swNoData {bayesImageS} | R Documentation |

## Simulate pixel labels using the Swendsen-Wang algorithm.

### 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

```
swNoData(beta, k, neighbors, blocks, niter = 1000, random = TRUE)
```

### 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. |

`niter` |
The number of iterations of the algorithm to perform. |

`random` |
Whether to initialize the labels using random or deterministic starting values. |

### 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. & Wang, J.-S. (1987) "Nonuniversal critical dynamics in Monte Carlo simulations" *Physical Review Letters* **58**(2), 86–88, DOI: doi: 10.1103/PhysRevLett.58.86

### Examples

```
# 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]
```

*bayesImageS*version 0.6-1 Index]