Wolff: Generate Random Samples from a Compound Potts Model by the...
In PottsUtils: Utility Functions of the Potts Models
Description
Usage
Arguments
Details
Value
References
See Also
Examples
Description
Generate random samples from a compound Potts model using the Wolff Algorithm.
Usage
1
Arguments
n
number of samples.
nvertex
number of vertices of a graph.
ncolor
number of colors each vertex can take.
neighbors
neighbors of a graph.
weights
weights between neighbors. One for each corresponding
component in neighbors. The default values are 1s for all.
beta
the parameter inverse temperature of the Potts model.
Details
We use the Wolff algorithm to generate random samples from a compound
Potts model. See rPotts1 for more
information on the compound Potts model.
Value
A nvertex by n matrix with the kth column being the kth
sample.
References
Ulli Wolff (1989)
Collective Monte Carlo Updating for Spin Systems
Physical Review Letters vol. 62, no. 4, 361-364
Dai Feng (2008)
Bayesian Hidden Markov Normal Mixture Models with Application to MRI
Tissue Classification
Ph. D. Dissertation, The University of Iowa
See Also
Examples
1
2
3
4
5
6
7
8
#Example 1: Generate 100 samples from a Potts model with the
# neighborhood structure corresponding to a
# second-order Markov random field defined on a
# 3*3 2D graph. The number of colors is 2.
# beta=0.7. All weights are equal to 1.
neighbors <- getNeighbors(mask=matrix(1, 3, 3), neiStruc=rep(2,4))
Wolff(n=100, nvertex=9, ncolor=2, neighbors, beta=0.7)
Example output
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
[1,] 2 2 2 1 1 1 2 1 2 2 2 1 2
[2,] 1 1 2 1 2 1 2 1 2 1 2 1 2
[3,] 1 1 2 1 2 1 2 1 2 1 2 1 2
[4,] 1 1 2 1 2 1 2 1 2 1 1 1 2
[5,] 1 1 2 1 2 1 2 1 2 1 2 1 2
[6,] 2 2 2 1 2 1 2 1 2 1 2 1 2
[7,] 1 1 2 1 2 1 2 1 2 2 2 1 1
[8,] 1 2 2 1 2 1 2 1 2 1 1 1 2
[9,] 2 2 2 1 2 1 2 1 2 1 2 1 2
[,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
[1,] 1 2 2 1 2 2 2 2 1 1 2 1
[2,] 1 2 2 1 2 2 1 2 1 2 2 1
[3,] 1 2 2 1 2 2 1 2 2 2 2 2
[4,] 1 1 1 1 2 2 1 1 1 1 2 1
[5,] 1 2 2 1 2 2 1 2 1 1 2 1
[6,] 1 2 2 1 2 2 1 1 1 1 2 1
[7,] 1 2 2 2 2 2 1 1 1 1 2 1
[8,] 1 2 1 1 1 1 1 1 1 1 2 1
[9,] 1 2 1 1 1 2 1 1 1 1 2 1
[,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
[1,] 1 2 2 1 2 1 2 2 1 2 2 2
[2,] 1 1 1 1 2 1 2 2 1 2 2 2
[3,] 2 2 2 1 2 1 2 2 1 2 1 1
[4,] 1 2 2 1 2 1 2 2 1 2 2 2
[5,] 1 2 2 1 2 1 1 2 1 2 1 1
[6,] 1 1 1 1 2 1 1 2 1 2 1 1
[7,] 1 1 1 1 2 1 1 2 1 2 1 2
[8,] 1 1 2 1 2 1 1 2 1 2 1 1
[9,] 2 2 2 1 2 1 1 2 1 2 1 1
[,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
[1,] 2 1 2 1 1 2 1 2 1 1 1 2
[2,] 2 1 2 2 1 2 1 1 1 2 1 2
[3,] 2 1 2 2 1 2 1 1 1 2 1 1
[4,] 2 1 2 1 1 2 1 2 1 2 1 2
[5,] 2 1 2 1 1 2 1 2 1 2 1 2
[6,] 2 1 2 1 1 2 1 2 1 2 1 2
[7,] 2 1 2 1 1 2 1 2 2 2 1 2
[8,] 2 1 2 1 1 2 1 2 1 2 1 2
[9,] 2 1 2 1 1 2 1 1 1 2 1 1
[,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61]
[1,] 1 2 1 2 1 2 2 1 2 1 2 1
[2,] 1 2 1 2 1 2 2 1 2 1 2 1
[3,] 1 2 1 2 1 2 1 1 2 1 2 1
[4,] 1 1 1 2 1 1 1 1 2 1 2 1
[5,] 1 2 1 2 1 2 2 1 2 1 2 1
[6,] 1 2 1 2 1 2 2 1 2 1 2 1
[7,] 2 2 1 2 2 2 2 1 2 1 2 1
[8,] 1 2 2 2 1 2 2 1 2 1 2 1
[9,] 1 2 1 2 2 2 2 1 2 1 2 1
[,62] [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73]
[1,] 2 1 2 1 2 2 2 1 1 1 1 1
[2,] 2 1 2 1 2 2 2 2 2 2 2 1
[3,] 2 1 2 1 2 2 2 2 1 2 2 1
[4,] 1 1 2 1 2 1 1 1 1 1 1 1
[5,] 2 1 2 1 2 2 2 2 1 1 2 1
[6,] 2 1 2 1 1 1 2 2 1 1 2 2
[7,] 2 1 2 2 2 2 2 2 1 1 1 1
[8,] 2 1 2 1 2 2 2 2 1 1 2 1
[9,] 2 1 2 1 2 2 2 2 1 1 2 1
[,74] [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85]
[1,] 1 2 1 2 1 2 1 2 2 1 2 1
[2,] 1 2 1 2 1 2 1 2 2 1 2 1
[3,] 1 2 1 2 1 1 1 1 2 1 1 1
[4,] 1 2 1 2 1 2 1 1 2 1 2 1
[5,] 1 2 1 2 1 2 1 1 2 1 2 1
[6,] 2 2 1 2 1 2 1 1 2 1 2 1
[7,] 1 2 1 2 1 2 1 1 2 1 2 2
[8,] 1 1 1 2 1 2 1 1 2 1 2 1
[9,] 2 2 1 2 1 2 1 1 1 1 2 1
[,86] [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97]
[1,] 2 2 2 1 2 2 1 2 1 2 2 1
[2,] 2 1 2 1 2 2 1 2 1 2 1 1
[3,] 2 1 2 1 2 2 1 1 1 2 1 1
[4,] 2 1 2 1 1 2 1 2 1 2 2 1
[5,] 2 1 2 1 2 2 1 2 1 2 2 1
[6,] 2 1 2 1 2 2 1 2 1 2 1 1
[7,] 2 1 2 2 2 2 1 1 1 2 2 1
[8,] 2 1 2 1 2 2 1 2 1 2 2 1
[9,] 2 1 2 1 2 2 1 1 1 2 2 1
[,98] [,99] [,100]
[1,] 2 1 1
[2,] 2 1 1
[3,] 1 1 1
[4,] 2 1 1
[5,] 2 1 1
[6,] 1 1 1
[7,] 2 2 2
[8,] 2 2 2
[9,] 2 2 1
PottsUtils documentation built on May 2, 2019, 6:45 a.m.
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Description Usage Arguments Details Value References See Also Examples
Description
Generate random samples from a compound Potts model using the Wolff Algorithm.
Usage
1 |
Arguments
n |
number of samples. |
nvertex |
number of vertices of a graph. |
ncolor |
number of colors each vertex can take. |
neighbors |
neighbors of a graph. |
weights |
weights between neighbors. One for each corresponding
component in |
beta |
the parameter inverse temperature of the Potts model. |
Details
We use the Wolff algorithm to generate random samples from a compound
Potts model. See rPotts1 for more
information on the compound Potts model.
Value
A nvertex by n matrix with the kth column being the kth
sample.
References
Ulli Wolff (1989) Collective Monte Carlo Updating for Spin Systems Physical Review Letters vol. 62, no. 4, 361-364
Dai Feng (2008) Bayesian Hidden Markov Normal Mixture Models with Application to MRI Tissue Classification Ph. D. Dissertation, The University of Iowa
See Also
Examples
1 2 3 4 5 6 7 8 | #Example 1: Generate 100 samples from a Potts model with the
# neighborhood structure corresponding to a
# second-order Markov random field defined on a
# 3*3 2D graph. The number of colors is 2.
# beta=0.7. All weights are equal to 1.
neighbors <- getNeighbors(mask=matrix(1, 3, 3), neiStruc=rep(2,4))
Wolff(n=100, nvertex=9, ncolor=2, neighbors, beta=0.7)
|
Example output
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
[1,] 2 2 2 1 1 1 2 1 2 2 2 1 2
[2,] 1 1 2 1 2 1 2 1 2 1 2 1 2
[3,] 1 1 2 1 2 1 2 1 2 1 2 1 2
[4,] 1 1 2 1 2 1 2 1 2 1 1 1 2
[5,] 1 1 2 1 2 1 2 1 2 1 2 1 2
[6,] 2 2 2 1 2 1 2 1 2 1 2 1 2
[7,] 1 1 2 1 2 1 2 1 2 2 2 1 1
[8,] 1 2 2 1 2 1 2 1 2 1 1 1 2
[9,] 2 2 2 1 2 1 2 1 2 1 2 1 2
[,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
[1,] 1 2 2 1 2 2 2 2 1 1 2 1
[2,] 1 2 2 1 2 2 1 2 1 2 2 1
[3,] 1 2 2 1 2 2 1 2 2 2 2 2
[4,] 1 1 1 1 2 2 1 1 1 1 2 1
[5,] 1 2 2 1 2 2 1 2 1 1 2 1
[6,] 1 2 2 1 2 2 1 1 1 1 2 1
[7,] 1 2 2 2 2 2 1 1 1 1 2 1
[8,] 1 2 1 1 1 1 1 1 1 1 2 1
[9,] 1 2 1 1 1 2 1 1 1 1 2 1
[,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
[1,] 1 2 2 1 2 1 2 2 1 2 2 2
[2,] 1 1 1 1 2 1 2 2 1 2 2 2
[3,] 2 2 2 1 2 1 2 2 1 2 1 1
[4,] 1 2 2 1 2 1 2 2 1 2 2 2
[5,] 1 2 2 1 2 1 1 2 1 2 1 1
[6,] 1 1 1 1 2 1 1 2 1 2 1 1
[7,] 1 1 1 1 2 1 1 2 1 2 1 2
[8,] 1 1 2 1 2 1 1 2 1 2 1 1
[9,] 2 2 2 1 2 1 1 2 1 2 1 1
[,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
[1,] 2 1 2 1 1 2 1 2 1 1 1 2
[2,] 2 1 2 2 1 2 1 1 1 2 1 2
[3,] 2 1 2 2 1 2 1 1 1 2 1 1
[4,] 2 1 2 1 1 2 1 2 1 2 1 2
[5,] 2 1 2 1 1 2 1 2 1 2 1 2
[6,] 2 1 2 1 1 2 1 2 1 2 1 2
[7,] 2 1 2 1 1 2 1 2 2 2 1 2
[8,] 2 1 2 1 1 2 1 2 1 2 1 2
[9,] 2 1 2 1 1 2 1 1 1 2 1 1
[,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61]
[1,] 1 2 1 2 1 2 2 1 2 1 2 1
[2,] 1 2 1 2 1 2 2 1 2 1 2 1
[3,] 1 2 1 2 1 2 1 1 2 1 2 1
[4,] 1 1 1 2 1 1 1 1 2 1 2 1
[5,] 1 2 1 2 1 2 2 1 2 1 2 1
[6,] 1 2 1 2 1 2 2 1 2 1 2 1
[7,] 2 2 1 2 2 2 2 1 2 1 2 1
[8,] 1 2 2 2 1 2 2 1 2 1 2 1
[9,] 1 2 1 2 2 2 2 1 2 1 2 1
[,62] [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73]
[1,] 2 1 2 1 2 2 2 1 1 1 1 1
[2,] 2 1 2 1 2 2 2 2 2 2 2 1
[3,] 2 1 2 1 2 2 2 2 1 2 2 1
[4,] 1 1 2 1 2 1 1 1 1 1 1 1
[5,] 2 1 2 1 2 2 2 2 1 1 2 1
[6,] 2 1 2 1 1 1 2 2 1 1 2 2
[7,] 2 1 2 2 2 2 2 2 1 1 1 1
[8,] 2 1 2 1 2 2 2 2 1 1 2 1
[9,] 2 1 2 1 2 2 2 2 1 1 2 1
[,74] [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85]
[1,] 1 2 1 2 1 2 1 2 2 1 2 1
[2,] 1 2 1 2 1 2 1 2 2 1 2 1
[3,] 1 2 1 2 1 1 1 1 2 1 1 1
[4,] 1 2 1 2 1 2 1 1 2 1 2 1
[5,] 1 2 1 2 1 2 1 1 2 1 2 1
[6,] 2 2 1 2 1 2 1 1 2 1 2 1
[7,] 1 2 1 2 1 2 1 1 2 1 2 2
[8,] 1 1 1 2 1 2 1 1 2 1 2 1
[9,] 2 2 1 2 1 2 1 1 1 1 2 1
[,86] [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97]
[1,] 2 2 2 1 2 2 1 2 1 2 2 1
[2,] 2 1 2 1 2 2 1 2 1 2 1 1
[3,] 2 1 2 1 2 2 1 1 1 2 1 1
[4,] 2 1 2 1 1 2 1 2 1 2 2 1
[5,] 2 1 2 1 2 2 1 2 1 2 2 1
[6,] 2 1 2 1 2 2 1 2 1 2 1 1
[7,] 2 1 2 2 2 2 1 1 1 2 2 1
[8,] 2 1 2 1 2 2 1 2 1 2 2 1
[9,] 2 1 2 1 2 2 1 1 1 2 2 1
[,98] [,99] [,100]
[1,] 2 1 1
[2,] 2 1 1
[3,] 1 1 1
[4,] 2 1 1
[5,] 2 1 1
[6,] 1 1 1
[7,] 2 2 2
[8,] 2 2 2
[9,] 2 2 1
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