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Re: TOTAL gives totally different result on identical array [message #76892 is a reply to message #76890]

Fri, 08 July 2011 10:25

Liam Gumley
Messages: 473
Registered: November 1994

Senior Member

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

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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