Partition function of a general Potts model defined on a rectangular h x w lattice (h ≤ w) with either a first order or a second order dependency structure and a small number of rows (up to 25 for 2-state models).
Usage
NC.mrf(h, w, param, ncolors = 2, nei = 4,
pot = NULL, top = NULL, left = NULL,
bottom = NULL, right = NULL, corner = NULL)
Arguments
h
the number of rows of the rectangular lattice.
w
the number of columns of the rectangular lattice.
param
numeric entry setting the interaction parameter (edges parameter)
ncolors
the number of states for the discrete random variables. By default, ncolors = 2.
nei
the number of neighbors. The latter must be one of nei = 4 or nei = 8, which respectively correspond to a first order and a second order dependency structure. By default, nei = 4.
pot
numeric entry setting homogeneous potential on singletons (vertices parameter). By default, pot = NULL
top, left, bottom, right, corner
numeric entry setting constant borders for the lattice. By default, top = NULL, left = NULL, bottom = NULL, right = NULL, corner = NULL.
References
Friel, N. and Rue, H. (2007). Recursive computing and simulation-free inference for general factorizable models. Biometrika, 94(3):661–672.
Reeves, R. and Pettitt, A. N. (2004). Efficient recursions for general factorisable models. Biometrika, 91(3):751–757.
See Also
The “GiRaF-introduction” vignette
Examples
# Dimension of the lattice
height <- 8
width <- 10
# Interaction parameter
Beta <- 0.6 # Isotropic configuration
# Beta <- c(0.6, 0.6) # Anisotropic configuration when nei = 4
# Beta <- c(0.6, 0.6, 0.6, 0.6) # Anisotropic configuration when nei = 8
# Number of colors
K <- 2
# Number of neighbors
G <- 4
# Optional potential on sites
potential <- runif(K,-1,1)
# Optional borders.
Top <- Bottom <- sample(0:(K-1), width, replace = TRUE)
Left <- Right <- sample(0:(K-1), height, replace = TRUE)
Corner <- sample(0:(K-1), 4, replace = TRUE)
# Partition function for the default setting
NC.mrf(h = height, w = width, param = Beta)
# When specifying the number of colors and neighbors
NC.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta)
# When specifying an optional potential on sites
NC.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta,
pot = potential)
# When specifying possible borders. The users will omit to mention all
# the non-existing borders
NC.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta,
top = Top, left = Left, bottom = Bottom, right = Right, corner = Corner)
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
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Type 'demo()' for some demos, 'help()' for on-line help, or
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> library(GiRaF)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GiRaF/NC.mrf.Rd_%03d_medium.png", width=480, height=480)
> ### Name: NC.mrf
> ### Title: Normalising constant of a Gibbs Random Field
> ### Aliases: NC.mrf
>
> ### ** Examples
>
> # Dimension of the lattice
> height <- 8
> width <- 10
>
> # Interaction parameter
> Beta <- 0.6 # Isotropic configuration
> # Beta <- c(0.6, 0.6) # Anisotropic configuration when nei = 4
> # Beta <- c(0.6, 0.6, 0.6, 0.6) # Anisotropic configuration when nei = 8
>
> # Number of colors
> K <- 2
> # Number of neighbors
> G <- 4
>
> # Optional potential on sites
> potential <- runif(K,-1,1)
> # Optional borders.
> Top <- Bottom <- sample(0:(K-1), width, replace = TRUE)
> Left <- Right <- sample(0:(K-1), height, replace = TRUE)
> Corner <- sample(0:(K-1), 4, replace = TRUE)
>
> # Partition function for the default setting
> NC.mrf(h = height, w = width, param = Beta)
[1] 3.541494e+45
>
> # When specifying the number of colors and neighbors
> NC.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta)
[1] 3.541494e+45
>
> # When specifying an optional potential on sites
> NC.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta,
+ pot = potential)
[1] 3.736054e+66
>
> # When specifying possible borders. The users will omit to mention all
> # the non-existing borders
> NC.mrf(h = height, w = width, ncolors = K, nei = G, param = Beta,
+ top = Top, left = Left, bottom = Bottom, right = Right, corner = Corner)
[1] 1.002689e+51
>
>
>
>
>
> dev.off()
null device
1
>