def test_Trace_MatAdd_doit():
# See issue sympy/sympy#9028
X = ImmutableMatrix([[1, 2, 3]] * 3)
Y = MatrixSymbol('Y', 3, 3)
q = MatAdd(X, 2 * X, Y, -3 * Y)
assert Trace(q).arg == q
assert Trace(q).doit() == 18 - 2 * Trace(Y)
def test_invariants():
A = MatrixSymbol('A', n, m)
B = MatrixSymbol('B', m, l)
X = MatrixSymbol('X', n, n)
objs = [Identity(n), ZeroMatrix(m, n), MatMul(A, B), MatAdd(A, A),
Transpose(A), Adjoint(A), Inverse(X), MatPow(X, 2), MatPow(X, -1),
MatPow(X, 0)]
for obj in objs:
assert obj == obj.__class__(*obj.args)
def test_Trace_doit_deep_False():
X = Matrix([[1, 2], [3, 4]])
assert Trace(X).doit(deep=False) == 5
q = MatPow(X, 2)
assert Trace(q).doit(deep=False).arg == q
q = MatAdd(X, 2 * X)
assert Trace(q).doit(deep=False).arg == q
q = MatMul(X, 2 * X)
assert Trace(q).doit(deep=False).arg == q
def test_doit_args():
A = ImmutableMatrix([[1, 2], [3, 4]])
B = ImmutableMatrix([[2, 3], [4, 5]])
assert MatAdd(A, MatPow(B, 2)).doit() == A + B**2
assert MatAdd(A, MatMul(A, B)).doit() == A + A * B
assert MatAdd(A, A).doit(deep=False) == 2 * A
assert (MatAdd(A, X, MatMul(A, B), Y,
MatAdd(2 * A, B)).doit() == MatAdd(X, Y, 3 * A + A * B + B))
def test_matadd_simplify():
A = MatrixSymbol('A', 1, 1)
assert simplify(MatAdd(A, ImmutableMatrix([[sin(x)**2 + cos(x)**2]]))) == \
MatAdd(A, ImmutableMatrix([[1]]))
def test_Trace_A_plus_B():
assert trace(A + B) == Trace(A) + Trace(B)
assert Trace(A + B).arg == MatAdd(A, B)
assert Trace(A + B).doit() == Trace(A) + Trace(B)
def test_matadd_of_matrices():
assert MatAdd(eye(2), 4 * eye(2),
eye(2)).doit() == ImmutableMatrix(6 * eye(2))
def test_matadd_sympify():
assert isinstance(MatAdd(eye(1), eye(1)).args[0], Basic)
def test_matadd():
pytest.raises(ShapeError, lambda: X + eye(1))
MatAdd(X, eye(1), check=False) # not raises
def test_sort_key():
assert MatAdd(Y, X).doit().args == (X, Y)
def test_doit_nested_MatrixExpr():
X = ImmutableMatrix([[1, 2], [3, 4]])
Y = ImmutableMatrix([[2, 3], [4, 5]])
assert MatPow(MatMul(X, Y), 2).doit() == (X * Y)**2
assert MatPow(MatAdd(X, Y), 2).doit() == (X + Y)**2