Multivariate Hawkes Model

using JumpProcesses, Graphs, Statistics, BenchmarkTools, Plots
using SciMLLogging
using OrdinaryDiffEq: Tsit5
fmt = :png
width_px, height_px = default(:size);

Model and example solutions

Let a graph with $V$ nodes, then the multivariate Hawkes process is characterized by $V$ point processes such that the conditional intensity rate of node $i$ connected to a set of nodes $E_i$ in the graph is given by:

\[ \lambda_i^\ast (t) = \lambda + \sum_{j \in E_i} \sum_{t_{n_j} < t} \alpha \exp \left[-\beta (t - t_{n_j}) \right]\]

This process is known as self-exciting, because the occurrence of an event $j$ at $t_{n_j}$ will increase the conditional intensity of all the processes connected to it by $\alpha$. The excited intensity then decreases at a rate proportional to $\beta$.

The conditional intensity of this process has a recursive formulation which can significantly speed the simulation. The recursive formulation for the univariate case is derived in Laub et al. [2]. We derive the compound case here. Let $t_{N_i} = \max \{ t_{n_j} < t \mid j \in E_i \}$ and

\[\begin{split} \phi_i^\ast (t) &= \sum_{j \in E_i} \sum_{t_{n_j} < t} \alpha \exp \left[-\beta (t - t_{N_i} + t_{N_i} - t_{n_j}) \right] \\ &= \exp \left[ -\beta (t - t_{N_i}) \right] \sum_{j \in E_i} \sum_{t_{n_j} \leq t_{N_i}} \alpha \exp \left[-\beta (t_{N_i} - t_{n_j}) \right] \\ &= \exp \left[ -\beta (t - t_{N_i}) \right] \left( \alpha + \phi_i^\ast (t_{N_i}) \right) \end{split}\]

Then the conditional intensity can be re-written in terms of $\phi_i^\ast (t_{N_i})$

\[ \lambda_i^\ast (t) = \lambda + \phi_i^\ast (t) = \lambda + \exp \left[ -\beta (t - t_{N_i}) \right] \left( \alpha + \phi_i^\ast (t_{N_i}) \right)\]

In Julia, we define a factory for the conditional intensity $\lambda_i$ which returns the brute-force or recursive versions of the intensity given node $i$ and network $g$.

function hawkes_rate(i::Int, g; use_recursion = false)
    @inline @inbounds function rate_recursion(u, p, t)
        λ, α, β, h, urate, ϕ = p
        urate[i] = λ + exp(-β*(t - h[i]))*ϕ[i]
        return urate[i]
    end

    @inline @inbounds function rate_brute(u, p, t)
        λ, α, β, h, urate = p
        x = zero(typeof(t))
        for j in g[i]
            for _t in reverse(h[j])
                ϕij = α * exp(-β * (t - _t))
                if ϕij ≈ 0
                    break
                end
                x += ϕij
            end
        end
        urate[i] = λ + x
        return urate[i]
    end

    if use_recursion
        return rate_recursion
    else
        return rate_brute
    end
end

hawkes_rate (generic function with 1 method)

Given the rate factory, we can create a jump factory which will create all the jumps in our model.

function hawkes_jump(i::Int, g; use_recursion = false)
    rate = hawkes_rate(i, g; use_recursion)
    urate = rate
    @inbounds rateinterval(u, p, t) = p[5][i] == p[1] ? typemax(t) : 2 / p[5][i]
    @inbounds lrate(u, p, t) = p[1]
    @inbounds function affect_recursion!(integrator)
        λ, α, β, h, _, ϕ = integrator.p
        for j in g[i]
            ϕ[j] *= exp(-β*(integrator.t - h[j]))
            ϕ[j] += α
            h[j] = integrator.t
        end
        integrator.u[i] += 1
    end
    @inbounds function affect_brute!(integrator)
        push!(integrator.p[4][i], integrator.t)
        integrator.u[i] += 1
    end
    return VariableRateJump(
        rate,
        use_recursion ? affect_recursion! : affect_brute!;
        lrate,
        urate,
        rateinterval
    )
end

function hawkes_jump(u, g; use_recursion = false)
    return [hawkes_jump(i, g; use_recursion) for i in 1:length(u)]
end

hawkes_jump (generic function with 2 methods)

We can then create a factory for Multivariate Hawkes JumpProblems. We can define two types of JumpProblems depending on the aggregator. The Direct() aggregator expects an ODEProblem since it cannot handle the SSAStepper with VariableRateJumps.

function f!(du, u, p, t)
    du .= 0
    nothing
end

function hawkes_problem(
    p,
    agg;
    vr_agg = VR_DirectFW(),
    u = [0.0],
    tspan = (0.0, 50.0),
    save_positions = (false, true),
    g = [[1]],
    use_recursion = false,
)
    oprob = ODEProblem(f!, u, tspan, p)
    jumps = JumpSet(; variable_jumps = hawkes_jump(u, g; use_recursion))
    jprob = JumpProblem(oprob, agg, jumps; vr_aggregator = vr_agg, save_positions = save_positions)
    return jprob
end

hawkes_problem (generic function with 1 method)

The Coevolve() aggregator knows how to handle the SSAStepper, so it accepts a DiscreteProblem.

function hawkes_problem(
        p,
        agg::Coevolve;
        u = [0.0],
        tspan = (0.0, 50.0),
        save_positions = (false, true),
        g = [[1]],
        use_recursion = false
)
    dprob = DiscreteProblem(u, tspan, p)
    jumps = JumpSet(; variable_jumps = hawkes_jump(u, g; use_recursion))
    jprob = JumpProblem(dprob, agg, jumps; dep_graph = g, save_positions = save_positions)
    return jprob
end

hawkes_problem (generic function with 2 methods)

Let's solve the problems defined so far. We sample a random graph from the Erdős-Rényi model. This model assumes that the probability of an edge between two nodes is independent of other edges, which we fix at $0.2$. For illustration purposes, we fix $V = 10$.

V = 10
G = erdos_renyi(V, 0.2, seed = 9103)
g = [neighbors(G, i) for i in 1:nv(G)]

10-element Vector{Graphs.FrozenVector{Int64}}:
 [4, 6, 7, 8]
 [8]
 [5]
 [1]
 [3, 6, 9]
 [1, 5, 8]
 [1]
 [1, 2, 6]
 [5]
 0-element Graphs.FrozenVector{Int64}

We fix the Hawkes parameters at $\lambda = 0.5 , \alpha = 0.1 , \beta = 2.0$ which ensures the process does not explode.

tspan = (0.0, 50.0)
u = [0.0 for i in 1:nv(G)]
p = (0.5, 0.1, 2.0)

(0.5, 0.1, 2.0)

Now, we instantiate the problems, find their solutions and plot the results.

algorithms = Tuple{Any, Any, Bool, String}[
(
    Direct(), Tsit5(), false, "Direct (brute-force)"),
(
    Coevolve(), SSAStepper(), false, "Coevolve (brute-force)"),
(
    Direct(), Tsit5(), true, "Direct (recursive)"),
(
    Coevolve(), SSAStepper(), true, "Coevolve (recursive)")
]

let fig = []
    for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms)
        @info label
        if use_recursion
            h = zeros(eltype(tspan), nv(G))
            urate = zeros(eltype(tspan), nv(G))
            ϕ = zeros(eltype(tspan), nv(G))
            _p = (p[1], p[2], p[3], h, ϕ, urate)
        else
            h = [eltype(tspan)[] for _ in 1:nv(G)]
            urate = zeros(eltype(tspan), nv(G))
            _p = (p[1], p[2], p[3], h, urate)
        end
        jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion)
        sol = solve(jump_prob, stepper)
        push!(fig, plot(sol.t, sol[1:V, :]', title = label, legend = false, format = fmt))
    end
    fig = plot(fig..., layout = (2, 2), format = fmt, size = (width_px, 2*height_px/2))
end

Alternative libraries

We benchmark JumpProcesses.jl against PiecewiseDeterministicMarkovProcesses.jl and Python Tick library.

In order to compare with the PiecewiseDeterministicMarkovProcesses.jl, we need to reformulate our jump problem as a Piecewise Deterministic Markov Process (PDMP). In this setting, we have two options.

The simple version only requires the conditional intensity. Like above, we define a brute-force and recursive approach. Following the library's specification we define the following functions.

function hawkes_rate_simple_recursion(rate, xc, xd, p, t, issum::Bool)
    λ, _, β, h, ϕ, g = p
    for i in 1:length(g)
        rate[i] = λ + exp(-β * (t - h[i])) * ϕ[i]
    end
    if issum
        return sum(rate)
    end
    return 0.0
end

function hawkes_rate_simple_brute(rate, xc, xd, p, t, issum::Bool)
    λ, α, β, h, g = p
    for i in 1:length(g)
        x = zero(typeof(t))
        for j in g[i]
            for _t in reverse(h[j])
                ϕij = α * exp(-β * (t - _t))
                if ϕij ≈ 0
                    break
                end
                x += ϕij
            end
        end
        rate[i] = λ + x
    end
    if issum
        return sum(rate)
    end
    return 0.0
end

function hawkes_affect_simple_recursion!(xc, xd, p, t, i::Int64)
    _, α, β, h, ϕ, g = p
    for j in g[i]
        ϕ[j] *= exp(-β * (t - h[j]))
        ϕ[j] += α
        h[j] = t
    end
end

function hawkes_affect_simple_brute!(xc, xd, p, t, i::Int64)
    push!(p[4][i], t)
end

hawkes_affect_simple_brute! (generic function with 1 method)

Since this is a library for PDMP, we also need to define the ODE problem. In the simple version, we simply set it to zero.

function hawkes_drate_simple(dxc, xc, xd, p, t)
    dxc .= 0
end

hawkes_drate_simple (generic function with 1 method)

Next, we create a factory for the Multivariate Hawkes PDMPCHVSimple problem.

import LinearAlgebra: I
using PiecewiseDeterministicMarkovProcesses
const PDMP = PiecewiseDeterministicMarkovProcesses

struct PDMPCHVSimple end

function hawkes_problem(p,
        agg::PDMPCHVSimple;
        u = [0.0],
        tspan = (0.0, 50.0),
        save_positions = (false, true),
        g = [[1]],
        use_recursion = true)
    xd0 = Array{Int}(u)
    xc0 = copy(u)
    nu = one(eltype(xd0)) * I(length(xd0))
    if use_recursion
        jprob = PDMPProblem(hawkes_drate_simple, hawkes_rate_simple_recursion,
            hawkes_affect_simple_recursion!, nu, xc0, xd0, p, tspan)
    else
        jprob = PDMPProblem(hawkes_drate_simple, hawkes_rate_simple_brute,
            hawkes_affect_simple_brute!, nu, xc0, xd0, p, tspan)
    end
    return jprob
end

push!(algorithms, (PDMPCHVSimple(), CHV(Tsit5()), false, "PDMPCHVSimple (brute-force)"));
push!(algorithms, (PDMPCHVSimple(), CHV(Tsit5()), true, "PDMPCHVSimple (recursive)"));

The full version requires that we describe how the conditional intensity changes with time which we derive below:

\[\begin{split} \frac{d \lambda_i^\ast (t)}{d t} &= -\beta \sum_{j \in E_i} \sum_{t_{n_j} < t} \alpha \exp \left[-\beta (t - t_{n_j}) \right] \\ &= -\beta \left( \lambda_i^\ast (t) - \lambda \right) \end{split}\]

function hawkes_drate_full(dxc, xc, xd, p, t)
    λ, α, β, _, _, g = p
    for i in 1:length(g)
        dxc[i] = -β * (xc[i] - λ)
    end
end

hawkes_drate_full (generic function with 1 method)

Next, we need to define the intensity rate and the jumps according to library's specification.

function hawkes_rate_full(rate, xc, xd, p, t, issum::Bool)
    λ, α, β, _, _, g = p
    if issum
        return sum(@view(xc[1:length(g)]))
    end
    rate[1:length(g)] .= @view xc[1:length(g)]
    return 0.0
end

function hawkes_affect_full!(xc, xd, p, t, i::Int64)
    λ, α, β, _, _, g = p
    for j in g[i]
        xc[i] += α
    end
end

hawkes_affect_full! (generic function with 1 method)

Finally, we create a factory for the Multivariate Hawkes PDMPCHVFull problem.

struct PDMPCHVFull end

function hawkes_problem(
        p,
        agg::PDMPCHVFull;
        u = [0.0],
        tspan = (0.0, 50.0),
        save_positions = (false, true),
        g = [[1]],
        use_recursion = true
)
    xd0 = Array{Int}(u)
    xc0 = [p[1] for i in 1:length(u)]
    nu = one(eltype(xd0)) * I(length(xd0))
    jprob = PDMPProblem(
        hawkes_drate_full, hawkes_rate_full, hawkes_affect_full!, nu, xc0, xd0, p, tspan)
    return jprob
end

push!(algorithms, (PDMPCHVFull(), CHV(Tsit5()), true, "PDMPCHVFull"));

The Python Tick library is installed by the folder setup hook and accessed with PyCall.jl. We define a factory for the Multivariate Hawkes PyTick problem.

const BENCHMARK_PYTHON::Bool = tryparse(Bool, get(ENV, "SCIMLBENCHMARK_PYTHON", "true"))

struct PyTick end

if BENCHMARK_PYTHON
    using PyCall
    @info "PyCall" PyCall.libpython PyCall.pyversion PyCall.conda

    function hawkes_problem(
            p,
            agg::PyTick;
            u = [0.0],
            tspan = (0.0, 50.0),
            save_positions = (false, true),
            g = [[1]],
            use_recursion = true
    )
        λ, α, β = p
        SimuHawkesSumExpKernels = pyimport("tick.hawkes")[:SimuHawkesSumExpKernels]
        jprob = SimuHawkesSumExpKernels(
            baseline = fill(λ, length(u)),
            adjacency = [i in j ? α / β : 0.0 for j in g, i in 1:length(u), u in 1:1],
            decays = [β],
            end_time = tspan[2],
            verbose = SciMLLogging.None(),
            force_simulation = true
        )
        return jprob
    end

    push!(algorithms, (PyTick(), nothing, true, "PyTick"));
end

8-element Vector{Tuple{Any, Any, Bool, String}}:
 (JumpProcesses.Direct(), OrdinaryDiffEqTsit5.Tsit5{typeof(OrdinaryDiffEqCo
re.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), FastBroa
dcast.Serial}(OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivi
al_limiter!, FastBroadcast.Serial()), 0, "Direct (brute-force)")
 (JumpProcesses.Coevolve(), JumpProcesses.SSAStepper(), 0, "Coevolve (brute
-force)")
 (JumpProcesses.Direct(), OrdinaryDiffEqTsit5.Tsit5{typeof(OrdinaryDiffEqCo
re.trivial_limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), FastBroa
dcast.Serial}(OrdinaryDiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivi
al_limiter!, FastBroadcast.Serial()), 1, "Direct (recursive)")
 (JumpProcesses.Coevolve(), JumpProcesses.SSAStepper(), 1, "Coevolve (recur
sive)")
 (Main.var"##WeaveSandBox#277".PDMPCHVSimple(), PiecewiseDeterministicMarko
vProcesses.CHV{OrdinaryDiffEqTsit5.Tsit5{typeof(OrdinaryDiffEqCore.trivial_
limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), FastBroadcast.Seria
l}}(OrdinaryDiffEqTsit5.Tsit5{typeof(OrdinaryDiffEqCore.trivial_limiter!), 
typeof(OrdinaryDiffEqCore.trivial_limiter!), FastBroadcast.Serial}(Ordinary
DiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, FastBroad
cast.Serial())), 0, "PDMPCHVSimple (brute-force)")
 (Main.var"##WeaveSandBox#277".PDMPCHVSimple(), PiecewiseDeterministicMarko
vProcesses.CHV{OrdinaryDiffEqTsit5.Tsit5{typeof(OrdinaryDiffEqCore.trivial_
limiter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), FastBroadcast.Seria
l}}(OrdinaryDiffEqTsit5.Tsit5{typeof(OrdinaryDiffEqCore.trivial_limiter!), 
typeof(OrdinaryDiffEqCore.trivial_limiter!), FastBroadcast.Serial}(Ordinary
DiffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, FastBroad
cast.Serial())), 1, "PDMPCHVSimple (recursive)")
 (Main.var"##WeaveSandBox#277".PDMPCHVFull(), PiecewiseDeterministicMarkovP
rocesses.CHV{OrdinaryDiffEqTsit5.Tsit5{typeof(OrdinaryDiffEqCore.trivial_li
miter!), typeof(OrdinaryDiffEqCore.trivial_limiter!), FastBroadcast.Serial}
}(OrdinaryDiffEqTsit5.Tsit5{typeof(OrdinaryDiffEqCore.trivial_limiter!), ty
peof(OrdinaryDiffEqCore.trivial_limiter!), FastBroadcast.Serial}(OrdinaryDi
ffEqCore.trivial_limiter!, OrdinaryDiffEqCore.trivial_limiter!, FastBroadca
st.Serial())), 1, "PDMPCHVFull")
 (Main.var"##WeaveSandBox#277".PyTick(), nothing, 1, "PyTick")

Now, we instantiate the problems, find their solutions and plot the results.

let fig = []
    for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms[5:end])
        @info label
        if algo isa PyTick
            _p = (p[1], p[2], p[3])
            jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion)
            jump_prob.reset()
            jump_prob.simulate()
            t = tspan[1]:0.1:tspan[2]
            N = [[sum(jumps .< _t) for _t in t] for jumps in jump_prob.timestamps]
            push!(fig, plot(t, N, title = label, legend = false, format = fmt))
        elseif algo isa PDMPCHVSimple
            if use_recursion
                h = zeros(eltype(tspan), nv(G))
                ϕ = zeros(eltype(tspan), nv(G))
                _p = (p[1], p[2], p[3], h, ϕ, g)
            else
                h = [eltype(tspan)[] for _ in 1:nv(G)]
                _p = (p[1], p[2], p[3], h, g)
            end
            jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion)
            sol = solve(jump_prob, stepper)
            push!(fig, plot(
                sol.time, sol.xd[1:V, :]', title = label, legend = false, format = fmt))
        elseif algo isa PDMPCHVFull
            _p = (p[1], p[2], p[3], nothing, nothing, g)
            jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion)
            sol = solve(jump_prob, stepper)
            push!(fig, plot(
                sol.time, sol.xd[1:V, :]', title = label, legend = false, format = fmt))
        end
    end
    fig = plot(fig..., layout = (2, 2), format = fmt, size = (width_px, 2*height_px/2))
end

Correctness: QQ-Plots

We check that the algorithms produce correct simulation by inspecting their QQ-plots. Point process theory says that transforming the simulated points using the compensator should produce points whose inter-arrival duration is distributed according to the exponential distribution (see Section 7.4 [1]).

The compensator of any point process is the integral of the conditional intensity $\Lambda_i^\ast(t) = \int_0^t \lambda_i^\ast(u) du$. The compensator for the Multivariate Hawkes process is defined below.

\[ \Lambda_i^\ast(t) = \lambda t + \frac{\alpha}{\beta} \sum_{j \in E_i} \sum_{t_{n_j} < t} ( 1 - \exp \left[-\beta (t - t_{n_j}) \right])\]

function hawkes_Λ(i::Int, g, p)
    @inline @inbounds function Λ(t, h)
        λ, α, β = p
        x = λ * t
        for j in g[i]
            for _t in h[j]
                if _t >= t
                    break
                end
                x += (α / β) * (1 - exp(-β * (t - _t)))
            end
        end
        return x
    end
    return Λ
end

function hawkes_Λ(g, p)
    return [hawkes_Λ(i, g, p) for i in 1:length(g)]
end

Λ = hawkes_Λ(g, p)

10-element Vector{Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, V
ector{Graphs.FrozenVector{Int64}}, Tuple{Float64, Float64, Float64}}}:
 (::Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, Vector{Graphs.F
rozenVector{Int64}}, Tuple{Float64, Float64, Float64}}) (generic function w
ith 1 method)
 (::Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, Vector{Graphs.F
rozenVector{Int64}}, Tuple{Float64, Float64, Float64}}) (generic function w
ith 1 method)
 (::Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, Vector{Graphs.F
rozenVector{Int64}}, Tuple{Float64, Float64, Float64}}) (generic function w
ith 1 method)
 (::Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, Vector{Graphs.F
rozenVector{Int64}}, Tuple{Float64, Float64, Float64}}) (generic function w
ith 1 method)
 (::Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, Vector{Graphs.F
rozenVector{Int64}}, Tuple{Float64, Float64, Float64}}) (generic function w
ith 1 method)
 (::Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, Vector{Graphs.F
rozenVector{Int64}}, Tuple{Float64, Float64, Float64}}) (generic function w
ith 1 method)
 (::Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, Vector{Graphs.F
rozenVector{Int64}}, Tuple{Float64, Float64, Float64}}) (generic function w
ith 1 method)
 (::Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, Vector{Graphs.F
rozenVector{Int64}}, Tuple{Float64, Float64, Float64}}) (generic function w
ith 1 method)
 (::Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, Vector{Graphs.F
rozenVector{Int64}}, Tuple{Float64, Float64, Float64}}) (generic function w
ith 1 method)
 (::Main.var"##WeaveSandBox#277".var"#Λ#hawkes_Λ##0"{Int64, Vector{Graphs.F
rozenVector{Int64}}, Tuple{Float64, Float64, Float64}}) (generic function w
ith 1 method)

We need a method for extracting the history from a simulation run. Below, we define such functions for each type of algorithm.

"""
Given an ODE solution `sol`, recover the timestamp in which events occurred. It
returns a vector with the history of each process in `sol`.

It assumes that `JumpProblem` was initialized with `save_positions` equal to
`(true, false)`, `(false, true)` or `(true, true)` such the system's state is
saved before and/or after the jump occurs; and, that `sol.u` is a
non-decreasing series that counts the total number of events observed as a
function of time.
"""
function histories(u, t)
    _u = permutedims(reduce(hcat, u))
    k = size(_u)[2]
    # computes a mask that show when total counts change
    mask = cat(fill(0.0, 1, k), _u[2:end, :] .- _u[1:(end - 1), :], dims = 1) .≈ 1
    h = Vector{typeof(t)}(undef, k)
    @inbounds for i in 1:k
        h[i] = t[mask[:, i]]
    end
    return h
end

function histories(sol::S) where {S <: ODESolution}
    # get u and permute the dimensions to get a matrix n x k with n obsevations and k processes.
    if sol.u[1] isa ExtendedJumpArray
        u = map((u) -> u.u, sol.u)
    else
        u = sol.u
    end
    return histories(u, sol.t)
end

function histories(sol::S) where {S <: PDMP.PDMPResult}
    return histories(sol.xd.u, sol.time)
end

function histories(sols)
    map(histories, sols)
end

histories (generic function with 4 methods)

We also need to compute the quantiles of the empirical distribution given a history of events hs, the compensator Λ and the target quantiles quant.

import Distributions: Exponential

"""
Computes the empirical and expected quantiles given a history of events `hs`,
the compensator `Λ` and the target quantiles `quant`.

The history `hs` is a vector with the history of each process. Alternatively,
the function also takes a vector of histories containing the histories from
multiple runs.

The compensator `Λ` can either be an homogeneous compensator function that
equally applies to all the processes in `hs`. Alternatively, it accepts a
vector of compensator that applies to each process.
"""
function qq(hs, Λ, quant = 0.01:0.01:0.99)
    _hs = apply_Λ(hs, Λ)
    T = typeof(hs[1][1][1])
    Δs = Vector{Vector{T}}(undef, length(hs[1]))
    for k in 1:length(Δs)
        _Δs = Vector{Vector{T}}(undef, length(hs))
        for i in 1:length(_Δs)
            _Δs[i] = _hs[i][k][2:end] .- _hs[i][k][1:(end - 1)]
        end
        Δs[k] = reduce(vcat, _Δs)
    end
    empirical_quant = map((_Δs) -> quantile(_Δs, quant), Δs)
    expected_quant = quantile(Exponential(1.0), quant)
    return empirical_quant, expected_quant
end

"""
Compute the compensator `Λ` value for each timestamp recorded in history `hs`.

The history `hs` is a vector with the history of each process. Alternatively,
the function also takes a vector of histories containing the histories from
multiple runs.

The compensator `Λ` can either be an homogeneous compensator function that
equally applies to all the processes in `hs`. Alternatively, it accepts a
vector of compensator that applies to each process.
"""
function apply_Λ(hs::V, Λ) where {V <: Vector{<:Number}}
    _hs = similar(hs)
    @inbounds for n in 1:length(hs)
        _hs[n] = Λ(hs[n], hs)
    end
    return _hs
end

function apply_Λ(k::Int, hs::V, Λ::A) where {V <: Vector{<:Vector{<:Number}}, A <: Array}
    @inbounds hsk = hs[k]
    @inbounds Λk = Λ[k]
    _hs = similar(hsk)
    @inbounds for n in 1:length(hsk)
        _hs[n] = Λk(hsk[n], hs)
    end
    return _hs
end

function apply_Λ(hs::V, Λ) where {V <: Vector{<:Vector{<:Number}}}
    _hs = similar(hs)
    @inbounds for k in 1:length(_hs)
        _hs[k] = apply_Λ(hs[k], Λ)
    end
    return _hs
end

function apply_Λ(hs::V, Λ::A) where {V <: Vector{<:Vector{<:Number}}, A <: Array}
    _hs = similar(hs)
    @inbounds for k in 1:length(_hs)
        _hs[k] = apply_Λ(k, hs, Λ)
    end
    return _hs
end

function apply_Λ(hs::V, Λ) where {V <: Vector{<:Vector{<:Vector{<:Number}}}}
    return map((_hs) -> apply_Λ(_hs, Λ), hs)
end

apply_Λ (generic function with 5 methods)

We can construct QQ-plots with a Plot recipe as follows.

@userplot QQPlot
@recipe function f(x::QQPlot)
    empirical_quant, expected_quant = x.args
    max_empirical_quant = maximum(maximum, empirical_quant)
    max_expected_quant = maximum(expected_quant)
    upperlim = ceil(maximum([max_empirical_quant, max_expected_quant]))
    @series begin
        seriestype := :line
        linecolor := :lightgray
        label --> ""
        (x) -> x
    end
    @series begin
        seriestype := :scatter
        aspect_ratio := :equal
        xlims := (0.0, upperlim)
        ylims := (0.0, upperlim)
        xaxis --> "Expected"
        yaxis --> "Empirical"
        markerstrokewidth --> 0
        markerstrokealpha --> 0
        markersize --> 1.5
        size --> (400, 500)
        label --> permutedims(["quantiles $i" for i in 1:length(empirical_quant)])
        expected_quant, empirical_quant
    end
end

Now, we simulate all of the algorithms we defined in the previous Section $250$ times to produce their QQ-plots.

let fig = []
    for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms)
        @info label
        if algo isa PyTick
            _p = (p[1], p[2], p[3])
        elseif algo isa PDMPCHVSimple
            if use_recursion
                h = zeros(eltype(tspan), nv(G))
                ϕ = zeros(eltype(tspan), nv(G))
                _p = (p[1], p[2], p[3], h, ϕ, g)
            else
                h = [eltype(tspan)[] for _ in 1:nv(G)]
                _p = (p[1], p[2], p[3], h, g)
            end
        elseif algo isa PDMPCHVFull
            _p = (p[1], p[2], p[3], nothing, nothing, g)
        else
            if use_recursion
                h = zeros(eltype(tspan), nv(G))
                ϕ = zeros(eltype(tspan), nv(G))
                urate = zeros(eltype(tspan), nv(G))
                _p = (p[1], p[2], p[3], h, urate, ϕ)
            else
                h = [eltype(tspan)[] for _ in 1:nv(G)]
                urate = zeros(eltype(tspan), nv(G))
                _p = (p[1], p[2], p[3], h, urate)
            end
        end
        jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion)
        runs = Vector{Vector{Vector{Number}}}(undef, 250)
        for n in 1:length(runs)
            if algo isa PyTick
                jump_prob.reset()
                jump_prob.simulate()
                runs[n] = jump_prob.timestamps
            else
                if ~(algo isa PDMPCHVFull)
                    if use_recursion
                        h .= 0
                        ϕ .= 0
                    else
                        for _h in h
                            empty!(_h)
                        end
                    end
                    if ~(algo isa PDMPCHVSimple)
                        urate .= 0
                    end
                end
                runs[n] = histories(solve(jump_prob, stepper))
            end
        end
        qqs = qq(runs, Λ)
        push!(fig, qqplot(
            qqs..., legend = false, aspect_ratio = :equal, title = label, fmt = fmt))
    end
    fig = plot(fig..., layout = (4, 2), fmt = fmt, size = (width_px, 4*height_px/2))
end

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Benchmarking performance

In this Section we benchmark all the algorithms introduced in the first Section.

We generate networks in the range from $1$ to $95$ nodes and simulate the Multivariate Hawkes process for $25$ units of time. We fix the Hawkes parameters at $\lambda = 0.5 , \alpha = 0.1 , \beta = 5.0$ which ensures the process does not explode. We simulate $50$ trajectories with a limit of ten seconds to complete execution for each configuration. Only configurations that complete all $50$ trajectories within that limit are plotted.

tspan = (0.0, 25.0)
p = (0.5, 0.1, 5.0)
Vs = append!([1], 5:5:95)
Gs = [erdos_renyi(V, 0.2, seed = 6221) for V in Vs]

bs = Vector{Vector{BenchmarkTools.Trial}}()

for (algo, stepper, use_recursion, label) in algorithms
    @info label
    global _stepper = stepper
    push!(bs, Vector{BenchmarkTools.Trial}())
    _bs = bs[end]
    for (i, G) in enumerate(Gs)
        local g = [neighbors(G, i) for i in 1:nv(G)]
        local u = [0.0 for i in 1:nv(G)]
        if algo isa PyTick
            _p = (p[1], p[2], p[3])
        elseif algo isa PDMPCHVSimple
            if use_recursion
                global h = zeros(eltype(tspan), nv(G))
                global ϕ = zeros(eltype(tspan), nv(G))
                _p = (p[1], p[2], p[3], h, ϕ, g)
            else
                global h = [eltype(tspan)[] for _ in 1:nv(G)]
                _p = (p[1], p[2], p[3], h, g)
            end
        elseif algo isa PDMPCHVFull
            _p = (p[1], p[2], p[3], nothing, nothing, g)
        else
            if use_recursion
                global h = zeros(eltype(tspan), nv(G))
                global urate = zeros(eltype(tspan), nv(G))
                global ϕ = zeros(eltype(tspan), nv(G))
                _p = (p[1], p[2], p[3], h, urate, ϕ)
            else
                global h = [eltype(tspan)[] for _ in 1:nv(G)]
                global urate = zeros(eltype(tspan), nv(G))
                _p = (p[1], p[2], p[3], h, urate)
            end
        end
        global jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion)
        trial = try
            if algo isa PyTick
                @benchmark($(jump_prob).simulate(),
                    setup=($(jump_prob).reset()),
                    samples=50,
                    evals=1,
                    seconds=10,)
            else
                if algo isa PDMPCHVFull
                    @benchmark(solve($jump_prob, $_stepper),
                        setup=(),
                        samples=50,
                        evals=1,
                        seconds=10,)
                elseif algo isa PDMPCHVSimple
                    if use_recursion
                        @benchmark(solve($jump_prob, $_stepper),
                            setup=(h .= 0; ϕ .= 0),
                            samples=50,
                            evals=1,
                            seconds=10,)
                    else
                        @benchmark(solve($jump_prob, $_stepper),
                            setup=([empty!(_h) for _h in h]),
                            samples=50,
                            evals=1,
                            seconds=10,)
                    end
                else
                    if use_recursion
                        @benchmark(solve($jump_prob, $_stepper),
                            setup=(h .= 0; urate .= 0; ϕ .= 0),
                            samples=50,
                            evals=1,
                            seconds=10,)
                    else
                        @benchmark(solve($jump_prob, $_stepper),
                            setup=([empty!(_h) for _h in h]; urate .= 0),
                            samples=50,
                            evals=1,
                            seconds=10,)
                    end
                end
            end
        catch e
            BenchmarkTools.Trial(
                BenchmarkTools.Parameters(samples = 50, evals = 1, seconds = 10),
            )
        end
        push!(_bs, trial)
        if (nv(G) == 1 || nv(G) % 10 == 0)
            median_time = length(trial) > 0 ?
                          "$(BenchmarkTools.prettytime(median(trial.times)))" :
                          "nan"
            println("algo=$(label), V = $(nv(G)), length = $(length(trial.times)), median time = $median_time")
        end
    end
end

algo=Direct (brute-force), V = 1, length = 50, median time = 129.204 μs
algo=Direct (brute-force), V = 10, length = 50, median time = 24.076 ms
algo=Direct (brute-force), V = 20, length = 43, median time = 219.219 ms
algo=Direct (brute-force), V = 30, length = 13, median time = 785.327 ms
algo=Direct (brute-force), V = 40, length = 5, median time = 2.081 s
algo=Direct (brute-force), V = 50, length = 3, median time = 4.513 s
algo=Direct (brute-force), V = 60, length = 2, median time = 7.631 s
algo=Direct (brute-force), V = 70, length = 1, median time = 14.146 s
algo=Direct (brute-force), V = 80, length = 1, median time = 24.925 s
algo=Direct (brute-force), V = 90, length = 1, median time = 39.603 s
algo=Coevolve (brute-force), V = 1, length = 50, median time = 5.450 μs
algo=Coevolve (brute-force), V = 10, length = 50, median time = 278.788 μs
algo=Coevolve (brute-force), V = 20, length = 50, median time = 1.374 ms
algo=Coevolve (brute-force), V = 30, length = 50, median time = 3.798 ms
algo=Coevolve (brute-force), V = 40, length = 50, median time = 10.286 ms
algo=Coevolve (brute-force), V = 50, length = 50, median time = 22.363 ms
algo=Coevolve (brute-force), V = 60, length = 50, median time = 42.490 ms
algo=Coevolve (brute-force), V = 70, length = 50, median time = 60.809 ms
algo=Coevolve (brute-force), V = 80, length = 50, median time = 118.536 ms
algo=Coevolve (brute-force), V = 90, length = 46, median time = 211.513 ms
algo=Direct (recursive), V = 1, length = 50, median time = 128.599 μs
algo=Direct (recursive), V = 10, length = 50, median time = 4.274 ms
algo=Direct (recursive), V = 20, length = 50, median time = 16.564 ms
algo=Direct (recursive), V = 30, length = 50, median time = 36.925 ms
algo=Direct (recursive), V = 40, length = 50, median time = 68.999 ms
algo=Direct (recursive), V = 50, length = 50, median time = 113.398 ms
algo=Direct (recursive), V = 60, length = 50, median time = 168.837 ms
algo=Direct (recursive), V = 70, length = 41, median time = 235.437 ms
algo=Direct (recursive), V = 80, length = 29, median time = 336.259 ms
algo=Direct (recursive), V = 90, length = 21, median time = 450.412 ms
algo=Coevolve (recursive), V = 1, length = 50, median time = 5.830 μs
algo=Coevolve (recursive), V = 10, length = 50, median time = 115.939 μs
algo=Coevolve (recursive), V = 20, length = 50, median time = 358.058 μs
algo=Coevolve (recursive), V = 30, length = 50, median time = 713.175 μs
algo=Coevolve (recursive), V = 40, length = 50, median time = 1.247 ms
algo=Coevolve (recursive), V = 50, length = 50, median time = 1.957 ms
algo=Coevolve (recursive), V = 60, length = 50, median time = 2.952 ms
algo=Coevolve (recursive), V = 70, length = 50, median time = 3.847 ms
algo=Coevolve (recursive), V = 80, length = 50, median time = 5.773 ms
algo=Coevolve (recursive), V = 90, length = 50, median time = 7.942 ms
algo=PDMPCHVSimple (brute-force), V = 1, length = 50, median time = 163.978
 μs
algo=PDMPCHVSimple (brute-force), V = 10, length = 50, median time = 6.460 
ms
algo=PDMPCHVSimple (brute-force), V = 20, length = 50, median time = 49.865
 ms
algo=PDMPCHVSimple (brute-force), V = 30, length = 50, median time = 174.40
9 ms
algo=PDMPCHVSimple (brute-force), V = 40, length = 25, median time = 402.16
9 ms
algo=PDMPCHVSimple (brute-force), V = 50, length = 12, median time = 881.40
2 ms
algo=PDMPCHVSimple (brute-force), V = 60, length = 6, median time = 1.686 s
algo=PDMPCHVSimple (brute-force), V = 70, length = 4, median time = 2.646 s
algo=PDMPCHVSimple (brute-force), V = 80, length = 2, median time = 5.093 s
algo=PDMPCHVSimple (brute-force), V = 90, length = 2, median time = 7.777 s
algo=PDMPCHVSimple (recursive), V = 1, length = 50, median time = 160.049 μ
s
algo=PDMPCHVSimple (recursive), V = 10, length = 50, median time = 593.076 
μs
algo=PDMPCHVSimple (recursive), V = 20, length = 50, median time = 1.239 ms
algo=PDMPCHVSimple (recursive), V = 30, length = 50, median time = 2.231 ms
algo=PDMPCHVSimple (recursive), V = 40, length = 50, median time = 3.321 ms
algo=PDMPCHVSimple (recursive), V = 50, length = 50, median time = 4.853 ms
algo=PDMPCHVSimple (recursive), V = 60, length = 50, median time = 6.859 ms
algo=PDMPCHVSimple (recursive), V = 70, length = 50, median time = 9.233 ms
algo=PDMPCHVSimple (recursive), V = 80, length = 50, median time = 13.131 m
s
algo=PDMPCHVSimple (recursive), V = 90, length = 50, median time = 18.022 m
s
algo=PDMPCHVFull, V = 1, length = 50, median time = 163.004 μs
algo=PDMPCHVFull, V = 10, length = 50, median time = 860.884 μs
algo=PDMPCHVFull, V = 20, length = 50, median time = 1.291 ms
algo=PDMPCHVFull, V = 30, length = 50, median time = 1.894 ms
algo=PDMPCHVFull, V = 40, length = 50, median time = 2.225 ms
algo=PDMPCHVFull, V = 50, length = 50, median time = 2.612 ms
algo=PDMPCHVFull, V = 60, length = 50, median time = 3.430 ms
algo=PDMPCHVFull, V = 70, length = 50, median time = 4.026 ms
algo=PDMPCHVFull, V = 80, length = 50, median time = 5.999 ms
algo=PDMPCHVFull, V = 90, length = 50, median time = 7.543 ms
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.10e-04 seconds.
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Done simulating using SimuHawkesSumExpKernels in 4.07e-04 seconds.
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Done simulating using SimuHawkesSumExpKernels in 3.95e-04 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.23e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.55e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.81e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.74e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.77e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.69e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.81e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.69e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.15e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.67e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.62e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.69e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.67e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.77e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.72e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.74e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.74e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.72e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.15e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.12e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.81e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.77e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.67e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.69e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.98e-05 seconds.
algo=PyTick, V = 1, length = 50, median time = 45.760 μs
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.31e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.96e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.72e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.08e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.77e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.03e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.10e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.74e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.29e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.67e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.67e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.86e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.84e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.81e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.65e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.67e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.74e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.93e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.96e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.74e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.65e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.77e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.15e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.58e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.58e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.63e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.67e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.15e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.65e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.89e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.32e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.17e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.15e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.36e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.44e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.96e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.34e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.20e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.36e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.32e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.06e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.77e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.82e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.05e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.58e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.34e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.53e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.84e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.46e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.03e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.27e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.82e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.70e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.32e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.46e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.10e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.86e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.46e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.53e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.82e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.44e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.67e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.25e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.56e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.34e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.22e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.72e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.94e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.29e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.22e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.05e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.67e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.41e-05 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.47e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.15e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.16e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.46e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.92e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.29e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.89e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.11e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.98e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.85e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.00e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.06e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.13e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.96e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.09e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.03e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.75e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.71e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.12e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.07e-04 seconds.
-----------------------------------------------------
algo=PyTick, V = 10, length = 50, median time = 216.048 μs
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.54e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.95e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.13e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.05e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.73e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.82e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.86e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.74e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.03e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.99e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.69e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.07e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.95e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.81e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.90e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.98e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.80e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.79e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.13e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.72e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.83e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.04e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.14e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.80e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.95e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.11e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.86e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.80e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.58e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.89e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.08e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.90e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.67e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.89e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.36e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.18e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.86e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.97e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.88e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.53e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.24e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.33e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.90e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.09e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.78e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.05e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.55e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.21e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.61e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.87e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.84e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.89e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.05e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.75e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.61e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.34e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.80e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.63e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.84e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.36e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.51e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.29e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.19e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.06e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.70e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.80e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.90e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.60e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.88e-04 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.83e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.18e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.12e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.58e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.39e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.80e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.25e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.98e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.64e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.17e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.33e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.69e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.25e-04 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.47e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.45e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.28e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.40e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.27e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.31e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.41e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.34e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.43e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.39e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.39e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
algo=PyTick, V = 20, length = 50, median time = 1.342 ms
Done simulating using SimuHawkesSumExpKernels in 1.38e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.23e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.54e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.23e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.22e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.34e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.30e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.26e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.35e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.30e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.20e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.52e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.44e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.20e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.24e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.33e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.34e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.29e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.40e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.30e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.30e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.52e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.25e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.29e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.23e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.29e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.34e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.32e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.37e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.37e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.18e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.33e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.39e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.26e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.47e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.14e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.27e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.39e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.36e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.17e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.57e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.59e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.35e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.45e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.62e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.27e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.51e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.60e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.56e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.37e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.58e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.62e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.55e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.60e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.54e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.64e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.47e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.43e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.53e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.51e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.61e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.51e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.50e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.52e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.59e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.43e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.41e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.54e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.39e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.34e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.45e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.33e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.20e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.56e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.68e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.54e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.52e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.49e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.39e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.19e-03 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.41e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.36e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.46e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.66e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.58e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.56e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.44e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.56e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.62e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.55e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.41e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.24e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.51e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.17e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.12e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.21e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.23e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.16e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.06e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.24e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.22e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.80e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.01e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.01e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.82e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.40e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.12e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.26e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.75e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.89e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.13e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.12e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.89e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.02e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.88e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.73e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.52e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.98e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.51e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.06e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.42e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.04e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.95e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.10e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.30e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.45e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.12e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.97e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.38e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.75e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.67e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.10e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.97e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.41e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.00e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.06e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.08e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.01e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.25e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.58e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
algo=PyTick, V = 30, length = 50, median time = 4.127 ms
Done simulating using SimuHawkesSumExpKernels in 4.38e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.17e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.15e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.27e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.97e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.26e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.05e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.48e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.65e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.60e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.15e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.11e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.71e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.33e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.36e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.72e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.85e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.56e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.34e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.07e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.62e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.62e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.43e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.94e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.40e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.55e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.01e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.00e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.49e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.03e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.71e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.60e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.64e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.56e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.97e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.49e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.66e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.20e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.18e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.39e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.12e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.74e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.55e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.67e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.86e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.42e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.39e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.32e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.11e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.30e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.92e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.57e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.68e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.13e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.03e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.64e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.93e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.06e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.98e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.08e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.03e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.37e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.07e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.01e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.05e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.00e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.06e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.05e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.09e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.00e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.89e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.66e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.01e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.87e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.87e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.02e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.12e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.69e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.03e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.24e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.08e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.12e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.02e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.93e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.64e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.33e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.16e-02 seconds.
algo=PyTick, V = 40, length = 50, median time = 10.288 ms
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.81e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.68e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.96e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.07e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 9.47e-03 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.03e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.02e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.53e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.54e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.59e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.54e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.58e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.31e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.57e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.56e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.63e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.33e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.61e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.56e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.41e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.52e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.52e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.35e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.54e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.40e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.49e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.48e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.48e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.37e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.49e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.45e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.43e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.56e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.38e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.48e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.46e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.36e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.43e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.48e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.44e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.47e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.42e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.42e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.46e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.48e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.57e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.38e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.14e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.27e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.24e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.33e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.25e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.42e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.10e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.29e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.39e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.24e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.16e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.30e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.29e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.25e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.06e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.15e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.23e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.09e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.00e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.23e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.29e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.19e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.37e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.19e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.25e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.12e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.30e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.17e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.28e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.19e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.22e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.09e-02 seconds.
-----------------------------------------------------
algo=PyTick, V = 50, length = 50, median time = 22.006 ms
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.17e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.11e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.19e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.14e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.25e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.20e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.18e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.21e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.18e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.37e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.19e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.20e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.19e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.22e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.19e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.29e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.16e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.99e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.39e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.14e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.09e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.07e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.45e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.44e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.28e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.06e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.40e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.37e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.17e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.19e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.25e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.33e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.20e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.13e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.39e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.56e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.41e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.49e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.17e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.22e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.35e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.84e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.05e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.25e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.21e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.15e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.49e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.11e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.29e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.33e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.55e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.33e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.83e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.38e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.17e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.41e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.06e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.35e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.23e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.10e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.23e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.19e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.16e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.06e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.38e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.26e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.25e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.26e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 3.37e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.49e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.90e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.79e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.88e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.95e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.42e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.86e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.47e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.39e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.95e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.12e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.88e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.60e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.33e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.70e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.68e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.62e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.72e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.87e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.62e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.55e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.55e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.53e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
algo=PyTick, V = 60, length = 50, median time = 46.863 ms
Done simulating using SimuHawkesSumExpKernels in 4.60e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.60e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.83e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.77e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.48e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.70e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.84e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.40e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.62e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.53e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.85e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.80e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.36e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.74e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.92e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.28e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.62e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.82e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.07e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.37e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.85e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.66e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.60e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.69e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.58e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.96e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.10e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 4.51e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.36e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.99e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.92e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.30e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.30e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.06e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.20e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.06e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.94e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.00e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.81e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.57e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.08e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.47e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.14e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.88e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.21e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.85e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.40e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.73e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.15e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.14e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.10e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.01e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.37e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.84e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.34e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.93e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.46e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.00e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.98e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.09e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.18e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.80e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.15e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.96e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.83e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.06e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.36e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.05e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.84e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.06e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.01e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.12e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.94e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.08e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.36e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.10e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.94e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 6.49e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 5.81e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.84e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.17e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.07e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.29e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.93e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.15e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.18e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.31e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.23e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.11e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.89e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.08e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.13e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.14e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.22e-02 seconds.
algo=PyTick, V = 70, length = 50, median time = 80.571 ms
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.16e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.84e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.76e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.14e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.17e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.45e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.10e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.65e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.41e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.82e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.66e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.19e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.78e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.90e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.96e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.11e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.82e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.88e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.84e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.12e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.85e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.07e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.04e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.93e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.80e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.47e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.69e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.81e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.63e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.16e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.85e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 7.76e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.12e-02 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.03e-02 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 8.48e-02 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.07e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.06e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.16e-01 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.22e-01 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.12e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.16e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.21e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.19e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.15e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.11e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.13e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.06e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.11e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.19e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.14e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.10e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.11e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.15e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.08e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.14e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.09e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.11e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.08e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.14e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.17e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.12e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.14e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.13e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.11e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.17e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.09e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.10e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.09e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.14e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.14e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.18e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.10e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.07e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.07e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.09e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.09e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.15e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.10e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.11e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.14e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.14e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.23e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.21e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.13e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.12e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.08e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.45e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.45e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.46e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.41e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.49e-01 seconds.
-----------------------------------------------------
algo=PyTick, V = 80, length = 50, median time = 149.130 ms
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.52e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.61e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.45e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.54e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.56e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.49e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.45e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.49e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.49e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.46e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.49e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.39e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.46e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.42e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.43e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.61e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.52e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.45e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.44e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.45e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.46e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.48e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.54e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.44e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.55e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.53e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.53e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.39e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.47e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.42e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.43e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.60e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.43e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.50e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.56e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.51e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.85e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.92e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.79e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.95e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.77e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.97e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.85e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.83e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.86e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.96e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.82e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.83e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.86e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.91e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.90e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.75e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.87e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.94e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.95e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.91e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.94e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.82e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.85e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.80e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.91e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.83e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.95e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.76e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.86e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.88e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.80e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.77e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.84e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.88e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.99e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.81e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.84e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.91e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.88e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.89e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.94e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.93e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.84e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.95e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.87e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.74e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.86e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.90e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
algo=PyTick, V = 90, length = 43, median time = 237.756 ms
Done simulating using SimuHawkesSumExpKernels in 1.85e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.96e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 1.88e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.39e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.30e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.40e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.44e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.47e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.29e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.38e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.49e-01 seconds.
-----------------------------------------------------
Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.49e-01 seconds.
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Launching simulation using SimuHawkesSumExpKernels...
Done simulating using SimuHawkesSumExpKernels in 2.41e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.17e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.36e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.46e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.33e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.39e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.31e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.45e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.23e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.42e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.25e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.39e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.32e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.31e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.49e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.29e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.29e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.38e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.48e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.47e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.45e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.38e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.42e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.31e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.31e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.34e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.41e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.43e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.39e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.24e-01 seconds.
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Done simulating using SimuHawkesSumExpKernels in 2.29e-01 seconds.
-----------------------------------------------------

let fig = plot(
        yscale = :log10,
        xlabel = "V",
        ylabel = "Time (ns)",
        legend_position = :outertopright,
        size = (800, 400),
    )
    for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms)
        _bs, _Vs = [], []
        for (j, b) in enumerate(bs[i])
            if length(b) == 50
                push!(_bs, median(b.times))
                push!(_Vs, Vs[j])
            end
        end
        plot!(_Vs, _bs, label = label)
    end
    title!("Simulations, 50 samples: nodes × time")
end

Benchmarking Variable Rate Aggregators

We benchmark the variable rate aggregators (VR_Direct, VR_DirectFW, VR_FRM) for the Multivariate Hawkes process, using the same setup as above: networks from $1$ to $95$ nodes, tspan = (0.0, 25.0), $\lambda = 0.5$, $\alpha = 0.1$, $\beta = 5.0$, and 50 trajectories with a 10-second limit per configuration. We test both recursive and brute-force formulations. VR_FRM is only run up to 40 nodes because constructing its per-jump callbacks becomes compilation-bound beyond that point; VR_Direct and VR_DirectFW are run over the full range. As above, only configurations that complete all 50 trajectories within the limit are plotted.

vr_aggs = [
    (VR_Direct(), Tsit5(), false, "VR_Direct (brute-force)"),
    (VR_DirectFW(), Tsit5(), false, "VR_DirectFW (brute-force)"),
    (VR_FRM(), Tsit5(), false, "VR_FRM (brute-force)"),
    (VR_Direct(), Tsit5(), true, "VR_Direct (recursive)"),
    (VR_DirectFW(), Tsit5(), true, "VR_DirectFW (recursive)"),
    (VR_FRM(), Tsit5(), true, "VR_FRM (recursive)"),
]

tspan = (0.0, 25.0)
p = (0.5, 0.1, 5.0)
Vs = append!([1], 5:5:95)
Gs = [erdos_renyi(V, 0.2, seed = 6221) for V in Vs]

vr_bs = Vector{Vector{BenchmarkTools.Trial}}()

for (vr_agg, stepper, use_recursion, label) in vr_aggs
    @info label
    global _stepper = stepper
    push!(vr_bs, Vector{BenchmarkTools.Trial}())
    _vr_bs = vr_bs[end]
    local benchmark_graphs = vr_agg isa VR_FRM ? Gs[Vs .<= 40] : Gs
    for (i, G) in enumerate(benchmark_graphs)
        local g = [neighbors(G, i) for i in 1:nv(G)]
        local u = [0.0 for i in 1:nv(G)]
        if use_recursion
            global h = zeros(eltype(tspan), nv(G))
            global urate = zeros(eltype(u), nv(G))
            global ϕ = zeros(eltype(tspan), nv(G))
            _p = (p[1], p[2], p[3], h, urate, ϕ)
        else
            global h = [eltype(tspan)[] for _ in 1:nv(G)]
            global urate = zeros(eltype(u), nv(G))
            _p = (p[1], p[2], p[3], h, urate)
        end
        global jump_prob = hawkes_problem(_p, Direct(); vr_agg, u, tspan, g, use_recursion)
        trial = try
            if use_recursion
                @benchmark(
                    solve($jump_prob, $_stepper),
                    setup = (h .= 0; urate .= 0; ϕ .= 0),
                    samples = 50,
                    evals = 1,
                    seconds = 10,
                )
            else
                @benchmark(
                    solve($jump_prob, $_stepper),
                    setup = ([empty!(_h) for _h in h]; urate .= 0),
                    samples = 50,
                    evals = 1,
                    seconds = 10,
                )
            end
        catch e
            BenchmarkTools.Trial(
                BenchmarkTools.Parameters(samples=50, evals=1, seconds=10),
            )
        end
        push!(_vr_bs, trial)
        if (nv(G) == 1 || nv(G) % 10 == 0)
            median_time =
                length(trial) > 0 ? "$(BenchmarkTools.prettytime(median(trial.times)))" : "nan"
            println("algo=$label, V=$(nv(G)), length=$(length(trial.times)), median time=$median_time")
        end
    end
end

algo=VR_Direct (brute-force), V=1, length=50, median time=102.504 μs
algo=VR_Direct (brute-force), V=10, length=50, median time=23.148 ms
algo=VR_Direct (brute-force), V=20, length=46, median time=204.947 ms
algo=VR_Direct (brute-force), V=30, length=13, median time=778.144 ms
algo=VR_Direct (brute-force), V=40, length=2, median time=9.693 s
algo=VR_Direct (brute-force), V=50, length=1, median time=15.576 s
algo=VR_Direct (brute-force), V=60, length=1, median time=29.830 s
algo=VR_Direct (brute-force), V=70, length=1, median time=44.285 s
algo=VR_Direct (brute-force), V=80, length=1, median time=73.456 s
algo=VR_Direct (brute-force), V=90, length=1, median time=93.266 s
algo=VR_DirectFW (brute-force), V=1, length=50, median time=122.564 μs
algo=VR_DirectFW (brute-force), V=10, length=50, median time=23.890 ms
algo=VR_DirectFW (brute-force), V=20, length=44, median time=219.268 ms
algo=VR_DirectFW (brute-force), V=30, length=13, median time=750.276 ms
algo=VR_DirectFW (brute-force), V=40, length=5, median time=1.972 s
algo=VR_DirectFW (brute-force), V=50, length=3, median time=4.694 s
algo=VR_DirectFW (brute-force), V=60, length=2, median time=9.207 s
algo=VR_DirectFW (brute-force), V=70, length=1, median time=14.169 s
algo=VR_DirectFW (brute-force), V=80, length=1, median time=26.920 s
algo=VR_DirectFW (brute-force), V=90, length=1, median time=41.537 s
algo=VR_FRM (brute-force), V=1, length=50, median time=191.819 μs
algo=VR_FRM (brute-force), V=10, length=50, median time=43.141 ms
algo=VR_FRM (brute-force), V=20, length=20, median time=491.024 ms
algo=VR_FRM (brute-force), V=30, length=7, median time=1.510 s
algo=VR_FRM (brute-force), V=40, length=4, median time=3.052 s
algo=VR_Direct (recursive), V=1, length=50, median time=112.794 μs
algo=VR_Direct (recursive), V=10, length=50, median time=1.555 ms
algo=VR_Direct (recursive), V=20, length=50, median time=4.379 ms
algo=VR_Direct (recursive), V=30, length=50, median time=9.635 ms
algo=VR_Direct (recursive), V=40, length=3, median time=4.229 s
algo=VR_Direct (recursive), V=50, length=2, median time=8.809 s
algo=VR_Direct (recursive), V=60, length=1, median time=15.412 s
algo=VR_Direct (recursive), V=70, length=1, median time=22.542 s
algo=VR_Direct (recursive), V=80, length=1, median time=37.941 s
algo=VR_Direct (recursive), V=90, length=1, median time=54.171 s
algo=VR_DirectFW (recursive), V=1, length=50, median time=152.909 μs
algo=VR_DirectFW (recursive), V=10, length=50, median time=4.156 ms
algo=VR_DirectFW (recursive), V=20, length=50, median time=15.445 ms
algo=VR_DirectFW (recursive), V=30, length=50, median time=35.565 ms
algo=VR_DirectFW (recursive), V=40, length=50, median time=66.082 ms
algo=VR_DirectFW (recursive), V=50, length=50, median time=106.545 ms
algo=VR_DirectFW (recursive), V=60, length=50, median time=159.418 ms
algo=VR_DirectFW (recursive), V=70, length=42, median time=223.982 ms
algo=VR_DirectFW (recursive), V=80, length=30, median time=311.325 ms
algo=VR_DirectFW (recursive), V=90, length=22, median time=436.956 ms
algo=VR_FRM (recursive), V=1, length=50, median time=263.018 μs
algo=VR_FRM (recursive), V=10, length=50, median time=30.114 ms
algo=VR_FRM (recursive), V=20, length=26, median time=372.696 ms
algo=VR_FRM (recursive), V=30, length=9, median time=1.193 s
algo=VR_FRM (recursive), V=40, length=5, median time=2.129 s

let fig = plot(
    yscale = :log10,
    xlabel = "V",
    ylabel = "Time (ns)",
    legend_position = :outertopright,
    size = (800, 400),
)
    for (i, (vr_agg, _, use_recursion, label)) in enumerate(vr_aggs)
        _bs, _Vs = [], []
        for (j, b) in enumerate(vr_bs[i])
            if length(b) == 50
                push!(_bs, median(b.times))
                push!(_Vs, Vs[j])
            end
        end
        plot!(_Vs, _bs, label=label)
    end
    title!("Variable Rate Simulations, 50 samples: nodes × time")
end

References

[1] D. J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods. Probability and Its Applications, An Introduction to the Theory of Point Processes. Springer-Verlag, 2 edition. doi:10.1007/b97277.

[2] Patrick J. Laub, Young Lee, and Thomas Taimre. The Elements of Hawkes Processes. Springer International Publishing. doi:10.1007/978-3-030-84639-8.

Appendix

These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.

To locally run this benchmark, do the following commands:

using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/HybridJumps","MultivariateHawkes.jmd")

Computer Information:

Julia Version 1.12.7
Commit 6d172b025e4 (2026-08-15 08:05 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, znver2)
  GC: Built with stock GC
Threads: 128 default, 1 interactive, 128 GC (on 128 virtual cores)
Environment:
  JULIA_NUM_THREADS = auto

Package Information:

Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/HybridJumps/Project.toml`
  [6e4b80f9] BenchmarkTools v1.8.0
⌃ [479239e8] Catalyst v16.4.3
  [8f4d0f93] Conda v1.10.3
  [864edb3b] DataStructures v0.19.6
⌃ [2b5f629d] DiffEqBase v7.21.2
  [459566f4] DiffEqCallbacks v4.19.4
  [31c24e10] Distributions v0.25.131
  [86223c79] Graphs v1.15.0
  [ccbc3e58] JumpProcesses v9.33.1
⌅ [b4f0291d] LazySets v5.3.0
⌃ [7ed4a6bd] LinearSolve v5.18.1
  [1dea7af3] OrdinaryDiffEq v7.8.1
⌅ [d96e819e] Parameters v0.12.3
  [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12
  [91a5bcdd] Plots v1.41.7
  [438e738f] PyCall v1.96.4
⌃ [731186ca] RecursiveArrayTools v4.5.2
  [31c91b34] SciMLBenchmarks v0.2.1 [loaded: `/home/crackauc/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/src/SciMLBenchmarks.jl` (v0.2.1) expected `/home/crackauc/.julia/packages/SciMLBenchmarks/ceJyd/src/SciMLBenchmarks.jl` (v0.2.1)]
  [a6db7da4] SciMLLogging v2.1.0
⌃ [860ef19b] StableRNGs v1.0.4
⌃ [90137ffa] StaticArrays v1.9.22
  [789caeaf] StochasticDiffEq v7.2.0
  [37e2e46d] LinearAlgebra v1.12.0
  [2f01184e] SparseArrays v1.12.0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated`

And the full manifest:

Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/HybridJumps/Manifest.toml`
  [47edcb42] ADTypes v1.24.0
  [14f7f29c] AMD v0.5.4
  [6e696c72] AbstractPlutoDingetjes v1.4.1
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.45
⌃ [79e6a3ab] Adapt v4.7.1
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.30.2
⌃ [4c555306] ArrayLayouts v1.13.0
⌃ [aae01518] BandedMatrices v1.13.0
  [6e4b80f9] BenchmarkTools v1.8.0
  [e2ed5e7c] Bijections v0.2.2
  [b2a6c25c] BinaryHeaps v1.1.0
  [caf10ac8] BipartiteGraphs v0.1.14
⌃ [8e7c35d0] BlockArrays v1.10.0
⌃ [70df07ce] BracketingNonlinearSolve v1.12.7
  [fa961155] CEnum v0.5.0
  [96374032] CRlibm v1.0.2
⌃ [479239e8] Catalyst v16.4.3
  [523fee87] CodecBzip2 v0.8.5
  [944b1d66] CodecZlib v0.7.9
  [35d6a980] ColorSchemes v3.31.0
  [3da002f7] ColorTypes v0.12.3
  [c3611d14] ColorVectorSpace v0.11.0
⌃ [5ae59095] Colors v0.13.1
⌅ [861a8166] Combinatorics v1.0.2
  [38540f10] CommonSolve v0.2.14
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.2.2
  [34da2185] Compat v4.18.1
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.8
  [8f4d0f93] Conda v1.10.3
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⌃ [77a26b50] DiffEqNoiseProcess v5.36.3
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⌃ [5b8099bc] DomainSets v0.8.2
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⌃ [f151be2c] EnzymeCore v0.8.21
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  [e2ba6199] ExprTools v0.1.11
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⌃ [c87230d0] FFMPEG v0.4.5
  [7034ab61] FastBroadcast v1.4.0
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  [a4df4552] FastPower v1.5.0
  [fa42c844] FastRounding v0.3.1
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⌅ [53c48c17] FixedPointNumbers v0.8.6
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  [a85aefff] FunctionMaps v0.1.2
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  [77dc65aa] FunctionWrappersWrappers v1.13.0
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  [46192b85] GPUArraysCore v0.2.1
  [28b8d3ca] GR v0.73.27
  [a0844989] Gamma v1.2.0
  [86223c79] Graphs v1.15.0
⌅ [eafb193a] Highlights v0.5.3
  [34004b35] HypergeometricFunctions v0.3.30
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  [d25df0c9] Inflate v0.1.5
⌅ [842dd82b] InlineStrings v1.4.6
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⌅ [d1acc4aa] IntervalArithmetic v0.21.2
⌃ [8197267c] IntervalSets v0.7.14
  [3587e190] InverseFunctions v0.1.17
  [41ab1584] InvertedIndices v1.3.1
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
  [692b3bcd] JLLWrappers v1.8.0
⌅ [682c06a0] JSON v0.21.4
  [ae98c720] Jieko v0.2.1
⌃ [4076af6c] JuMP v1.31.2
  [ccbc3e58] JumpProcesses v9.33.1
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⌃ [87fe0de2] LineSearch v0.1.18
⌃ [7ed4a6bd] LinearSolve v5.18.1
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  [1914dd2f] MacroTools v0.5.16
  [b8f27783] MathOptInterface v1.54.0
  [bb5d69b7] MaybeInplace v0.1.8
  [442fdcdd] Measures v0.3.3
  [e1d29d7a] Missings v1.2.0
⌃ [7771a370] ModelingToolkitBase v1.77.0
⌅ [2e0e35c7] Moshi v0.3.9
  [46d2c3a1] MuladdMacro v0.2.7
  [102ac46a] MultivariatePolynomials v0.5.20
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  [d8a4904e] MutableArithmetics v1.8.1
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⌃ [be0214bd] NonlinearSolveBase v2.54.0
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⌅ [bac558e1] OrderedCollections v1.8.2 [loaded: v2.0.2]
  [1dea7af3] OrdinaryDiffEq v7.8.1
⌃ [6ad6398a] OrdinaryDiffEqBDF v2.4.11
⌃ [bbf590c4] OrdinaryDiffEqCore v4.18.0
  [50262376] OrdinaryDiffEqDefault v2.6.2
⌃ [4302a76b] OrdinaryDiffEqDifferentiation v3.12.3
⌃ [127b3ac7] OrdinaryDiffEqNonlinearSolve v2.9.8
⌃ [43230ef6] OrdinaryDiffEqRosenbrock v2.7.4
  [b4bd8bb3] OrdinaryDiffEqRosenbrockTableaus v2.4.2
⌃ [2d112036] OrdinaryDiffEqSDIRK v2.9.6
⌃ [b1df2697] OrdinaryDiffEqTsit5 v2.1.4
⌃ [79d7bb75] OrdinaryDiffEqVerner v2.4.1
  [90014a1f] PDMats v0.11.41
⌅ [d96e819e] Parameters v0.12.3
⌅ [69de0a69] Parsers v2.8.8
  [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12
  [ccf2f8ad] PlotThemes v3.3.0
⌃ [995b91a9] PlotUtils v1.5.0
  [91a5bcdd] Plots v1.41.7
  [e409e4f3] PoissonRandom v0.4.13
  [2dfb63ee] PooledArrays v1.4.3
  [d236fae5] PreallocationTools v1.7.1
  [aea7be01] PrecompileTools v1.3.4
  [21216c6a] Preferences v1.6.0
⌃ [08abe8d2] PrettyTables v3.4.8
  [27ebfcd6] Primes v0.5.7
  [43287f4e] PtrArrays v1.4.0
  [0c0d3e7f] PureKLU v1.6.0
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  [379f33d0] ReachabilityBase v0.3.6
  [988b38a3] ReadOnlyArrays v0.2.0
  [795d4caa] ReadOnlyDicts v1.0.1
⌃ [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
⌃ [731186ca] RecursiveArrayTools v4.5.2
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.4.0
  [9fe22ead] RespecializeParams v1.3.0
  [79098fc4] Rmath v0.9.0
⌃ [f2b01f46] Roots v3.0.8
  [5eaf0fd0] RoundingEmulator v0.2.1
⌃ [7e49a35a] RuntimeGeneratedFunctions v0.5.26
  [9dfe8606] SCCNonlinearSolve v1.15.4
⌃ [0bca4576] SciMLBase v3.56.0
  [31c91b34] SciMLBenchmarks v0.2.1 [loaded: `/home/crackauc/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/src/SciMLBenchmarks.jl` (v0.2.1) expected `/home/crackauc/.julia/packages/SciMLBenchmarks/ceJyd/src/SciMLBenchmarks.jl` (v0.2.1)]
  [19f34311] SciMLJacobianOperators v0.1.19
  [a6db7da4] SciMLLogging v2.1.0
⌃ [c0aeaf25] SciMLOperators v1.30.1
  [431bcebd] SciMLPublic v1.3.0
  [53ae85a6] SciMLStructures v1.10.5
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  [91c51154] SentinelArrays v1.4.10
  [3cc68bcd] SetRounding v0.2.1
  [efcf1570] Setfield v1.1.2
  [992d4aef] Showoff v1.1.1
⌃ [727e6d20] SimpleNonlinearSolve v2.14.5
  [699a6c99] SimpleTraits v0.9.6
  [ed01d8cd] Sobol v1.5.0
  [a2af1166] SortingAlgorithms v1.2.3
  [a57abbd0] SparseColumnPivotedQR v2.1.8
  [0a514795] SparseMatrixColorings v0.4.28
  [276daf66] SpecialFunctions v2.9.0
⌃ [860ef19b] StableRNGs v1.0.4
  [0c0c59c1] StarAlgebras v0.3.0
⌃ [90137ffa] StaticArrays v1.9.22
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.5
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.13
  [4c63d2b9] StatsFuns v2.2.1
  [789caeaf] StochasticDiffEq v7.2.0
  [19c5a474] StochasticDiffEqCore v2.2.3
  [0520c28c] StochasticDiffEqHighOrder v2.2.0
  [ebf54054] StochasticDiffEqIIF v2.1.0
  [5080b986] StochasticDiffEqImplicit v2.2.1
  [aefaaa88] StochasticDiffEqLeaping v2.1.0
  [90dbc90e] StochasticDiffEqLevyArea v2.1.1
  [d15fe365] StochasticDiffEqLowOrder v2.0.5
  [8c95a807] StochasticDiffEqMilstein v2.1.1
  [db241ea8] StochasticDiffEqROCK v2.1.1
⌃ [49714585] StochasticDiffEqRODE v2.1.1
  [af2a2fcd] StochasticDiffEqWeak v2.2.1
  [69024149] StringEncodings v0.3.7
⌅ [892a3eda] StringManipulation v0.5.0
  [c3572dad] Sundials v6.7.1
  [2efcf032] SymbolicIndexingInterface v0.3.55
  [19f23fe9] SymbolicLimits v1.2.1
⌃ [d1185830] SymbolicUtils v4.48.0
⌃ [0c5d862f] Symbolics v7.41.1
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.14.0
  [ed4db957] TaskLocalValues v0.1.3
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v2.0.0
  [1c621080] TestItems v1.1.0
  [a759f4b9] TimerOutputs v1.2.2
  [3bb67fe8] TranscodingStreams v0.11.3
  [410a4b4d] Tricks v0.1.13
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [41fe7b60] Unzip v0.2.0
  [81def892] VersionParsing v1.3.0
  [d30d5f5c] WeakCacheSets v0.1.0
  [44d3d7a6] Weave v0.10.12
  [ddb6d928] YAML v0.4.17
  [6e34b625] Bzip2_jll v1.0.9+0
  [4e9b3aee] CRlibm_jll v1.0.1+0
⌃ [83423d85] Cairo_jll v1.18.7+0
  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.8.4+0
⌅ [b22a6f82] FFMPEG_jll v8.1.2+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.14.3+1
  [559328eb] FriBidi_jll v1.0.17+0
  [0656b61e] GLFW_jll v3.5.1+0
⌅ [e8aa6df9] GLPK_jll v5.0.1+1
  [d2c73de3] GR_jll v0.73.27+0
⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [7746bdde] Glib_jll v2.88.3+0
  [3b182d85] Graphite2_jll v1.3.16+0
  [2e76f6c2] HarfBuzz_jll v100.14004.0+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [aacddb02] JpegTurbo_jll v3.2.0+1
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.2.0+0
  [1d63c593] LLVMOpenMP_jll v23.1.1+0
  [aae0fff6] LSODA_jll v0.1.2+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.42.0+0
  [89763e89] Libtiff_jll v4.7.3+0
  [38a345b3] Libuuid_jll v2.42.0+0
  [856f044c] MKL_jll v2025.2.0+0
  [e7412a2a] Ogg_jll v1.3.6+0
  [656ef2d0] OpenBLAS32_jll v0.3.34+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.6.1+0
  [36c8627f] Pango_jll v1.58.2+0
  [30392449] Pixman_jll v0.46.4+0
  [c0090381] Qt6Base_jll v6.10.2+2
  [629bc702] Qt6Declarative_jll v6.10.2+2
  [ce943373] Qt6ShaderTools_jll v6.10.2+1
  [6de9746b] Qt6Svg_jll v6.10.2+0
  [e99dba38] Qt6Wayland_jll v6.10.2+1
  [f50d1b31] Rmath_jll v0.5.2+0
  [ca45d3f4] SuiteSparse32_jll v7.12.1+1
  [fb77eaff] Sundials_jll v7.5.0+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.24.0+0
  [ffd25f8a] XZ_jll v5.8.4+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.13+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.8+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
  [a51aa0fd] Xorg_libXi_jll v1.8.4+0
  [d1454406] Xorg_libXinerama_jll v1.1.7+0
  [ec84b674] Xorg_libXrandr_jll v1.5.6+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.2.0+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.47.0+2
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
  [a4ae2306] libaom_jll v3.15.1+0
  [0ac62f75] libass_jll v0.17.5+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [8e53e030] libdrm_jll v2.4.134+0
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
⌃ [b53b4c65] libpng_jll v1.6.58+0
  [9a156e7d] libva_jll v2.23.0+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
  [1317d2d5] oneTBB_jll v2022.3.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.7.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.1
  [de0858da] Printf v1.11.0
  [9abbd945] Profile v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.3.1+2
  [781609d7] GMP_jll v6.3.0+2
  [deac9b47] LibCURL_jll v8.15.0+0
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.11.4
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.6+0
  [efcefdf7] PCRE2_jll v10.44.0+1
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.15.0+0
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.7.0+0
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`