def test_Trace_MatAdd_doit(): # See issue #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_Trace_doit_deep_False(): X = Matrix([[1, 2], [3, 4]]) 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_trace_constant_factor(): # Issue 9052: gave 2*Trace(MatMul(A)) instead of 2*Trace(A) assert trace(2 * A) == 2 * Trace(A) X = ImmutableMatrix([[1, 2], [3, 4]]) assert trace(MatMul(2, X)) == 10
def test_Trace_MatPow_doit(): X = Matrix([[1, 2], [3, 4]]) assert Trace(X).doit() == 5 q = MatPow(X, 2) assert Trace(q).arg == q assert Trace(q).doit() == 29
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_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())