user_guide:tutorials:latest:random

Differences

This shows you the differences between two versions of the page.


—user_guide:tutorials:latest:random [2023/11/06 10:57] (current) – created - external edit 127.0.0.1
Line 1: Line 1:
 +====== Random Constructions ======
 +
 +===== Random points on the unit sphere =====
 +
 +The easiest way to randomly construct a polytope is by sampling points on the unit sphere. The following chooses 100 points on the unit sphere in 3-space.
 +
 +<code perl>
 +> $p1=rand_sphere(3,100);
 +> print $p1->SIMPLICIAL;
 +true
 +</code>
 +===== Random points sampled from a normal distribution =====
 +
 +A second way to randomly construct a polytope is by sampling points by a standard normal distribution. The following chooses 100 points sampled from the standard normal distribution in 3-space.
 +
 +<code perl>
 +> $p2 = rand_normal(3, 100);
 +> print $p2 -> SIMPLICIAL, "\n", $p2 -> F_VECTOR;
 +true
 +24 66 44
 +</code>
 +With probability one such polytopes under either distribution are simplicial.
 +
 +===== Random polytopes with are neither simplicial nor simple =====
 +
 +<code perl>
 +> ($d,$m,$n) = (4,50,30);
 +> $p1=rand_sphere($d,$m);
 +> $p2=polarize($p1);
 +> $p3=new Polytope(POINTS=>rand_vert($p2->VERTICES,$n));
 +> print $p3->SIMPLICIAL, " ", $p3->SIMPLE, "\n", $p3->F_VECTOR;
 +false false
 +30 162 251 119
 +</code>