It would be nice to have a `progress` keyword for time estimation about integrals.jl HOT 7 CLOSED

It's a bit more difficult in this case because it's not clear how to measure the progress, since it's a convergence criteria not stepping across time and thus there's no clear percentage of the computation already done.

from integrals.jl.

We can show percentage of convergence reached for both abstol and reltol separately, in such way user have some idea of what is happening and can estimate time for integration to complete.

from integrals.jl.

That is a cool idea! Unfortunately, the libraries that Integrals.jl wraps do not support callbacks that would allow for this kind query of the estimated error. If your integrals take very long to converge, is there a better algorithm that could integrate them with fewer function evaluations?

from integrals.jl.

That is a cool idea! Unfortunately, the libraries that Integrals.jl wraps do not support callbacks that would allow for this kind query of the estimated error. If your integrals take very long to converge, is there a better algorithm that could integrate them with fewer function evaluations?

I am using CubatureJLh() i tried also VEGAS but performance was not that great since I dont have big dimensions, only two, and need to integrate vectors, if you have any recomendation i am happy to try them out :)

Closing issue as can not be implemented.

from integrals.jl.

@Yaraslaut In 2D I would recommend a quadrature or cubature for faster convergence. Other than that, the optimal algorithm will depend on your integrand. If it is very smooth, CubatureJLp() would be favorable, since it reuses function evaluations. However if you tried CubatureJLh() this would be because your integrand is localized somewhere. If it is localized around points, I would recommend CubatureJLh(). However, if it is localized around curves, then doing nested 1d integration will have better computational complexity because of the number of cubes versus intervals it takes to adaptively tile a nearly singular surface in many versus one dimension. The quadgk! routine may be your friend in the case of curves.

from integrals.jl.

@Yaraslaut In 2D I would recommend a quadrature or cubature for faster convergence. Other than that, the optimal algorithm will depend on your integrand. If it is very smooth, CubatureJLp() would be favorable, since it reuses function evaluations. However if you tried CubatureJLh() this would be because your integrand is localized somewhere. If it is localized around points, I would recommend CubatureJLh(). However, if it is localized around curves, then doing nested 1d integration will have better computational complexity because of the number of cubes versus intervals it takes to adaptively tile a nearly singular surface in many versus one dimension. The quadgk! routine may be your friend in the case of curves.

Thanks for pointing out to some usefull places, I will definitely try to use quadgk!
One of the drawbacks i see in it is the lack of parallel computing especially in the nested case

Edit:
I found out that some batch procedure exist inside QuadGK.jl, hope i can figure out how to use it

from integrals.jl.

The batch procedure in quadgk is new but it doesn't support in-place integrands. However if the arrays you need to integrate are small you could use StaticArrays.jl with the batch interface. On the other hand if your arrays are too big for static arrays, then the integrand is likely expensive and would be another candidate for parallelization

from integrals.jl.