# Copyright (C) 2010, Jesper Friis
# (see accompanying license files for details).
"""Definition of the Spacegroup class.

This module only depends on NumPy and the space group database.
"""

import os
import warnings
from functools import lru_cache, total_ordering
from types import SimpleNamespace
from typing import Union

import numpy as np

from ase.utils import deprecated

__all__ = ['Spacegroup']


class SpacegroupError(Exception):
    """Base exception for the spacegroup module."""


class SpacegroupNotFoundError(SpacegroupError):
    """Raised when given space group cannot be found in data base."""


class SpacegroupValueError(SpacegroupError):
    """Raised when arguments have invalid value."""


# Type alias
_SPACEGROUP = Union[int, str, 'Spacegroup']


@total_ordering
class Spacegroup:
    """A space group class.

    The instances of Spacegroup describes the symmetry operations for
    the given space group.

    Example:

    >>> from ase.spacegroup import Spacegroup
    >>>
    >>> sg = Spacegroup(225)
    >>> print('Space group', sg.no, sg.symbol)
    Space group 225 F m -3 m
    >>> sg.scaled_primitive_cell
    array([[ 0. ,  0.5,  0.5],
           [ 0.5,  0. ,  0.5],
           [ 0.5,  0.5,  0. ]])
    >>> sites, kinds = sg.equivalent_sites([[0,0,0]])
    >>> sites
    array([[ 0. ,  0. ,  0. ],
           [ 0. ,  0.5,  0.5],
           [ 0.5,  0. ,  0.5],
           [ 0.5,  0.5,  0. ]])
    """
    @property
    def no(self):
        """Space group number in International Tables of Crystallography."""
        return self._no

    @property
    def symbol(self):
        """Hermann-Mauguin (or international) symbol for the space group."""
        return self._symbol

    @property
    def setting(self):
        """Space group setting. Either one or two."""
        return self._setting

    @property
    def lattice(self):
        """Lattice type.

        P     primitive
        I     body centering, h+k+l=2n
        F     face centering, h,k,l all odd or even
        A,B,C single face centering, k+l=2n, h+l=2n, h+k=2n
        R     rhombohedral centering, -h+k+l=3n (obverse); h-k+l=3n (reverse)
        """
        return self._symbol[0]

    @property
    def centrosymmetric(self):
        """Whether a center of symmetry exists."""
        return self._centrosymmetric

    @property
    def scaled_primitive_cell(self):
        """Primitive cell in scaled coordinates.

        Matrix with the primitive vectors along the rows.
        """
        return self._scaled_primitive_cell

    @property
    def reciprocal_cell(self):
        """

        Tree Miller indices that span all kinematically non-forbidden
        reflections as a matrix with the Miller indices along the rows.
        """
        return self._reciprocal_cell

    @property
    def nsubtrans(self):
        """Number of cell-subtranslation vectors."""
        return len(self._subtrans)

    @property
    def nsymop(self):
        """Total number of symmetry operations."""
        scale = 2 if self.centrosymmetric else 1
        return scale * len(self._rotations) * len(self._subtrans)

    @property
    def subtrans(self):
        """Translations vectors belonging to cell-sub-translations."""
        return self._subtrans

    @property
    def rotations(self):
        """Symmetry rotation matrices.

        The invertions are not included for centrosymmetrical crystals.
        """
        return self._rotations

    @property
    def translations(self):
        """Symmetry translations.

        The invertions are not included for centrosymmetrical crystals.
        """
        return self._translations

    def __init__(self, spacegroup: _SPACEGROUP, setting=1, datafile=None):
        """Returns a new Spacegroup instance.

        Parameters:

        spacegroup : int | string | Spacegroup instance
            The space group number in International Tables of
            Crystallography or its Hermann-Mauguin symbol. E.g.
            spacegroup=225 and spacegroup='F m -3 m' are equivalent.
        setting : 1 | 2
            Some space groups have more than one setting. `setting`
            determines Which of these should be used.
        datafile : None | string
            Path to database file. If `None`, the the default database
            will be used.
        """
        if isinstance(spacegroup, Spacegroup):
            for k, v in spacegroup.__dict__.items():
                setattr(self, k, v)
            return
        if not datafile:
            datafile = get_datafile()
        namespace = _read_datafile(spacegroup, setting, datafile)
        self._no = namespace._no
        self._symbol = namespace._symbol
        self._setting = namespace._setting
        self._centrosymmetric = namespace._centrosymmetric
        self._scaled_primitive_cell = namespace._scaled_primitive_cell
        self._reciprocal_cell = namespace._reciprocal_cell
        self._subtrans = namespace._subtrans
        self._rotations = namespace._rotations
        self._translations = namespace._translations

    def __repr__(self):
        return 'Spacegroup(%d, setting=%d)' % (self.no, self.setting)

    def todict(self):
        return {'number': self.no, 'setting': self.setting}

    def __str__(self):
        """Return a string representation of the space group data in
        the same format as found the database."""
        retval = []
        # no, symbol
        retval.append('%-3d   %s\n' % (self.no, self.symbol))
        # setting
        retval.append('  setting %d\n' % (self.setting))
        # centrosymmetric
        retval.append('  centrosymmetric %d\n' % (self.centrosymmetric))
        # primitive vectors
        retval.append('  primitive vectors\n')
        for i in range(3):
            retval.append('   ')
            for j in range(3):
                retval.append(' %13.10f' % (self.scaled_primitive_cell[i, j]))
            retval.append('\n')
        # primitive reciprocal vectors
        retval.append('  reciprocal vectors\n')
        for i in range(3):
            retval.append('   ')
            for j in range(3):
                retval.append(' %3d' % (self.reciprocal_cell[i, j]))
            retval.append('\n')
        # sublattice
        retval.append('  %d subtranslations\n' % self.nsubtrans)
        for i in range(self.nsubtrans):
            retval.append('   ')
            for j in range(3):
                retval.append(' %13.10f' % (self.subtrans[i, j]))
            retval.append('\n')
        # symmetry operations
        nrot = len(self.rotations)
        retval.append('  %d symmetry operations (rot+trans)\n' % nrot)
        for i in range(nrot):
            retval.append(' ')
            for j in range(3):
                retval.append(' ')
                for k in range(3):
                    retval.append(' %2d' % (self.rotations[i, j, k]))
                retval.append('  ')
            for j in range(3):
                retval.append(' %13.10f' % self.translations[i, j])
            retval.append('\n')
        retval.append('\n')
        return ''.join(retval)

    def __eq__(self, other):
        return self.no == other.no and self.setting == other.setting

    def __ne__(self, other):
        return not self.__eq__(other)

    def __lt__(self, other):
        return self.no < other.no or (self.no == other.no
                                      and self.setting < other.setting)

    def __index__(self):
        return self.no

    __int__ = __index__

    def get_symop(self):
        """Returns all symmetry operations (including inversions and
        subtranslations) as a sequence of (rotation, translation)
        tuples."""
        symop = []
        parities = [1]
        if self.centrosymmetric:
            parities.append(-1)
        for parity in parities:
            for subtrans in self.subtrans:
                for rot, trans in zip(self.rotations, self.translations):
                    newtrans = np.mod(trans + subtrans, 1)
                    symop.append((parity * rot, newtrans))
        return symop

    def get_op(self):
        """Returns all symmetry operations (including inversions and
        subtranslations), but unlike get_symop(), they are returned as
        two ndarrays."""
        if self.centrosymmetric:
            rot = np.tile(np.vstack((self.rotations, -self.rotations)),
                          (self.nsubtrans, 1, 1))
            trans = np.tile(np.vstack((self.translations, -self.translations)),
                            (self.nsubtrans, 1))
            trans += np.repeat(self.subtrans, 2 * len(self.rotations), axis=0)
            trans = np.mod(trans, 1)
        else:
            rot = np.tile(self.rotations, (self.nsubtrans, 1, 1))
            trans = np.tile(self.translations, (self.nsubtrans, 1))
            trans += np.repeat(self.subtrans, len(self.rotations), axis=0)
            trans = np.mod(trans, 1)
        return rot, trans

    def get_rotations(self):
        """Return all rotations, including inversions for
        centrosymmetric crystals."""
        if self.centrosymmetric:
            return np.vstack((self.rotations, -self.rotations))
        else:
            return self.rotations

    def equivalent_reflections(self, hkl):
        """Return all equivalent reflections to the list of Miller indices
        in hkl.

        Example:

        >>> from ase.spacegroup import Spacegroup
        >>> sg = Spacegroup(225)  # fcc
        >>> sg.equivalent_reflections([[0, 0, 2]])
        array([[ 0,  0, -2],
               [ 0, -2,  0],
               [-2,  0,  0],
               [ 2,  0,  0],
               [ 0,  2,  0],
               [ 0,  0,  2]])
        """
        hkl = np.array(hkl, dtype='int', ndmin=2)
        rot = self.get_rotations()
        n, nrot = len(hkl), len(rot)
        R = rot.transpose(0, 2, 1).reshape((3 * nrot, 3)).T
        refl = np.dot(hkl, R).reshape((n * nrot, 3))
        ind = np.lexsort(refl.T)
        refl = refl[ind]
        diff = np.diff(refl, axis=0)
        mask = np.any(diff, axis=1)
        return np.vstack((refl[:-1][mask], refl[-1, :]))

    def equivalent_lattice_points(self, uvw):
        """Return all lattice points equivalent to any of the lattice points
        in `uvw` with respect to rotations only.

        Only equivalent lattice points that conserves the distance to
        origo are included in the output (making this a kind of real
        space version of the equivalent_reflections() method).

        Example:

        >>> from ase.spacegroup import Spacegroup
        >>> sg = Spacegroup(225)  # fcc
        >>> sg.equivalent_lattice_points([[0, 0, 2]])
        array([[ 0,  0, -2],
               [ 0, -2,  0],
               [-2,  0,  0],
               [ 2,  0,  0],
               [ 0,  2,  0],
               [ 0,  0,  2]])

        """
        uvw = np.array(uvw, ndmin=2)
        rot = self.get_rotations()
        n, nrot = len(uvw), len(rot)
        directions = np.dot(uvw, rot).reshape((n * nrot, 3))
        ind = np.lexsort(directions.T)
        directions = directions[ind]
        diff = np.diff(directions, axis=0)
        mask = np.any(diff, axis=1)
        return np.vstack((directions[:-1][mask], directions[-1:]))

    def symmetry_normalised_reflections(self, hkl):
        """Returns an array of same size as *hkl*, containing the
        corresponding symmetry-equivalent reflections of lowest
        indices.

        Example:

        >>> from ase.spacegroup import Spacegroup
        >>> sg = Spacegroup(225)  # fcc
        >>> sg.symmetry_normalised_reflections([[2, 0, 0], [0, 2, 0]])
        array([[ 0,  0, -2],
               [ 0,  0, -2]])
        """
        hkl = np.array(hkl, dtype=int, ndmin=2)
        normalised = np.empty(hkl.shape, int)
        R = self.get_rotations().transpose(0, 2, 1)
        for i, g in enumerate(hkl):
            gsym = np.dot(R, g)
            j = np.lexsort(gsym.T)[0]
            normalised[i, :] = gsym[j]
        return normalised

    def unique_reflections(self, hkl):
        """Returns a subset *hkl* containing only the symmetry-unique
        reflections.

        Example:

        >>> from ase.spacegroup import Spacegroup
        >>> sg = Spacegroup(225)  # fcc
        >>> sg.unique_reflections([[ 2,  0,  0],
        ...                        [ 0, -2,  0],
        ...                        [ 2,  2,  0],
        ...                        [ 0, -2, -2]])
        array([[2, 0, 0],
               [2, 2, 0]])
        """
        hkl = np.array(hkl, dtype=int, ndmin=2)
        hklnorm = self.symmetry_normalised_reflections(hkl)
        perm = np.lexsort(hklnorm.T)
        iperm = perm.argsort()
        xmask = np.abs(np.diff(hklnorm[perm], axis=0)).any(axis=1)
        mask = np.concatenate(([True], xmask))
        imask = mask[iperm]
        return hkl[imask]

    def equivalent_sites(self,
                         scaled_positions,
                         onduplicates='error',
                         symprec=1e-3,
                         occupancies=None):
        """Returns the scaled positions and all their equivalent sites.

        Parameters:

        scaled_positions: list | array
            List of non-equivalent sites given in unit cell coordinates.

        occupancies: list | array, optional (default=None)
            List of occupancies corresponding to the respective sites.

        onduplicates : 'keep' | 'replace' | 'warn' | 'error'
            Action if `scaled_positions` contain symmetry-equivalent
            positions of full occupancy:

            'keep'
               ignore additional symmetry-equivalent positions
            'replace'
                replace
            'warn'
                like 'keep', but issue an UserWarning
            'error'
                raises a SpacegroupValueError

        symprec: float
            Minimum "distance" betweed two sites in scaled coordinates
            before they are counted as the same site.

        Returns:

        sites: array
            A NumPy array of equivalent sites.
        kinds: list
            A list of integer indices specifying which input site is
            equivalent to the corresponding returned site.

        Example:

        >>> from ase.spacegroup import Spacegroup
        >>> sg = Spacegroup(225)  # fcc
        >>> sites, kinds = sg.equivalent_sites([[0, 0, 0], [0.5, 0.0, 0.0]])
        >>> sites
        array([[ 0. ,  0. ,  0. ],
               [ 0. ,  0.5,  0.5],
               [ 0.5,  0. ,  0.5],
               [ 0.5,  0.5,  0. ],
               [ 0.5,  0. ,  0. ],
               [ 0. ,  0.5,  0. ],
               [ 0. ,  0. ,  0.5],
               [ 0.5,  0.5,  0.5]])
        >>> kinds
        [0, 0, 0, 0, 1, 1, 1, 1]
        """
        if onduplicates not in ('keep', 'replace', 'warn', 'error'):
            raise SpacegroupValueError(
                'Argument "onduplicates" must be one of: '
                '"keep", "replace", "warn" or "error".'
            )

        scaled = np.array(scaled_positions, ndmin=2)
        rotations, translations = zip(*self.get_symop())
        rotations = np.array(rotations)
        translations = np.array(translations)

        def find_orbit(point: np.ndarray) -> np.ndarray:
            """Find crystallographic orbit of the given point."""
            candidates = ((rotations @ point) + translations % 1.0) % 1.0
            orbit = [candidates[0]]
            for member in candidates[1:]:
                diff = member - orbit
                diff -= np.rint(diff)
                if not np.any(np.all(np.abs(diff) < symprec, axis=1)):
                    orbit.append(member)
            return np.array(orbit)

        orbits = []
        for kind, pos in enumerate(scaled):
            for i, (kind0, positions0) in enumerate(orbits):
                diff = pos - positions0
                diff -= np.rint(diff)
                if np.any(np.all(np.abs(diff) < symprec, axis=1)):
                    if onduplicates == 'keep':
                        pass
                    elif onduplicates == 'replace':
                        orbits[i] = (kind, positions0)
                    elif onduplicates == 'warn':
                        warnings.warn(
                            'scaled_positions %d and %d are equivalent' %
                            (kind0, kind))
                    elif onduplicates == 'error':
                        raise SpacegroupValueError(
                            'scaled_positions %d and %d are equivalent' %
                            (kind0, kind))
                    break
            else:
                orbits.append((kind, find_orbit(pos)))

        kinds = []
        sites = []
        for kind, orbit in orbits:
            kinds.extend(len(orbit) * [kind])
            sites.append(orbit)

        return np.concatenate(sites, axis=0), kinds

    def symmetry_normalised_sites(self,
                                  scaled_positions,
                                  map_to_unitcell=True):
        """Returns an array of same size as *scaled_positions*,
        containing the corresponding symmetry-equivalent sites of
        lowest indices.

        If *map_to_unitcell* is true, the returned positions are all
        mapped into the unit cell, i.e. lattice translations are
        included as symmetry operator.

        Example:

        >>> from ase.spacegroup import Spacegroup
        >>> sg = Spacegroup(225)  # fcc
        >>> sg.symmetry_normalised_sites([[0.0, 0.5, 0.5], [1.0, 1.0, 0.0]])
        array([[ 0.,  0.,  0.],
               [ 0.,  0.,  0.]])
        """
        scaled = np.array(scaled_positions, ndmin=2)
        normalised = np.empty(scaled.shape, float)
        rot, trans = self.get_op()
        for i, pos in enumerate(scaled):
            sympos = np.dot(rot, pos) + trans
            if map_to_unitcell:
                # Must be done twice, see the scaled_positions.py test
                sympos %= 1.0
                sympos %= 1.0
            j = np.lexsort(sympos.T)[0]
            normalised[i, :] = sympos[j]
        return normalised

    def unique_sites(self,
                     scaled_positions,
                     symprec=1e-3,
                     output_mask=False,
                     map_to_unitcell=True):
        """Returns a subset of *scaled_positions* containing only the
        symmetry-unique positions.  If *output_mask* is True, a boolean
        array masking the subset is also returned.

        If *map_to_unitcell* is true, all sites are first mapped into
        the unit cell making e.g. [0, 0, 0] and [1, 0, 0] equivalent.

        Example:

        >>> from ase.spacegroup import Spacegroup
        >>> sg = Spacegroup(225)  # fcc
        >>> sg.unique_sites([[0.0, 0.0, 0.0],
        ...                  [0.5, 0.5, 0.0],
        ...                  [1.0, 0.0, 0.0],
        ...                  [0.5, 0.0, 0.0]])
        array([[ 0. ,  0. ,  0. ],
               [ 0.5,  0. ,  0. ]])
        """
        scaled = np.array(scaled_positions, ndmin=2)
        symnorm = self.symmetry_normalised_sites(scaled, map_to_unitcell)
        perm = np.lexsort(symnorm.T)
        iperm = perm.argsort()
        xmask = np.abs(np.diff(symnorm[perm], axis=0)).max(axis=1) > symprec
        mask = np.concatenate(([True], xmask))
        imask = mask[iperm]
        if output_mask:
            return scaled[imask], imask
        else:
            return scaled[imask]

    def tag_sites(self, scaled_positions, symprec=1e-3):
        """Returns an integer array of the same length as *scaled_positions*,
        tagging all equivalent atoms with the same index.

        Example:

        >>> from ase.spacegroup import Spacegroup
        >>> sg = Spacegroup(225)  # fcc
        >>> sg.tag_sites([[0.0, 0.0, 0.0],
        ...               [0.5, 0.5, 0.0],
        ...               [1.0, 0.0, 0.0],
        ...               [0.5, 0.0, 0.0]])
        array([0, 0, 0, 1])
        """
        scaled = np.array(scaled_positions, ndmin=2)
        scaled %= 1.0
        scaled %= 1.0
        tags = -np.ones((len(scaled), ), dtype=int)
        mask = np.ones((len(scaled), ), dtype=bool)
        rot, trans = self.get_op()
        i = 0
        while mask.any():
            pos = scaled[mask][0]
            sympos = np.dot(rot, pos) + trans
            # Must be done twice, see the scaled_positions.py test
            sympos %= 1.0
            sympos %= 1.0
            m = ~np.all(np.any(np.abs(scaled[np.newaxis, :, :] -
                                      sympos[:, np.newaxis, :]) > symprec,
                               axis=2),
                        axis=0)
            assert not np.any((~mask) & m)
            tags[m] = i
            mask &= ~m
            i += 1
        return tags


def get_datafile():
    """Return default path to datafile."""
    return os.path.join(os.path.dirname(__file__), 'spacegroup.dat')


def format_symbol(symbol):
    """Returns well formatted Hermann-Mauguin symbol as extected by
    the database, by correcting the case and adding missing or
    removing dublicated spaces."""
    fixed = []
    s = symbol.strip()
    s = s[0].upper() + s[1:].lower()
    for c in s:
        if c.isalpha():
            if len(fixed) and fixed[-1] == '/':
                fixed.append(c)
            else:
                fixed.append(' ' + c + ' ')
        elif c.isspace():
            fixed.append(' ')
        elif c.isdigit():
            fixed.append(c)
        elif c == '-':
            fixed.append(' ' + c)
        elif c == '/':
            fixed.append(c)
    s = ''.join(fixed).strip()
    return ' '.join(s.split())


# Functions for parsing the database. They are moved outside the
# Spacegroup class in order to make it easier to later implement
# caching to avoid reading the database each time a new Spacegroup
# instance is created.


def _skip_to_blank(f, spacegroup, setting):
    """Read lines from f until a blank line is encountered."""
    while True:
        line = f.readline()
        if not line:
            raise SpacegroupNotFoundError(
                f'invalid spacegroup `{spacegroup}`, setting `{setting}` not '
                'found in data base')
        if not line.strip():
            break


def _skip_to_nonblank(f, spacegroup, setting):
    """Read lines from f until a nonblank line not starting with a
    hash (#) is encountered and returns this and the next line."""
    while True:
        line1 = f.readline()
        if not line1:
            raise SpacegroupNotFoundError(
                'invalid spacegroup %s, setting %i not found in data base' %
                (spacegroup, setting))
        line1.strip()
        if line1 and not line1.startswith('#'):
            line2 = f.readline()
            break
    return line1, line2


def _read_datafile_entry(spg, no, symbol, setting, f):
    """Read space group data from f to spg."""

    floats = {'0.0': 0.0, '1.0': 1.0, '0': 0.0, '1': 1.0, '-1': -1.0}
    for n, d in [(1, 2), (1, 3), (2, 3), (1, 4), (3, 4), (1, 6), (5, 6)]:
        floats[f'{n}/{d}'] = n / d
        floats[f'-{n}/{d}'] = -n / d

    spg._no = no
    spg._symbol = symbol.strip()
    spg._setting = setting
    spg._centrosymmetric = bool(int(f.readline().split()[1]))
    # primitive vectors
    f.readline()
    spg._scaled_primitive_cell = np.array(
        [
            [float(floats.get(s, s)) for s in f.readline().split()]
            for _ in range(3)
        ],
        dtype=float,
    )
    # primitive reciprocal vectors
    f.readline()
    spg._reciprocal_cell = np.array([[int(i) for i in f.readline().split()]
                                     for i in range(3)],
                                    dtype=int)
    # subtranslations
    nsubtrans = int(f.readline().split()[0])
    spg._subtrans = np.array(
        [
            [float(floats.get(t, t)) for t in f.readline().split()]
            for _ in range(nsubtrans)
        ],
        dtype=float,
    )
    # symmetry operations
    nsym = int(f.readline().split()[0])
    symop = np.array(
        [
            [float(floats.get(s, s)) for s in f.readline().split()]
            for _ in range(nsym)
        ],
        dtype=float,
    )
    spg._rotations = np.array(symop[:, :9].reshape((nsym, 3, 3)), dtype=int)
    spg._translations = symop[:, 9:]


@lru_cache
def _read_datafile(spacegroup, setting, datafile):
    with open(datafile, encoding='utf-8') as fd:
        return _read_f(spacegroup, setting, fd)


def _read_f(spacegroup, setting, f):
    if isinstance(spacegroup, int):
        pass
    elif isinstance(spacegroup, str):
        spacegroup = ' '.join(spacegroup.strip().split())
        compact_spacegroup = ''.join(spacegroup.split())
    else:
        raise SpacegroupValueError('`spacegroup` must be of type int or str')
    while True:
        line1, line2 = _skip_to_nonblank(f, spacegroup, setting)
        _no, _symbol = line1.strip().split(None, 1)
        _symbol = format_symbol(_symbol)
        compact_symbol = ''.join(_symbol.split())
        _setting = int(line2.strip().split()[1])
        _no = int(_no)

        condition = (
            (isinstance(spacegroup, int) and _no == spacegroup
             and _setting == setting)
            or (isinstance(spacegroup, str)
                and compact_symbol == compact_spacegroup) and
            (setting is None or _setting == setting))

        if condition:
            namespace = SimpleNamespace()
            _read_datafile_entry(namespace, _no, _symbol, _setting, f)
            return namespace
        else:
            _skip_to_blank(f, spacegroup, setting)


def parse_sitesym_element(element):
    """Parses one element from a single site symmetry in the form used
    by the International Tables.

    Examples:

    >>> parse_sitesym_element("x")
    ([(0, 1)], 0.0)
    >>> parse_sitesym_element("-1/2-y")
    ([(1, -1)], -0.5)
    >>> parse_sitesym_element("z+0.25")
    ([(2, 1)], 0.25)
    >>> parse_sitesym_element("x-z+0.5")
    ([(0, 1), (2, -1)], 0.5)



    Parameters
    ----------

    element: str
      Site symmetry like "x" or "-y+1/4" or "0.5+z".


    Returns
    -------

    list[tuple[int, int]]
      Rotation information in the form '(index, sign)' where index is
      0 for "x", 1 for "y" and 2 for "z" and sign is '1' for a positive
      entry and '-1' for a negative entry. E.g. "x" is '(0, 1)' and
      "-z" is (2, -1).

    float
      Translation information in fractional space. E.g. "-1/4" is
      '-0.25' and "1/2" is '0.5' and "0.75" is '0.75'.


    """
    element = element.lower()
    is_positive = True
    is_frac = False
    sng_trans = None
    fst_trans = []
    snd_trans = []
    rot = []

    for char in element:
        if char == "+":
            is_positive = True
        elif char == "-":
            is_positive = False
        elif char == "/":
            is_frac = True
        elif char in "xyz":
            rot.append((ord(char) - ord("x"), 1 if is_positive else -1))
        elif char.isdigit() or char == ".":
            if sng_trans is None:
                sng_trans = 1.0 if is_positive else -1.0
            if is_frac:
                snd_trans.append(char)
            else:
                fst_trans.append(char)

    trans = 0.0 if not fst_trans else (sng_trans * float("".join(fst_trans)))
    if is_frac:
        trans /= float("".join(snd_trans))

    return rot, trans


def parse_sitesym_single(sym, out_rot, out_trans, sep=",",
                         force_positive_translation=False):
    """Parses a single site symmetry in the form used by International
    Tables and overwrites 'out_rot' and 'out_trans' with data.

    Parameters
    ----------

    sym: str
      Site symmetry in the form used by International Tables
      (e.g. "x,y,z", "y-1/2,x,-z").

    out_rot: np.array
      A 3x3-integer array representing rotations (changes are made inplace).

    out_rot: np.array
      A 3-float array representing translations (changes are made inplace).

    sep: str
      String separator ("," in "x,y,z").

    force_positive_translation: bool
      Forces fractional translations to be between 0 and 1 (otherwise
      negative values might be accepted). Defaults to 'False'.


    Returns
    -------

    Nothing is returned: 'out_rot' and 'out_trans' are changed inplace.


    """
    out_rot[:] = 0.0
    out_trans[:] = 0.0

    for i, element in enumerate(sym.split(sep)):
        e_rot_list, e_trans = parse_sitesym_element(element)
        for rot_idx, rot_sgn in e_rot_list:
            out_rot[i][rot_idx] = rot_sgn
        out_trans[i] = \
            (e_trans % 1.0) if force_positive_translation else e_trans


def parse_sitesym(symlist, sep=',', force_positive_translation=False):
    """Parses a sequence of site symmetries in the form used by
    International Tables and returns corresponding rotation and
    translation arrays.

    Example:

    >>> symlist = [
    ...     'x,y,z',
    ...     '-y+1/2,x+1/2,z',
    ...     '-y,-x,-z',
    ...     'x-1/4, y-1/4, -z'
    ... ]
    >>> rot, trans = parse_sitesym(symlist)
    >>> rot
    array([[[ 1,  0,  0],
            [ 0,  1,  0],
            [ 0,  0,  1]],
    <BLANKLINE>
           [[ 0, -1,  0],
            [ 1,  0,  0],
            [ 0,  0,  1]],
    <BLANKLINE>
           [[ 0, -1,  0],
            [-1,  0,  0],
            [ 0,  0, -1]],
    <BLANKLINE>
           [[ 1,  0,  0],
            [ 0,  1,  0],
            [ 0,  0, -1]]])
    >>> trans
    array([[ 0.  ,  0.  ,  0.  ],
           [ 0.5 ,  0.5 ,  0.  ],
           [ 0.  ,  0.  ,  0.  ],
           [-0.25, -0.25,  0.  ]])
    """

    nsym = len(symlist)
    rot = np.zeros((nsym, 3, 3), dtype='int')
    trans = np.zeros((nsym, 3))

    for i, sym in enumerate(symlist):
        parse_sitesym_single(
            sym, rot[i], trans[i], sep=sep,
            force_positive_translation=force_positive_translation)

    return rot, trans


def spacegroup_from_data(no=None,
                         symbol=None,
                         setting=None,
                         centrosymmetric=None,
                         scaled_primitive_cell=None,
                         reciprocal_cell=None,
                         subtrans=None,
                         sitesym=None,
                         rotations=None,
                         translations=None,
                         datafile=None):
    """Manually create a new space group instance.  This might be
    useful when reading crystal data with its own spacegroup
    definitions."""
    if no is not None and setting is not None:
        spg = Spacegroup(no, setting, datafile)
    elif symbol is not None:
        spg = Spacegroup(symbol, None, datafile)
    else:
        raise SpacegroupValueError('either *no* and *setting* '
                                   'or *symbol* must be given')
    if not isinstance(sitesym, list):
        raise TypeError('sitesym must be a list')

    have_sym = False
    if centrosymmetric is not None:
        spg._centrosymmetric = bool(centrosymmetric)
    if scaled_primitive_cell is not None:
        spg._scaled_primitive_cell = np.array(scaled_primitive_cell)
    if reciprocal_cell is not None:
        spg._reciprocal_cell = np.array(reciprocal_cell)
    if subtrans is not None:
        spg._subtrans = np.atleast_2d(subtrans)
    if sitesym is not None:
        spg._rotations, spg._translations = parse_sitesym(sitesym)
        have_sym = True
    if rotations is not None:
        spg._rotations = np.atleast_3d(rotations)
        have_sym = True
    if translations is not None:
        spg._translations = np.atleast_2d(translations)
        have_sym = True
    if have_sym:
        if spg._rotations.shape[0] != spg._translations.shape[0]:
            raise SpacegroupValueError('inconsistent number of rotations and '
                                       'translations')
    return spg


@deprecated(
    '`get_spacegroup` has been deprecated due to its misleading output. '
    'The returned `Spacegroup` object has symmetry operations for a '
    'standard setting regardress of the given `Atoms` object. '
    'See https://gitlab.com/ase/ase/-/issues/1534 for details. '
    'Please use `ase.spacegroup.symmetrize.check_symmetry` or `spglib` '
    'directly to get the symmetry operations for the given `Atoms` object.'
)
def get_spacegroup(atoms, symprec=1e-5):
    """Determine the spacegroup to which belongs the Atoms object.

    This requires spglib: https://atztogo.github.io/spglib/ .

    .. warning::
        The returned ``Spacegroup`` object has symmetry operations for a
        standard setting regardless of the given ``Atoms`` object.
        See https://gitlab.com/ase/ase/-/issues/1534 for details.

    .. deprecated:: 3.24.0
        Please use ``ase.spacegroup.symmetrize.check_symmetry`` or ``spglib``
        directly to get the symmetry operations for the given ``Atoms`` object.

    Parameters:

    atoms: Atoms object
        Types, positions and unit-cell.
    symprec: float
        Symmetry tolerance, i.e. distance tolerance in Cartesian
        coordinates to find crystal symmetry.

    The Spacegroup object is returned.
    """

    # Example:
    # (We don't include the example in docstring to appease doctests
    #  when import fails)
    # >>> from ase.build import bulk
    # >>> atoms = bulk("Cu", "fcc", a=3.6, cubic=True)
    # >>> sg = get_spacegroup(atoms)
    # >>> sg
    # Spacegroup(225, setting=1)
    # >>> sg.no
    # 225

    import spglib

    sg = spglib.get_spacegroup((atoms.get_cell(), atoms.get_scaled_positions(),
                                atoms.get_atomic_numbers()),
                               symprec=symprec)
    if sg is None:
        raise RuntimeError('Spacegroup not found')
    sg_no = int(sg[sg.find('(') + 1:sg.find(')')])
    return Spacegroup(sg_no)