# Re: [Rd] the incredible lightness of crossprod

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Fri 28 Jan 2005 - 07:23:39 EST

On Thu, 27 Jan 2005, Paul Gilbert wrote:

> A few weeks ago I noticed
>
>> z <- matrix(rnorm(20000),10000,2)
>
>> system.time(for (i in 1:1000) apply(z,2,sum))
> [1] 13.44 0.48 14.08 0.00 0.00
>
>> system.time(for (i in 1:1000) rep(1,10000) %*% z)
> [1] 6.46 0.11 6.84 0.00 0.00

So both run in a few milliseconds for rather large problems.

> which seemed completely contrary to all my childhood teachings. Now
>
>> system.time(for (i in 1:1000) crossprod(rep(1,10000), z))
> [1] 1.90 0.12 2.24 0.00 0.00
>
> makes sense because it is suppose to be faster than %*% , but why is apply so
> slow?

`so slow' sic: what are you going to do in the 7ms you saved?

> (And should I go back and change apply in my code everywhere or is this
> likely to reverse again?)

It's not likely. apply is an R-level loop, and %*% is a C-level one. However, %*% is not supposed to be much slower than crossprod, and the devil is in the details of how the BLAS is implemented: the code is very similar.

That %*% was faster than apply has been true in all my (17 years) of S/R experience. Your childhood may predate S3, of course.

I still think one should use row/colSums for clarity with acceptable efficiency. It must be very unusual for these operations to be a dominant part of a calculation, so let's not lose proportion here.

> Paul Gilbert
>
>
> Patrick Burns wrote:
>
>> The following is at least as much out of intellectual curiosity
>> as for practical reasons.
>> On reviewing some code written by novices to R, I came
>> across:
>>
>> crossprod(x, y)[1,1]
>>
>> I thought, "That isn't a very S way of saying that, I wonder
>> what the penalty is for using 'crossprod'." To my surprise the
>> penalty was substantially negative. Handily the client had S-PLUS
>> as well -- there the sign of the penalty was as I had expected, but
>> the order of magnitude was off.
>>
>> Here are the timings of 1 million computations on vectors of
>> length 1000. This is under Windows, R version 1.9.1 and S-PLUS
>> 6.2 (on the same machine).
>>
>> Command R S-PLUS
>> sum(x * y) 28.61 97.6
>> crossprod(x, y)[1,1] 6.77 2256.2
>>
>>
>> Another example is when computing the sums of the columns of a
>> matrix. For example:
>>
>> set.seed(1)
>> jjm <- matrix(rnorm(600), 5)
>>
>> Timings for this under Windows 2000 with R version 2.0.1 (on an
>> old chip running at about 0.7Ghz) for 100,000 computations are:
>>
>> apply(jjm, 2, sum) 536.59
>> colSums(jjm) 18.26
>> rep(1,5) %*% jjm 15.41
>> crossprod(rep(1,5), jjm) 13.16
>>
>> (These timings seem to be stable across R versions and on at least
>> one Linux platform.)
>>
>> Andy Liaw showed another example of 'crossprod' being fast a couple
>> days ago on R-help.
>>
>> Questions for those with a more global picture of the code:
>>
>> * Is the speed advantage of 'crossprod' inherent, or is it because
>> more care has been taken with its implementation than the other
>> functions?
>>
>> * Is 'crossprod' faster than 'sum(x * y)' because 'crossprod' is
>> going to BLAS while 'sum' can't?
>>
>> * Would it make sense to (essentially) use 'crossprod' in
>> 'colSums' and its friends at least for the special case of matrices?
>>
>> Patrick Burns
>>
>> Burns Statistics
>> patrick@burns-stat.com
>> +44 (0)20 8525 0696
>> http://www.burns-stat.com
>> (home of S Poetry and "A Guide for the Unwilling S User")
>>
>> ______________________________________________
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>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>
>
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>
>

```--
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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Received on Fri Jan 28 06:38:46 2005

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