"Hit and Run" and "Shake and Bake" for Sampling Uniformly from Convex Shapes
Bounding box rejection sampler
Calculate a bounding box
Generate a seed point
Create transformation matrices
Eliminate redundant linear constraints
Find extreme points
Find the closest face (constraint) to an interior point of a polytope.
Find an interior point
Find vertices of the polytope
Constraint formulation utility functions
"Hit and Run" sampler
"Hit and Run" sampling
"Hit and Run" sampler
Sample uniformly from an n-hypersphere
"Shake and Bake" sampler
"Shake and Bake" sampler
Create constraints that define the (n-1)-simplex
Transform points on an (n-1)-simplex to n-dimensional space
Sample uniformly from a simplex
Calculate the basis for the solution space of a system of linear equat...
Apply a transformation to a set of linear constraints.
The "Hit and Run" Markov Chain Monte Carlo method for sampling uniformly from convex shapes defined by linear constraints, and the "Shake and Bake" method for sampling from the boundary of such shapes. Includes specialized functions for sampling normalized weights with arbitrary linear constraints. Tervonen, T., van Valkenhoef, G., Basturk, N., and Postmus, D. (2012) <doi:10.1016/j.ejor.2012.08.026>. van Valkenhoef, G., Tervonen, T., and Postmus, D. (2014) <doi:10.1016/j.ejor.2014.06.036>.