[R] Re: numerical integration {better than integrate(.)} ?

[Jim Lindsey]

> 
> {{I first wanted to send this to R-devel; 
>   but then thought, maybe first hear of you all.. 
>   and added a bit more
> 
>   Still could ask on R-devel later -- MM}
> 
> - In R, there's currently the "integrate" package from Mike Meyer, ported to
>   R by Thomas Lumley which really relies on multi-dimensional integration
>   "adapt" and is not particularly efficient for integrating simple 1d functions.
>   It stops with error/warning many times when I try to use it.
>   Also, it does not allow indefinite integrals (eg. from 0 to infty)
> 
> - MASS package has "area" which is there ``mainly for illustrative purposes''
> 
> - Jim Lindsey's non-CRAN "rmutil" package has  `int()'  which looks great,
>   judged from the help (int.Rd), allowing to choose between Romberg and
>   TOMS 614 methods, allowing for indefinite integrals and singularities at
>   the end point(s).
>   On the other hand, the C code seems somewhat complicated, and (for romberg.c),
>   quite a bit nested  (romberg -> evalRfn -> ..; interp) and completely
>   without comments. 
> 
>   [Yes: TOMS 614 has the copyright problem; but together with many more TOMS
>         routines in R...]
>   The (considerable!) drawback with  int() is that you don't get a
>   precision estimate back, but maybe that would be easy..
>   
> - For nice functions, very fast and accurate Gaussian integration should be 
>   "easy" to implement, and I remember having seen source for S, years ago,
>   but can't find it easily now.
>   The source would be so small that we could just include it in R's base
>   package (and this might be true for other integration utilities). 
> 
> I would propose to include in R a hopefully simple, 
> and `accurate in good cases'
> integrate() function [ different name?] for numerical integration of 1d
> functions. 
> 
> e.g. I want to be able to have things like
> 
>      integrate(function(x) dt(x,df=2), 0, Inf)
>      integrate(function(x) x*sqrt(x) dnorm(x), 0, 10, eps = 1e-10)
> 
> work
> [it *does* work with Jim's  int()  
>     ((when one uses character "infty" instead of Inf)),

That was written before Inf was in R and is obviously easy to fix.

>  but in my experience, one needs a long time of parameter fiddling to make
>  it produce a proper result with current integrate()]
> 
> Comments?
> Ideas?
> Jim, would you mind if e.g. I took your  int() & romberg code and
>  changed it by adding comments, probably change the UI a bit (argument
>  names; default values,..)?

Absolutely no problem. All of my code is wide open to the R community.
  Jim
> 
> MM
> 
>   
> 

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