hitandrun (version 0.5-6)

bbReject: Bounding box rejection sampler

Description

Generates uniform random variates over a convex polytope defined by a set of linear constraints by generating uniform variates over a bounding box and rejecting those outside the polytope.

Usage

bbReject(lb, ub, constr, N, homogeneous=FALSE, transform=NULL)

Arguments

lb

Lower bound for each dimension (not including homogeneous coordinate)

ub

Upper bound for each dimension (not including homogeneous coordinate)

constr

Constraint definition (see details)

N

Number of samples to generate

homogeneous

Whether constr and transform are given in homogeneous coordinate representation (see details)

transform

Transformation matrix to apply to the generated samples (optional)

Value

A list, containing:

samples

A matrix containing the generated samples as rows.

rejectionRate

The mean number of samples rejected for each accepted sample.

Details

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

See Also

createBoundBox

harConstraints simplex.createTransform simplex.createConstraints

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)

# create a bounding box that contains the polytope
lb <- c(0, 0)
ub <- c(1, 1)

# sample 10,000 points
samples <- bbReject(lb, ub, constr, 1E4)$samples

# Check dimension of result
stopifnot(dim(samples) == c(1E4, 2))

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

# Check that x_1 + x_2 <= 1
stopifnot(samples[,1] + samples[,2] <= 1)

# }
# NOT RUN {
plot(samples)
# }
# NOT RUN {
# }