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)

../../_images/plot_tmatrix_1d.png
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

pi,i−1=0.5dmin⁡{1.0,e−(Ei−1−Ei)},pi,i+1=0.5dmin⁡{1.0,e−(Ei+1−Ei)},pi,i=1.0−pi,i−1−pi,i+1.\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}