From 15d0cbc7868a9f06b46fea6dfe63efeb7f25bdca Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Tue, 6 Feb 2024 18:41:17 +0100
Subject: [PATCH 01/17] rem mutable + add Ref(x)

---
 .gitignore           | 4 +++-
 src/KernelDensity.jl | 2 ++
 src/interp.jl        | 3 +--
 src/univariate.jl    | 2 +-
 4 files changed, 7 insertions(+), 4 deletions(-)

diff --git a/.gitignore b/.gitignore
index ae3a70e3..291b930a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,4 @@
 examples/.ipynb_checkpoints/*
-Manifest.toml
\ No newline at end of file
+Manifest.toml
+.vscode/settings.json
+tmp.jl
diff --git a/src/KernelDensity.jl b/src/KernelDensity.jl
index 722e118d..b6201c8a 100644
--- a/src/KernelDensity.jl
+++ b/src/KernelDensity.jl
@@ -12,6 +12,8 @@ export kde, kde_lscv, UnivariateKDE, BivariateKDE, InterpKDE, pdf
 
 abstract type AbstractKDE end
 
+Base.broadcastable(x::AbstractKDE) = Ref(x)
+
 include("univariate.jl")
 include("bivariate.jl")
 include("interp.jl")
diff --git a/src/interp.jl b/src/interp.jl
index 05e648e6..4503e43d 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -1,12 +1,11 @@
 import Interpolations: interpolate, scale
 
-mutable struct InterpKDE{K,I} <: AbstractKDE
+struct InterpKDE{K,I} <: AbstractKDE
     kde::K
     itp::I
     InterpKDE{K,I}(kde::K, itp::I) where {K,I} = new{K,I}(kde, itp)
 end
 
-
 function InterpKDE(kde::UnivariateKDE, opts...)
     itp_u = interpolate(kde.density, opts...)
     itp = scale(itp_u, kde.x)
diff --git a/src/univariate.jl b/src/univariate.jl
index 5f71a809..993c4339 100644
--- a/src/univariate.jl
+++ b/src/univariate.jl
@@ -13,7 +13,7 @@ sum(density) * step(x) ≈ 1
 
 $(FIELDS)
 """
-mutable struct UnivariateKDE{R<:AbstractRange} <: AbstractKDE
+struct UnivariateKDE{R<:AbstractRange} <: AbstractKDE
     "Gridpoints for evaluating the density."
     x::R
     "Kernel density at corresponding gridpoints `x`."

From cd7723ea3a238b4153781f076f3b63cc1303a263 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 01:09:09 +0100
Subject: [PATCH 02/17] broadcast

---
 .gitignore    | 1 +
 Project.toml  | 5 +++++
 src/interp.jl | 5 +++--
 3 files changed, 9 insertions(+), 2 deletions(-)

diff --git a/.gitignore b/.gitignore
index 291b930a..d66bf271 100644
--- a/.gitignore
+++ b/.gitignore
@@ -2,3 +2,4 @@ examples/.ipynb_checkpoints/*
 Manifest.toml
 .vscode/settings.json
 tmp.jl
+Project.toml
diff --git a/Project.toml b/Project.toml
index e0df42fe..7a9ff6df 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,10 +4,15 @@ authors = ["Simon Byrne and various contributors"]
 version = "0.6.8"
 
 [deps]
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
 Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
+Loess = "4345ca2d-374a-55d4-8d30-97f9976e7612"
+LsqFit = "2fda8390-95c7-5789-9bda-21331edee243"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 
 [compat]
diff --git a/src/interp.jl b/src/interp.jl
index 4503e43d..cb125f20 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -23,9 +23,10 @@ function InterpKDE(kde::BivariateKDE, opts...)
 end
 InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Line(OnGrid()))))
 
+pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)
 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]
+Base.broadcasted(::typeof(pdf),k::UnivariateKDE,xs) = InterpKDE(k).itp.(xs)
 
-pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)
 pdf(k::BivariateKDE,x,y) = pdf(InterpKDE(k),x,y)
+pdf(ik::InterpKDE,xs::AbstractVector,ys::AbstractVector) = [ik.itp(x,y) for x in xs, y in ys]

From eee2128baa87705113c893fb3d1a4b5360581e08 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 01:39:55 +0100
Subject: [PATCH 03/17] Update interp.jl

---
 src/interp.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/interp.jl b/src/interp.jl
index cb125f20..435a9acc 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -26,7 +26,7 @@ InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Li
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)
 pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
 pdf(ik::InterpKDE,xs::AbstractVector) = [ik.itp(x) for x in xs]
-Base.broadcasted(::typeof(pdf),k::UnivariateKDE,xs) = InterpKDE(k).itp.(xs)
+Base.broadcast(::typeof(pdf),k::UnivariateKDE,xs) = InterpKDE(k).itp.(xs)
 
 pdf(k::BivariateKDE,x,y) = pdf(InterpKDE(k),x,y)
 pdf(ik::InterpKDE,xs::AbstractVector,ys::AbstractVector) = [ik.itp(x,y) for x in xs, y in ys]

From 976c63088369cdc97fd249989725a0cf403fa2ec Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 14:53:33 +0100
Subject: [PATCH 04/17] interface tests

---
 src/interp.jl     | 17 ++++++++++++-----
 src/univariate.jl |  2 +-
 test/interp.jl    | 16 ++++++++++++++++
 3 files changed, 29 insertions(+), 6 deletions(-)

diff --git a/src/interp.jl b/src/interp.jl
index cb125f20..e8e1afc9 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -1,6 +1,6 @@
 import Interpolations: interpolate, scale
 
-struct InterpKDE{K,I} <: AbstractKDE
+mutable struct InterpKDE{K,I} <: AbstractKDE
     kde::K
     itp::I
     InterpKDE{K,I}(kde::K, itp::I) where {K,I} = new{K,I}(kde, itp)
@@ -23,10 +23,17 @@ function InterpKDE(kde::BivariateKDE, opts...)
 end
 InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Line(OnGrid()))))
 
-pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)
 pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
-pdf(ik::InterpKDE,xs::AbstractVector) = [ik.itp(x) for x in xs]
-Base.broadcasted(::typeof(pdf),k::UnivariateKDE,xs) = InterpKDE(k).itp.(xs)
+
+# interface implementation
+# it should be consistent with Distributions.pdf
+
+pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)
+Base.broadcasted(::typeof(pdf),k::UnivariateKDE,xs) = Base.broadcasted(InterpKDE(k).itp, xs)
+pdf(ik::InterpKDE,xs::AbstractVector) = pdf.(ik, xs)
 
 pdf(k::BivariateKDE,x,y) = pdf(InterpKDE(k),x,y)
-pdf(ik::InterpKDE,xs::AbstractVector,ys::AbstractVector) = [ik.itp(x,y) for x in xs, y in ys]
+pdf(ik::InterpKDE,xs::AbstractVector,ys::AbstractVector) = ik.itp.(xs,ys')
+pdf(k::BivariateKDE, M) = pdf(InterpKDE(k),M)
+pdf(ik::InterpKDE, M::AbstractArray{<:Real, 1}) = ik.itp(M[1],M[2])
+pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
diff --git a/src/univariate.jl b/src/univariate.jl
index 993c4339..5f71a809 100644
--- a/src/univariate.jl
+++ b/src/univariate.jl
@@ -13,7 +13,7 @@ sum(density) * step(x) ≈ 1
 
 $(FIELDS)
 """
-struct UnivariateKDE{R<:AbstractRange} <: AbstractKDE
+mutable struct UnivariateKDE{R<:AbstractRange} <: AbstractKDE
     "Gridpoints for evaluating the density."
     x::R
     "Kernel density at corresponding gridpoints `x`."
diff --git a/test/interp.jl b/test/interp.jl
index ed93d914..1a917145 100644
--- a/test/interp.jl
+++ b/test/interp.jl
@@ -23,3 +23,19 @@ k = kde(([0.0],[0.0]), bandwidth=(1.0, 1.0))
 @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])
+
+@testset "pdf method interface" begin
+    k = kde([-1., 1.])
+    ik = InterpKDE(k)
+
+    @test pdf.(k, [0., 1.]) ≈ [pdf(k, 0.), pdf(k, 1.)] ≈ pdf.(k,[0., 1.]) ≈ [pdf(ik, 0.), pdf(ik, 1.)]
+    @test all( pdf.(k, (0., 1.)) .≈ (pdf(k, 0.), pdf(k, 1.)) )
+    @test pdf.(k, [0. 1.; 2. -1.]) ≈ [pdf(k, 0.) pdf(k, 1.); pdf(k, 2.) pdf(k, -1.)]
+
+    k2d = kde(([-1., 1.], [0., 1.]))
+    ik2d = InterpKDE(k2d)
+
+    @test pdf(k2d, [0.5, 0.1]) ≈ pdf(k2d, 0.5, 0.1) ≈ pdf(ik2d, 0.5, 0.1)
+    @test pdf(k2d, [0.5 1.; 0.1 1.]) ≈ [pdf(ik2d, 0.5, 0.1), pdf(ik2d, 1., 1.)]
+    @test pdf(k2d, [0.5; 1. ;;; 0.1; 1.]) ≈ [pdf(ik2d, 0.5, 1.) pdf(ik2d, 0.1, 1.)]
+end
\ No newline at end of file

From e00c4ccd5c48ad3a5ffc7e26e9d5a1a1b9202882 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 16:12:44 +0100
Subject: [PATCH 05/17] Update interp.jl

---
 src/interp.jl | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/src/interp.jl b/src/interp.jl
index e8e1afc9..b294827f 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -30,10 +30,9 @@ pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
 
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)
 Base.broadcasted(::typeof(pdf),k::UnivariateKDE,xs) = Base.broadcasted(InterpKDE(k).itp, xs)
-pdf(ik::InterpKDE,xs::AbstractVector) = pdf.(ik, xs)
 
 pdf(k::BivariateKDE,x,y) = pdf(InterpKDE(k),x,y)
 pdf(ik::InterpKDE,xs::AbstractVector,ys::AbstractVector) = ik.itp.(xs,ys')
 pdf(k::BivariateKDE, M) = pdf(InterpKDE(k),M)
-pdf(ik::InterpKDE, M::AbstractArray{<:Real, 1}) = ik.itp(M[1],M[2])
+pdf(ik::InterpKDE, V::AbstractVector) = ik.itp(V[1],V[2])
 pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )

From 6ba8bad9e553e27a6ffca65462c9f6240427d2b8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 18:06:20 +0100
Subject: [PATCH 06/17] comments

---
 src/interp.jl  | 8 ++++++--
 test/interp.jl | 2 +-
 2 files changed, 7 insertions(+), 3 deletions(-)

diff --git a/src/interp.jl b/src/interp.jl
index b294827f..ed5c0aa6 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -25,14 +25,18 @@ InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Li
 
 pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
 
-# interface implementation
+# pdf interface implementation
 # it should be consistent with Distributions.pdf
 
+# 1 dimension
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)
 Base.broadcasted(::typeof(pdf),k::UnivariateKDE,xs) = Base.broadcasted(InterpKDE(k).itp, xs)
 
+# 2 dimensions
 pdf(k::BivariateKDE,x,y) = pdf(InterpKDE(k),x,y)
 pdf(ik::InterpKDE,xs::AbstractVector,ys::AbstractVector) = ik.itp.(xs,ys')
 pdf(k::BivariateKDE, M) = pdf(InterpKDE(k),M)
-pdf(ik::InterpKDE, V::AbstractVector) = ik.itp(V[1],V[2])
 pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
+
+# any dimension
+pdf(ik::InterpKDE, V::AbstractVector) = ik.itp(V...)
diff --git a/test/interp.jl b/test/interp.jl
index 1a917145..d2f7c4a6 100644
--- a/test/interp.jl
+++ b/test/interp.jl
@@ -35,7 +35,7 @@ k = kde(([0.0],[0.0]), bandwidth=(1.0, 1.0))
     k2d = kde(([-1., 1.], [0., 1.]))
     ik2d = InterpKDE(k2d)
 
-    @test pdf(k2d, [0.5, 0.1]) ≈ pdf(k2d, 0.5, 0.1) ≈ pdf(ik2d, 0.5, 0.1)
+    @test pdf(k2d, [0.5, 0.1]) ≈ pdf(k2d, [0.5; 0.1]) ≈ pdf(k2d, 0.5, 0.1) ≈ pdf(ik2d, 0.5, 0.1)
     @test pdf(k2d, [0.5 1.; 0.1 1.]) ≈ [pdf(ik2d, 0.5, 0.1), pdf(ik2d, 1., 1.)]
     @test pdf(k2d, [0.5; 1. ;;; 0.1; 1.]) ≈ [pdf(ik2d, 0.5, 1.) pdf(ik2d, 0.1, 1.)]
 end
\ No newline at end of file

From a06b49a71ba0343f063c5d14b07b48924546a3fc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 18:16:55 +0100
Subject: [PATCH 07/17] Update interp.jl

---
 src/interp.jl | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/interp.jl b/src/interp.jl
index ed5c0aa6..b92525b4 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -23,11 +23,15 @@ function InterpKDE(kde::BivariateKDE, opts...)
 end
 InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Line(OnGrid()))))
 
-pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
 
 # pdf interface implementation
 # it should be consistent with Distributions.pdf
 
+# any dimension
+pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
+pdf(ik::InterpKDE, V::AbstractVector) = ik.itp(V...)
+pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
+
 # 1 dimension
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)
 Base.broadcasted(::typeof(pdf),k::UnivariateKDE,xs) = Base.broadcasted(InterpKDE(k).itp, xs)
@@ -36,7 +40,3 @@ Base.broadcasted(::typeof(pdf),k::UnivariateKDE,xs) = Base.broadcasted(InterpKDE
 pdf(k::BivariateKDE,x,y) = pdf(InterpKDE(k),x,y)
 pdf(ik::InterpKDE,xs::AbstractVector,ys::AbstractVector) = ik.itp.(xs,ys')
 pdf(k::BivariateKDE, M) = pdf(InterpKDE(k),M)
-pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
-
-# any dimension
-pdf(ik::InterpKDE, V::AbstractVector) = ik.itp(V...)

From 9fd648a0462e69c99f6a6ba607651b457ec429b0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 19:33:13 +0100
Subject: [PATCH 08/17] Update Project.toml

---
 Project.toml | 5 -----
 1 file changed, 5 deletions(-)

diff --git a/Project.toml b/Project.toml
index 7a9ff6df..e0df42fe 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,15 +4,10 @@ authors = ["Simon Byrne and various contributors"]
 version = "0.6.8"
 
 [deps]
-BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
 Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
-Loess = "4345ca2d-374a-55d4-8d30-97f9976e7612"
-LsqFit = "2fda8390-95c7-5789-9bda-21331edee243"
-Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
-Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 
 [compat]

From b30a95025b9c1bc5f3536d54b77685b75f034a9c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 19:43:18 +0100
Subject: [PATCH 09/17] Update interp.jl

---
 test/interp.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/interp.jl b/test/interp.jl
index d2f7c4a6..cbdeb7c5 100644
--- a/test/interp.jl
+++ b/test/interp.jl
@@ -13,7 +13,7 @@ k = kde((X,Y))
 # 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, k.x) ≈ k.density
 @test pdf(k, -10.0) ≤ pdf(Normal(), -10.0)
 @test pdf(k, +10.0) ≤ pdf(Normal(), +10.0)
 

From 9974b8c935156c1d622284d1b8012f4bb3b7a035 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 19:47:56 +0100
Subject: [PATCH 10/17] tests update

---
 test/interp.jl | 48 +++++++++++++++++++++++++-----------------------
 1 file changed, 25 insertions(+), 23 deletions(-)

diff --git a/test/interp.jl b/test/interp.jl
index cbdeb7c5..3b02de07 100644
--- a/test/interp.jl
+++ b/test/interp.jl
@@ -1,28 +1,30 @@
 using Test
 using KernelDensity
 
-X = randn(100)
-Y = randn(100)
-
-k = kde(X)
-@test pdf(k, k.x) ≈ k.density
-
-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])
+@testset "interpolation computation" begin
+    X = randn(100)
+    Y = randn(100)
+
+    k = kde(X)
+    @test pdf.(k, k.x) ≈ k.density
+
+    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])
+end
 
 @testset "pdf method interface" begin
     k = kde([-1., 1.])
@@ -38,4 +40,4 @@ k = kde(([0.0],[0.0]), bandwidth=(1.0, 1.0))
     @test pdf(k2d, [0.5, 0.1]) ≈ pdf(k2d, [0.5; 0.1]) ≈ pdf(k2d, 0.5, 0.1) ≈ pdf(ik2d, 0.5, 0.1)
     @test pdf(k2d, [0.5 1.; 0.1 1.]) ≈ [pdf(ik2d, 0.5, 0.1), pdf(ik2d, 1., 1.)]
     @test pdf(k2d, [0.5; 1. ;;; 0.1; 1.]) ≈ [pdf(ik2d, 0.5, 1.) pdf(ik2d, 0.1, 1.)]
-end
\ No newline at end of file
+end

From eac3b90ca3840977407d3527d8d25980eb323074 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 20:02:14 +0100
Subject: [PATCH 11/17] Update interp.jl

---
 src/interp.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/interp.jl b/src/interp.jl
index b92525b4..3f2e726a 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -34,7 +34,7 @@ pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, d
 
 # 1 dimension
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)
-Base.broadcasted(::typeof(pdf),k::UnivariateKDE,xs) = Base.broadcasted(InterpKDE(k).itp, xs)
+Base.Broadcast.broadcasted(::typeof(pdf),k::UnivariateKDE,xs) = Base.Broadcast.broadcasted(InterpKDE(k).itp, xs)
 
 # 2 dimensions
 pdf(k::BivariateKDE,x,y) = pdf(InterpKDE(k),x,y)

From d3ade85b48fa4ac7a7c959ea86a49535f13e0ea6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Wed, 7 Feb 2024 23:49:47 +0100
Subject: [PATCH 12/17] trying Compat for eachslice in Julia 1.0

---
 Project.toml         | 1 +
 src/KernelDensity.jl | 1 +
 src/interp.jl        | 2 +-
 3 files changed, 3 insertions(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index e0df42fe..e9ed4a9d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,6 +11,7 @@ Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 
 [compat]
+Compat = "2.2.0"
 Distributions = "0.23, 0.24, 0.25"
 DocStringExtensions = "0.8, 0.9"
 FFTW = "1"
diff --git a/src/KernelDensity.jl b/src/KernelDensity.jl
index b6201c8a..61cde468 100644
--- a/src/KernelDensity.jl
+++ b/src/KernelDensity.jl
@@ -4,6 +4,7 @@ using DocStringExtensions: TYPEDEF, FIELDS
 using StatsBase
 using Distributions
 using Interpolations
+using Compat
 
 import Distributions: twoπ, pdf
 import FFTW: rfft, irfft
diff --git a/src/interp.jl b/src/interp.jl
index 3f2e726a..a404ec7d 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -30,7 +30,7 @@ InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Li
 # any dimension
 pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
 pdf(ik::InterpKDE, V::AbstractVector) = ik.itp(V...)
-pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
+@compat pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
 
 # 1 dimension
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)

From 8d44f99d30d570338b1bd9948a249f69a952076d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Thu, 8 Feb 2024 00:02:56 +0100
Subject: [PATCH 13/17] remove Compat

---
 Project.toml         | 1 -
 src/KernelDensity.jl | 1 -
 src/interp.jl        | 2 +-
 3 files changed, 1 insertion(+), 3 deletions(-)

diff --git a/Project.toml b/Project.toml
index e9ed4a9d..e0df42fe 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,7 +11,6 @@ Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 
 [compat]
-Compat = "2.2.0"
 Distributions = "0.23, 0.24, 0.25"
 DocStringExtensions = "0.8, 0.9"
 FFTW = "1"
diff --git a/src/KernelDensity.jl b/src/KernelDensity.jl
index 61cde468..b6201c8a 100644
--- a/src/KernelDensity.jl
+++ b/src/KernelDensity.jl
@@ -4,7 +4,6 @@ using DocStringExtensions: TYPEDEF, FIELDS
 using StatsBase
 using Distributions
 using Interpolations
-using Compat
 
 import Distributions: twoπ, pdf
 import FFTW: rfft, irfft
diff --git a/src/interp.jl b/src/interp.jl
index a404ec7d..3f2e726a 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -30,7 +30,7 @@ InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Li
 # any dimension
 pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
 pdf(ik::InterpKDE, V::AbstractVector) = ik.itp(V...)
-@compat pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
+pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
 
 # 1 dimension
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)

From 84eaa9689b7272e5da9ccbab765dae88bd7bd3eb Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Mon, 11 Mar 2024 19:33:52 +0100
Subject: [PATCH 14/17] adding Compat

---
 Project.toml  | 2 ++
 src/interp.jl | 4 +++-
 2 files changed, 5 insertions(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index e0df42fe..e3bd9594 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,6 +4,7 @@ authors = ["Simon Byrne and various contributors"]
 version = "0.6.8"
 
 [deps]
+Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
@@ -17,6 +18,7 @@ FFTW = "1"
 Interpolations = "0.9, 0.10, 0.11, 0.12, 0.13, 0.14, 0.15"
 StatsBase = "0.33, 0.34"
 julia = "1"
+Compat = "3.22, 4"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/src/interp.jl b/src/interp.jl
index 3f2e726a..ea56df1b 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -1,5 +1,7 @@
+import Compat: @compat
 import Interpolations: interpolate, scale
 
+
 mutable struct InterpKDE{K,I} <: AbstractKDE
     kde::K
     itp::I
@@ -30,7 +32,7 @@ InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Li
 # any dimension
 pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
 pdf(ik::InterpKDE, V::AbstractVector) = ik.itp(V...)
-pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
+pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = @compat pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
 
 # 1 dimension
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)

From 60db7b0a93687f9a586d7086883383623b118601 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Mon, 11 Mar 2024 19:58:20 +0100
Subject: [PATCH 15/17] Compat ver

---
 Project.toml  | 2 +-
 src/interp.jl | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Project.toml b/Project.toml
index e3bd9594..c43890d0 100644
--- a/Project.toml
+++ b/Project.toml
@@ -18,7 +18,7 @@ FFTW = "1"
 Interpolations = "0.9, 0.10, 0.11, 0.12, 0.13, 0.14, 0.15"
 StatsBase = "0.33, 0.34"
 julia = "1"
-Compat = "3.22, 4"
+Compat = "2.2.0, 4"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/src/interp.jl b/src/interp.jl
index ea56df1b..c4498242 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -1,4 +1,4 @@
-import Compat: @compat
+import Compat: eachslice
 import Interpolations: interpolate, scale
 
 
@@ -32,7 +32,7 @@ InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Li
 # any dimension
 pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
 pdf(ik::InterpKDE, V::AbstractVector) = ik.itp(V...)
-pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = @compat pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
+pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
 
 # 1 dimension
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)

From 8b0126c67426cf1ed8761e0edf8730032d717e00 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Mon, 11 Mar 2024 23:19:52 +0100
Subject: [PATCH 16/17] rem Compat, eachslice to maplices + reshape

---
 Project.toml  | 2 --
 src/interp.jl | 3 +--
 2 files changed, 1 insertion(+), 4 deletions(-)

diff --git a/Project.toml b/Project.toml
index c43890d0..e0df42fe 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,7 +4,6 @@ authors = ["Simon Byrne and various contributors"]
 version = "0.6.8"
 
 [deps]
-Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
@@ -18,7 +17,6 @@ FFTW = "1"
 Interpolations = "0.9, 0.10, 0.11, 0.12, 0.13, 0.14, 0.15"
 StatsBase = "0.33, 0.34"
 julia = "1"
-Compat = "2.2.0, 4"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/src/interp.jl b/src/interp.jl
index c4498242..748dbc90 100644
--- a/src/interp.jl
+++ b/src/interp.jl
@@ -1,4 +1,3 @@
-import Compat: eachslice
 import Interpolations: interpolate, scale
 
 
@@ -32,7 +31,7 @@ InterpKDE(kde::BivariateKDE) = InterpKDE(kde::BivariateKDE, BSpline(Quadratic(Li
 # any dimension
 pdf(ik::InterpKDE,x::Real...) = ik.itp(x...)
 pdf(ik::InterpKDE, V::AbstractVector) = ik.itp(V...)
-pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = pdf.(ik,eachslice(M, dims=ntuple(i->i+1, N-1)) )
+pdf(ik::InterpKDE, M::AbstractArray{<:Real, N}) where N = reshape(mapslices(v->pdf(ik, v), M, dims = 1), size(M)[2:end])
 
 # 1 dimension
 pdf(k::UnivariateKDE,x) = pdf(InterpKDE(k),x)

From 8cd5a1c6c1ae1bae7620948319900d92a79f556a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20=C5=9Al=C4=99zak?=
 <128084860+jaksle@users.noreply.github.com>
Date: Mon, 11 Mar 2024 23:36:05 +0100
Subject: [PATCH 17/17] alternative to ;;;

---
 test/interp.jl | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/test/interp.jl b/test/interp.jl
index 3b02de07..b2ea5411 100644
--- a/test/interp.jl
+++ b/test/interp.jl
@@ -39,5 +39,12 @@ end
 
     @test pdf(k2d, [0.5, 0.1]) ≈ pdf(k2d, [0.5; 0.1]) ≈ pdf(k2d, 0.5, 0.1) ≈ pdf(ik2d, 0.5, 0.1)
     @test pdf(k2d, [0.5 1.; 0.1 1.]) ≈ [pdf(ik2d, 0.5, 0.1), pdf(ik2d, 1., 1.)]
-    @test pdf(k2d, [0.5; 1. ;;; 0.1; 1.]) ≈ [pdf(ik2d, 0.5, 1.) pdf(ik2d, 0.1, 1.)]
+    @static if VERSION >= v"1.1"
+        @test pdf(k2d, [0.5; 1. ;;; 0.1; 1.]) ≈ [pdf(ik2d, 0.5, 1.) pdf(ik2d, 0.1, 1.)]
+    else
+        M = zeros(2, 1, 2)
+        M[:,1,1] .= [0.5, 1]
+        M[:,1,2] .= [0.1, 1]
+        @test pdf(k2d, M) ≈ [pdf(ik2d, 0.5, 1.) pdf(ik2d, 0.1, 1.)]
+    end
 end