Evaluate many different integrands over the different domain

[WWXkenmo]

Feature

Desired Behavior / Functionality

Hey,

Thanks for developing this module. Recently I am trying to deal with an integration problem, which require to integrate many different integrands over different domain. For example, I have a set of function [f_1(t; a1, b1), f_2(t; a2, b2), ..., f_n(t; an, bn)], that means each function has the same form but just has difference in parameters, what I want to do is integrating f_1,..., f_n with each function has specific integrate domain (n). so the output would still a n-dimensional tensor, with each elements is the integration results of f_i

I have tracked the PR, and seems integrate on the same domain has been implement (#160), so I am wondering if this feature could be realized. If could, this tool could be applied on more scenarios.

Thanks,
Ken

[gomezzz]

Hi @WWXkenmo thanks for reaching out!

Yes, it is definitely related to #160 , I don't think it is yet support but implementing it should be quite manageable, I think. Would you be interested in implementing it?

@ilan-gold you are probably better qualified to answer this in general than me, what are your thoughts on this? :)

[WWXkenmo]

Hi,

After working on code today, I think I have figure out this issue, it could be easily down by Integration by substitution.
that is, for n th function (domain), we could represent the t_n as t*t_scale_n + t0_n, in which t_scale_n = t_n - t0_n, so, for every t_n, we substitute as the function of t, then we could use a fixed domain for t ([0, 1]), and each domain would be specific by the index ([t0_n, t_n]). But be aware of the rule of integration, the integrand need to multiply the t_scale_n, but t_scale_n and t0_n now could be the new parameter, which is feasible using current vectorised method #160.

It could be down externally, but it also could be integrated in the module. I would glad to help, but maybe in the next week?

Best,
Ken

[ilan-gold]

@WWXkenmo If I understand you correctly, I think I have an identical use-case. I wrote a custom integrator and it works very well. @gomezzz If I understand @WWXkenmo correctly, I would be happy to contribute what I have. Basically, it lets you change the domain of integration for each of the vectorized integrands. If this is not something we want to support, then I can just make the changes that let me build this custom integrator and send @WWXkenmo the code separately.

[gomezzz]

@ilan-gold can be closed now, I think, right? :)

[ilan-gold]

At long last

[ilan-gold]

Also I have spoken to @WWXkenmo - I can help him IRL if he wants but what he wants to do is now possible via an API.