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plefka.jl
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plefka.jl
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using ComponentArrays
using LinearAlgebra
using Random
using CUDA
using IfElse
include("plefka_functions.jl")
"""
this code is an implementation of paper
[1] Aguilera, M, Moosavi, SA & Shimazaki H (2021).
A unifying framework for mean-field theories of asymmetric kinetic Ising systems.
Nature Communications 12:1197; https://doi.org/10.1038/s41467-021-20890.
"""
############################
### Kinetic Ising Model ###
############################
abstract type AbstractIsingModel{T} end
abstract type AbstractIsingCache{T} end
struct Ising{T} <: AbstractIsingModel{T}
sze::Int
H::AbstractArray{T,1}
J::AbstractArray{T,2}
Beta::T
s::AbstractArray{T,1}
end
struct IsingCache_v0{T} <: AbstractIsingCache{T}
h::AbstractArray{T,1}
r::AbstractArray{T,1}
end
function randomizeState(::Type{T}, sze::Int, rng::AbstractRNG ) where T
Array{T}(rand(rng, (-1,1), sze))
end
function Ising(::Type{T}, sze::Int, rng::AbstractRNG=Random.default_rng()) where T
Ising{T}(sze, zeros(T, sze), zeros(T, sze, sze), T(1), randomizeState(T, sze, rng))
end
function IsingCache_v0(::Type{T}, sze::Int) where T
IsingCache_v0{T}(zeros(T, sze), zeros(T, sze))
end
function randomFields!(ising::Ising{T}, rng::AbstractRNG=Random.default_rng()) where T
ising.H .= rand(rng, T, ising.sze).*2 .- 1
end
function randomWiring!(ising::Ising{T}, rng::AbstractRNG=Random.default_rng()) where T
ising.J .= randn(rng, T, ising.sze, ising.sze )
end
function randomizeState!(ising::Ising{T}, rng::AbstractRNG=Random.default_rng()) where T
ising.s .= randomizeState(T, ising.sze, rng)
end
function parallelUpdate!(ising::Ising{T}, rng::AbstractRNG) where T
h = (ising.H + ising.J*ising.s) * T(2*ising.Beta)
r = rand(rng, T, ising.sze)
ising.s .= ifelse.( sigmoid.(h)>=r, T(1), T(-1) )
return nothing
end
function parallelUpdate_cpu!(ising::Ising{T}, ising_cache::IsingCache_v0{T}, rng::AbstractRNG=Random.default_rng()) where T
# benchmark is 11.029 s 640.62 KiB, 30_000 allocs
copy!(ising_cache.h, ising.H)
mul!(ising_cache.h, ising.J, ising.s, T(2*ising.Beta), T(2*ising.Beta))
@turbo for i in eachindex(ising.s)
r = rand(rng,T)
ising.s[i] = ifelse(sigmoid(ising_cache.h[i])>=r, T(1), T(-1))
# ising.s[i] = sign(r - sigmoid(ising_cache.h[i])
end
return nothing
end
function sigmoid(x)
1 / (exp(-x)+1)
end
function parallelUpdate_gpu!(ising::Ising{T}, ising_cache::IsingCache_v0{T}, rng::AbstractRNG=CURAND.default_rng()) where T
# benchmark is 471.232 ms, 1.48 MiB 27_000 allocs
copy!(ising_cache.h, ising.H)
mul!(ising_cache.h, ising.J, ising.s, T(2*ising.Beta), T(2*ising.Beta))
rand!(rng, ising_cache.r)
ising.s .= ifelse.( sigmoid.(ising_cache.h).>=ising_cache.r, T(1), T(-1) )
# ising.s .= sign.(ising_cache.r .- sigmoid.(ising_cache.h))
return nothing
end
function copy_gpu(y,x)
index = (blockIdx().x - Int32(1)) * blockDim().x + threadIdx().x
stride = gridDim().x * blockDim().x
i = index
while i<=length(y)
@inbounds y[i] = x[i]
i += stride
end
return
end
function gpu(a::Array{T,N}) where {T,N}
CuArray{T}(a)
end
function gpu(ising::Ising{T}) where{T}
H = ising.H |> gpu
J = ising.J |> gpu
s = ising.s |> gpu
Ising{T}(ising.sze, H, J, ising.Beta, s)
end
function gpu(ising_cache::IsingCache_v0{T}) where{T}
h = ising_cache.h |> gpu
r = ising_cache.r |> gpu
IsingCache_v0{T}(h, r)
end
##########################
### Mean Ising Model ###
##########################
abstract type AbstractMeanIsingAlgorithm end
struct MeanIsingModel{T,Alg<:AbstractMeanIsingAlgorithm}
sze::Int
m::AbstractArray{T,1}
C::AbstractArray{T,2}
D::AbstractArray{T,2}
m_p::AbstractArray{T,1}
C_p::AbstractArray{T,2}
D_p::AbstractArray{T,2}
algorithm::Alg
end
function MeanIsingModel(::Type{T}, sze::Int, alg::AbstractMeanIsingAlgorithm) where T
MeanIsingModel{T, typeof(alg)}(
sze,
zeros(T, sze),
zeros(T, sze, sze),
zeros(T, sze, sze),
zeros(T, sze),
zeros(T, sze, sze),
zeros(T, sze, sze),
alg
)
end
function initialize_state!(mean_ising::MeanIsingModel{T, Alg}, m::AbstractArray{T,1}) where {T, Alg}
mean_ising.m .= m
mean_ising.m_p .= copy(mean_ising.m)
mean_ising.C .= diagm(1 .- m.^2)
mean_ising.C_p .= copy(mean_ising.C)
mean_ising.D .= zeros(T, mean_ising.sze, mean_ising.sze)
mean_ising.D_p .= copy(mean_ising.D)
end
function initialize_state!(mean_ising::MeanIsingModel{T, Alg}) where {T, Alg}
m .= zeros(T, mean_ising.sze)
initialize_state!(mean_ising, m)
end
##########################
### Plefka Expansions ###
##########################
abstract type AbstractIsingPlefkaExpansion{T} <: AbstractMeanIsingAlgorithm end
"""
Plefka[t-1,t] order 2
"""
struct IsingPlefka_t1_t{T} <: AbstractIsingPlefkaExpansion{T}
# cache::ComponentArray
end
function update_P!(ising::Ising{T}, mean_ising::MeanIsingModel{T,Alg}) where {T, Alg<:IsingPlefka_t1_t}
mean_ising.m_p .= copy(mean_ising.m)
mean_ising.m .= update_m_P_t1_t_o2(ising.H, ising.J, mean_ising.m_p)
mean_ising.C .= update_C_P_t1_t_o2(ising.H, ising.J, mean_ising.m, mean_ising.m_p)
mean_ising.D .= update_D_P_t1_t_o2(ising.H, ising.J, mean_ising.m, mean_ising.m_p)
end
"""
Plefka[t] order 2
"""
struct IsingPlefka_t{T} <: AbstractIsingPlefkaExpansion{T}
# cache::ComponentArray
end
function update_P!(ising::Ising{T}, mean_ising::MeanIsingModel{T,Alg}) where {T, Alg<:IsingPlefka_t}
mean_ising.m_p .= copy(mean_ising.m)
mean_ising.C_p .= copy(mean_ising.C)
mean_ising.m .= update_m_P_t_o2(ising.H, ising.J, mean_ising.m_p, mean_ising.C_p)
mean_ising.C .= update_C_P_t_o2(ising.H, ising.J, mean_ising.m, mean_ising.C_p)
mean_ising.D .= update_D_P_t_o2(ising.H, ising.J, mean_ising.m, mean_ising.m_p, mean_ising.C_p)
end
"""
Plefka[t-1] order 1
"""
struct IsingPlefka_t1{T} <: AbstractIsingPlefkaExpansion{T}
# cache::ComponentArray
end
function update_P!(ising::Ising{T}, mean_ising::MeanIsingModel{T,Alg}) where {T, Alg<:IsingPlefka_t1}
mean_ising.m_p .= copy(mean_ising.m)
mean_ising.C_p .= copy(mean_ising.C)
mean_ising.m .= update_m_P_t1_o1(ising.H, ising.J, mean_ising.m_p)
mean_ising.C .= update_C_P_t1_o1(ising.H, ising.J, mean_ising.m, mean_ising.m_p, mean_ising.C_p)
mean_ising.D .= update_D_P_t1_o1(ising.H, ising.J, mean_ising.m_p, mean_ising.C_p)
end
"""
Plefka2[t] order 2
"""
struct IsingPlefka2_t{T} <: AbstractIsingPlefkaExpansion{T}
# cache::ComponentArray
end
function update_P!(ising::Ising{T}, mean_ising::MeanIsingModel{T,Alg}) where {T, Alg<:IsingPlefka2_t}
mean_ising.m_p .= copy(mean_ising.m)
mean_ising.C_p .= copy(mean_ising.C)
mean_ising.D_p .= copy(mean_ising.D)
m, D = update_D_P2_t_o2(ising.H, ising.J, mean_ising.m_p, mean_ising.C_p, mean_ising.D_p)
mean_ising.m .= m
mean_ising.D .= D
mean_ising.C .= update_C_P2_t_o2(ising.H, ising.J, mean_ising.m, mean_ising.m_p, mean_ising.C_p)
end