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    "info": {
        "author": "St\u00e9phane Caron",
        "author_email": "stephane.caron@lirmm.fr",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 5 - Production/Stable",
            "Intended Audience :: Developers",
            "Intended Audience :: Science/Research",
            "License :: OSI Approved :: GNU Lesser General Public License v3 (LGPLv3)",
            "Operating System :: OS Independent",
            "Programming Language :: Python",
            "Programming Language :: Python :: 2",
            "Programming Language :: Python :: 3",
            "Topic :: Scientific/Engineering :: Mathematics"
        ],
        "description": "This library implements common operations over `convex polyhedra <https://en.wikipedia.org/wiki/Convex_polyhedron>`_ such\nas `polytope projection <https://scaron.info/doc/pypoman/index.html#module-pypoman.projection>`_, `double description <https://scaron.info/doc/pypoman/index.html#module-pypoman.duality>`_ (conversion between\nhalfspace and vertex representations), computing the `Chebyshev center <https://scaron.info/doc/pypoman/index.html#chebyshev-center>`_,\netc.\n\nSee the complete `API documentation <https://scaron.info/doc/pypoman/>`_ for details.\n\nExamples\n--------\n\nVertex enumeration\n~~~~~~~~~~~~~~~~~~\n\nWe can compute the list of vertices of a polytope described in halfspace\nrepresentation by ``A * x <= b``:\n\n.. code:: python\n\n    import numpy\n    import pypoman\n\n    A = numpy.array([\n        [-1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],\n        [0, -1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],\n        [0,  0, -1,  0,  0,  0,  0,  0,  0,  0,  0,  0],\n        [0,  0,  0, -1,  0,  0,  0,  0,  0,  0,  0,  0],\n        [0,  0,  0,  0, -1,  0,  0,  0,  0,  0,  0,  0],\n        [0,  0,  0,  0,  0, -1,  0,  0,  0,  0,  0,  0],\n        [0,  0,  0,  0,  0,  0, -1,  0,  0,  0,  0,  0],\n        [0,  0,  0,  0,  0,  0,  0, -1,  0,  0,  0,  0],\n        [0,  0,  0,  0,  0,  0,  0,  0, -1,  0,  0,  0],\n        [0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  0,  0],\n        [0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1,  0],\n        [0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1],\n        [1,  1,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0],\n        [0,  0,  0,  1,  1,  1,  0,  0,  0,  0,  0,  0],\n        [0,  0,  0,  0,  0,  0,  1,  1,  1,  0,  0,  0],\n        [0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  1],\n        [1,  0,  0,  1,  0,  0,  1,  0,  0,  1,  0,  0],\n        [0,  1,  0,  0,  1,  0,  0,  1,  0,  0,  1,  0],\n        [0,  0,  1,  0,  0,  1,  0,  0,  1,  0,  0,  1]])\n    b = numpy.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 2, 3])\n    vertices = pypoman.compute_polytope_vertices(A, b)\n\nPolytope projection\n~~~~~~~~~~~~~~~~~~~\n\nLet us project an n-dimensional polytope over ``x = [x_1 ... x_n]`` onto its\nfirst two coordinates ``proj(x) = [x_1 x_2]``:\n\n.. code:: python\n\n    import pypoman\n    from numpy import array, eye, ones, vstack, zeros\n\n    n = 10  # dimension of the original polytope\n    p = 2   # dimension of the projected polytope\n\n    # Original polytope:\n    # - inequality constraints: \\forall i, |x_i| <= 1\n    # - equality constraint: sum_i x_i = 0\n    A = vstack([+eye(n), -eye(n)])\n    b = ones(2 * n)\n    C = ones(n).reshape((1, n))\n    d = array([0])\n    ineq = (A, b)  # A * x <= b\n    eq = (C, d)    # C * x == d\n\n    # Projection is proj(x) = [x_0 x_1]\n    E = zeros((p, n))\n    E[0, 0] = 1.\n    E[1, 1] = 1.\n    f = zeros(p)\n    proj = (E, f)  # proj(x) = E * x + f\n\n    vertices = pypoman.project_polytope(proj, ineq, eq, method='bretl')\n\n    if __name__ == \"__main__\":   # plot projected polytope\n        import pylab\n        pylab.ion()\n        pylab.figure()\n        pypoman.plot_polygon(vertices)",
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        "keywords": "convex,polyhedron,polyhedra,polytope,projection,duality",
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