[R] vectorizing the integrate function

ravi rv15| @end|ng |rom y@hoo@@e
Sun Aug 11 01:01:01 CEST 2019 

 Bert,Thanks a lot. This meets all my expectations for the moment. Thanks.Ravi

    On Sunday, 11 August 2019, 00:52:02 CEST, Bert Gunter <bgunter.4567 using gmail.com> wrote:  
 
 Cleaner, I think, is to use ?expand.grid and ?do.call, noting that any n-column data frame is also an n-component list.
Using your example as before:
> f2 <- function(a,b,m)integrate(function(x){exp(-a*x^3-b*x^2-m*x)},lower =0,upper = Inf)
> fv <- Vectorize(f2,vectorize.args=c("a","b","m"),SIMPLIFY=TRUE)
 ## Now use expand.grid to get all combinations of a,b, and m in a data frame
> allvals <- expand.grid(a=a, b=b, m=m)## Here's what it looks like (note the **named** columns to avoid problems)> head(allvals)
    a b  m
1 0.0 5 10
2 0.5 5 10
3 1.0 5 10
4 0.0 6 10
5 0.5 6 10
6 1.0 6 10## etc.  3 x 6 x 3 = 54 rows in all
## now use do.call to do fv() on these three column vectors (considered as a list of 3 components)
> results <- do.call(fv, allvals)
## So what does results look like?
> class(results)
[1] "matrix"
> dim(results)
[1]  5 54
> dimnames(results)[[1]]
[1] "value"        "abs.error"    "subdivisions" "message"      "call"      

## So the first row of the matrix contains the values. If you extract them by results[1, ], 
## you'll find, however, that it's a list of 54 components, each of which is a vector with
## one value. So unlist it first to avoid this:
> vals <- unlist(results[1,])
> vals
 [1] 0.09207851 0.09193111 0.09178672 0.09083412 0.09070066 0.09056960 0.08966646 0.08954474
 [9] 0.08942499 0.08856628 0.08845459 0.08834454 0.08752598 0.08742295 0.08732131 0.08653926
[17] 0.08644379 0.08634949 0.06403081 0.06398995 0.06394947 0.06356740 0.06352890 0.06349075
[25] 0.06312099 0.06308463 0.06304856 0.06269028 0.06265583 0.06262164 0.06227409 0.06224138
[33] 0.06220891 0.06187141 0.06184029 0.06180937 0.04883372 0.04881874 0.04880384 0.04861813
[41] 0.04860372 0.04858939 0.04840766 0.04839378 0.04837997 0.04820203 0.04818865 0.04817532
[49] 0.04800099 0.04798808 0.04797521 0.04780433 0.04779185 0.04777941
You can either convert this into an array or just add it as a column to allvals. The results are listed in 
the order given there.
Cheers,BertBert 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 3:03 PM Rui Barradas <ruipbarradas using sapo.pt> wrote:

Hello,

The following code might not be the best way of computing the integrals 
for all combinations of the arguments but it gets the job done and I 
believe it's readable code.


f2 <- function(a, b, c){
   integrate(function(x) {exp(-a*x^3 - b*x^2 - c*x)},
             lower = 0, upper = Inf)
}

f2_all_args <- function(a, b, c){
   lapply(a, function(.a)
     lapply(b, function(.b)
       lapply(c, function(.c)
         f2(.a, .b, .c)[1:2]
       )
     )
   )
}

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)

res <- f2_all_args(a, b, m)

r <- array(0, c(3, 6, 3))
r.error <- array(0, c(3, 6, 3))

for(i in seq_along(a)){
   res_i <- res[[i]]
   for(j in seq_along(b)){
     res_i_j <- res_i[[j]]
     for(k in seq_along(m)){
       r[i, j, k] <- res_i_j[[k]]$value
       r.error[i, j, k] <- res_i_j[[k]]$abs.error
     }
   }
}


Hope this helps,

Rui Barradas


Às 21:14 de 10/08/19, ravi via R-help escreveu:
>   Bert,Thanks a lot for your help. I have a few follow-up questions (shown in the comment lines).  Numerical values and error for a (i) vector and (ii) array.
> 
> 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(a,b,m)integrate(function(x){exp(-a*x^3-b*x^2-m*x)},lower=0,upper = Inf)
> fv <- Vectorize(f2,vectorize.args=c("a","b","m"),SIMPLIFY=TRUE)
> 
> r1 <- fv(a,b,m)
> # How to get just the numerical results as an array
> # for scalar values of a,b and m, I can get it with
> 
> #s <- integrate(f,0,Inf)$value
> # How do I get this for a vector
> 
> # Finally, if I want an array for all the values of a, b and m, how should I proceed?
> r <- array(0,c(3,6,3))
> r.error <- array(0,c(3,6,3))
> # I want the results of the vectorized integrate function in the above arrays. How do I extract these values?
> 
> 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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