latte_count uses LattE's count function to count the (integer) lattice
points in a polytope and compute Ehrhart polynomials.
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, ...)
| spec | Specification, see details and examples |
|---|---|
| dir | Directory to place the files in, without an ending / |
| quiet | Show latte output? |
| mpoly | When opts = "--ehrhart-polynomial", return the mpoly version of it |
| ... | Additional arguments to pass to the function, see count --help at the command line to see examples. Note that dashes - should be specified with underscores _ |
The count. If the count is a number has less than 10 digits, an integer is returned. If the number has 10 or more digits, an integer in a character string is returned. You may want to use the gmp package's as.bigz to parse it.
The specification should be one of the following: (1) a character string or strings containing an inequality in the mpoly expression format (see examples), (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 a character vector is supplied, (1) and (4) are distinguished by the number of strings.
Behind the scenes, count works by writing a latte file and running count on it. 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 LattE code and then run count on it.
if (has_latte()) { spec <- c("x + y <= 10", "x >= 1", "y >= 1") latte_count(spec) # 45 latte_count(spec, quiet = FALSE) # 45 latte_count(spec, dilation = 10) # 3321 latte_count(spec, homog = TRUE) # 45 # by default, the output from LattE is in list.files(tempdir()) list.files(tempdir(), recursive = TRUE) # ehrhart polynomials latte_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 series latte_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 function latte_count(spec, multivariate_generating_function = TRUE) # by vertices spec <- list(c(1,1), c(10,1), c(1,10), c(10,10)) latte_count(spec) latte_count(spec, vrep = TRUE) code <- " 5 3 1 -1 0 1 0 -1 1 -1 -1 0 1 0 0 0 1 " latte_count(code) # for Ax <= b, see this example from the latte manual p.10 A <- 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)) }#> Ray Support Algorithm. #> The codimension is 3 #> #> Left = 1, Col = 3, Size = 3 Time: 0.00 #> Left = 1, Col = 3, Size = 3, Time: 0.00 #> 45#> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #> #>#> Time for reading and preprocessing: 0 sec #> Time for computing vertices and supporting cones: 0 sec #> Time for irrationalizing general cones: 0 sec #> Time for dualizing general cones: 0 sec #> Time for triangulating cones into simplicial cones: 0 sec #> Time for Barvinok decomposition and residue calculation: 0 sec #> Total time: 0 sec #> Total number of simplicial cones: 3 #> Total number of unimodular cones: 3 #> Maximum depth of the decomposition tree: 0 #>#>#> [1] 3