dikin_walk: Dikin Walk
In walkr: Random Walks in the Intersection of Hyperplanes and the N-Simplex

Description Usage Arguments Value Examples

This function implements the Dikin Walk using the Hessian of the Log barrier function. Note that a $r$ of 1 guarantees that the ellipsoid generated won't leave our polytope $K$ (see Theorems online)

1 2	dikin_walk(A, b, x0 = list(), points, r = 1, thin = 1, burn = 0, chains = 1)

`A`	is the lhs of Ax <= b
`b`	is the rhs of Ax <= b
`x0`	is the starting point (a list of points)
`points`	is the number of points we want to sample
`r`	is the radius of the ellipsoid (1 by default)
`thin`	every thin-th point is stored
`burn`	the first burn points are deleted
`chains`	is the number of chains we run

a list of chains of the sampled points, each chain being a matrix object with each column as a point

A <- rbind(c(1, 0), c(0, 1))
b <- c(1, 1)    
sampled_points <- dikin_walk(A = A, b = b, points = 10, x0 = list(c(0.5,0.5)))

## Not run: 
## note that this Ax <= b is different from Ax=b that the 
## user specifies for walkr (see transformation section in vignette) 
dikin_walk(A = A, b = b, x0, points = 100, 
           r = 1thin = 1, burn = 0, chains = 1) 

## End(Not run)