| Re: vectorising versus loops [message #38218 is a reply to message #38145] |
Mon, 23 February 2004 15:42   |
nasalmon
Messages: 33
Registered: August 2003
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Craig Markwardt <craigmnet@REMOVEcow.physics.wisc.edu> wrote in message news:<onfzd3vttk.fsf@cow.physics.wisc.edu>...
> nasalmon@onetel.net.uk (Neil) writes:
>> Does anyone know what the speed increase factor is in IDL programmes
>> when going from "do loops" to full vectorisation of arrays? I know all
>> programmes are different and not every process lends itself to
>> vectorisation. However, there must be some rule of thumb, ie speed
>> going as a linear function of the number of array elements times some
>> factor.
>
> A very simple rule of thumb is to vectorize when the overhead of doing
> a FOR loop passes your "pain" threshold. Example: a one million
> iterations of an "empty" loop like this:
>
> for i = 0L, 1000000L do begin & x = 0 & end
>
> takes 0.25 sec on a reasonably modern machine I use. On an older
> machine it takes 1.5 sec. You can do the same, and decide when the
> loop overhead time per iteration passes your personal threshold. Bear
> in mind that if you do multiple executions of the loop, you should
> multiply that in.
Craig,
yes many thanks for this valuable information. One of the problems i
have is that the condition in the WHERE statement has to contain the
counter in the "do loop", that is basically why i put it in the "do
loop" to start with. Is there any way i can make the condition depend
on the counter, ie the vector index.
best regards,
Neil
>
> Whether or not I go over my personal pain threshold, I tend to be
> picky and try to vectorize anyway. My personal approach is to remove
> the innermost loop and vectorize where possible.
>
>
>> Also, are there any tricks to play if you want to vectorise loops that
>> have IF statement decision in them, or any general rules for neat
>> vectorisation of looped programmes?
>
> Yes, there are several. You can use WHERE:
>
> ; Example, square root of DATA
> result = data*0 ;; Initialize result
> wh = where(data GE 0, ct) ;; Find non-negative data values
> if ct GT 0 then result(wh) = sqrt(data(wh)) ;; compute sqrt
>
> This can get cumbersome sometimes, especially because the RESULT needs
> to be initiiazed. In the square root example above, we don't need to
> use WHERE(), since we can use other features of IDL like the threshold
> operator.
>
> result = sqrt(data > 0) ;; Make all negative values of DATA zero
>
> This is clearly more simple, faster, and easier to understand.
>
> Another technique is to use a "mask" variable to set offending numbers
> to zero. For example, when computing the gaussian function, one often
> wants to limit the argument of the exponential to prevent overflows.
>
> ;; Example: compute gaussian function of X (mean=xmean, sigma=sigma)
> arg = -0.5*((x-xmean)/sigma)^2
> mask = abs(arg) LT 50 ;; Arbitrary limit of < sqrt(50) sigma
>
> result = exp(arg*mask) / (2*!dpi*sqrt(sigma)) ;; WRONG
>
> Ah, but if you look carefully, multiplying by MASK will make an
> argument of 0, so RESULT will be 1 in those positions. We have
> avoided the under/overflow, but now the result is incorrect. This is
> easily remedied however, since we can multiply by MASK again to set
> these values to zero:
>
> result = mask*exp(arg*mask) / (2*!dpi*sqrt(sigma)) ;; CORRECT
>
> Hope those examples give you some ideas. Good luck!
> Craig
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