PottsUtils (version 0.2-1)

getBlocks: Get Blocks of a Graph

Description

Obtain blocks of vertices of a 1D, 2D, or 3D graph, in order to use the conditional independence to speed up the simulation (checkerboard idea).

Usage

getBlocks(mask, nblock)

Arguments

mask

a vector, matrix, or 3D array specifying vertices of a graph. Vertices of value 1 are within the graph and 0 are not.

nblock

a scalar specifying the number of blocks. Right now, for a 2D graph nblock could be either 2 or 4, and for a 3D graph nblock could be either 2 or 8.

Value

• A list with the number of components equal to nblock. Each component consists of vertices within the same block.

Details

The vertices within each block are mutually independent given the vertices in other blocks. Some blocks could be empty.

References

Darren J. Wilkinson Parallel Bayesian Computation Handbook of Parallel Computing and Statistics 481-512 Marcel Dekker/CRC Press 2005

Examples

#Example 1: split a line into 2 blocks
  getBlocks(mask=c(1,1,1,1,0,0,1,1,0), nblock=2)

  #Example 2: split a \eqn{4 \times 4} 2D graph into 4 blocks in order
  #           to use the checkerboard idea for a neighborhood structure
  #           corresponding to the second-order Markov random field.
  getBlocks(mask=matrix(1, nrow=4, ncol=4), nblock=4)

  #Example 3: split a \eqn{3 \times 3 \times 3} 3D graph into 8 blocks
  #           in order to use the checkerboard idea for a neighborhood
  #           structure based on the 18 neighbors definition, where the
  #           neighbors of a vertex comprise its available
  #           adjacencies sharing the same edges or faces.
  mask <- array(1, dim=rep(3,3))
  getBlocks(mask, nblock=8)