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Re: TOTAL gives totally different result on identical array [message #76888 is a reply to message #76886]

Fri, 08 July 2011 11:33

Foldy Lajos
Messages: 268
Registered: October 2001

Senior Member

On Fri, 8 Jul 2011, Liam Gumley wrote:

> On Jul 8, 10:44 am, FÖLDY Lajos <fo...@rmki.kfki.hu> wrote:
>> It will be very slow. But it's IDL, vectorize it!
>
> The pairwise summation algorithm is sometimes recommended as a faster
> solution:
>
> http://en.wikipedia.org/wiki/Pairwise_summation
>
> Here is an IDL implementation (with very little testing!)
>
> FUNCTION PAIRWISE_SUM, X
> compile_opt idl2
> forward_function pairwise_sum
> np = 100
> nx = n_elements(x)
> if (nx le np) then begin
> ;- Naieve summation
> s = total(x, /double)
> endif else begin
> ;- Divide and conquer: recursively sum two halves of the array
> m = floor(nx / 2)
> s = pairwise_sum(x[0:m-1]) + pairwise_sum(x[m:*])
> endelse
> return, s
> END
>

Recursive calls are slow, you can make it much faster:

function chunk_sum, x
compile_opt idl2
forward_function chunk_sum
np = 100
nx = n_elements(x)
nchunk = nx / np
sums = dblarr(nchunk+1)
for j=0, nchunk-1 do sums[j] = total(x[j*np:(j+1)*np-1], /double)
left = nx - nchunk * np
if left gt 0 then sums[nchunk] = total(x[nchunk*np, *], /double)
if nchunk gt np then s=chunk_sum(sums) else s=total(sums)
return, s
end

IDL> test
Kahan sum result
0.00000
Elapsed time (seconds) = 7.1223309

Pairwise sum result
0.0000000
Elapsed time (seconds) = 1.1735301

Chunk sum result
0.0000000
Elapsed time (seconds) = 0.34169912

regards,
Lajos

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[Message index]

		Re: TOTAL gives totally different result on identical array By: Michael Galloy on Fri, 08 July 2011 12:10
		Re: TOTAL gives totally different result on identical array By: Liam Gumley on Fri, 08 July 2011 11:48
		Re: TOTAL gives totally different result on identical array By: Foldy Lajos on Fri, 08 July 2011 11:33
		Re: TOTAL gives totally different result on identical array By: Fabzou on Fri, 08 July 2011 10:46
		Re: TOTAL gives totally different result on identical array By: Liam Gumley on Fri, 08 July 2011 10:25
		Re: TOTAL gives totally different result on identical array By: Foldy Lajos on Fri, 08 July 2011 08:44
		Re: TOTAL gives totally different result on identical array By: Liam Gumley on Fri, 08 July 2011 07:37
		Aw: Re: TOTAL gives totally different result on identical array By: M. Suklitsch on Fri, 08 July 2011 05:55
		Re: TOTAL gives totally different result on identical array By: Fabzou on Fri, 08 July 2011 03:34

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