def test_vectorSpaceBasis_2():
f1 = MultiPower(np.array([[[0,0,1],[0,3/20,0],[0,0,0]],
[[0,0,0],[-3/40,1,0],[0,0,0]],
[[0,0,0],[0,0,0],[0,0,0]]]))
f2 = MultiPower(np.array([[[3/16,-5/2,0],[0,3/16,0],[0,0,0]],
[[0,0,1],[0,0,0],[0,0,0]],
[[0,0,0],[0,0,0],[0,0,0]]]))
f3 = MultiPower(np.array([[[0,1,1/2],[0,3/40,1],[0,0,0]],
[[-1/2,20/3,0],[-3/80,0,0],[0,0,0]],
[[0,0,0],[0,0,0],[0,0,0]]]))
f4 = MultiPower(np.array([[[3/32,-7/5,0,1],[-3/16,83/32,0,0],[0,0,0,0],[0,0,0,0]],
[[3/40,-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]]]))
f5 = 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]]]))
f6 = MultiPower(np.array([[[0,0,0],[0,0,0],[1,0,0]],
[[0,-8/3,0],[0,0,0],[0,0,0]],
[[0,0,0],[0,0,0],[0,0,0]]]))
G = [f1, f2, f3, f4, f5, f6]
basis = rf.vectorSpaceBasis(G)[0]
trueBasis = [(0,0,0),(1,0,0),(0,1,0),(1,1,0),(0,0,1),(0,0,2),(1,0,1),(0,1,1)]
assert (len(basis) == len(trueBasis)) and (m in basis for m in trueBasis), \
"Failed on MultiPower in 3 vars."
def test_vectorSpaceBasis():
f1 = MultiPower(np.array([[0,-1.5,.5],[-1.5,1.5,0],[1,0,0]]))
f2 = MultiPower(np.array([[0,0,0],[-1,0,1],[0,0,0]]))
f3 = MultiPower(np.array([[0,-1,0,1],[0,0,0,0],[0,0,0,0],[0,0,0,0]]))
G = [f1, f2, f3]
basis = rf.vectorSpaceBasis(G)[0]
trueBasis = [(0,0), (1,0), (0,1), (1,1), (0,2)]
assert (len(basis) == len(trueBasis)) and (m in basis for m in trueBasis), \
"Failed on MultiPower in 2 vars."
def testMultMatrix_2():
f1 = MultiPower(np.array([[0,-1.5,.5],[-1.5,1.5,0],[1,0,0]]))
f2 = MultiPower(np.array([[0,0,0],[-1,0,1],[0,0,0]]))
f3 = MultiPower(np.array([[0,-1,0,1],[0,0,0,0],[0,0,0,0],[0,0,0,0]]))
GB = [f1, f2, f3]
VB = rf.vectorSpaceBasis(GB)[0]
x = MultiPower(np.array([[0],[1]]))
y = MultiPower(np.array([[0,1]]))
mx_Eig = np.linalg.eigvals(rf.multMatrix(x, GB, VB))
my_Eig = np.linalg.eigvals(rf.multMatrix(y, GB, VB))
assert(len(mx_Eig) == 5)
assert(len(my_Eig) == 5)
assert(np.allclose(mx_Eig, [-1., 2., 1., 1., 0.]))
assert(np.allclose(my_Eig, [1., -1., 1., -1., 0.]))
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))