qutip/qutip

__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