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rosimulationfast.jl
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rosimulationfast.jl
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using LinearAlgebra, Distributions, FLoops
mutable struct Parameters{T <: AbstractFloat}
N::Int #number of particles
M::Int #number of measures
L::T #length of the box
σ::T #particle diameter
ϵ::T #maximum size of the kick
κ::T #blending between BRO and RO
η::T #polydispersity
Nb::Int #number of cells per side linkedlist
end
function Parameters(N::Int, M::Int, L::T, ϵ::T; σ::T = one(T), κ::T = one(T),
η::T = zero(T)) where T <: AbstractFloat
return Parameters(N, M, L, σ, ϵ, κ, η, Int(fld(L, σ)))
end
mutable struct Config{T <: AbstractFloat}
pos::Vector{Tuple{T, T}} #position of all particles
active::Vector{Bool} #list of active particles
sizes::Vector{T} #sizes of the particle
end
mutable struct Measures{T <: AbstractFloat}
pos::Vector{Vector{Tuple{T, T}}} #stored positions
active::Vector{T} #stored order parameter
sampletimes::Vector{Int} #time instant of each measurement
end
#Method for dynamics
abstract type Model end
struct RO <: Model end
struct BRO <: Model end
confacfrac(conf::Config) = sum(conf.active) / length(conf.pos)
function pbcdist(x₁::T, x₂::T, L::T) where T <: AbstractFloat
if x₁ - x₂ > L / 2.0
return x₁ - x₂ - L
elseif x₁ - x₂ < - L / 2.0
return x₁ - x₂ + L
else
return x₁ - x₂
end
end
"""
dist(p₁::Tuple{T, T}, p₂::Tuple{T, T}, L::T) where T <: AbstractFloat
Compute the minimum image distance between pair of particles in a box of size `L`.
"""
function dist(p₁::Tuple{T, T}, p₂::Tuple{T, T}, L::T) where T <: AbstractFloat
return (pbcdist(p₁[1], p₂[1], L), pbcdist(p₁[2], p₂[2], L))
end
function deltafill!(𝜹::Vector{Tuple{T, T}}, conf::Config, L::T, i::Int, j::Int, ϵ::T,
::Type{RO}) where T <: AbstractFloat
#Random kick
𝜹[i], 𝜹[j] = map(randn, (T, T)), map(randn, (T, T))
nothing
end
function deltafill!(𝜹::Vector{Tuple{T, T}}, conf::Config, L::T, i::Int, j::Int, ϵ::T,
::Type{BRO}) where T <: AbstractFloat
#Evaluate distance (with PBC)
dij = dist(conf.pos[i], conf.pos[j], L)
dnij = rand(Uniform(0.0, ϵ)) .* dij ./ norm(dij)
#Update 𝜹
𝜹[i] = 𝜹[i] .+ dnij
𝜹[j] = 𝜹[j] .- dnij
nothing
end
"""
linkedlist(𝜹::Vector{Tuple{T, T}}, conf::Config, par::Parameters,
head::Vector{Int}, lscl::Vector{Int},
model::Type{W} = RO) where T <: AbstractFloat where W <: Model
Implement the linked-list algorithm to check for overlapping particles and compute displacements.
"""
function linkedlist(𝜹::Vector{Tuple{T, T}}, conf::Config, par::Parameters,
head::Vector{Int}, lscl::Vector{Int},
model::Type{W} = RO) where T <: AbstractFloat where W <: Model
#Define parameters
N = par.N
Nb = par.Nb
L = par.L
mc, mc1 = [1, 1], [1, 1]
rc = L / Nb
rshift = zeros(T, 2)
#LIST CONSTRUCTOR
#Reset the headers
@inbounds for c ∈ 1 : Nb^2
head[c] = -1
end
#Scan atoms to construct headers and linked lists
@inbounds for i ∈ 1 : N
#Vector cell index to which this atom belongs
mc[1], mc[2] = Int(fld(conf.pos[i][1], rc)), Int(fld(conf.pos[i][2], rc))
#Translate the vector cell index, mc, to a scalar cell index
c = Nb * mc[1] + mc[2] + 1
#Link to the previous occupant (or EMPTY (-1) if you're the 1st)
lscl[i] = head[c]
#The last one goes to the header
head[c] = i
end
#INTERACTION COMPUTATION
#Scan inner cells
@inbounds for mc[1] ∈ 0 : Nb - 1, mc[2] ∈ 0 : Nb - 1
#Calculate a scalar index
c = Nb * mc[1] + mc[2] + 1
#Scan the neighbor cells (including itself) of cell c
@inbounds for mc1[1] ∈ mc[1] - 1 : mc[1] + 1, mc1[2] ∈ mc[2] - 1 : mc[2] + 1
#Periodic boundary condition by shifting coordinates
@inbounds for a ∈ 1 : 2
if mc1[a] < 0
rshift[a] = -L
elseif mc1[a] ≥ Nb
rshift[a] = L
else
rshift[a] = zero(T)
end
end
#Calculate the scalar cell index of the neighbor cell (with PBC)
c1 = ((mc1[1] + Nb) % Nb) * Nb + ((mc1[2] + Nb) % Nb) + 1
#Scan atom i in cell c
i = head[c]
while (i != -1)
#Scan atom j in cell c1
j = head[c1]
while (j != -1)
#Avoid double counting
if i < j
#Define distace between particles
Δr = conf.pos[i] .- (conf.pos[j] .+ (rshift[1], rshift[2]))
#Check for collisions
if norm(Δr) ≤ (conf.sizes[i] + conf.sizes[j]) / 2.0
#Update 𝜹 for active particles
deltafill!(𝜹, conf, par.L, i, j, par.ϵ, model)
end
end
j = lscl[j]
end
i = lscl[i]
end
end
end
#Check for active particles
active = findall(a -> !iszero(a), sum.(𝜹))
#Return list of actives
return active
end
"""
initialconf(par::Parameters, 𝐗₀::Vector{Tuple{T, T}},
𝜹::Vector{Tuple{T, T}}, head::Vector{Int}, lscl::Vector{Int},
model::Type{W} = RO) where T <: AbstractFloat where W <: Model
Return the initial configuration.
"""
function initialconf(par::Parameters, 𝐗₀::Vector{Tuple{T, T}},
𝜹::Vector{Tuple{T, T}}, head::Vector{Int}, lscl::Vector{Int},
model::Type{W} = RO) where T <: AbstractFloat where W <: Model
#Generate sizes
N = par.N
sizes = rand(Normal(par.σ, sqrt(par.η * par.σ)), N)
#Initialisation
conf = Config(fill((zero(T), zero(T)), N), zeros(Bool, N), sizes)
conf.pos = 𝐗₀
#Check for collisions
active = linkedlist(𝜹, conf, par, head, lscl, model)
conf.active[active] .= true
return conf
end
"""
initialmeas(par::Parameters, conf::Config, sampletimes::Vector{Int},
Mp::Int, T::DataType)
Return the initial measure.
"""
function initialmeas(par::Parameters, conf::Config, sampletimes::Vector{Int},
Mp::Int, T::DataType)
#Initialisation
N, M = par.N, par.M
meas = Measures(fill(fill((zero(T), zero(T)), N), Mp), zeros(T, M), sampletimes)
#First measure
meas.active[1] = confacfrac(conf)
meas.pos[1] = copy(conf.pos)
return meas
end
"""
update!(conf::Config, par::Parameters, 𝜹::Vector{Tuple{T, T}},
head::Vector{Int}, lscl::Vector{Int},
model::Type{W} = RO) where T <: AbstractFloat where W <: Model
Updates configuration `conf` at each time step.
"""
function update!(conf::Config, par::Parameters, 𝜹::Vector{Tuple{T, T}},
head::Vector{Int}, lscl::Vector{Int},
model::Type{W} = RO) where T <: AbstractFloat where W <: Model
#Reset 𝜹
N = par.N
@inbounds for i ∈ 1 : N
𝜹[i] = (zero(T), zero(T))
end
#Check for collisions
active = linkedlist(𝜹, conf, par, head, lscl, model)
#Update all positions (with PBC)
X₂ = [conf.pos[i] .+ 𝜹[i] for i ∈ 1 : N]
conf.pos = [X₂[i] .- fld.(X₂[i], par.L) .* par.L for i ∈ 1 : N]
#Update actives
conf.active .= false
conf.active[active] .= true
nothing
end
"""
whentomeasure(t₀::Int, tmax::Int, nmeas::Int;
slope::T = 1.0) where T <: AbstractFloat
Define when to store samples.
"""
function whentomeasure(t₀::Int, tmax::Int, nmeas::Int;
slope::T = 1.0) where T <: AbstractFloat
#Create sampletimes and fix extrema
sampletimes = zeros(Int, nmeas)
sampletimes[end], sampletimes[1] = t₀, tmax
#Power law sampling
rng = LinRange(0, 1, nmeas)
for m ∈ 2 : nmeas - 1
sampletimes[m] = Int(floor(-rng[m]^slope * (tmax - t₀) + tmax))
end
#Finishing
return unique!(reverse!(sampletimes))
end
"""
simulation(N::Int, #number of particles
tmax::Int, #number of time steps
L::T; #length of the box
t₀::Int = 0, #termalisation time
nmeas::Int = Int(floor(log(2, (tmax - t₀)))), #number of measurements (approximate)
slope::T = 1.0, #slope of the sampling
Δm::Int = 1, #intervals to store full configurations
sampletimes::Vector{Int} = whentomeasure(t₀, tmax, nmeas, slope = slope), #optional custom sampletimes
σ::T = 1.0, #particle diameter
ϵ::T = 0.5, #maximum size of the kick
κ::T = 1.0, #blending between BRO and RO
η::T = 0.0, #polydispersity
𝐗₀::Vector{Tuple{T, T}} = [L .* map(rand, (T, T)) for i ∈ 1 : N], #initial configuration
model::Type{W} = RO) where T <: AbstractFloat where W <: Model
Main code for a single simulation.
"""
function simulation(N::Int, #number of particles
tmax::Int, #number of time steps
L::T; #length of the box
t₀::Int = 0, #termalisation time
nmeas::Int = Int(floor(log(2, (tmax - t₀)))), #number of measurements (approximate)
slope::T = 1.0, #slope of the sampling
Δm::Int = 1, #intervals to store full configurations
sampletimes::Vector{Int} = whentomeasure(t₀, tmax, nmeas, slope = slope), #optional custom sampletimes
σ::T = 1.0, #particle diameter
ϵ::T = 0.5, #maximum size of the kick
κ::T = 1.0, #blending between BRO and RO
η::T = 0.0, #polydispersity
𝐗₀::Vector{Tuple{T, T}} = [L .* map(rand, (T, T)) for i ∈ 1 : N], #initial configuration
model::Type{W} = RO) where T <: AbstractFloat where W <: Model
#INISIALISATION
#Define parameters
M = length(sampletimes)
Mp = length(1 : Δm : M)
par = Parameters(N, M, L, ϵ, σ = σ, κ = κ, η = η)
Δt = [sampletimes[m] - sampletimes[m - 1] for m ∈ 2 : M]
Δm = M ÷ Mp
#Initialse arrays
head = - ones(Int, par.Nb^2)
lscl = - ones(Int, N)
𝜹 = [(zero(T), zero(T)) for i ∈ 1 : N]
conf = initialconf(par, 𝐗₀, 𝜹, head, lscl, model)
#Update until termalisation
@inbounds for t ∈ 1 : t₀
update!(conf, par, 𝜹, head, lscl, model)
end
#First measurement
meas = initialmeas(par, conf, sampletimes, Mp, T)
#MAIN LOOP
mp = 2
@inbounds for m ∈ 2 : M
#Update between two measurements
@inbounds for t ∈ 1 : Δt[m - 1]
update!(conf, par, 𝜹, head, lscl, model)
#Break in case of absorbing state
iszero(confacfrac(conf)) && break
end
#Measure active particles
meas.active[m] = confacfrac(conf)
#Store complete configuration once every Δm
if iszero((m - 1) % Δm)
meas.pos[mp] = copy(conf.pos)
mp += 1
end
#Fill in case of absorbing state
if iszero(confacfrac(conf))
meas.pos[mp : Mp] .= [meas.pos[mp - 1]]
break
end
end
#Store the last configuration
meas.pos[Mp] = copy(conf.pos)
return meas
end
"""
runs(n::Int, #number of simulations
N::Int, #number of particles
tmax::Int, #number of time steps
L::T; #length of the box
t₀::Int = 0, #termalisation time
nmeas::Int = Int(floor(log(2, (tmax - t₀)))), #number of measurements (approximate)
Δm::Int = 10, #intervals to store full configurations
sampletimes::Vector{Int} = whentomeasure(t₀, tmax, nmeas), #optional custom sampletimes
σ::T = 1.0, #particle diameter
ϵ::T = 0.5, #maximum size of the kick
κ::T = 1.0, #blending between BRO and RO
η::T = 0.0, #polydispersity
𝐗₀::Vector{Tuple{T, T}} = [L .* map(rand, (T, T)) for i ∈ 1 : N], #initial configuration
model::Type{W} = RO, #dynamical rule
verbose::Bool = false, #debug
ncores::Int = Threads.nthreads()) where T <: AbstractFloat where W <: Model
Run `n`simulations simultaneously using `ncores` processors.
"""
function runs(n::Int, #number of simulations
N::Int, #number of particles
tmax::Int, #number of time steps
L::T; #length of the box
t₀::Int = 0, #termalisation time
nmeas::Int = Int(floor(log(2, (tmax - t₀)))), #number of measurements (approximate)
Δm::Int = 10, #intervals to store full configurations
sampletimes::Vector{Int} = whentomeasure(t₀, tmax, nmeas), #optional custom sampletimes
σ::T = 1.0, #particle diameter
ϵ::T = 0.5, #maximum size of the kick
κ::T = 1.0, #blending between BRO and RO
η::T = 0.0, #polydispersity
𝐗₀::Vector{Tuple{T, T}} = [L .* map(rand, (T, T)) for i ∈ 1 : N], #initial configuration
model::Type{W} = RO, #dynamical rule
verbose::Bool = false, #debug
ncores::Int = Threads.nthreads()) where T <: AbstractFloat where W <: Model
res = Vector{Measures}(undef, n)
@floop ThreadedEx(basesize = n ÷ ncores) for k ∈ 1 : n
res[k] = simulation(N, tmax, L, t₀ = t₀, nmeas = nmeas, Δm = Δm, sampletimes = sampletimes, σ = σ, ϵ = ϵ, κ = κ, η = η, 𝐗₀ = 𝐗₀, model = model)
verbose && println("sim = $k on thread $(Threads.threadid())")
end
return res
end
nothing