Interface of KernelDensity.pdf is not consistent with Distributions.pdf

[jaksle]

I've noticed KernelDensity.pdf cannot be used in the same way as Distributions.pdf. I think this is very confusing for users and is a potential source of errors. In particular, pdf.(kde::UnivariateKDE, x::Vector) and pdf(kde::BivariateKDE, M::Matrix) do not work.

I could try adding them if there is agreement it should be done.

[tpapp]

Yes, it is unfortunate that the package defines a pdf method that works on vectors. This predates broadcasting (I think). It would be best to remove pdf(ik::InterpKDE,xs::AbstractVector) & friends and make things work with broadcasting.

As for pdf(kde::BivariateKDE, M::Matrix), I would very much prefer the solution as above combined with eachcol and/or eachrow. There is no preferred/canonical way to iterate over vectors in matrices in Julia, it is best to be explicit.

[jaksle]

I will look at this. Leaving it as it is would be asking for problems later, e.g. when more dimensional kde would be implemented. I'd strictly comply with the Distributions.jl interface.

[jaksle]

This is actually simpler than I thought. The pdf method for vectors was not a problem. The problem was broadcast had no information about the types UnivariateKDE and InterpKDE. You only need to add information they are scalars

Base.broadcastable(s::InterpKDE) = Ref(s)

the same for UnivariateKDE. But then, the broadcast is very slow as it calculates interpolation for each point separately. Fortunately, fixing it is even simpler, but requires a breaking change: making InterpKDE non-mutable. Then the compiler knows making those interpolations is the same call and broadcast becomes fast, actually 50% faster than the old vector method!

I'd like to stress now I see no reasonable reason as why InterpKDE was mutable. It seems completely useless trying to modify it. The same for other KDE types; changing that behaviour is not required for this problem, but I suspect this can cause efficiency problems in other circumstances.

Adding matrix argument was done in pull request #102. Together this would make KernelDensity comply with Distributions.