Volume Approximation and Sampling of Convex Polytopes

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Documentation for package ‘volesti’ version 1.1.2-7

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compute_indicators Compute an indicator for each time period that describes the state of a market.
copula Construct a copula using uniform sampling from the unit simplex
direct_sampling Sample perfect uniformly distributed points from well known convex bodies: (a) the unit simplex, (b) the canonical simplex, (c) the boundary of a hypersphere or (d) the interior of a hypersphere.
exact_vol Compute the exact volume of (a) a zonotope (b) an arbitrary simplex in V-representation or (c) if the volume is known and declared by the input object.
frustum_of_simplex Compute the percentage of the volume of the simplex that is contained in the intersection of a half-space and the simplex.
gen_cross Generator function for cross polytopes
gen_cube Generator function for hypercubes
gen_prod_simplex Generator function for product of simplices
gen_rand_hpoly Generator function for random H-polytopes
gen_rand_vpoly Generator function for random V-polytopes
gen_rand_zonotope Generator function for zonotopes
gen_simplex Generator function for simplices
gen_skinny_cube Generator function for skinny hypercubes
Hpolytope An R class to represent an H-polytope
Hpolytope-class An R class to represent an H-polytope
inner_ball Compute an inscribed ball of a convex polytope
read_sdpa_format_file Read a SDPA format file
rotate_polytope Apply a random rotation to a convex polytope (H-polytope, V-polytope, zonotope or intersection of two V-polytopes)
round_polytope Apply rounding to a convex polytope (H-polytope, V-polytope or a zonotope)
sample_points Sample uniformly or normally distributed points from a convex Polytope (H-polytope, V-polytope, zonotope or intersection of two V-polytopes).
Spectrahedron An R class to represent a Spectrahedron
Spectrahedron-class An R class to represent a Spectrahedron
volume The main function for volume approximation of a convex Polytope (H-polytope, V-polytope, zonotope or intersection of two V-polytopes)
Vpolytope An R class to represent a V-polytope
Vpolytope-class An R class to represent a V-polytope
VpolytopeIntersection An R class to represent the intersection of two V-polytopes
VpolytopeIntersection-class An R class to represent the intersection of two V-polytopes
write_sdpa_format_file Write a SDPA format file
Zonotope An R class to represent a Zonotope
Zonotope-class An R class to represent a Zonotope
zonotope_approximation A function to over-approximate a zonotope with PCA method and to evaluate the approximation by computing a ratio of fitness.