function tmatrix_metropolis1d¶
- deeptime.data.tmatrix_metropolis1d(energies, d=1.0)¶
Transition matrix describing the Metropolis chain jumping between neighbors in a discrete 1D energy landscape.
(Source code, png, hires.png, pdf)
- Parameters:
energies ((M,) ndarray) – Energies in units of kT
d (float (optional)) – Diffusivity of the chain, d in (0, 1]
- Returns:
P – Transition matrix of the Markov chain
- Return type:
(M, M) ndarray
Notes
Transition probabilities are computed as
\[\begin{aligned} p_{i,i-1} &= 0.5 d \min \left\{ 1.0, \mathrm{e}^{-(E_{i-1} - E_i)} \right\}, \\ p_{i,i+1} &= 0.5 d \min \left\{ 1.0, \mathrm{e}^{-(E_{i+1} - E_i)} \right\}, \\ p_{i,i} &= 1.0 - p_{i,i-1} - p_{i,i+1}. \end{aligned}\]