R help - Jan 2016 - Multiple Integrals

Dear R-helpers,

I'm looking for a quick way to calculate triple integrals.

I have tried something like this example:

f <- function(x,y,z) dnorm(x)*dnorm(y)*dnorm(z)
llim <- -Inf
ulim <- Inf
integrate(function(z)
{
  sapply(z,function(z)
  {
    integrate(function(y)
    {
      sapply(y, function(y)
      {
        integrate(function(x) f(x,y,z), llim, ulim)$value
      })
    }, llim, ulim)$value
  })
},llim,ulim)

I'm not sure if there are other ways faster than this one.
Any help will be appreciated.

Thanks,
L.M.

	[[alternative HTML version deleted]]

On 07/01/16 13:03, Lu?sa Freitas wrote:
> Dear R-helpers,
>
> I'm looking for a quick way to calculate triple integrals.
>
> I have tried something like this example:
>
> f <- function(x,y,z) dnorm(x)*dnorm(y)*dnorm(z)
> llim <- -Inf
> ulim <- Inf
> integrate(function(z)
> {
>    sapply(z,function(z)
>    {
>      integrate(function(y)
>      {
>        sapply(y, function(y)
>        {
>          integrate(function(x) f(x,y,z), llim, ulim)$value
>        })
>      }, llim, ulim)$value
>    })
> },llim,ulim)
>
> I'm not sure if there are other ways faster than this one.
> Any help will be appreciated.
GIYF.  Searching on "multiple integration r" led me very quickly to
the
R2Cuba package for multidimensional numerical integration, which will 
presumably do what you want.  (I have not tried it out; that's your job.)

cheers,

Rolf Turner

-- 
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276

> On Jan 6, 2016, at 8:37 PM, Rolf Turner <r.turner at auckland.ac.nz>
wrote:
> 
> On 07/01/16 13:03, Lu?sa Freitas wrote:
>> Dear R-helpers,
>> 
>> I'm looking for a quick way to calculate triple integrals.
>> 
>> I have tried something like this example:
>> 
>> f <- function(x,y,z) dnorm(x)*dnorm(y)*dnorm(z)
>> llim <- -Inf
>> ulim <- Inf
>> integrate(function(z)
>> {
>>   sapply(z,function(z)
>>   {
>>     integrate(function(y)
>>     {
>>       sapply(y, function(y)
>>       {
>>         integrate(function(x) f(x,y,z), llim, ulim)$value
>>       })
>>     }, llim, ulim)$value
>>   })
>> },llim,ulim)
>> 
>> I'm not sure if there are other ways faster than this one.
>> Any help will be appreciated.
> 
> GIYF.  Searching on "multiple integration r" led me very quickly
to the R2Cuba package for multidimensional numerical integration, which will
presumably do what you want.  (I have not tried it out; that's your job.)
I have not tried that package out but I can report satisfactory experience with
the r package 'cubature'.

-- 
David.
> 
> cheers,
> 
> Rolf Turner
> 
> -- 
> Technical Editor ANZJS
> Department of Statistics
> University of Auckland
> Phone: +64-9-373-7599 ext. 88276
> 
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