msmtools.generation.transition_matrix_metropolis_1d

msmtools.generation.transition_matrix_metropolis_1d(E, d=1.0)

Transition matrix describing the Metropolis chain jumping between neighbors in a discrete 1D energy landscape.

Parameters:

• E ((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 .. math:

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}.