forked from JuliaGaussianProcesses/KernelFunctions.jl
-
Notifications
You must be signed in to change notification settings - Fork 1
/
test_kernels.jl
161 lines (159 loc) · 6.29 KB
/
test_kernels.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
using Test
using LinearAlgebra
using KernelFunctions
using SpecialFunctions
x = rand()*2; v1 = rand(3); v2 = rand(3); id = IdentityTransform()
@testset "Kappa functions of kernels" begin
@testset "Constant" begin
@testset "ZeroKernel" begin
k = ZeroKernel()
@test eltype(k) == Any
@test kappa(k,2.0) == 0.0
end
@testset "WhiteKernel" begin
k = WhiteKernel()
@test eltype(k) == Any
@test kappa(k,1.0) == 1.0
@test kappa(k,0.0) == 0.0
end
@testset "ConstantKernel" begin
c = 2.0
k = ConstantKernel(c)
@test eltype(k) == Any
@test kappa(k,1.0) == c
@test kappa(k,0.5) == c
end
end
@testset "Exponential" begin
@testset "SqExponentialKernel" begin
k = SqExponentialKernel()
@test kappa(k,x) ≈ exp(-x)
@test k(v1,v2) ≈ exp(-norm(v1-v2)^2)
@test kappa(SqExponentialKernel(),x) == kappa(k,x)
# l = 0.5
# k = SqExponentialKernel(l)
# @test k(v1,v2) ≈ exp(-l^2*norm(v1-v2)^2)
# v = rand(3)
# k = SqExponentialKernel(v)
# @test k(v1,v2) ≈ exp(-norm(v.*(v1-v2))^2)
end
@testset "ExponentialKernel" begin
k = ExponentialKernel()
@test kappa(k,x) ≈ exp(-x)
@test k(v1,v2) ≈ exp(-norm(v1-v2))
@test kappa(ExponentialKernel(),x) == kappa(k,x)
# l = 0.5
# k = ExponentialKernel(l)
# @test k(v1,v2) ≈ exp(-l*norm(v1-v2))
# v = rand(3)
# k = ExponentialKernel(v)
# @test k(v1,v2) ≈ exp(-norm(v.*(v1-v2)))
end
@testset "GammaExponentialKernel" begin
k = GammaExponentialKernel(2.0)
@test kappa(k,x) ≈ exp(-(x)^(k.γ))
@test k(v1,v2) ≈ exp(-norm(v1-v2)^(2k.γ))
@test kappa(GammaExponentialKernel(),x) == kappa(k,x)
# l = 0.5
# k = GammaExponentialKernel(l,1.5)
# @test k(v1,v2) ≈ exp(-l^(3.0)*norm(v1-v2)^(3.0))
# v = rand(3)
# k = GammaExponentialKernel(v,3.0)
# @test k(v1,v2) ≈ exp(-norm(v.*(v1-v2)).^6.0)
#Coherence :
@test KernelFunctions._kernel(GammaExponentialKernel(1.0),v1,v2) ≈ KernelFunctions._kernel(SqExponentialKernel(),v1,v2)
@test KernelFunctions._kernel(GammaExponentialKernel(0.5),v1,v2) ≈ KernelFunctions._kernel(ExponentialKernel(),v1,v2)
end
end
@testset "Exponentiated" begin
@testset "ExponentiatedKernel" begin
k = ExponentiatedKernel()
@test kappa(k,x) ≈ exp(x)
@test kappa(k,-x) ≈ exp(-x)
@test k(v1,v2) ≈ exp(dot(v1,v2))
end
end
@testset "Matern" begin
@testset "MaternKernel" begin
ν = 2.0
k = MaternKernel(ν)
matern(x,ν) = 2^(1-ν)/gamma(ν)*(sqrt(2ν)*x)^ν*besselk(ν,sqrt(2ν)*x)
@test kappa(k,x) ≈ matern(x,ν)
@test kappa(k,0.0) == 1.0
@test kappa(MaternKernel(ν),x) == kappa(k,x)
end
@testset "Matern32Kernel" begin
k = Matern32Kernel()
@test kappa(k,x) ≈ (1+sqrt(3)*x)exp(-sqrt(3)*x)
@test k(v1,v2) ≈ (1+sqrt(3)*norm(v1-v2))exp(-sqrt(3)*norm(v1-v2))
@test kappa(Matern32Kernel(),x) == kappa(k,x)
end
@testset "Matern52Kernel" begin
k = Matern52Kernel()
@test kappa(k,x) ≈ (1+sqrt(5)*x+5/3*x^2)exp(-sqrt(5)*x)
@test k(v1,v2) ≈ (1+sqrt(5)*norm(v1-v2)+5/3*norm(v1-v2)^2)exp(-sqrt(5)*norm(v1-v2))
@test kappa(Matern52Kernel(),x) == kappa(k,x)
end
@testset "Coherence Materns" begin
@test kappa(MaternKernel(0.5),x) ≈ kappa(ExponentialKernel(),x)
@test kappa(MaternKernel(1.5),x) ≈ kappa(Matern32Kernel(),x)
@test kappa(MaternKernel(2.5),x) ≈ kappa(Matern52Kernel(),x)
end
end
@testset "Polynomial" begin
c = randn();
@testset "LinearKernel" begin
k = LinearKernel()
@test kappa(k,x) ≈ x
@test k(v1,v2) ≈ dot(v1,v2)
@test kappa(LinearKernel(),x) == kappa(k,x)
end
@testset "PolynomialKernel" begin
k = PolynomialKernel()
@test kappa(k,x) ≈ x^2
@test k(v1,v2) ≈ dot(v1,v2)^2
@test kappa(PolynomialKernel(),x) == kappa(k,x)
#Coherence test
@test kappa(PolynomialKernel(1.0,c),x) ≈ kappa(LinearKernel(c),x)
end
end
@testset "RationalQuadratic" begin
@testset "RationalQuadraticKernel" begin
k = RationalQuadraticKernel()
@test kappa(k,x) ≈ (1.0+x/2.0)^-2
@test k(v1,v2) ≈ (1.0+norm(v1-v2)^2/2.0)^-2
@test kappa(RationalQuadraticKernel(),x) == kappa(k,x)
end
@testset "GammaRationalQuadraticKernel" begin
k = GammaRationalQuadraticKernel()
@test kappa(k,x) ≈ (1.0+x^2.0/2.0)^-2
@test k(v1,v2) ≈ (1.0+norm(v1-v2)^4.0/2.0)^-2
@test kappa(GammaRationalQuadraticKernel(),x) == kappa(k,x)
a = 1.0 + rand()
#Coherence test
@test kappa(GammaRationalQuadraticKernel(a,1.0),x) ≈ kappa(RationalQuadraticKernel(a),x)
end
end
@testset "Transformed/Scaled Kernel" begin
s = rand()
k = SqExponentialKernel()
kt = KernelFunctions.TransformedKernel(k,ScaleTransform(s))
ks = KernelFunctions.ScaledKernel(k,s)
@test KernelFunctions.kappa(kt,v1,v2) == KernelFunctions.kappa(KernelFunctions.transform(k,ScaleTransform(s)),v1,v2)
@test KernelFunctions.metric(kt) == KernelFunctions.metric(k)
@test kappa(ks,x) == s*kappa(k,x)
@test kappa(ks,x) == kappa(s*k,x)
end
@testset "KernelCombinations" begin
k1 = LinearKernel()
k2 = SqExponentialKernel()
X = rand(2,2)
@testset "KernelSum" begin
k = k1 + k2
@test KernelFunctions.metric(k) == [KernelFunctions.DotProduct(),KernelFunctions.SqEuclidean()]
@test length(k) == 2
end
@testset "KernelProduct" begin
end
end
end