Calculate Exponential Stochastic Matrix

Given a distance matrix from calcVinEll, calculate a stochastic matrix where one step movement probabilities follow an exponential density.

calcExpKernel(distMat, rate)

Arguments

distMat	Distance matrix from calcVinEll
rate	Rate parameter of Exponential distribution

Details

The distribution and density functions for the exponential kernel are given below: $$ F(x)=1-e^{-\lambda x} $$ $$ f(x)=\lambda e^{-\lambda x} $$ where \(\lambda\) is the rate parameter of the exponential distribution.

Examples

# setup distance matrix
# two-column matrix with latitude/longitude, in degrees
latLong = cbind(runif(n = 5, min = 0, max = 90),
                runif(n = 5, min = 0, max = 180))

# Vincenty Ellipsoid  distance formula
distMat = calcVinEll(latLongs = latLong)

# calculate exponential distribution over distances
#  rate is just for example
kernMat = calcExpKernel(distMat = distMat, rate = 10)