From 69f4f3302880aa74d6a9513c77d4cc91ae224010 Mon Sep 17 00:00:00 2001
From: Oskar Laverny <oskar.laverny@gmail.com>
Date: Tue, 24 Oct 2023 17:38:53 +0200
Subject: [PATCH 1/5] Remove AlphaStableDistributions

---
 Project.toml                                |  2 -
 src/ArchimedeanCopulas/GumbelCopula.jl      |  2 +-
 src/Copulas.jl                              | 49 ++++++++++-------
 src/univariate_distributions/AlphaStable.jl | 60 +++++++++++++++++++++
 4 files changed, 91 insertions(+), 22 deletions(-)
 create mode 100644 src/univariate_distributions/AlphaStable.jl

diff --git a/Project.toml b/Project.toml
index b31aa137..7b6dabc9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,7 +4,6 @@ authors = ["Oskar Laverny"]
 version = "0.1.11"
 
 [deps]
-AlphaStableDistributions = "f20549b4-2d50-407f-863c-cdd202ba59a3"
 Cubature = "667455a9-e2ce-5579-9412-b964f529a492"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -18,7 +17,6 @@ StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 TaylorSeries = "6aa5eb33-94cf-58f4-a9d0-e4b2c4fc25ea"
 
 [compat]
-AlphaStableDistributions = "1"
 Cubature = "1.5"
 Distributions = "0.25"
 ForwardDiff = "0.10"
diff --git a/src/ArchimedeanCopulas/GumbelCopula.jl b/src/ArchimedeanCopulas/GumbelCopula.jl
index 447072aa..9dffe04d 100644
--- a/src/ArchimedeanCopulas/GumbelCopula.jl
+++ b/src/ArchimedeanCopulas/GumbelCopula.jl
@@ -23,7 +23,7 @@ GumbelCopula(d,θ) = θ >= 1 ? GumbelCopula{d,typeof(θ)}(θ) : @error "Theta mu
 τ(C::GumbelCopula) = ifelse(isfinite(C.θ), (C.θ-1)/C.θ, 1)
 τ⁻¹(::Type{GumbelCopula},τ) =ifelse(τ == 1, Inf, 1/(1-τ))
 
-radial_dist(C::GumbelCopula) = AlphaStableDistributions.AlphaStable(α = 1/C.θ, β = 1,scale = cos(π/(2C.θ))^C.θ, location = (C.θ == 1 ? 1 : 0))
+radial_dist(C::GumbelCopula) = AlphaStable(α = 1/C.θ, β = 1,scale = cos(π/(2C.θ))^C.θ, location = (C.θ == 1 ? 1 : 0))
 
 
 # S(α, β, γ , δ) denotes a stable distribution in
diff --git a/src/Copulas.jl b/src/Copulas.jl
index eca3ed81..d0f0943a 100644
--- a/src/Copulas.jl
+++ b/src/Copulas.jl
@@ -2,9 +2,9 @@ module Copulas
 
 
 @doc let
-       path = joinpath(dirname(@__DIR__), "README.md")
-       include_dependency(path)
-       read(path, String)
+    path = joinpath(dirname(@__DIR__), "README.md")
+    include_dependency(path)
+    read(path, String)
 end Copulas
 
     import Base
@@ -18,7 +18,6 @@ end Copulas
     import ForwardDiff
     import Cubature
     import MvNormalCDF
-    import AlphaStableDistributions
     using PrecompileTools 
 
     # Standard copulas and stuff. 
@@ -33,6 +32,7 @@ end Copulas
     # These three distributions might be merged in Distrbutions.jl one day. 
     include("univariate_distributions/Sibuya.jl")
     include("univariate_distributions/Logarithmic.jl")
+    include("univariate_distributions/AlphaStable.jl")
 
     # Elliptical copulas
     include("EllipticalCopula.jl")
@@ -64,20 +64,31 @@ end Copulas
            WCopula,
            SurvivalCopula
 
-     # PrecompileTools stuff
-     @setup_workload begin
-       biv_cops = [GaussianCopula([1 0.7; 0.7 1]), TCopula(2,[1 0.7; 0.7 1]),ClaytonCopula(2,7),JoeCopula(2,3),GumbelCopula(2,8),FrankCopula(2,0.5), AMHCopula(2,0.7)]
-       @compile_workload begin
-           for C in biv_cops
-              u = Random.rand(C,10)
-              pdf(C,[0.5,0.5])
-              cdf(C,[0.5,0.5])
-              D = SklarDist(C,[Gamma(1,1),Normal(1,1)])
-              u = Random.rand(D,10)
-              pdf(D,[0.5,0.5])
-              cdf(D,[0.5,0.5])
-           end
-       end
-   end
+    # PrecompileTools stuff
+    @setup_workload begin
+        biv_cops = [
+            GaussianCopula([1 0.7; 0.7 1]),
+            TCopula(2,[1 0.7; 0.7 1]),
+            ClaytonCopula(2,7),
+            JoeCopula(2,3),
+            GumbelCopula(2,8),
+            FrankCopula(2,0.5),
+            AMHCopula(2,0.7),
+            WCopula(2),
+            IndependentCopula(2), 
+            MCopula(2)
+        ]
+        @compile_workload begin
+            for C in biv_cops
+                u = Random.rand(C,10)
+                pdf(C,[0.5,0.5])
+                cdf(C,[0.5,0.5])
+                D = SklarDist(C,[Gamma(1,1),Normal(1,1)])
+                u = Random.rand(D,10)
+                pdf(D,[0.5,0.5])
+                cdf(D,[0.5,0.5])
+            end
+        end
+    end
 
 end
diff --git a/src/univariate_distributions/AlphaStable.jl b/src/univariate_distributions/AlphaStable.jl
new file mode 100644
index 00000000..dfd2154a
--- /dev/null
+++ b/src/univariate_distributions/AlphaStable.jl
@@ -0,0 +1,60 @@
+##########
+########## Copied from https://github.com/org-arl/AlphaStableDistributions.jl
+########## To avoid too many dependencies and fasten the package. 
+########## Probably we can do better by integrating with them... but they use too much. 
+##########
+
+Base.@kwdef struct AlphaStable{T} <: Distributions.ContinuousUnivariateDistribution
+    α::T = 1.5
+    β::T = zero(α)
+    scale::T = one(α)
+    location::T = zero(α)
+end
+
+AlphaStable(α::Integer, β::Integer, scale::Integer, location::Integer) = AlphaStable(float(α), float(β), float(scale), float(location))
+function AlphaStable(α,β,scale,location)
+    αT,βT,scaleT,locationT =  promote(α,β,scale,location)
+    AlphaStable(αT,βT,scaleT,locationT)
+end
+Distributions.params(d::AlphaStable) = (d.α, d.β, d.scale, d.location)
+
+"""
+Generate independent stable random numbers.
+
+:param α: characteristic exponent (0.1 to 2.0)
+:param β: skew (-1 to +1)
+:param scale: scale parameter
+:param loc: location parameter (mean for α > 1, median/mode when β=0)
+
+
+This implementation is based on the method in J.M. Chambers, C.L. Mallows
+and B.W. Stuck, "A Method for Simulating Stable Random Variables," JASA 71 (1976): 340-4.
+McCulloch's MATLAB implementation (1996) served as a reference in developing this code.
+"""
+function Base.rand(rng::Distributions.AbstractRNG, d::AlphaStable{T}) where {T<:AbstractFloat} 
+    α=d.α; β=d.β; sc=d.scale; loc=d.location
+    (α < 0.1 || α > 2) && throw(DomainError(α, "α must be in the range 0.1 to 2"))
+    abs(β) > 1 && throw(DomainError(β, "β must be in the range -1 to 1"))
+    # added eps(T) to prevent DomainError: x ^ y where x < 0
+    ϕ = (rand(rng, T) - T(0.5)) * π * (one(T) - eps(T))
+    if α == one(T) && β == zero(T)
+        return loc + sc * tan(ϕ)
+    end
+    w = -log(rand(rng, T))
+    α == 2 && (return loc + 2*sc*sqrt(w)*sin(ϕ))
+    β == zero(T) && (return loc + sc * ((cos((one(T)-α)*ϕ) / w)^(one(T)/α - one(T)) * sin(α * ϕ) / cos(ϕ)^(one(T)/α)))
+    cosϕ = cos(ϕ)
+    if abs(α - one(T)) > 1e-8
+        ζ = β * tan(π * α / 2)
+        aϕ = α * ϕ
+        a1ϕ = (one(T) - α) * ϕ
+        return loc + sc * ((((sin(aϕ) + ζ * cos(aϕ))/cosϕ) * ((cos(a1ϕ) + ζ*sin(a1ϕ)) / (w*cosϕ))^((one(T)-α)/α)))
+    end
+    bϕ = π/2 + β*ϕ
+    x = 2/π * (bϕ * tan(ϕ) - β * log(π/2*w*cosϕ/bϕ))
+    α == one(T) || (x += β * tan(π*α/2))
+    return loc + sc * x
+end
+
+Base.eltype(::Type{<:AlphaStable{T}}) where {T<:AbstractFloat} = T
+

From 3e74a5c82c8404b59303bbba9277cbad6f0697c0 Mon Sep 17 00:00:00 2001
From: Oskar Laverny <oskar.laverny@gmail.com>
Date: Wed, 25 Oct 2023 10:52:39 +0200
Subject: [PATCH 2/5] Remove precompiletools

---
 Project.toml   |  2 --
 src/Copulas.jl | 28 ----------------------------
 2 files changed, 30 deletions(-)

diff --git a/Project.toml b/Project.toml
index 7b6dabc9..e7d3a527 100644
--- a/Project.toml
+++ b/Project.toml
@@ -9,7 +9,6 @@ Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 GSL = "92c85e6c-cbff-5e0c-80f7-495c94daaecd"
 MvNormalCDF = "37188c8d-bc69-4638-b057-733e744175ec"
-PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
@@ -22,7 +21,6 @@ Distributions = "0.25"
 ForwardDiff = "0.10"
 GSL = "1"
 MvNormalCDF = "0.2, 0.3"
-PrecompileTools = "1"
 Roots = "1, 2"
 SpecialFunctions = "2"
 StatsBase = "0.33, 0.34"
diff --git a/src/Copulas.jl b/src/Copulas.jl
index d0f0943a..2f25dbf3 100644
--- a/src/Copulas.jl
+++ b/src/Copulas.jl
@@ -18,7 +18,6 @@ end Copulas
     import ForwardDiff
     import Cubature
     import MvNormalCDF
-    using PrecompileTools 
 
     # Standard copulas and stuff. 
     include("utils.jl")
@@ -64,31 +63,4 @@ end Copulas
            WCopula,
            SurvivalCopula
 
-    # PrecompileTools stuff
-    @setup_workload begin
-        biv_cops = [
-            GaussianCopula([1 0.7; 0.7 1]),
-            TCopula(2,[1 0.7; 0.7 1]),
-            ClaytonCopula(2,7),
-            JoeCopula(2,3),
-            GumbelCopula(2,8),
-            FrankCopula(2,0.5),
-            AMHCopula(2,0.7),
-            WCopula(2),
-            IndependentCopula(2), 
-            MCopula(2)
-        ]
-        @compile_workload begin
-            for C in biv_cops
-                u = Random.rand(C,10)
-                pdf(C,[0.5,0.5])
-                cdf(C,[0.5,0.5])
-                D = SklarDist(C,[Gamma(1,1),Normal(1,1)])
-                u = Random.rand(D,10)
-                pdf(D,[0.5,0.5])
-                cdf(D,[0.5,0.5])
-            end
-        end
-    end
-
 end

From ddcbaaa2605b77201bf05bf88c907d43dfcce891 Mon Sep 17 00:00:00 2001
From: Oskar Laverny <oskar.laverny@gmail.com>
Date: Wed, 25 Oct 2023 11:18:34 +0200
Subject: [PATCH 3/5] add tests

---
 test/old_precompile_workflow.jl | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)
 create mode 100644 test/old_precompile_workflow.jl

diff --git a/test/old_precompile_workflow.jl b/test/old_precompile_workflow.jl
new file mode 100644
index 00000000..92186c08
--- /dev/null
+++ b/test/old_precompile_workflow.jl
@@ -0,0 +1,21 @@
+
+@testitem "standard functionality test" begin
+    biv_cops = [
+        GaussianCopula([1 0.7; 0.7 1]),
+        TCopula(2,[1 0.7; 0.7 1]),
+        ClaytonCopula(2,7),
+        JoeCopula(2,3),
+        GumbelCopula(2,8),
+        FrankCopula(2,0.5),
+        AMHCopula(2,0.7)
+    ]
+    for C in biv_cops
+        u = Random.rand(C,10)
+        pdf(C,[0.5,0.5])
+        cdf(C,[0.5,0.5])
+        D = SklarDist(C,[Gamma(1,1),Normal(1,1)])
+        u = Random.rand(D,10)
+        pdf(D,[0.5,0.5])
+        cdf(D,[0.5,0.5])
+    end
+end

From 1be5dfac18387e50454de383ab46c00c01509eab Mon Sep 17 00:00:00 2001
From: Oskar Laverny <oskar.laverny@gmail.com>
Date: Wed, 25 Oct 2023 11:21:27 +0200
Subject: [PATCH 4/5] typo in test

---
 test/old_precompile_workflow.jl | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/test/old_precompile_workflow.jl b/test/old_precompile_workflow.jl
index 92186c08..3687f200 100644
--- a/test/old_precompile_workflow.jl
+++ b/test/old_precompile_workflow.jl
@@ -1,5 +1,6 @@
 
 @testitem "standard functionality test" begin
+    using Random, Distributions
     biv_cops = [
         GaussianCopula([1 0.7; 0.7 1]),
         TCopula(2,[1 0.7; 0.7 1]),
@@ -18,4 +19,5 @@
         pdf(D,[0.5,0.5])
         cdf(D,[0.5,0.5])
     end
+    @test true
 end

From 9288f337e72eb23961bcb0edfd1fbedb0a368829 Mon Sep 17 00:00:00 2001
From: Oskar Laverny <oskar.laverny@gmail.com>
Date: Wed, 25 Oct 2023 11:35:12 +0200
Subject: [PATCH 5/5] up test

---
 test/old_precompile_workflow.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/test/old_precompile_workflow.jl b/test/old_precompile_workflow.jl
index 3687f200..4db0eb5d 100644
--- a/test/old_precompile_workflow.jl
+++ b/test/old_precompile_workflow.jl
@@ -16,8 +16,8 @@
         cdf(C,[0.5,0.5])
         D = SklarDist(C,[Gamma(1,1),Normal(1,1)])
         u = Random.rand(D,10)
-        pdf(D,[0.5,0.5])
-        cdf(D,[0.5,0.5])
+        pdf(D,[0.5,0])
+        cdf(D,[0.5,0])
     end
     @test true
 end