[R] vectorizing the integrate function

ravi rv15| @end|ng |rom y@hoo@@e
Sun Aug 11 00:56:38 CEST 2019

 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:  
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  

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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