def testMultMatrix():
f1 = MultiPower(
np.array([[[5, 0, 0], [0, 0, 0], [0, 0, 0]],
[[0, -2, 0], [0, 0, 0], [0, 0, 0]],
[[1, 0, 0], [0, 0, 0], [0, 0, 0]]]))
f2 = MultiPower(
np.array([[[1, 0, 0], [0, 1, 0], [0, 0, 0]],
[[0, 0, 0], [0, 0, 0], [1, 0, 0]],
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]]))
f3 = MultiPower(
np.array([[[0, 0, 0], [0, 0, 0], [3, 0, 0]],
[[0, -8, 0], [0, 0, 0], [0, 0, 0]],
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]]))
F = [f1, f2, f3]
Gr = Groebner(F)
GB = Gr.solve()
VB = rf.vectorSpaceBasis(GB)
x = MultiPower(np.array([[0], [1]]))
y = MultiPower(np.array([[0, 1]]))
z = MultiPower(np.array([[[0, 1]]]))
mx_RealEig = [eig.real for eig in \
np.linalg.eigvals(rf.multMatrix(x, GB, VB)) if (eig.imag == 0)]
my_RealEig = [eig.real for eig in \
np.linalg.eigvals(rf.multMatrix(y, GB, VB)) if (eig.imag==0)]
mz_RealEig = [eig.real for eig in \
np.linalg.eigvals(rf.multMatrix(z, GB, VB)) if (eig.imag==0)]
assert (len(mx_RealEig) == 2)
assert (len(my_RealEig) == 2)
assert (len(mz_RealEig) == 2)
assert (np.allclose(mx_RealEig, [-1.100987715, .9657124563], atol=1.e-8))
assert (np.allclose(my_RealEig, [-2.878002536, -2.81249605], atol=1.e-8))
assert (np.allclose(mz_RealEig, [3.071618528, -2.821182227], atol=1.e-8))
def test_solve():
#First Test
A = MultiPower(np.array([[-10, 0], [0, 1], [1, 0]]))
B = MultiPower(np.array([[-26, 0, 0], [0, 0, 1], [0, 0, 0], [1, 0, 0]]))
C = MultiPower(
np.array([[-70, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0],
[1, 0, 0, 0]]))
grob = Groebner([A, B, C])
X = MultiPower(np.array([[-2.], [1.]]))
Y = MultiPower(np.array([[-3., 1.]]))
x1, y1 = grob.solve()
assert (np.any([X == i and Y == j for i, j in permutations((x1, y1), 2)]))
#Second Test
A = MultiPower(
np.array([[[[
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
]],
[[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
]]],
[[[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
]],
[[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
]]]]))
B = MultiPower(
np.array([[[[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
]]],
[[[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
]],
[[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
]]]]))
C = MultiPower(
np.array([[[[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
]],
[[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
]],
[[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
]]]]))
grob = Groebner([A, B, C])
w1, x1, y1, z1 = grob.solve()
W = MultiPower(
np.array([[[[0.], [0.]], [[0.], [0.]], [[0.], [0.]], [[1.], [0.]]],
[[[0.], [-1.]], [[0.], [0.]], [[0.], [0.]], [[0.], [0.]]]]))
X = MultiPower(
np.array([[[[0., 0., 0., 0., 0., 1.], [-1., 0., 0., 0., 0., 0.]]]]))
Y = MultiPower(np.array([[[[0.], [0.], [1.]], [[-1.], [0.], [0.]]]]))
Z = MultiPower(
np.array([[[[0.], [0.]], [[0.], [0.]], [[0.], [1.]]],
[[[-1.], [0.]], [[0.], [0.]], [[0.], [0.]]]]))
assert (np.any([
W == i and X == j and Y == k and Z == l
for i, j, k, l in permutations((w1, x1, y1, z1), 4)
]))
#Third Test
A = MultiPower(np.array([[-1, 0, 1], [0, 0, 0]]))
B = MultiPower(np.array([[-1, 0, 0], [0, 1, 0], [1, 0, 0]]))
grob = Groebner([A, B])
x1, y1 = grob.solve()
assert (np.any([A == i and B == j for i, j in permutations((x1, y1), 2)]))
#Fourth Test
A = MultiPower(np.array([[-10, 0], [0, 1], [1, 0]]))
B = MultiPower(np.array([[-25, 0, 0], [0, 0, 1], [0, 0, 0], [1, 0, 0]]))
C = MultiPower(
np.array([[-70, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0],
[1, 0, 0, 0]]))
grob = Groebner([A, B, C])
X = MultiPower(np.array([[1.]]))
x1 = grob.solve()
assert (X == x1[0])
#Fifth Test
A = MultiPower(np.array([[1, 1], [0, 0]]))
B = MultiPower(np.array([[1, 0], [1, 0]]))
C = MultiPower(np.array([[1, 0], [1, 0], [0, 1]]))
grob = Groebner([A, B, C])
X = MultiPower(np.array([[1.]]))
x1 = grob.solve()
assert (X == x1[0])