content: __all__ = ['qpt_plot', 'qpt_plot_combined', 'qpt']
  
  from numpy import hstack, real, imag
  import scipy.linalg as la
  from . import tensor, spre, spost, stack_columns, unstack_columns
  from .visualization import matrix_histogram
  import itertools
  
  try:
      import matplotlib.pyplot as plt
  except:
      pass
  
  
  def _index_permutations(size_list):
      """
      Generate a list with all index permutations.
  
      Parameters
      ----------
      size_list : list
          A list that contains the sizes for each composite system.
  
      Returns
      -------
      perm_idx : list
          List containing index permutations.
  
      """
      return itertools.product(*[range(N) for N in size_list])
  
  
  def qpt_plot(chi, lbls_list, title=None, fig=None, axes=None):
      """
      Visualize the quantum process tomography chi matrix. Plot the real and
      imaginary parts separately.
  
      Parameters
      ----------
      chi : array
          Input QPT chi matrix.
      lbls_list : list
          List of labels for QPT plot axes.
      title : str, optional
          Plot title.
      fig : figure instance, optional
          User defined figure instance used for generating QPT plot.
      axes : list of figure axis instance, optional
          User defined figure axis instance (list of two axes) used for
          generating QPT plot.
  
      Returns
      -------
      fig, ax : tuple
          A tuple of the matplotlib figure and axes instances used to produce
          the figure.
  
      """
  
      if axes is None or len(axes) != 2:
          if fig is None:
              fig = plt.figure(figsize=(16, 8))
  
          ax1 = fig.add_subplot(1, 2, 1, projection='3d', position=[0, 0, 1, 1])
          ax2 = fig.add_subplot(1, 2, 2, projection='3d', position=[0, 0, 1, 1])
  
          axes = [ax1, ax2]
  
      xlabels = []
      for inds in _index_permutations([len(lbls) for lbls in lbls_list]):
          xlabels.append("".join([lbls_list[k][inds[k]]
                                  for k in range(len(lbls_list))]))
  
      matrix_histogram(real(chi), xlabels, xlabels, limits=[-1, 1], ax=axes[0])
      axes[0].set_title(r"real($\chi$)")
  
      matrix_histogram(imag(chi), xlabels, xlabels, limits=[-1, 1], ax=axes[1])
      axes[1].set_title(r"imag($\chi$)")
  
      if title and fig:
          fig.suptitle(title)
  
      return fig, axes
  
  
  def qpt_plot_combined(chi, lbls_list, title=None,
                        fig=None, ax=None, figsize=(8, 6),
                        threshold=None):
      """
      Visualize the quantum process tomography chi matrix. Plot bars with
      height and color corresponding to the absolute value and phase,
      respectively.
  
      Parameters
      ----------
      chi : array
          Input QPT chi matrix.
  
      lbls_list : list
          List of labels for QPT plot axes.
  
      title : str, optional
          Plot title.
  
      fig : figure instance, optional
          User defined figure instance used for generating QPT plot.
  
      figsize : (int, int), default: (8, 6)
          Size of the figure when the ``fig`` is not provided.
  
      ax : figure axis instance, optional
          User defined figure axis instance used for generating QPT plot
          (alternative to the fig argument).
  
      threshold: float, optional
          Threshold for when bars of smaller height should be transparent. If
          not set, all bars are colored according to the color map.
  
      Returns
      -------
      fig, ax : tuple
          A tuple of the matplotlib figure and axes instances used to produce
          the figure.
      """
  
      if ax is None:
          if fig is None:
              fig = plt.figure(figsize=figsize)
          ax = fig.add_subplot(1, 1, 1, projection='3d', position=[0, 0, 1, 1])
  
      xlabels = []
      for inds in _index_permutations([len(lbls) for lbls in lbls_list]):
          xlabels.append("".join(
              [lbls_list[k][inds[k]] for k in range(len(lbls_list))]))
  
      if not title:
          title = r"$\chi$"
  
      matrix_histogram(chi, xlabels, xlabels, bar_style='abs',
                       color_style='phase',
                       options={'threshold': threshold}, ax=ax)
      ax.set_title(title)
  
      return fig, ax
  
  
  def qpt(U, op_basis_list):
      """
      Calculate the quantum process tomography chi matrix for a given (possibly
      nonunitary) transformation matrix U, which transforms a density matrix in
      vector form according to:
  
          vec(rho) = U * vec(rho0)
  
          or
  
          rho = unstack_columns(U * stack_columns(rho0))
  
      U can be calculated for an open quantum system using the QuTiP propagator
      function.
  
      Parameters
      ----------
      U : Qobj
          Transformation operator. Can be calculated using QuTiP propagator
          function.
  
      op_basis_list : list
          A list of Qobj's representing the basis states.
  
      Returns
      -------
      chi : array
          QPT chi matrix
  
      """
  
      E_ops = []
      # loop over all index permutations
      for inds in _index_permutations([len(ops) for ops in op_basis_list]):
          # loop over all composite systems
          E_op_list = [op_basis_list[k][inds[k]] for k in range(len(
              op_basis_list))]
          E_ops.append(tensor(E_op_list))
      EE_ops = [spre(E1) * spost(E2.dag()) for E1 in E_ops for E2 in E_ops]
      M = hstack([EE.full().ravel('F')[:, None] for EE in EE_ops])
      Uvec = U.full().ravel('F')
      chi_vec = la.solve(M, Uvec)
      return chi_vec.reshape(U.shape).T
  