def test_block_lu_decomposition():
A = MatrixSymbol('A', n, n)
B = MatrixSymbol('B', n, m)
C = MatrixSymbol('C', m, n)
D = MatrixSymbol('D', m, m)
X = BlockMatrix([[A, B], [C, D]])
#LDU decomposition
L, D, U = X.LDUdecomposition()
assert block_collapse(L*D*U) == X
#UDL decomposition
U, D, L = X.UDLdecomposition()
assert block_collapse(U*D*L) == X
#LU decomposition
L, U = X.LUdecomposition()
assert block_collapse(L*U) == X
