being optimized with respect to the code itself, is designed to be multi-threaded so that it can split work off into chunks and run them in parallel on multi-core machines. Here, the tcrossprod() function was run in parallel on my machine, and so the elapsed time was about a quarter of the time that was “charged” to the CPU(s).

David’s tweet indicated that when using Microsoft R Open, which is a custom built binary of R, that the (I assume?) elapsed time is 2.5 seconds. Looking at the attached link, it appears that Microsoft’s R Open is linked against Intel’s Math Kernel Library (MKL) which contains, among other things, an optimized BLAS for Intel chips. I don’t know what kind of computer David was running on, but assuming it was similarly high-powered as mine, it would suggest Intel’s MKL sees slightly better performance. But either way, both Accelerate and MKL achieve that speed up through custom-coding of the BLAS routines and multi-threading on multi-core systems.

If you’re going to be doing any linear algebra in R (and you will), it’s important to link to an optimized BLAS. Otherwise, you’re just wasting time unnecessarily. Besides Accelerate (Mac) and Intel MKL, theres AMD’s ACML library for AMD chips and the ATLAS library which is a general purpose tunable library. Also Goto’s BLAS is optimized but is not under active development.

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