"""Kohn-Sham single particle excitations realated objects.

"""
import sys
import json
import numpy as np
from copy import copy

from ase.units import Bohr, Hartree, alpha

import gpaw.mpi as mpi
from gpaw.utilities import packed_index
from gpaw.lrtddft.excitation import Excitation, ExcitationList, get_filehandle
from gpaw.pair_density import PairDensity
from gpaw.fd_operators import Gradient
from gpaw.utilities.tools import coordinates


class KSSingles(ExcitationList):
    """Kohn-Sham single particle excitations

    Input parameters:

    calculator:
      the calculator object after a ground state calculation

    nspins:
      number of spins considered in the calculation
      Note: Valid only for unpolarised ground state calculation

    eps:
      Minimal occupation difference for a transition (default 0.001)

    istart:
      First occupied state to consider
    jend:
      Last unoccupied state to consider
    energy_range:
      The energy range [emin, emax] or emax for KS transitions to use as basis
    """
    def __init__(self,
                 restrict={},
                 log=None,
                 txt=None):
        ExcitationList.__init__(self, log=log, txt=txt)
        self.world = mpi.world

        self.restrict = KSSRestrictor()
        self.restrict.update(restrict)

    def calculate(self, atoms, nspins=None):
        calculator = atoms.calc
        self.calculator = calculator

        # LCAO calculation requires special actions
        self.lcao = calculator.wfs.mode == 'lcao'

        # deny hybrids as their empty states are wrong
#        gsxc = calculator.hamiltonian.xc
#        hybrid = hasattr(gsxc, 'hybrid') and gsxc.hybrid > 0.0
#        assert(not hybrid)

        # ensure correctly initialized wave functions
        calculator.converge_wave_functions()
        self.world = calculator.wfs.world

        # parallelization over bands not yet supported
        assert calculator.wfs.bd.comm.size == 1

        # do the evaluation
        self.select(nspins)

        trkm = self.get_trk()
        self.log('KSS {0} transitions (restrict={1})'.format(
            len(self), self.restrict))
        self.log('KSS TRK sum %g (%g,%g,%g)' %
                 (np.sum(trkm) / 3., trkm[0], trkm[1], trkm[2]))
        pol = self.get_polarizabilities(lmax=3)
        self.log('KSS polarisabilities(l=0-3) %g, %g, %g, %g' %
                 tuple(pol.tolist()))
        return self

    @staticmethod
    def emin_emax(energy_range):
        emin = -sys.float_info.max
        emax = sys.float_info.max
        if energy_range is not None:
            try:
                emin, emax = energy_range
                emin /= Hartree
                emax /= Hartree
            except TypeError:
                emax = energy_range / Hartree
        return emin, emax

    def select(self, nspins=None):
        """Select KSSingles according to the given criterium."""

        # criteria
        emin, emax = self.restrict.emin_emax()
        istart = self.restrict['istart']
        jend = self.restrict['jend']
        eps = self.restrict['eps']

        if not hasattr(self, 'calculator'):  # I'm read from a file
            # throw away all not needed entries
            for i, ks in reversed(list(enumerate(self))):
                if ((ks.fij / ks.weight) <= eps or
                   ks.i < istart or ks.j > jend or
                   ks.energy < emin or ks.energy > emax):
                    del self[i]
            return None

        paw = self.calculator
        wfs = paw.wfs
        self.dtype = wfs.dtype
        self.kpt_u = wfs.kpt_u

        if not self.lcao and self.kpt_u[0].psit_nG is None:
            raise RuntimeError('No wave functions in calculator!')

        # here, we need to take care of the spins also for
        # closed shell systems (Sz=0)
        # vspin is the virtual spin of the wave functions,
        #       i.e. the spin used in the ground state calculation
        # pspin is the physical spin of the wave functions
        #       i.e. the spin of the excited states
        self.nvspins = wfs.nspins
        self.npspins = wfs.nspins
        fijscale = 1
        ispins = [0]
        nks = wfs.kd.nibzkpts * wfs.kd.nspins
        if self.nvspins < 2:
            if (nspins or 0) > self.nvspins:
                self.npspins = nspins
                fijscale = 0.5
                ispins = [0, 1]
                nks *= 2

        kpt_comm = self.calculator.wfs.kd.comm
        nbands = len(self.kpt_u[0].f_n)

        # select
        take = np.zeros((nks, nbands, nbands), dtype=int)
        u = 0
        for ispin in ispins:
            for k in range(wfs.kd.nibzkpts):
                q = k - wfs.kd.k0
                for s in range(wfs.nspins):
                    if q >= 0 and q < wfs.kd.mynk:
                        kpt = wfs.kpt_qs[q][s]
                        for i in range(nbands):
                            for j in range(i + 1, nbands):
                                fij = (kpt.f_n[i] - kpt.f_n[j]) / kpt.weight
                                epsij = kpt.eps_n[j] - kpt.eps_n[i]
                                if (fij > eps and
                                    epsij >= emin and epsij < emax and
                                        i >= istart and j <= jend):
                                    take[u, i, j] = 1
                    u += 1
        kpt_comm.sum(take)

        self.log()
        self.log('Kohn-Sham single transitions')
        self.log()

        # calculate in parallel
        u = 0
        for ispin in ispins:
            for k in range(wfs.kd.nibzkpts):
                q = k - wfs.kd.k0
                for s in range(wfs.kd.nspins):
                    for i in range(nbands):
                        for j in range(i + 1, nbands):
                            if take[u, i, j]:
                                if q >= 0 and q < wfs.kd.mynk:
                                    kpt = wfs.kpt_qs[q][s]
                                    pspin = max(kpt.s, ispin)
                                    self.append(
                                        KSSingle(i, j, pspin, kpt, paw,
                                                 fijscale=fijscale,
                                                 dtype=self.dtype))
                                else:
                                    self.append(KSSingle(i, j, pspin=0,
                                                         kpt=None, paw=paw,
                                                         dtype=self.dtype))
                    u += 1

        # distribute
        for kss in self:
            kss.distribute()

    @classmethod
    def read(cls, filename=None, fh=None, restrict={}, log=None):
        """Read myself from a file"""
        assert (filename is not None) or (fh is not None)

        def fail(f):
            raise RuntimeError(f.name + ' does not contain ' +
                               cls.__class__.__name__ + ' data')
        if fh is None:
            f = get_filehandle(cls, filename)

            # there can be other information, i.e. the LrTDDFT header
            try:
                content = f.read()
                f.seek(content.index('# KSSingles'))
                del content
                f.readline()
            except ValueError:
                fail(f)
        else:
            f = fh
            # we assume to be at the right place and read the header
            if not f.readline().strip() == '# KSSingles':
                fail(f)

        words = f.readline().split()
        n = int(words[0])
        kssl = cls(log=log)
        if len(words) == 1:
            # very old output style for real wave functions (finite systems)
            kssl.dtype = float
            restrict_from_file = {}
        else:
            if words[1].startswith('complex'):
                kssl.dtype = complex
            else:
                kssl.dtype = float
            restrict_from_file = json.loads(f.readline())
            if not isinstance(restrict_from_file, dict):  # old output style
                restrict_from_file = {'eps': restrict_from_file}
        kssl.npspins = 1
        for i in range(n):
            kss = KSSingle(string=f.readline(), dtype=kssl.dtype)
            kssl.append(kss)
            kssl.npspins = max(kssl.npspins, kss.pspin + 1)

        if fh is None:
            f.close()

        kssl.update()
        kssl.restrict.update(restrict_from_file)
        if len(restrict):
            kssl.restrict.update(restrict)
            kssl.select()

        return kssl

    def update(self):
        istart = self[0].i
        jend = 0
        npspins = 1
        nvspins = 1
        for kss in self:
            istart = min(kss.i, istart)
            jend = max(kss.j, jend)
            if kss.pspin == 1:
                npspins = 2
            if kss.spin == 1:
                nvspins = 2
        self.restrict.update({'istart': istart, 'jend': jend})
        self.npspins = npspins
        self.nvspins = nvspins

        if hasattr(self, 'energies'):
            del self.energies

    def set_arrays(self):
        if hasattr(self, 'energies'):
            return
        energies = []
        fij = []
        me = []
        mur = []
        muv = []
        magn = []
        for k in self:
            energies.append(k.energy)
            fij.append(k.fij)
            me.append(k.me)
            mur.append(k.mur)
            if k.muv is not None:
                muv.append(k.muv)
            if k.magn is not None:
                magn.append(k.magn)
        self.energies = np.array(energies)
        self.fij = np.array(fij)
        self.me = np.array(me)
        self.mur = np.array(mur)
        if len(muv):
            self.muv = np.array(muv)
        else:
            self.muv = None
        if len(magn):
            self.magn = np.array(magn)
        else:
            self.magn = None

    def write(self, filename=None, fh=None):
        """Write current state to a file.

        'filename' is the filename. If the filename ends in .gz,
        the file is automatically saved in compressed gzip format.

        'fh' is a filehandle. This can be used to write into already
        opened files.
        """
        if self.world.rank != 0:
            return

        if fh is None:
            f = get_filehandle(self, filename, mode='w')
        else:
            f = fh

        f.write('# KSSingles\n')
        f.write('{0} {1}\n'.format(len(self), np.dtype(self.dtype)))
        f.write(json.dumps(self.restrict.values) + '\n')
        for kss in self:
            f.write(kss.outstring())
        if fh is None:
            f.close()

    def overlap(self, ov_nn, other):
        """Matrix element overlaps determined from wave function overlaps.

        Parameters
        ----------
        ov_nn: array
            Wave function overlap factors from a displaced calculator.
            Index 0 corresponds to our own wavefunctions conjugated and
            index 1 to the others' wavefunctions

        Returns
        -------
        ov_pp: array
            Overlap corresponding to matrix elements.
            Index 0 corresponds to our own matrix elements conjugated and
            index 1 to the others' matrix elements
        """
        n0 = len(self)
        n1 = len(other)
        ov_pp = np.zeros((n0, n1), dtype=ov_nn.dtype)
        i1_p = [ex.i for ex in other]
        j1_p = [ex.j for ex in other]
        for p0, ex0 in enumerate(self):
            ov_pp[p0, :] = ov_nn[ex0.i, i1_p].conj() * ov_nn[ex0.j, j1_p]
        return ov_pp


class KSSRestrictor:
    """Object to handle KSSingles restrictions"""
    defaults = {'eps': 0.01,
                'istart': 0,
                'jend': sys.maxsize,
                'energy_range': None}

    def __init__(self, dictionary={}):
        self._vals = {}
        self.update(dictionary)

    def __getitem__(self, index):
        assert index in self.defaults
        return self._vals.get(index, self.defaults[index])

    def __setitem__(self, index, value):
        assert index in self.defaults
        self._vals[index] = value

    def update(self, dictionary):
        for key, value in dictionary.items():
            self[key] = value

    def emin_emax(self):
        emin = -sys.float_info.max
        emax = sys.float_info.max
        if self['energy_range'] is not None:
            try:
                emin, emax = self['energy_range']
                emin /= Hartree
                emax /= Hartree
            except TypeError:
                emax = self['energy_range'] / Hartree
        return emin, emax

    def __ge__(self, other):
        """am I less or equal restricting than the other?"""
        emin, emax = self.emin_emax()
        omin, omax = other.emin_emax()
        res = (emin <= omin) & (emax >= omax)

        res &= self['istart'] <= other['istart']
        res &= self['jend'] >= other['jend']
        res &= self['eps'] < other['eps']

        return res

    @property
    def values(self):
        return dict(self._vals)

    def __str__(self):
        return str(self.values)


class KSSingle(Excitation, PairDensity):
    """Single Kohn-Sham transition containing all its indices

      pspin=physical spin
      spin=virtual  spin, i.e. spin in the ground state calc.
      kpt=the Kpoint object
      fijscale=weight for the occupation difference::
      me  = sqrt(fij*epsij) * <i|r|j>
      mur = - <i|r|a>
      muv = - <i|nabla|a>/omega_ia with omega_ia>0
      magn = <i|[r x nabla]|a> / (2 m_e c)
    """

    def __init__(self, iidx=None, jidx=None, pspin=None, kpt=None,
                 paw=None, string=None, fijscale=1, dtype=float):
        """
        iidx: index of occupied state
        jidx: index of empty state
        pspin: physical spin
        kpt: kpoint object,
        paw: calculator,
        string: string to be initialized from
        fijscale:
        dtype: dtype of matrix elements
        """
        if string is not None:
            self.fromstring(string, dtype)
            return None

        # normal entry

        PairDensity.__init__(self, paw)
        PairDensity.initialize(self, kpt, iidx, jidx)

        self.pspin = pspin

        self.energy = 0.0
        self.fij = 0.0

        self.me = np.zeros((3), dtype=dtype)
        self.mur = np.zeros((3), dtype=dtype)
        self.muv = np.zeros((3), dtype=dtype)
        self.magn = np.zeros((3), dtype=dtype)

        self.kpt_comm = paw.wfs.kd.comm

        # leave empty if not my kpt
        if kpt is None:
            return

        wfs = paw.wfs
        gd = wfs.gd

        self.energy = kpt.eps_n[jidx] - kpt.eps_n[iidx]
        self.fij = (kpt.f_n[iidx] - kpt.f_n[jidx]) * fijscale

        # calculate matrix elements -----------

        # length form ..........................

        # course grid contribution
        # <i|r|j> is the negative of the dipole moment (because of negative
        # e- charge)
        me = - gd.calculate_dipole_moment(self.get())

        # augmentation contributions
        ma = np.zeros(me.shape, dtype=dtype)
        pos_av = paw.atoms.get_positions() / Bohr
        for a, P_ni in kpt.P_ani.items():
            Ra = pos_av[a]
            Pi_i = P_ni[self.i].conj()
            Pj_i = P_ni[self.j]
            Delta_pL = wfs.setups[a].Delta_pL
            ni = len(Pi_i)
            ma0 = 0
            ma1 = np.zeros(me.shape, dtype=me.dtype)
            for i in range(ni):
                for j in range(ni):
                    pij = Pi_i[i] * Pj_i[j]
                    ij = packed_index(i, j, ni)
                    # L=0 term
                    ma0 += Delta_pL[ij, 0] * pij
                    # L=1 terms
                    if wfs.setups[a].lmax >= 1:
                        # see spherical_harmonics.py for
                        # L=1:y L=2:z; L=3:x
                        ma1 += np.array([Delta_pL[ij, 3], Delta_pL[ij, 1],
                                         Delta_pL[ij, 2]]) * pij
            ma += np.sqrt(4 * np.pi / 3) * ma1 + Ra * np.sqrt(4 * np.pi) * ma0
        gd.comm.sum(ma)

        self.me = np.sqrt(self.energy * self.fij) * (me + ma)
        self.mur = - (me + ma)

        # velocity form .............................

        if self.lcao:
            self.wfi = _get_and_distribute_wf(wfs, iidx, kpt.k, pspin)
            self.wfj = _get_and_distribute_wf(wfs, jidx, kpt.k, pspin)

        me = np.zeros(self.mur.shape, dtype=dtype)

        # get derivatives
        dtype = self.wfj.dtype
        dwfj_cg = gd.empty((3), dtype=dtype)
        if not hasattr(gd, 'ddr'):
            gd.ddr = [Gradient(gd, c, dtype=dtype, n=2).apply
                      for c in range(3)]
        for c in range(3):
            gd.ddr[c](self.wfj, dwfj_cg[c], kpt.phase_cd)
            me[c] = gd.integrate(self.wfi.conj() * dwfj_cg[c])

        # XXX is this the best choice, maybe center of mass?
        origin = 0.5 * np.diag(paw.wfs.gd.cell_cv)

        # augmentation contributions

        # <psi_i|grad|psi_j>
        ma = np.zeros(me.shape, dtype=me.dtype)
        # Ra x <psi_i|grad|psi_j> for magnetic transition dipole
        mRa = np.zeros(me.shape, dtype=me.dtype)
        for a, P_ni in kpt.P_ani.items():
            Pi_i = P_ni[self.i].conj()
            Pj_i = P_ni[self.j]
            nabla_iiv = paw.wfs.setups[a].nabla_iiv
            ma_c = np.zeros(me.shape, dtype=me.dtype)
            for c in range(3):
                for i1, Pi in enumerate(Pi_i):
                    for i2, Pj in enumerate(Pj_i):
                        ma_c[c] += Pi * Pj * nabla_iiv[i1, i2, c]
            mRa += np.cross(paw.atoms[a].position / Bohr - origin, ma_c)
            ma += ma_c
        gd.comm.sum(ma)
        gd.comm.sum(mRa)

        self.muv = - (me + ma) / self.energy

        # magnetic transition dipole ................

        # m_ij = -(1/2c) <i|L|j> = i/2c <i|r x p|j>
        # see Autschbach et al., J. Chem. Phys., 116, 6930 (2002)

        r_cg, r2_g = coordinates(gd, origin=origin)
        magn = np.zeros(me.shape, dtype=dtype)

        # <psi_i|r x grad|psi_j>
        wfi_g = self.wfi.conj()
        for ci in range(3):
            cj = (ci + 1) % 3
            ck = (ci + 2) % 3
            magn[ci] = gd.integrate(wfi_g * r_cg[cj] * dwfj_cg[ck] -
                                    wfi_g * r_cg[ck] * dwfj_cg[cj])

        # augmentation contributions
        # <psi_i| r x nabla |psi_j>
        # = <psi_i| (r - Ra + Ra) x nabla |psi_j>
        # = <psi_i| (r - Ra) x nabla |psi_j> + Ra x <psi_i| nabla |psi_j>

        ma = np.zeros(magn.shape, dtype=magn.dtype)
        for a, P_ni in kpt.P_ani.items():
            Pi_i = P_ni[self.i].conj()
            Pj_i = P_ni[self.j]
            rxnabla_iiv = paw.wfs.setups[a].rxnabla_iiv
            for c in range(3):
                for i1, Pi in enumerate(Pi_i):
                    for i2, Pj in enumerate(Pj_i):
                        ma[c] += Pi * Pj * rxnabla_iiv[i1, i2, c]
        gd.comm.sum(ma)

        self.magn = alpha / 2. * (magn + ma + mRa)

    def distribute(self):
        """Distribute results to all cores."""
        self.spin = self.kpt_comm.sum(self.spin)
        self.pspin = self.kpt_comm.sum(self.pspin)
        self.k = self.kpt_comm.sum(self.k)
        self.weight = self.kpt_comm.sum(self.weight)
        self.energy = self.kpt_comm.sum(self.energy)
        self.fij = self.kpt_comm.sum(self.fij)

        self.kpt_comm.sum(self.me)
        self.kpt_comm.sum(self.mur)
        self.kpt_comm.sum(self.muv)
        self.kpt_comm.sum(self.magn)

    def __add__(self, other):
        """Add two KSSingles"""
        result = copy(self)
        result.me = self.me + other.me
        result.mur = self.mur + other.mur
        result.muv = self.muv + other.muv
        result.magn = self.magn + other.magn
        return result

    def __sub__(self, other):
        """Subtract two KSSingles"""
        result = copy(self)
        result.me = self.me - other.me
        result.mur = self.mur - other.mur
        result.muv = self.muv - other.muv
        result.magn = self.magn - other.magn
        return result

    def __rmul__(self, x):
        return self.__mul__(x)

    def __mul__(self, x):
        """Multiply a KSSingle with a number"""
        assert isinstance(x, (float, int))
        result = copy(self)
        result.me = self.me * x
        result.mur = self.mur * x
        result.muv = self.muv * x
        result.magn = self.magn * x
        return result

    def __truediv__(self, x):
        return self.__mul__(1. / x)

    __div__ = __truediv__

    def fromstring(self, string, dtype=float):
        l = string.split()
        self.i = int(l.pop(0))
        self.j = int(l.pop(0))
        self.pspin = int(l.pop(0))
        self.spin = int(l.pop(0))
        if dtype == float:
            self.k = 0
            self.weight = 1
        else:
            self.k = int(l.pop(0))
            self.weight = float(l.pop(0))
        self.energy = float(l.pop(0))
        self.fij = float(l.pop(0))
        self.mur = np.array([dtype(l.pop(0)) for i in range(3)])
        self.me = - self.mur * np.sqrt(self.energy * self.fij)
        self.muv = self.magn = None
        if len(l):
            self.muv = np.array([dtype(l.pop(0)) for i in range(3)])
        if len(l):
            self.magn = np.array([dtype(l.pop(0)) for i in range(3)])
        return None

    def outstring(self):
        if self.mur.dtype == float:
            string = '{0:d} {1:d}  {2:d} {3:d}  {4:.10g} {5:f}'.format(
                self.i, self.j, self.pspin, self.spin, self.energy, self.fij)
        else:
            string = (
                '{0:d} {1:d}  {2:d} {3:d} {4:d} {5:.10g}  {6:g} {7:g}'.format(
                    self.i, self.j, self.pspin, self.spin, self.k,
                    self.weight, self.energy, self.fij))
        string += '  '

        def format_me(me):
            string = ''
            if me.dtype == float:
                for m in me:
                    string += ' {0:.5e}'.format(m)
            else:
                for m in me:
                    string += ' {0.real:.5e}{0.imag:+.5e}j'.format(m)
            return string

        string += '  ' + format_me(self.mur)
        if self.muv is not None:
            string += '  ' + format_me(self.muv)
        if self.magn is not None:
            string += '  ' + format_me(self.magn)
        string += '\n'

        return string

    def __str__(self):
        string = '# <KSSingle> %d->%d %d(%d) eji=%g[eV]' % \
            (self.i, self.j, self.pspin, self.spin,
             self.energy * Hartree)
        if self.me.dtype == float:
            string += ' (%g,%g,%g)' % (self.me[0], self.me[1], self.me[2])
        else:
            string += ' kpt={0:d} w={1:g}'.format(self.k, self.weight)
            string += ' ('
            # use velocity form
            s = - np.sqrt(self.energy * self.fij)
            for c, m in enumerate(s * self.me):
                string += '{0.real:.5e}{0.imag:+.5e}j'.format(m)
                if c < 2:
                    string += ','
            string += ')'
        return string

    def __eq__(self, other):
        """KSSingles are considred equal when their indices are equal."""
        return (self.pspin == other.pspin and self.k == other.k and
                self.i == other.i and self.j == other.j)

    def __hash__(self):
        """Hash similar to __eq__"""
        if not hasattr(self, 'hash'):
            self.hash = hash((self.spin, self.k, self.i, self.j))
        return self.hash

    #
    # User interface: ##
    #

    def get_weight(self):
        return self.fij


def _get_and_distribute_wf(wfs, n, k, s):
    gd = wfs.gd
    wf = wfs.get_wave_function_array(n=n, k=k, s=s, realspace=True,
                                     periodic=False)
    if wfs.world.rank != 0:
        wf = gd.empty(dtype=wfs.dtype, global_array=True)
    wf = np.ascontiguousarray(wf)
    wfs.world.broadcast(wf, 0)
    wfd = gd.empty(dtype=wfs.dtype, global_array=False)
    wfd = gd.distribute(wf)
    return wfd
