latticeDensity (version 1.2.7)

Tkp: Compute the vector T^k*p

Description

TranMat is the transition matrix of the random walk on the lattice. By multiplying by the probability density p at time t, you get the probability density at time t+1. Thus, to get the probability density after k steps, pk, compute pk = Tkp1. This application of finite Markov processes is described in Barry and McIntyre (2011).

Usage

Tkp(TranMat, k, p)

Value

A vector of probabilities.

Arguments

TranMat

Transition matrix returned by makeTmatrix.

k

The number of steps in the diffusion.

p

A numerical vector of length equal to the number of nodes, of initial probabilities.

Author

Ronald P. Barry

References

Ronald P. Barry, Julie McIntyre. Estimating animal densities and home range in regions with irregular boundaries and holes: A lattice-based alternative to the kernel density estimator. Ecological Modelling 222 (2011) 1666-1672.

Examples

plot.new()
data(polygon1)
nodeFillingOutput <- nodeFilling(poly=polygon1, node_spacing=0.015)
formLatticeOutput <- formLattice(nodeFillingOutput)
Pointdata <- splancs::csr(polygon1,75)
Pointdata <- Pointdata[Pointdata[,1]<0.5, ]
init_prob <- addObservations(formLatticeOutput, Pointdata)
TranMat <- makeTmatrix(formLatticeOutput, M = 0.5, sparse=TRUE)
p10 <- Tkp(TranMat, k=10, p=init_prob$init_prob)
head(cbind(init_prob$init_prob, p10))