Merge pull request #61 from Element-126/interpolations-v0.9

Support Interpolations v0.9

Author: simonbyrne

REQUIRE

@@ -2,5 +2,5 @@ julia 0.7
 StatsBase
 Distributions
 Optim 0.16
-Interpolations
+Interpolations 0.9 0.10-
 FFTW

src/interp.jl

@@ -10,21 +10,23 @@ end
 function InterpKDE(kde::UnivariateKDE, opts...)
     itp_u = interpolate(kde.density, opts...)
     itp = scale(itp_u, kde.x)
-    InterpKDE{typeof(kde),typeof(itp)}(kde, itp)
+    etp = extrapolate(itp, zero(eltype(kde.density)))
+    InterpKDE{typeof(kde),typeof(etp)}(kde, etp)
 end
-InterpKDE(kde::UnivariateKDE) = InterpKDE(kde, BSpline(Quadratic(Line())), OnGrid())
+InterpKDE(kde::UnivariateKDE) = InterpKDE(kde, BSpline(Quadratic(Line(OnGrid()))))
 
 
 function InterpKDE(kde::BivariateKDE, opts...)
     itp_u = interpolate(kde.density,opts...)
     itp = scale(itp_u, kde.x, kde.y)
-    InterpKDE{typeof(kde),typeof(itp)}(kde, itp)
+    etp = extrapolate(itp, zero(eltype(kde.density)))
+    InterpKDE{typeof(kde),typeof(etp)}(kde, etp)
 end
-InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Line())), OnGrid())
+InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Line(OnGrid()))))
 
-pdf(ik::InterpKDE,x::Real...) = ik.itp[x...]
-pdf(ik::InterpKDE,xs::AbstractVector) = [ik.itp[x] for x in xs]
-pdf(ik::InterpKDE,xs::AbstractVector,ys::AbstractVector) = [ik.itp[x,y] for x in xs, y in ys]
+pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
+pdf(ik::InterpKDE,xs::AbstractVector) = [ik.itp(x) for x in xs]
+pdf(ik::InterpKDE,xs::AbstractVector,ys::AbstractVector) = [ik.itp(x,y) for x in xs, y in ys]
 
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)
 pdf(k::BivariateKDE,x,y) = pdf(InterpKDE(k),x,y)

test/interp.jl

@@ -9,3 +9,17 @@ k = kde(X)
 
 k = kde((X,Y))
 @test pdf(k, k.x, k.y) ≈ k.density
+
+# Try to evaluate the KDE outside the interpolation domain
+# The KDE is allowed to be zero, but it should not be greater than the exact solution
+k = kde([0.0], bandwidth=1.0)
+@test pdf(k, k.x) ≈ k.density
+@test pdf(k, -10.0) ≤ pdf(Normal(), -10.0)
+@test pdf(k, +10.0) ≤ pdf(Normal(), +10.0)
+
+k = kde(([0.0],[0.0]), bandwidth=(1.0, 1.0))
+@test pdf(k, k.x, k.y) ≈ k.density
+@test pdf(k, -10.0, 0.0) ≤ pdf(MvNormal(2, 1.0), [-10.0, 0.0])
+@test pdf(k, +10.0, 0.0) ≤ pdf(MvNormal(2, 1.0), [+10.0, 0.0])
+@test pdf(k, 0.0, -10.0) ≤ pdf(MvNormal(2, 1.0), [0.0, -10.0])
+@test pdf(k, 0.0, +10.0) ≤ pdf(MvNormal(2, 1.0), [0.0, +10.0])