def test_transpose():
Sq = MatrixSymbol('Sq', n, n)
assert transpose(A) == Transpose(A)
assert Transpose(A).shape == (m, n)
assert Transpose(A * B).shape == (l, n)
assert transpose(Transpose(A)) == A
assert isinstance(Transpose(Transpose(A)), Transpose)
assert adjoint(Transpose(A)) == Adjoint(Transpose(A))
assert conjugate(Transpose(A)) == Adjoint(A)
assert Transpose(eye(3)).doit() == eye(3)
assert Transpose(S(5)).doit() == S(5)
assert Transpose(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3],
[2, 4]])
assert transpose(trace(Sq)) == trace(Sq)
assert trace(Transpose(Sq)) == trace(Sq)
assert Transpose(Sq)[0, 1] == Sq[1, 0]
assert Transpose(A * B).doit() == Transpose(B) * Transpose(A)
def test_trace():
assert isinstance(Trace(A), Trace)
assert not isinstance(Trace(A), MatrixExpr)
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).doit() == (0 + 0) + (1 + 1) + (2 + 2)
raises(TypeError, lambda: Trace(S.One))
assert Trace(A).arg is A
def test_adjoint():
assert adjoint(A * B) == Adjoint(B) * Adjoint(A)
assert adjoint(2 * A * B) == 2 * Adjoint(B) * Adjoint(A)
assert adjoint(2 * I * C) == -2 * I * Adjoint(C)
M = Matrix(2, 2, [1, 2 + I, 3, 4])
MA = Matrix(2, 2, [1, 3, 2 - I, 4])
assert adjoint(M) == MA
assert adjoint(2 * M) == 2 * MA
assert adjoint(MatMul(2, M)) == MatMul(2, MA).doit()
def test_adjoint():
Sq = MatrixSymbol('Sq', n, n)
assert Adjoint(A).shape == (m, n)
assert Adjoint(A * B).shape == (l, n)
assert Adjoint(Adjoint(A)) == A
assert Adjoint(eye(3)) == eye(3)
assert Adjoint(S(5)) == S(5)
assert Adjoint(Matrix([[1, 2], [3, 4]])) == Matrix([[1, 3], [2, 4]])
assert Adjoint(Trace(Sq)) == conjugate(Trace(Sq))
assert Trace(Adjoint(Sq)) == conjugate(Trace(Sq))
assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0])
def test_adjoint():
Sq = MatrixSymbol("Sq", n, n)
assert Adjoint(A).shape == (m, n)
assert Adjoint(A * B).shape == (l, n)
assert adjoint(Adjoint(A)) == A
assert isinstance(Adjoint(Adjoint(A)), Adjoint)
assert conjugate(Adjoint(A)) == Transpose(A)
assert transpose(Adjoint(A)) == Adjoint(Transpose(A))
assert Adjoint(eye(3)).doit() == eye(3)
assert Adjoint(S(5)).doit() == S(5)
assert Adjoint(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]])
assert adjoint(trace(Sq)) == conjugate(trace(Sq))
assert trace(adjoint(Sq)) == conjugate(trace(Sq))
assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0])
assert Adjoint(A * B).doit() == Adjoint(B) * Adjoint(A)