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]]) 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 _______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users |
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 :
-- 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 _______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users |
Sorry the ode call should be (y0 first, then x0) y = ode(-1,x0,x1,list(f,x1,y1,d1)) The elapsed time seems OK:
--> tic;y =
ode(-1,x0,x1,list(f,x1,y1,d1));toc
ans = 0.002235 S.
Le 11/02/2020 à 08:17, Stéphane
Mottelet a écrit :
-- 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 _______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users |
Stéphane, Thanks for your solution. I've found another solution that is even slightly faster: I've modified the function intsplin(), changing both instances of sum by cumsum (and some formal details), so the same interpolator is used for the whole set of data. Regards, Federico Miyara On 11/02/2020 04:23, Stéphane Mottelet
wrote:
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