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    Metadata details:
    filename: vert2lcon.m
    path of file: ./repos/Swan/polytopes_2017_10_04_v1.9
    
    the code of the file until where you have to start completion: function [A,b,Aeq,beq]=vert2lcon(V,tol)
%An extension of Michael Kleder's vert2con function, used for finding the 
%linear constraints defining a polyhedron in R^n given its vertices. This 
%wrapper extends the capabilities of vert2con to also handle cases where the 
%polyhedron is not solid in R^n, i.e., where the polyhedron is defined by 
%both equality and inequality constraints.
% 
%SYNTAX:
%
%  [A,b,Aeq,beq]=vert2lcon(V,TOL)
%
%The rows of the N x n matrix V are a series of N vertices of a polyhedron
%in R^n. TOL is a rank-estimation tolerance (Default = 1e-10).
%
%Any point x inside the polyhedron will/must satisfy
%  
%   A*x  <= b
%   Aeq*x = beq
%
%up to machine precision issues.
%
%
%EXAMPLE: 
%
%Consider V=eye(3) corresponding to the 3D region defined 
%by x+y+z=1, x>=0, y>=0, z>=0.
%
% 
%   >>[A,b,Aeq,beq]=vert2lcon(eye(3))
%
%
%     A =
% 
%         0.4082   -0.8165    0.4082
%         0.4082    0.4082   -0.8165
%        -0.8165    0.4082    0.4082
% 
% 
%     b =
% 
%         0.4082
%         0.4082
%         0.4082
% 
% 
%     Aeq =
% 
%         0.5774    0.5774    0.5774
% 
% 
%     beq =
% 
%         0.5774


  %%initial stuff
  
    if nargin<2, tol=1e-10; end

    
    
function [A,b] = vert2con(V,tol)
% VERT2CON - convert a set of points to the set of inequality constraints
%            which most tightly contain the points; i.e., create
%            constraints to bound the convex hull of the given points
%
% [A,b] = vert2con(V)
%
% V = a set of points, each ROW of which is one point
% A,b = a set of constraints such that A*x <= b defines
%       the region of space enclosing the convex hull of
%       the given points
%
% For n dimensions:
% V = p x n matrix (p vertices, n dimensions)
% A = m x n matrix (m constraints, n dimensions)
% b = m x 1 vector (m constraints)
%
% NOTES: (1) In higher dimensions, duplicate constraints can
%            appear. This program detects duplicates at up to 6
%            digits of precision, then returns the unique constraints.
%        (2) See companion function CON2VERT.
%        (3) ver 1.0: initial version, June 2005.
%        (4) ver 1.1: enhanced redundancy checks, July 2005
%        (5) Written by Michael Kleder, 
%
%Modified by Matt Jacobson - March 29,2011
% 


k = convhulln(V);
c = mean(V(unique(k),:));


V = bsxfun(@minus,V,c);
A  = nan(size(k,1),size(V,2));

dim=size(V,2);
ee=ones(size(k,2),1);
rc=0;

for ix = 1:size(k,1)
    F = V(k(ix,:),:);
    if lindep(F,tol) == dim
        rc=rc+1;
        A(rc,:)=F\ee;
    end