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
[[alternative HTML version deleted]]
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 at 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
>
>
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
[[alternative HTML version deleted]]
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 at
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 at 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
? ? ? ? [[alternative HTML version deleted]]
______________________________________________
R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
[[alternative HTML version deleted]]
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 at
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 at 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
? ? ? ? [[alternative HTML version deleted]]
______________________________________________
R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
[[alternative HTML version deleted]]
Dear ravi, In your example, the function "f" is linear to a, b, and c. Is this the general case in your task? If it is, you can save *lots* of computation taking advantage of the linearity. Lei On Sat, 10 Aug 2019 at 19:20, ravi via R-help <r-help at 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 > > > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.
Hi all,I would like to thank every one who has responded to my question. I have
received valuable help.Linus, the function that I gave here is just a toy
function. I think that is possible even to find an analytical solution. I chose
that just to include many constant parameters. I wanted to find out how I can
vectorize. I have obtained nice answers from Bert and I appreciate the help. I
knew even previously that the vectorizing primarily improves the readability of
the code. Thanks Bert for making it crystal clear that the looping is still at
the interpreted level of R.Thanks,Ravi
On Sunday, 11 August 2019, 12:24:43 CEST, Linus Chen <linus.l.chen at
gmail.com> wrote:
Dear ravi,
In your example, the function "f" is linear to a, b, and c.
Is this the general case in your task?
If it is, you can save? *lots* of computation taking advantage of the linearity.
Lei
On Sat, 10 Aug 2019 at 19:20, ravi via R-help <r-help at 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
>
>
>
>
>? ? ? ? [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
[[alternative HTML version deleted]]