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Stationary solution of a Leslie matrix

Source: R/further-regression.R
tda_spmod.Rd

TDA's spmod: iterates a population vector under the Leslie matrix built from age-specific fertility (first row) and survivor rates (subdiagonal) until the age distribution is stationary. Verified in the suite against R's eigen: the growth factor equals the dominant eigenvalue and the stationary vector the normalized dominant eigenvector.

Usage

tda_spmod(
  fertility,
  survival,
  start = rep(1, length(fertility)),
  tolf = 1e-08,
  mxit = 500,
  ...
)

Arguments

fertility, survival, start

numeric vectors of equal length: age-specific fertility, survivor rates (last entry unused), and the starting population.

tolf

convergence tolerance.

mxit

iteration cap.

...

passed to tda_run.

Value

list with growth (the dominant eigenvalue) and stationary (the stable age distribution, summing to 1).

Examples

r <- tda_spmod(c(0, .4, .3, .1), c(.9, .8, .7, 0), rep(1, 4))
r
#> <tda_leslie>
#> growth: 0.8320931 
#> stationary: 0.2502305 0.2706518 0.2602130 0.2189047 
L <- rbind(c(0, .4, .3, .1), cbind(diag(c(.9, .8, .7)), 0))
stopifnot(abs(r$growth - Re(eigen(L)$values[1])) < 1e-5)