Corrected Matern inference bug : fixes #7

Author: theogf

src/kernels/matern.jl

@@ -1,26 +1,26 @@
 """
-    MaternKernel([[ρ=1],ν=3/2])
+    MaternKernel([ρ=1.0,[ν=1.0]])
 
 The matern kernel is an isotropic Mercer kernel given by the formula:
 
 ```
-    κ(x,y) = 2^{1-ν}/Γ(ν)*(√(2ν)‖x-y‖/ρ)^ν K_ν(√(2ν)‖x-y‖/ρ)
+    κ(x,y) = 2^{1-ν}/Γ(ν)*(√(2ν)‖x-y‖)^ν K_ν(√(2ν)‖x-y‖)
 ```
 
-For `ν=n+1/2, n=0,1,2,...` it can be simplified (it will be converted automatically).
-`ρ` is a lengthscale parameter.
+For `ν=n+1/2, n=0,1,2,...` it can be simplified and you should instead use `ExponentialKernel` for `n=0`, `Matern32Kernel`, for `n=1`, Matern52Kernel for `n=2` and `SqExponentialKernel` for `n=∞`.
+`ρ` is the lengthscale parameter(s) or the transform object.
 
 # Examples
 
 ```jldoctest; setup = :(using KernelFunctions)
 julia> MaternKernel()
-Matern3_2Kernel{Float64,Float64}(1.0)
+MaternKernel{Float64,Float64}(1.0,1.0)
 
 julia> MaternKernel(2.0f0,3.0)
 MaternKernel{Float32,Float32}(2.0,3.0)
 
-julia> MaternKernel([2.0,3.0],5/2)
-Matern5_2Kernel{Float64,Array{Float64}}([2.0,3.0])
+julia> MaternKernel([2.0,3.0],2.5)
+MaternKernel{Float64,Array{Float64}}([2.0,3.0],2.5)
 ```
 """
 struct MaternKernel{T,Tr<:Transform} <: Kernel{T,Tr}
@@ -34,47 +34,17 @@ end
 
 function MaternKernel(ρ::T₁=1.0,ν::T₂=1.5) where {T₁<:Real,T₂<:Real}
     @check_args(MaternKernel, ν, ν > zero(T₂), "ν > 0")
-    if ν == 0.5
-        ExponentialKernel{T₁,ScaleTransform{T₁}}(ScaleTransform(ρ))
-    elseif ν == 1.5
-        Matern32Kernel{T₁,ScaleTransform{T₁}}(ScaleTransform(ρ))
-    elseif ν == 2.5
-        Matern52Kernel{T₁,ScaleTransform{T₁}}(ScaleTransform(ρ))
-    elseif ν == Inf
-        SquaredExponentialKernel{T₁,ScaleTransform{T₁}}(ScaleTransform(ρ))
-    else
-        MaternKernel{T₁,ScaleTransform{T₁}}(ScaleTransform(ρ),ν)
-    end
+    MaternKernel{T₁,ScaleTransform{T₁}}(ScaleTransform(ρ),ν)
 end
 
 function MaternKernel(ρ::A,ν::T=1.5) where {A<:AbstractVector{<:Real},T<:Real}
     @check_args(MaternKernel, ν, ν > zero(T), "ν > 0")
-    if ν == 0.5
-        ExponentialKernel{eltype(A),ScaleTransform{A}}(ScaleTransform(ρ))
-    elseif ν == 1.5
-        Matern32Kernel{eltype(A),ScaleTransform{A}}(ScaleTransform(ρ))
-    elseif ν == 2.5
-        Matern52Kernel{eltype(A),ScaleTransform{A}}(ScaleTransform(ρ))
-    elseif ν == Inf
-        SquaredExponentialKernel{eltype(A),ScaleTransform{A}}(ScaleTransform(ρ))
-    else
-        MaternKernel{eltype(A),ScaleTransform{A}}(ScaleTransform(ρ),ν)
-    end
+    MaternKernel{eltype(A),ScaleTransform{A}}(ScaleTransform(ρ),ν)
 end
 
-function MaternKernel(t::T₁,ν::T₂=1.5) where {T₁<:Transform,T₂<:Real}
-    @check_args(MaternKernel, ν, ν > zero(T₂), "ν > 0")
-    if ν == 0.5
-        ExponentialKernel{eltype(t),T₁}(t)
-    elseif ν == 1.5
-        Matern32Kernel{eltype(t),T₁}(t)
-    elseif ν == 2.5
-        Matern52Kernel{eltype(t),T₁}(t)
-    elseif ν == Inf
-        SquaredExponentialKernel{eltype(t),T₁}(t)
-    else
-        MaternKernel{eltype(t),T₁}(t,ν)
-    end
+function MaternKernel(t::Tr,ν::T=1.5) where {Tr<:Transform,T<:Real}
+    @check_args(MaternKernel, ν, ν > zero(T), "ν > 0")
+    MaternKernel{eltype(t),Tr}(t,ν)
 end
 
 @inline kappa(κ::MaternKernel, d::Real) where {T} = exp((1.0-κ.ν)*logtwo - lgamma(κ.ν) - κ.ν*log(sqrt(2κ.ν)*d))*besselk(κ.ν,sqrt(2κ.ν)*d)
@@ -96,8 +66,8 @@ function Matern32Kernel(ρ::A) where {A<:AbstractVector{<:Real}}
     Matern32Kernel{eltype(A),ScaleTransform{A}}(ScaleTransform(ρ))
 end
 
-function Matern32Kernel(t::Transform)
-    Matern52Kernel{eltype(A),ScaleTransform{A}}(t)
+function Matern32Kernel(t::Tr) where {Tr<:Transform}
+    Matern52Kernel{eltype(Tr),Tr}(t)
 end
 
 @inline kappa(κ::Matern32Kernel, d::T) where {T<:Real} = (1+sqrt(3)*d)*exp(-sqrt(3)*d)
@@ -118,8 +88,8 @@ function Matern52Kernel(ρ::A) where {A<:AbstractVector{<:Real}}
     Matern52Kernel{eltype(A),ScaleTransform{A}}(ScaleTransform(ρ))
 end
 
-function Matern52Kernel(t::Transform)
-    Matern52Kernel{eltype(A),ScaleTransform{A}}(t)
+function Matern52Kernel(t::Tr) where {Tr<:Transform}
+    Matern52Kernel{eltype(Tr),Tr}(t)
 end
 
 @inline kappa(κ::Matern52Kernel, d::Real) where {T} = (1+sqrt(5)*d+5*d^2/3)*exp(-sqrt(5)*d)