stephane-caron/pypoman

Python module for polyhedral geometry

Polyhedron manipulation in Python

This library allows common operations over convex polyhedra such as polytope projection and vertex enumeration. Check out the API documentation for details.

Installation

Install system packages for Python and GLPK, for instance for Debian-based Linux distributions:

$ sudo apt-get install cython libglpk-dev python python-dev python-pip

Then, install the library by:

$ pip install pypoman

Some functions, such as point-polytope projection and polygon intersection, are optional and not installed by default. To enable all of them, run:

$ pip install pypoman[all]

Examples

Vertex enumeration

We can compute the list of vertices of a polytope described in halfspace representation by $A x \leq b$:

import numpy as np
from pypoman import compute_polytope_vertices

A = np.array([
    [-1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
    [0, -1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],
    [0,  0, -1,  0,  0,  0,  0,  0,  0,  0,  0,  0],
    [0,  0,  0, -1,  0,  0,  0,  0,  0,  0,  0,  0],
    [0,  0,  0,  0, -1,  0,  0,  0,  0,  0,  0,  0],
    [0,  0,  0,  0,  0, -1,  0,  0,  0,  0,  0,  0],
    [0,  0,  0,  0,  0,  0, -1,  0,  0,  0,  0,  0],
    [0,  0,  0,  0,  0,  0,  0, -1,  0,  0,  0,  0],
    [0,  0,  0,  0,  0,  0,  0,  0, -1,  0,  0,  0],
    [0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  0,  0],
    [0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  0],
    [0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1],
    [1,  1,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0],
    [0,  0,  0,  1,  1,  1,  0,  0,  0,  0,  0,  0],
    [0,  0,  0,  0,  0,  0,  1,  1,  1,  0,  0,  0],
    [0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  1],
    [1,  0,  0,  1,  0,  0,  1,  0,  0,  1,  0,  0],
    [0,  1,  0,  0,  1,  0,  0,  1,  0,  0,  1,  0],
    [0,  0,  1,  0,  0,  1,  0,  0,  1,  0,  0,  1]])
b = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 2, 3])

vertices = compute_polytope_vertices(A, b)

Halfspace enumeration

The other way round, assume we know the vertices of a polytope, and want to get its halfspace representation $A x \leq b$.

import numpy as np
from pypoman import compute_polytope_halfspaces

vertices = map(
    np.array,
    [[1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [0, 1, 1]],
)

A, b = compute_polytope_halfspaces(vertices)

Polytope projection

Let us project an $n$-dimensional polytope $A x \leq b$ over $x = [x_1\ \ldots\ x_n]$ onto its first two coordinates $proj(x) = [x_1 x_2]$:

from numpy import array, eye, ones, vstack, zeros
from pypoman import plot_polygon, project_polytope

n = 10  # dimension of the original polytope
p = 2   # dimension of the projected polytope

# Original polytope:
# - inequality constraints: \forall i, |x_i| <= 1
# - equality constraint: sum_i x_i = 0
A = vstack([+eye(n), -eye(n)])
b = ones(2 * n)
C = ones(n).reshape((1, n))
d = array([0])
ineq = (A, b)  # A * x <= b
eq = (C, d)    # C * x == d

# Projection is proj(x) = [x_0 x_1]
E = zeros((p, n))
E[0, 0] = 1.
E[1, 1] = 1.
f = zeros(p)
proj = (E, f)  # proj(x) = E * x + f

vertices = project_polytope(proj, ineq, eq, method='bretl')

We can then plot the projected polytope:

import pylab

pylab.ion()
pylab.figure()
plot_polygon(vertices)

See also

• A short introduction to Polyhedra and polytopes
• Komei Fukuda's Frequently Asked Questions in Polyhedral Computation
• The Polyhedron class in Sage
• StabiliPy: a Python package implementing a more general recursive method for polytope projection

pypoman's Issues

Pypoman with integer variables

Hello!

Really nice to find this amazing tool! but Im new at MIP and I want to know if Does this library supports integer variables? and if it does how can i compute then?

Greetings for this amazing job!
Stay safe!

pypi package doesn't include project_point_to_polytope

If I install 0.5.4 from pypi, the resulting package does not include project_point_to_polytope. If I build from source, also version 0.5.4, the resulting package does have it.

That function was committed in Oct. 2021 and at that time, setup.py's version was at 0.5.4.

Would it be possible to release a new version with that function?

Possible to include support for projection of point to onto polytope?

pypoman has the ability to do polytope projection onto a lower dimensional space, however is there a means of projecting a point onto a given polytope? This is sometimes called the minimum norm point in a polytope problem.

@stephane-caron I was wondering if this feature would be in the scope of the package and, also, whether you had any intuition/advice on how one might accomplish this? I know that one can reformulate as a convex QP, e.g.

import numpy as np
from qpsolvers import solve_qp
from pypoman import compute_polytope_halfspaces

## The point to project 
x0 = np.array([0.5, 5.2])

## The polygon 
P = np.array([[0, 0], [3,0], [4,5], [2,6], [0,4]])

## Reduction to QP
q = -np.reshape(x0, (2,1)) 
A, b = compute_polytope_halfspaces(P)
y = solve_qp(P=np.eye(2), q=q, G=A, h=b.reshape((len(b), 1)), verbose=True, solver="cvxopt")
print("QP solution: y = {}".format(y))

import matplotlib.pyplot as plt 
plt.gca().set_aspect('equal')
plt.plot(*(np.vstack([x, x[0,:]])).T)
plt.scatter(*x0, c = 'red')
plt.scatter(*y, c = 'green')
plt.arrow(*x0.T, *(y-x0).T, width=0.025)

But this requires converting the convex hull to the H-form of the polytope and apparently there exist methods (Philip Wolfe's algorithm, possibly a subcomputation of the GJK algorithm, etc.) to do this using only the V-form, though I've been unable to find a nice implementation

Installation of pycddlib dependency on MacOS

I tried to install pypoman on MacOS v11.6 within a virtual environment with Python version 3.8.9. I started by installing cython and gplk using:

brew install cython
brew install gplk

and then installed scipy with pip install scipy. However, pip install pypoman gives the following error

$ pip install pypoman
Collecting pypoman
  Using cached pypoman-0.5.4-py3-none-any.whl
Collecting pycddlib
  Using cached pycddlib-2.1.4.tar.gz (265 kB)
  Preparing metadata (setup.py) ... done
Collecting cvxopt
  Using cached cvxopt-1.2.7-cp38-cp38-macosx_10_9_x86_64.whl (3.1 MB)
Building wheels for collected packages: pycddlib
  Building wheel for pycddlib (setup.py) ... error
  ERROR: Command errored out with exit status 1:
   command: /Users/3054363/PycharmProjects/setz/venv/bin/python -u -c 'import io, os, sys, setuptools, tokenize; sys.argv[0] = '"'"'/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py'"'"'; __file__='"'"'/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py'"'"';f = getattr(tokenize, '"'"'open'"'"', open)(__file__) if os.path.exists(__file__) else io.StringIO('"'"'from setuptools import setup; setup()'"'"');code = f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' bdist_wheel -d /private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-wheel-6ht_j0yq
       cwd: /private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/
  Complete output (29 lines):
  /Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/__init__.py:148: SetuptoolsDeprecationWarning: setup_requires is deprecated. Supply build dependencies using PEP 517 pyproject.toml build-requires.
    warnings.warn(
  Traceback (most recent call last):
    File "<string>", line 1, in <module>
    File "/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py", line 107, in <module>
      setup(
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/__init__.py", line 158, in setup
      _install_setup_requires(attrs)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/__init__.py", line 153, in _install_setup_requires
      dist.fetch_build_eggs(dist.setup_requires)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/dist.py", line 806, in fetch_build_eggs
      resolved_dists = pkg_resources.working_set.resolve(
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/pkg_resources/__init__.py", line 766, in resolve
      dist = best[req.key] = env.best_match(
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/pkg_resources/__init__.py", line 1051, in best_match
      return self.obtain(req, installer)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/pkg_resources/__init__.py", line 1063, in obtain
      return installer(requirement)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/dist.py", line 877, in fetch_build_egg
      return fetch_build_egg(self, req)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/installer.py", line 80, in fetch_build_egg
      wheel.install_as_egg(dist_location)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/wheel.py", line 95, in install_as_egg
      self._install_as_egg(destination_eggdir, zf)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/wheel.py", line 103, in _install_as_egg
      self._convert_metadata(zf, destination_eggdir, dist_info, egg_info)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/wheel.py", line 124, in _convert_metadata
      os.mkdir(destination_eggdir)
  FileExistsError: [Errno 17] File exists: '/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/.eggs/Cython-0.29.24-py3.8-macosx-10.14-x86_64.egg'
  ----------------------------------------
  ERROR: Failed building wheel for pycddlib
  Running setup.py clean for pycddlib
  ERROR: Command errored out with exit status 1:
   command: /Users/3054363/PycharmProjects/setz/venv/bin/python -u -c 'import io, os, sys, setuptools, tokenize; sys.argv[0] = '"'"'/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py'"'"'; __file__='"'"'/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py'"'"';f = getattr(tokenize, '"'"'open'"'"', open)(__file__) if os.path.exists(__file__) else io.StringIO('"'"'from setuptools import setup; setup()'"'"');code = f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' clean --all
       cwd: /private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32
  Complete output (29 lines):
  /Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/__init__.py:148: SetuptoolsDeprecationWarning: setup_requires is deprecated. Supply build dependencies using PEP 517 pyproject.toml build-requires.
    warnings.warn(
  Traceback (most recent call last):
    File "<string>", line 1, in <module>
    File "/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py", line 107, in <module>
      setup(
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/__init__.py", line 158, in setup
      _install_setup_requires(attrs)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/__init__.py", line 153, in _install_setup_requires
      dist.fetch_build_eggs(dist.setup_requires)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/dist.py", line 806, in fetch_build_eggs
      resolved_dists = pkg_resources.working_set.resolve(
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/pkg_resources/__init__.py", line 766, in resolve
      dist = best[req.key] = env.best_match(
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/pkg_resources/__init__.py", line 1051, in best_match
      return self.obtain(req, installer)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/pkg_resources/__init__.py", line 1063, in obtain
      return installer(requirement)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/dist.py", line 877, in fetch_build_egg
      return fetch_build_egg(self, req)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/installer.py", line 80, in fetch_build_egg
      wheel.install_as_egg(dist_location)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/wheel.py", line 95, in install_as_egg
      self._install_as_egg(destination_eggdir, zf)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/wheel.py", line 103, in _install_as_egg
      self._convert_metadata(zf, destination_eggdir, dist_info, egg_info)
    File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/wheel.py", line 124, in _convert_metadata
      os.mkdir(destination_eggdir)
  FileExistsError: [Errno 17] File exists: '/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/.eggs/Cython-0.29.24-py3.8-macosx-10.14-x86_64.egg'
  ----------------------------------------
  ERROR: Failed cleaning build dir for pycddlib
Failed to build pycddlib
Installing collected packages: pycddlib, cvxopt, pypoman
    Running setup.py install for pycddlib ... error
    ERROR: Command errored out with exit status 1:
     command: /Users/3054363/PycharmProjects/setz/venv/bin/python -u -c 'import io, os, sys, setuptools, tokenize; sys.argv[0] = '"'"'/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py'"'"'; __file__='"'"'/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py'"'"';f = getattr(tokenize, '"'"'open'"'"', open)(__file__) if os.path.exists(__file__) else io.StringIO('"'"'from setuptools import setup; setup()'"'"');code = f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' install --record /private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-record-0zuwcfj8/install-record.txt --single-version-externally-managed --compile --install-headers /Users/3054363/PycharmProjects/setz/venv/include/site/python3.8/pycddlib
         cwd: /private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/
    Complete output (29 lines):
    /Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/__init__.py:148: SetuptoolsDeprecationWarning: setup_requires is deprecated. Supply build dependencies using PEP 517 pyproject.toml build-requires.
      warnings.warn(
    Traceback (most recent call last):
      File "<string>", line 1, in <module>
      File "/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py", line 107, in <module>
        setup(
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/__init__.py", line 158, in setup
        _install_setup_requires(attrs)
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/__init__.py", line 153, in _install_setup_requires
        dist.fetch_build_eggs(dist.setup_requires)
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/dist.py", line 806, in fetch_build_eggs
        resolved_dists = pkg_resources.working_set.resolve(
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/pkg_resources/__init__.py", line 766, in resolve
        dist = best[req.key] = env.best_match(
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/pkg_resources/__init__.py", line 1051, in best_match
        return self.obtain(req, installer)
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/pkg_resources/__init__.py", line 1063, in obtain
        return installer(requirement)
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/dist.py", line 877, in fetch_build_egg
        return fetch_build_egg(self, req)
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/installer.py", line 80, in fetch_build_egg
        wheel.install_as_egg(dist_location)
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/wheel.py", line 95, in install_as_egg
        self._install_as_egg(destination_eggdir, zf)
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/wheel.py", line 103, in _install_as_egg
        self._convert_metadata(zf, destination_eggdir, dist_info, egg_info)
      File "/Users/3054363/PycharmProjects/setz/venv/lib/python3.8/site-packages/setuptools/wheel.py", line 124, in _convert_metadata
        os.mkdir(destination_eggdir)
    FileExistsError: [Errno 17] File exists: '/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/.eggs/Cython-0.29.24-py3.8-macosx-10.14-x86_64.egg'
    ----------------------------------------
ERROR: Command errored out with exit status 1: /Users/3054363/PycharmProjects/setz/venv/bin/python -u -c 'import io, os, sys, setuptools, tokenize; sys.argv[0] = '"'"'/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py'"'"'; __file__='"'"'/private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-install-wf69f8bg/pycddlib_ee6ee3ac177c42c487f886b285492f32/setup.py'"'"';f = getattr(tokenize, '"'"'open'"'"', open)(__file__) if os.path.exists(__file__) else io.StringIO('"'"'from setuptools import setup; setup()'"'"');code = f.read().replace('"'"'\r\n'"'"', '"'"'\n'"'"');f.close();exec(compile(code, __file__, '"'"'exec'"'"'))' install --record /private/var/folders/xf/r_jhy8wd01s9nr6zqnzh6f1xnv1_63/T/pip-record-0zuwcfj8/install-record.txt --single-version-externally-managed --compile --install-headers /Users/3054363/PycharmProjects/setz/venv/include/site/python3.8/pycddlib Check the logs for full command output.

Error in `python': double free or corruption

I am trying to run the polytope projection example:

import numpy as np
import pylab
import pypoman

n = 10  # dimension of the original polytope
p = 2   # dimension of the projected polytope

# Original polytope:
# - inequality constraints: \forall i, |x_i| <= 1
# - equality constraint: sum_i x_i = 0
A = np.vstack([+np.eye(n), -np.eye(n)])
b = np.ones(2 * n)
C = np.ones(n).reshape((1, n))
d = np.array([0])
ineq = (A, b)  # A * x <= b
eq = (C, d)    # C * x == d

# Projection is proj(x) = [x_0 x_1]
E = np.zeros((p, n))
E[0, 0] = 1.
E[1, 1] = 1.
f = np.zeros(p)
proj = (E, f)  # proj(x) = E * x + f

vertices = pypoman.project_polytope(proj, ineq, eq, method='bretl')

if __name__ == "__main__":   # plot projected polytope
    pylab.ion()
    pylab.figure()
    pypoman.plot_polygon(vertices)
    print('Done!')

However, I am greeted with this error message:

*** Error in `python': double free or corruption (!prev): 0x0000000002380660 ***
======= Backtrace: =========
/lib/x86_64-linux-gnu/libc.so.6(+0x777e5)[0x7f07e26b67e5]
/lib/x86_64-linux-gnu/libc.so.6(+0x8037a)[0x7f07e26bf37a]
/lib/x86_64-linux-gnu/libc.so.6(cfree+0x4c)[0x7f07e26c353c]
python[0x4a9675]
python(PyEval_EvalFrameEx+0x67a8)[0x4c25d8]
python(PyEval_EvalCodeEx+0x306)[0x4b9ab6]
python(PyEval_EvalFrameEx+0x58b7)[0x4c16e7]
python(PyEval_EvalCodeEx+0x306)[0x4b9ab6]
python(PyEval_EvalFrameEx+0x58b7)[0x4c16e7]
python(PyEval_EvalCodeEx+0x306)[0x4b9ab6]
python(PyEval_EvalFrameEx+0x58b7)[0x4c16e7]
python(PyEval_EvalCodeEx+0x306)[0x4b9ab6]
python(PyEval_EvalFrameEx+0x58b7)[0x4c16e7]
python(PyEval_EvalCodeEx+0x306)[0x4b9ab6]
python(PyEval_EvalFrameEx+0x58b7)[0x4c16e7]
python(PyEval_EvalCodeEx+0x306)[0x4b9ab6]
python(PyEval_EvalFrameEx+0x58b7)[0x4c16e7]
python(PyEval_EvalCodeEx+0x306)[0x4b9ab6]
python[0x4eb30f]
python(PyRun_FileExFlags+0x82)[0x4e5422]
python(PyRun_SimpleFileExFlags+0x186)[0x4e3cd6]
python(Py_Main+0x612)[0x493ae2]
/lib/x86_64-linux-gnu/libc.so.6(__libc_start_main+0xf0)[0x7f07e265f830]
python(_start+0x29)[0x4933e9]
======= Memory map: ========
00400000-006de000 r-xp 00000000 08:03 5244123                            /usr/bin/python2.7
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01cd2000-02df7000 rw-p 00000000 00:00 0                                  [heap]
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7f07c0586000-7f07c05b5000 r-xp 00000000 08:03 4485697                    /home/henrique/.local/lib/python2.7/site-packages/cvxopt/base.so
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7f07e2c51000-7f07e2d51000 rw-p 00000000 00:00 0 
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7f07e2e09000-7f07e2e0a000 rw-p 00000000 00:00 0 
7f07e2e0a000-7f07e2e0b000 rwxp 00000000 00:00 0 
7f07e2e0b000-7f07e2e4b000 rw-p 00000000 00:00 0 
7f07e2e4b000-7f07e2e4c000 r--p 00025000 08:03 7213513                    /lib/x86_64-linux-gnu/ld-2.23.so
7f07e2e4c000-7f07e2e4d000 rw-p 00026000 08:03 7213513                    /lib/x86_64-linux-gnu/ld-2.23.so
7f07e2e4d000-7f07e2e4e000 rw-p 00000000 00:00 0 
7ffefc26e000-7ffefc293000 rw-p 00000000 00:00 0                          [stack]
7ffefc3d4000-7ffefc3d7000 r--p 00000000 00:00 0                          [vvar]
7ffefc3d7000-7ffefc3d9000 r-xp 00000000 00:00 0                          [vdso]
ffffffffff600000-ffffffffff601000 r-xp 00000000 00:00 0                  [vsyscall]
[1]    17376 abort (core dumped)  python example_polytope_projection.py

Is this a known issue? I can run the vertex enumeration example just fine.

Also, it might help to know that I can run all the pymanoid examples, i.e., inverse_kinematics.py, posture_generation.py, and wrench_cone.py, except the multi_contact_walking.py.
When I try to run multi_contact_walking.py I get the same Error in `python': double free or corruption message.

P.s. I am on Ubuntu 16.04.

compute_polytope_vertices does not work for large matrices

Problem:

Using the exact same code as in the documentation, but using :
A: 114x14 matrix,
b: a 114x1 matrix,
the function compute_polytope_vertices(A,b) returns an empty array, like if it does not find any vertice of the polytope.
Yet, the two matrices used come from a real problem in which I am pretty sure A and b define a not-empty polytope.

Reproduce the problem:

A = np.array(
                [
                    [-2751, -2434, -2753, 3633, 1745, 273, 1941, -2848, -73, 1805, 1496, 1615, -2906, -2793],
                    [-2159, -2029, -2137, 3219, 1239, 81, 1488, -2141, -51, 1349, 1110, 1090, -2184, -2149],
                    [-976, -953, -963, -1641, 823, -1025, 3697, -956, -4, 2119, 735, -98, -967, -963],
                    [1079, 1075, 1074, 2226, -703, 1085, -3991, 1060, 5, -2225, -793, 372, 1073, 1073],
                    [-1079, -1075, -1074, -2226, 703, -1085, 3991, -1060, -5, 2225, 793, -372, -1073, -1073],
                    [1033, 1039, 1032, 2317, -580, 1017, -3778, 1017, 5, -2077, -752, 476, 1029, 1031],
                    [-1033, -1039, -1032, -2317, 580, -1017, 3778, -1017, -5, 2077, 752, -476, -1029, -1031],
                    [344, -217, 59, 4074, -5481, 476, -1039, 152, -1, -2287, -271, -8685, 169, 92],
                    [4830, 4446, 4714, -6473, -3006, -38, -3406, 4727, 119, -3150, -2589, -2743, 4818, 4742],
                    [-2645, -2889, -2681, -8515, 2621, -118, 1884, -2530, -47, 2029, 1147, 2962, -2581, -2652],
                    [2576, 2362, 2282, -5413, -1505, -103, -1288, 2163, 41, -1297, -882, -1595, 2225, 2266],
                    [430, 1586, 1676, -3653, -995, -126, -855, 1624, 29, -860, -597, -1054, 1704, 1683],
                    [865, -6537, -3019, 1819, -2655, 469, -728, -1735, 1, -1186, -275, -3653, -1512, -2592],
                    [-6085, -5890, -5983, -5640, 4596, -6947, 11761, -5951, -59, 9474, 7106, -213, -6020, -5991],
                    [974, 5915, 5032, -9482, -1643, -438, -1870, 4493, 69, -1747, -1373, -1492, 4616, 4912],
                    [1167, 6992, 5698, -9742, -1505, -511, -1879, 4962, 72, -1719, -1402, -1277, 5070, 5522],
                    [-1684, -1209, -1384, 7054, 2227, -166, 1289, -1393, -27, 1498, 737, 2689, -1441, -1400],
                    [-2222, -2748, -2457, -7019, -5186, -88, -4046, -2289, -103, -4070, -984, -5616, -2333, -2419],
                    [-869, 18201, -17551, 1705, 2053, 275, 1149, -10410, -39, 1335, 764, 2510, -5258, -9010],
                    [405, -6065, 12248, -827, -910, -158, -530, 4897, 19, -607, -360, -1102, 3050, 16631],
                    [224, -2666, 16105, -464, -485, -98, -290, 3932, 11, -328, -199, -584, 1659, 26096],
                    [-272, 4655, 12242, 559, 638, 96, 364, -559, -12, 420, 244, 776, -2375, -37504],
                    [373, -6784, -26190, -768, -891, -126, -505, -613, 17, -584, -337, -1087, 3401, -49448],
                    [570, -10076, -26656, -1175, -1351, -198, -768, 133, 25, -886, -514, -1645, 5122, -46987],

                    [-373, 6784, 26190, 768, 891, 126, 505, 613, -17, 584, 337, 1087, -3401, 49448],
                    [-473, 7946, 22635, 976, 1109, 170, 634, -1012, -22, 731, 426, 1348, -4167, 46460],
                    [-570, 10076, 26656, 1175, 1351, 198, 768, -133, -25, 886, 514, 1645, -5122, 46987],
                    [597, -9991, -18189, -1169, -1330, -223, -766, 17224, 27, -881, -519, -1614, 2299, -9249],
                    [-597, 9991, 18189, 1169, 1330, 223, 766, -17224, -27, 881, 519, 1614, -2299, 9249],
                    [478, -8222, -22763, -986, -1126, -169, -642, 675, 22, -741, -430, -1370, 0, 0],
                    [-478, 8222, 22763, 986, 1126, 169, 642, -675, -22, 741, 430, 1370, 0, 0],
                    [1653, 1846, 1735, 2696, 3484, 1661, 4226, 1672, 178, 4090, 6117, 3152, 1688, 1721],
                    [-6457, -7622, -6959, -12885, -17407, -5738, -21606, -6593, -990, -20704, -27702, -15512, -6683,
                     -6876],
                    [-4257, -5789, -4955, -17703, -11726, 10530, -8394, -4466, -167, -8638, -1404, -13078, -4597,
                     -4847],
                    [588, 470, 533, 179, -922, 1222, -1790, 560, -10, -1545, -4882, -534, 560, 541],
                    [-588, -470, -533, -179, 922, -1222, 1790, -560, 10, 1545, 4882, 534, -560, -541],
                    [-8913, -9574, -9467, -4749, -2558, 6891, -676, -9138, -163, -1081, 532, -3496, -9441, -9447],
                    [-9766, -10166, -10181, -4218, -1967, 9356, 75, -9926, -212, -396, 1287, -2993, -10207, -10176],
                    [-3914, -5870, -4994, -6461, -3861, 4834, -2554, -4283, -13, -2756, -1388, -4490, -4595, -4870],
                    [-3576, -9529, -6370, -4420, -3904, 94, -2186, -4068, 55, -2537, -1370, -4768, -4554, -5886],
                    [-2196, -9555, -7950, -2930, -2877, -118, -1604, -5076, 46, -1866, -1028, -3518, -6995, -7643],
                    [-573, -1818, 4836, -3332, -3025, -628, -1871, 6422, 69, -2094, -1297, -3604, 8263, 5719],
                    [-1201, -12437, -7255, -3219, -3395, -358, -1922, -925, 62, -2223, -1266, -4138, -835, -6032],
                    [-788, 2180, 4443, 215, 262, 2, 137, 10125, -4, 163, 85, 325, 1075, 4476],
                    [-92, 12983, 10039, 1303, 1654, 94, 875, 1627, -25, 1039, 557, 2048, -3009, 8437],
                    [14, 9036, 10430, 298, 531, -35, 245, 3243, -5, 308, 141, 677, -96, 9589],
                    [-181, 13821, 7727, 1450, 1825, 120, 974, 626, -29, 1153, 623, 2258, -3522, 5839],
                    [262, 9037, 23315, 256, 560, -135, 222, 18682, -1, 299, 106, 733, -16142, 24758],
                    [227, 8938, 23894, 297, 591, -119, 245, 17575, -3, 323, 124, 768, -15654, 29876],
                    [432, -2658, -47, -4573, -3411, 233, -1807, 838, 42, -2146, -1078, -4220, 1079, 269],

                    [-683, -2290, 4313, -2972, -2877, -554, -1735, 5943, 63, -1960, -1192, -3451, 7747, 5196],
                    [-575, 13860, 23596, 1870, 2106, 234, 1182, 13994, -38, 1371, 779, 2573, 48845, 26067],
                    [9030, 5959, 7296, -3859, -4443, -17143, -6047, 8207, 638, -5499, -6617, -3599, 7860, 7473],
                    [9030, 5960, 7296, -3860, -4443, -17144, -6047, 8208, 638, -5499, -6617, -3599, 7861, 7474],
                    [-7094, -11508, -13483, -3590, -3259, -87, -1914, -14290, 51, -2180, -1236, -3934, -14657, -13775],
                    [869, -18201, 17551, -1705, -2053, -275, -1149, 10410, 39, -1335, -764, -2510, 5258, 9010],
                    [680, 918, 787, 582, -3044, 246, -796, 726, 6, -2954, -304, 2206, 732, 771],
                    [-2081, -3089, -2539, -579, 12025, -318, 1943, -2295, -33, 3945, 952, -3701, -2313, -2472],
                    [2081, 3089, 2539, 579, -12025, 318, -1943, 2295, 33, -3945, -952, 3701, 2313, 2472],
                    [406, 549, 470, 339, 3759, 145, -472, 432, 4, -1733, -182, 1343, 437, 460],
                    [-1404, -1978, -1660, -1236, -18567, -160, 4088, -1512, -33, -10910, 959, -6702, -1528, -1620],
                    [1091, 1157, 1110, 2501, -14607, 744, -2152, 1074, 8, -4701, -636, 15124, 1088, 1103],
                    [3122, 4358, 3676, 2295, 1608, 743, -3743, 3363, 48, -4391, -1603, 18961, 3394, 3592],
                    [-1836, -2404, -2086, -3466, -9729, -343, -20987, -1927, -110, -15928, 2273, -6802, -1952, -2046],
                    [-8134, -9434, -8695, -18002, -16233, -4982, -6438, -8284, -181, -7689, 9462, -18359, -8383, -8601],
                    [8134, 9434, 8695, 18002, 16233, 4982, 6438, 8284, 181, 7689, -9462, 18359, 8383, 8601],
                    [6486, 6884, 6648, 16459, 3034, 5784, -7101, 6472, 93, -4114, -7255, 7443, 6547, 6616],
                    [6211, 6202, 6192, 17375, -2208, 6584, -10303, 6114, 70, -7797, -7154, 2476, 6185, 6187],
                    [-750, -736, -741, -1642, 812, -783, 4103, -734, -2, 2064, 535, -144, -743, -741],
                    [-812, -764, -788, -1789, 1474, -966, 4321, -789, 3, 3129, 436, 167, -797, -790],
                    [-5866, -6537, -6151, -8547, -13973, -5537, -22713, -5939, 79, -22343, 1160, -11312, -5990, -6102],
                    [5866, 6537, 6151, 8547, 13973, 5537, 22713, 5939, -79, 22343, -1160, 11312, 5990, 6102],
                    [-3713, -4738, -4164, -9658, -13060, -253, -12245, -3862, -155, -11179, 9360, -12317, -3921, -4091],
                    [3713, 4738, 4164, 9658, 13060, 253, 12245, 3862, 155, 11179, -9360, 12317, 3921, 4091],
                    [5178, 5772, 5430, 7539, 12369, 4886, 17503, 5242, -69, 20015, -1023, 9994, 5287, 5387],
                    [4988, 6507, 5649, 6268, 11820, 1417, -6290, 5231, 84, -1563, -3041, 21078, 5290, 5543],
                    [-4988, -6507, -5649, -6268, -11820, -1417, 6290, -5231, -84, 1563, 3041, -21078, -5290, -5543],

                    [27, -516, -942, -55, -65, -10, -37, 21556, 1, -43, -25, -80, 169, -436],
                    [99, -2659, -4101, -716, -678, -255, -447, -13728, 20, -491, -330, -793, -2786, -4074],
                    [13604, 14405, 13924, 17915, 21082, 15357, 24375, 13632, -738, 25000, 25593, 19569, 13726, 13863],
                    [-13604, -14405, -13924, -17915, -21082, -15357, -24375, -13632, 738, -25000, -25593, -19569,
                     -13726, -13863],
                    [8345, 7908, 8133, 5906, 5149, 6088, 4298, 8256, -4403, 4360, 3646, 5554, 8231, 8162],
                    [-23391, -24200, -23674, -28499, -28737, -30569, -29212, -23305, -2144, -28476, -30499, -28476,
                     -23463, -23606],
                    [-28932, -27486, -28255, -20747, -18234, -21270, -15401, -28692, 946, -15617, -13229, -19584,
                     -28585, -28354],
                    [28932, 27486, 28255, 20747, 18234, 21270, 15401, 28692, -946, 15617, 13229, 19584, 28585, 28354],
                    [15217, 14571, 15132, 10852, 9656, 10621, 8234, 15584, -368, 8335, 7221, 10336, 15340, 15204],
                    [160, 206, 180, 181, 1085, 76, -251, 168, 1, 8246, -70, 533, 170, 177],
                    [-690, -797, -737, -942, -2419, -570, -643, -705, 6, -9549, 107, -1584, -711, -729],
                    [-103, -133, -117, -117, -702, -49, 163, -109, -1, 16456, 45, -345, -110, -115],
                    [0, 0, 0, 0, 0, 0, 0, 0, 0, 14947, 0, 0, 0, 0],
                    [-43, -85, -62, 8, -1039, 59, 626, -51, -4, -10518, 81, -377, -51, -59],
                    [33, 17, 25, 86, -398, 82, 405, 29, -3, -12064, 37, -85, 29, 25],
                    [-662, -284, -461, -4067, 4609, -446, 1209, -509, -6, 2188, 412, 6618, -528, -479],
                    [738, -588, 99, 8135, -16298, 2324, -4947, 351, -18, -7975, -1113, -21603, 376, 179],
                    [662, 284, 461, 4067, -4609, 446, -1209, 509, 6, -2188, -412, -6618, 528, 479],
                    [-7783, -8589, -8122, -11137, -17317, -7679, -23045, -7863, 137, -28332, 11, -14235, -7928, -8062],
                    [6457, 7622, 6959, 12885, 17407, 5738, 21606, 6593, 990, 20704, 27702, 15512, 6683, 6876],

                    [8207, 9256, 8653, 14323, 17365, 8720, 20211, 8307, 827, 18972, 28760, 16081, 8401, 8576],
                    [557, 1736, 1086, 6408, 13189, -5173, 17235, 768, 198, 15165, -5768, 10971, 810, 1005],
                    [2837, 2496, 2675, 2929, -3907, 5194, -16064, 2744, -273, -12992, -29, -586, 2751, 2697],
                    [-792, 159, -361, 3484, 10186, -5899, 15759, -608, 185, 13635, -4592, 7779, -582, -426],
                    [-4360, -3743, -4068, -2003, 3769, -10184, 8155, -4201, -12, 6925, 12203, 1761, -4208, -4108],
                    [3359, 2692, 3048, 582, -4936, 8857, -8828, 3200, -13, -7588, -13422, -3056, 3200, 3092],
                    [7783, 8589, 8122, 11137, 17317, 7679, 23045, 7863, -137, 28332, -11, 14235, 7928, 8062],
                    [-8207, -9256, -8653, -14323, -17365, -8720, -20211, -8307, -827, -18972, -28760, -16081, -8401,
                     -8576],
                    [-557, -1736, -1086, -6408, -13189, 5173, -17235, -768, -198, -15165, 5768, -10971, -810, -1005],
                    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100000],
                    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100000],
                    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100000, 0],
                    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100000, 0],
                    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100000, 100000],
                    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100000, -100000],
                    [100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000,
                     100000, 100000],
                    [-100000, -100000, -100000, -100000, -100000, -100000, -100000, -100000, -100000, -100000, -100000,
                     -100000, -100000, -100000]
                ]
            )

            b = np.array([17700000, 16900000, 24000000, 17500000, 24700000, 17400000, 24800000, 38000000, 67500000,
                          46100000, 39100000, 19300000, 99600000, 107400000, 46400000, 50200000,
                          25100000, 41900000, 257800000, 129100000, 121600000, 89400000, 158800000,
                          155300000, 104300000, 100200000, 108000000, 116700000, 134800000, 156500000,
                          106800000, 36200000, 89200000, 149100000, 26100000, 38300000, 64500000,
                          73100000, 79800000, 87400000, 82400000, 69900000, 135900000, 64400000,
                          103400000, 73600000, 114800000, 107300000, 103300000, 68600000, 71100000,
                          194800000, 60700000, 60700000, 79600000, 286600000, 23100000, 12400000,
                          62800000, 25600000, 69400000, 111400000, 142100000, 91600000, 89400000,
                          160600000, 108500000, 87000000, 27500000, 27800000, 98600000, 150800000,
                          92300000, 157100000, 116300000, 157100000, 66200000, 118800000, 28900000,
                          158700000, 67100000, 22800000, 56800000, 173900000, 63700000, 34200000,
                          19900000, 9900000, 23700000, 23900000, 23500000, 28300000, 35300000,
                          99500000, 32300000, 98400000, 171200000, 168800000, 165900000, 63700000,
                          151300000, 136600000, 103600000, 154400000, 91100000, 122500000, 100000000,
                          100000000, 100000000, 100000000, 0, 0, 0, 0])

            vertices = compute_polytope_vertices(A,b)

Question:
@stephane-caron and the developer team, do you have any idea how to solve this issue ?

Can't find a solution that's not full-dimensional

In the attached example, pypoman incorrectly says that the first LP is feasible but the second is not. However, they should both be feasible. In going from the first LP to the second, all I have done is added one new variable (first column of A_2) and two new constraints (last two rows of A_2 and last two entries of b_2) enforcing that the new variable be zero. Therefore, we can take a solution from the first LP and append a zero to the beginning to get a solution to the second LP. Yet when I enumerate the vertices, the second one comes up empty. The problem has something to do with decimal precision; if you round each decimal entry of b_2 to one less decimal place, the problem disappears. FYI, I am using Python 3.8.5.
pypoman_bug.zip