baptiste auguie <baptiste.auguie <at> googlemail.com> writes:
>
> Dear list,
>
> I'm seeking some advice regarding a particular numerical integration I
> wish to perform.
>
> The integrand f takes two real arguments x and y and returns a vector
> of constant length N. The range of integration is [0, infty) for x and
> [a,b] (finite) for y. Since the integrand has values in R^N I did not
> find a built-in function to perform numerical quadrature, so I wrote
> my own after some inspiration from a post in R-help,
The function adaptIntegral() in the 'cubature' package integrates
multi-valued functions over n-dimensional finite hypercubes, as do the
functions in 'R2Cuba'.
If the hypercube is (partly) infinite, a transformation such as x --> 1/x
per infinite axis (as in NR) has to be applied.
For two dimensions, another approach could be to apply the integrate()
function twice, because this 1-dimensional integration function can handle
infinite intervals.
Hint: First inegrate over the finite dimension(s).
Example: Integrate sin(x)/exp(y) for 0 <= x <= pi, 0 <= y <= Inf (value: 2)
----
f1 <- function(y) 1/exp(y)
f2 <- function(x) sin(x) * integrate(f1, 0, Inf)$value
integrate(f2, 0, pi)
# 2 with absolute error < 2.2e-14
----
Note that the absolute error is not correct, as the first integration has
its own error term. You have to do your own error estimation.
Hans Werner
>
> [...]
>
> So it seems to work. I wonder though if I may have missed an easier
> (and more reliable) way to perform such integration using base
> functions or an add-on package that I may have overlooked.
>
> Best regards,
>
> baptiste
>
>
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