def test_multiplication_neutral_element(self, shape):
length = functools.reduce(operator.mul, shape)
a = Matrix(shape, range(length))
assert a * Matrix(shape, 1) == a
assert a * 1 == a
assert a * 1.0 == a
def test_distributivity(self, shape):
length = functools.reduce(operator.mul, shape)
a = Matrix(shape, range(length))
b = Matrix(shape, range(1, length + 1))
c = Matrix(shape, range(2, length + 2))
assert a * (b + c) == a * b + a * c
def test_addition_inverse(self, shape):
length = functools.reduce(operator.mul, shape)
a = Matrix(shape, range(length))
b = Matrix(shape, range(1, length + 1))
assert -a == Matrix(a.shape, (-s for s in a))
assert a + -b == a - b
assert a + +b == a + b
def test_all_close(self, shape):
epsilon = 7 / 3 - 4 / 3 - 1
a = Matrix(shape, epsilon)
b = Matrix(shape, 0)
c = 0
d = 0.0
assert a.all_close(b) is True
assert a.all_close(c) is True
assert a.all_close(d) is True
def test_multiplication_commutativity(self, shape):
length = functools.reduce(operator.mul, shape)
a = Matrix(shape, range(1, length + 1))
b = Matrix(shape, range(4, length + 4))
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, shape):
length = functools.reduce(operator.mul, shape)
a = Matrix(shape, range(length))
b = Matrix(shape, range(1, length + 1))
c = 5
d = 5.0
assert a + b == b + a
assert a + c == c + a
assert a + d == d + a
def test_multiplication_associativity(self, shape):
length = functools.reduce(operator.mul, shape)
a = Matrix(shape, range(length))
b = Matrix(shape, range(1, length + 1))
c = Matrix(shape, range(2, length + 2))
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_addition_associativity(self, shape):
length = functools.reduce(operator.mul, shape)
a = Matrix(shape, range(length))
b = Matrix(shape, range(1, length + 1))
c = Matrix(shape, range(2, length + 2))
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_total_ordering(self, shape):
length = functools.reduce(operator.mul, shape)
a = Matrix(shape, 0)
b = Matrix(shape, -1)
c = Matrix(shape, range(1, length + 1))
assert a == a
assert a >= a
assert a <= a
assert a > b
assert a >= b
assert b < a
assert b <= a
assert a != b
assert a != c
def test_transpose(self, shape):
length = functools.reduce(operator.mul, shape)
a = Matrix(shape, range(length))
assert a == a.t.t
assert a.shape == a.t.shape[::-1]
for i, j in itertools.product(range(a.shape[0]), range(a.shape[1])):
assert a[i, j] == a.t[j, i]
def test_is_close(self, shape):
epsilon = 7 / 3 - 4 / 3 - 1
a = Matrix(shape, epsilon)
b = Matrix(shape, 0)
c = 0
d = 0.0
assert a.is_close(b) == Matrix(shape, 1, data_type="B")
assert a.is_close(c) == Matrix(shape, 1, data_type="B")
assert a.is_close(d) == Matrix(shape, 1, data_type="B")
def test_instantiation(self, shape):
Matrix(shape)
Matrix(shape, data_type="f", transposed=False)
Matrix(shape, 2)
Matrix(shape, range(shape[0] * shape[1]))
Matrix(shape, list(range(shape[0] * shape[1])))
a = Matrix(shape)
assert Matrix(shape, a._data)._data is a._data
def test_determinant(self, shape):
a = Matrix(shape)
if a.is_square and not a.is_scalar:
if a.shape[0] <= 4:
assert a.determinant() == 1
else:
with pytest.raises(NotImplementedError):
a.determinant()
else:
with pytest.raises(ValueError):
a.determinant()
def test_multiplication_inverse(self, shape):
length = functools.reduce(operator.mul, shape)
a = Matrix(shape, range(1, length + 1))
b = Matrix(shape, range(4, length + 4))
assert all_close(
Matrix(shape, 1) / a, Matrix(a.shape, (1 / s for s in a)))
assert all_close(1 / a, Matrix(a.shape, (1 / s for s in a)))
assert all_close(1.0 / a, Matrix(a.shape, (1 / s for s in a)))
assert all_close(a * (Matrix(shape, 1) / b), a / b)
assert all_close(a * (1 / b), a / b)
assert all_close(a * (1.0 / b), a / b)
def test_setitem(self):
m = Matrix((4, 4), range(16))
m[0, 1] = 100
assert m[0, 1] == 100
m = Matrix((4, 4), range(16))
m[1, :3] = Matrix((1, 3), 100)
assert m[1, :3] == Matrix((1, 3), 100)
m = Matrix((4, 4), range(16))
m[:2, :2] = (100, 100, 100, 100)
assert m[:2, :2] == Matrix((2, 2), 100)
m = Matrix((4, 4), range(16))
m[0, (0, 1, 3)] = 100
assert m[0, (0, 1, 3)] == Matrix((1, 3), 100)
def test_from_iterable(self):
data = ((0, 1), (2, 3))
assert Matrix.from_iterable(data) == Matrix((2, 2), range(4))
data = (0, 1, 2, 3)
assert Matrix.from_iterable(data) == Matrix((4, 1), range(4))
data = ((0, 1), (0, 1, 2))
with pytest.raises(ValueError):
Matrix.from_iterable(data)
def test_dot_product_inverse(self):
a = Matrix((2, 2), (4, 3, 2, 1))
b = Matrix((2, 2), (-0.5, 1.5, 1, -2))
assert a @ b == Matrix.identity(2)
assert b @ a == Matrix.identity(2)
def test_is_scalar(self):
assert Matrix((4, 4)).is_scalar is False
assert Matrix((4, 1)).is_scalar is False
assert Matrix((1, 4)).is_scalar is False
assert Matrix((1, 1)).is_scalar is True
def test_multiplication_shapes(self):
with pytest.raises(ValueError):
Matrix((2, 2)) * Matrix((3, 3))
with pytest.raises(ValueError):
Matrix((2, 2)) / Matrix((3, 3))
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_is_row_vector(self):
assert Matrix((4, 4)).is_row_vector is False
assert Matrix((4, 1)).is_row_vector is False
assert Matrix((1, 4)).is_row_vector is True
assert Matrix((1, 1)).is_row_vector is False
def test_matrix(self):
assert Quaternion().matrix == Matrix.identity(4)
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_dot_product_vectors(self):
assert Matrix((1, 3), 1) @ Matrix((3, 1), 1) == 3
def test_is_square(self):
assert Matrix((4, 4)).is_square is True
assert Matrix((4, 1)).is_square is False
assert Matrix((1, 4)).is_square is False
assert Matrix((1, 1)).is_square is True
def test_dot_product_shapes(self):
with pytest.raises(ValueError):
Matrix((4, 3)) @ Matrix((2, 2))
def test_dot_distributivity(self):
a = Matrix((2, 2), range(4))
b = Matrix((2, 2), range(1, 5))
c = Matrix((2, 2), range(2, 6))
assert a @ (b + c) == a @ b + a @ c
def test_length(self, shape):
assert len(Matrix(shape)) == functools.reduce(operator.mul, shape)
def test_dot_product_associativity(self):
a = Matrix((2, 2), range(4))
b = Matrix((2, 2), range(1, 5))
c = Matrix((2, 2), range(2, 6))
assert b @ (a @ c) == (b @ a) @ c
def test_dot_product_neutral_element(self):
a = Matrix((2, 2), range(4))
b = Matrix.identity(2)
assert a @ b == a
assert a @ b == b @ a