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).permute_rows(p, 'backward') - 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).permute_rows(p, 'backward') - testmat == zeros(4)
# non-square
testmat = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
L, U, p = testmat.LUdecomposition(rankcheck=False)
assert L.is_lower
assert U.is_upper
assert (L * U).permute_rows(p, 'backward') - testmat == zeros(4, 3)
# square and singular
testmat = Matrix([[1, 2, 3], [2, 4, 6], [4, 5, 6]])
L, U, p = testmat.LUdecomposition(rankcheck=False)
assert L.is_lower
assert U.is_upper
assert (L * U).permute_rows(p, 'backward') - testmat == zeros(3)
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).permute_rows(p, 'backward') - M == zeros(3)
mL = Matrix((
(1, 0, 0),
(2, 3, 0),
))
assert mL.is_lower is True
assert mL.is_upper is False
mU = Matrix((
(1, 2, 3),
(0, 4, 5),
))
assert mU.is_lower is False
assert mU.is_upper is True
# 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
M = Matrix([[0, 0, 1], [2, 3, 0], [3, 1, 4]])
P, L, Dee, U = M.LUdecompositionFF()
assert P * M == L * Dee.inv() * U
# issue 15794
M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
raises(ValueError, lambda: M.LUdecomposition_Simple(rankcheck=True))
