[Scilab-users] Strange behavior of explicit vs implicit iteration

[Stéphane Mottelet]

Hi Frederico,

Rouding stuff is not a simple issue, but it's clear that your are not 
doing the computations in the same order, which could explain the 
difference. Here is a simpler example showing that the result depends on 
the order in which computations are done:

--> x=rand(10,1,"normal");

--> sum([1;x])-sum([x;1])
  ans  =

   -2.220D-16

Floating point addition is NOT associative. See e.g. 
https://en.wikipedia.org/wiki/Round-off_error

S.

Le 25/04/2022 à 10:00, Federico Miyara a écrit :
>
> Dear All,
>
> Here I have the following script, where I compute the same thing using 
> two iteration methods:
>
> alfa  =  rand(1,10);
> Rpr  =  rand();
> R  =  rand();
> Z  =  rand(10,200);  
>
> G  =  zeros(1,200);
> for  i=1:200
>     A  =  0;
>     B  =  0;
>     for  k  =  1:10
>        A  =  A  +  Rpr*alfa(k)  /  (Z(k,i)  +  alfa(k)*(1  -  alfa(k))*R);   
>        B  =  B  +  Rpr*(1  -  alfa(k))  /  (Z(k,i)  +  alfa(k)*(1  -  alfa(k))*R);
>     end
>     G(i)  =  (1  +  A)  /  (1  +  B);
> end
>
> A  =  1;
> B  =  1;
> for  k  =  1:10
>     A  =  A  +  Rpr*alfa(k)  ./  (Z(k,:)  +  alfa(k)*(1  -  alfa(k))*R);   
>     B  =  B  +  Rpr*(1  -  alfa(k))  ./  (Z(k,:)  +  alfa(k)*(1  -  alfa(k))*R);
> end
> G1  =  A  ./  B;
>
> [M,  ind]  =  max(abs(G- G1))
> However, the last line shows that there are differences between both 
> methods. They are tiny (near %eps), but I can't find nor imagine which 
> is the reason.
>
> NOTE: I kept the original formulas as in the script where the problem 
> arised but changed the data. When I tried to use a simpler formula 
> there was no difference.
>
> Any idea?
>
> Regards,
>
> Federico Miyara
>
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-- 
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet
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