def test_LU_example4_4x3():
A = Matrix([[1, 0, 2, 3],
[2, -1, 3, 6],
[1, 4, 4, 0]])
L, U = lu(A)
assert (L @ U) == A
L, U = lu(A.T)
assert (L @ U) == A.T
def test_LU_example1_2x2():
A = Matrix([[3, 1],
[4, 2]])
L, U = lu(A)
assert L == Matrix([[1, 0],
[4/3, 1]])
assert U == Matrix([[3, 1],
[0, 0.6666666666666667]])
assert (L @ U) == A
def lu_inv(A):
"""
Calculating matrix inverse using LU-factorization:
A = LU
A @ A_inv = I
LU @ A_inv = I
L (U @ A_inv) = I
(U @ A_inv) = L_inv
A_inv = L_inv @ U_inv
:param A: matrix
:return:
"""
nrow, ncol = A.shape
if nrow != ncol:
print("Matrix is not invertible")
return None
L, U = lu(A)
I = eye(nrow)
Y = solve(L, I)
A_inv = solve(U, Y)
return A_inv
def test_LU_example3_3x3():
A = Matrix([[2, 6, 2],
[-3, -8, 0],
[4, 9, 2]])
L, U = lu(A)
assert (L @ U) == A
def test_LU_example2_3x3_zero_row():
A = Matrix([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
L, U = lu(A)
assert (L @ U) == A