Hello Tryer.
What you are trying to achieve seems to be what the ppl_lcdd demo program (which is distributed along with the PPL) does. Here is an excerpt from its man page:
NAME ppl_lcdd - a PPL-based program for vertex/facet enumeration of convex polyhedra
SYNOPSIS ppl_lcdd [OPTION]... [FILE]
DESCRIPTION Reads an H-representation (resp., a V-representation) of a polyhedron and generates a V-representation (resp., an H-representation) of the same polyhedron.
See the cddlib Reference Manual for information on the file formats.
Regarding your other question, the PPL can be compiled for Windows using MinGW. It can also be compiled for Linux and the resulting executable can be run also under WSL. I recommend you use the version of PPL available in the devel branch of the Git repository available at
git://git.bugseng.com/ppl/ppl.git
Kind regards,
Roberto
On 06/03/22 13:43, anoninus wrote:
Hello,
For a project I am working on with a collaborator, I have the extreme points and the rays of a polyhedron. I have to obtain the facetious representation of this polyhedron. That is, I want a simple V to H conversion.
I have been working with polymake so far. My working code is:
#include <polymake/Main.h> #include <polymake/Matrix.h> #include <polymake/SparseMatrix.h> #include <polymake/Rational.h> using namespace polymake; int main(int argc, const char* argv[]) { try { Main pm; pm.set_application("polytope"); BigObject p("Polytope<Rational>"); std::vectorstd::string CoordinateLabels = { "extravar", "x1", "x2", "x3", "x4", "x5", "x6"}; std::vector<std::vector<Int>> Points; std::vector<Int> point; point = { 1,0,1,1,0,0,1 }; Points.push_back(point); point = { 1,1,0,0,1,1,0 }; Points.push_back(point); point = { 1,0,0,1,1,0,1 }; Points.push_back(point); point = { 1,1,0,0,1,1,0 }; Points.push_back(point); point = { 1,0,1,1,0,0,1 }; Points.push_back(point); point = { 1,1,0,0,1,1,0 }; Points.push_back(point); point = { 1,0,1,1,0,0,1 }; Points.push_back(point); point = { 1,0,0,0,1,1,1 }; Points.push_back(point); point = { 0,1,0,0,0,0,0 }; Points.push_back(point); point = { 0,0,1,0,0,0,0 }; Points.push_back(point); point = { 0,0,0,1,0,0,0 }; Points.push_back(point); point = { 0,0,0,0,1,0,0 }; Points.push_back(point); point = { 0,0,0,0,0,1,0 }; Points.push_back(point); point = { 0,0,0,0,0,0,1 }; Points.push_back(point); p.take("VERTICES") << Points; const Matrix<Rational> f = p.give("FACETS"); cout << "facets" << endl << f << endl; cout << "Dimension of the facets matrix are " << f.rows() << " and " << f.cols() << endl; cout << "Printing the facets for easy reading" << endl; for (int i = 0; i < f.rows(); i++) { cout << " Facet " << i << ": "; Rational rhs = f(i, 0); for (int j = 1; j < f.cols(); j++) { Rational coef = f(i, j); if (coef.is_zero() == false) { cout << " + (" << coef << " " << CoordinateLabels[j] << ") "; } } cout << " >= - (" << rhs << ")" << endl; } const Matrix<Rational> affine_hull = p.give("AFFINE_HULL"); cout << "affine hull" << endl << affine_hull << endl; cout << "Dimension of the affine hull matrix are " << affine_hull.rows() << " and " << affine_hull.cols() << endl; cout << "Printing the affine hull for easy reading" << endl; for (int i = 0; i < affine_hull.rows(); i++) { printf("AffineHull %d: ", i); Rational rhs = affine_hull(i, 0); for (int j = 1; j < affine_hull.cols(); j++) { Rational coef = affine_hull(i, j); if (coef.is_zero() == false) { cout << " + (" << coef << " " << CoordinateLabels[j] << ") "; } } cout << " = - (" << rhs << ")" << endl; } } catch (const std::exception& ex) { std::cerr << "ERROR: " << ex.what() << endl; return 1; } return 0; }
The code can also be seen on godbolt at : https://godbolt.org/z/Ko7zq4z64 https://godbolt.org/z/Ko7zq4z64
The output of the above program is:
polymake: used package ppl The Parma Polyhedra Library ([[wiki:external_software#PPL]]): A C++ library for convex polyhedra and other numerical abstractions. http://www.cs.unipr.it/ppl/ http://www.cs.unipr.it/ppl/
facets -1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 -1 0 1 0 1 0 0 -1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 -1 1 0 0 0 0 1 0 0 0 0 0 0 1 -1 0 0 0 1 0 1 -1 0 0 0 0 1 1 1 0 0 0 0 0 0
Dimension of the facets matrix are 13 and 7 Printing the facets for easy reading Facet 0: + (1 x3) + (1 x5) >= - (-1) Facet 1: + (1 x3) >= - (0) Facet 2: + (1 x2) >= - (0) Facet 3: + (1 x2) + (1 x4) >= - (-1) Facet 4: + (1 x3) + (1 x4) >= - (-1) Facet 5: + (1 x4) >= - (0) Facet 6: + (1 x5) >= - (0) Facet 7: + (1 x1) >= - (0) Facet 8: + (1 x1) + (1 x6) >= - (-1) Facet 9: + (1 x6) >= - (0) Facet 10: + (1 x4) + (1 x6) >= - (-1) Facet 11: + (1 x5) + (1 x6) >= - (-1) Facet 12: >= - (1) affine hull
Dimension of the affine hull matrix are 0 and 7 Printing the affine hull for easy reading I have two queries:
(1) Is there a simple example that shows how the equivalent of the above functionality can be obtained in PPL via C/C+ code? I have looked at the PPL user manual, but I have to admit that it is quite forbidding in its size and details and it is not fully clear where in the document complete C/C++ examples are. I admit that this is possibly my lack of delving too deep into the manual.
I also notice that Polymake has solved this problem by calling PPL behind the scenes.
(2) Can the PPL code I write on Linux/WSL be used on a Windows Machine as well? I ask this because this is not a possibility in Polymake. Indeed, I was guided towards PPL as a result of my query on the Polymake forum. Polymake code cannot run on a Windows machine. I was wondering if PPL has this capability as suggested there. Please see that discussion at:
https://forum.polymake.org/viewtopic.php?f=8&p=3919 https://forum.polymake.org/viewtopic.php?f=8&p=3919
Thanks. Tryer
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