import torch
from torch import Tensor
import torch.utils.data
import math
import numpy as np
from collections import defaultdict
from typing import Tuple, NamedTuple, Optional
from .nn import SpeciesEnergies


def pad(species):
    """Put different species together into single tensor.

    If the species are from molecules of different number of total atoms, then
    ghost atoms with atom type -1 will be added to make it fit into the same
    shape.

    Arguments:
        species (:class:`collections.abc.Sequence`): sequence of species.
            Species must be of shape ``(N, A)``, where ``N`` is the number of
            3D structures, ``A`` is the number of atoms.

    Returns:
        :class:`torch.Tensor`: species batched together.
    """
    max_atoms = max([s.shape[1] for s in species])
    padded_species = []
    for s in species:
        natoms = s.shape[1]
        if natoms < max_atoms:
            padding = torch.full((s.shape[0], max_atoms - natoms), -1,
                                 dtype=torch.long, device=s.device)
            s = torch.cat([s, padding], dim=1)
        padded_species.append(s)
    return torch.cat(padded_species)


def pad_atomic_properties(atomic_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:
        species_coordinates (:class:`collections.abc.Sequence`): sequence of
             atomic properties.
        padding_values (dict): the value to fill to pad tensors to same size
    """
    keys = list(atomic_properties[0])
    anykey = keys[0]
    max_atoms = max(x[anykey].shape[1] for x in atomic_properties)
    padded = {k: [] for k in keys}
    for p in atomic_properties:
        num_molecules = 1
        for v in p.values():
            assert num_molecules in {1, v.shape[0]}, 'Number of molecules in different atomic properties mismatch'
            if v.shape[0] != 1:
                num_molecules = v.shape[0]
        for k, v in p.items():
            shape = list(v.shape)
            padatoms = max_atoms - shape[1]
            shape[1] = padatoms
            padding = v.new_full(shape, padding_values[k])
            v = torch.cat([v, padding], dim=1)
            shape = list(v.shape)
            shape[0] = num_molecules
            v = v.expand(*shape)
            padded[k].append(v)
    return {k: torch.cat(v) for k, v in padded.items()}


# @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.to(coordinates_cell.dtype)
    # 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_from_dataset(self, atomic_properties, properties):
        """Compute atomic self energies from dataset.

        Least-squares solution to a linear equation is calculated to output
        ``self_energies`` when ``self_energies = None`` is passed to
        :class:`torchani.EnergyShifter`
        """
        species = atomic_properties['species']
        energies = properties['energies']
        present_species_ = present_species(species)
        X = (species.unsqueeze(-1) == present_species_).sum(dim=1).to(torch.double)
        # Concatenate a vector of ones to find fit intercept
        if self.fit_intercept:
            X = torch.cat((X, torch.ones(X.shape[0], 1).to(torch.double)), dim=-1)
        y = energies.unsqueeze(dim=-1)
        coeff_, _, _, _ = np.linalg.lstsq(X, y, rcond=None)
        return coeff_.squeeze(-1)

    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 subtract_from_dataset(self, atomic_properties, properties):
        """Transformer for :class:`torchani.data.BatchedANIDataset` that
        subtract self energies.
        """
        if self.self_energies is None:
            self_energies = self.sae_from_dataset(atomic_properties, properties)
            self.self_energies = torch.tensor(self_energies, dtype=torch.double)

        species = atomic_properties['species']
        energies = properties['energies']
        device = energies.device
        energies = energies.to(torch.double) - self.sae(species).to(device)
        properties['energies'] = energies
        return atomic_properties, properties

    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).to(energies.device)
        return SpeciesEnergies(species, energies.to(sae.dtype) + sae)


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

    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):
        """Convert species from squence 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 orthogonal but not normalized, MDN modes are normalized
    but not orthogonal. MWN modes are orthonormal, but they correspond
    to mass weighted cartesian coordinates (x' = sqrt(m)x).
    """
    if unit != 'cm^-1':
        raise ValueError('Only 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
    wavenumbers = frequencies * 17092

    # 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 4.3597482
    fconstants = eigenvalues * rmasses * 4.3597482  # 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)


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