def test_addition_inverse(self):
a = Quaternion(1, 2, 3, 4)
b = Quaternion(2, 3, 4, 5)
assert -a == Quaternion(-1, -2, -3, -4)
assert a + -b == a - b
assert a + +b == a + b
def test_multiplication_commutativity(self):
a = Quaternion(1, 2, 3, 4)
b = Quaternion(2, 3, 4, 5)
c = 5
d = 5.0
assert a * b == b * a
assert a * c == c * a
assert a * d == d * a
def test_addition_commutativity(self):
a = Quaternion(1, 2, 3, 4)
b = Quaternion(2, 3, 4, 5)
c = 5
d = 5.0
assert a + b == b + a
assert a + c == c + a
assert a + d == d + a
def test_addition_associativity(self):
a = Quaternion(1, 2, 3, 4)
b = Quaternion(2, 3, 4, 5)
c = Quaternion(3, 4, 5, 6)
d = 5
e = 6
f = 5.0
g = 6.0
assert b + (a + c) == (b + a) + c
assert d + (a + e) == (d + a) + e
assert f + (a + g) == (f + a) + g
def test_multiplication_associativity(self):
a = Quaternion(1, 2, 3, 4)
b = Quaternion(2, 3, 4, 5)
c = Quaternion(3, 4, 5, 6)
d = 5
e = 6
f = 5.0
g = 6.0
assert b * (a * c) == (b * a) * c
assert d * (a * e) == (d * a) * e
assert f * (a * g) == (f * a) * g
def test_multiplication_inverse(self):
a = Quaternion(1, 2, 3, 4)
b = Quaternion(2, 3, 4, 5)
assert all_close(
Quaternion(1, 1, 1, 1) / a,
Quaternion(1 / a.qi, 1 / a.qj, 1 / a.qk, 1 / a.qr))
assert all_close(1 / a,
Quaternion(1 / a.qi, 1 / a.qj, 1 / a.qk, 1 / a.qr))
assert all_close(1.0 / a,
Quaternion(1 / a.qi, 1 / a.qj, 1 / a.qk, 1 / a.qr))
assert all_close(a * (Quaternion(1, 1, 1, 1) / b), a / b)
assert all_close(a * (1 / b), a / b)
assert all_close(a * (1.0 / b), a / b)
def test_quaternion_product_associativity(self):
a = Quaternion(1, 2, 3, 4)
b = Quaternion(2, 3, 4, 5)
c = Quaternion(3, 4, 5, 6)
assert b @ (a @ c) == (b @ a) @ c
def test_quaternion_product_inverse(self):
a = Quaternion(2, 2, 2, 2)
b = a.inverse()
assert a @ b == Quaternion()
assert b @ a == Quaternion()
def test_quaternion_product_neutral_element(self):
a = Quaternion(1, 2, 3, 4)
b = Quaternion()
assert a @ b == a
assert a @ b == b @ a
def test_distributivity(self):
a = Quaternion(1, 2, 3, 4)
b = Quaternion(2, 3, 4, 5)
c = Quaternion(3, 4, 5, 6)
assert a * (b + c) == a * b + a * c
def test_conjugate(self):
assert Quaternion(1, 2, 3, 4).t == Quaternion(-1, -2, -3, 4)
def test_properties(self):
a = Quaternion(1, 2, 3, 4)
assert a.qi == 1
assert a.qj == 2
assert a.qk == 3
assert a.qr == 4
def test_multiplication_neutral_element(self):
a = Quaternion(1, 2, 3, 4)
assert a * Quaternion(1, 1, 1, 1) == a
assert a * 1 == a
assert a * 1.0 == a
def test_matrix(self):
assert Quaternion().matrix == Matrix.identity(4)
def test_quaternion_distributivity(self):
a = Quaternion(1, 2, 3, 4)
b = Quaternion(2, 3, 4, 5)
c = Quaternion(3, 4, 5, 6)
assert a @ (b + c) == a @ b + a @ c
def test_addition_neutral_element(self):
a = Quaternion(1, 2, 3, 4)
assert a + Quaternion(0, 0, 0, 0) == a
assert a + 0 == a
assert a + 0.0 == a
def test_slerp(self):
a = Quaternion(1, 0, 0, 1)
b = Quaternion(0, 1, 0, 1)
assert Quaternion.slerp(a, b, 0.0) == a / a.norm()
assert Quaternion.slerp(a, b, 1.0) == b / b.norm()
def test_transform(self):
a = Quaternion(0, 0, 0, 1)
b = Matrix((4, 1), (1, 2, 3, 4))
assert a.transform(b) == b
def test_norm(self):
assert Quaternion().norm() == 1
assert Quaternion(1, 1, 1, 1).norm() == 2
def test_equality(self):
assert Quaternion() == Quaternion()
assert Quaternion(1, 2, 3, 4) == Quaternion(1, 2, 3, 4)
def test_quaternion_vectors(self):
a = Quaternion(0, 0, 0, 1)
b = Matrix((4, 1), (1, 2, 3, 4))
assert a @ b @ a.inverse() == Quaternion(1, 2, 3, 4)
def test_instantiation(self):
Quaternion()
Quaternion(qi=0, qj=0, qk=0, qr=1, data_type="f")