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)]]))
Q = 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.I) == A.I
assert block_collapse(X.inverse()) == BlockMatrix([[
(-B * D.I * C + A).I, -A.I * B * (D + -C * A.I * B).I
], [-(D - C * A.I * B).I * C * A.I, (D - C * A.I * B).I]])
assert isinstance(X.inverse(), Inverse)
assert not X.is_Identity
Z = BlockMatrix([[Identity(n), B], [C, D]])
assert not Z.is_Identity
def test_block_plus_ident():
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]])
assert bc_block_plus_ident(X+Identity(m+n)) == \
BlockDiagMatrix(Identity(n), Identity(m)) + X
def test_Trace():
assert isinstance(Trace(A), Trace)
assert not isinstance(Trace(A), MatrixExpr)
pytest.raises(ShapeError, lambda: Trace(C))
assert trace(eye(3)) == 3
assert trace(Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])) == 15
assert adjoint(Trace(A)) == trace(Adjoint(A))
assert conjugate(Trace(A)) == trace(Adjoint(A))
assert transpose(Trace(A)) == Trace(A)
A / Trace(A) # Make sure this is possible
# Some easy simplifications
assert trace(Identity(5)) == 5
assert trace(ZeroMatrix(5, 5)) == 0
assert trace(2 * A * B) == 2 * Trace(A * B)
assert trace(A.T) == trace(A)
i, j = symbols('i j')
F = FunctionMatrix(3, 3, Lambda((i, j), i + j))
assert trace(F) == (0 + 0) + (1 + 1) + (2 + 2)
pytest.raises(TypeError, lambda: Trace(S.One))
assert Trace(A).arg is A
assert str(trace(A)) == str(Trace(A).doit())
def test_eval_determinant():
assert det(Matrix()) == 1
assert det(Identity(n)) == 1
assert det(ZeroMatrix(n, n)) == 0
assert det(Transpose(A)) == det(A)