Makorv state models

msmgenerate(nframe::Int, T, pi_i)
            states = zeros(typeof(nframe), nframe)

Randomly samples a state trajectory from the the given transition matrix, and equilibrium probabilities of states.

Examples

julia> T, pi_i = msmtransitionmatrix(C)
julia> states = msmgenerate(1000, T, pi_i)

msmgenerate(nframe, T, pi_i, emission) -> states, observations

Randomly samples a state trajectory and observations from the given transition matrix, equilibrium probabilities of states, and emissions.

Examples

julia> T, pi_i = msmtransitionmatrix(C)
julia> states, observations = msmgenerate(1000, T, pi_i, emission)

msmcountmatrix(indexOfCluster; tau=1) -> C::Matrix

Transition count matrix from a sinlgle binned trajectory or a set of binned trajectories. indexOfCluster is a vector or a set of vectors containing binned trajectorie(s). Returns count matrix for transitions from state i to state j in a time step of tau.

Examples

julia> ta = mdload("ak.dcd")
julia> X = compute_distancemap(ta["atomname CA"])
julia> F = clusterkcenters(X)
julia> c = msmcountmatrix(F.indexOfCluster, tau=10)

msmtransitionmatrix(C; TOLERANCE=10^(-4), verbose=true) -> T::Matrix, p::Vector

Estimate the transition probability matrix from count matrix C. Detailed balance is implicitly imposed in the estimation.

Returns the transition probability matrix and the equilibrium probabilities of states.

Examples

julia> ta = mdload("ak.dcd")
julia> X = compute_distancemap(ta["atomname CA"])
julia> F = clusterkcenters(X)
julia> C = msmcountmatrix(F.indexOfCluster, tau=10)
julia> T, p = msmtransitionmatrix(C)

References

This routines uses the reversible maximum likelihood estimator described in 
K. A. Beauchamp, G. R. Bowman, T. J. Lane, L. Maibaum, I. S. Haque, and V. S. Pande, 
MSMBuilder2: Modeling Conformational Dynamics on the Picosecond to Millisecond Scale, 
J. Chem. Theory Comput. 7, 3412 (2011).

msmviterbi(observation, T, p, log_emission) -> states::Vector

Viterbi algorithm estimates the most probable hidden state sequence from the observation data. observations is a set of observed vectors. T, p are the transition probabilities and equilibrium probabilities, respectively. log_emission is a matrix whose rows correspond to states, and columns correspond to observations.

Returns the maximum likelihood state sequence.

Examples

julia> nframe = 1000
julia> states, observations = msmgenerate(nframe, T, pi_i, emission)
julia> states_estimated = msmviterbi(T, pi_i, emission, observation)

msmbaumwelch(observations, T_init, p_init, emission_init; TOLERANCE=10.0^(-4), MAXITERATION=Inf64) -> T::Matrix, p::Vector, emission::Matrix

Baum-Welch algorithm estimates the most probable transition probabilities from the given observation data. In this function, detailed balance is implicitly imposed in the estimation, so the equilibrium probabilities can be determined from the estimated transition probabilities. Also, unlike the original Baum-Welch algorithm, the emission is NOT estimated in this function, because the emission probabilites are usually known a priori in cases of molecular experiments. observations is a set of observed vectors. T_init, p_init are initial transition probabilities and equilibrium probabilities, respectively. emission_init is a matrix whose rows correspond to states, and columns correspond to observations.

Returns the transition probability matrix, the equilibrium probabilities of states, and the emission probabilities (though the emission does not change).

Examples

julia> ta = mdload("ak.dcd")
julia> X = compute_distancemap(ta["atomname CA"])
julia> F = clusterkcenters(X)
julia> C = msmcountmatrix(F.indexOfCluster, tau=10)
julia> T, p = msmtransitionmatrix(C)

References

The algorithm of this routines is based on the descriptions in PRML book by C. Bishop. 

msmplot(T; pi_i=nothing, x=nothing, y=nothing, filename=nothing, 
        edgewidth_scale=10.0, arrow_scale=0.1, nodesize=0.5, fontsize=10, names=[], dpi=100)

Visualize the graphical structure of the given Markov state model parameters. T is a transition probability matrix whose elements Tij represents the probablity of transition from state i to j. T should satisfy the detailed balance condition. pi_i is a vector whose elements are equilibrium probabilities of states. x and y are X and Y coordinates of states, respectively.

Examples

julia> nstate = 5
julia> T, pi_i = msmtransitionmatrix(rand(nstate, nstate))
julia> x = rand(nstate); y = rand(nstate)
julia> msmplot(T, pi_i=pi_i, x=x, y=y)