CollectionMatrix

class CollectionMatrix

The collection matrix is triple banded when the macrostate can only increase or decrease by a single “bin” in the macrostate order parameter. For example, one cannot use a triple banded collection matrix if insertions of both single and pairs of particles are attempted. Single or pair only would be fine.

The collection matrix was slightly reformulated to not require the middle band by making the elements intensive. Thus, instead of storing C0, C1 and C2, we store P_down=C0/(C0+C1+C2) and P_up=C2/(C0+C1+C2). Note that C0+C1+C2 is simply the number of trials starting from that macrostate. Thus, this new, intensive collection matrix is now double banded.

The first index of the matrix is the macrostate. The second is the state change as follows:

• 0: macrostate decrease

• 1: macrostate increase

Arguments

• delta_ln_prob_guess: if the CollectionMatrix lacks transitions to compute a delta_ln_prob, use this value instead (default: 0). This guess can affect the initial convergence. When a simulation starts at low macrostate, a negative number encourages acceptance of macrostates that have not yet been visited. And for high macrostate, a positive number may help. If the value is too large, a very low probability trial may be accepted, creating a large free energy difference that will make it difficult to sample the reverse transition. If a simulation appears “stuck” in a subset of the macrostate range, then the guess may be too large.

• visits_per_delta_ln_prob_boost: In the case where a guess is needed, if “n” attempts to increase the macrostate, decrease delta_ln_prob_guess by 0.01 per “n”. Alternatively, if “n” attempts to decrease macrostate, increase delta_ln_prob_guess by 0.01 per “n”. If visits_per_delta_ln_prob_boost is -1, do nothing (default: -1).

• exp_for_boost: ratio of neighboring probabilities must be within 10^exp or 10^-exp for boosting. If -1, ignore (default: 2).