[Scilab-users] Int3D / Triple integration

[Stéphane Mottelet]

Le 02/04/2021 à 12:53, arctica1963 a écrit :
> Hi Stephane,
>
> At the moment I am just trying to understand how Scilab works with triple
> integration of f(x,y,z) with limits for xyz.

Ok, when you say "limits" for xyz you mean that each variable varies in 
a given constant interval, that's what I meant by the rectangular 
parallelepiped [x1,x2] x [y1,y2] x [z1,z2]. In fact it is a pity that 
Scilab does not handle this case but only the more general case of a 
collection of (eventually disconnected) tetrahedrons. However, cutting 
your parallepiped in 5 (https://www.geogebra.org/m/C3TjXxFY)  is enough 
to use int3d, since they will be recursively divided to attain the 
required precision:

deff('v=f(xyz,numfun)','v=xyz(1)^2+xyz(2)^2+xyz(3)^2')
xlim=[0  1];
ylim=[0  1];
zlim=[0  1];
[x,y,z]=ndgrid(xlim,ylim,zlim);
i  =  [5  8  2  3
      5  8  2  6
      5  8  3  7
      5  2  3  1
      2  3  8  4]';
[result,err]  =  int3d(x(i),y(i),z(i),f) --> result result = 1.0000000 --> err err = 
1.110D-14

S.

> Lester
>
>
>
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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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