enumerate.vertices: Enumerate the vertices of a polytope.
In vertexenum: Vertex Enumeration of Polytopes

Description Usage Arguments Value Note Author(s) Examples

Returns a d by n + 1 dimensional matrix representing the d vertices of the polytope represented by Ax <= b.

1	enumerate.vertices(A, b, warn_if_open=FALSE)

`A`	An `m` by `n` matrix.
`b`	A `m` by `1` vector.
`warn_if_open`	Boolean.

A d by n + 1 dimensional matrix. The rows of this matrix represent the d vertices of the polytope represented by the system Ax <= b. If the optional argument warn_if_open is set to TRUE, then a warning will be printed if the system of inequalities is not closed, i.e. if it contains an extreme ray.

This is a port of the lrs library for vertex enumeration (http://cgm.cs.mcgill.ca/~avis/C/lrs.html). The source was written by David Avis.

Robert Robere robere@cs.toronto.edu

library(vertexenum)
## example vertex enumeration
## the system Ax <= b represents a unit square, with
## the lower left corner at the origin

A <- rbind(c(-1, 0), c(0, 1), c(1, 0), c(0, -1))
b <- c(0, 1, 1, 0)
## outputs a 4 x 2 matrix, each row corresponds to a vertex
enumerate.vertices(A, b)

## second example
## this is a unit square, with lower left corner at the origin, missing
## a facet on the right side
A <- rbind(c(-1, 0), c(0, 1), c(0, -1))
b <- c(0, 1, 0)

## outputs a 2 x 2 matrix, each row corresponds to a vertex
## will print a warning, since the input set described by Ax <= b
## is not closed
enumerate.vertices(A, b, warn_if_open=TRUE)

     [,1] [,2]
[1,]    1    0
[2,]    0    0
[3,]    1    1
[4,]    0    1
[1] "Input system contains an extreme ray."
     [,1] [,2]
[1,]    0    0
[2,]    0    1