coverage: 86.08%. first build
when pulling 9e0279b on Ericgig:solver.faster_normalizations
into 12bf7f7 on qutip:master.

Are there any use cases where the state is an operator and we want to use norm instead of tr? If no, we could just do isoper(state) instead of state._isherm.

As a side note, in cases with non-Hermitian "density matrices", it probably does not make much sense to normalize the output in any way. That is, I don't think it matters too much whether we use norm or tr in such a case, because probably neither is intended by the user... (But maybe there are some use cases I am not aware of?)

The only operator we normalise are density matrices, so isoper work as well. Propagator computation turn the normalisation off. Other cases should only happen when the user pass an arbitrary super operator. I which case they probably don't want any normalisation on our side.

My issue is that in these cases, we still set the isherm flag while not having any ideas what the user is trying to do:

>>> H = qt.qeye(2) * 1j
>>> L = qt.spre(H)
>>> qt.mesolve(L, qt.basis(2,1), [0, 1]).final_state
Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=Dense, isherm=True
Qobj data =
[[0.+0.j         0.+0.j        ]
 [0.+0.j         1.+1.55740849j]]

We don't set the flag when the input are super operators? We try to check if the Liouvillian preserve hermiticity (not easy for time dependant operator)? Junk in, junk out?

My issue is that in these cases, we still set the isherm flag while not having any ideas what the user is trying to do:

We don't set the flag when the input are super operators? We try to check if the Liouvillian preserve hermiticity (not easy for time dependant operator)? Junk in, junk out?

A problem can also happen if the input is not a superoperator:

H = qt.sigmaz() + 1j * qt.sigmax()
initial = qt.ket2dm(qt.basis(2, 0))
qt.mesolve(H, initial, [0, 1], c_ops=[qt.sigmam()]).final_state
> Quantum object: dims=[[2], [2]], shape=(2, 2), type='oper', dtype=Dense, isherm=True
> Qobj data =
> [[ 0.51118445+0.j         -0.11358048+0.24945183j]
>  [ 0.11358048+0.24945183j  0.32517255+0.j        ]]