RationalQuadraticKernel and GammaRationalQuadraticKernel implementations

[molet]

I would be interested if there is a particular reason of implementing RationalQuadraticKernel as:

κ(x,y)=(1+||x−y||²/α)^(-α)

instead of:

κ(x,y)=(1+||x−y||²/(2α))^(-α)

Most of the implementations I have seen are using the latter form and I'm wondering if KernelFunctions.jl could use it as well in order to make comparisons easier.

Also, this is the docstring of GammaRationalQuadraticKernel:

"""
`GammaRationalQuadraticKernel([ρ=1.0[,α=2.0[,γ=2.0]]])`
The Gamma-rational-quadratic kernel is an isotropic Mercer kernel given by the formula:

    κ(x,y)=(1+ρ^(2γ)||x−y||^(2γ)/α)^(-α)

where `α` is a shape parameter of the Euclidean distance and `γ` is another shape parameter.
"""

However, there is no such variable ρ that can be defined in the actual constructor:

struct GammaRationalQuadraticKernel{Tα<:Real, Tγ<:Real} <: SimpleKernel
    α::Vector{Tα}
    γ::Vector{Tγ}
    function GammaRationalQuadraticKernel(;alpha::Tα=2.0, gamma::Tγ=2.0, α::Tα=alpha, γ::Tγ=gamma) where {Tα<:Real, Tγ<:Real}
        @check_args(GammaRationalQuadraticKernel, α, α > one(Tα), "α > 1")
        @check_args(GammaRationalQuadraticKernel, γ, γ >= one(Tγ), "γ >= 1")
        return new{Tα, Tγ}([α], [γ])
    end
end

It might have been forgotten in the implementation or - if skipping it was intentional - it would be nice to update the docstring.

[willtebbutt]

Most of the implementations I have seen are using the latter form and I'm wondering if KernelFunctions.jl could use it as well in order to make comparisons easier.

This probably relates to #158 -- I guess I just missed this when I was reviewing everything.

[devmotion]

This is fixed now: the definition of RationalQuadraticKernel was changed as suggested above and the docstring of GammaRationalQuadraticKernel (renamed to GammaRationalKernel) was fixed.