On May 31, 2014, at 3:17 PM, Yuriy Strilets wrote:
> Dear All,
>
>
>
> I would appreciate if someone could give any hint/ provide a solution if
> it's possible in R to create such a function where many similar
> mathematical expressions organized in a given way.
>
> For example, to create a function: f(x)=(...(((x^x)^x)^x)...^x)^x (x is
> encountered n times). Or another example:
> g(x)=sin(x)*sin(x^2)*sin(x^3)*...*sin(x^n).
You should look at:
?funprog
There are several example of repeated applications of a functional argument.
Also composition of list of functions.
One instance:
Iterate <- function(f, n = 1)
function(x) Reduce(Funcall, rep.int(list(f), n), x, right = TRUE)
Iterate(function(x) x^1.1, 30)(1.01)
--
David
>
>
> When we are interested in a computation of any specific value of that
> function given a particular value of x, there is no any issue, and
> corresponding function value is computed in a straightforward way. For
> example of f(x) defined above:
>
> f<-function(x, n) {
>
> p<-x
>
> for (i in 1:n) {
>
> p<-p^x
>
> }
>
> print(p)
>
> }
>
>
>
> The issue is when we want to use a function "in general" with no particular
> x given.
>
>
> The whole question can be converted to a very short question (solution for
> which one is assumed to be a solution for primary question):
>
> - to integrate a function f(x)=(...(((x^x)^x)^x)...^x)^x (x is encountered
> n times) on the interval (0,1).
>
>
>
> Thanks a lot in advance for any ideas.
>
> I really believe that this doable with R syntax.
>
>
>
> Best Regards,
>
> Yuriy
>
> [[alternative HTML version deleted]]
>
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David Winsemius
Alameda, CA, USA
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