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Volume computation and sampling

About

The volesti package provides R with functions for volume estimation and sampling. In particular, it provides an R interface for the C++ library volesti.

volesti computes approximations of volume of polytopes given as a set of points or linear inequalities or as a Minkowski sum of segments (zonotopes). There are algorithms for volume approximation as well as algorithms for sampling, rounding and rotating polytopes. Last but not least, volesti provides implementations of geometric algorithms to compute the score of a portfolio given asset returns and to detect financial crises in stock markets.

Download and install

The latest stable version is available from CRAN.
The latest development version is available on Github www.github.com/GeomScale/volume_approximation
Install volesti by running:

install.packages("volesti")

The package-dependencies are: Rcpp, RcppEigen, BH.

Documentation

Credits

Copyright (c) 2012-2020 Vissarion Fisikopoulos
Copyright (c) 2018-2020 Apostolos Chalkis

You may redistribute or modify the software under the GNU Lesser General Public License as published by Free Software Foundation, either version 3 of the License, or (at your option) any later version. It is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY.

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Version

Install

install.packages('volesti')

Monthly Downloads

382

Version

1.1.1

License

LGPL-3

Maintainer

Vissarion Fisikopoulos

Last Published

June 22nd, 2020

Functions in volesti (1.1.1)

gen_prod_simplex

Generator function for product of simplices

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_rand_zonotope

Generator function for zonotopes

file_to_polytope

function to get an ine or an ext file and returns the corresponding polytope

Generator function for random V-polytopes

Generator function for cross polytopes

Generator function for hypercubes

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

Generator function for simplices

gen_skinny_cube

Generator function for skinny hypercubes

Internal rcpp function for the rounding of a convex polytope

compute_indicators

Compute an indicator for each time period that describes the state of a market.

Construct a copula using uniform sampling from the unit simplex

Compute an inscribed ball of a convex polytope

Sample uniformly or normally distributed points from a convex Polytope (H-polytope, V-polytope, zonotope or intersection of two V-polytopes).

loadSdpaFormatFile

Read a SDPA format file

Generator function for random H-polytopes

The main function for volume approximation of a convex Polytope (H-polytope, V-polytope, zonotope or intersection of two V-polytopes)

writeSdpaFormatFile

Write a SDPA format file

An internal Rccp function as a polytope generator

readSdpaFormatFile

Read a SDPA format file

An Rcpp class to represent zonotopes, exposed to R via modules.

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.

An internal Rccp function for the over-approximation of a zonotope

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.

zonotope_approximation

A function to over-approximate a zonotope with PCA method and to evaluate the approximation by computing a ratio of fitness.

rotate_polytope

Apply a random rotation to a convex polytope (H-polytope, V-polytope, zonotope or intersection of two V-polytopes)

An internal Rccp function for the random rotation of a convex polytope

Rcpp_VpolytopeIntersection

An Rcpp class to represent the intersection of two V-polytope, exposed to R via modules.

An R class to represent spectrahedra.

An Rcpp class to represent H-polytopes, exposed to R via modules.

An R class to represent H-polytopes.

VpolytopeIntersection

An R class to represent the intersection of two V-polytopes.

An R class to represent zonotopes.

Rcpp_Spectrahedron

An Rcpp class to represent spectrahedra, exposed to R via modules.

An R class to represent V-polytopes.

An Rcpp class to represent V-polytopes, exposed to R via modules.