Add Mahalanobis distance-based kernel

Author: sharanry

src/KernelFunctions.jl

@@ -14,6 +14,7 @@ export ExponentiatedKernel
 export MaternKernel, Matern32Kernel, Matern52Kernel
 export LinearKernel, PolynomialKernel
 export RationalQuadraticKernel, GammaRationalQuadraticKernel
+export MahaKernel
 export KernelSum, KernelProduct
 export TransformedKernel, ScaledKernel
 
@@ -44,7 +45,7 @@ include("distances/dotproduct.jl")
 include("distances/delta.jl")
 include("transform/transform.jl")
 
-for k in ["exponential","matern","polynomial","constant","rationalquad","exponentiated"]
+for k in ["exponential","matern","polynomial","constant","rationalquad","exponentiated","maha"]
     include(joinpath("kernels",k*".jl"))
 end
 include("kernels/transformedkernel.jl")

src/kernels/maha.jl

@@ -0,0 +1,21 @@
+"""
+    MahaKernel(; ell::Real=1.0, p::Real=1.0)
+
+    Mahalanobis distance-based kernel given by
+```math
+    κ(x,y) =  k(r^2), r^2 = maha(x,P,y) = (x-y)'*inv(P)*(x-y)
+```
+where the matrix P is the metric.
+
+"""
+struct MahaKernel{T<:Real} <: BaseKernel
+    P
+    function MahaKernel(P::AbstractMatrix{T}) where {T<:Real}
+        @assert size(P)[1] == size(P)[2], "P should be a square matrix"
+        new{T}(P)
+    end
+end
+
+kappa(κ::MahaKernel, d::T) where {T<:Real} = d 
+
+metric(κ::MahaKernel) = Mahalanobis(κ.P)