Add Cosine Kernel (#45)

* Add Cosine Kernel

* Update src/kernels/cosine.jl

Co-Authored-By: willtebbutt <[email protected]>

* Update src/kernels/cosine.jl

Co-Authored-By: David Widmann <[email protected]>

* Modify Cosine to be parameter-less

* Add tests

* Update Docstring

* Change metric to Euclidean

* Use cospi, change scaling factor to pi and update tests.

Co-authored-by: willtebbutt <[email protected]>
Co-authored-by: David Widmann <[email protected]>

Author: 3 people

src/KernelFunctions.jl

@@ -44,7 +44,7 @@ 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","cosine"]
     include(joinpath("kernels",k*".jl"))
 end
 include("kernels/transformedkernel.jl")
@@ -53,7 +53,6 @@ include("matrix/kernelmatrix.jl")
 include("kernels/kernelsum.jl")
 include("kernels/kernelproduct.jl")
 include("approximations/nystrom.jl")
-
 include("generic.jl")
 
 include("zygote_adjoints.jl")

src/kernels/cosine.jl

@@ -0,0 +1,14 @@
+"""
+    CosineKernel
+
+The cosine kernel is a stationary kernel for a sinusoidal given by
+```
+    κ(x,y) = cos( π * (x-y) )
+```
+
+"""
+struct CosineKernel <: BaseKernel end
+
+kappa(κ::CosineKernel, d::Real) = cospi(d)
+
+metric(::CosineKernel) = Euclidean()

test/test_kernels.jl

@@ -26,6 +26,15 @@ x = rand()*2; v1 = rand(3); v2 = rand(3); id = IdentityTransform()
             @test kappa(k,0.5) == c
         end
     end
+    @testset "Cosine" begin
+        k = CosineKernel()
+        @test eltype(k) == Any
+        @test kappa(k, 1.0) ≈ -1.0 atol=1e-5
+        @test kappa(k, 2.0) ≈ 1.0 atol=1e-5
+        @test kappa(k, 1.5) ≈ 0.0 atol=1e-5
+        @test kappa(k,x) ≈ cospi(x) atol=1e-5
+        @test k(v1, v2) ≈ cospi(sqrt(sum(abs2.(v1-v2)))) atol=1e-5
+    end
     @testset "Exponential" begin
         @testset "SqExponentialKernel" begin
             k = SqExponentialKernel()
@@ -133,8 +142,8 @@ x = rand()*2; v1 = rand(3); v2 = rand(3); id = IdentityTransform()
         ks = ScaledKernel(k,s)
         @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(kt,v1,v2) ≈ kappa(k,s*v1,s*v2) atol=1e-5
+        @test kappa(ktard,v1,v2) ≈ kappa(transform(k,ARDTransform(v)),v1,v2) atol=1e-5
         @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)