[R] vectorizing the integrate function

[Bert Gunter]

Ravi:

I believe you are under a misconception. The Vectorize() function
vectorizes the function call, **but it does not vectorize the computation
by moving loops down to the C level**, which is typically what is meant
when it is recommended that R users use inbuilt vectorized functions when
possible to move looping from the interpreted (R) level to the compiled (C
level) code. That is, mapply() -- and thus Vectorize, which is just a
wrapper for mapply -- is still looping at the interpreted level and
therefore is essentially the same as explicit iterative or *apply loops. It
may be a bit faster or slower, depending, but not the orders of magnitude
faster that one can get with true vectorized (at the C level) code.

Finally, if you want to just add the integration results to the allvals
list, here's a
slightly different one-liner to do it:

> allvals$vals <- unlist(with(allvals,fv(a,b,m))[1,])
> head(allvals)
    a b  m       vals
1 0.0 5 10 0.09207851
2 0.5 5 10 0.09193111
3 1.0 5 10 0.09178672
4 0.0 6 10 0.09083412
5 0.5 6 10 0.09070066
6 1.0 6 10 0.09056960

or the one liner using the previous do.call() construction that just
extracts the vector of values:

> vals <- unlist(do.call(fv,allvals)[1,])
Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Sat, Aug 10, 2019 at 3:56 PM ravi <rv15i using yahoo.se> wrote:

> Rui,
> Thanks for your help in getting the result with for loops. That is useful,
> but I have a complicated integral and I am interested in improving the
> performance with the benefit of vectorization.
>
> In the solution from Bert, I would like to know how I can extract the
> numerical vector from the function fv. That is, extract the fv$value as a
> vector. I can then perhaps try to improvise and extend it to arrays.
> Thanks,
> Ravi
>
> On Saturday, 10 August 2019, 20:03:22 CEST, Bert Gunter <
> bgunter.4567 using gmail.com> wrote:
>
>
> Ravi:
>
> First of all, you're calling Vectorize incorrectly. The first argument
> must be a function *name*, not a function call. Here's what you need to do
> (and thanks for the reprex -- wouldn't have been able to help without it!):
>
> f2 <- function(a,b,c)integrate(function(x){exp(-a*x^3-b*x^2-c*x)},lower
> =0,upper = Inf)
> fv <- Vectorize(f2,vectorize.args=c("a","b","c"),SIMPLIFY=TRUE)
>
> Second of all, as you may realize, the vectorization uses mapply() and so
> vectorizes the c(a,b,c) triplet "in parallel," which will "recycle" shorter
> arguments to the length of longer. Hence you will get 6 results from your
> example:
>
> > fv(a,b,m)
>              [,1]         [,2]         [,3]        [,4]         [,5]
>   [,6]
> value        0.09207851   0.0635289    0.04837997  0.08856628   0.06224138
>   0.04777941
> abs.error    3.365173e-08 3.108388e-06 1.00652e-09 3.284876e-09
> 1.796619e-08 6.348142e-09
> subdivisions 2            1            2           2            2
>    2
> message      "OK"         "OK"         "OK"        "OK"         "OK"
>   "OK"
> call         Expression   Expression   Expression  Expression   Expression
>   Expression
>
> Cheers,
> Bert
>
> Bert Gunter
>
> "The trouble with having an open mind is that people keep coming along and
> sticking things into it."
> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>
>
> On Sat, Aug 10, 2019 at 10:20 AM ravi via R-help <r-help using r-project.org>
> wrote:
>
> Hi all,I am having some difficulties in vectorizing the integrate
> function. Let me explain with an example.
> a <- 10; b <- 3; c <- 4
> f <- function(x) {exp(-a*x^3-b*x^2-c*x)}
> integrate(f,0,Inf) # works fine
>
> My difficulties start when I want to vectorize.
>
> # attempts to vectorize fail
> a <- seq(from=0,to=1,by=0.5)
> b <- seq(from=5,to=10,by=1)
> m <- seq(from=10,to=20,by=5)
> f2 <- function(x,a,b,c) {exp(-a*x^3-b*x^2-m*x)}
> fv <-
> Vectorize(integrate(f2,0,Inf),vectorize.args=c("a","b","m"),SIMPLIFY=TRUE)
>
> I want the result as a 3-d array with dimensions of the lengths of a, b
> and c. I have tried several variants but am not having much luck. Will
> appreciate any help that I can get.
> Thanks,Ravi Sutradhara
>
>
>
>
>
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>
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