deeptime.markov.tools.flux.flux_matrix

deeptime.markov.tools.flux.flux_matrix(T, pi, qminus, qplus, netflux=True)

Compute the TPT flux network for the reaction A–>B.

Parameters:

  • T ((M, M) ndarray) – transition matrix

  • pi ((M,) ndarray) – Stationary distribution corresponding to T

  • qminus ((M,) ndarray) – Backward comittor

  • qplus ((M,) ndarray) – Forward committor

  • netflux (boolean) – True: net flux matrix will be computed False: gross flux matrix will be computed

Returns:

flux – Matrix of flux values between pairs of states.

Return type:

(M, M) ndarray

See also

committor.forward_committor, committor.backward_committor

Notes

Computation of the flux network relies on transition path theory (TPT) [1]. Here we use discrete transition path theory [2] in the transition matrix formulation [3]. The central object used in transition path theory is the forward and backward comittor function.

The TPT (gross) flux is defined as

\[f_{ij}=\left \{ \begin{array}{rl} \pi_i q_i^{(-)} p_{ij} q_j^{(+)} & i \neq j \\ 0 & i=j \end{array} \right . \]

The TPT net flux is then defined as

\[f_{ij}=\max\{f_{ij} - f_{ji}, 0\} \:\:\:\forall i,j. \]

References