def test_cube(self):
# Halfspaces of the cube:
halfspaces = np.array([
[-1., 0., 0., 0.], # x >= 0
[1., 0., 0., -1.], # x <= 1
[0., -1., 0., 0.], # y >= 0
[0., 1., 0., -1.], # y <= 1
[0., 0., -1., 0.], # z >= 0
[0., 0., 1., -1.]
]) # z <= 1
point = np.array([0.5, 0.5, 0.5])
hs = qhull.HalfspaceIntersection(halfspaces, point)
# qhalf H0.5,0.5,0.5 o < input.txt
qhalf_points = np.array([[-2, 0, 0], [2, 0, 0], [0, -2, 0], [0, 2, 0],
[0, 0, -2], [0, 0, 2]])
qhalf_facets = [[2, 4, 0], [4, 2, 1], [5, 2, 0], [2, 5, 1], [3, 4, 1],
[4, 3, 0], [5, 3, 1], [3, 5, 0]]
assert len(qhalf_facets) == len(hs.dual_facets)
for a, b in zip(qhalf_facets, hs.dual_facets):
assert set(a) == set(b) # facet orientation can differ
assert_allclose(hs.dual_points, qhalf_points)
def test_cube_halfspace_intersection(self):
halfspaces = np.array([[-1.0, 0.0, 0.0], [0.0, -1.0, 0.0],
[1.0, 0.0, -1.0], [0.0, 1.0, -1.0]])
feasible_point = np.array([0.5, 0.5])
points = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]])
hull = qhull.HalfspaceIntersection(halfspaces, feasible_point)
assert_allclose(hull.intersections, points)
def test_cube_halfspace_intersection(self, dt):
halfspaces = np.array([[-1, 0, 0], [0, -1, 0], [1, 0, -2], [0, 1, -2]],
dtype=dt)
feasible_point = np.array([1, 1], dtype=dt)
points = np.array([[0.0, 0.0], [2.0, 0.0], [0.0, 2.0], [2.0, 2.0]])
hull = qhull.HalfspaceIntersection(halfspaces, feasible_point)
assert_allclose(hull.intersections, points)
def test_incremental(self):
#Cube
halfspaces = np.array([[0., 0., -1., -0.5], [0., -1., 0., -0.5],
[-1., 0., 0., -0.5], [1., 0., 0., -0.5],
[0., 1., 0., -0.5], [0., 0., 1., -0.5]])
#Cut each summit
extra_normals = np.array([[1., 1., 1.], [1., 1., -1.], [1., -1., 1.],
[1, -1., -1.]])
offsets = np.array([[-1.]] * 8)
extra_halfspaces = np.hstack((np.vstack(
(extra_normals, -extra_normals)), offsets))
feas_point = np.array([0., 0., 0.])
inc_hs = qhull.HalfspaceIntersection(halfspaces,
feas_point,
incremental=True)
inc_res_hs = qhull.HalfspaceIntersection(halfspaces,
feas_point,
incremental=True)
for i, ehs in enumerate(extra_halfspaces):
inc_hs.add_halfspaces(ehs[np.newaxis, :])
inc_res_hs.add_halfspaces(ehs[np.newaxis, :], restart=True)
total = np.vstack((halfspaces, extra_halfspaces[:i + 1, :]))
hs = qhull.HalfspaceIntersection(total, feas_point)
assert_allclose(inc_hs.halfspaces, inc_res_hs.halfspaces)
assert_allclose(inc_hs.halfspaces, hs.halfspaces)
#Direct computation and restart should have points in same order
assert_allclose(hs.intersections, inc_res_hs.intersections)
#Incremental will have points in different order than direct computation
self.assert_unordered_allclose(inc_hs.intersections,
hs.intersections)
inc_hs.close()
def test_self_dual_polytope_intersection(self):
fname = os.path.join(os.path.dirname(__file__), 'data',
'selfdual-4d-polytope.txt')
ineqs = np.genfromtxt(fname)
halfspaces = -np.hstack((ineqs[:, 1:], ineqs[:, :1]))
feas_point = np.array([0., 0., 0., 0.])
hs = qhull.HalfspaceIntersection(halfspaces, feas_point)
assert_equal(hs.intersections.shape, (24, 4))
assert_almost_equal(hs.dual_volume, 32.0)
assert_equal(len(hs.dual_facets), 24)
for facet in hs.dual_facets:
assert_equal(len(facet), 6)
dists = halfspaces[:, -1] + halfspaces[:, :-1].dot(feas_point)
self.assert_unordered_allclose((halfspaces[:, :-1].T/dists).T, hs.dual_points)
points = itertools.permutations([0., 0., 0.5, -0.5])
for point in points:
assert_equal(np.sum((hs.intersections == point).all(axis=1)), 1)