First commit with. Details the organization of the code.

Two folders:
- core/ which contains the essential files for the packages
- tests/ which contains tests and benchmarks of other packages / methods

For now on:
- we wrote minimal tests in tests/ (a simulation of SIR model) that should run for
a first minimal version of the package
- we described in core/ the general structure of essential
types, how they articulate each others and the minimum methods we should
implement for a first version that runs the tests.

core/MarkovProcesses.jl

+module MarkovProcesses
+
+import Base: +, -, getfield, getindex
+
+export Model, ContinuousTimeModel, DiscreteTimeModel
+export simulate, set_param!, get_param
+include("model.jl")
+
+export Observations, AbstractTrajectory
+export +,-,δ,get_obs_variables
+include("observations.jl")
+
+end
+

core/model.jl

+
+abstract type Model end 
+abstract type ContinuousTimeModel <: Model end 
+abstract type DiscreteTimeModel <: Model end 
+
+function check_consistency(m::Model) end
+function simulate(m::Model, n::Int; bound::Real = Inf)::AbstractObservations end
+function set_param!(m::Model, p::AbstractVector{Real})::Nothing end
+function get_param(m::Model)::AbstractVector{Real} end
+

core/observations.jl

+
+abstract type AbstractTrajectory end
+ContinuousObservations = AbstractVector{AbstractTrajectory}
+
+struct Trajectory <: AbstractTrajectory
+    m::ContinuousTimeModel
+    values::AbstractMatrix{Real}
+    times::AbstractMatrix{Real}
+    transitions::AbstractVector{Union{String,Missing,Nothing}}
+end
+
+struct ObservedTrajectory <: AbstractTrajectory
+    m::ContinuousTimeModel
+    values::AbstractMatrix{Real}
+    times::AbstractMatrix{Real}
+end
+
+function +(σ1::AbstractTrajectory,σ2::AbstractTrajectory) end
+function -(σ1::AbstractTrajectory,σ2::AbstractTrajectory) end
+function δ(σ1::AbstractTrajectory,t::Real) end
+function get_obs_variables(σ::Trajectory) end
+function get_obs_variables(σ::ObservedTrajectory) end
+function get_values(σ::AbstractTrajectory, variable::String) end
+function get_times(σ::AbstractTrajectory, variable::String) end
+function getindex(σ::AbstractTrajectory, idx::String) end
+

tests/load_module.jl

+
+using MarkovProcesses
+

tests/models/sir.jl

+
+import StaticArrays: SVector, SMatrix, @SMatrix
+
+State = SVector{3, Int}
+Parameters = SVector{2, Real}
+
+d=3
+dobs=1
+k=2
+dict=Dict("S" => 1, "I" => 2, "R" => 3)
+l_name_param = ["ki", "kr"]
+p = Parameters(0.0012, 0.05)
+x0 = State(95, 5, 0)
+
+function f(xn::State, p::Parameters, tn::Real)
+    a1 = p[1] * xn[1] * xn[2]
+    a2 = p[2] * xn[2]
+    l_a = SVector(a1, a2)
+    asum = sum(l_a)
+    # column-major order
+    l_nu = @SMatrix [-1.0 0.0;
+                     1.0 -1.0;
+                     0.0 1.0]
+    
+    u1, u2 = rand(), rand()
+    tau = - log(u1) / asum
+    b_inf = 0.0
+    b_sup = a1
+    reaction = 0
+    for i = 1:2
+        if b_inf < asum*u2 < b_sup
+            reaction = i
+            break
+        end
+        b_inf += l_a[i]
+        b_sup += l_a[i+1]
+    end
+ 
+    nu = l_nu[:,reaction]
+    xnplus1 = State(xn[1]+nu[1], xn[2]+nu[2], xn[3]+nu[3])
+    tnplus1 = tn + tau
+    transition = "R$(reaction)"
+
+    return xnplus1
+end
+
+g = SVector(1)
+
+# Gamma should be constructed automatically in the case of 
+
+#m = Model(d,dobs,k,dict,l_name,param,p,x0,f,g)
+

tests/sim_sir.jl

+
+using MarkovProcesses 
+using PyPlot
+
+include("models/sir.jl")
+
+σ = simulate(SIR)
+plt.figure()
+plot(σ["S,times"], σ["S,values"])
+plt.savefig("sim_sir.png")
+plt.close()
+