Matrix exponential of a movement generator, exactly or by implicit solve

Turns an instantaneous rate matrix into transition fractions. This is the single point where SPoRC decides how a matrix exponential is evaluated, so that Get_Movement and every move_timing = 2 operator in model_transition.R share one convention.

Usage

mat_exp(A, expm_nsub = 0)

Arguments

A

Square matrix, dense or sparse, numeric or advector. The generator whose exponential is wanted, already scaled by whatever time step the caller intends (i.e. this returns \(e^{A}\), not \(e^{A\Delta}\)).

expm_nsub

Integer. 0 (default) evaluates \(e^{A}\) with Matrix::expm. A power of two \(n \ge 1\) uses the implicit (backward Euler) scheme with \(n\) substeps (faster but loses acurracy).

Value

A plain dense matrix of the same dimension as A.