DOC: Add method details/reference to scipy.integrate.dblquad and scipy.integrate.tplquad

[ShantanuDash]

Reference issue

Closes #13872

What does this implement/fix?

Add method details/reference to the documentation of scipy.integrate.dblquad and scipy.integrate.tplquad

Additional information

Both scipy.integrate.dblquad and scipy.integrate.tplquad wrap scipy.integrate.nquad to perform double and triple integration (definite) respectively. This was previously unclear, see here

[rgommers]

Hi @ShantanuDash, thanks for working on this. This doesn't yet address the issue though. nquad is not a method. The request is to look at the actual numerical method used (as implemented in QUADPACK) and then add some details like the name of the method and a reference to the original paper about this method.

[ShantanuDash]

@rgommers thanks a lot for informing! I am absolutely new to this. Will look into QUADPACK and would follow up.

[ShantanuDash]

@rgommers the quad function calls different QUADPACK routines depending on the parameters, each of which subsequently uses different routines. Here's the original documentation. . So should i add something like this and specify how exactly different QUADPACKS routines are called and then add the original QUADPACK documentation as reference?

[rgommers]

So should i add something like this and specify how exactly different QUADPACKS routines are called and then add the original QUADPACK documentation as reference?

Yes that sounds about right. Check which routines are called exactly, and then a phrasing like on Wikipedia like "uses global adaptive quadrature based on 21-point Gauss–Kronrod quadrature within each subinterval, with acceleration by Peter Wynn's epsilon algorithm." (not sure that's the correct one, just stole it from the QAGS).

[mdhaber]

Hi @ShantanuDash were you still interested in finishing this? If so, I can resolve the merge conflicts for you.

[mdhaber]

The referenced issue is closed, so I'll close this PR.