content: import pytest
  import collections
  import functools
  import numpy as np
  import qutip
  from qutip.core.data import CSR, Dense
  import qutip.core.data as _data
  
  # We want to test the broadcasting rules for `qutip.expect` for a whole bunch
  # of different systems, without having to repeatedly specify the systems over
  # and over again.  We first store a small number of test cases for known
  # expectation value in the most bundled-up form, because it's easier to unroll
  # these by applying the expected broadcasting rules explicitly ourselves than
  # performing the inverse operation.
  #
  # We store a single test case in a record type, just to keep things neatly
  # together while we're munging them, so it's clear at all times what
  # constitutes a valid test case.
  
  _Case = collections.namedtuple('_Case', ['operator', 'state', 'expected'])
  
  
  def _case_to_dm(case):
      return case._replace(state=[x.proj() for x in case.state])
  
  
  def _unwrap(list_):
      """Unwrap lists until we reach the first non-list element."""
      out = list_
      while isinstance(out, list):
          out = out[0]
      return out
  
  
  def _case_id(case):
      op_part = 'qubit' if _unwrap(case.operator).dims[0][0] == 2 else 'basis'
      state_part = 'ket' if _unwrap(case.state).dims[1][0] == 1 else 'dm'
      return op_part + "-" + state_part
  
  
  # This is the minimal set of test cases, with a Fock system and a qubit system
  # both in ket form and dm form.  The reference expectations are a 2D array
  # which would be found by broadcasting `operator` against `state` and applying
  # `qutip.expect` to the pairs.
  _dim = 5
  _num, _a = qutip.num(_dim), qutip.destroy(_dim)
  _sx, _sz, _sp = qutip.sigmax(), qutip.sigmaz(), qutip.sigmap()
  _known_fock = _Case([_num, _a],
                      [qutip.fock(_dim, n) for n in range(_dim)],
                      np.array([np.arange(_dim), np.zeros(_dim)]))
  _known_qubit = _Case([_sx, _sz, _sp],
                       [qutip.basis(2, 0), qutip.basis(2, 1)],
                       np.array([[0, 0], [1, -1], [0, 0]]))
  _known_cases = [_known_fock, _case_to_dm(_known_fock),
                  _known_qubit, _case_to_dm(_known_qubit)]
  
  
  class TestKnownExpectation:
      def pytest_generate_tests(self, metafunc):
          """
          Perform the parametrisation over the test cases, performing the
          explicit broadcasting into separate test cases when required.
  
          We detect whether to perform explicit broadcasting over one of the
          arguments of the `_Case` by looking for a singular/plural name of the
          parameter in the test.  If the parameter is singular, then we manually
          perform the broadcasting rule for that fixture, and parametrise over
          the resulting list, taking care to pick out the correct parts of the
          reference array.
          """
          cases = _known_cases
          op_name, state_name = 'operator', 'state'
          if op_name not in metafunc.fixturenames:
              op_name += 's'
          else:
              cases = [_Case(op, case.state, expected)
                       for case in cases
                       for op, expected in zip(case.operator, case.expected)]
          if state_name not in metafunc.fixturenames:
              state_name += 's'
          else:
              cases = [_Case(case.operator, state, expected)
                       for case in cases
                       for state, expected in zip(case.state, case.expected.T)]
          metafunc.parametrize([op_name, state_name, 'expected'], cases,
                               ids=[_case_id(case) for case in cases])
  
      def test_operator_by_basis(self, operator, state, expected):
          result = qutip.expect(operator, state)
          assert result == expected
          assert isinstance(result, float if operator.isherm else complex)
  
      def test_broadcast_operator_list(self, operators, state, expected):
          result = qutip.expect(operators, state)
          assert len(result) == len(operators)
          for part, operator, expected_part in zip(result, operators, expected):
              assert isinstance(part, float if operator.isherm else complex)
              assert part == expected_part
  
      def test_broadcast_state_list(self, operator, states, expected):
          result = qutip.expect(operator, states)
          expected_dtype = np.float64 if operator.isherm else np.complex128
          assert isinstance(result, np.ndarray)
          assert result.dtype == expected_dtype
          assert list(result) == list(expected)
  
      def test_broadcast_both_lists(self, operators, states, expected):
          result = qutip.expect(operators, states)
          assert len(result) == len(operators)
          for part, operator, expected_part in zip(result, operators, expected):
              expected_dtype = np.float64 if operator.isherm else np.complex128
              assert isinstance(part, np.ndarray)
              assert part.dtype == expected_dtype
              assert list(part) == list(expected_part)
  
  
  @pytest.mark.repeat(5)
  @pytest.mark.parametrize("hermitian", [False, True], ids=['complex', 'real'])
  @pytest.mark.parametrize("op_type", [CSR, Dense], ids=['csr', 'dense'])
  @pytest.mark.parametrize("state_type", [CSR, Dense], ids=['csr', 'dense'])
  def test_equivalent_to_matrix_element(hermitian, op_type, state_type):
      dimension = 20
      state = qutip.rand_ket(dimension, 0.3).to(op_type)
      op = qutip.rand_herm(dimension, 0.2).to(state_type)
      if not hermitian:
          op = op + 1j*qutip.rand_herm(dimension, 0.1).to(state_type)
      expected = state.dag() * op * state
      assert abs(qutip.expect(op, state) - expected) < 1e-14
  
  
  @pytest.mark.parametrize("solve", [
      pytest.param(qutip.sesolve, id="sesolve"),
      pytest.param(functools.partial(qutip.mesolve, c_ops=[qutip.qzero(2)]),
                   id="mesolve"),
  ])
  def test_compatibility_with_solver(solve):
      e_ops = [getattr(qutip, 'sigma'+x)() for x in 'xyzmp']
      e_ops += [lambda t, psi: np.sin(t)]
      h = qutip.sigmax()
      state = qutip.basis(2, 0)
      times = np.linspace(0, 10, 101)
      options = {"store_states":True}
      result = solve(h, state, times, e_ops=e_ops, options=options)
      direct, states = result.expect, result.states
      indirect = qutip.expect(e_ops[:-1], states)
      # check measurement operators based on quantum objects
      assert len(direct)-1 == len(indirect)
      for direct_, indirect_ in zip(direct, indirect):
          assert len(direct_) == len(indirect_)
          assert isinstance(direct_, np.ndarray)
          assert isinstance(indirect_, np.ndarray)
          assert direct_.dtype == indirect_.dtype
          np.testing.assert_allclose(np.array(direct_), indirect_, atol=1e-12)
          # test measurement operators based on lambda functions
          direct_ = direct[-1]
          indirect_ = np.sin(times)
          assert len(direct_) == len(indirect_)
          assert isinstance(direct_, np.ndarray)
          assert isinstance(indirect_, np.ndarray)
          assert direct_.dtype == indirect_.dtype
          np.testing.assert_allclose(np.array(direct_), indirect_, atol=1e-12)
  
  
  def test_no_real_casting(monkeypatch):
      sz = qutip.sigmaz() # the choice of the matrix does not matter
      assert isinstance(qutip.expect(sz, sz), float)
      with qutip.CoreOptions(auto_real_casting=False):
          assert isinstance(qutip.expect(sz, sz), complex)
  
  
  def test_no_real_casting_multiple_states(monkeypatch):
      sz = qutip.sigmaz() # the choice of the matrix does not matter
      assert isinstance(qutip.expect(sz, [sz])[0], float)
      with qutip.CoreOptions(auto_real_casting=False):
          assert isinstance(qutip.expect(sz, [sz])[0], complex)
  