deeptime.markov.tools.analysis.expected_counts¶
- deeptime.markov.tools.analysis.expected_counts(T, p0, N)¶
Compute expected transition counts for Markov chain with n steps.
- Parameters:
T ((M, M) ndarray or sparse matrix) – Transition matrix
p0 ((M,) ndarray) – Initial (probability) vector
N (int) – Number of steps to take
- Returns:
EC – Expected value for transition counts after N steps
- Return type:
(M, M) ndarray or sparse matrix
Notes
Expected counts can be computed via the following expression
\[\mathbb{E}[C^{(N)}]=\sum_{k=0}^{N-1} \text{diag}(p^{T} T^{k}) T\]Examples
>>> import numpy as np >>> from deeptime.markov.tools.analysis import expected_counts
>>> T = np.array([[0.9, 0.1, 0.0], [0.5, 0.0, 0.5], [0.0, 0.1, 0.9]]) >>> p0 = np.array([1.0, 0.0, 0.0]) >>> N = 100 >>> EC = expected_counts(T, p0, N)
>>> EC array([[45.44616147, 5.0495735 , 0. ], [ 4.50413223, 0. , 4.50413223], [ 0. , 4.04960006, 36.44640052]])