Hello everyone, I have a very basic question. I’m looking for the most efficient way to perform the following very classical integral: [image] For now I’m using hquadrature of the cubature package in two steps. This works, but I’m not sure whether this is the most efficient way. More generally…

You can use a change of variables in general. However, since your problem is separable in x and u, you should take advantage of that, eg approximate the integral of g(u)du from 0 to x as some G(x), similarly for f, and then F(a)G(x) is your answer. (BTW, does the forum allow LaTeX now? or was that …

Thanks for your answer, Ok, I will stick with two-step approach then. BTW, yes, it’s an image. :slight_smile:

Why is the problem separable? The integration is over the x variable which is the limit of integration of the second integral. In any case, your suggestion has been accepted.

[image] mzaffalon: Why is the problem separable? The integration is over the x variable which is the limit of integration of the second integral. The way I read this notation is that the dx closes the scope for the x, so the second x is a free variable. I am aware that some people follow a di…

[image] Olivier_Merchiers: Ok, I will stick with two-step approach then. I would recommend trying a change of variables to turn the integration region into a rectangle. For example, let y=u/x, so that the integral becomes [image] In general, a 2d cubature code can be more efficient than nes…

Thank you very much @stevengj for your answer. That was exactly the information I was looking for. I know in matlab you can actually use a function handle to define an integration region. I was wondering if something similar was possible with one of the julia packages. Thanks again

[image] Olivier_Merchiers: I know in matlab you can actually use a function handle to define an integration region. I’m not sure what you’re referring to — as far as I can tell, Matlab doesn’t include multi-dimensional integration routines.

This is what I found for Matlab R2017a https://fr.mathworks.com/help/matlab/ref/integral2.html#btbbuxy-3 In older versions I used quad2d In both versions you could pass a function handle (anonymous function) as an integration bound. I quickly checked the publications cited at the end of the pag…

There is no way to compute non rectangular Integral in julia??? this is the way that I do it in python: func = lambda x,y: xy integ = integrate.dblquad(x2,0,t,lambda x :x, lambda y: t)[0] and this is the way that I do in matlab: func = @(x,y) xy; integ = integral2(func,0,t,@(t1) t1,t); but I …

2D integration over non-rectangular domain using cubature

New to Julia

dpsanders April 5, 2017, 8:43pm 6

It’s quite natural, once you get used to it, to think of as “\int dx” as the operator “integrate the following function with respect to x”

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2D integration over non-rectangular domain using cubature

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