[Rd] the incredible lightness of crossprod

[Patrick Burns]

On my machine the versions are all precompiled R, and I would
be very surprised if the same were not the case on the client's
machine.  That is, no specially compiled BLAS.

Douglas Bates wrote:

> 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?
>
>
> For a numeric matrix crossprod ends up calling level 3 BLAS; either 
> dsyrk for the single argument case or dgemm for the two argument case. 
> Especially in accelerated versions of the BLAS like Atlas or Goto's 
> BLAS, those routines are hideously efficient and that's where you are 
> seeing the big gain in speed.
>
> By the way, you didn't mention if you had an accelerated BLAS 
> installed with R.  Do you?
>
>
>