createSeedPoint: Generate a seed point

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

Generate a seed point

Description

Generate a seed point inside a polytope given by a set of linear constraints.

Usage

createSeedPoint(constr, homogeneous=FALSE, randomize=FALSE, method="slacklp")

Arguments

constr	Constraint definition
homogeneous	Whether constr is given in homogeneous coordinate representation
randomize	If TRUE, randomize the starting point
method	How to obtain the starting point: "slacklp" for a linear program that maximizes the minimum slack, or "vertices" for a weighted average of the vertices of the polytope

Details

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

• The "slacklp" method solves a linear program that maximizes the minimum slack on the inequality constraints. When randomized, the slack on each constraint is randomly rescaled before maximization.

• The "vertices" method enumerates all vertices of the polytope and then calculates the weighted arithmetic mean of this set of points. If ‘randomize’ is set, the weights are randomly generated, otherwise they are all equal and the generated point is the centroid of the polytope.

Value

A coordinate vector in the appropriate coordinate system.

Author(s)

Gert van Valkenhoef

See Also

har

findExtremePoints findVertices

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)

x0 <- createSeedPoint(constr)
stopifnot(x0 >= 0)
stopifnot(sum(x0) <= 1)

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