Simulate pixel labels using the Swendsen-Wang algorithm.

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Description

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.

Usage

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swNoData(beta, k, neighbors, blocks, slices = c(0, nrow(neighbors)),
  niter = 1000)

Arguments

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.

slices

Deprecated.

niter

The number of iterations of the algorithm to perform.

Value

A list containing the following elements:

alloc

An n by k matrix containing the number of times that pixel i was allocated to label j.

z

An (n+1) by k matrix containing the final sample from the Potts model after niter iterations of Swendsen-Wang.

sum

An niter by 1 matrix containing the sum of like neighbors, i.e. the sufficient statistic of the Potts model, at each iteration.

References

Swendsen, R. H. and Wang, J.-S. 1987 "Nonuniversal critical dynamics in Monte Carlo simulations" Physical Review Letters 58(2), 86–88, DOI: 10.1103/PhysRevLett.58.86

See Also

SW

Examples

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# 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$z
res.sw$sum[200]