R help - Oct 2011 - About an integral univariate problem

Hello all R users

I want to calculate this univariate integral:
exp(-x)*sum(y^x)  respect to x  from 0 to 3  where y is a vector y=(2,3,5).
In fact, the original y vector has a large number of elements but I propose
with 3 elements.

I know that I can resolve this problem doing

fun <- function(x) exp(-x)*(2^x+3^x+5^x)
integrate(fun,0,3)

When the y vector has a large number of elements the last solution is not
possible,
if I use this another way I can not obtain the true answer

   y <- c(2,3,5)
fun1 <- function(x) exp(-x)*sum(y^x)
integrate(fun1,0,3)

Someone could give me a help with the problem?
Thanks.


Freddy Hernández Barajas

	[[alternative HTML version deleted]]

How about adding an additional argument to fun?

R> fun <- function(x, y) exp(-x)*sum(y^x)
R> y <- c(2,3,5)
R> integrate(fun, 0, 3, y)
[1] 346.853 with absolute error < 3.9e-12
Michael

On Tue, Oct 18, 2011 at 10:01 AM, Freddy Hernandez Barajas
<fhernanb at gmail.com> wrote:
> Hello all R users
>
> I want to calculate this univariate integral:
> exp(-x)*sum(y^x) ?respect to x ?from 0 to 3 ?where y is a vector y=(2,3,5).
> In fact, the original y vector has a large number of elements but I propose
> with 3 elements.
>
> I know that I can resolve this problem doing
>
> fun <- function(x) exp(-x)*(2^x+3^x+5^x)
> integrate(fun,0,3)
>
> When the y vector has a large number of elements the last solution is not
> possible,
> if I use this another way I can not obtain the true answer
>
> ? y <- c(2,3,5)
> fun1 <- function(x) exp(-x)*sum(y^x)
> integrate(fun1,0,3)
>
> Someone could give me a help with the problem?
> Thanks.
>
>
> Freddy Hern?ndez Barajas
>
> ? ? ? ?[[alternative HTML version deleted]]
>
>
> ______________________________________________
> R-help at r-project.org mailing list
> 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.
>
>

Your original code was not directly vectorizible (and I should have
noted that): this should work:

fnc <- function(x, y) {
    z <- outer(y, x, FUN = "^")
    exp(-x) * colSums(z)
}
y <- c(2,3,5)
integrate(fnc, 0, 3, y)

This should work and sorry for the initial confusion.

Michael

On Tue, Oct 18, 2011 at 11:05 AM, Freddy Hernandez Barajas
<fhernanb at gmail.com> wrote:
> Thanks for the response.
>
> But there is a problem, the value of the integral is approximately 14.02
and
> the proposed procedure gives 346.85
>
> Freddy Hern?ndez Barajas
>
>
>
> 2011/10/18 R. Michael Weylandt <michael.weylandt at gmail.com>
>>
>> How about adding an additional argument to fun?
>>
>> R> fun <- function(x, y) exp(-x)*sum(y^x)
>> R> y <- c(2,3,5)
>> R> integrate(fun, 0, 3, y)
>> [1] 346.853 with absolute error < 3.9e-12
>> Michael
>>
>> On Tue, Oct 18, 2011 at 10:01 AM, Freddy Hernandez Barajas
>> <fhernanb at gmail.com> wrote:
>> > Hello all R users
>> >
>> > I want to calculate this univariate integral:
>> > exp(-x)*sum(y^x) ?respect to x ?from 0 to 3 ?where y is a vector
>> > y=(2,3,5).
>> > In fact, the original y vector has a large number of elements but
I
>> > propose
>> > with 3 elements.
>> >
>> > I know that I can resolve this problem doing
>> >
>> > fun <- function(x) exp(-x)*(2^x+3^x+5^x)
>> > integrate(fun,0,3)
>> >
>> > When the y vector has a large number of elements the last solution
is
>> > not
>> > possible,
>> > if I use this another way I can not obtain the true answer
>> >
>> > ? y <- c(2,3,5)
>> > fun1 <- function(x) exp(-x)*sum(y^x)
>> > integrate(fun1,0,3)
>> >
>> > Someone could give me a help with the problem?
>> > Thanks.
>> >
>> >
>> > Freddy Hern?ndez Barajas
>> >
>> > ? ? ? ?[[alternative HTML version deleted]]
>> >
>> >
>> > ______________________________________________
>> > R-help at r-project.org mailing list
>> > 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.
>> >
>> >
>
>