search

markovmodel / msmtools

Tools for estimating and analyzing Markov state models
GNU Lesser General Public License v3.0
40 stars 27 forks source link

how the backward_committor is calculated? #113

Closed zhanghaomiao closed 6 years ago

zhanghaomiao commented 6 years ago

when the backward_committor is calculated, you use the adjoint of the generator matrix

I Know when the transition probablity matrix is not reversible, the backward_committor is not 1-forward_committor, but how backward_committor is calculated in this way? I can't find any reference about it.

marscher commented 6 years ago

@trendelkampschroer Are these equations taken from some text book or have you derived these yourself?

franknoe commented 6 years ago

You can find the equations for a transition matrix in the SI of this paper (copied below): http://www.pnas.org/content/106/45/19011

I don't think msmtools uses 1-forward committors to compute the backward committor unless you have a reversible matrix. The expression above is probably used to compute coefficients for the linear solver. If in doubt, please refer to the line of code.

image

zhanghaomiao commented 6 years ago

@franknoe @marscher Thanks, I get it.