gen_rand_hpoly

This function generates a \(d\)-dimensional polytope in H-representation with \(m\) facets. We pick \(m\) random hyperplanes tangent on the \(d\)-dimensional unit hypersphere as facets.

Provides an R interface for 'volesti' C++ package. 'volesti' computes estimations of volume
of polytopes given by (i) a set of points, (ii) linear inequalities or (iii) Minkowski sum of segments
(a.k.a. zonotopes). There are three algorithms for volume estimation as well as algorithms
for sampling, rounding and rotating polytopes. Moreover, 'volesti' provides algorithms for
estimating copulas useful in computational finance. Methods implemented in 'volesti' are described
in A. Chalkis and V. Fisikopoulos (2022) <doi:10.32614/RJ-2021-077> and references therein.

Vissarion Fisikopoulos

volesti

Volume Approximation and Sampling of Convex Polytopes

Apostolos Chalkis

gen_rand_hpoly function

<dl><dt>dimension</dt>
<dd>The dimension of the convex polytope.</dd>
<dt>nfacets</dt>
<dd>The number of the facets.</dd>
<dt>generator</dt>
<dd>A list that could contain two elements.<dl>
<dt>constants </dt>
<dd>To declare how to set the constants \(b_i\) for each facets: (i) 'sphere', each hyperplane is tangent to the hypersphere of radius 10, (ii) 'uniform' for each \(b_i\) the generator picks a uniform number from \((0,1)\). The defalut value is 'sphere'.</dd></dl></dd><dt>seed </dt>
<dd>Optional. A fixed seed for the number generator.</dd>
</dl>

Arguments

Generator function for random H-polytopes — gen_rand_hpoly

<dl>

<dt>dimension</dt>
<dd>The dimension of the convex polytope.</dd>


<dt>nfacets</dt>
<dd>The number of the facets.</dd>


<dt>generator</dt>
<dd>A list that could contain two elements.<dl>
<dt>constants </dt>
<dd>To declare how to set the constants \(b_i\) for each facets: (i) 'sphere', each hyperplane is tangent to the hypersphere of radius 10, (ii) 'uniform' for each \(b_i\) the generator picks a uniform number from \((0,1)\). The defalut value is 'sphere'.</dd>

<dt>seed </dt>
<dd>Optional. A fixed seed for the number generator.</dd>


</dl></dd>

</dl>

gen_rand_hpoly: Generator function for random H-polytopes

Description

Usage

Value

Arguments

Examples