# -*- coding: utf-8 -*-
"""
Created on Wed May 29 11:23:46 2013

@author: dcriger
"""

from __future__ import division

import numpy as np
import pytest

from qutip import (
    Qobj, basis, identity, sigmax, sigmay, qeye, create, rand_super,
    rand_super_bcsz, rand_dm, tensor, super_tensor, kraus_to_choi,
    to_super, to_choi, to_kraus, to_chi, to_stinespring, operator_to_vector,
    vector_to_operator, sprepost, destroy, CoreOptions
)
from qutip.core.gates import swap


tol = 1e-8


def assert_kraus_equivalence(a, b, tol=tol):
    assert a.shape == b.shape
    assert a.dims == b.dims
    assert a.type == b.type
    # Kraus operators may vary by a global phase.  Let's find the first
    # non-zero element, set the phase such that that element has the same phase
    # in both, and then compare.  We have to take care to find the first
    # element.
    a, b = a.full(), b.full()
    a_nz = np.nonzero(np.abs(a) > tol)
    if len(a_nz[0]) == 0:
        np.testing.assert_allclose(b, 0, atol=tol)
    a_el, b_el = a[a_nz[0][0], a_nz[1][0]], b[a_nz[0][0], a_nz[1][0]]
    assert b_el != 0
    b *= (a_el / np.abs(a_el)) / (b_el / np.abs(b_el))
    np.testing.assert_allclose(a, b)


@pytest.fixture(scope="function", params=[2, 3, 7])
def dimension(request):
    # There are also some cases in the file where this fixture is explicitly
    # overridden by a more local mark.  That is deliberate.
    return request.param


@pytest.fixture(scope="function", params=[
    pytest.param(rand_super, id="super"),
    pytest.param(rand_super_bcsz, id="super_bcz")
])
def superoperator(request, dimension):
    return request.param(dimension)


class TestSuperopReps:
    """
    A test class for the QuTiP function for applying superoperators to
    subsystems.
    """

    def test_SuperChoiSuper(self, superoperator):
        """
        Superoperator: Converting superoperator to Choi matrix and back.
        """
        choi_matrix = to_choi(superoperator)
        test_supe = to_super(choi_matrix)

        # Assert both that the result is close to expected, and has the right
        # type.
        assert (test_supe - superoperator).norm() < tol
        assert choi_matrix.type == "super" and choi_matrix.superrep == "choi"
        assert test_supe.type == "super" and test_supe.superrep == "super"

    @pytest.mark.parametrize('dimension', [2, 4])
    def test_SuperChoiChiSuper(self, dimension):
        """
        Superoperator: Converting two-qubit superoperator through
        Choi and chi representations goes back to right superoperator.
        """
        superoperator = super_tensor(
            rand_super(dimension), rand_super(dimension),
        )

        choi_matrix = to_choi(superoperator)
        chi_matrix = to_chi(choi_matrix)
        test_supe = to_super(chi_matrix)

        # Assert both that the result is close to expected, and has the right
        # type.
        assert (test_supe - superoperator).norm() < tol
        assert choi_matrix.type == "super" and choi_matrix.superrep == "choi"
        assert chi_matrix.type == "super" and chi_matrix.superrep == "chi"
        assert test_supe.type == "super" and test_supe.superrep == "super"

    def test_ChoiKrausChoi(self, superoperator):
        """
        Superoperator: Convert superoperator to Choi matrix and back.
        """
        choi_matrix = to_choi(superoperator)
        kraus_ops = to_kraus(choi_matrix)
        test_choi = kraus_to_choi(kraus_ops)

        # Assert both that the result is close to expected, and has the right
        # type.
        assert (test_choi - choi_matrix).norm() < tol
        assert choi_matrix.type == "super" and choi_matrix.superrep == "choi"
        assert test_choi.type == "super" and test_choi.superrep == "choi"

    def test_NonSquareKrausSuperChoi(self):
        """
        Superoperator: Convert non-square Kraus operator to Super + Choi matrix
        and back.
        """
        zero = np.array([[1], [0]], dtype=complex)
        one = np.array([[0], [1]], dtype=complex)
        zero_log = np.kron(np.kron(zero, zero), zero)
        one_log = np.kron(np.kron(one, one), one)
        # non-square Kraus operator (isometry)
        kraus = Qobj(zero_log @ zero.T + one_log @ one.T)
        super = sprepost(kraus, kraus.dag())
        choi = to_choi(super)
        op1 = to_kraus(super)
        op2 = to_kraus(choi)
        op3 = to_super(choi)
        assert choi.type == "super" and choi.superrep == "choi"
        assert super.type == "super" and super.superrep == "super"
        assert_kraus_equivalence(op1[0], kraus, tol=1e-8)
        assert_kraus_equivalence(op2[0], kraus, tol=1e-8)
        assert abs((op3 - super).norm()) < 1e-8

    def test_NeglectSmallKraus(self):
        """
        Superoperator: Convert Kraus to Choi matrix and back. Neglect tiny
        Kraus operators.
        """
        zero = np.array([[1], [0]], dtype=complex)
        one = np.array([[0], [1]], dtype=complex)
        zero_log = np.kron(np.kron(zero, zero), zero)
        one_log = np.kron(np.kron(one, one), one)
        # non-square Kraus operator (isometry)
        kraus = Qobj(zero_log @ zero.T + one_log @ one.T)
        super = sprepost(kraus, kraus.dag())
        # 1 non-zero Kraus operator the rest are zero
        sixteen_kraus_ops = to_kraus(super, tol=0.0)
        # default is tol=1e-9
        one_kraus_op = to_kraus(super)
        assert len(sixteen_kraus_ops) == 16
        assert len(one_kraus_op) == 1
        assert_kraus_equivalence(one_kraus_op[0], kraus, tol=tol)

    def test_SuperPreservesSelf(self, superoperator):
        """
        Superoperator: to_super(q) returns q if q is already a
        supermatrix.
        """

        assert superoperator is to_super(superoperator)

    def test_ChoiPreservesSelf(self, superoperator):
        """
        Superoperator: to_choi(q) returns q if q is already Choi.
        """
        choi = to_choi(superoperator)
        assert choi is to_choi(choi)

    def test_random_iscptp(self, superoperator):
        """
        Superoperator: Randomly generated superoperators are
        correctly reported as CPTP and HP.
        """
        with CoreOptions(atol=1e-9):
            assert superoperator.iscptp
            assert superoperator.ishp

    @pytest.mark.parametrize(['qobj', 'hp', 'cp', 'tp'], [
        pytest.param(sprepost(destroy(2), create(2)), True, True, False),
        pytest.param(sprepost(destroy(2), destroy(2)), False, False, False),
        pytest.param(qeye(2), True, True, True),
        pytest.param(sigmax(), True, True, True),
        pytest.param(tensor(sigmax(), qeye(2)), True, True, True),
        pytest.param(0.5 * (to_super(tensor(sigmax(), qeye(2)))
                            + to_super(tensor(qeye(2), sigmay()))),
                     True, True, True,
                     id="linear combination of bipartite unitaries"),
        pytest.param(Qobj(swap(), type='super', superrep='choi'),
                     True, False, True,
                     id="partial transpose map"),
        pytest.param(Qobj(qeye(4)*0.9, type='super'), True, True, False,
                     id="subnormalized map"),
        pytest.param(basis(2, 0), False, False, False, id="ket"),
    ])
    def test_known_iscptp(self, qobj, hp, cp, tp):
        """
        Superoperator: ishp, iscp, istp and iscptp known cases.
        """
        assert qobj.ishp == hp
        assert qobj.iscp == cp
        assert qobj.istp == tp
        assert qobj.iscptp == (cp and tp)

    def test_choi_tr(self):
        """
        Superoperator: Trace returned by to_choi matches docstring.
        """
        for dims in range(2, 5):
            assert abs(to_choi(identity(dims)).tr() - dims) < tol


    # Conjugation by a creation operator
    a = create(2).dag()
    S = sprepost(a, a.dag())

    # A single off-diagonal element
    S_ = sprepost(a, a)

    # Check that a linear combination of bipartite unitaries is CPTP and HP.
    S_U = (
        to_super(tensor(sigmax(), identity(2))) +
        to_super(tensor(identity(2), sigmay()))
    ) / 2

    # The partial transpose map, whose Choi matrix is SWAP
    ptr_swap = Qobj(swap(), type='super', superrep='choi')

    # Subnormalized maps (representing erasure channels, for instance)
    subnorm_map = Qobj(identity(4) * 0.9, type='super', superrep='super')

    @pytest.mark.parametrize(['qobj',  'shouldhp', 'shouldcp', 'shouldtp'], [
        pytest.param(S, True, True, False, id="conjugatio by create op"),
        pytest.param(S_, False, False, False, id="single off-diag"),
        pytest.param(identity(2), True, True, True, id="Identity"),
        pytest.param(sigmax(), True, True, True, id="Pauli X"),
        pytest.param(
            tensor(sigmax(), identity(2)), True, True, True,
            id="bipartite system",
        ),
        pytest.param(
            S_U, True, True, True, id="linear combination of bip. unitaries",
        ),
        pytest.param(ptr_swap,  True, False, True, id="partial transpose map"),
        pytest.param(subnorm_map, True, True, False, id="subnorm map"),
        pytest.param(basis(2), False, False, False, id="not an operator"),

    ])
    def test_known_iscptp(self, qobj, shouldhp, shouldcp, shouldtp):
        """
        Superoperator: ishp, iscp, istp and iscptp known cases.
        """
        assert qobj.ishp == shouldhp
        assert qobj.iscp == shouldcp
        assert qobj.istp == shouldtp
        assert qobj.iscptp == (shouldcp and shouldtp)

    def test_choi_tr(self, dimension):
        """
        Superoperator: Trace returned by to_choi matches docstring.
        """
        assert abs(to_choi(identity(dimension)).tr() - dimension) <= tol

    def test_stinespring_cp(self, dimension):
        """
        Stinespring: A and B match for CP maps.
        """
        superop = rand_super_bcsz(dimension)
        A, B = to_stinespring(superop)

        assert (A - B).norm() < tol

    @pytest.mark.repeat(3)
    def test_stinespring_agrees(self, dimension):
        """
        Stinespring: Partial Tr over pair agrees w/ supermatrix.
        """

        map = rand_super_bcsz(dimension)
        state = rand_dm(dimension)

        S = to_super(map)
        A, B = to_stinespring(map)

        q1 = vector_to_operator(
            S * operator_to_vector(state)
        )
        # FIXME: problem if Kraus index is implicitly
        #        ptraced!
        q2 = (A * state * B.dag()).ptrace((0,))

        assert (q1 - q2).norm('tr') <= tol

    def test_stinespring_dims(self, dimension):
        """
        Stinespring: Check that dims of channels are preserved.
        """
        chan = super_tensor(to_super(sigmax()), to_super(qeye(dimension)))
        A, B = to_stinespring(chan)
        assert A.dims == [[2, dimension, 1], [2, dimension]]
        assert B.dims == [[2, dimension, 1], [2, dimension]]

    @pytest.mark.parametrize('dimension', [2, 4, 8])
    def test_chi_choi_roundtrip(self, dimension):

        superop = rand_super_bcsz(dimension)
        superop = to_chi(superop)
        rt_superop = to_chi(to_choi(superop))
        dif = (rt_superop - superop).norm()

        assert dif == pytest.approx(0, abs=1e-7)
        assert rt_superop.type == superop.type
        assert rt_superop.dims == superop.dims

    chi_sigmax = [
        [0, 0, 0, 0],
        [0, 4, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0]
    ]
    chi_diag2 = [
        [4, 0, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0]
    ]
    rotX_pi_4 = (-1j * sigmax() * np.pi / 4).expm()
    chi_rotX_pi_4 = [
        [2, 2j, 0, 0],
        [-2j, 2, 0, 0],
        [0, 0, 0, 0],
        [0, 0, 0, 0]
    ]

    @pytest.mark.parametrize(['superop', 'chi_expected'], [
        pytest.param(sigmax(), chi_sigmax),
        pytest.param(to_super(sigmax()), chi_sigmax),
        pytest.param(qeye(2), chi_diag2),
        pytest.param(rotX_pi_4, chi_rotX_pi_4)
    ])
    def test_chi_known(self, superop, chi_expected):
        """
        Superoperator: Chi-matrix for known cases is correct.
        """
        chi_actual = to_chi(superop)
        chiq = Qobj(
            chi_expected, dims=[[[2], [2]], [[2], [2]]], superrep='chi',
        )
        assert (chi_actual - chiq).norm() < tol
