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Update of stochastic matrix is strange

even though index is not reversed...

julia> mp.A
2×2 MMatrix{2, 2, Float64, 4} with indices SOneTo(2)×SOneTo(2):
 1.0  0.00100141
 0.0  0.998999

Setting :

using Revise
using Random
using LinearAlgebra
using ARHMM

using StaticArrays
using Distributions

function data_generation(n, A, prop_list)
    x = SVector{1, Float64}([0.0])
    z = 1
    xs = [x]
    zs = [z]
    for i in 1:n
        cat = Categorical(A[:, z])
        z_next = rand(cat)
        x_next = prop_list[z](x)
        x, z = x_next, z_next
        push!(xs, SVector{1, Float64}(x))
        push!(zs, z)
    end
    return xs, zs
end

Random.seed!(0)
prop1 = LinearPropagator(Diagonal([1.0]), Diagonal([0.1^2]), [0.4])
prop2 = LinearPropagator(Diagonal([1.0]), Diagonal([0.1^2]), [-0.4])
prop_list = [prop1, prop2]
A = [0.6 0.0;
     0.4 1.0]

xs, zs = data_generation(1000, A, prop_list)
A_pred_init = [0.9 0.0;
               0.1 1.0]
prop1_init = LinearPropagator(Diagonal([1.0]), Diagonal([0.5^2]), [0.2])
prop2_init = LinearPropagator(Diagonal([1.0]), Diagonal([0.3^2]), [-0.5])
prop_list_init = [prop1_init, prop2_init]
mp = ModelParameters(1, A_pred_init, prop_list_init)

z_ests = nothing
for _ in 1:1 # if more than 2, usually likelihood will be static
    global z_ests
    z_ests, zz_ests, log_likeli = compute_hidden_states(mp, xs)
    update_model_parameters!(mp, z_ests, zz_ests, xs)
end
z_preds = [argmax(z) for z in z_ests];