def test_solve_linear_system_and_get_back_to_earth():
# We need to solve this linear system in order to fly back to the Earth.
# Don't ask how, it just works.
s = """| 1 1 1 |
| 0 2 5 |
| 2 5 -1 |"""
X = str_to_array(s)
Y = [[6], [-4], [27]]
det = determinant(X)
I, J = len(X), len(X[0])
def cofactor(X, i, j):
sgn = (-1)**(i + j)
minor = determinant(submatrix(X, i, j))
return sgn * minor
cofactor_matrix = [[cofactor(X, i, j) for j in range(J)] for i in range(I)]
adjucate_matrix = transpose(cofactor_matrix)
det = determinant(X)
X_inverse = mul(adjucate_matrix, 1 / det)
result = matmul(X_inverse, Y)
expected = [[5], [3], [-2]]
assert numpy.isclose(result, expected).all()
print("Congratulations! You just solved the linear system and can fly "
"back to Earth :-)")
def test_100x99_with_99x200_multiplication(self):
numpy.random.seed(sum(ord(c) for c in "Drink more coffee"))
X = numpy.random.randint(-5, +6, (100, 99)).tolist()
Y = numpy.random.randint(-5, +6, (99, 200)).tolist()
expected = numpy.matmul(X, Y).tolist()
result = matmul(X, Y)
assert result == expected
def test_100x100_with_100x_1_multiplication(self):
numpy.random.seed(420)
X = numpy.random.randint(-5, +6, (100, 100)).tolist()
Y = numpy.random.randint(-5, +6, (100, 1)).tolist()
expected = numpy.matmul(X, Y).tolist()
result = matmul(X, Y)
assert result == expected
def test_simple_4x4_multiplication(self):
X = [[5, 1, 7, 1], [9, 4, 4, 2], [7, 4, 5, 1], [7, 5, 8, 8]]
Y = [[6, 8, 2, 4], [1, 5, 8, 1], [8, 7, 1, 4], [8, 6, 7, 9]]
expected = [
[95, 100, 32, 58],
[106, 132, 68, 74],
[94, 117, 58, 61],
[175, 185, 118, 137],
]
result = matmul(X, Y)
assert result == expected
def test_identity_2x2_returns_same_value(self):
X = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
Y = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
result = matmul(X, Y)
assert result == [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
def test_simple_2x2_multiplication(self):
X = [[1, 2], [3, 4]]
Y = [[5, 6], [7, 8]]
result = matmul(X, Y)
assert result == [[19, 22], [43, 50]]