import torch
from torch import Tensor
import torch.utils.data
import math
from collections import defaultdict
from typing import Tuple, NamedTuple, Optional
from torchani.units import sqrt_mhessian2invcm, sqrt_mhessian2milliev, mhessian2fconst
from .nn import SpeciesEnergies


def empty_list():
    return []


def stack_with_padding(properties, padding):
    output = defaultdict(empty_list)
    for p in properties:
        for k, v in p.items():
            output[k].append(torch.as_tensor(v))
    for k, v in output.items():
        if v[0].dim() == 0:
            output[k] = torch.stack(v)
        else:
            output[k] = torch.nn.utils.rnn.pad_sequence(v, True, padding[k])
    return output


def broadcast_first_dim(properties):
    num_molecule = 1
    for k, v in properties.items():
        shape = list(v.shape)
        n = shape[0]
        if num_molecule != 1:
            assert n == 1 or n == num_molecule, "unable to broadcast"
        else:
            num_molecule = n
    for k, v in properties.items():
        shape = list(v.shape)
        shape[0] = num_molecule
        properties[k] = v.expand(shape)
    return properties


def pad_atomic_properties(properties, padding_values=defaultdict(lambda: 0.0, species=-1)):
    """Put a sequence of atomic properties together into single tensor.

    Inputs are `[{'species': ..., ...}, {'species': ..., ...}, ...]` and the outputs
    are `{'species': padded_tensor, ...}`

    Arguments:
        properties (:class:`collections.abc.Sequence`): sequence of properties.
        padding_values (dict): the value to fill to pad tensors to same size
    """
    vectors = [k for k in properties[0].keys() if properties[0][k].dim() > 1]
    scalars = [k for k in properties[0].keys() if properties[0][k].dim() == 1]
    padded_sizes = {k: max(x[k].shape[1] for x in properties) for k in vectors}
    num_molecules = [x[vectors[0]].shape[0] for x in properties]
    total_num_molecules = sum(num_molecules)
    output = {}
    for k in scalars:
        output[k] = torch.stack([x[k] for x in properties])
    for k in vectors:
        tensor = properties[0][k]
        shape = list(tensor.shape)
        device = tensor.device
        dtype = tensor.dtype
        shape[0] = total_num_molecules
        shape[1] = padded_sizes[k]
        output[k] = torch.full(shape, padding_values[k], device=device, dtype=dtype)
        index0 = 0
        for n, x in zip(num_molecules, properties):
            original_size = x[k].shape[1]
            output[k][index0: index0 + n, 0: original_size, ...] = x[k]
            index0 += n
    return output


# @torch.jit.script
def present_species(species):
    """Given a vector of species of atoms, compute the unique species present.

    Arguments:
        species (:class:`torch.Tensor`): 1D vector of shape ``(atoms,)``

    Returns:
        :class:`torch.Tensor`: 1D vector storing present atom types sorted.
    """
    # present_species, _ = species.flatten()._unique(sorted=True)
    present_species = species.flatten().unique(sorted=True)
    if present_species[0].item() == -1:
        present_species = present_species[1:]
    return present_species


def strip_redundant_padding(atomic_properties):
    """Strip trailing padding atoms.

    Arguments:
        atomic_properties (dict): properties to strip

    Returns:
        dict: same set of properties with redundant padding atoms stripped.
    """
    species = atomic_properties['species']
    non_padding = (species >= 0).any(dim=0).nonzero().squeeze()
    for k in atomic_properties:
        atomic_properties[k] = atomic_properties[k].index_select(1, non_padding)
    return atomic_properties


def map2central(cell, coordinates, pbc):
    """Map atoms outside the unit cell into the cell using PBC.

    Arguments:
        cell (:class:`torch.Tensor`): tensor of shape (3, 3) of the three
            vectors defining unit cell:

            .. code-block:: python

                tensor([[x1, y1, z1],
                        [x2, y2, z2],
                        [x3, y3, z3]])

        coordinates (:class:`torch.Tensor`): Tensor of shape
            ``(molecules, atoms, 3)``.

        pbc (:class:`torch.Tensor`): boolean vector of size 3 storing
            if pbc is enabled for that direction.

    Returns:
        :class:`torch.Tensor`: coordinates of atoms mapped back to unit cell.
    """
    # Step 1: convert coordinates from standard cartesian coordinate to unit
    # cell coordinates
    inv_cell = torch.inverse(cell)
    coordinates_cell = torch.matmul(coordinates, inv_cell)
    # Step 2: wrap cell coordinates into [0, 1)
    coordinates_cell -= coordinates_cell.floor() * pbc
    # Step 3: convert from cell coordinates back to standard cartesian
    # coordinate
    return torch.matmul(coordinates_cell, cell)


class EnergyShifter(torch.nn.Module):
    """Helper class for adding and subtracting self atomic energies

    This is a subclass of :class:`torch.nn.Module`, so it can be used directly
    in a pipeline as ``[input->AEVComputer->ANIModel->EnergyShifter->output]``.

    Arguments:
        self_energies (:class:`collections.abc.Sequence`): Sequence of floating
            numbers for the self energy of each atom type. The numbers should
            be in order, i.e. ``self_energies[i]`` should be atom type ``i``.
        fit_intercept (bool): Whether to calculate the intercept during the LSTSQ
            fit. The intercept will also be taken into account to shift energies.
    """

    def __init__(self, self_energies, fit_intercept=False):
        super(EnergyShifter, self).__init__()

        self.fit_intercept = fit_intercept
        if self_energies is not None:
            self_energies = torch.tensor(self_energies, dtype=torch.double)

        self.register_buffer('self_energies', self_energies)

    def sae(self, species):
        """Compute self energies for molecules.

        Padding atoms will be automatically excluded.

        Arguments:
            species (:class:`torch.Tensor`): Long tensor in shape
                ``(conformations, atoms)``.

        Returns:
            :class:`torch.Tensor`: 1D vector in shape ``(conformations,)``
            for molecular self energies.
        """
        intercept = 0.0
        if self.fit_intercept:
            intercept = self.self_energies[-1]

        self_energies = self.self_energies[species]
        self_energies[species == torch.tensor(-1, device=species.device)] = torch.tensor(0, device=species.device, dtype=torch.double)
        return self_energies.sum(dim=1) + intercept

    def forward(self, species_energies: Tuple[Tensor, Tensor],
                cell: Optional[Tensor] = None,
                pbc: Optional[Tensor] = None) -> SpeciesEnergies:
        """(species, molecular energies)->(species, molecular energies + sae)
        """
        species, energies = species_energies
        sae = self.sae(species)
        return SpeciesEnergies(species, energies + sae)


class ChemicalSymbolsToInts:
    r"""Helper that can be called to convert chemical symbol string to integers

    On initialization the class should be supplied with a :class:`list` (or in
    general :class:`collections.abc.Sequence`) of :class:`str`. The returned
    instance is a callable object, which can be called with an arbitrary list
    of the supported species that is converted into a tensor of dtype
    :class:`torch.long`. Usage example:

    .. code-block:: python

       from torchani.utils import ChemicalSymbolsToInts


       # We initialize ChemicalSymbolsToInts with the supported species
       species_to_tensor = ChemicalSymbolsToInts(['H', 'C', 'Fe', 'Cl'])

       # We have a species list which we want to convert to an index tensor
       index_tensor = species_to_tensor(['H', 'C', 'H', 'H', 'C', 'Cl', 'Fe'])

       # index_tensor is now [0 1 0 0 1 3 2]


    .. warning::

        If the input is a string python will iterate over
        characters, this means that a string such as 'CHClFe' will be
        intepreted as 'C' 'H' 'C' 'l' 'F' 'e'. It is recommended that you
        input either a :class:`list` or a :class:`numpy.ndarray` ['C', 'H', 'Cl', 'Fe'],
        and not a string. The output of a call does NOT correspond to a
        tensor of atomic numbers.

    Arguments:
        all_species (:class:`collections.abc.Sequence` of :class:`str`):
            sequence of all supported species, in order.
    """

    def __init__(self, all_species):
        self.rev_species = {s: i for i, s in enumerate(all_species)}

    def __call__(self, species):
        r"""Convert species from sequence of strings to 1D tensor"""
        rev = [self.rev_species[s] for s in species]
        return torch.tensor(rev, dtype=torch.long)

    def __len__(self):
        return len(self.rev_species)


def _get_derivatives_not_none(x: Tensor, y: Tensor, retain_graph: Optional[bool] = None, create_graph: bool = False) -> Tensor:
    ret = torch.autograd.grad([y.sum()], [x], retain_graph=retain_graph, create_graph=create_graph)[0]
    assert ret is not None
    return ret


def hessian(coordinates: Tensor, energies: Optional[Tensor] = None, forces: Optional[Tensor] = None) -> Tensor:
    """Compute analytical hessian from the energy graph or force graph.

    Arguments:
        coordinates (:class:`torch.Tensor`): Tensor of shape `(molecules, atoms, 3)`
        energies (:class:`torch.Tensor`): Tensor of shape `(molecules,)`, if specified,
            then `forces` must be `None`. This energies must be computed from
            `coordinates` in a graph.
        forces (:class:`torch.Tensor`): Tensor of shape `(molecules, atoms, 3)`, if specified,
            then `energies` must be `None`. This forces must be computed from
            `coordinates` in a graph.

    Returns:
        :class:`torch.Tensor`: Tensor of shape `(molecules, 3A, 3A)` where A is the number of
        atoms in each molecule
    """
    if energies is None and forces is None:
        raise ValueError('Energies or forces must be specified')
    if energies is not None and forces is not None:
        raise ValueError('Energies or forces can not be specified at the same time')
    if forces is None:
        assert energies is not None
        forces = -_get_derivatives_not_none(coordinates, energies, create_graph=True)
    flattened_force = forces.flatten(start_dim=1)
    force_components = flattened_force.unbind(dim=1)
    return -torch.stack([
        _get_derivatives_not_none(coordinates, f, retain_graph=True).flatten(start_dim=1)
        for f in force_components
    ], dim=1)


class FreqsModes(NamedTuple):
    freqs: Tensor
    modes: Tensor


class VibAnalysis(NamedTuple):
    freqs: Tensor
    modes: Tensor
    fconstants: Tensor
    rmasses: Tensor


def vibrational_analysis(masses, hessian, mode_type='MDU', unit='cm^-1'):
    """Computing the vibrational wavenumbers from hessian.

    Note that normal modes in many popular software packages such as
    Gaussian and ORCA are output as mass deweighted normalized (MDN).
    Normal modes in ASE are output as mass deweighted unnormalized (MDU).
    Some packages such as Psi4 let ychoose different normalizations.
    Force constants and reduced masses are calculated as in Gaussian.

    mode_type should be one of:
    - MWN (mass weighted normalized)
    - MDU (mass deweighted unnormalized)
    - MDN (mass deweighted normalized)

    MDU modes are not orthogonal, and not normalized,
    MDN modes are not orthogonal, and normalized.
    MWN modes are orthonormal, but they correspond
    to mass weighted cartesian coordinates (x' = sqrt(m)x).
    """
    if unit == 'meV':
        unit_converter = sqrt_mhessian2milliev
    elif unit == 'cm^-1':
        unit_converter = sqrt_mhessian2invcm
    else:
        raise ValueError('Only meV and cm^-1 are supported right now')

    assert hessian.shape[0] == 1, 'Currently only supporting computing one molecule a time'
    # Solving the eigenvalue problem: Hq = w^2 * T q
    # where H is the Hessian matrix, q is the normal coordinates,
    # T = diag(m1, m1, m1, m2, m2, m2, ....) is the mass
    # We solve this eigenvalue problem through Lowdin diagnolization:
    # Hq = w^2 * Tq ==> Hq = w^2 * T^(1/2) T^(1/2) q
    # Letting q' = T^(1/2) q, we then have
    # T^(-1/2) H T^(-1/2) q' = w^2 * q'
    inv_sqrt_mass = (1 / masses.sqrt()).repeat_interleave(3, dim=1)  # shape (molecule, 3 * atoms)
    mass_scaled_hessian = hessian * inv_sqrt_mass.unsqueeze(1) * inv_sqrt_mass.unsqueeze(2)
    if mass_scaled_hessian.shape[0] != 1:
        raise ValueError('The input should contain only one molecule')
    mass_scaled_hessian = mass_scaled_hessian.squeeze(0)
    eigenvalues, eigenvectors = torch.symeig(mass_scaled_hessian, eigenvectors=True)
    angular_frequencies = eigenvalues.sqrt()
    frequencies = angular_frequencies / (2 * math.pi)
    # converting from sqrt(hartree / (amu * angstrom^2)) to cm^-1 or meV
    wavenumbers = unit_converter(frequencies)

    # Note that the normal modes are the COLUMNS of the eigenvectors matrix
    mw_normalized = eigenvectors.t()
    md_unnormalized = mw_normalized * inv_sqrt_mass
    norm_factors = 1 / torch.norm(md_unnormalized, dim=1)  # units are sqrt(AMU)
    md_normalized = md_unnormalized * norm_factors.unsqueeze(1)

    rmasses = norm_factors**2  # units are AMU
    # The conversion factor for Ha/(AMU*A^2) to mDyne/(A*AMU) is about 4.3597482
    fconstants = mhessian2fconst(eigenvalues) * rmasses  # units are mDyne/A

    if mode_type == 'MDN':
        modes = (md_normalized).reshape(frequencies.numel(), -1, 3)
    elif mode_type == 'MDU':
        modes = (md_unnormalized).reshape(frequencies.numel(), -1, 3)
    elif mode_type == 'MWN':
        modes = (mw_normalized).reshape(frequencies.numel(), -1, 3)

    return VibAnalysis(wavenumbers, modes, fconstants, rmasses)


def get_atomic_masses(species):
    r"""Convert a tensor of znumbers into a tensor of atomic masses

    Atomic masses supported are the first 119 elements, and are taken from:

    Atomic weights of the elements 2013 (IUPAC Technical Report). Meija, J.,
    Coplen, T., Berglund, M., et al. (2016). Pure and Applied Chemistry, 88(3), pp.
    265-291. Retrieved 30 Nov. 2016, from doi:10.1515/pac-2015-0305

    They are all consistent with those used in ASE

    Arguments:
        species (:class:`torch.Tensor`): tensor with atomic numbers

    Returns:
        :class:`torch.Tensor`: Tensor of dtype :class:`torch.double`, with
        atomic masses, with the same shape as the input.
    """
    # Note that there should not be any atoms with index zero, because that is
    # not an element
    assert len((species == 0).nonzero()) == 0
    default_atomic_masses = torch.tensor(
            [0.        ,   1.008     ,   4.002602  ,   6.94      , # noqa
             9.0121831 ,  10.81      ,  12.011     ,  14.007     , # noqa
            15.999     ,  18.99840316,  20.1797    ,  22.98976928, # noqa
            24.305     ,  26.9815385 ,  28.085     ,  30.973762  , # noqa
            32.06      ,  35.45      ,  39.948     ,  39.0983    , # noqa
            40.078     ,  44.955908  ,  47.867     ,  50.9415    , # noqa
            51.9961    ,  54.938044  ,  55.845     ,  58.933194  , # noqa
            58.6934    ,  63.546     ,  65.38      ,  69.723     , # noqa
            72.63      ,  74.921595  ,  78.971     ,  79.904     , # noqa
            83.798     ,  85.4678    ,  87.62      ,  88.90584   , # noqa
            91.224     ,  92.90637   ,  95.95      ,  97.90721   , # noqa
           101.07      , 102.9055    , 106.42      , 107.8682    , # noqa
           112.414     , 114.818     , 118.71      , 121.76      , # noqa
           127.6       , 126.90447   , 131.293     , 132.90545196, # noqa
           137.327     , 138.90547   , 140.116     , 140.90766   , # noqa
           144.242     , 144.91276   , 150.36      , 151.964     , # noqa
           157.25      , 158.92535   , 162.5       , 164.93033   , # noqa
           167.259     , 168.93422   , 173.054     , 174.9668    , # noqa
           178.49      , 180.94788   , 183.84      , 186.207     , # noqa
           190.23      , 192.217     , 195.084     , 196.966569  , # noqa
           200.592     , 204.38      , 207.2       , 208.9804    , # noqa
           208.98243   , 209.98715   , 222.01758   , 223.01974   , # noqa
           226.02541   , 227.02775   , 232.0377    , 231.03588   , # noqa
           238.02891   , 237.04817   , 244.06421   , 243.06138   , # noqa
           247.07035   , 247.07031   , 251.07959   , 252.083     , # noqa
           257.09511   , 258.09843   , 259.101     , 262.11      , # noqa
           267.122     , 268.126     , 271.134     , 270.133     , # noqa
           269.1338    , 278.156     , 281.165     , 281.166     , # noqa
           285.177     , 286.182     , 289.19      , 289.194     , # noqa
           293.204     , 293.208     , 294.214], # noqa
        dtype=torch.double, device=species.device) # noqa
    masses = default_atomic_masses[species]
    return masses


PERIODIC_TABLE = """
    H                                                                                                                           He
    Li  Be                                                                                                  B   C   N   O   F   Ne
    Na  Mg                                                                                                  Al  Si  P   S   Cl  Ar
    K   Ca  Sc                                                          Ti  V   Cr  Mn  Fe  Co  Ni  Cu  Zn  Ga  Ge  As  Se  Br  Kr
    Rb  Sr  Y                                                           Zr  Nb  Mo  Tc  Ru  Rh  Pd  Ag  Cd  In  Sn  Sb  Te  I   Xe
    Cs  Ba  La  Ce  Pr  Nd  Pm  Sm  Eu  Gd  Tb  Dy  Ho  Er  Tm  Yb  Lu  Hf  Ta  W   Re  Os  Ir  Pt  Au  Hg  Tl  Pb  Bi  Po  At  Rn
    Fr  Ra  Ac  Th  Pa  U   Np  Pu  Am  Cm  Bk  Cf  Es  Fm  Md  No  Lr  Rf  Db  Sg  Bh  Hs  Mt  Ds  Rg  Cn  Nh  Fl  Mc  Lv  Ts  Og
    """.strip().split()


__all__ = ['pad_atomic_properties', 'present_species', 'hessian',
           'vibrational_analysis', 'strip_redundant_padding',
           'ChemicalSymbolsToInts', 'get_atomic_masses']
