def test_a_submatrix_of_a_3x3_matrix_is_a_2x2_matrix():
# Given
A = Matrix(1, 5, 0,
-3, 2, 7,
0, 6, -3)
# Then
assert A.submatrix(0, 2) == Matrix(-3, 2,
0, 6)
def test_raise_exception_when_inverse_of_a_noninvertible_matrix():
A = Matrix(-4, 2, -2, -3,
9, 6, 2, 6,
0, -5, 1, -5,
0, 0, 0, 0)
assert not A.is_invertible()
with pytest.raises(NonInvertibleMatrixError):
A.inverse()
def testing_an_invertible_matrix_for_invertibility():
# Given
A = Matrix(6, 4, 4, 4,
5, 5, 7, 6,
4, -9, 3, -7,
9, 1, 7, -6)
# Then
assert A.determinant() == -2120
assert A.is_invertible()
def test_a_3x3_matrix_ought_to_be_representable():
# Given
M = Matrix(-3, 5, 0,
1, -2, -7,
0, 1, 1)
# Then
assert M.at(0, 0) == -3
assert M.at(1, 1) == -2
assert M.at(2, 2) == 1
def test_calculating_a_minor_of_a_3x3_matrix():
# Given
A = Matrix(3, 5, 0,
2, -1, -7,
6, -1, 5)
B = A.submatrix(1, 0)
# Then
assert B.determinant() == 25
assert A.minor(1, 0) == 25
def testing_a_noninvertible_matrix_for_invertibility():
# Given
A = Matrix(-4, 2, -2, -3,
9, 6, 2, 6,
0, -5, 1, -5,
0, 0, 0, 0)
# Then
assert A.determinant() == 0
assert not A.is_invertible()
def test_a_2x2_matrix_ought_to_be_representable():
# Given
M = Matrix(-3, 5,
1, -2)
# Then
assert M.at(0, 0) == -3
assert M.at(0, 1) == 5
assert M.at(1, 0) == 1
assert M.at(1, 1) == -2
def test_calculating_the_determinant_of_a_3x3_matrix():
# Given
A = Matrix(1, 2, 6,
-5, 8, -4,
2, 6, 4)
# Then
assert A.cofactor(0, 0) == 56
assert A.cofactor(0, 1) == 12
assert A.cofactor(0, 2) == -46
assert A.determinant() == -196
def test_a_submatrix_of_a_4x4_matrix_is_a_3x3_matrix():
# Given
A = Matrix(-6, 1, 1, 6,
-8, 5, 8, 6,
-1, 0, 8, 2,
-7, 1, -1, 1)
# Then
assert A.submatrix(2, 1) == Matrix(-6, 1, 6,
-8, 8, 6,
-7, -1, 1)
def test_transposing_a_matrix():
# Given
A = Matrix(0, 9, 3, 0,
9, 8, 0, 8,
1, 8, 5, 3,
0, 0, 5, 8)
# Then
assert A.transpose() == Matrix(0, 9, 1, 0,
9, 8, 8, 0,
3, 0, 5, 5,
0, 8, 3, 8)
def test_calculating_the_inverse_of_a_third_matrix():
# Given
A = Matrix(9, 3, 0, 9,
-5, -2, -6, -3,
-4, 9, 6, 4,
-7, 6, 6, 2)
# Then
assert A.inverse() == Matrix(-0.04074, -0.07778, 0.14444, -0.22222,
-0.07778, 0.03333, 0.36667, -0.33333,
-0.02901, -0.14630, -0.10926, 0.12963,
0.17778, 0.06667, -0.26667, 0.33333)
def test_calculating_the_inverse_of_another_matrix():
# Given
A = Matrix(8, -5, 9, 2,
7, 5, 6, 1,
-6, 0, 9, 6,
-3, 0, -9, -4)
# Then
assert A.inverse() == Matrix(-0.15385, -0.15385, -0.28205, -0.53846,
-0.07692, 0.12308, 0.02564, 0.03077,
0.35897, 0.35897, 0.43590, 0.92308,
-0.69231, -0.69231, -0.76923, -1.92308)
def test_matrix_equality_with_identical_matrices():
# Given
A = Matrix(1, 2, 3, 4,
5, 6, 7, 8,
9, 8, 7, 6,
5, 4, 3, 2)
B = Matrix(1, 2, 3, 4,
5, 6, 7, 8,
9, 8, 7, 6,
5, 4, 3, 2)
# Then
assert A == B
def test_calculating_the_determinant_of_a_4x4_matrix():
# Given
A = Matrix(-2, -8, 3, 5,
-3, 1, 7, 3,
1, 2, -9, 6,
-6, 7, 7, -9)
# Then
assert A.cofactor(0, 0) == 690
assert A.cofactor(0, 1) == 447
assert A.cofactor(0, 2) == 210
assert A.cofactor(0, 3) == 51
assert A.determinant() == -4071
def test_matrix_equality_with_different_matrices():
# Given
A = Matrix(1, 2, 3, 4,
5, 6, 7, 8,
9, 8, 7, 6,
5, 4, 3, 2)
B = Matrix(2, 3, 4, 5,
6, 7, 8, 9,
8, 7, 6, 5,
4, 3, 2, 1)
# Then
assert A != B
def test_multiplying_a_product_by_its_inverse():
# Given
A = Matrix(3, -9, 7, 3,
3, -8, 2, -9,
-4, 4, 4, 1,
-6, 5, -1, 1)
B = Matrix(8, 2, 2, 2,
3, -1, 7, 0,
7, 0, 5, 4,
6, -2, 0, 5)
C = A * B
# Then
assert C * B.inverse() == A
def test_multiplying_two_matrices():
# Given
A = Matrix(1, 2, 3, 4,
5, 6, 7, 8,
9, 8, 7, 6,
5, 4, 3, 2)
B = Matrix(-2, 1, 2, 3,
3, 2, 1, -1,
4, 3, 6, 5,
1, 2, 7, 8)
# Then
assert A * B == Matrix(20, 22, 50, 48,
44, 54, 114, 108,
40, 58, 110, 102,
16, 26, 46, 42)
def test_multiplying_a_matrix_by_the_identity_matrix():
# Given
A = Matrix(0, 1, 2, 4,
1, 2, 4, 8,
2, 4, 8, 16,
4, 8, 16, 32)
# Then
assert A * identity_matrix() == A
def view_transform(f, to, up):
forward = (to - f).normalize()
upn = up.normalize()
left = forward.cross(upn)
true_up = left.cross(forward)
orientation = Matrix(left.x, left.y, left.z, 0, true_up.x, true_up.y,
true_up.z, 0, -forward.x, -forward.y, -forward.z, 0,
0, 0, 0, 1)
return orientation * translation(-f.x, -f.y, -f.z)
def test_equivalence_matrix_with_no_matrix_object():
A = Matrix(1, 2, 3, 4,
5, 6, 7, 8,
9, 8, 7, 6,
5, 4, 3, 2)
assert A != [[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 8, 7, 6],
[5, 4, 3, 2]]
def test_a_matrix_multiplied_by_a_tuple():
# Given
A = Matrix(1, 2, 3, 4,
2, 4, 4, 2,
8, 6, 4, 1,
0, 0, 0, 1)
b = Tuple(1, 2, 3, 1)
# Then
assert A * b == Tuple(18, 24, 33, 1)
def test_an_arbitray_view_transformation():
# Given
f = Point(1, 3, 2)
to = Point(4, -2, 8)
up = Vector(1, 1, 0)
# When
t = view_transform(f, to, up)
# Then
assert t == Matrix(-0.50709, 0.50709, 0.67612, -2.36643, 0.76772, 0.60609,
0.12122, -2.82843, -0.35857, 0.59761, -0.71714, 0.00000,
0.00000, 0.00000, 0.00000, 1.00000)
def test_calculating_a_cofactor_of_a_3x3_matrix():
# Given
A = Matrix(3, 5, 0,
2, -1, -7,
6, -1, 5)
# Then
assert A.minor(0, 0) == -12
assert A.cofactor(0, 0) == -12
assert A.minor(1, 0) == 25
assert A.cofactor(1, 0) == -25
def test_calculating_the_inverse_of_a_matrix():
# Given
A = Matrix(-5, 2, 6, -8,
1, -5, 1, 8,
7, 7, -6, -7,
1, -3, 7, 4)
B = A.inverse()
# Then
assert A.determinant() == 532
assert A.cofactor(2, 3) == -160
assert equal(B.at(3, 2), -160/532)
assert A.cofactor(3, 2) == 105
assert equal(B.at(2, 3), 105/532)
assert B == Matrix(0.21805, 0.45113, 0.24060, -0.04511,
-0.80827, -1.45677, -0.44361, 0.52068,
-0.07895, -0.22368, -0.05263, 0.19737,
-0.52256, -0.81391, -0.30075, 0.30639)
def test_constructing_and_inspecting_a_4x4_matrix():
# Given
M = Matrix(1, 2, 3, 4,
5.5, 6.5, 7.5, 8.5,
9, 10, 11, 12,
13.5, 14.5, 15.5, 16.5)
# Then
assert M.at(0, 0) == 1
assert M.at(0, 3) == 4
assert M.at(1, 0) == 5.5
assert M.at(1, 2) == 7.5
assert M.at(2, 2) == 11
assert M.at(3, 0) == 13.5
assert M.at(3, 2) == 15.5
def scaling(x, y, z):
return Matrix(x, 0, 0, 0, 0, y, 0, 0, 0, 0, z, 0, 0, 0, 0, 1)
def translation(x, y, z):
return Matrix(1, 0, 0, x, 0, 1, 0, y, 0, 0, 1, z, 0, 0, 0, 1)
def shearing(xy, xz, yx, yz, zx, zy):
return Matrix(1, xy, xz, 0, yx, 1, yz, 0, zx, zy, 1, 0, 0, 0, 0, 1)
def rotation_z(radian):
return Matrix(cos(radian), -sin(radian), 0, 0, sin(radian), cos(radian), 0,
0, 0, 0, 1, 0, 0, 0, 0, 1)
def test___repr__():
A = Matrix(3, -9, 7, 3,
3, -8, 2, -9,
-4, 4, 4, 1,
-6, 5, -1, 1)
assert A.__repr__() == """\