The algorithm of Swendsen & Wang (1987) forms clusters of neighbouring pixels, then updates all of the labels within a cluster to the same value. When simulating from the prior, such as a Potts model without an external field, this algorithm is very efficient.
swNoData(beta, k, neighbors, blocks, niter = 1000, random = TRUE)
| beta | The inverse temperature parameter of the Potts model. |
|---|---|
| k | The number of unique labels. |
| neighbors | A matrix of all neighbors in the lattice, one row per pixel. |
| blocks | A list of pixel indices, dividing the lattice into independent blocks. |
| niter | The number of iterations of the algorithm to perform. |
| random | Whether to initialize the labels using random or deterministic starting values. |
A list containing the following elements:
allocAn n by k matrix containing the number of times that pixel i was allocated to label j.
zAn (n+1) by k matrix containing the final sample from the Potts model after niter iterations of Swendsen-Wang.
sumAn niter by 1 matrix containing the sum of like neighbors, i.e. the sufficient statistic of the Potts model, at each iteration.
Swendsen, R. H. & Wang, J.-S. (1987) "Nonuniversal critical dynamics in Monte Carlo simulations" Physical Review Letters 58(2), 86--88, DOI: 10.1103/PhysRevLett.58.86
# Swendsen-Wang for a 2x2 lattice neigh <- matrix(c(5,2,5,3, 1,5,5,4, 5,4,1,5, 3,5,2,5), nrow=4, ncol=4, byrow=TRUE) blocks <- list(c(1,4), c(2,3)) res.sw <- swNoData(0.7, 3, neigh, blocks, niter=200) res.sw$z#> [,1] [,2] [,3] #> [1,] 1 0 0 #> [2,] 1 0 0 #> [3,] 1 0 0 #> [4,] 0 0 1 #> [5,] 0 0 0res.sw$sum[200]#> [1] 2