Added docs

Author: theogf

docs/src/api.md

@@ -28,6 +28,7 @@ LinearKernel
 PolynomialKernel
 RationalQuadraticKernel
 GammaRationalQuadraticKernel
+PeriodicKernel
 ZeroKernel
 ConstantKernel
 WhiteKernel

docs/src/kernels.md

@@ -91,6 +91,14 @@ The [Polynomial Kernel](@ref KernelFunctions.PolynomialKernel) is defined as
   k(x,x';c,d) = \left(\langle x,x'\rangle + c\right)^d
 ```
 
+## Periodic Kernels
+
+### PeriodicKernel
+
+```math
+  k(x,x';r) = \exp\left(-0.5 \sum_i (sin (π(x_i - x'_i))/r_i)^2\right)
+```
+
 ## Constant Kernels
 
 ### ConstantKernel

src/kernels/periodic.jl

@@ -1,8 +1,11 @@
 """
     PeriodicKernel(r::AbstractVector)
     PeriodicKernel(dims::Int)
+    PeriodicKernel(T::DataType, dims::Int)
+
+Periodic Kernel as described in http://www.inference.org.uk/mackay/gpB.pdf eq. 47.
 ```
-    κ(x,y) = exp(-2 * sum_i(sin (π(x_i - y_i))/r_i))
+    κ(x,y) = exp( - 0.5 sum_i(sin (π(x_i - y_i))/r_i))
 ```
 """
 struct PeriodicKernel{T} <: BaseKernel
@@ -19,4 +22,6 @@ PeriodicKernel(T::DataType, dims::Int = 1) = PeriodicKernel(r = ones(T, dims))
 
 metric(κ::PeriodicKernel) = Sinus(κ.r)
 
-kappa(κ::PeriodicKernel, d::Real) = exp(-0.5 * d)
+kappa(κ::PeriodicKernel, d::Real) = exp(- 0.5d)
+
+Base.show(io::IO, κ::PeriodicKernel) = print(io, "Periodic Kernel, length(r) = $(length(κ.r))")

test/kernels/periodic.jl

@@ -6,4 +6,5 @@
     @test k(v1, v2) ≈ exp(-0.5 * sum(abs2, sinpi.(v1 - v2) ./ r))
     @test k(v1, v2) == k(v2, v1)
     @test PeriodicKernel(3)(v1, v2) == PeriodicKernel(r = ones(3))(v1, v2)
+    @test_nowarn println(k)
 end