latter

latter is an R package that makes back-end connections to LattE and 4ti2. Most of its functions were previously part of the algstat package, but have been pulled out and improved upon.

It is currently being developed.

Note: the following assumes you have LattE and 4ti2 installed and latter recognizes their path.

library(latter)
#> LattE found in /Applications/latte/dest/bin
#> 4ti2 found in /Applications/latte/dest/bin

Lattice point counting

Most LattE programs are available as functions in latter. For example, count() uses LattE's count to determine the number of integer points in a polytope:

count(c("x + y <= 10", "x >= 0", "y >= 0"))
#> [1] 66

It's easy to confirm the solution with a simple visualization:

library(ggplot2); theme_set(theme_bw())
polytope <- data.frame(x = c(0,10,0), y = c(0,0,10))
points   <- expand.grid(x = 0:10, y = 0:10)
points   <- subset(points, x + y <= 10)
points$number <- 1:nrow(points)
ggplot(aes(x = x, y = y), data = polytope) +
  geom_polygon(fill = "red", alpha = .2) + 
  geom_text(aes(y = y + .25, label = number), size = 3.5, data = points) +
  geom_point(data = points) + 
  coord_equal()

Integer programming

In addition to table counting, it can also do integer programming with LattE's latte-maximize and latte-minimize programs. To do this, it uses tools from mpoly:

latte_max("-2 x + 3 y", c("x + y <= 10", "x >= 0", "y >= 0"))
#> $par
#>  x  y 
#>  0 10 
#> 
#> $value
#> [1] 30
latte_min("-2 x + 3 y", c("x + y <= 10", "x >= 0", "y >= 0"))
#> $par
#>  x  y 
#> 10  0 
#> 
#> $value
#> [1] -20

We can check that the solution given above is correct, but the value is not. So, it needs some more work:

points$objective <- with(points, -2*x + 3*y)
ggplot(aes(x = x, y = y), data = polytope) +
  geom_polygon(fill = "red", alpha = .2) + 
  geom_point(aes(size = objective), data = points) + 
  coord_equal()

Installation

Installing latter

• From Github (dev version):

if (!("devtools" %in% installed.packages())) install.packages("devtools")
devtools::install_github("dkahle/mpoly")
devtools::install_github("dkahle/latter")

Installing supporting software

Coming soon! See the links above for direct information.