# msmtools.flux.flux_matrix¶

msmtools.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 flux – Matrix of flux values between pairs of states. (M, M) ndarray

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].

committor.forward_committor(), committor.backward_committor()

Notes

Computation of the flux network relies on transition path theory (TPT). The central object used in transition path theory is the forward and backward comittor function.

The TPT (gross) flux is defined as

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

The TPT net flux is then defined as

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

References

 [1] W. E and E. Vanden-Eijnden. Towards a theory of transition paths. J. Stat. Phys. 123: 503-523 (2006)
 [2] P. Metzner, C. Schuette and E. Vanden-Eijnden. Transition Path Theory for Markov Jump Processes. Multiscale Model Simul 7: 1192-1219 (2009)
 [3] F. Noe, Ch. Schuette, E. Vanden-Eijnden, L. Reich and T. Weikl: Constructing the Full Ensemble of Folding Pathways from Short Off-Equilibrium Simulations. Proc. Natl. Acad. Sci. USA, 106, 19011-19016 (2009)