fundamental_matrix {exactLTRE}

Fundamental matrix

Description

Calculate the fundamental matrix. The fundamental matrix, generally referred to as N, contains the expected number of timesteps that an individual will spend in each age, stage, or size class of the matrix throughout their lifespan, given their current class. In the fundamental matrix, the current state is the column, and the future states are in the rows. For an age-classified matrix, this should be lower triangular.

Usage

fundamental_matrix(Umat)

Arguments

Umat

The survival components of the population projection matrix.

Value

The fundamental matrix, containing the expected number of timesteps that an individual will spend in each class of the population, given their current state. This matrix will have the same size as the input matrix.

Examples

A1<- matrix(data=c(0,0.8,0, 0,0,0.7, 5,0,0.2), nrow=3, ncol=3)
U1<- A1
U1[1,3]<- 0
# the upper right corner represents adult fertility in this model. U1, the
# survival matrix, contains all the transitions *except* for fertility.
N1<- fundamental_matrix(U1)