latticeDensity (version 1.2.7)

makeTmatrix: Create the transition matrix for the diffusion.

Description

This function generates a transition matrix for the diffusion process on the lattice.

Usage

makeTmatrix(formLatticeOutput, M = 0.5, sparse = TRUE)

Value

An NxN transition matrix, where N is the number of nodes.

Arguments

formLatticeOutput

A formLatticeOutput object, returned by the functions formLattice or by the function editLattice.

M

A smoothing parameter. It is the maximum probability that the random walk moves from the node in a single step. It is a maximum probability in the sense that this is the movement probability for nodes not near a boundary. Of course, near a boundary movement will be constrained proportional to how many neighbors the node has. Thus if interior nodes have eight neighbors, a node with only four neighbors will move half as often. Since the number of steps k also determines smoothing, M is usually left at 0.5. Note that values of M=1 or M=0 can lead to pathological results. The paper of Barry and McIntyre (2011) shows the exact construction of the transition matrix.

sparse

logical. If TRUE, then uses sparse matrix computations from packages spdep and spam. If FALSE, uses full matrix computations. The use of sparse matrices is almost always more efficient.

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. <doi:10.1016/j.ecolmodel.2011.02.016>

Examples

plot.new()
data(polygon1)
nodeFillingOutput <- nodeFilling(poly=polygon1, node_spacing=0.02)
formLatticeOutput <- formLattice(nodeFillingOutput)
Pointdata <- splancs::csr(polygon1,75)
Pointdata <- Pointdata[Pointdata[,1]<0.5,]
poly.area <- splancs::areapl(polygon1)
init_prob <- addObservations(formLatticeOutput, Pointdata)
T = makeTmatrix(formLatticeOutput, M = 0.5, sparse=TRUE)
p10 <- Tkp(T, 10, p=init_prob$init_prob)
head(cbind(init_prob$init_prob, p10))