InvDistMat function

Inverse distance matrix

This function calculates the inverse distances, with a given cutoff distance and a positive exponent.

InvDistMat(distMat, distCutOff = NULL, powr = 1, mevn = FALSE)

Arguments

• distMat: distance matrix
• distCutOff: cutoff distance. Default = the maximal value from the distance matrix.
• powr: power (positive exponent), default = 1
• mevn: logical, default FALSE. If TRUE, max-eigenvalue normalization is performed.

Returns

• W: weights matrix (Default, not normalized)

Details

W is an nxn matrix with elements $w_{ij}$, i,j=1,..n, where $w_{ij}=1/d_{ij}^\gamma$, if $0 <= d_{ij} < D$ and $w_{ij}=0$, if $d_{ij} > D$ or $i = j$. D is the distance cutoff point (maximum radius of influence), $d_{ij}$ is the distance between spatial units i and j, and $\gamma$ is the value for the exponent (e.g. $\gamma$ = 1, 2, 3, 4,...).

Examples

## distance between centroids of NUTS3 regions in Germany (in meters)
data(gN3dist, package = "SDPDmod")
## inverse distance matrix with cutoff 100000 meters
W1    <- InvDistMat(distMat = gN3dist, distCutOff = 100000)
dist2 <- gN3dist/1000 ##distance in km
## normalized distance matrix with cutoff 100km
W2    <- InvDistMat(distMat = dist2, distCutOff=100, powr = 2, mevn = TRUE)

Author(s)

Rozeta Simonovska