def test_matthias_zonotopes():
'tests from_centered_zonotope constructor'
# zonotopes from Figure 2 of "On Computing the Minkowski Difference of Zonotopes" by Matthias Althoff
# Z_m (shifted due to lack of center in our constructor)
m = lpset.from_centered_zonotope([[1, 0], [0, 1], [1, 1]])
expected = [[-2, -2], [-2, 0], [0, 2], [2, 2], [2, 0], [0, -2]]
assert_verts_equals(m.verts(), expected)
# Z_{s,1}
s1 = lpset.from_centered_zonotope([[0.5, -0.25], [0, 0.25]])
expected = [[-0.5, 0], [-0.5, 0.5], [0.5, 0], [0.5, -0.5]]
assert_verts_equals(s1.verts(), expected)
# Z_{s,2}
s2 = lpset.from_centered_zonotope([[0.5, -0.5], [0, 0.5]])
#s2.plot()
#plt.show()
expected = [[-0.5, 0], [-0.5, 1.0], [0.5, 0], [0.5, -1.0]]
assert_verts_equals(s2.verts(), expected)
# Z_{s,3}
s3 = lpset.from_centered_zonotope([[2.0, -0.5], [0, 0.5]])
expected = [[-2.0, 0], [-2.0, 1.0], [2.0, 0], [2.0, -1.0]]
assert_verts_equals(s3.verts(), expected)
def test_mindiff_3d():
'test minkowski difference in 3d'
m = lpset.from_centered_zonotope([[1, 1, 1], [1, 0, 0], [0, 1, 0],
[0, 0, 1]])
s = lpset.from_centered_zonotope([[-1 / 3, 1 / 3, 1 / 3], [1 / 3, 0, 0],
[0, 1 / 3, 0], [0, 0, 1 / 3]])
p_in = m.find_point_in_diff(s)
print(p_in)
assert False
def test_intersection():
'test the lpset intersection'
m = lpset.from_centered_zonotope([[1, 1, 1], [1, 0, 0], [0, 1, 0],
[0, 0, 1]])
s = lpset.from_centered_zonotope([[-1 / 3, 1 / 3, 1 / 3], [1 / 3, 0, 0],
[0, 1 / 3, 0], [0, 0, 1 / 3]])
inter = lpset.intersection(m, s)
verts_s = s.verts3d()
verts_inter = lpplot.get_verts3d(inter)
assert_verts_equals(verts_s, verts_inter)
def test_mindiff_2d():
'test minkowski difference in 2d'
# Z_m (shifted due to lack of center in our constructor)
m = lpset.from_centered_zonotope([[1, 0], [0, 1], [1, 1]])
# Z_{s,1}
s1 = lpset.from_centered_zonotope([[0.5, -0.25], [0, 0.25]])
p_in = m.find_point_in_diff(s1)
print(p_in)
assert False
def test_minkowski_difference():
'test minkowski difference'
# tests from Figure 2 of "On Computing the Minkowski Difference of Zonotopes" by Matthias Althoff
# Z_m (shifted due to lack of center in our constructor)
z_m = lpset.from_centered_zonotope([[1, 0], [0, 1], [1, 1]])
# Z_{s,1}
z_s1 = lpset.from_centered_zonotope([[0.5, -0.25], [0, 0.25]])
z_d1 = z_m.clone().minkowski_difference(z_s1)
z_m.plot(':')
z_s1.plot('-')
z_d1.plot('--')
plt.show()
def test_complement_lps():
'test getting the complement lps'
m = lpset.from_centered_zonotope([[1, 1, 1], [1, 0, 0], [0, 1, 0],
[0, 0, 1]])
c = m.get_complement_lpsets()
assert len(c) == 8
def test_2d_zonotope():
'simple zonotope test'
m = lpset.from_centered_zonotope([[1, 1], [0, 1]])
m.plot()
plt.show()
expected = [[-1, -2], [-1, 0], [1, 2], [1, 0]]
assert_verts_equals(m.verts(), expected)
def test_chull_hard():
'test convex hull operation'
m = lpset.from_centered_zonotope([[1, 0], [0, 1], [1, 1]])
# Z_{s,1}
s1 = lpset.from_centered_zonotope([[0.5, -0.25], [0, 0.25]])
# Z_{s,2}
s2 = lpset.from_centered_zonotope([[0.5, -0.5], [0, 0.5]])
# s = s1
s = s2
#combined = lpset.minkowski_sum([m, s1])
combined = lpset.minkowski_sum([m, s])
lam = -0.1
slack = 0.1
c = lpset.from_forced_chull(m, combined, lam=lam, slack=slack)
a_index = c.lpi.names.index('a')
direction_vec = [0] * a_index + [1]
c.lpi.set_minimize_direction(direction_vec, offset=0)
val = c.lpi.minimize(columns=[a_index])[0]
print(f"min_val of a: {val}")
direction_vec = [0] * a_index + [-1]
c.lpi.set_minimize_direction(direction_vec, offset=0)
val = c.lpi.minimize(columns=[a_index])[0]
print(f"max_val of a: {val}")
m.plot('b:')
s.plot('r:')
combined.plot('k--')
c.plot('g-')
plt.show()
assert False
def test_minkowski_dif_twogen():
'test the minkowski difference from a zonotope with two linearly dependent generators'
z = lpset.from_centered_zonotope([[0, 1], [0, -1]])
expected = [[-2, 0], [2, 0]]
assert_verts_equals(z.verts(), expected)
b = lpset.from_box([[-0.1, 0.1]])
dif = z.clone().minkowski_difference(b)
expected = [[-1.9, 0], [1.9, 0]]
assert_verts_equals(dif.verts(), expected)
def test_3d_zonotope_plot():
'test verts3d on zonotope'
# zonotope from Figure 6 of "On Computing the Minkowski Difference of Zonotopes" by Matthias Althoff
m = lpset.from_centered_zonotope([[1, 1, 1], [1, 0, 0], [0, 1, 0],
[0, 0, 1]])
#s = lpset.from_zonotope([0, 0, 0], [[-1/3, 1/3, 1/3], [1/3, 0, 0], [0, 1/3, 0], [0, 0, 1/3]])
verts = m.verts3d()
assert len(verts) == 14
# figure should work
fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
m.plot3d(ax)
plt.show()
assert False