findExtremePoints: Find extreme points

In hitandrun: "Hit and Run" and "Shake and Bake" for Sampling Uniformly from Convex Shapes

Find extreme points

Description

Find extreme points of a polytope given by a set of linear constraints along each dimension.

Usage

findExtremePoints(constr, homogeneous=FALSE)

Arguments

constr	Constraint definition
homogeneous	Whether constr is given in homogeneous coordinate representation

Details

See har for a description of the constraint definition and the homogeneous coordinate representation.

For n-dimensional coordinate vectors, solves 2n LPs to find the extreme points along each dimension.

Value

A matrix, in which each row is a coordinate vector in the appropriate coordinate system.

Author(s)

Gert van Valkenhoef

See Also

har

findInteriorPoint findVertices

lpcdd

Examples

# constraints: x_1 >= 0, x_2 >= 0, x_1 + x_2 <= 1
A <- rbind(c(-1, 0), c(0, -1), c(1, 1))
b <- c(0, 0, 1)
d <- c("<=", "<=", "<=")
constr <- list(constr=A, rhs=b, dir=d)

findExtremePoints(constr, homogeneous=FALSE)

hitandrun documentation built on May 28, 2022, 1:09 a.m.