[Scilab-users] Command integrate() is too slow under certain expressions

[Stéphane Mottelet]

Hello,

The usual way to compute a primitive would be to use ode, like this:

function  out=f(x, y, x1, y1, d1)
     out  =  interp(x,x1,y1,d1)
endfunction

x0  =  0
x1  =  0:0.01:2*%pi;
y1  =  sin(x1);

d1  =  splin(x1,y1);

y  =  ode(x0,-1,x1,list(f,x1,y1,d1))

Your proposition is very slow because you are recomputing the spline 
many times.

S.

Le 10/02/2020 à 20:52, Federico Miyara a écrit :
>
> Dear all,
>
> The function integrate() is very handy to obtain a numerical primtive 
> of a function, particularly useful when there is no closed form for 
> the primitive or it is too involved. According to the documentation
>
>     x = integrate(expr, v, x0, x1 [, atol [, rtol]])
>
>     expr: a character string defining a Scilab expression.
>     v:    a character string, the integration variable name
>
>
> However there is a case that would be interesting to handle, and it is 
> when one has a set of experimental (or simulated) data xk, yk. Here 
> there is no expression defining a function.
>
> One way to circumvent this is using as the expression some sort of 
> interpolator such as
>
> x = integrate("interp1(xk, yk, x, ''spline'')", "x", x0, x1)
>
> This works, but for some reason I don't quite understand it is very slow.
>
> For instance,
>
> x0 = 0
> x1 = 0:0.01:2*%pi;
> y1 = sin(x1);
>
> tic
> X = integrate("interp1(x1, y1, x, ''spline'')", "x", x0, x1);
> toc
>
> Requires 27 s to execute. In the meantime, control is seemingly 
> returned to the console, one can enter instructions, but then the 
> program freezes until the integrate comand finishes.
>
> Changing "spline" to "linear" even worsens it rising to 33 s.
>
> Has anybody an idea of what can be happening?
>
> Maybe it computes the full interpolator for each single point? Even if 
> so, I have only 629 values of the independent variable.
>
> 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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