deeptime.markov.tools¶

Package containing various low-level tools that are used for estimating and analyzing Markov state models. This package is a fork of MSMTools.

MSM estimation¶

This module (deeptime.markov.tools.estimation) contains utility functions dealing with MSM estimation from data.

count_matrix(dtraj, lag[, sliding, ...])

Generate a count matrix from given microstate trajectory.

`connected_sets`(C[, directed])	Compute connected sets of microstates.
`largest_connected_set`(C[, directed])	Largest connected component for a directed graph with edge-weights given by the count matrix.
`largest_connected_submatrix`(C[, directed, lcc])	Compute the count matrix on the largest connected set.
`is_connected`(C[, directed])	Check connectivity of the given matrix.

`transition_matrix`(C[, reversible, mu, ...])	Estimate the transition matrix from the given countmatrix.
`rate_matrix`(C[, dt, method, sparsity, ...])	Estimate a reversible rate matrix from a count matrix.
`log_likelihood`(C, T)	Log-likelihood of the count matrix given a transition matrix.
`tmatrix_cov`(C[, k])	Covariance tensor for non-reversible transition matrix posterior.
`error_perturbation`(C, S)	Error perturbation for given sensitivity matrix.

tmatrix_sampler(C[, reversible, mu, T0, ...])

Generate transition matrix sampler object.

`bootstrap_counts`(dtrajs, lagtime[, corrlength])	Generates a randomly resampled count matrix given the input coordinates.
`bootstrap_trajectories`(trajs, correlation_length)	Generates a randomly resampled trajectory segments.

`prior_neighbor`(C[, alpha])	Neighbor prior for the given count matrix.
`prior_const`(C[, alpha])	Constant prior for given count matrix.
`prior_rev`(C[, alpha])	Prior counts for sampling of reversible transition matrices.

This module (deeptime.markov.tools.analysis) contains functions to analyze a created Markov model, which is specified with a transition matrix T.

`is_transition_matrix`(T[, tol])	Check if the given matrix is a transition matrix.
`is_rate_matrix`(K[, tol])	Check if the given matrix is a rate matrix.
`is_connected`(T[, directed])	Check connectivity of the given matrix.
`is_reversible`(T[, mu, tol])	Check reversibility of the given transition matrix.

Decomposition routines use the scipy LAPACK bindings for dense numpy-arrays and the ARPACK bindings for scipy sparse matrices.

`stationary_distribution`(T[, ncv, mode, ...])	Compute stationary distribution of stochastic matrix T.
`eigenvalues`(T[, k, ncv, reversible, mu])	Find eigenvalues of the transition matrix.
`eigenvectors`(T[, k, right, ncv, reversible, mu])	Compute eigenvectors of given transition matrix.
`rdl_decomposition`(T[, k, norm, ncv, ...])	Compute the decomposition into eigenvalues, left and right eigenvectors.
`timescales`(T[, tau, k, ncv, reversible, mu])	Compute implied time scales of given transition matrix.

`expected_counts`(T, p0, N)	Compute expected transition counts for Markov chain with n steps.
`expected_counts_stationary`(T, N[, mu])	Expected transition counts for Markov chain in equilibrium.

mfpt(T, target[, origin, tau, mu])

Mean first passage times (from a set of starting states - optional) to a set of target states.

`committor`(T, A, B[, forward, mu])	Compute the committor between sets of microstates.
`pcca_memberships`(T, m)	Compute meta-stable sets using PCCA++.
`hitting_probability`(T, target)	Computes the hitting probabilities for all states to the target states.

`fingerprint_correlation`(T, obs1[, obs2, ...])	Dynamical fingerprint for equilibrium correlation experiment.
`fingerprint_relaxation`(T, p0, obs[, tau, k, ncv])	Dynamical fingerprint for relaxation experiment.
`expectation`(T, a[, mu])	Equilibrium expectation value of a given observable.
`correlation`(T, obs1[, obs2, times, k, ncv])	Time-correlation for equilibrium experiment.
`relaxation`(T, p0, obs[, times, k])	Relaxation experiment.

`stationary_distribution_sensitivity`(T, j)	Sensitivity matrix of a stationary distribution element.
`eigenvalue_sensitivity`(T, k)	Sensitivity matrix of a specified eigenvalue.
`timescale_sensitivity`(T, k)	Sensitivity matrix of a specified time-scale.
`eigenvector_sensitivity`(T, k, j[, right])	Sensitivity matrix of a selected eigenvector element.
`mfpt_sensitivity`(T, target, i)	Sensitivity matrix of the mean first-passage time from specified state.
`committor_sensitivity`(T, A, B, i[, forward])	Sensitivity matrix of a specified committor entry.
`expectation_sensitivity`(T, a)	Sensitivity of expectation value of observable A=(a_i).

This module (deeptime.markov.tools.flux) contains functions to compute reactive flux networks and find dominant reaction pathways in such networks.

`flux_matrix`(T, pi, qminus, qplus[, netflux])	Compute the TPT flux network for the reaction A-->B.
`to_netflux`(flux)	Compute the netflux from the gross flux.
`flux_production`(F)	Returns the net flux production for all states
`flux_producers`(F[, rtol, atol])	Return indexes of states that are net flux producers.
`flux_consumers`(F[, rtol, atol])	Return indexes of states that are net flux producers.
`coarsegrain`(F, sets)	Coarse-grains the flux to the given sets.

`total_flux`(F[, A])	Compute the total flux, or turnover flux, that is produced by
`rate`(totflux, pi, qminus)	Transition rate for reaction A to B.
`mfpt`(totflux, pi, qminus)	Mean first passage time for reaction A to B.

pathways(F, A, B[, fraction, maxiter])

Decompose flux network into dominant reaction paths.