[R] Integration with 'adapt'

[Rodrigo Drummond]

Thank you for your answer to my question.
Here is a reproducible example of the problem:

> A<-2
> B<--1
> C<-1
> linf<-c(-10,-1,0.0003)
> lsup<-c(10,1,0.0004)
> Integrand1<-function(v)
{exp(-1*(A*v[1]^2-B*v[1]+C+(((v[1]-v[2])^2)/(2*v[3]^2))))/(K*v[3])}
> Const<-adapt(3,linf,lsup,functn=Integrand1)$value
Warning message:
Ifail=2, lenwrk was too small. -- fix adapt() !
 Check the returned relerr! in: adapt(3, linf, lsup, functn = Integrand1)

The problem is related to the small range of the third variable,
(0.0003-0.0004), so I tried the change of variables z2<-z/(max(z)-min(z)):

> rang=0.0004-0.0003
> linf[3]<-linf[3]/rang
> lsup[3]<-lsup[3]/rang
> Integrand1<-function(v)
{exp(-1*(A*v[1]^2-B*v[1]+C+(((v[1]-v[2])^2)/(2*(rang^2)*(v[3]^2)))))/(K*v[3])}
> #With the change of variables, the constant "rang" appears in the function.
> Const<-adapt(3,linf,lsup,functn=Integrand1)$value
Warning message:
Ifail=2, lenwrk was too small. -- fix adapt() !
 Check the returned relerr! in: adapt(3, linf, lsup, functn = Integrand1)

And the problem persists, probably because of the small value of "rang",
what can be checked below:

> rang<-.01
> Integrand1<-function(v)
{exp(-1*(A*v[1]^2-B*v[1]+C+(((v[1]-v[2])^2)/(2*(rang^2)*(v[3]^2)))))/(K*v[3])}
> #The same function as before, with a bigger value for "rang"
> Const<-adapt(3,linf,lsup,functn=Integrand1)$value
> Const
[1] 8.766637e-05

How can I evaluate the integral, even with small values of rang?
Thanks a lot for your help.
Best regards.
Rodrigo Drummond



>>>>>> "Rodrigo" == Rodrigo Drummond <rduarte at unicamp.br>
>>>>>>     on Tue, 27 Jul 2004 15:31:07 -0300 (BRT) writes:
>
>     Rodrigo> Hi all, I need to calculate a multidimensional
>     Rodrigo> integration on R. I am using the command
>     Rodrigo> "adapt" (from library adapt), although
>
> it's a "package", not a library.
>
>     Rodrigo> sometimes I get the following error message:
>
>     Rodrigo> Ifail=2, lenwrk was too small. -- fix adapt() !
>     Rodrigo> Check the returned relerr! in: adapt(3, linf, lsup,
>     Rodrigo> functn = Integrando1)
>
> If you could give as a *reproducible* example,
>
> we (the adapt authors) would have chance to do what the above
> message says, namely "fix adapt()" ..
>
>
>     Rodrigo> I guess it happens because the domain of
>     Rodrigo> integration is too small,
>
> maybe, maybe not. We need an example we can reproduce, see above.
>
>     Rodrigo> although I tried a change of variables to avoid
>     Rodrigo> this problem and it didn’t help. The command adapt
>     Rodrigo> calls a fortran routine, but I don’t know fortran
>     Rodrigo> enough to fix the problem.
>
> Martin Maechler, ETH Zurich
>


____________________________________________
Rodrigo D. Drummond
Laboratorio Genoma Funcional
Centro de Biologia Molecular e Eng. Genetica
Universidade Estadual de Campinas
Caixa Postal 6010
13083-875 - Campinas - SP - Brasil
Tel: xx-19-3788-1119 Fax: xx-19-3788-1089