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Hello, I am trying to use mbar for a project in Julia and I have some trouble reproducing the free energy of the harmonic oscillator. Here is a MWE:

using Revise 
using MDToolbox
using LinearAlgebra:norm
using Random
# include("mbar_src.jl")

N = 1 # dimension of the walk.
xo = zeros(N)
Ns = Int(1e5)
krange = [25; 16; 9; 4; 1; 1]
orange = [0.; 1.; 2.; 3.; 4.; 5.]
u = Array{Vector{Float64},2}(undef, length(krange),length(orange)) 
for (j,k) in enumerate(krange)
    v = [randn(N)/sqrt(k) for i in 1:Ns]
    for n in eachindex(orange)
        u[j,n] = map(x -> 0.5*k*norm(x .- orange[n])^2, v)
    end
end

f = mbar(u)

# theoretical free energy: 
f_ho(k) = -0.5*N*log(2π/k)  
fv = f_ho.(krange) 
fv = fv .- fv[1]

@show abs.(f-fv)

Unfortunately the vector f is not giving the correct energy. Do you have any insight?

Thank you

EDIT: I saw that you need a K x K state to do the computation. I updated the code but it still doesn't match the correct levels.