def test_plane_through_points(self):
# n-dimensional case
for n in range(2, 10):
points = [p for p in np.eye(n)]
a, d = plane_through_points(points)
np.testing.assert_array_almost_equal(a, np.ones(n) / np.sqrt(n))
self.assertAlmostEqual(d, 1. / np.sqrt(n))
# 2d case through origin
points = [np.array([1., -1.]), np.array([-1., 1.])]
a, d = plane_through_points(points)
self.assertAlmostEqual(a[0] / a[1], 1.)
self.assertAlmostEqual(d, 0.)
def _get_inner_simplex(A, b, vertices, tol=1.e-7):
"""
Constructs a simplex contained in the porjection.
Arguments
----------
A : numpy.ndarray
Left-hand side of the inequalities describing the higher dimensional polytope.
b : numpy.ndarray
Right-hand side of the inequalities describing the higher dimensional polytope.
vertices : list of numpy.ndarray
List of two vertices of the projection.
tol : float
Maximal expansion of a facet to consider it a facet of the projection.
Returns
----------
vertices : list of numpy.ndarray
List of vertices of the simplex contained in the projection.
"""
# initialize LPs
n = vertices[0].shape[0]
# expand increasing at every iteration the dimension of the space
for i in range(2, n+1):
a, d = plane_through_points([v[:i,:] for v in vertices])
f = np.vstack((a, np.zeros((A.shape[1]-i, 1))))
sol = linear_program(f, A, b)
# check the length of the expansion wrt to the plane, if zero expand in the opposite direction
expansion = np.abs(a.T.dot(sol['argmin'][:i, :]) - d) # >= 0
if expansion < tol:
lp.f = - lp.f
sol = lp.solve()
vertices.append(sol['argmin'][:n,:])
return vertices