[Tests] Large refactor and upgrade of the testing framework. (#232)

* Commit every changes availiables...

* let's comit everything before having issuesw with it

* Restore specific tests

* restore tests

* bugfix

src/SubsetCopula.jl

@@ -64,7 +64,7 @@ end
 function SubsetCopula(C::FGMCopula{d,Tθ}, dims::Tuple{Int64, Int64}) where {d,Tθ}
     i = 1
     for indices in Combinatorics.combinations(1:d, 2)
-        all(indices .∈ dims) && return FGMCopula(2,C.θ[i])
+        all(indices .∈ Ref(dims)) && return FGMCopula(2,C.θ[i])
         i = i+1
     end
     @error("Somethings wrong...")

test/ArchimedeanCopulas.jl

@@ -0,0 +1,115 @@
+
+@testitem "Archimedeans - Fix sampled values" begin
+    using Random, Distributions
+    using StableRNGs
+    rng = StableRNG(123)
+    @test rand(rng, AMHCopula(3,0.6)          ) ≈ [0.6100194232653313, 0.2812460189425596, 0.10333020320732342]
+    @test rand(rng, AMHCopula(4,-0.3)         ) ≈ [0.6794797200689908, 0.2392452398851621, 0.6025427563179961, 0.2844305227337651]
+    @test rand(rng, ClaytonCopula(2,-0.7)     ) ≈ [0.6275520653528824, 0.163616179546588]
+    @test rand(rng, ClaytonCopula(3,-0.1)     ) ≈ [0.3881011762518264, 0.5656986324924199, 0.2940237224994986]
+    @test rand(rng, ClaytonCopula(4,7)        ) ≈ [0.4939026426425556, 0.5327344049793008, 0.508779929573844, 0.458289642358837]
+    @test rand(rng, FrankCopula(2,-5)         ) ≈ [0.7336303867890769, 0.19556711408763564]
+    @test rand(rng, FrankCopula(3,12)         ) ≈ [0.705387567921179, 0.8641668940713177, 0.815244058863104]
+    @test rand(rng, FrankCopula(4,6)          ) ≈ [0.9003228944757687, 0.8260436103707566, 0.9133247903512886, 0.7994891654043613]
+    @test rand(rng, FrankCopula(4,30)         ) ≈ [0.3923476356094088, 0.4382518570496335, 0.39700820876188975, 0.3908555957587312]
+    @test rand(rng, FrankCopula(4,37)         ) ≈ [0.7303681473348445, 0.6898271742903759, 0.7264896311455771, 0.7294073988977854]
+    @test rand(rng, FrankCopula(4,150)        ) ≈ [0.43642655973527883, 0.42188653827683725, 0.41316130988739547, 0.42762193255859465]
+    @test rand(rng, JoeCopula(3,7)            ) ≈ [0.5527859698950577, 0.5839844253671289, 0.6067932545327556]
+    @test rand(rng, GumbelCopula(4,7)         ) ≈ [0.781761681793509, 0.7444203095073173, 0.8307664734410207, 0.7495821288234644]
+    @test rand(rng, GumbelCopula(4,20)        ) ≈ [0.5482947180691102, 0.5460490383319109, 0.5159827606532166, 0.6002166337095293]
+    @test rand(rng, GumbelCopula(4,100)       ) ≈ [0.8199684741926241, 0.81488028576667, 0.8161867411368382, 0.8187239187339411]
+    @test rand(rng, GumbelBarnettCopula(3,0.7)) ≈ [0.33125926946816414, 0.31478129636784674, 0.48594013921379653]
+    @test rand(rng, InvGaussianCopula(4,0.05) ) ≈ [0.4777472572394352, 0.5714072783562308, 0.8312697205666382, 0.5291602862226205]
+    @test rand(rng, InvGaussianCopula(3,8)    ) ≈ [0.5325775326824974, 0.4876131855666078, 0.5207906451760111]
+end
+
+@testitem "Archimedean - Fix Kendall correlation" begin
+    using Random
+    using StableRNGs
+    rng = StableRNG(123)
+
+    @test Copulas.Debye(0.5,1) ≈ 0.8819271567906056
+    @test Copulas.τ⁻¹(FrankCopula, 0.6) ≈ 7.929642284264058
+    @test Copulas.τ⁻¹(GumbelCopula, 0.5) ≈ 2.
+    @test Copulas.τ⁻¹(ClaytonCopula, 1/3) ≈ 1.
+    @test Copulas.τ⁻¹(AMHCopula, 1/4) ≈ 0.8384520912688538
+    @test Copulas.τ⁻¹(AMHCopula, 0.) ≈ 0.
+    @test Copulas.τ⁻¹(AMHCopula, 1/3+0.0001) ≈ 1.
+    @test Copulas.τ⁻¹(AMHCopula, -2/11) ≈ -1.
+    @test Copulas.τ⁻¹(AMHCopula, -0.1505) ≈ -0.8 atol=1.0e-3
+    @test Copulas.τ⁻¹(FrankCopula, -0.3881) ≈ -4. atol=1.0e-3
+    @test Copulas.τ⁻¹(ClaytonCopula, -1/3) ≈ -.5 atol=1.0e-5
+end
+
+@testitem "Archimedeans - Fix Spearman correlation" begin
+
+    @test Copulas.ρ(ClaytonCopula(2,3.)) ≈ 0.78645 atol=1.0e-4
+    @test Copulas.ρ(ClaytonCopula(2,0.001)) ≈ 0. atol=1.0e-2
+    @test Copulas.ρ(GumbelCopula(2,3.)) ≈ 0.8489 atol=1.0e-4
+
+    @test_broken Copulas.ρ⁻¹(ClaytonCopula, 1/3) ≈ 0.58754 atol=1.0e-5
+    @test_broken Copulas.ρ⁻¹(ClaytonCopula, 0.01) ≈ 0. atol=1.0e-1
+    @test_broken Copulas.ρ⁻¹(ClaytonCopula, -0.4668) ≈ -.5 atol=1.0e-3
+
+    @test_broken Copulas.ρ⁻¹(GumbelCopula, 0.5) ≈ 1.5410704204332681
+    @test_broken Copulas.ρ⁻¹(GumbelCopula, 0.0001) == 1.
+
+    @test_broken Copulas.ρ⁻¹(FrankCopula, 1/3) ≈ 2.116497 atol=1.0e-5
+    @test_broken Copulas.ρ⁻¹(FrankCopula, -0.5572) ≈ -4. atol=1.0e-3
+
+    @test_broken Copulas.ρ⁻¹(AMHCopula, 0.2) ≈ 0.5168580913147318
+    @test_broken Copulas.ρ⁻¹(AMHCopula, 0.) ≈ 0. atol=1.0e-4
+    @test_broken Copulas.ρ⁻¹(AMHCopula, 0.49) ≈ 1 atol=1.0e-4
+    @test_broken Copulas.ρ⁻¹(AMHCopula, -0.273) ≈ -1 atol=1.0e-4
+    @test_broken Copulas.ρ⁻¹(AMHCopula, -0.2246) ≈ -0.8 atol=1.0e-3
+end
+
+@testitem "Testing empirical tail values of certain copula samples" begin
+    using StableRNGs
+    using Distributions
+    rng = StableRNG(123)
+
+    function tail(v1::Vector{T}, v2::Vector{T}, tail::String, α::T = 0.002) where T <: Real
+        if tail == "l"
+            return sum((v1 .< α) .* (v2 .< α))./(length(v1)*α)
+        elseif tail == "r"
+            return sum((v1 .> (1-α)) .* (v2 .> (1-α)))./(length(v1)*α)
+        end
+        0.
+    end
+
+    @testset "tail dependencies test" begin
+        v1 = vcat(zeros(5), 0.5*ones(5), zeros(5), 0.5*ones(70), ones(5), 0.5*ones(5), ones(5));
+        v2 = vcat(zeros(10), 0.5*ones(80), ones(10))
+        @test tail(v1, v2,  "l", 0.1) ≈ 0.5
+        @test tail(v1, v2, "r", 0.1) ≈ 0.5
+    end
+
+    @testset "Gumbel" begin
+        rng = StableRNG(123)
+        x = rand(rng,GumbelCopula(3,2.), 100_000)
+        @test_broken tail(x[:,1], x[:,2], "r") ≈ 2-2^(1/2) atol=1.0e-1
+        @test_broken tail(x[:,1], x[:,2], "r") ≈ 2-2^(1/2) atol=1.0e-1
+        @test tail(x[:,1], x[:,2], "l", 0.00001) ≈ 0.
+        @test tail(x[:,1], x[:,3], "l", 0.00001) ≈ 0.
+    end
+    @testset "Clayton" begin
+        rng = StableRNG(123)
+        x = rand(rng,ClaytonCopula(3,1.), 100_000)
+        @test_broken tail(x[:,1], x[:,2], "l") ≈ 2.0^(-1) atol=1.0e-1
+        @test_broken tail(x[:,1], x[:,3], "l") ≈ 2.0^(-1) atol=1.0e-1
+        @test tail(x[:,1], x[:,2], "r", 0.0001) ≈ 0
+    end
+    @testset "AMH" begin
+        rng = StableRNG(123)
+        x = rand(rng,AMHCopula(3,0.8), 100_000)
+        @test tail(x[:,1], x[:,2], "l", 0.0001) ≈ 0
+        @test tail(x[:,1], x[:,2], "r", 0.0001) ≈ 0
+    end
+    @testset "Frank" begin
+        rng = StableRNG(123)
+        x = rand(rng,FrankCopula(3,0.8), 100_000)
+        @test tail(x[:,1], x[:,2], "l", 0.0001) ≈ 0
+        @test tail(x[:,1], x[:,2], "r", 0.0001) ≈ 0
+    end
+end

test/ClaytonCopula.jl

@@ -0,0 +1,28 @@
+@testitem "Fix values of bivariate ClaytonCopula: τ, cdf, pdf and contructor" begin
+    using Distributions
+
+    # Fix a few cdf and pdf values: 
+    x = [0:0.25:1;]
+    y = x
+    cdf1 = [0.0, 0.1796053020267749, 0.37796447300922725, 0.6255432421712244, 1.0]
+    cdf2 = [0.0, 0.0, 0.17157287525381, 0.5358983848622453, 1.0]
+    pdf1 = [Inf, 2.2965556205046926, 1.481003649342278, 1.614508582188617, 3.0]
+    pdf2 = [Inf, 0.0, 1.0, 2 / 3, 0.5]
+    for i in 1:5
+        @test cdf(ClaytonCopula(2,2),[x[i],y[i]]) ≈ cdf1[i]
+        @test cdf(ClaytonCopula(2,-0.5),[x[i],y[i]]) ≈ cdf2[i]
+        @test pdf(ClaytonCopula(2,2),[x[i],y[i]]) ≈ pdf1[i]
+        @test pdf(ClaytonCopula(2,-0.5),[x[i],y[i]]) ≈ pdf2[i]
+    end
+
+    # Fix a few tau values: 
+    @test Copulas.τ(ClaytonCopula(2,-0.5)) == -1 / 3
+    @test Copulas.τ(ClaytonCopula(2,2)) == 0.5
+    @test Copulas.τ(ClaytonCopula(2,10)) == 10 / 12
+
+    # Fix constructor behavior: 
+    @test isa(ClaytonCopula(2,0), IndependentCopula)
+    @test isa(ClaytonCopula(2,-0.7), ClaytonCopula)
+    @test isa(ClaytonCopula(2,-1), WCopula)
+    @test isa(ClaytonCopula(2,Inf), MCopula)
+end

test/Constructor_Errors.jl

@@ -0,0 +1,10 @@
+@testitem "Constructors errors on wrong inputs" begin
+    using LinearAlgebra
+    @test_throws LinearAlgebra.PosDefException GaussianCopula([1 2.0; 2 1])
+    @test_throws LinearAlgebra.PosDefException TCopula(10,[1 2.0; 2 1])
+    @test_throws ArgumentError PlackettCopula(-0.5)
+    @test_throws ArgumentError FGMCopula(1,0.5)
+    @test_throws ArgumentError FGMCopula(3,[-1.5,2.0,3.1,1.2])
+    @test_throws ArgumentError FGMCopula(1,[0.8,0.2,0.5,0.4])
+end
+