analysis - MSM analysis functions (msmtools.analysis)¶
This module contains functions to analyze a created Markov model, which is specified with a transition matrix T.
Validation¶
is_transition_matrix(T[, tol]) |
Check if the given matrix is a transition matrix. |
is_tmatrix(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¶
Decomposition routines use the scipy LAPACK bindings for dense numpy-arrays and the ARPACK bindings for scipy sparse matrices.
stationary_distribution(T) |
Compute stationary distribution of stochastic matrix T. |
statdist(T) |
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¶
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. |
Passage times¶
mfpt(T, target[, origin, tau, mu]) |
Mean first passage times (from a set of starting states - optional) to a set of target states. |
Committors and PCCA¶
committor(T, A, B[, forward, mu]) |
Compute the committor between sets of microstates. |
pcca(T, m) |
Compute meta-stable sets using PCCA++ _[1] and return the membership of all states to these sets. |
Fingerprints¶
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, maxtime, ...]) |
Time-correlation for equilibrium experiment. |
relaxation(T, p0, obs[, times, k, ncv]) |
Relaxation experiment. |
Sensitivity analysis¶
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). |