hitandrun (version 0.5-6)

createSeedPoint: 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

Value

A coordinate vector in the appropriate coordinate system.

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.

See Also

har

findExtremePoints findVertices

Examples

# NOT RUN {
# 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)
# }