algstat (version 0.0.2)

markov: Compute a Markov Basis with 4ti2

Description

A Markov basis of a matrix A is computed with the markov function of 4ti2, obtained with the LattE-integrale bundle.

Usage

markov(mat, format = c("mat", "vec", "tab"), dim = NULL, all = FALSE, dir = tempdir(), opts = "-parb", quiet = TRUE, dbName)

Arguments

mat

a matrix; for example the output of hmat

format

how the moves should be returned (if "mat", moves are columns)

dim

the dimension to be used in vec2tab if format = "tab" is used, oftentimes a vector of the number of levels of each variable in order

all

if TRUE, all moves (+ and -) are given. if FALSE, only the + moves are given.

dir

directory to place the files in, without an ending /

opts

options for markov

quiet

show 4ti2 output

dbName

the name of the model in the markov bases database, http://markov-bases.de, see examples

Value

a matrix containing the Markov basis as its columns (for easy addition to tables)

References

Drton, M., B. Sturmfels, and S. Sullivant (2009). Lectures on Algebraic Statistics, Basel: Birkhauser Verlag AG.

Examples

## Not run: 
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# # 2x2 independence example
# # following convention, the first index indicates rows
# varlvls <- c(2,2)
# facets <- list(1,2)
# ( A <- hmat(varlvls, facets) )
# markov(A)
# markov(A, "vec")
# markov(A, "tab", varlvls)
# markov(A, "tab", varlvls, TRUE)
# 
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# # 3x3 independence example
# # following convention, the first index indicates rows
# varlvls <- c(3,3)
# facets <- list(1,2)
# ( A <- hmat(varlvls, facets) )
# markov(A)
# markov(A, "vec")
# markov(A, "tab", varlvls)
# markov(A, "tab", varlvls, TRUE)
# 
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# # LAS example 1.2.1, p.12 (2x3 independence)
# varlvls <- c(2,3)
# facets <- list(1, 2)
# ( A <- hmat(varlvls, facets) )
# markov(A, "tab", varlvls)
# # Prop 1.2.2 says that there should be
# 2*choose(2, 2)*choose(3,2) # = 6
# # moves.
# markov(A, "tab", varlvls, TRUE)
# 
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# # LAS example 1.2.12, p.17  (no 3-way interaction)
# varlvls <- c(2,2,2)
# facets <- list(c(1,2), c(1,3), c(2,3))
# ( A <- hmat(varlvls, facets) )
# markov(A)
# 
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# # LAS example 1.2.12, p.16  (no 3-way interaction)
# varlvls <- c(2,2,2,2)
# facets <- list(c(1,2), c(1,4), c(2,3))
# ( A <- hmat(varlvls, facets) )
# markov(A)
# markov(A, "tab", varlvls) # hard to understand
# tableau(markov(A), varlvls)
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# # using the markov bases database, must be connected to internet
# # A <- markov(dbName = "ind3-3")
# B <- markov(hmat(c(3,3), list(1,2)))
# # all(A == B)
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# markov(diag(1, 10))
# 
# ## End(Not run)