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 first index of the matrix is the macrostate. The second is the state change as follows:
0: macrostate decrease
1: macrostate constant
2: macrostate increase
Beware that the computed probability distribution from this collection matrix may contain spurious values at the two most extreme ends. These two extreme ends are the two pairs of the two lowest and highest indices, respectively. For example, at the highest macrostate, a transition to the next highest macrostate is immediately rejected and thus the macrostate increase part of the collection matrix is zero due to this constraint. However, this would not be the case if the higher macrostate values were allowed. The constraint thus affects the probability at the most extreme values, and these values should be discarded. There are exceptions such as the case with zero particles. In this case, there cannot be less than zero particles so the constraint is physically meaningful and the probability at this macrostate is correct.
increment(const int macro, const int state_change, const double add)¶
Add value for a given macrostate and state change.
Update the ln_prob according to the collection matrix.
Return the matrix.