def test_LUdecomp():
testmat = Matrix([[0, 2, 5, 3], [3, 3, 7, 4], [8, 4, 0, 2], [-2, 6, 3, 4]])
L, U, p = testmat.LUdecomposition()
assert L.is_lower()
assert U.is_upper()
assert (L * U).permuteBkwd(p) - testmat == zeros(4)
testmat = Matrix([[6, -2, 7, 4], [0, 3, 6, 7], [1, -2, 7, 4],
[-9, 2, 6, 3]])
L, U, p = testmat.LUdecomposition()
assert L.is_lower()
assert U.is_upper()
assert (L * U).permuteBkwd(p) - testmat == zeros(4)
x, y, z = Symbol('x'), Symbol('y'), Symbol('z')
M = Matrix(((1, x, 1), (2, y, 0), (y, 0, z)))
L, U, p = M.LUdecomposition()
assert L.is_lower()
assert U.is_upper()
assert (L * U).permuteBkwd(p) - M == zeros(3)
# test FF LUdecomp
M = Matrix([[1, 3, 3], [3, 2, 6], [3, 2, 2]])
P, L, Dee, U = M.LUdecompositionFF()
assert P * M == L * Dee.inv() * U
M = Matrix([[1, 2, 3, 4], [3, -1, 2, 3], [3, 1, 3, -2], [6, -1, 0, 2]])
P, L, Dee, U = M.LUdecompositionFF()
assert P * M == L * Dee.inv() * U
