Movatterモバイル変換

Type:	Package
Title:	Interface to 'LattE' and '4ti2'
Version:	0.2.2
Maintainer:	David Kahle <david@kahle.io>
Description:	Back-end connections to 'LattE' (https://www.math.ucdavis.edu/~latte/) for counting lattice points and integration inside convex polytopes and '4ti2' (http://www.4ti2.de/) for algebraic, geometric, and combinatorial problems on linear spaces and front-end tools facilitating their use in the 'R' ecosystem.
License:	GPL-2
URL:	https://github.com/dkahle/latte
BugReports:	https://github.com/dkahle/latte/issues
SystemRequirements:	LattE <https://www.math.ucdavis.edu/~latte/>, 4ti2<http://www.4ti2.de/>
Imports:	magrittr, stringr, mpoly, ggplot2, memoise, dplyr, usethis,glue
Suggests:	knitr, rmarkdown
RoxygenNote:	7.3.2
Encoding:	UTF-8
NeedsCompilation:	no
Packaged:	2025-06-09 05:07:18 UTC; david_kahle
Author:	David Kahle [aut, cph, cre], Luis Garcia [aut, cph], Ruriko Yoshida [aut, cph]
Repository:	CRAN
Date/Publication:	2025-06-09 05:20:02 UTC

Unified interface to calling LattE

Description

Unified interface to calling LattE

Usage

call_latte(  which_exe,  input_file,  project_dir,  opts = list(),  stdout = "stdout",  stderr = "stderr",  shell = FALSE)

Arguments

Value

invisible()

Generate a configuration matrix

Description

genmodel runs 4ti2's genmodel program to compute the configuration matrix Acorresponding to graphical statistical models given by a simplicial complexand levels on the nodes.

Usage

genmodel(varlvls, facets, dir = tempdir(), quiet = TRUE, shell = FALSE, ...)

Arguments

Value

The configuration matrix of the model provided

Examples

if (has_4ti2()) {varlvls <- rep(2, 2)facets <- list(1, 2)genmodel(varlvls, facets)genmodel(varlvls, facets, quiet = FALSE)varlvls <- rep(3, 3)facets <- list(1:2, 2:3, c(3,1))genmodel(varlvls, facets)# compare this to algstat's hmat function}

Iterated Kronecker product

Description

Compute the Kronecker product of several matrices.

Usage

kprod(..., FUN = `*`)

Arguments

Details

If kronecker is the function that computes A x B, kprod computes A x B x Cand so on; it's a wrapper of Reduce and kronecker.

Value

A matrix that is the kronecker product of the specified matrices(from left to right).

Examples

kprod(diag(2), t(ones(2)))kprod(t(ones(2)), diag(2))kprod(diag(2), t(ones(2)), t(ones(2)))kprod(t(ones(2)), diag(2), t(ones(2)))kprod(t(ones(2)), t(ones(2)), diag(2))# cf. aoki, hara, and takemura p.13rbind(  kprod(diag(2), t(ones(2))),  kprod(t(ones(2)), diag(2)))

R Interface to LattE and 4ti2

Description

Back-end connections to LattE (https://www.math.ucdavis.edu/~latte/)and 4ti2 (http://www.4ti2.de/) executables and front-end toolsfacilitating their use in the R ecosystem.

Count integer points in a polytope

Description

latte_count uses LattE's count function to count the (integer) latticepoints in a polytope and compute Ehrhart polynomials.

Usage

count_core(spec, dir = tempdir(), quiet = TRUE, mpoly = TRUE, ...)latte_count(spec, dir = tempdir(), quiet = TRUE, mpoly = TRUE, ...)latte_fcount(spec, dir = tempdir(), quiet = TRUE, mpoly = TRUE, ...)

Arguments

Details

The specification should be one of the following: (1) a character string orstrings containing an inequality in the mpoly expression format (seeexamples), (2) a list of vertices, (3) a list of A and b for the equation Ax<= b (see examples), or (4) raw code for LattE's count program. If acharacter vector is supplied, (1) and (4) are distinguished by the number ofstrings.

Behind the scenes, count works by writing a latte file and running count onit. If a specification other than a length one character is given to it(which is considered to be the code), count attempts to convert it into LattEcode and then run count on it.

Value

The count. If the count is a number has less than 10 digits, aninteger is returned. If the number has 10 or more digits, an integer in acharacter string is returned. You may want to use the gmp package's as.bigzto parse it.

Examples

if (has_latte()) {spec <- c("x + y <= 10", "x >= 1", "y >= 1")latte_count(spec) # 45latte_count(spec, quiet = FALSE) # 45latte_count(spec, dilation = 10) # 3321latte_count(spec, homog = TRUE) # 45# by default, the output from LattE is inlist.files(tempdir())list.files(tempdir(), recursive = TRUE)# ehrhart polynomialslatte_count(spec, ehrhart_polynomial = TRUE)latte_count(spec, ehrhart_polynomial = TRUE, mpoly = FALSE)# ehrhart series (raw since mpoly can't handle rational functions)latte_count(spec, ehrhart_series = TRUE)# simplified ehrhart series - not yet implemented#latte_count(spec, simplified_ehrhart_polynomial = TRUE)# first terms of the ehrhart serieslatte_count(spec, ehrhart_taylor = 1)# latte_count(spec, ehrhart_taylor = 2)# latte_count(spec, ehrhart_taylor = 3)# latte_count(spec, ehrhart_taylor = 4)# multivariate generating functionlatte_count(spec, multivariate_generating_function = TRUE)# by verticesspec <- list(c(1,1), c(10,1), c(1,10), c(10,10))latte_count(spec)latte_count(spec, vrep = TRUE)code <- "5 31 -1  01  0 -11 -1 -10  1  00  0  1"latte_count(code)# for Ax <= b, see this example from the latte manual p.10A <- matrix(c(   1,  0,   0,  1,   1,  1,  -1,  0,   0, -1), nrow = 5, byrow = TRUE)b <- c(1, 1, 1, 0, 0)latte_count(list(A = A, b = b))}

Format/read/write a matrix in latte's style

Description

format_latte() formats a matrix in latte's style.write_latte() writes a latte-formatted file to file.read_latte() reads a latte-formatted file from disk.

Usage

format_latte(mat, file)write_latte(mat, file)write.latte(mat, file)read_latte(file, format = c("mat", "Ab"))read.latte(file, format = c("mat", "Ab"))

Arguments

Value

• format_latte() – A character string of the matrix inlatte format.

• write_latte() – An invisible characterstring of the formatted output.

• read_latte() – An integer matrix.

Examples

(mat <- matrix(sample(9), 3, 3))format_latte(mat)cat(format_latte(mat))(file <- file.path(tempdir(), "foo.hrep"))write_latte(mat, file)file.show(file)read_latte(file)read_latte(file, "Ab")attr(mat, "linearity") <- c(1, 3)attr(mat, "nonnegative") <- 2matformat_latte(mat)cat(format_latte(mat))write_latte(mat, file)file.show(file)read_latte(file)file.remove(file)

Solve an integer progam with LattE

Description

latte_max() andlatte_min() use LattE'slatte-maximize andlatte-minimize functions to find the maximum or minimum of a linearobjective function over the integers points in a polytope (i.e. satisfyinglinearity constraints). This makes use of the digging algorithm; see theLattE manual athttps://www.math.ucdavis.edu/~latte/ for details.

Usage

latte_optim(  objective,  constraints,  type = c("max", "min"),  method = c("lp", "cones"),  dir = tempdir(),  opts = "",  quiet = TRUE,  shell = FALSE)latte_max(  objective,  constraints,  method = c("lp", "cones"),  dir = tempdir(),  opts = "",  quiet = TRUE)latte_min(  objective,  constraints,  method = c("lp", "cones"),  dir = tempdir(),  opts = "",  quiet = TRUE)

Arguments

Value

A named list with componentspar, a named-vector of optimizingarguments, andvalue, the value of the objective function at the optimialpoint.

Examples

if (has_latte()) {latte_max(  "-2 x + 3 y",   c("x + y <= 10", "x >= 0", "y >= 0"))latte_max(  "-2 x + 3 y",   c("x + y <= 10", "x >= 0", "y >= 0"),  quiet = FALSE)df <- expand.grid("x" = 0:10, "y" = 0:10)df <- subset(df, x + y <= 10L)df$objective <- with(df, -2*x + 3*y)library("ggplot2")ggplot(df, aes(x, y, size = objective)) +  geom_point()latte_min(  "-2 x + 3 y",  c("x + y <= 10", "x >= 0", "y >= 0"),  method = "cones")latte_min("-2 x - 3 y - 4 z", c(  "3 x + 2 y + z <= 10",  "2 x + 5 y + 3 z <= 15",  "x >= 0", "y >= 0", "z >= 0"), "cones", quiet = FALSE)}

Compute a basis with 4ti2

Description

4ti2 provides several executables that can be used to generate bases for aconfiguration matrix A. See the references for details.

Usage

basis(exec, memoise = TRUE)zbasis(  A,  format = c("mat", "vec", "tab"),  dim = NULL,  all = FALSE,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  dbName = NULL,  ...)markov(  A,  format = c("mat", "vec", "tab"),  dim = NULL,  all = FALSE,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  dbName = NULL,  ...)groebner(  A,  format = c("mat", "vec", "tab"),  dim = NULL,  all = FALSE,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  dbName = NULL,  ...)hilbert(  A,  format = c("mat", "vec", "tab"),  dim = NULL,  all = FALSE,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  dbName = NULL,  ...)graver(  A,  format = c("mat", "vec", "tab"),  dim = NULL,  all = FALSE,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  dbName = NULL,  ...)fzbasis(  A,  format = c("mat", "vec", "tab"),  dim = NULL,  all = FALSE,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  dbName = NULL,  ...)fmarkov(  A,  format = c("mat", "vec", "tab"),  dim = NULL,  all = FALSE,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  dbName = NULL,  ...)fgroebner(  A,  format = c("mat", "vec", "tab"),  dim = NULL,  all = FALSE,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  dbName = NULL,  ...)fhilbert(  A,  format = c("mat", "vec", "tab"),  dim = NULL,  all = FALSE,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  dbName = NULL,  ...)fgraver(  A,  format = c("mat", "vec", "tab"),  dim = NULL,  all = FALSE,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  dbName = NULL,  ...)

Arguments

Value

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

References

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

Examples

if (has_4ti2()) {# basic input and output for the 3x3 independence example(A <- rbind(  kprod(diag(3), ones(1,3)),  kprod(ones(1,3), diag(3))))markov(A, p = "arb")# you can get the output formatted in different ways:markov(A, p = "arb", all = TRUE)markov(A, p = "arb", "vec")markov(A, p = "arb", "tab", c(3, 3))tableau(markov(A, p = "arb"), dim = c(3, 3)) # tableau notation# you can add options by listing them off# to see the options available to you by function,# go to http://www.4ti2.demarkov(A, p = "arb")# the basis functions are automatically cached for future use.# (note that it doesn't persist across sessions.)A <- rbind(  kprod(  diag(4), ones(1,4), ones(1,4)),  kprod(ones(1,4),   diag(4), ones(1,4)),  kprod(ones(1,4), ones(1,4),   diag(4)))system.time(markov(A, p = "arb"))system.time(markov(A, p = "arb"))# the un-cashed versions begin with an "f"# (think: "forgetful" markov)system.time(fmarkov(A, p = "arb"))system.time(fmarkov(A, p = "arb"))# you can see the command line code by typing shell = TRUE# and the standard output wiht quiet = FALSE# we illustrate these with fmarkov because otherwise it's cached(A <- rbind(  kprod(diag(2), ones(1,4)),  kprod(ones(1,4), diag(2))))fmarkov(A, p = "arb", shell = TRUE)fmarkov(A, p = "arb", quiet = FALSE)# compare the bases for the 3x3x3 no-three-way interaction modelA <- rbind(  kprod(  diag(3),   diag(3), ones(1,3)),  kprod(  diag(3), ones(1,3),   diag(3)),  kprod(ones(1,3),   diag(3),   diag(3)))str(  zbasis(A, p = "arb")) #    8 elements = ncol(A) - qr(A)$rankstr(  markov(A, p = "arb")) #   81 elementsstr(groebner(A, p = "arb")) #  110 elementsstr(  graver(A))            #  795 elements# the other bases are also cachedA <- rbind(  kprod(  diag(3), ones(1,3), ones(1,2)),  kprod(ones(1,3),   diag(3), ones(1,2)),  kprod(ones(1,3), ones(1,3),   diag(2)))system.time( graver(A))system.time( graver(A))system.time(fgraver(A))system.time(fgraver(A))# LAS ex 1.2.1, p.12 : 2x3 independence(A <- rbind(  kprod(diag(2), ones(1,3)),  kprod(ones(1,2), diag(3))))markov(A, p = "arb", "tab", c(3, 3))# Prop 1.2.2 says that there should be2*choose(2, 2)*choose(3,2) # = 6# moves (up to +-1)markov(A, p = "arb", "tab", c(3, 3), TRUE)# LAS example 1.2.12, p.17  (no 3-way interaction)(A <- rbind(  kprod(  diag(2),   diag(2), ones(1,2)),  kprod(  diag(2), ones(1,2),   diag(2)),  kprod(ones(1,2),   diag(2),   diag(2))))plot_matrix(A)markov(A, p = "arb")groebner(A, p = "arb")graver(A)tableau(markov(A, p = "arb"), dim = c(2,2,2))# using the markov bases database, must be connected to internet# commented out for predictable and fast cran checks time# A <- markov(dbName = "ind3-3")# B <- markov(rbind(#   kprod(diag(3), ones(1,3)),#   kprod(ones(1,3), diag(3))# ), p = "arb")# all(A == B)# possible issues# markov(diag(1, 10))# zbasis(diag(1, 10), "vec")# groebner(diag(1, 10), "vec", all = TRUE)# graver(diag(1, 10), "vec", all = TRUE)# graver(diag(1, 4), "tab", all = TRUE, dim = c(2,2))}

Ones

Description

Make an array of ones

Usage

ones(...)

Arguments

Value

An integer array of ones

Examples

ones(5)ones(5, 1)ones(1, 5)ones(2, 3)ones(2, 3, 2)str(ones(5))

Set paths to LattE and 4ti2 executables

Description

These are helper functions that deal with pathing to external programs andasking if they are present. When latte is loaded it attempts to find LattEand 4ti2 executables by looking for environment variables specifying them,i.e. their paths as specified in your.Renviron file.

Usage

set_latte_path(path)set_4ti2_path(path)get_4ti2_path()get_latte_path()has_4ti2()has_latte()missing_4ti2_stop()missing_latte_stop()

Arguments

Details

For easiest use, you'll want to specify the paths of LattE and 4ti2executables in your⁠~/.Renviron⁠ file. They should look something like

⁠LATTE=/Applications/latte/bin⁠

⁠FOURTITWO=/Applications/latte/bin⁠

You can set these permanently withusethis::edit_r_environ().

You can change these for the current session using, e.g.,set_latte_path(),which accepts a character string or, if missing, usesfile.choose() to letyou interactively; you just select an arbitrary executable.

Value

A logical(1) or character(1) containing the path.

Author(s)

David Kahledavid@kahle.io

Examples

has_4ti2()if (has_4ti2()) get_4ti2_path()has_latte()if (has_4ti2()) get_latte_path()# you can set these paths permanently with the following. note that you'll # need to re-start the R session afterwards or simply pass the path into, # e.g., set_latte_path(). see below for more details on that.if (interactive()) edit_r_environ()# you can change these in your current session with set_latte_path() andif (had_latte <- has_latte()) old_latte_path <- get_latte_path()set_latte_path("/path/to/latte")get_latte_path()if (had_latte) set_latte_path(old_latte_path)get_latte_path()

Plot a matrix

Description

plot_matrix is a R variant of Matlab'sspy function.

Usage

plot_matrix(A)

Arguments

Value

a ggplot object

Author(s)

David Kahledavid@kahle.io

Examples

# the no-three-way interaction configuration(A <- kprod(ones(1,3), diag(3), ones(3)))plot_matrix(A)if (has_4ti2()) {plot_matrix(markov(A))(A <- genmodel(c(2L, 2L), list(1L, 2L)))plot_matrix(A)plot_matrix(markov(A))(A <- genmodel(c(5L, 5L), list(1L, 2L)))plot_matrix(A)plot_matrix(markov(A))}

Compute the primitive partition identities

Description

ppi runs 4ti2's ppi program to compute the primitive partition identities,that is, the Graver basis of 1:N.

Usage

ppi(N, dir = tempdir(), quiet = TRUE, shell = FALSE, ...)

Arguments

Value

A matrix containing the basis as its columns (for easy addition totables)

See Also

graver()

Examples

if (has_4ti2()) {ppi(3)t(ppi(3)) %*% 1:3plot_matrix(ppi(3))graver(t(1:3))plot_matrix(graver(t(1:3)))ppi(5, quiet = FALSE, shell = TRUE)}

Pretty printing of tableau output.

Description

Pretty printing of tableau output.

Usage

## S3 method for class 'tableau'print(x, ...)

Arguments

Value

Invisible string of the printed object.

Examples

# see ?tableau

Solve a linear system over the rationals

Description

qsolve runs 4ti2's qsolve program to compute theconfiguration matrix A corresponding to graphical statisticalmodels given by a simplicial complex and levels on the nodes.

Usage

qsolve(mat, rel, sign, dir = tempdir(), quiet = TRUE, shell = FALSE, ...)

Arguments

Value

The configuration matrix of the model provided

Examples

if (has_4ti2()) {# x + y > 0# x + y < 0mat <- rbind(  c( 1,  1),  c( 1,  1))rel <- c(">", "<")sign <- c(0, 0)qsolve(mat, rel, sign, p = "arb")qsolve(mat, rel, sign, p = "arb", quiet = FALSE)qsolve(mat, rel, sign, p = "arb", shell = TRUE)}

Objects exported from other packages

Description

These objects are imported from other packages. Follow the linksbelow to see their documentation.

usethis

edit_r_environ

Array to vector conversion

Description

Convert an array into a vector.

Usage

tab2vec(tab)

Arguments

Details

This function converts an array (or a multi-way contingency table) into avector, using a consistent ordering of the cells. The ordering of the cellsis lexicographical and cannot be specified by the user.

Value

a Named integer vector. The names correspond to the cell indices inthe table.

See Also

vec2tab()

Examples

a <- array(1:6, c(1,2,3))tab2vec(a)data(Titanic)tab2vec(Titanic)Titanic[1,1,1,1]Titanic[1,1,1,2]

Tableau Notation for Markov

Description

Print the tableau notation for a Markov move. See the referenceprovided, p. 13.

Usage

tableau(move, dim)

Arguments

Value

an object of class tableau

References

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

Examples

vec <- matrix(c(1, -1, -1, 1), nrow = 4)varlvls <- c(2, 2)tableau(vec, varlvls)

Vector to array conversion

Description

Convert a vector into an array given a set of dimensions; it therefore simplywrapsbase::aperm() andbase::array().

Usage

vec2tab(vec, dim)

Arguments

Details

This function converts an array (or a multi-way contingency table) into avector, using a consistent ordering of the cells. The ordering of the cellsis lexicographic and cannot be specified by the user.

Value

An array

See Also

tab2vec(),base::aperm(),base::array()

Examples

data(Titanic)str( Titanic )str( tab2vec(Titanic) )# convert it back into a table (names are removed)vec2tab(  tab2vec(Titanic),   dim(Titanic))# check that they are the sameall( vec2tab(tab2vec(Titanic), dim(Titanic)) == Titanic )

Solve a linear system over the integers

Description

zsolve runs 4ti2's zsolve program to compute the configuration matrix Acorresponding to graphical statistical models given by a simplicial complexand levels on the nodes.

Usage

zsolve(  mat,  rel,  rhs,  sign,  lat,  lb,  ub,  dir = tempdir(),  quiet = TRUE,  shell = FALSE,  ...)

Arguments

Value

The configuration matrix of the model provided

Examples

if (has_4ti2()) {mat <- rbind(  c( 1, -1),  c(-3,  1),  c( 1,  1))rel <- c("<", "<", ">")rhs <- c(2, 1, 1)sign <- c(0, 1)zsolve(mat, rel, rhs, sign)zsolve(mat, rel, rhs, sign, quiet = FALSE)zsolve(mat, rel, rhs, sign, shell = TRUE)zsolve(mat, rel, rhs, sign, p = "gmp", quiet = FALSE)}