[R] Integration of functions with a vector argument

[Bert Gunter]

If you haven't already done so, you may wish to have a look here:

https://cran.r-project.org/web/views/NumericalMathematics.html#differentiation-and-integration

(Or perhaps in other related subtopics in the Numerical Math task view)

Cheers,
Bert

On Thu, Jun 20, 2024 at 8:37 AM Ivan Krylov via R-help <r-help using r-project.org>
wrote:

> В Tue, 18 Jun 2024 23:12:03 +0000
> "Levine, Michael" <mlevins using purdue.edu> пишет:
>
> > I have heard of several packages used for numerical integration in R -
> > cubature that you mentioned, mvQuad, and pracma.  My impression is
> > that you think that Cubature is the best in your opinion. Is that so?
>
> Yes, but the preference is not very strong. My own numerical
> integration experience is limited to using QUADPACK in a project where
> everything had to be rewritten in Fortran for speed.
>
> I trust the code of the 'cubature' library by Steven G. Johnson (whose
> work includes FFTW and NLopt) and the 'Cuba' library by Thomas Hahn.
> The 'cubature' R package wraps these two libraries. Unfortunately, as
> you see, its documentation can be lacking.
>
> Like 'cubature', the 'mvQuad' package won't require a significant
> rewrite of the integrand because it expects its functions to take
> matrices of arguments. Unfortunately, the two packages differ in the
> meanings they assign to the matrices: in 'cubature', individual
> arguments of the function correspond to the rows of the first argument,
> while in 'mvQuad', they must be in the columns.
>
> The 'mvQuad' package requires manual adjustments to the generated
> quadratures using rescale(...), which may be not very convenient.
>
> The 'pracma' package contains implementations of a lot of excellent
> methods (I've trusted it before for its other functions), but the (two-
> or three-argument) integrand will have to be rewritten to accept
> separate arrays (of arbitrary shape?) instead of a single matrix.
>
> > If yes, do you know of any detailed discussion of this package beyond
> > the two vignettes available on CRAN?
>
> I don't know how much it can help, but more information about the
> underlying code for 'cubature' can be found at
> <https://github.com/stevengj/cubature> and <https://feynarts.de/cuba/>.
>
> --
> Best regards,
> Ivan
>
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