class MarkovStateModel¶

class deeptime.markov.msm.MarkovStateModel(transition_matrix, stationary_distribution=None, reversible=None, n_eigenvalues=None, ncv=None, count_model=None, transition_matrix_tolerance=1e-08, lagtime=None)¶

Markov model with a given transition matrix.

Parameters:

transition_matrix ((n,n) array_like) – The transition matrix.
stationary_distribution (ndarray(n), optional, default=None) – Stationary distribution. Can be optionally given in case if it was already computed.
reversible (bool, optional, default=None) – Whether the transition matrix is reversible with respect to its stationary distribution. If None (default), will be determined from the transition matrix.
n_eigenvalues (int, optional, default=None) – The number of eigenvalues / eigenvectors to be kept. If set to None, it depends on the transition matrix. If it is densely stored (in terms of a numpy array), all eigenvectors and eigenvalues are computed. If it is sparse, only the 10 largest eigenvalues with corresponding eigenvectors are computed.
ncv (int optional, default=None) – Relevant for eigenvalue decomposition of reversible transition matrices. It is the number of Lanczos vectors generated, ncv must be greater than n_eigenvalues; it is recommended that ncv > 2*neig.
count_model (TransitionCountModel, optional, default=None) – In case the MSM was estimated from data, the transition count model can be provided for statistical information about the data. Some properties of the model require a count model so that they can be computed.
transition_matrix_tolerance (float, default=1e-8) – The tolerance under which a matrix is still considered a transition matrix (only non-negative elements and row sums of 1).
lagtime (int, optional, default=None) – The lagtime of this MSM. If there is a count model, the MSM assumes the lagtime of the count model, otherwise falls back to the lagtime set via this constructor argument or a lagtime of 1 if no lagtime is provided at all.

`count_model`	Returns a transition count model, can be None.
`empirical_koopman_model`	Yields a `CovarianceKoopmanModel` based on the count matrix of this Markov state model.
`has_count_model`	Yields whether this Markov state model has a count model.
`is_real`	Checks if all eigenvalues as well as eigenvectors/functions are real.
`koopman_model`	Yields a `CovarianceKoopmanModel` based on the transition matrix and stationary
`lagtime`	The lagtime this model was estimated at.
`n_eigenvalues`	number of eigenvalues to compute.
`n_states`	Number of active states on which all computations and estimations are done
`ncv`	Number of Lanczos vectors used when computing the partial eigenvalue decomposition
`reversible`	Returns whether the MarkovStateModel is reversible
`sparse`	Returns whether the MarkovStateModel is sparse
`stationary`	Whether the MSM is stationary, i.e. whether the initial distribution is the stationary distribution of the hidden transition matrix.
`stationary_distribution`	The stationary distribution on the MarkovStateModel states
`transition_matrix`	The transition matrix on the active set.
`transition_matrix_tolerance`	The tolerance under which a matrix is considered a transition matrix.

`ck_test`(models, n_metastable_sets[, ...])	Validates a model estimated at lag time tau by testing its predictions for longer lag times.
`committor_backward`(A, B)	Backward committor from set A to set B
`committor_forward`(A, B)	Forward committor (also known as p_fold or splitting probability) from set A to set B.
`compute_state_indices`(dtrajs)	Generates a trajectory/time indices for the given list of states.
`compute_trajectory_weights`(dtrajs)	Uses the MarkovStateModel to assign a probability weight to each trajectory frame.
`copy`()	Makes a deep copy of this model.
`correlation`(a[, b, maxtime, k, ncv])	Time-correlation for equilibrium experiment.
`eigenvalues`([k])	Compute or fetch the transition matrix eigenvalues.
`eigenvectors_left`([k])	Compute the left transition matrix eigenvectors
`eigenvectors_right`([k])	Compute the right transition matrix eigenvectors
`expectation`(a)	Equilibrium expectation value of a given observable.
`fingerprint_correlation`(a[, b, k, ncv])	Dynamical fingerprint for equilibrium time-correlation experiment.
`fingerprint_relaxation`(p0, a[, k, ncv])	Dynamical fingerprint for perturbation/relaxation experiment.
`get_params`([deep])	Get the parameters.
`hmm`(dtrajs, nhidden[, return_estimator])	Estimates a hidden Markov state model as described in [1].
`mfpt`(A, B)	Mean first passage times from set A to set B, in units of the input trajectory time step.
`pcca`(n_metastable_sets)	Runs PCCA+ [2] to compute a metastable decomposition of MarkovStateModel states.
`propagate`(p0, k)	Propagates the initial distribution p0 k times
`reactive_flux`(source_states, target_states)	A->B reactive flux from transition path theory (TPT)
`relaxation`(p0, a[, maxtime, k, ncv])	Simulates a perturbation-relaxation experiment.
`score`([dtrajs, r, dim])	Scores the MSM using the dtrajs using the variational approach for Markov processes.
`set_params`(**params)	Set the parameters of this estimator.
`simulate`(n_steps[, start, stop, dt, seed])	Generates a realization of the Markov Model.
`submodel`(states)	Restricts this markov state model to a subset of states by taking a submatrix of the transition matrix and re-normalizing it, as well as restricting the stationary distribution and count model if given.
`timescales`([k])	Relaxation timescales corresponding to the eigenvalues.
`to_koopman_model`([empirical, epsilon])	Computes the SVD of the symmetrized Koopman operator in the analytical or empirical distribution, returns as Koopman model.
`update_stationary_distribution`(value)	Explicitly sets the stationary distribution, re-normalizes
`update_transition_matrix`(value)	Sets the transition matrix and invalidates all cached and derived properties.