Convert Stochastic Matrix to Rate Matrix

Given a stochastic matrix, return the rate matrix (infinitesimal generator) that would generate it when exponentiated over the interval of unit time.

movement_prob2rate(tau)

Arguments

tau	a row normalized stochastic matrix

Value

a list with two elements: gamma negative diagonal of the rate matrix, mat matrix of row normalized off-diagonal elements

Details

Warning: if the matrix provided has diagonal-only rows (i.e., the location is independent), the rate matrix will return 0 in that row, as there is no movement rate that can generate that scenario.

Examples

  # generate random matrix for example
  #  This represents a 3-node landscape, with random movement between nodes
  moveMat <- matrix(data = runif(n = 9), nrow = 3, ncol = 3)
  moveMat <- moveMat/rowSums(moveMat)

  moveRate <- movement_prob2rate(tau = moveMat)