import numpy as np
from ase.units import Ha
from gpaw.mpi import world
from gpaw.response import ResponseContext
from gpaw.response.coulomb_kernels import CoulombKernel
from gpaw.response.screened_interaction import initialize_w_calculator
from gpaw.response import timer
from gpaw.response.pw_parallelization import Blocks1D
from gpaw.response.pair import KPointPairFactory
from gpaw.wannier90 import read_uwan


def ibz2bz_map(qd):
    """ Maps each k in BZ to corresponding k in IBZ. """
    out_map = [[] for _ in range(qd.nibzkpts)]
    for iK in range(qd.nbzkpts):
        ik = qd.bz2ibz_k[iK]
        out_map[ik].append(iK)
    return out_map


def initialize_w_model(chi0calc, truncation=None, integrate_gamma=0,
                       q0_correction=False, txt='w_model.out',
                       eta=None, world=world, timer=None):
    """ Helper function to initialize ModelInteraction

    Parameters
    ----------
    chi0calc: Chi0Calculator
    truncation: str
        Coulomb truncation scheme. Can be either 2D, 1D, 0D or None.
    integrate_gamma: int
        Method to integrate the Coulomb interaction. 1 is a numerical
        integration at all q-points with G=[0,0,0] - this breaks the
        symmetry slightly. 0 is analytical integration at q=[0,0,0] only -
        this conserves the symmetry. integrate_gamma=2 is the same as 1,
        but the average is only carried out in the non-periodic directions.
    q0_correction: bool
        Analytic correction to the q=0 contribution applicable to 2D
        systems.
    txt: str
        Filename of output files.
    world: MPI comm
    timer: ResponseContext timer
    """
    gs = chi0calc.gs
    wcontext = ResponseContext(txt=txt,
                               comm=world, timer=timer)
    coulomb = CoulombKernel.from_gs(gs, truncation=truncation)
    if eta is not None:
        eta /= Ha
    wcalc = initialize_w_calculator(chi0calc,
                                    wcontext,
                                    coulomb=coulomb,
                                    xc='RPA',
                                    integrate_gamma=integrate_gamma,
                                    q0_correction=q0_correction,
                                    eta=eta)
    return ModelInteraction(wcalc)


class ModelInteraction:

    def __init__(self, wcalc):
        """Class to compute interaction matrix in Wannier basis

        Parameters
        ----------
        wcalc: WCalculator
        """

        self.wcalc = wcalc
        self.gs = wcalc.gs
        self.context = self.wcalc.context
        self.qd = self.wcalc.qd

    @timer('Calculate W in Wannier')
    def calc_in_Wannier(self, chi0calc, Uwan_mnk, bandrange, spin=0):
        """Calculates the screened interaction matrix in Wannier basis.
        NOTE: Does not work with SOC!

        Parameters:
        ----------
        chi0calc: Chi0Calculator
        Uwan_mnk: cmplx or str
            Wannier transformation matrix. if str name of wannier90 output
            m: Wannier index, n: bandindex, k: k-index
        bandrange: int
            range of bands that the wannier functions were constructed from
        spin: int
            spin index (0 or 1)

        Documentation
        -------------

        W_n1,n2;n3,n4(R=0, w) =
        <w^*_{n1,R=0} w_{n2, R=0} | W(r,r',w) |w^*_{n3,R=0} w_{n4, R=0} >

        w_{n R} = V/(2pi)^3 int_{BZ} dk e^{-kR} psi^w_{nk}
        psi^w_{nk} = sum_m U_nm(k) psi^{KS}_{mk}

        In this implementation we compute W_n1,n2;n3,n4(R=0) efficiently
        by expressing it in terms of the reduced Wannier density matrices

        A_{n1,n2,q} = sum_{k} rhowan^{n1,k}_{n2, k+q}

        where the Wannier density matrix is calculated from the usual
        density matrix
        rho^{m1,k}_{m2 k+q} = < psi_{m1,k} | e^{i(q+G)r} | psi_{m2, k+q} >
        and the Wannier transformation matrices U_{nm}(k) as

        rhowan^{n1, k}_{n2, k+q} =
        = sum_{m1, m5} U^*_{n1,m1}(k) U_{n2, m2}(k+q) rho^{m1,k}_{m2 k+q}
        """

        ibz2bz = ibz2bz_map(self.gs.kd)

        # Create pair_factory with nblocks = 1
        pair_factory = KPointPairFactory(self.gs, self.context)
        pair_calc = pair_factory.pair_calculator()

        if isinstance(Uwan_mnk, str):
            # read w90 transformation matrix from file
            seed = Uwan_mnk
            Uwan_mnk, nk, nwan, nband = read_uwan(seed,
                                                  self.gs.kd,
                                                  dis=False)
            if bandrange[1] - bandrange[0] > nband:
                Uwan_mnk, nk, nwan, nband = read_uwan(seed,
                                                      self.gs.kd,
                                                      dis=True)
        else:
            nk = Uwan_mnk.shape[2]
            nband = Uwan_mnk.shape[1]
            nwan = Uwan_mnk.shape[0]

        assert nk == self.gs.kd.nbzkpts
        assert bandrange[1] - bandrange[0] == nband
        wd = chi0calc.wd
        nfreq = len(wd)

        # Find frequency range for block distributed arrays
        blockdist = chi0calc.chi0_body_calc.get_blockdist()
        blocks1d = Blocks1D(blockdist.blockcomm, nfreq)
        mynfreq = blocks1d.nlocal
        self.intrablockcomm = blockdist.intrablockcomm

        # Variable that will store the screened interaction in Wannier basis
        Wwan_wijkl = np.zeros([mynfreq, nwan, nwan, nwan, nwan], dtype=complex)

        for iq, q_c in enumerate(self.gs.kd.ibzk_kc):
            self.context.print('iq = ', iq, '/', self.gs.kd.nibzkpts)
            # Calculate chi0 and W for IBZ k-point q
            self.context.print('calculating chi0...')
            self.context.timer.start('chi0')
            chi0 = chi0calc.calculate(q_c)
            self.context.timer.stop('chi0')
            qpd = chi0.qpd
            self.context.print('calculating W_wGG...')
            W_wGG = self.wcalc.calculate_W_wGG(chi0,
                                               fxc_mode='GW',
                                               only_correlation=False)
            pawcorr = chi0calc.chi0_body_calc.pawcorr

            self.context.print('Projecting to localized Wannier basis...')
            # Loop over all equivalent k-points
            for iQ in ibz2bz[iq]:
                Q_c = self.wcalc.qd.bzk_kc[iQ]
                assert self.wcalc.qd.where_is_q(Q_c,
                                                self.wcalc.qd.bzk_kc) == iQ

                A_mnG = self.get_reduced_wannier_density_matrix(spin,
                                                                Q_c,
                                                                iq,
                                                                bandrange,
                                                                pawcorr,
                                                                qpd,
                                                                pair_calc,
                                                                pair_factory,
                                                                Uwan_mnk)
                if self.qd.time_reversal_k[iQ]:
                    # TR corresponds to complex conjugation
                    A_mnG = A_mnG.conj()

                Wwan_wijkl += np.einsum('ijk,lkm,pqm->lipjq',
                                        A_mnG.conj(),
                                        W_wGG,
                                        A_mnG,
                                        optimize='optimal')

        # factor from three BZ summations and taking from Hartree to eV
        # and volume factor from matrix element in PW basis
        factor = Ha / self.gs.kd.nbzkpts**3 / self.gs.volume
        Wwan_wijkl *= factor
        self.context.write_timer()

        return wd.omega_w * Ha, blocks1d.all_gather(Wwan_wijkl)

    @timer('get_reduced_wannier_density_matrix')
    def get_reduced_wannier_density_matrix(self, spin, Q_c, iq, bandrange,
                                           pawcorr, qpd, pair_calc,
                                           pair_factory, Uwan_mnk):
        """
        Returns sum_k sum_(m1,m2) U_{n1m1}* U_{n2m2} rho^{m1 k}_{m2 k-q}(G)
        where rho is the usual density matrix and U are wannier tranformation
        matrices.
        """
        nG = qpd.ngmax
        nwan = Uwan_mnk.shape[0]
        A_mnG = np.zeros([nwan, nwan, nG], dtype=complex)

        # Parallell sum over k-points
        for iK1 in self.myKrange():
            kpt1 = pair_factory.get_k_point(spin, iK1,
                                            bandrange[0],
                                            bandrange[1])
            iK2 = self.gs.kd.find_k_plus_q(Q_c, [kpt1.K])[0]
            kpt2 = pair_factory.get_k_point(spin, iK2,
                                            bandrange[0],
                                            bandrange[1])

            # Calculate density matrix
            rholoc, iqloc, sign = self.get_density_matrix(kpt1,
                                                          kpt2,
                                                          pawcorr,
                                                          qpd,
                                                          pair_calc)
            assert iqloc == iq

            # Rotate to Wannier basis and sum to get reduced Wannier
            # density matrix A
            A_mnG += np.einsum('ia,jb,abG->ijG',
                               Uwan_mnk[:, :, iK1].conj(),
                               Uwan_mnk[:, :, iK2],
                               rholoc)
        self.intrablockcomm.sum(A_mnG)
        return A_mnG

    def get_density_matrix(self, kpt1, kpt2, pawcorr, qpd, pair_calc):
        from gpaw.response.g0w0 import QSymmetryOp, get_nmG

        symop, iq = QSymmetryOp.get_symop_from_kpair(
            self.gs.kd, self.qd, kpt1, kpt2)
        nG = qpd.ngmax
        mypawcorr, I_G = symop.apply_symop_q(
            qpd, pawcorr, kpt1, kpt2)

        rho_mnG = np.zeros((len(kpt1.eps_n), len(kpt2.eps_n), nG),
                           complex)
        for m in range(len(rho_mnG)):
            rho_mnG[m] = get_nmG(kpt1, kpt2, mypawcorr, m, qpd, I_G, pair_calc)

        return rho_mnG, iq, symop.sign

    def myKrange(self, rank=None):
        if rank is None:
            rank = self.intrablockcomm.rank
        nK = self.gs.kd.nbzkpts
        myKsize = -(-nK // self.intrablockcomm.size)
        myKrange = range(rank * myKsize,
                         min((rank + 1) * myKsize, nK))
        # myKsize = len(myKrange)
        return myKrange
