Iterate a Leslie matrix

Projects an age-structured population forward using a Leslie matrix – TDA's mpit/mpit1. Row i of fertility_survival holds (fertility[i], survival[i]): fertility[i] is the birth rate contributed by age class i (used only for class 1 of the next generation); survival[i] is the fraction of age class i that survives into age class i + 1 (survival[n], the last row, is unused). tda_mpit1 adds a constant vector immigration to every age class after each projection step.

Usage

tda_mpit(fertility_survival, population, iterations, dir = tempfile("tda"))

tda_mpit1(
  fertility_survival,
  population,
  immigration,
  iterations,
  dir = tempfile("tda")
)

Arguments

fertility_survival

an n x 2 numeric matrix, columns (fertility, survival) as above.

population

the initial population vector, length n.

iterations

how many projection steps to take.

dir

working directory.

immigration

for tda_mpit1, a constant vector added to the population after each step, length n.

Value

A matrix with iterations + 1 rows (the initial population, then one row per step) and n columns.

See also

Other matrix algebra: tda_mcel(), tda_mcent(), tda_mch(), tda_mcross(), tda_mdiag(), tda_mev(), tda_mevs(), tda_midf(), tda_midf1(), tda_midf2(), tda_midf3(), tda_minvs(), tda_mkmet(), tda_mkp(), tda_mmul(), tda_mnc(), tda_mnrow(), tda_mpbl(), tda_mpfit(), tda_mpinv(), tda_mple(), tda_mpz(), tda_mscal1(), tda_msqrtd(), tda_msvd(), tda_mwvec()

Examples

F <- rbind(c(0, 0), c(2, 0.5), c(1, 0.3))
tda_mpit(F, c(100, 50, 20), iterations = 3)
#>      [,1] [,2] [,3]
#> [1,]  100   50   20
#> [2,]  120    0   25
#> [3,]   25    0    0
#> [4,]    0    0    0