def test_squareBlockMatrix():
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]])
Y = BlockMatrix([[A]])
assert X.is_square
assert (block_collapse(X + Identity(m + n)) == BlockMatrix(
[[A + Identity(n), B], [C, D + Identity(m)]]))
X + Identity(m + n)
assert (X + MatrixSymbol('Q', n + m, n + m)).is_MatAdd
assert (X * MatrixSymbol('Q', n + m, n + m)).is_MatMul
assert block_collapse(Y.inverse()) == A.inverse()
assert block_collapse(X.inverse()) == BlockMatrix(
[[(-B * D.inverse() * C + A).inverse(),
-A.inverse() * B * (D + -C * A.inverse() * B).inverse()],
[
-(D - C * A.inverse() * B).inverse() * C * A.inverse(),
(D - C * A.inverse() * B).inverse()
]])
assert isinstance(X.inverse(), Inverse)
assert not X.is_Identity
Z = BlockMatrix([[Identity(n), B], [C, D]])
assert not Z.is_Identity
def test_multiplication():
A = MatrixSymbol('A', n, m)
B = MatrixSymbol('B', m, l)
C = MatrixSymbol('C', n, n)
assert (2*A*B).shape == (n, l)
assert (A*0*B) == ZeroMatrix(n, l)
pytest.raises(ShapeError, lambda: B*A)
assert (2*A).shape == A.shape
assert A * ZeroMatrix(m, m) * B == ZeroMatrix(n, l)
assert C * Identity(n) * C.inverse() == Identity(n)
assert B/2 == Rational(1, 2)*B
pytest.raises(NotImplementedError, lambda: 2/B)
A = MatrixSymbol('A', n, n)
B = MatrixSymbol('B', n, n)
assert Identity(n) * (A + B) == A + B