From 1889f7d60b9a94f3e23d24120f2b13d26d06ea9a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 25 Oct 2022 17:15:32 +0200
Subject: [PATCH 01/14] Stable version of product and test

---
 src/kernels/kernelproduct.jl  | 5 ++++-
 test/kernels/kernelproduct.jl | 4 ++++
 2 files changed, 8 insertions(+), 1 deletion(-)

diff --git a/src/kernels/kernelproduct.jl b/src/kernels/kernelproduct.jl
index 990b4a1bb..c95c1126e 100644
--- a/src/kernels/kernelproduct.jl
+++ b/src/kernels/kernelproduct.jl
@@ -45,8 +45,11 @@ Base.length(k::KernelProduct) = length(k.kernels)
 
 (κ::KernelProduct)(x, y) = prod(k(x, y) for k in κ.kernels)
 
+_hadamard(f::Tf, x::Tuple) where {Tf} = f(first(x)) .* _hadamard(f, Base.tail(x))
+_hadamard(f::Tf, x::Tuple{Tx}) where {Tf,Tx} = f(only(x))
+
 function kernelmatrix(κ::KernelProduct, x::AbstractVector)
-    return reduce(hadamard, kernelmatrix(k, x) for k in κ.kernels)
+    return _hadamard(Base.Fix2(kernelmatrix, x), κ.kernels)
 end
 
 function kernelmatrix(κ::KernelProduct, x::AbstractVector, y::AbstractVector)
diff --git a/test/kernels/kernelproduct.jl b/test/kernels/kernelproduct.jl
index 1c50d52d9..a05da5f91 100644
--- a/test/kernels/kernelproduct.jl
+++ b/test/kernels/kernelproduct.jl
@@ -19,4 +19,8 @@
         KernelProduct(SqExponentialKernel(), LinearKernel(; c=c))
     end
     test_params(k1 * k2, (k1, k2))
+
+    nested_k = RBFKernel() * ((LinearKernel() + CosineKernel() * RBFKernel()) ∘ SelectTransform(1))
+    x = RowVecs(rand(10, 2))
+    @test (@inferred kernelmatrix(nested_k, x)) isa Matrix{Float64}
 end

From 530fce700251f78be5899128da6a80cd75ffc8dd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 25 Oct 2022 17:44:14 +0200
Subject: [PATCH 02/14] Cleanup

---
 src/kernels/kernelproduct.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/kernels/kernelproduct.jl b/src/kernels/kernelproduct.jl
index c95c1126e..fa4c40b4a 100644
--- a/src/kernels/kernelproduct.jl
+++ b/src/kernels/kernelproduct.jl
@@ -45,11 +45,11 @@ Base.length(k::KernelProduct) = length(k.kernels)
 
 (κ::KernelProduct)(x, y) = prod(k(x, y) for k in κ.kernels)
 
-_hadamard(f::Tf, x::Tuple) where {Tf} = f(first(x)) .* _hadamard(f, Base.tail(x))
-_hadamard(f::Tf, x::Tuple{Tx}) where {Tf,Tx} = f(only(x))
+_hadamard(f, ks::Tuple, x) = f(first(ks), x) .* _hadamard(f, Base.tail(ks), x)
+_hadamard(f, ks::Tuple{Tx}, x) where {Tx} = f(only(ks), x)
 
 function kernelmatrix(κ::KernelProduct, x::AbstractVector)
-    return _hadamard(Base.Fix2(kernelmatrix, x), κ.kernels)
+    return _hadamard(kernelmatrix, κ.kernels, x)
 end
 
 function kernelmatrix(κ::KernelProduct, x::AbstractVector, y::AbstractVector)

From 8de3e73404a21a52b73c7b8d6dbfeb0a157bebcd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 25 Oct 2022 17:48:16 +0200
Subject: [PATCH 03/14] Update test/kernels/kernelproduct.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 test/kernels/kernelproduct.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/test/kernels/kernelproduct.jl b/test/kernels/kernelproduct.jl
index a05da5f91..10bb8276f 100644
--- a/test/kernels/kernelproduct.jl
+++ b/test/kernels/kernelproduct.jl
@@ -20,7 +20,8 @@
     end
     test_params(k1 * k2, (k1, k2))
 
-    nested_k = RBFKernel() * ((LinearKernel() + CosineKernel() * RBFKernel()) ∘ SelectTransform(1))
+    nested_k =
+        RBFKernel() * ((LinearKernel() + CosineKernel() * RBFKernel()) ∘ SelectTransform(1))
     x = RowVecs(rand(10, 2))
     @test (@inferred kernelmatrix(nested_k, x)) isa Matrix{Float64}
 end

From e92e14fcce550b58bc615cf64456be53e5e27bba Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 25 Oct 2022 18:04:02 +0200
Subject: [PATCH 04/14] Bump version

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 4b68161dd..591d1f6ad 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "KernelFunctions"
 uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
-version = "0.10.48"
+version = "0.10.49"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"

From 68bde159f1380194c1cb6f63a514ee3207dd1751 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Sat, 29 Oct 2022 16:35:16 +0200
Subject: [PATCH 05/14] Generalize approach to all functions

---
 src/kernels/kernelproduct.jl | 10 ++++++----
 src/kernels/kernelsum.jl     | 12 ++++++------
 2 files changed, 12 insertions(+), 10 deletions(-)

diff --git a/src/kernels/kernelproduct.jl b/src/kernels/kernelproduct.jl
index fa4c40b4a..ce54b37b3 100644
--- a/src/kernels/kernelproduct.jl
+++ b/src/kernels/kernelproduct.jl
@@ -45,19 +45,21 @@ Base.length(k::KernelProduct) = length(k.kernels)
 
 (κ::KernelProduct)(x, y) = prod(k(x, y) for k in κ.kernels)
 
-_hadamard(f, ks::Tuple, x) = f(first(ks), x) .* _hadamard(f, Base.tail(ks), x)
-_hadamard(f, ks::Tuple{Tx}, x) where {Tx} = f(only(ks), x)
+_hadamard(f, ks::Tuple, args...) = f(first(ks), args...) .* _hadamard(f, Base.tail(ks), args...)
+_hadamard(f, ks::Tuple{Tx}, args...) where {Tx} = f(only(ks), args...)
+
+(κ::KernelProduct)(x, y) = _hadamard((k, x, y) -> k(x, y), κ.kernels, x, y)
 
 function kernelmatrix(κ::KernelProduct, x::AbstractVector)
     return _hadamard(kernelmatrix, κ.kernels, x)
 end
 
 function kernelmatrix(κ::KernelProduct, x::AbstractVector, y::AbstractVector)
-    return reduce(hadamard, kernelmatrix(k, x, y) for k in κ.kernels)
+    return _hadamard(kernelmatrix, κ.kernels, x, y)
 end
 
 function kernelmatrix_diag(κ::KernelProduct, x::AbstractVector)
-    return reduce(hadamard, kernelmatrix_diag(k, x) for k in κ.kernels)
+    return _hadamard(kernelmatrix_diag, κ.kernels, x, y)
 end
 
 function kernelmatrix_diag(κ::KernelProduct, x::AbstractVector, y::AbstractVector)
diff --git a/src/kernels/kernelsum.jl b/src/kernels/kernelsum.jl
index 2ca25370c..29966cb12 100644
--- a/src/kernels/kernelsum.jl
+++ b/src/kernels/kernelsum.jl
@@ -43,21 +43,21 @@ end
 
 Base.length(k::KernelSum) = length(k.kernels)
 
-_sum(f::Tf, x::Tuple) where {Tf} = f(x[1]) + _sum(f, Base.tail(x))
-_sum(f::Tf, x::Tuple{Tx}) where {Tf,Tx} = f(x[1])
+_sum(f, ks::Tuple, args...) = f(first(ks), args...) + _sum(f, Base.tail(ks). args...)
+_sum(f, ks::Tuple{Tx}, args...) where {Tx} = f(only(ks), args...)
 
-(κ::KernelSum)(x, y) = _sum(k -> k(x, y), κ.kernels)
+(κ::KernelSum)(x, y) = _sum((k, x, y) -> k(x, y), κ.kernels, x, y)
 
 function kernelmatrix(κ::KernelSum, x::AbstractVector)
-    return _sum(Base.Fix2(kernelmatrix, x), κ.kernels)
+    return _sum(kernelmatrix, κ.kernels, x)
 end
 
 function kernelmatrix(κ::KernelSum, x::AbstractVector, y::AbstractVector)
-    return _sum(k -> kernelmatrix(k, x, y), κ.kernels)
+    return _sum(kernelmatrix, κ.kernels, x, y)
 end
 
 function kernelmatrix_diag(κ::KernelSum, x::AbstractVector)
-    return _sum(Base.Fix2(kernelmatrix_diag, x), κ.kernels)
+    return _sum(k -> kernelmatrix_diag(k, x), κ.kernels)
 end
 
 function kernelmatrix_diag(κ::KernelSum, x::AbstractVector, y::AbstractVector)

From ff2ec8853ba5fa888f36e13beeac592ed3997cc6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Sat, 29 Oct 2022 18:15:49 +0200
Subject: [PATCH 06/14] Refactor TestUtils

---
 src/TestUtils.jl              | 150 ++++++++++++++++++++++------------
 src/kernels/kernelproduct.jl  |   4 +-
 src/kernels/kernelsum.jl      |   2 +-
 test/kernels/kernelproduct.jl |  10 +--
 test/kernels/kernelsum.jl     |  39 ++++-----
 test/runtests.jl              |   2 +-
 6 files changed, 120 insertions(+), 87 deletions(-)

diff --git a/src/TestUtils.jl b/src/TestUtils.jl
index 357375dbf..b746e7433 100644
--- a/src/TestUtils.jl
+++ b/src/TestUtils.jl
@@ -86,18 +86,94 @@ function test_interface(
     @test kernelmatrix_diag!(tmp_diag, k, x0, x1) ≈ kernelmatrix_diag(k, x0, x1)
 end
 
-function test_interface(
-    rng::AbstractRNG, k::Kernel, ::Type{Vector{T}}; kwargs...
+
+"""
+    test_interface([rng::AbstractRNG], k::Kernel, ::Type{T}=Float64; kwargs...) where {T}
+
+Run the [`test_interface`](@ref) tests for randomly generated inputs of types `Vector{T}`,
+`Vector{Vector{T}}`, `ColVecs{T}`, and `RowVecs{T}`.
+
+For other input types, please provide the data manually.
+
+The keyword arguments are forwarded to the invocations of [`test_interface`](@ref) with the
+randomly generated inputs.
+"""
+function test_interface(k::Kernel, T::Type=Float64; kwargs...)
+    return test_interface(Random.GLOBAL_RNG, k, T; kwargs...)
+end
+
+function test_interface(rng::AbstractRNG, k::Kernel, T::Type=Float64; kwargs...)
+    return test_with_type(test_interface, rng, k, T; kwargs...)
+end
+
+"""
+test_type_stability(
+    k::Kernel,
+    x0::AbstractVector,
+    x1::AbstractVector,
+    x2::AbstractVector
+)
+
+Run type stability checks over `k(x,y)` and the different functions of the API (`kernelmatrix`, `kernelmatrix_diag`).
+`x0` and `x1` should be of the same length with different values, while `x0` and `x2` should be of different lengths.
+"""
+function test_type_stability(k::Kernel, x0::AbstractVector, x1::AbstractVector, x2::AbstractVector)
+    # Ensure that we have the required inputs.
+    @assert length(x0) == length(x1)
+    @assert length(x0) ≠ length(x2)
+    # @test @inferred(k(first(x0), first(x1))) isa Real
+    @test @inferred(kernelmatrix(k, x0)) isa AbstractMatrix
+    @test @inferred(kernelmatrix(k, x0, x2)) isa AbstractMatrix
+    @test @inferred(kernelmatrix_diag(k, x0)) isa AbstractVector
+    @test @inferred(kernelmatrix_diag(k, x0, x1)) isa AbstractVector
+end
+
+function test_type_stability(k::Kernel, ::Type{T}=Float64; kwargs...) where {T}
+    return test_type_stability(Random.GLOBAL_RNG, k, T; kwargs...)
+end
+
+function test_type_stability(rng::AbstractRNG, k::Kernel, ::Type{T}; kwargs...) where {T}
+    return test_with_type(test_type_stability, rng, k, T; kwargs...)
+end
+
+"""
+    test_with_type(f, rng::AbstractRNG, k::Kernel, ::Type{T}; kwargs...) where {T<:Real}
+
+Run the functions `f`, (for example [`test_interface`](@ref) or [`test_type_stable`](@ref)) for randomly generated inputs of types `Vector{T}`,
+`Vector{Vector{T}}`, `ColVecs{T}`, and `RowVecs{T}`.
+
+For other input types, please provide the data manually.
+
+The keyword arguments are forwarded to the invocations of `f` with the
+randomly generated inputs.
+"""
+function test_with_type(f, rng::AbstractRNG, k::Kernel, ::Type{T}; kwargs...) where {T}
+    @testset "Vector{$T}" begin
+        test_with_type(f, rng, k, Vector{T}; kwargs...)
+    end
+    @testset "ColVecs{$T}" begin
+        test_with_type(f, rng, k, ColVecs{T}; kwargs...)
+    end
+    @testset "RowVecs{$T}" begin
+        test_with_type(f, rng, k, RowVecs{T}; kwargs...)
+    end
+    @testset "Vector{Vector{$T}}" begin
+        test_with_type(f, rng, k, Vector{Vector{T}}; kwargs...)
+    end
+end
+
+function test_with_type(
+    f, rng::AbstractRNG, k::Kernel, ::Type{Vector{T}}; kwargs...
 ) where {T<:Real}
-    return test_interface(
+    return f(
         k, randn(rng, T, 11), randn(rng, T, 11), randn(rng, T, 13); kwargs...
     )
 end
 
-function test_interface(
-    rng::AbstractRNG, k::MOKernel, ::Type{Vector{Tuple{T,Int}}}; dim_out=3, kwargs...
+function test_with_type(
+    f, rng::AbstractRNG, k::MOKernel, ::Type{Vector{Tuple{T,Int}}}; dim_out=3, kwargs...
 ) where {T<:Real}
-    return test_interface(
+    return f(
         k,
         [(randn(rng, T), rand(rng, 1:dim_out)) for i in 1:11],
         [(randn(rng, T), rand(rng, 1:dim_out)) for i in 1:11],
@@ -106,10 +182,10 @@ function test_interface(
     )
 end
 
-function test_interface(
-    rng::AbstractRNG, k::Kernel, ::Type{<:ColVecs{T}}; dim_in=2, kwargs...
+function test_with_type(
+    f, rng::AbstractRNG, k::Kernel, ::Type{<:ColVecs{T}}; dim_in=2, kwargs...
 ) where {T<:Real}
-    return test_interface(
+    return f(
         k,
         ColVecs(randn(rng, T, dim_in, 11)),
         ColVecs(randn(rng, T, dim_in, 11)),
@@ -118,10 +194,10 @@ function test_interface(
     )
 end
 
-function test_interface(
-    rng::AbstractRNG, k::Kernel, ::Type{<:RowVecs{T}}; dim_in=2, kwargs...
+function test_with_type(
+    f, rng::AbstractRNG, k::Kernel, ::Type{<:RowVecs{T}}; dim_in=2, kwargs...
 ) where {T<:Real}
-    return test_interface(
+    return f(
         k,
         RowVecs(randn(rng, T, 11, dim_in)),
         RowVecs(randn(rng, T, 11, dim_in)),
@@ -130,10 +206,10 @@ function test_interface(
     )
 end
 
-function test_interface(
-    rng::AbstractRNG, k::Kernel, ::Type{<:Vector{Vector{T}}}; dim_in=2, kwargs...
+function test_with_type(
+    f, rng::AbstractRNG, k::Kernel, ::Type{<:Vector{Vector{T}}}; dim_in=2, kwargs...
 ) where {T<:Real}
-    return test_interface(
+    return f(
         k,
         [randn(rng, T, dim_in) for _ in 1:11],
         [randn(rng, T, dim_in) for _ in 1:11],
@@ -142,8 +218,8 @@ function test_interface(
     )
 end
 
-function test_interface(rng::AbstractRNG, k::Kernel, ::Type{Vector{String}}; kwargs...)
-    return test_interface(
+function test_with_type(f, rng::AbstractRNG, k::Kernel, ::Type{Vector{String}}; kwargs...)
+    return f(
         k,
         [randstring(rng) for _ in 1:3],
         [randstring(rng) for _ in 1:3],
@@ -152,10 +228,10 @@ function test_interface(rng::AbstractRNG, k::Kernel, ::Type{Vector{String}}; kwa
     )
 end
 
-function test_interface(
-    rng::AbstractRNG, k::Kernel, ::Type{ColVecs{String}}; dim_in=2, kwargs...
+function test_with_type(
+    f, rng::AbstractRNG, k::Kernel, ::Type{ColVecs{String}}; dim_in=2, kwargs...
 )
-    return test_interface(
+    return f(
         k,
         ColVecs([randstring(rng) for _ in 1:dim_in, _ in 1:3]),
         ColVecs([randstring(rng) for _ in 1:dim_in, _ in 1:3]),
@@ -164,38 +240,8 @@ function test_interface(
     )
 end
 
-function test_interface(k::Kernel, T::Type{<:AbstractVector}; kwargs...)
-    return test_interface(Random.GLOBAL_RNG, k, T; kwargs...)
-end
-
-"""
-    test_interface([rng::AbstractRNG], k::Kernel, ::Type{T}; kwargs...) where {T<:Real}
-
-Run the [`test_interface`](@ref) tests for randomly generated inputs of types `Vector{T}`,
-`Vector{Vector{T}}`, `ColVecs{T}`, and `RowVecs{T}`.
-
-For other input types, please provide the data manually.
-
-The keyword arguments are forwarded to the invocations of [`test_interface`](@ref) with the
-randomly generated inputs.
-"""
-function test_interface(rng::AbstractRNG, k::Kernel, ::Type{T}; kwargs...) where {T<:Real}
-    @testset "Vector{$T}" begin
-        test_interface(rng, k, Vector{T}; kwargs...)
-    end
-    @testset "ColVecs{$T}" begin
-        test_interface(rng, k, ColVecs{T}; kwargs...)
-    end
-    @testset "RowVecs{$T}" begin
-        test_interface(rng, k, RowVecs{T}; kwargs...)
-    end
-    @testset "Vector{Vector{T}}" begin
-        test_interface(rng, k, Vector{Vector{T}}; kwargs...)
-    end
-end
-
-function test_interface(k::Kernel, T::Type{<:Real}=Float64; kwargs...)
-    return test_interface(Random.GLOBAL_RNG, k, T; kwargs...)
+function test_with_type(f, k::Kernel, T::Type{<:Real}; kwargs...)
+    return test_with_type(f, Random.GLOBAL_RNG, k, T; kwargs...)
 end
 
 """
diff --git a/src/kernels/kernelproduct.jl b/src/kernels/kernelproduct.jl
index ce54b37b3..7a42725fe 100644
--- a/src/kernels/kernelproduct.jl
+++ b/src/kernels/kernelproduct.jl
@@ -59,11 +59,11 @@ function kernelmatrix(κ::KernelProduct, x::AbstractVector, y::AbstractVector)
 end
 
 function kernelmatrix_diag(κ::KernelProduct, x::AbstractVector)
-    return _hadamard(kernelmatrix_diag, κ.kernels, x, y)
+    return _hadamard(kernelmatrix_diag, κ.kernels, x)
 end
 
 function kernelmatrix_diag(κ::KernelProduct, x::AbstractVector, y::AbstractVector)
-    return reduce(hadamard, kernelmatrix_diag(k, x, y) for k in κ.kernels)
+    return _hadamard(kernelmatrix_diag, κ.kernels, x, y)
 end
 
 function Base.show(io::IO, κ::KernelProduct)
diff --git a/src/kernels/kernelsum.jl b/src/kernels/kernelsum.jl
index 29966cb12..51199b3e8 100644
--- a/src/kernels/kernelsum.jl
+++ b/src/kernels/kernelsum.jl
@@ -43,7 +43,7 @@ end
 
 Base.length(k::KernelSum) = length(k.kernels)
 
-_sum(f, ks::Tuple, args...) = f(first(ks), args...) + _sum(f, Base.tail(ks). args...)
+_sum(f, ks::Tuple, args...) = f(first(ks), args...) + _sum(f, Base.tail(ks), args...)
 _sum(f, ks::Tuple{Tx}, args...) where {Tx} = f(only(ks), args...)
 
 (κ::KernelSum)(x, y) = _sum((k, x, y) -> k(x, y), κ.kernels, x, y)
diff --git a/test/kernels/kernelproduct.jl b/test/kernels/kernelproduct.jl
index 10bb8276f..b2cdea042 100644
--- a/test/kernels/kernelproduct.jl
+++ b/test/kernels/kernelproduct.jl
@@ -10,8 +10,8 @@
     )
 
     # Standardised tests.
-    TestUtils.test_interface(k, Float64)
-    TestUtils.test_interface(ConstantKernel(; c=1.0) * WhiteKernel(), Vector{String})
+    test_interface(k, Float64)
+    test_interface(ConstantKernel(; c=1.0) * WhiteKernel(), Vector{String})
     test_ADs(
         x -> KernelProduct(SqExponentialKernel(), LinearKernel(; c=exp(x[1]))), rand(1)
     )
@@ -20,8 +20,6 @@
     end
     test_params(k1 * k2, (k1, k2))
 
-    nested_k =
-        RBFKernel() * ((LinearKernel() + CosineKernel() * RBFKernel()) ∘ SelectTransform(1))
-    x = RowVecs(rand(10, 2))
-    @test (@inferred kernelmatrix(nested_k, x)) isa Matrix{Float64}
+    nested_k = RBFKernel() * (LinearKernel() + CosineKernel() * RBFKernel())
+    test_type_stability(nested_k)
 end
diff --git a/test/kernels/kernelsum.jl b/test/kernels/kernelsum.jl
index 716343ef7..11ae1dcd2 100644
--- a/test/kernels/kernelsum.jl
+++ b/test/kernels/kernelsum.jl
@@ -4,39 +4,28 @@
     k = KernelSum(k1, k2)
     @test k == KernelSum([k1, k2]) == KernelSum((k1, k2))
     @test length(k) == 2
-    @test string(k) == (
+    @test repr(k) == (
         "Sum of 2 kernels:\n" *
         "\tLinear Kernel (c = 0.0)\n" *
         "\tSquared Exponential Kernel (metric = Euclidean(0.0))"
     )
 
     # Standardised tests.
-    TestUtils.test_interface(k, Float64)
-    TestUtils.test_interface(ConstantKernel(; c=1.5) * WhiteKernel(), Vector{String})
-    test_ADs(x -> KernelSum(SqExponentialKernel(), LinearKernel(; c=exp(x[1]))), rand(1))
-    test_interface_ad_perf(2.4, StableRNG(123456)) do c
-        KernelSum(SqExponentialKernel(), LinearKernel(; c=c))
-    end
+    test_interface(k, Float64)
+    test_interface(ConstantKernel(; c=1.5) + WhiteKernel(), Vector{String})
+    # test_ADs(x -> KernelSum(SqExponentialKernel(), LinearKernel(; c=exp(x[1]))), rand(1))
+    # test_interface_ad_perf(2.4, StableRNG(123456)) do c
+        # KernelSum(SqExponentialKernel(), LinearKernel(; c=c))
+    # end
 
-    test_params(k1 + k2, (k1, k2))
+    # test_params(k1 + k2, (k1, k2))
 
     # Regression tests for https://github.com//issues/458
-    @testset "Type stability" begin
-        function check_type_stability(k)
-            @test (@inferred k(0.1, 0.2)) isa Real
-            x = rand(10)
-            y = rand(10)
-            @test (@inferred kernelmatrix(k, x)) isa Matrix{<:Real}
-            @test (@inferred kernelmatrix(k, x, y)) isa Matrix{<:Real}
-            @test (@inferred kernelmatrix_diag(k, x)) isa Vector{<:Real}
-            @test (@inferred kernelmatrix_diag(k, x, y)) isa Vector{<:Real}
-        end
-        @testset for k in (
-            RBFKernel() + RBFKernel() * LinearKernel(),
-            RBFKernel() + RBFKernel() * ExponentialKernel(),
-            RBFKernel() * (LinearKernel() + ExponentialKernel()),
-        )
-            check_type_stability(k)
-        end
+    @testset for k in (
+        RBFKernel() + RBFKernel() * LinearKernel(),
+        RBFKernel() + RBFKernel() * ExponentialKernel(),
+        RBFKernel() * (LinearKernel() + ExponentialKernel()),
+    )
+        test_type_stability(k)
     end
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index dd6eb2d8a..0fe962648 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -20,7 +20,7 @@ using Compat: only
 
 using KernelFunctions: SimpleKernel, metric, kappa, ColVecs, RowVecs, TestUtils
 
-using KernelFunctions.TestUtils: test_interface, example_inputs
+using KernelFunctions.TestUtils: test_interface, test_type_stability, example_inputs
 
 # The GROUP is used to run different sets of tests in parallel on the GitHub Actions CI.
 # If you want to introduce a new group, ensure you also add it to .github/workflows/ci.yml

From 6bcd8cd8f906f1c2e0d636ef9538f8c6ad9e3dab Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Sat, 29 Oct 2022 18:17:04 +0200
Subject: [PATCH 07/14] Uncomment tests

---
 test/kernels/kernelsum.jl | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/test/kernels/kernelsum.jl b/test/kernels/kernelsum.jl
index 11ae1dcd2..cfe239717 100644
--- a/test/kernels/kernelsum.jl
+++ b/test/kernels/kernelsum.jl
@@ -13,12 +13,12 @@
     # Standardised tests.
     test_interface(k, Float64)
     test_interface(ConstantKernel(; c=1.5) + WhiteKernel(), Vector{String})
-    # test_ADs(x -> KernelSum(SqExponentialKernel(), LinearKernel(; c=exp(x[1]))), rand(1))
-    # test_interface_ad_perf(2.4, StableRNG(123456)) do c
-        # KernelSum(SqExponentialKernel(), LinearKernel(; c=c))
-    # end
+    test_ADs(x -> KernelSum(SqExponentialKernel(), LinearKernel(; c=exp(x[1]))), rand(1))
+    test_interface_ad_perf(2.4, StableRNG(123456)) do c
+        KernelSum(SqExponentialKernel(), LinearKernel(; c=c))
+    end
 
-    # test_params(k1 + k2, (k1, k2))
+    test_params(k1 + k2, (k1, k2))
 
     # Regression tests for https://github.com//issues/458
     @testset for k in (

From 1baa148576dddccdb5b36f691a75897562bd8b3c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Sat, 29 Oct 2022 18:17:41 +0200
Subject: [PATCH 08/14] Update src/TestUtils.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 src/TestUtils.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/TestUtils.jl b/src/TestUtils.jl
index b746e7433..811e3e461 100644
--- a/src/TestUtils.jl
+++ b/src/TestUtils.jl
@@ -86,7 +86,6 @@ function test_interface(
     @test kernelmatrix_diag!(tmp_diag, k, x0, x1) ≈ kernelmatrix_diag(k, x0, x1)
 end
 
-
 """
     test_interface([rng::AbstractRNG], k::Kernel, ::Type{T}=Float64; kwargs...) where {T}
 

From 2bb2c5d370c44ccb8bfe534620d5f7fe053bb4e4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Sat, 29 Oct 2022 18:17:51 +0200
Subject: [PATCH 09/14] Update src/kernels/kernelproduct.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 src/kernels/kernelproduct.jl | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/kernels/kernelproduct.jl b/src/kernels/kernelproduct.jl
index 7a42725fe..a99a455f8 100644
--- a/src/kernels/kernelproduct.jl
+++ b/src/kernels/kernelproduct.jl
@@ -45,7 +45,9 @@ Base.length(k::KernelProduct) = length(k.kernels)
 
 (κ::KernelProduct)(x, y) = prod(k(x, y) for k in κ.kernels)
 
-_hadamard(f, ks::Tuple, args...) = f(first(ks), args...) .* _hadamard(f, Base.tail(ks), args...)
+function _hadamard(f, ks::Tuple, args...)
+    return f(first(ks), args...) .* _hadamard(f, Base.tail(ks), args...)
+end
 _hadamard(f, ks::Tuple{Tx}, args...) where {Tx} = f(only(ks), args...)
 
 (κ::KernelProduct)(x, y) = _hadamard((k, x, y) -> k(x, y), κ.kernels, x, y)

From e32c368e01a77dc7bb5f54e4002a4f08c96f1abc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Sat, 29 Oct 2022 18:18:09 +0200
Subject: [PATCH 10/14] Update src/TestUtils.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 src/TestUtils.jl | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/src/TestUtils.jl b/src/TestUtils.jl
index 811e3e461..293a7bed0 100644
--- a/src/TestUtils.jl
+++ b/src/TestUtils.jl
@@ -164,9 +164,7 @@ end
 function test_with_type(
     f, rng::AbstractRNG, k::Kernel, ::Type{Vector{T}}; kwargs...
 ) where {T<:Real}
-    return f(
-        k, randn(rng, T, 11), randn(rng, T, 11), randn(rng, T, 13); kwargs...
-    )
+    return f(k, randn(rng, T, 11), randn(rng, T, 11), randn(rng, T, 13); kwargs...)
 end
 
 function test_with_type(

From 9401778e240fddbec0ebe0136346cb63ee1a1097 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Sat, 29 Oct 2022 18:18:21 +0200
Subject: [PATCH 11/14] Update src/TestUtils.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 src/TestUtils.jl | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/TestUtils.jl b/src/TestUtils.jl
index 293a7bed0..f898e9079 100644
--- a/src/TestUtils.jl
+++ b/src/TestUtils.jl
@@ -116,7 +116,9 @@ test_type_stability(
 Run type stability checks over `k(x,y)` and the different functions of the API (`kernelmatrix`, `kernelmatrix_diag`).
 `x0` and `x1` should be of the same length with different values, while `x0` and `x2` should be of different lengths.
 """
-function test_type_stability(k::Kernel, x0::AbstractVector, x1::AbstractVector, x2::AbstractVector)
+function test_type_stability(
+    k::Kernel, x0::AbstractVector, x1::AbstractVector, x2::AbstractVector
+)
     # Ensure that we have the required inputs.
     @assert length(x0) == length(x1)
     @assert length(x0) ≠ length(x2)

From 25798dc4864155e7cecb6a73f6a35fd32e5dd8ba Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 1 Nov 2022 13:14:08 +0100
Subject: [PATCH 12/14] Fix formatting and missing definition in kernel sum

---
 src/TestUtils.jl         | 18 +++++++++---------
 src/kernels/kernelsum.jl |  5 +++--
 2 files changed, 12 insertions(+), 11 deletions(-)

diff --git a/src/TestUtils.jl b/src/TestUtils.jl
index f898e9079..b76b8279a 100644
--- a/src/TestUtils.jl
+++ b/src/TestUtils.jl
@@ -106,15 +106,16 @@ function test_interface(rng::AbstractRNG, k::Kernel, T::Type=Float64; kwargs...)
 end
 
 """
-test_type_stability(
-    k::Kernel,
-    x0::AbstractVector,
-    x1::AbstractVector,
-    x2::AbstractVector
-)
+    test_type_stability(
+        k::Kernel,
+        x0::AbstractVector,
+        x1::AbstractVector,
+        x2::AbstractVector,
+    )
 
-Run type stability checks over `k(x,y)` and the different functions of the API (`kernelmatrix`, `kernelmatrix_diag`).
-`x0` and `x1` should be of the same length with different values, while `x0` and `x2` should be of different lengths.
+Run type stability checks over `k(x,y)` and the different functions of the API 
+(`kernelmatrix`, `kernelmatrix_diag`). `x0` and `x1` should be of the same 
+length with different values, while `x0` and `x2` should be of different lengths.
 """
 function test_type_stability(
     k::Kernel, x0::AbstractVector, x1::AbstractVector, x2::AbstractVector
@@ -122,7 +123,6 @@ function test_type_stability(
     # Ensure that we have the required inputs.
     @assert length(x0) == length(x1)
     @assert length(x0) ≠ length(x2)
-    # @test @inferred(k(first(x0), first(x1))) isa Real
     @test @inferred(kernelmatrix(k, x0)) isa AbstractMatrix
     @test @inferred(kernelmatrix(k, x0, x2)) isa AbstractMatrix
     @test @inferred(kernelmatrix_diag(k, x0)) isa AbstractVector
diff --git a/src/kernels/kernelsum.jl b/src/kernels/kernelsum.jl
index 51199b3e8..3b0f1b5cd 100644
--- a/src/kernels/kernelsum.jl
+++ b/src/kernels/kernelsum.jl
@@ -48,6 +48,7 @@ _sum(f, ks::Tuple{Tx}, args...) where {Tx} = f(only(ks), args...)
 
 (κ::KernelSum)(x, y) = _sum((k, x, y) -> k(x, y), κ.kernels, x, y)
 
+
 function kernelmatrix(κ::KernelSum, x::AbstractVector)
     return _sum(kernelmatrix, κ.kernels, x)
 end
@@ -57,11 +58,11 @@ function kernelmatrix(κ::KernelSum, x::AbstractVector, y::AbstractVector)
 end
 
 function kernelmatrix_diag(κ::KernelSum, x::AbstractVector)
-    return _sum(k -> kernelmatrix_diag(k, x), κ.kernels)
+    return _sum(kernelmatrix_diag, κ.kernels, x)
 end
 
 function kernelmatrix_diag(κ::KernelSum, x::AbstractVector, y::AbstractVector)
-    return _sum(k -> kernelmatrix_diag(k, x, y), κ.kernels)
+    return _sum(kernelmatrix_diag, κ.kernels, x, y)
 end
 
 function Base.show(io::IO, κ::KernelSum)

From ecd055658775f6a6eab49df2d3cc3a38a71d622c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 1 Nov 2022 13:15:31 +0100
Subject: [PATCH 13/14] Additional formatting

---
 src/TestUtils.jl | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/TestUtils.jl b/src/TestUtils.jl
index b76b8279a..cd14ec718 100644
--- a/src/TestUtils.jl
+++ b/src/TestUtils.jl
@@ -138,9 +138,10 @@ function test_type_stability(rng::AbstractRNG, k::Kernel, ::Type{T}; kwargs...)
 end
 
 """
-    test_with_type(f, rng::AbstractRNG, k::Kernel, ::Type{T}; kwargs...) where {T<:Real}
+    test_with_type(f, rng::AbstractRNG, k::Kernel, ::Type{T}; kwargs...) where {T}
 
-Run the functions `f`, (for example [`test_interface`](@ref) or [`test_type_stable`](@ref)) for randomly generated inputs of types `Vector{T}`,
+Run the functions `f`, (for example [`test_interface`](@ref) or
+[`test_type_stable`](@ref)) for randomly generated inputs of types `Vector{T}`,
 `Vector{Vector{T}}`, `ColVecs{T}`, and `RowVecs{T}`.
 
 For other input types, please provide the data manually.

From f647b40eebf97aa058f679f8758429ffa2c15cec Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Tue, 1 Nov 2022 13:16:16 +0100
Subject: [PATCH 14/14]  Moar formatting

---
 src/kernels/kernelsum.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/kernels/kernelsum.jl b/src/kernels/kernelsum.jl
index 3b0f1b5cd..77709502c 100644
--- a/src/kernels/kernelsum.jl
+++ b/src/kernels/kernelsum.jl
@@ -48,7 +48,6 @@ _sum(f, ks::Tuple{Tx}, args...) where {Tx} = f(only(ks), args...)
 
 (κ::KernelSum)(x, y) = _sum((k, x, y) -> k(x, y), κ.kernels, x, y)
 
-
 function kernelmatrix(κ::KernelSum, x::AbstractVector)
     return _sum(kernelmatrix, κ.kernels, x)
 end