simplex.createConstraints: Create constraints that define the (n-1)-simplex

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

Create constraints that define the (n-1)-simplex

Description

This function takes a transformation matrix from the plane coincident with the (n-1) simplex and (optionally) additional constraints defined in n-dimensional space, and generates a set of constraints defining the simplex and (optionally) the additional constraints in the (n-1)-dimensional homogeneous coordinate system.

Usage

simplex.createConstraints(transform, userConstr=NULL)

Arguments

transform	Transformation matrix
userConstr	Additional constraints

Details

The transformation of the constraint matrix to (n-1)-dimensional homogeneous coordinates is a necessary preprocessing step for applying "Hit and Run" to subsets of the simplex defined by userConstr.

Value

A set of constraints in the (n-1)-dimensional homogeneous coordinate system.

Author(s)

Gert van Valkenhoef

See Also

simplex.createTransform har harConstraints

Examples

n <- 3
userConstr <- mergeConstraints(
	ordinalConstraint(3, 1, 2), ordinalConstraint(3, 2, 3))

transform <- simplex.createTransform(n)
constr <- simplex.createConstraints(transform, userConstr)
seedPoint <- createSeedPoint(constr, homogeneous=TRUE)

N <- 10000
samples <- har(seedPoint, constr, N, 1, homogeneous=TRUE, transform=transform)$samples

# Check dimension
stopifnot(dim(samples) == c(N, n))

# Check that w_i >= w_i+1
stopifnot(sapply(1:(n-1), function(i) {
	all(samples[,i]>=samples[,i+1])
}))

# Check that w_i >= 0
stopifnot(samples >= 0)

# Check that sum_i w_i = 1
E <- 1E-12
stopifnot(apply(samples, 1, sum) > 1 - E)
stopifnot(apply(samples, 1, sum) < 1 + E)

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