def test_with_almost_converged_stat_dist(self):
""" test for #106 """
from msmtools.analysis import committor, is_reversible
from msmtools.flux import tpt, flux_matrix, to_netflux, ReactiveFlux
T = np.array([[
0.2576419223095193, 0.2254214623509954, 0.248270708174756,
0.2686659071647294
],
[
0.2233847186210225, 0.2130434781715344,
0.2793477268264001, 0.284224076381043
],
[
0.2118717275169231, 0.2405661227681972,
0.2943396213976011, 0.2532225283172787
],
[
0.2328617711043517, 0.2485926610067547,
0.2571819311236834, 0.2613636367652102
]])
mu = np.array([
0.2306979668517676, 0.2328013892993006, 0.2703312416016573,
0.2661694022472743
])
assert is_reversible(T)
np.testing.assert_allclose(mu.dot(T), mu)
np.testing.assert_equal(mu.dot(T), T.T.dot(mu))
A = [0]
B = [1]
# forward committor
qplus = committor(T, A, B, forward=True, mu=mu)
# backward committor
if is_reversible(T, mu=mu):
qminus = 1.0 - qplus
else:
qminus = committor(T, A, B, forward=False, mu=mu)
tpt_obj = tpt(T, A, B)
tpt_obj.major_flux(1.0)
# gross flux
grossflux = flux_matrix(T, mu, qminus, qplus, netflux=False)
# net flux
netflux = to_netflux(grossflux)
F = ReactiveFlux(A,
B,
netflux,
mu=mu,
qminus=qminus,
qplus=qplus,
gross_flux=grossflux)
F.pathways(1.0)
def calc_committor(T, source, target, forward=None):
"""Calculate forward or backward committor for each node between source and target.
Parameters
----------
T : 2D numpy.ndarray.
Row stochastic transition matrix.
source : list.
Source of probability flux. Committor value i will be the probability of leaving source and reaching node i
before reaching target or source again.
target : list.
Sink of probability flux. Committor value i will be the probability of reaching target from node i before
reaching source.
forward : bool.
If True, forward committor is calculated. If False, backward committor is calculated.
Returns
-------
committor : 1D numpy.ndarray.
Committor values in order of transition matrix.
"""
committor = mana.committor(T, source, target, forward=forward)
return committor
def committor(self, source, target, forward=True):
"""Compute the committor between sets of states.
Parameters
----------
source : Set
The set of source states.
target : Set
The set of target states.
forward : bool, optional
If true, compute the forward committor (default). If false,
compute the backward committor.
Returns
-------
(M,) ndarray
Vector of committor probabilities.
"""
source = [self.index(state) for state in set(source)]
target = [self.index(state) for state in set(target)]
return msmana.committor(self.jump_matrix,
source,
target,
forward=forward)
def setUp(self):
P = np.array([[0.8, 0.15, 0.05, 0.0,
0.0], [0.1, 0.75, 0.05, 0.05, 0.05],
[0.05, 0.1, 0.8, 0.0, 0.05], [0.0, 0.2, 0.0, 0.8, 0.0],
[0.0, 0.02, 0.02, 0.0, 0.96]])
P = csr_matrix(P)
A = [0]
B = [4]
mu = statdist(P)
qminus = committor(P, A, B, forward=False, mu=mu)
qplus = committor(P, A, B, forward=True, mu=mu)
self.A = A
self.B = B
self.F = flux_matrix(P, mu, qminus, qplus, netflux=True)
self.paths = [
np.array([0, 1, 4]),
np.array([0, 2, 4]),
np.array([0, 1, 2, 4])
]
self.capacities = [
0.0072033898305084252, 0.0030871670702178975,
0.00051452784503631509
]
def test_backward_comittor(self):
P = self.bdc.transition_matrix_sparse()
un = committor(P, list(range(10)), list(range(90, 100)), forward=False)
u = self.bdc.committor_backward(9, 90)
assert_allclose(un, u)
def test_backward_comittor(self):
P = self.bdc.transition_matrix()
un = committor(P, [0, 1], [8, 9], forward=False)
u = self.bdc.committor_backward(1, 8)
assert_allclose(un, u)
def tpt(T, A, B, mu=None, qminus=None, qplus=None, rate_matrix=False):
r""" Computes the A->B reactive flux using transition path theory (TPT)
Parameters
----------
T : (M, M) ndarray or scipy.sparse matrix
Transition matrix (default) or Rate matrix (if rate_matrix=True)
A : array_like
List of integer state labels for set A
B : array_like
List of integer state labels for set B
mu : (M,) ndarray (optional)
Stationary vector
qminus : (M,) ndarray (optional)
Backward committor for A->B reaction
qplus : (M,) ndarray (optional)
Forward committor for A-> B reaction
rate_matrix = False : boolean
By default (False), T is a transition matrix.
If set to True, T is a rate matrix.
Returns
-------
tpt: msmtools.flux.ReactiveFlux object
A python object containing the reactive A->B flux network
and several additional quantities, such as stationary probability,
committors and set definitions.
Notes
-----
The central object used in transition path theory is
the forward and backward comittor function.
TPT (originally introduced in [1]) for continous systems has a
discrete version outlined in [2]. Here, we use the transition
matrix formulation described in [3].
See also
--------
msmtools.analysis.committor, ReactiveFlux
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)
"""
import msmtools.analysis as msmana
if len(A) == 0 or len(B) == 0:
raise ValueError('set A or B is empty')
n = T.shape[0]
if len(A) > n or len(B) > n or max(A) > n or max(B) > n:
raise ValueError(
'set A or B defines more states, than given transition matrix.')
if (rate_matrix is False) and (not msmana.is_transition_matrix(T)):
raise ValueError('given matrix T is not a transition matrix')
if (rate_matrix is True):
raise NotImplementedError(
'TPT with rate matrix is not yet implemented - But it is very simple, so feel free to do it.'
)
# we can compute the following properties from either dense or sparse T
# stationary dist
if mu is None:
mu = msmana.stationary_distribution(T)
# forward committor
if qplus is None:
qplus = msmana.committor(T, A, B, forward=True)
# backward committor
if qminus is None:
if msmana.is_reversible(T, mu=mu):
qminus = 1.0 - qplus
else:
qminus = msmana.committor(T, A, B, forward=False, mu=mu)
# gross flux
grossflux = flux_matrix(T, mu, qminus, qplus, netflux=False)
# net flux
netflux = to_netflux(grossflux)
# construct flux object
from .reactive_flux import ReactiveFlux
F = ReactiveFlux(A,
B,
netflux,
mu=mu,
qminus=qminus,
qplus=qplus,
gross_flux=grossflux)
# done
return F