volesti (version 1.0.0)

round_polytope: Apply rounding to a convex polytope (H-polytope, V-polytope or a zonotope)

Description

Given a convex H or V polytope or a zonotope as input this functionbrings the polytope in well rounded position based on minimum volume enclosing ellipsoid of a pointset.

Usage

round_polytope(P, WalkType = NULL, walk_step = NULL, radius = NULL)

Arguments

P

A convex polytope. It is an object from class (a) Hpolytope or (b) Vpolytope or (c) Zonotope.

WalkType

Optional. A string that declares the random walk method: a) 'CDHR' for Coordinate Directions Hit-and-Run, b) 'RDHR' for Random Directions Hit-and-Run or c) 'BW' for Ball Walk. The default walk is 'CDHR'.

walk_step

Optional. The number of the steps for the random walk. The default value is \(\lfloor 10 + d/10\rfloor\).

radius

Optional. The radius for the ball walk.

Value

A list with 2 elements: (a) a polytope of the same class as the input polytope class and (b) the element "round_value" which is the determinant of the square matrix of the linear transformation that was applied on the polytope that is given as input.

Examples

# NOT RUN {
# rotate a H-polytope (2d unit simplex)
A = matrix(c(-1,0,0,-1,1,1), ncol=2, nrow=3, byrow=TRUE)
b = c(0,0,1)
P = Hpolytope$new(A, b)
listHpoly = round_polytope(P)

# rotate a V-polytope (3d unit cube) using Random Directions HnR with step equal to 50
P = GenCube(3, 'V')
ListVpoly = round_polytope(P, WalkType = 'RDHR', walk_step = 50)

# round a 2-dimensional zonotope defined by 6 generators using ball walk
Z = GenZonotope(2,6)
ListZono = round_polytope(Z, WalkType = 'BW')
# }