Skip to content

Commit

Permalink
Merge pull request #47 from org-arl/fix-rand
Browse files Browse the repository at this point in the history 
Fix bugs
  • Loading branch information
@ymtoo
ymtoo authored Jun 6, 2023
2 parents f5b082c + 8ed5754 commit 90960b2
Show file tree
Hide file tree
Showing 3 changed files with 54 additions and 42 deletions.
2 changes: 1 addition & 1 deletion Project.toml
View file
Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
name = "AlphaStableDistributions"
uuid = "f20549b4-2d50-407f-863c-cdd202ba59a3"
authors = ["Fredrik Bagge Carlson", "Too Yuen Min"]
version = "1.1.5"
version = "1.1.6"

[deps]
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
Expand Down
63 changes: 32 additions & 31 deletions src/AlphaStableDistributions.jl
View file
Original file line number Diff line number Diff line change
Expand Up @@ -172,22 +172,22 @@ const ϕ₃ = [
1.908 1.908 1.908 1.908 1.908
]
const ϕ₅ = [
0.0 0.0 0.0 0.0 0.0
0.0 -0.017 -0.032 -0.049 -0.064
0.0 -0.030 -0.061 -0.092 -0.123
0.0 -0.043 -0.088 -0.132 -0.179
0.0 -0.056 -0.111 -0.170 -0.232
0.0 -0.066 -0.134 -0.206 -0.283
0.0 -0.075 -0.154 -0.241 -0.335
0.0 -0.084 -0.173 -0.276 -0.390
0.0 -0.090 -0.192 -0.310 -0.447
0.0 -0.095 -0.208 -0.346 -0.508
0.0 -0.098 -0.223 -0.383 -0.576
0.0 -0.099 -0.237 -0.424 -0.652
0.0 -0.096 -0.250 -0.469 -0.742
0.0 -0.089 -0.262 -0.520 -0.853
0.0 -0.078 -0.272 -0.581 -0.997
0.0 -0.061 -0.279 -0.659 -1.198
0.0 -0.061 -0.279 -0.659 -1.198
0.0 -0.078 -0.272 -0.581 -0.997
0.0 -0.089 -0.262 -0.52 -0.853
0.0 -0.096 -0.25 -0.469 -0.742
0.0 -0.099 -0.237 -0.424 -0.652
0.0 -0.098 -0.223 -0.383 -0.576
0.0 -0.095 -0.208 -0.346 -0.508
0.0 -0.09 -0.192 -0.31 -0.447
0.0 -0.084 -0.173 -0.276 -0.39
0.0 -0.075 -0.154 -0.241 -0.335
0.0 -0.066 -0.134 -0.206 -0.283
0.0 -0.056 -0.111 -0.17 -0.232
0.0 -0.043 -0.088 -0.132 -0.179
0.0 -0.03 -0.061 -0.092 -0.123
0.0 -0.017 -0.032 -0.049 -0.064
0.0 0.0 0.0 0.0 0.0
]

"""
Expand Down Expand Up @@ -221,7 +221,7 @@ function Distributions.fit(::Type{<:AlphaStable}, x::AbstractArray{T}, alg=Quick
c = (p[6]-p[2]) / itp₃(α, abs(β))
itp₄ = interpolate((_α, _β), ϕ₅, Gridded(Linear()))
ζ = p[4] + c * sign(β) * itp₄(α, abs(β))
if abs(α - 1.0) < 0.1
if abs(α - 1.0) < 0.05
δ = ζ
else
δ = ζ - β * c * tan(π*α/2)
Expand All @@ -237,6 +237,7 @@ end
Distributions.params(d::SymmetricAlphaStable) = (d.α, d.scale, d.location)
Distributions.cf(d::SymmetricAlphaStable, t::Real) = cf(AlphaStable(d), t)
Random.rand(rng::AbstractRNG, d::SymmetricAlphaStable) = rand(rng, AlphaStable(d))
Base.eltype(::Type{<:SymmetricAlphaStable{T}}) where {T<:AbstractFloat} = T

function AlphaStable(d::SymmetricAlphaStable)
AlphaStable(α=d.α,scale=d.scale,location=d.location)
Expand Down Expand Up @@ -290,29 +291,29 @@ 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::AbstractRNG, d::AlphaStable{T}) where {T<:AbstractFloat}
α=d.α; β=d.β; scale=d.scale; loc=d.location
function Base.rand(rng::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"))
ϕ = (rand(rng, T) - 0.5) * π
# 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 + scale * tan(ϕ)
return loc + sc * tan(ϕ)
end
w = -log(rand(rng, T))
α == 2 && (return loc + 2*scale*sqrt(w)*sin(ϕ))
β == zero(T) && (return loc + scale * ((cos((1-α)*ϕ) / w)^(one(T)/α - one(T)) * sin(α * ϕ) / cos(ϕ)^(one(T)/α)))
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 + scale * (( (sin(aϕ) + ζ * cos(aϕ))/cosϕ * ((cos(a1ϕ) + ζ*sin(a1ϕ))) / ((w*cosϕ)^((1-α)/α)) ))
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 + scale * x
return loc + sc * x
end

Base.eltype(::Type{<:AlphaStable{T}}) where {T<:AbstractFloat} = T
Expand Down Expand Up @@ -466,10 +467,10 @@ with memory", Signal Processing, Volume 131, Pages 271-279, 2017.
"""
function Distributions.fit(d::Type{<:AlphaSubGaussian}, x::AbstractVector{T}, m::Integer; p=one(T)) where T
d1 = fit(AlphaStable, x)
α = d1.α; scale=d1.scale
α = d1.α; sc=d1.scale
cov = zeros(T, m+1, m+1)
xlen = length(x)
c = ((sum(x->abs(x)^p, x)/xlen)^(1/p))/scale
c = ((sum(x->abs(x)^p, x)/xlen)^(1/p))/sc
for i in 1:m
tempxlen = xlen-mod(xlen, i)
xtemp = reshape(x[1:end-mod(xlen, i)], i, tempxlen÷i)
Expand All @@ -478,11 +479,11 @@ function Distributions.fit(d::Type{<:AlphaSubGaussian}, x::AbstractVector{T}, m:
tempxlen = size(xtemp, 1)*size(xtemp, 2)
end
xtemp = reshape(xtemp', 2, tempxlen÷2)
@views r = (2/(c^p))*(scale^(2-p))*(xtemp[1, :]'*((sign.(xtemp[2, :]).*(abs.(xtemp[2, :]).^(p-1)))))/(tempxlen/2)
@views r = (2/(c^p))*(sc^(2-p))*(xtemp[1, :]'*((sign.(xtemp[2, :]).*(abs.(xtemp[2, :]).^(p-1)))))/(tempxlen/2)
cov[diagind(cov, i)] .+= r
end
cov = (cov+cov')+2*(scale^2)*I(m+1)
cov ./= 2*scale^2
cov = (cov+cov')+2*(sc^2)*I(m+1)
cov ./= 2*sc^2
AlphaSubGaussian(α=α, R=cov, n=length(x))
end

Expand Down
31 changes: 21 additions & 10 deletions test/runtests.jl
View file
Original file line number Diff line number Diff line change
Expand Up @@ -76,20 +76,31 @@ end
sampletypes = [Float32,Float64]
stabletypes = [AlphaStable,SymmetricAlphaStable]
αs = [0.6:0.1:2,1:0.1:2]
betas = [-1:0.5:1,0.0]
sc = 2.0
for sampletype ∈ sampletypes
for (i, stabletype) in enumerate(stabletypes)
for α in αs[i]
d1 = AlphaStable(α=sampletype(α))
s = rand(rng,d1, 200000)
@test eltype(s) == sampletype
for β in betas[i]
d1 = if stabletype == AlphaStable
stabletype(α=sampletype(α), β=sampletype(β), scale=sampletype(sc))
else
stabletype(α=sampletype(α), scale=sampletype(sc))
end
s = rand(rng, d1, 10^6)
@test eltype(s) == sampletype

d2 = fit(stabletype, s)
@test typeof(d2.α) == sampletype
d2 = fit(stabletype, s)
@test typeof(d2.α) == sampletype

@test d1.α ≈ d2.α rtol=0.1
stabletype != SymmetricAlphaStable && @test d1.β ≈ d2.β atol=0.2
@test d1.scale ≈ d2.scale rtol=0.1
@test d1.location ≈ d2.location atol=0.1
@test d1.α ≈ d2.α rtol=0.1
if (stabletype != SymmetricAlphaStable) && (α != 2)
@test d1.β ≈ d2.β atol=0.2
end
# the quantile method is less accurate
@test d1.scale ≈ d2.scale rtol=0.2 * sc
@test d1.location ≈ d2.location atol=0.9 * sc
end
end

xnormal = rand(rng,Normal(3.0, 4.0), 96000)
Expand Down Expand Up @@ -119,7 +130,7 @@ end
@test d3.α ≈ α rtol=0.2
@test d3.β ≈ 0 atol=0.2
@test d3.scale ≈ 1 rtol=0.2
@test d3.location ≈ 0 atol=0.1
@test d3.location ≈ 0 atol=0.2
end

d4 = AlphaSubGaussian(α=1.5, n=96000)
Expand Down

0 comments on commit 90960b2

Please sign in to comment.