Prepare Instantaneous Movement (Generator) Matrix

Converts a sparse adjacency-weighted matrix (output of the habitat-taxis step in simmar) into an instantaneous transition rate matrix (generator matrix) suitable for matrix exponentiation via expm::expm. The diagonal is set to minus the column sums so that each column sums to zero, as required for a continuous-time Markov chain.

Usage

prep_movement(multiplier, resolution)

Arguments

multiplier: multiplier for adjacency matrix
resolution: spatial resolution
time_step: time step in question

Value

A sparse matrix with the same dimensions as multiplier, with diagonal elements set to \(-\sum_{i \neq j} m_{ij}\) (negative column sums of the off-diagonal).

a prepared movement matrix

Details

Movement in marlin is modelled as a diffusion-taxis process following Thorson & Barnett (2017). The habitat taxis component modifies the off-diagonal elements of the base diffusion matrix to reflect drift towards high-quality habitat. prep_movement completes the generator matrix by filling in the diagonal, after which expm::expm is called to obtain the discrete-time transition matrix over one time step.

References