content: """
  Unit tests for QuTiP partial transpose functions.
  """
  
  import numpy as np
  
  from qutip import Qobj, partial_transpose, tensor, rand_dm
  from qutip.partial_transpose import _partial_transpose_reference
  
  
  def test_partial_transpose_bipartite():
      """partial transpose of bipartite systems"""
  
      rho = Qobj(np.arange(16).reshape(4, 4), dims=[[2, 2], [2, 2]])
  
      # no transpose
      rho_pt = partial_transpose(rho, [0, 0])
      assert (np.abs(np.max(rho_pt.full() - rho.full())) < 1e-12)
  
      # partial transpose subsystem 1
      rho_pt = partial_transpose(rho, [1, 0])
      rho_pt_expected = np.array([[0, 1,  8,  9],
                                  [4, 5, 12, 13],
                                  [2, 3, 10, 11],
                                  [6, 7, 14, 15]])
      assert (np.abs(np.max(rho_pt.full() - rho_pt_expected)) < 1e-12)
  
      # partial transpose subsystem 2
      rho_pt = partial_transpose(rho, [0, 1])
      rho_pt_expected = np.array([[0, 4, 2, 6],
                                  [1, 5, 3, 7],
                                  [8, 12, 10, 14],
                                  [9, 13, 11, 15]])
      assert (np.abs(np.max(rho_pt.full() - rho_pt_expected)) < 1e-12)
  
      # full transpose
      rho_pt = partial_transpose(rho, [1, 1])
      assert (np.abs(np.max(rho_pt.full() - rho.trans().full())) < 1e-12)
  
  
  def test_partial_transpose_comparison():
      """partial transpose: comparing sparse and dense implementations"""
  
      N = 10
      rho = tensor(rand_dm(N, density=0.5), rand_dm(N, density=0.5))
  
      # partial transpose of system 1
      rho_pt1 = partial_transpose(rho, [1, 0], method="dense")
      rho_pt2 = partial_transpose(rho, [1, 0], method="sparse")
      np.abs(np.max(rho_pt1.full() - rho_pt1.full())) < 1e-12
  
      # partial transpose of system 2
      rho_pt1 = partial_transpose(rho, [0, 1], method="dense")
      rho_pt2 = partial_transpose(rho, [0, 1], method="sparse")
      np.abs(np.max(rho_pt1.full() - rho_pt2.full())) < 1e-12
  
  
  def test_partial_transpose_randomized():
      """partial transpose: randomized tests on tripartite system"""
  
      rho = tensor(rand_dm(2, density=1),
                   rand_dm(2, density=1),
                   rand_dm(2, density=1))
  
      mask = np.random.randint(2, size=3)
  
      rho_pt_ref = _partial_transpose_reference(rho, mask)
  
      rho_pt1 = partial_transpose(rho, mask, method="dense")
      np.abs(np.max(rho_pt1.full() - rho_pt_ref.full())) < 1e-12
  
      rho_pt2 = partial_transpose(rho, mask, method="sparse")
      np.abs(np.max(rho_pt2.full() - rho_pt_ref.full())) < 1e-12
  