Calculate Exponential Stochastic Matrix

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

Usage

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)