besselJ derivative inaccuracy

[kaskr]

Thought these were carefully tested in TMB, but just came across this:

library(RTMB)
f <- function(p) besselJ(6, p)
F <- MakeTape(f,1)
f(5)
## [1] 0.3620871
F(5) ## OK
## [1] 0.3620871
numDeriv::grad(f,5)
## [1] -0.08149916
F$jacobian(5) ## Wrong!
##           [,1]
##[1,] -0.6882948

Might be relevant to go back and have a look at https://www.admb-project.org/developers/workshops/seattle-2016/Kristensen_Anders_Report.pdf

[kaskr]

Very likely a convergence issue as described on page 31 of the report under 'series convergence':

Edit: Only a problem for integer values, i.e. these are correct:

> F$jacobian(5+1e-12)
            [,1]
[1,] -0.08142719
> F$jacobian(5-1e-12)
            [,1]
[1,] -0.08149916

So, very likely a 'pointwise special case' issue as described on page 31.