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Last data update: 2014.03.03

R: Create the transition matrix for the diffusion.

makeTmatrix

R Documentation

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)

Arguments

`formLatticeOutput`	a `formLatticeOutput` object, returned by the functions `formLattice` or by the function `editLattice`.
`M`	a smoothing parameter. It is the probability that the random walk stays on the same node in a single step. 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.

Value

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

Author(s)

Ronald P. Barry <rpbarry@alaska.edu>

References

Ronald P. Barry, Julie McIntyre. Estimation 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=0.02)
formLatticeOutput = formLattice(nodeFillingOutput)

Pointdata = csr(polygon1,100)
Pointdata = Pointdata[Pointdata[,1]<0.5,]

poly.area = areapl(polygon1)

init.prob = addObservations(formLatticeOutput, Pointdata)
T = makeTmatrix(formLatticeOutput, M = 0.5, sparse=TRUE)
p10 = Tkp(T,10,p=init.prob$init.prob)
cbind(init.prob$init.prob,p10)