# makeTmatrix: Create the transition matrix for the diffusion. In latticeDensity: Density Estimation and Nonparametric Regression on Irregular Regions

## Description

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

## Usage

 `1` ```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 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.

## Value

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

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

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```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)) ```

latticeDensity documentation built on April 18, 2021, 5:06 p.m.