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Re: TOTAL gives totally different result on identical array [message #76890 is a reply to message #76888]

Fri, 08 July 2011 10:46

Fabzou
Messages: 76
Registered: November 2010

Member

Thank you very much for these functions.

Do you suggest to use PAIRWISE_SUM systematically? Is it possible to
make a generic function such as:

function robust_total, x

if (*statement to define*) then return, PAIRWISE_SUM(X) $
else return, total(X)

end

Thank you for your help!

Fabien

On 07/08/2011 07:25 PM, Liam Gumley wrote:
> On Jul 8, 10:44 am, Fï¿½LDY 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
>
> Increasing the value of NP makes the algorithm faster, but potentially
> decreases accuracy. Here's a challenging test case:
>
> PRO TEST
>
> vec = 100 ^ (10.0 * randomu(123456, 10000000))
> help, vec
> print, 'MIN = ', min(vec), ' MAX = ',
> max(vec)
>
> print
> print, 'TOTAL result'
> print, total(vec) - total(reverse(vec))
>
> print
> print, 'TOTAL double precision result'
> print, total(vec, /double) - total(reverse(vec), /double)
>
> print
> print, 'Kahan sum result'
> t1 = systime(1)
> result = kahansum(vec) - kahansum(reverse(vec))
> t2 = systime(1)
> print, result
> print, 'Elapsed time (seconds) = ', t2 -
> t1
>
> print
> print, 'Pairwise sum result'
> t1 = systime(1)
> result = pairwise_sum(vec) - pairwise_sum(reverse(vec))
> t2 = systime(1)
> print, result
> print, 'Elapsed time (seconds) = ', t2 -
> t1
>
> END
>
> Results of the test case:
>
> IDL> test
> % Compiled module: TEST.
> VEC FLOAT = Array[10000000]
> MIN = 1.00000 MAX = 9.99996e+19
>
> TOTAL result
> % Compiled module: REVERSE.
> -2.30584e+18
>
> TOTAL double precision result
> -2.5769804e+10
>
> Kahan sum result
> % Compiled module: KAHANSUM.
> 0.00000
> Elapsed time (seconds) = 5.7468300
>
> Pairwise sum result
> % Compiled module: PAIRWISE_SUM.
> 0.0000000
> Elapsed time (seconds) = 0.89422798
>
> Cheers,
> Liam.
> Practical IDL Programming (in print for 10 years!)
> http://www.gumley.com/

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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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