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Mar 20, 2020
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3 changes: 2 additions & 1 deletion src/kernels/exponential.jl
Original file line number Diff line number Diff line change
Expand Up @@ -20,6 +20,7 @@ Base.show(io::IO,::SqExponentialKernel) = print(io,"Squared Exponential Kernel")
## Aliases ##
const RBFKernel = SqExponentialKernel
const GaussianKernel = SqExponentialKernel
const SEKernel = SqExponentialKernel

"""
`ExponentialKernel([ρ=1.0])`
Expand Down Expand Up @@ -48,7 +49,7 @@ The γ-exponential kernel is an isotropic Mercer kernel given by the formula:
"""
struct GammaExponentialKernel{Tγ<:Real} <: BaseKernel
γ::Vector{Tγ}
function GammaExponentialKernel(;γ::T=2.0) where {T<:Real}
function GammaExponentialKernel(;gamma::T=2.0, γ::T=gamma) where {T<:Real}
@check_args(GammaExponentialKernel, γ, γ >= zero(T), "γ > 0")
return new{T}([γ])
end
Expand Down
13 changes: 9 additions & 4 deletions src/kernels/matern.jl
Original file line number Diff line number Diff line change
Expand Up @@ -8,15 +8,20 @@ For `ν=n+1/2, n=0,1,2,...` it can be simplified and you should instead use [`Ex
"""
struct MaternKernel{Tν<:Real} <: BaseKernel
ν::Vector{Tν}
function MaternKernel(;ν::T=1.5) where {T<:Real}
function MaternKernel(;nu::T=1.5, ν::T=nu) where {T<:Real}
@check_args(MaternKernel, ν, ν > zero(T), "ν > 0")
return new{T}([ν])
end
end

@inline function kappa(κ::MaternKernel, d::Real)
ν = first(κ.ν)
iszero(d) ? one(d) : exp((one(d)-ν)*logtwo-logabsgamma(ν)[1] + ν*log(sqrt(2ν)*d)+log(besselk(ν,sqrt(2ν)*d)))
iszero(d) ? one(d) :
exp(
(one(d) - ν) * logtwo - logabsgamma(ν)[1] +
ν * log(sqrt(2ν) * d) +
log(besselk(ν, sqrt(2ν) * d))
)
end

metric(::MaternKernel) = Euclidean()
Expand All @@ -30,7 +35,7 @@ The matern 3/2 kernel is an isotropic Mercer kernel given by the formula:
"""
struct Matern32Kernel <: BaseKernel end

kappa(κ::Matern32Kernel, d::Real) = (1+sqrt(3)*d)*exp(-sqrt(3)*d)
kappa(κ::Matern32Kernel, d::Real) = (1 + sqrt(3) * d) * exp(-sqrt(3) * d)

metric(::Matern32Kernel) = Euclidean()

Expand All @@ -43,6 +48,6 @@ The matern 5/2 kernel is an isotropic Mercer kernel given by the formula:
"""
struct Matern52Kernel <: BaseKernel end

kappa(κ::Matern52Kernel, d::Real) = (1+sqrt(5)*d+5*d^2/3)*exp(-sqrt(5)*d)
kappa(κ::Matern52Kernel, d::Real) = (1 + sqrt(5) * d + 5 * d^2 / 3) * exp(-sqrt(5) * d)

metric(::Matern52Kernel) = Euclidean()
4 changes: 2 additions & 2 deletions src/kernels/rationalquad.jl
Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,7 @@ where `α` is a shape parameter of the Euclidean distance. Check [`GammaRational
"""
struct RationalQuadraticKernel{Tα<:Real} <: BaseKernel
α::Vector{Tα}
function RationalQuadraticKernel(;α::T=2.0) where {T}
function RationalQuadraticKernel(;alpha::T=2.0, α::T=alpha) where {T}
@check_args(RationalQuadraticKernel, α, α > zero(T), "α > 1")
return new{T}([α])
end
Expand All @@ -29,7 +29,7 @@ where `α` is a shape parameter of the Euclidean distance and `γ` is another sh
struct GammaRationalQuadraticKernel{Tα<:Real, Tγ<:Real} <: BaseKernel
α::Vector{Tα}
γ::Vector{Tγ}
function GammaRationalQuadraticKernel(;α::Tα=2.0, γ::Tγ=2.0) where {Tα<:Real, Tγ<:Real}
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])
Expand Down
11 changes: 8 additions & 3 deletions test/test_kernels.jl
Original file line number Diff line number Diff line change
Expand Up @@ -44,6 +44,7 @@ x = rand()*2; v1 = rand(3); v2 = rand(3); id = IdentityTransform()
@test kappa(k,x) ≈ exp(-(x)^(γ))
@test k(v1,v2) ≈ exp(-norm(v1-v2)^(2γ))
@test kappa(GammaExponentialKernel(),x) == kappa(k,x)
@test GammaExponentialKernel(gamma=γ).γ == [γ]
#Coherence :
@test KernelFunctions._kernel(GammaExponentialKernel(γ=1.0),v1,v2) ≈ KernelFunctions._kernel(SqExponentialKernel(),v1,v2)
@test KernelFunctions._kernel(GammaExponentialKernel(γ=0.5),v1,v2) ≈ KernelFunctions._kernel(ExponentialKernel(),v1,v2)
Expand All @@ -62,6 +63,7 @@ x = rand()*2; v1 = rand(3); v2 = rand(3); id = IdentityTransform()
ν = 2.0
k = MaternKernel(ν=ν)
matern(x,ν) = 2^(1-ν)/gamma(ν)*(sqrt(2ν)*x)^ν*besselk(ν,sqrt(2ν)*x)
@test MaternKernel(nu=ν).ν == [ν]
@test kappa(k,x) ≈ matern(x,ν)
@test kappa(k,0.0) == 1.0
@test kappa(MaternKernel(ν=ν),x) == kappa(k,x)
Expand Down Expand Up @@ -103,17 +105,20 @@ x = rand()*2; v1 = rand(3); v2 = rand(3); id = IdentityTransform()
end
@testset "RationalQuadratic" begin
@testset "RationalQuadraticKernel" begin
k = RationalQuadraticKernel()
α = 2.0
k = RationalQuadraticKernel(α=α)
@test RationalQuadraticKernel(alpha=α).α == [α]
@test kappa(k,x) ≈ (1.0+x/2.0)^-2
@test k(v1,v2) ≈ (1.0+norm(v1-v2)^2/2.0)^-2
@test kappa(RationalQuadraticKernel(),x) == kappa(k,x)
@test kappa(RationalQuadraticKernel(α=α),x) == kappa(k,x)
end
@testset "GammaRationalQuadraticKernel" begin
k = GammaRationalQuadraticKernel()
@test kappa(k,x) ≈ (1.0+x^2.0/2.0)^-2
@test k(v1,v2) ≈ (1.0+norm(v1-v2)^4.0/2.0)^-2
@test kappa(GammaRationalQuadraticKernel(),x) == kappa(k,x)
a = 1.0 + rand()
@test GammaRationalQuadraticKernel(alpha=a).α == [a]
#Coherence test
@test kappa(GammaRationalQuadraticKernel(α=a,γ=1.0),x) ≈ kappa(RationalQuadraticKernel(α=a),x)
end
Expand All @@ -128,7 +133,7 @@ x = rand()*2; v1 = rand(3); v2 = rand(3); id = IdentityTransform()
@test kappa(kt,v1,v2) == kappa(transform(k,ScaleTransform(s)),v1,v2)
@test kappa(kt,v1,v2) == kappa(transform(k,s),v1,v2)
@test kappa(kt,v1,v2) == kappa(k,s*v1,s*v2)
@test kappa(ktard,v1,v2) == kappa(transform(k,ARDTransform(v)),v1,v2)
@test kappa(ktard,v1,v2) kappa(transform(k,ARDTransform(v)),v1,v2)
@test kappa(ktard,v1,v2) == kappa(transform(k,v),v1,v2)
@test kappa(ktard,v1,v2) == kappa(k,v.*v1,v.*v2)
@test KernelFunctions.metric(kt) == KernelFunctions.metric(k)
Expand Down