Propogate the time evolution of a population vector.
Parameters:
T : ndarray or sparse matrix
A transition matrix
NumSteps : int
How many timesteps to iterate
initial_populations : ndarray
The initial population vector
observable_vector : ndarray
Vector containing the state-wise averaged property of some observable.
Can be used to propagate properties such as fraction folded, ensemble
average RMSD, etc. Default: None
Returns:
X : ndarray
Final population vector, after propagation
obslist : list
list of floats of length equal to the number of steps, giving the mean value
of the observable (dot product of ObservableVector and populations) at
each timestep