# direct_sampling: Sample perfect uniformly distributed points from well known... In volesti: Volume Approximation and Sampling of Convex Polytopes

## Description

The d-dimensional unit simplex is the set of points \vec{x}\in \R^d, s.t.: ∑_i x_i≤q 1, x_i≥q 0. The d-dimensional canonical simplex is the set of points \vec{x}\in \R^d, s.t.: ∑_i x_i = 1, x_i≥q 0.

## Usage

 1 direct_sampling(body, n) 

## Arguments

 body A list to request exact uniform sampling from special well known convex bodies through the following input parameters: type A string that declares the type of the body for the exact sampling: a) 'unit_simplex' for the unit simplex, b) 'canonical_simplex' for the canonical simplex, c) 'hypersphere' for the boundary of a hypersphere centered at the origin, d) 'ball' for the interior of a hypersphere centered at the origin. dimension An integer that declares the dimension when exact sampling is enabled for a simplex or a hypersphere. radius The radius of the d-dimensional hypersphere. The default value is 1. seed A fixed seed for the number generator. n The number of points that the function is going to sample.

## Value

A d\times n matrix that contains, column-wise, the sampled points from the convex polytope P.

## References

R.Y. Rubinstein and B. Melamed, “Modern simulation and modeling” Wiley Series in Probability and Statistics, 1998.

A Smith, Noah and W Tromble, Roy, “Sampling Uniformly from the Unit Simplex,” Center for Language and Speech Processing Johns Hopkins University, 2004.

## Examples

 1 2 # 100 uniform points from the 2-d unit ball points = direct_sampling(n = 100, body = list("type" = "ball", "dimension" = 2)) 

volesti documentation built on July 14, 2021, 5:11 p.m.