trajectory.jl

# Top-level Lp distance function
"""
`dist_lp(l_σ1, l_σ2; verbose, p, str_stat_list, str_stat_trajectory)`   

Function that computes Lp distance between two set of any dimensional trajectories.
...
# Arguments
- `l_σ1::Vector{AbstractTrajectory}` is the first set of trajectories. l_σ2 is the second.
- `verbose::Bool` If `true`, launch a verbose execution of the computation. 
- `str_stat_list::String` allows to set the statistic to apply on the distances of the trajectories. 
It is salso called linkage function in clustering field. Only "mean" is available for now on.
...
"""
function dist_lp(l_σ1::Vector{<:AbstractTrajectory}, l_σ2::Vector{<:AbstractTrajectory};  
                 verbose::Bool = false, p::Int = 1, str_stat_list::String = "mean", str_stat_trajectory::String = "mean")
    if str_stat_list == "mean"
        return dist_lp_mean(l_σ1, l_σ2; verbose = verbose, p = p, str_stat_trajectory = str_stat_trajectory)
    end
    error("Unrecognized statistic in dist_lp")
end

"""
`dist_lp(σ1, σ2; verbose, p, str_stat)`   

Function that computes Lp distance between two trajectories of any dimension.
It computes Lp distances for each observed variable (contained in `get_obs_var(σ)`). and then apply a statistic on these distances.
Requires `get_obs_var(σ1) == get_obs_var(σ2)`, it is verified if they are simulated from the same model.
...
# Arguments
- `σ1::AbstractTrajectory` is the first trajectory. σ2 is the second.
- `verbose::Bool` If `true`, launch a verbose execution of the computation. 
- `str_stat::String` allows to set the statistic to apply on the distances computed  of the trajectories. 
Only "mean" is available for now on.
...
"""
function dist_lp(σ1::AbstractTrajectory, σ2::AbstractTrajectory;  
                 verbose::Bool = false, p::Int = 1, str_stat::String = "mean")
    if str_stat == "mean"
        return dist_lp_mean(σ1, σ2; verbose = verbose, p = p)
    end
    error("Unrecognized statistic in dist_lp")
end

"""
`dist_lp(σ1, σ2, var; verbose, p, str_stat)`   

Function that computes Lp distance between two trajectories of any dimension.
It computes Lp distances for each observed variable (contained in `get_obs_var(σ)`). and then apply a statistic on these distances.
Requires `get_obs_var(σ1) == get_obs_var(σ2)`, it is verified if they are simulated from the same model.
...
# Arguments
- `σ1::AbstractTrajectory` is the first trajectory. σ2 is the second.
- `var::String` is an observed variable. Have to be contained in `get_obs_var(σ1)` and `get_obs_var(σ2)`.
- `verbose::Bool` If `true`, launch a verbose execution of the computation. 
...
"""
function dist_lp(σ1::AbstractTrajectory, σ2::AbstractTrajectory, var::String; 
                 verbose::Bool = false, p::Int = 1)
    if !isbounded(σ1) || !isbounded(σ2)
        @warn "Lp distance computed on unbounded trajectories. Result should be wrong"
    end
    return dist_lp(σ1[var], times(σ1), σ2[var], times(σ2); verbose = false, p = p)
end

# Distance function. Vectorized version
function dist_lp(x_obs::Vector{Int}, t_x::Vector{Float64}, y_obs::Vector{Int}, t_y::Vector{Float64}; 
                 verbose::Bool = false, p::Int = 1)
    current_y_obs = y_obs[1]
    current_t_y = t_y[2]