[R] ADAPTIVE QUADRATURE WEIGHTS AND NODES

[spencerg]

      Beyond what Doug said, if you have a specific R function that does 
adaptive quadrature, you could read the code for that function.  You can 
get that without comments by typing the function name at a commands 
prompt.  To get the source code with comments, you can download the 
appropriate source code in *.tar.gz format from your favorite CRAN 
mirror.  If the function you want is in the base system, click "R 
Sources -> R-2.9.0.tar.gz" from your favorite CRAN mirror.  For a 
contributed packages, click "Packages" two lines below "R Sources". 


      The following will search help files for "adaptive quadrature": 

library(RSiteSearch)
aq <- RSiteSearch.function('adaptive quadrature')
summary(aq)
HTML(aq)

     
      Hope this helps. 
      Spencer Graves

Douglas Bates wrote:
> On Fri, May 8, 2009 at 7:07 AM, Boikanyo Makubate
> <boikanyo at stats.gla.ac.uk> wrote:
>
>   
>> Can anyone help me on how to get the nodes and weights of the adaptive quadrature
>> using R.
>>     
>
> You need to be more specific about which quadrature formula.  I'm
> guessing that you probably have Gauss-Hermite quadrature in mind
> because it is used when a density is approximated by a Gaussian
> density (the "adaptive" modifier refers to a process where the
> conditional mode and conditional variance are determined, given values
> of parameters).  In that case you could start at
>
> http://en.wikipedia.org/wiki/Gauss-Hermite_Quadrature
>
> for the theory.
>
> There is C code in the lme4 package to compute the nodes and weights
> for Gauss-Hermite quadrature but we haven't written a public interface
> to it.  You can try, for example
>
>   
>> library(lme4)
>> .Call("lme4_ghq", 7)
>>     
> [[1]]
> [1]  2.6519614  1.6735516  0.8162879  0.0000000 -0.8162879 -1.6735516 -2.6519614
>
> [[2]]
> [1] 0.0009717812 0.0545155828 0.4256072526 0.8102646176 0.4256072526
> [6] 0.0545155828 0.0009717812
>
> to get the nodes and the weights for a 7-point Gauss-Hermite
> quadrature.  (There are two versions of the Hermite polynomials, the
> physicist's version where the kernel is exp(-x^2) and the
> probabilist's version where the kernel is exp(-(x^2)/2).  I'm pretty
> sure these are from the physicist's version.)
>
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