From 5b9127aead7220a5602693fc32104ccd0647e8d5 Mon Sep 17 00:00:00 2001
From: Oskar Laverny <oskar.laverny@gmail.com>
Date: Mon, 30 Oct 2023 18:52:29 +0100
Subject: [PATCH] Adding test for random generation + fixed bug

---
 Project.toml                | 2 +-
 src/WilliamsonTransforms.jl | 6 ++++--
 test/testing_the_paper.jl   | 5 +++++
 3 files changed, 10 insertions(+), 3 deletions(-)

diff --git a/Project.toml b/Project.toml
index a9f55fd..0b0b0c1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "WilliamsonTransforms"
 uuid = "48feb556-9bdd-43a2-8e10-96100ec25e22"
 authors = ["Oskar Laverny <oskar.laverny@gmail.com> and contributors"]
-version = "0.0.1"
+version = "0.0.2"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
diff --git a/src/WilliamsonTransforms.jl b/src/WilliamsonTransforms.jl
index 2d24014..ee6ca60 100644
--- a/src/WilliamsonTransforms.jl
+++ b/src/WilliamsonTransforms.jl
@@ -101,7 +101,9 @@ function Distributions.cdf(d::𝒲₋₁, x::Real)
     c_ϕ = taylor(d.ϕ, x, d.d, typeof(x))
     c_ϕ[end] = max(c_ϕ[end], 0)
     for k in 0:(d.d-1)
-        rez += (-1)^k * x^k * c_ϕ[k+1]
+        if c_ϕ[k+1] != 0 # We need c_ϕ = 0 to dominate x = Inf
+            rez += (-1)^k * x^k * c_ϕ[k+1]
+        end
     end
     return 1-rez
 end
@@ -112,6 +114,6 @@ function Distributions.logpdf(d::𝒲₋₁, x::Real)
 end
 function Distributions.rand(rng::Distributions.AbstractRNG, d::𝒲₋₁)
     u = rand(rng)
-    Roots.find_zero(x -> (Distributions.cdf(d,x) - u), (0, Inf))
+    Roots.find_zero(x -> (Distributions.cdf(d,x) - u), (0.0, Inf))
 end
 end
diff --git a/test/testing_the_paper.jl b/test/testing_the_paper.jl
index 1fdb39b..523c700 100644
--- a/test/testing_the_paper.jl
+++ b/test/testing_the_paper.jl
@@ -5,6 +5,8 @@
     ϕ(x, d) = max((1-x)^(d-1),zero(x))
     Xhat = 𝒲₋₁(x -> ϕ(x,d),d)
     ϕhat = 𝒲(X,d)
+
+    rand(Xhat,10)
     
     @test maximum(abs.([cdf(X,x) - cdf(Xhat,x) for x in 0:0.01:10*d])) <= sqrt(eps(Float64))
     @test maximum(abs.([ϕ(x, d) - ϕhat(x) for x in 0:0.01:10])) <= sqrt(eps(Float64))
@@ -17,6 +19,8 @@ end
         ϕ(x) = exp(-x)
         Xhat = 𝒲₋₁(ϕ,d)
         ϕhat = 𝒲(X,d)
+
+        rand(Xhat,10)
     
         @test maximum(abs.([cdf(X,x) - cdf(Xhat,x) for x in 0:0.01:3*d])) <= sqrt(eps(Float64))
         @test maximum(abs.([ϕ(x) - ϕhat(x) for x in 0:0.01:10])) <= sqrt(eps(Float64))
@@ -65,6 +69,7 @@ end
         (2, -1.0)
     )
         Xhat = 𝒲₋₁(x -> ϕ(x,θ),d)
+        rand(Xhat,10)
         @test maximum(abs.([F(x,θ,d) - cdf(Xhat,x) for x in 0:0.01:10])) <= sqrt(eps(Float64))
     end