def trajectory_weights(self):
r"""Uses the HMSM to assign a probability weight to each trajectory frame.
This is a powerful function for the calculation of arbitrary observables in the trajectories one has
started the analysis with. The stationary probability of the MSM will be used to reweigh all states.
Returns a list of weight arrays, one for each trajectory, and with a number of elements equal to
trajectory frames. Given :math:`N` trajectories of lengths :math:`T_1` to :math:`T_N`, this function
returns corresponding weights:
.. math::
(w_{1,1}, ..., w_{1,T_1}), (w_{N,1}, ..., w_{N,T_N})
that are normalized to one:
.. math::
\sum_{i=1}^N \sum_{t=1}^{T_i} w_{i,t} = 1
Suppose you are interested in computing the expectation value of a function :math:`a(x)`, where :math:`x`
are your input configurations. Use this function to compute the weights of all input configurations and
obtain the estimated expectation by:
.. math::
\langle a \rangle = \sum_{i=1}^N \sum_{t=1}^{T_i} w_{i,t} a(x_{i,t})
Or if you are interested in computing the time-lagged correlation between functions :math:`a(x)` and
:math:`b(x)` you could do:
.. math::
\langle a(t) b(t+\tau) \rangle_t = \sum_{i=1}^N \sum_{t=1}^{T_i} w_{i,t} a(x_{i,t}) a(x_{i,t+\tau})
Returns
-------
The normalized trajectory weights. Given :math:`N` trajectories of lengths :math:`T_1` to :math:`T_N`,
returns the corresponding weights:
.. math::
(w_{1,1}, ..., w_{1,T_1}), (w_{N,1}, ..., w_{N,T_N})
"""
# compute stationary distribution, expanded to full set
statdist = self.stationary_distribution_obs
statdist = _np.append(statdist, [
-1
]) # add a zero weight at index -1, to deal with unobserved states
# histogram observed states
import msmtools.dtraj as msmtraj
hist = 1.0 * msmtraj.count_states(self.discrete_trajectories_obs,
ignore_negative=True)
# simply read off stationary distribution and accumulate total weight
W = []
wtot = 0.0
for dtraj in self.discrete_trajectories_obs:
w = statdist[dtraj] / hist[dtraj]
W.append(w)
wtot += _np.sum(W)
# normalize
for w in W:
w /= wtot
# done
return W
def __init__(self, dtrajs):
# TODO: extensive input checking!
from pyemma.util.types import ensure_dtraj_list
# discrete trajectories
self._dtrajs = ensure_dtraj_list(dtrajs)
## basic count statistics
# histogram
from msmtools.dtraj import count_states
self._hist = count_states(self._dtrajs, ignore_negative=True)
# total counts
self._total_count = np.sum(self._hist)
# number of states
self._nstates = msmest.number_of_states(dtrajs)
# not yet estimated
self._counted_at_lag = False
def __init__(self, dtrajs):
from pyerna.util.types import ensure_dtraj_list
# discrete trajectories
self._dtrajs = ensure_dtraj_list(dtrajs)
# TODO: extensive input checking!
if any([np.any(d < -1) for d in self._dtrajs]):
raise ValueError('Discrete trajectory contains elements < -1.')
## basic count statistics
# histogram
from msmtools.dtraj import count_states
self._hist = count_states(self._dtrajs, ignore_negative=True)
# total counts
self._total_count = np.sum(self._hist)
# number of states
self._nstates = msmest.number_of_states(dtrajs)
# not yet estimated
self._counted_at_lag = False
