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# Source code for ase.ga.bulk_mutations

    """Mutation operations intended for bulk structures.
    If you find this implementation useful in your work,
    please consider citing:
        M. Van den Bossche, Henrik Gronbeck, B. Hammer,
        J. Chem. Theory Comput., doi:10.1021/acs.jctc.8b00039
    in addition to the papers mentioned in the docstrings."""
    import inspect
    import json
    import numpy as np
    from random import gauss
    from ase.data import covalent_radii
    from ase.neighborlist import NeighborList
    from ase.build import niggli_reduce
    from ase.ga.offspring_creator import OffspringCreator, CombinationMutation
    from ase.ga.utilities import (atoms_too_close, atoms_too_close_two_sets,
                                  gather_atoms_by_tag)
    from ase.ga.bulk_utilities import get_rotation_matrix
    from scipy.spatial.distance import cdist

    class StrainMutation(OffspringCreator):
        """ Mutates a candidate by applying a randomly generated strain.

        For more information, see also:

          * `Glass, Oganov, Hansen, Comp. Phys. Comm. 175 (2006) 713-720`__

            __ https://doi.org/10.1016/j.cpc.2006.07.020

          * `Lonie, Zurek, Comp. Phys. Comm. 182 (2011) 372-387`__

            __ https://doi.org/10.1016/j.cpc.2010.07.048

        After initialization of the mutation, a scaling volume
        (to which each mutated structure is scaled before checking the
        constraints) is typically generated from the population,
        which is then also occasionally updated in the course of the
        GA run.

        Parameters:

        blmin: dict
               The closest allowed interatomic distances on the form:
               {(Z, Z*): dist, ...}, where Z and Z* are atomic numbers.

        cellbounds: ase.ga.bulk_utilities.CellBounds instance
                    Describing limits on the cell shape, see
                    :class:`~ase.ga.bulk_utilities.CellBounds`.

        stddev: float
                Standard deviation used in the generation of the
                strain matrix elements.

        use_tags: boolean
                  Whether to use the atomic tags to preserve molecular identity.
        """

        def __init__(self, blmin, cellbounds=None, stddev=0.7, use_tags=False,
                     verbose=False):
            OffspringCreator.__init__(self, verbose)
            self.blmin = blmin
            self.cellbounds = cellbounds
            self.stddev = stddev
            self.use_tags = use_tags
            self.scaling_volume = None
            self.descriptor = 'StrainMutation'
            self.min_inputs = 1

        def update_scaling_volume(self, population, w_adapt=0.5, n_adapt=0):
            """Function to initialize or update the scaling volume in a GA run."""
            if not n_adapt:
                # if not set, take best 20% of the population
                n_adapt = int(round(0.2 * len(population)))
            v_new = np.mean([a.get_volume() for a in population[:n_adapt]])

            if not self.scaling_volume:
                self.scaling_volume = v_new
            else:
                volumes = [self.scaling_volume, v_new]
                weights = [1 - w_adapt, w_adapt]
                self.scaling_volume = np.average(volumes, weights=weights)

        def get_new_individual(self, parents):
            f = parents[0]

            indi = self.mutate(f)
            if indi is None:
                return indi, 'mutation: strain'

            indi = self.initialize_individual(f, indi)
            indi.info['data']['parents'] = [f.info['confid']]

            return self.finalize_individual(indi), 'mutation: strain'

        def mutate(self, atoms):
            """ Does the actual mutation. """
            cell_ref = atoms.get_cell()
            pos_ref = atoms.get_positions()
            vol = atoms.get_volume()
            if self.use_tags:
                tags = atoms.get_tags()
                gather_atoms_by_tag(atoms)
                pos = atoms.get_positions()

            mutant = atoms.copy()
            if self.cellbounds is not None:
                if not self.cellbounds.is_within_bounds(cell_ref):
                    niggli_reduce(mutant)

            count = 0
            too_close = True
            maxcount = 1000
            while too_close and count < maxcount:
                mutant.set_cell(cell_ref, scale_atoms=False)
                mutant.set_positions(pos_ref)

                # generating the strain matrix:
                strain = np.identity(3)
                for i in range(3):
                    for j in range(i + 1):
                        if i == j:
                            strain[i, j] += gauss(0, self.stddev)
                        else:
                            epsilon = 0.5 * gauss(0, self.stddev)
                            strain[i, j] += epsilon
                            strain[j, i] += epsilon

                # applying the strain:
                cell_new = np.dot(strain, cell_ref)

                # volume scaling:
                v = abs(np.linalg.det(cell_new))
                if self.scaling_volume is None:
                    cell_new *= (vol / v)**(1. / 3)
                else:
                    cell_new *= (self.scaling_volume / v)**(1. / 3)

                # check cell dimensions:
                if not self.cellbounds.is_within_bounds(cell_new):
                    continue

                if self.use_tags:
                    transfo = np.linalg.solve(cell_ref, cell_new)
                    for tag in np.unique(tags):
                        select = np.where(tags == tag)
                        cop = np.mean(pos[select], axis=0)
                        disp = np.dot(cop, transfo) - cop
                        mutant.positions[select] += disp

                mutant.set_cell(cell_new, scale_atoms=not self.use_tags)

                # check distances:
                too_close = atoms_too_close(mutant, self.blmin,
                                            use_tags=self.use_tags)
                count += 1

            if count == maxcount:
                mutant = None

            return mutant

    class PermuStrainMutation(CombinationMutation):
        """ Combination of PermutationMutation and StrainMutation.

        For more information, see also:

          * `Lonie, Zurek, Comp. Phys. Comm. 182 (2011) 372-387`__

            __ https://doi.org/10.1016/j.cpc.2010.07.048

        Parameters:

        permutationmutation: OffspringCreator instance
                             A mutation that permutes atom types.

        strainmutation: OffspringCreator instance
                        A mutation that mutates by straining.
        """

        def __init__(self, permutationmutation, strainmutation, verbose=False):
            super(PermuStrainMutation, self).__init__(permutationmutation,
                                                      strainmutation,
                                                      verbose=verbose)
            self.descriptor = 'permustrain'

    class TagFilter:
        ''' Filter which constrains same-tag atoms to behave
            like internally rigid moieties '''

        def __init__(self, atoms):
            self.atoms = atoms
            gather_atoms_by_tag(self.atoms)
            self.tags = self.atoms.get_tags()
            self.unique_tags = np.unique(self.tags)
            self.n = len(self.unique_tags)

        def get_positions(self):
            all_pos = self.atoms.get_positions()
            cop_pos = np.zeros((self.n, 3))
            for i in range(self.n):
                indices = np.where(self.tags == self.unique_tags[i])
                cop_pos[i] = np.average(all_pos[indices], axis=0)
            return cop_pos

        def set_positions(self, positions, **kwargs):
            cop_pos = self.get_positions()
            all_pos = self.atoms.get_positions()
            assert np.all(np.shape(positions) == np.shape(cop_pos))
            for i in range(self.n):
                indices = np.where(self.tags == self.unique_tags[i])
                shift = positions[i] - cop_pos[i]
                all_pos[indices] += shift
            self.atoms.set_positions(all_pos, **kwargs)

        def get_forces(self, *args, **kwargs):
            f = self.atoms.get_forces()
            forces = np.zeros((self.n, 3))
            for i in range(self.n):
                indices = np.where(self.tags == self.unique_tags[i])
                forces[i] = np.sum(f[indices], axis=0)
            return forces

        def get_masses(self):
            m = self.atoms.get_masses()
            masses = np.zeros(self.n)
            for i in range(self.n):
                indices = np.where(self.tags == self.unique_tags[i])
                masses[i] = np.sum(m[indices])
            return masses

        def __len__(self):
            return self.n

    class PairwiseHarmonicPotential:
        """ Parent class for interatomic potentials of the type
            E(r_ij) = 0.5 * k_ij * (r_ij - r0_ij) ** 2 """

        def __init__(self, atoms, rcut=10.):
            self.atoms = atoms
            self.pos0 = atoms.get_positions()
            self.rcut = rcut

            # build neighborlist
            nat = len(self.atoms)
            self.nl = NeighborList([self.rcut / 2.] * nat, skin=0., bothways=True,
                                   self_interaction=False)
            self.nl.update(self.atoms)

            self.calculate_force_constants()

        def calculate_force_constants(self):
            msg = 'Child class needs to define a calculate_force_constants() ' \
                  'method which computes the force constants and stores them ' \
                  'in self.force_constants (as a list which contains, for every ' \
                  'atom, a list of the atom\'s force constants with its neighbors.'
            raise NotImplementedError(msg)

        def get_forces(self, atoms):
            pos = atoms.get_positions()
            cell = atoms.get_cell()
            forces = np.zeros_like(pos)

            for i, p in enumerate(pos):
                indices, offsets = self.nl.get_neighbors(i)
                p = pos[indices] + np.dot(offsets, cell)
                r = cdist(p, [pos[i]])
                v = (p - pos[i]) / r
                p0 = self.pos0[indices] + np.dot(offsets, cell)
                r0 = cdist(p0, [self.pos0[i]])
                dr = r - r0
                forces[i] = np.dot(self.force_constants[i].T, dr * v)

            return forces

    def get_number_of_valence_electrons(Z):
        """ Return the number of valence electrons for the element with
            atomic number Z, simply based on its periodic table group """
        groups = [[], [1, 3, 11, 19, 37, 55, 87], [2, 4, 12, 20, 38, 56, 88],
                  [21, 39, 57, 89]]

        for i in range(9):
            groups.append(i + np.array([22, 40, 72, 104]))

        for i in range(6):
            groups.append(i + np.array([5, 13, 31, 49, 81, 113]))

        for i, group in enumerate(groups):
            if Z in group:
                nval = i if i < 13 else i - 10
                break
        else:
            raise ValueError('Z=%d not included in this dataset.' % Z)

        return nval

    class BondElectroNegativityModel(PairwiseHarmonicPotential):
        """ Pairwise harmonic potential where the force constants are
            determined using the "bond electronegativity" model, see:

          * `Lyakhov, Oganov, Valle, Comp. Phys. Comm. 181 (2010) 1623-1632`__

            __ https://dx.doi.org/10.1016/j.cpc.2010.06.007

          * `Lyakhov, Oganov, Phys. Rev. B 84 (2011) 092103`__

            __ https://dx.doi.org/10.1103/PhysRevB.84.092103

        """

        def calculate_force_constants(self):
            cell = self.atoms.get_cell()
            pos = self.atoms.get_positions()
            num = self.atoms.get_atomic_numbers()
            nat = len(self.atoms)
            nl = self.nl

            # computing the force constants
            s_norms = []
            valence_states = []
            r_cov = []
            for i in range(nat):
                indices, offsets = nl.get_neighbors(i)
                p = pos[indices] + np.dot(offsets, cell)
                r = cdist(p, [pos[i]])
                r_ci = covalent_radii[num[i]]
                s = 0.
                for j, index in enumerate(indices):
                    d = r[j] - r_ci - covalent_radii[num[index]]
                    s += np.exp(-d / 0.37)
                s_norms.append(s)
                valence_states.append(get_number_of_valence_electrons(num[i]))
                r_cov.append(r_ci)

            self.force_constants = []
            for i in range(nat):
                indices, offsets = nl.get_neighbors(i)
                p = pos[indices] + np.dot(offsets, cell)
                r = cdist(p, [pos[i]])[:, 0]
                fc = []
                for j, ii in enumerate(indices):
                    d = r[j] - r_cov[i] - r_cov[ii]
                    chi_ik = 0.481 * valence_states[i] / (r_cov[i] + 0.5 * d)
                    chi_jk = 0.481 * valence_states[ii] / (r_cov[ii] + 0.5 * d)
                    cn_ik = s_norms[i] / np.exp(-d / 0.37)
                    cn_jk = s_norms[ii] / np.exp(-d / 0.37)
                    fc.append(np.sqrt(chi_ik * chi_jk / (cn_ik * cn_jk)))
                self.force_constants.append(np.array(fc))

    class SoftMutation(OffspringCreator):
        """
        Mutates the structure by displacing it along the lowest (nonzero)
        frequency modes found by vibrational analysis, as in:

        * `Lyakhov, Oganov, Valle, Comp. Phys. Comm. 181 (2010) 1623-1632`__

          __ https://dx.doi.org/10.1016/j.cpc.2010.06.007

        As in the reference above, the next-lowest mode is used if the
        structure has already been softmutated along the current-lowest
        mode.

        Parameters:

        blmin: dict
               The closest allowed interatomic distances on the form:
               {(Z, Z*): dist, ...}, where Z and Z* are atomic numbers.

        bounds: list
                Lower and upper limits (in Angstrom) for the largest
                atomic displacement in the structure. For a given mode,
                the algorithm starts at zero amplitude and increases
                it until either blmin is violated or the largest
                displacement exceeds the provided upper bound).
                If the largest displacement in the resulting structure
                is lower than the provided lower bound, the mutant is
                considered too similar to the parent and None is
                returned.

        calculator: ASE calculator object
                    The calculator to be used in the vibrational
                    analysis. The default is to use a calculator
                    based on pairwise harmonic potentials with force
                    constants from the "bond electronegativity"
                    model described in the reference above.
                    Any calculator with a working :func:`get_forces()`
                    method will work.

        rcut: float
              Cutoff radius in Angstrom for the pairwise harmonic
              potentials.

        used_modes_file: str or None
                         Name of json dump file where previously used
                         modes will be stored (and read). If None,
                         no such file will be used. Default is to use
                         the filename 'used_modes.json'.

        use_tags: boolean
                  Whether to use the atomic tags to preserve molecular identity.
        """

        def __init__(self, blmin, bounds=[0.5, 2.0],
                     calculator=BondElectroNegativityModel, rcut=10.,
                     used_modes_file='used_modes.json', use_tags=False,
                     verbose=False):
            OffspringCreator.__init__(self, verbose)
            self.blmin = blmin
            self.bounds = bounds
            self.calc = calculator
            self.rcut = rcut
            self.used_modes_file = used_modes_file
            self.use_tags = use_tags
            self.descriptor = 'SoftMutation'

            self.used_modes = {}
            if self.used_modes_file is not None:
                try:
                    self.read_used_modes(self.used_modes_file)
                except IOError:
                    # file doesn't exist (yet)
                    pass

        def _get_hessian(self, atoms, dx):
            """
            Returns the Hessian matrix d2E/dxi/dxj using a first-order
            central difference scheme with displacements dx.
            """
            N = len(atoms)
            pos = atoms.get_positions()
            hessian = np.zeros((3 * N, 3 * N))

            for i in range(3 * N):
                row = np.zeros(3 * N)
                for direction in [-1, 1]:
                    disp = np.zeros(3)
                    disp[i % 3] = direction * dx
                    pos_disp = np.copy(pos)
                    pos_disp[i // 3] += disp
                    atoms.set_positions(pos_disp)
                    f = atoms.get_forces()
                    row += -1 * direction * f.flatten()

                row /= (2. * dx)
                hessian[i] = row

            hessian += np.copy(hessian).T
            hessian *= 0.5
            atoms.set_positions(pos)

            return hessian

        def _calculate_normal_modes(self, atoms, dx=0.02, massweighing=False):
            """Performs the vibrational analysis."""
            hessian = self._get_hessian(atoms, dx)
            if massweighing:
                m = np.array([np.repeat(atoms.get_masses()**-0.5, 3)])
                hessian *= (m * m.T)

            eigvals, eigvecs = np.linalg.eigh(hessian)
            modes = {eigval: eigvecs[:, i] for i, eigval in enumerate(eigvals)}
            return modes

        def animate_mode(self, atoms, mode, nim=30, amplitude=1.0):
            """Returns an Atoms object showing an animation of the mode."""
            pos = atoms.get_positions()
            mode = mode.reshape(np.shape(pos))
            animation = []
            for i in range(nim):
                newpos = pos + amplitude * mode * np.sin(i * 2 * np.pi / nim)
                image = atoms.copy()
                image.positions = newpos
                animation.append(image)
            return animation

        def read_used_modes(self, filename):
            """ Read used modes from json file. """
            with open(filename, 'r') as f:
                modes = json.load(f)
                self.used_modes = {int(k): modes[k] for k in modes}
            return

        def write_used_modes(self, filename):
            """ Dump used modes to json file. """
            with open(filename, 'w') as f:
                json.dump(self.used_modes, f)
            return

        def get_new_individual(self, parents):
            f = parents[0]

            indi = self.mutate(f)
            if indi is None:
                return indi, 'mutation: soft'

            indi = self.initialize_individual(f, indi)
            indi.info['data']['parents'] = [f.info['confid']]

            return self.finalize_individual(indi), 'mutation: soft'

        def mutate(self, atoms):
            """ Does the actual mutation. """
            a = atoms.copy()

            if inspect.isclass(self.calc):
                assert issubclass(self.calc, PairwiseHarmonicPotential)
                calc = self.calc(atoms, rcut=self.rcut)
            else:
                calc = self.calc
            a.set_calculator(calc)

            if self.use_tags:
                a = TagFilter(a)

            pos = a.get_positions()
            modes = self._calculate_normal_modes(a)

            # Select the mode along which we want to move the atoms;
            # The first 3 translational modes as well as previously
            # applied modes are discarded.

            keys = np.array(sorted(modes))
            index = 3
            confid = atoms.info['confid']
            if confid in self.used_modes:
                while index in self.used_modes[confid]:
                    index += 1
                self.used_modes[confid].append(index)
            else:
                self.used_modes[confid] = [index]

            if self.used_modes_file is not None:
                self.write_used_modes(self.used_modes_file)

            key = keys[index]
            mode = modes[key].reshape(np.shape(pos))

            # Find a suitable amplitude for translation along the mode;
            # at every trial amplitude both positive and negative
            # directions are tried.

            mutant = atoms.copy()
            amplitude = 0.
            increment = 0.1
            direction = 1
            largest_norm = np.max(np.apply_along_axis(np.linalg.norm, 1, mode))

            def expand(atoms, positions):
                if isinstance(atoms, TagFilter):
                    a.set_positions(positions)
                    return a.atoms.get_positions()
                else:
                    return positions

            while amplitude * largest_norm < self.bounds[1]:
                pos_new = pos + direction * amplitude * mode
                pos_new = expand(a, pos_new)
                mutant.set_positions(pos_new)
                mutant.wrap()
                too_close = atoms_too_close(mutant, self.blmin,
                                            use_tags=self.use_tags)
                if too_close:
                    amplitude -= increment
                    pos_new = pos + direction * amplitude * mode
                    pos_new = expand(a, pos_new)
                    mutant.set_positions(pos_new)
                    mutant.wrap()
                    break

                if direction == 1:
                    direction = -1
                else:
                    direction = 1
                    amplitude += increment

            if amplitude * largest_norm < self.bounds[0]:
                mutant = None

            return mutant

    class RotationalMutation(OffspringCreator):
        """ Mutates a candidate by applying random rotations
        to multi-atom moieties in the structure (atoms with
        the same tag are considered part of one such moiety).
        Only performs whole-molecule rotations, no internal
        rotations.

        For more information, see also:

          * `Zhu Q., Oganov A.R., Glass C.W., Stokes H.T,
            Acta Cryst. (2012), B68, 215-226.`__

            __ https://dx.doi.org/10.1107/S0108768112017466

        Parameters:

        blmin: dict
               The closest allowed interatomic distances on the form:
               {(Z, Z*): dist, ...}, where Z and Z* are atomic numbers.

        n_top: int or None
               The number of atoms to optimize (None = include all).

        fraction: float
                  Fraction of the moieties to be rotated.

        tags: None or list of integers
              Specifies, respectively, whether all moieties or only those
              with matching tags are eligible for rotation.

        min_angle: float
                   Minimal angle (in radians) for each rotation;
                   should lie in the interval [0, pi].

        test_dist_to_slab: boolean
                           Whether also the distances to the slab
                           should be checked to satisfy the blmin.
        """

        def __init__(self, blmin, n_top=None, fraction=0.33, tags=None,
                     min_angle=1.57, test_dist_to_slab=True, verbose=False):
            OffspringCreator.__init__(self, verbose)
            self.blmin = blmin
            self.n_top = n_top
            self.fraction = fraction
            self.tags = tags
            self.min_angle = min_angle
            self.test_dist_to_slab = test_dist_to_slab
            self.descriptor = 'RotationalMutation'
            self.min_inputs = 1

        def get_new_individual(self, parents):
            f = parents[0]

            indi = self.mutate(f)
            if indi is None:
                return indi, 'mutation: rotational'

            indi = self.initialize_individual(f, indi)
            indi.info['data']['parents'] = [f.info['confid']]

            return self.finalize_individual(indi), 'mutation: rotational'

        def mutate(self, atoms):
            """ Does the actual mutation. """
            N = len(atoms) if self.n_top is None else self.n_top
            slab = atoms[:len(atoms) - N]
            atoms = atoms[-N:]

            mutant = atoms.copy()
            gather_atoms_by_tag(mutant)
            pos = mutant.get_positions()
            tags = mutant.get_tags()
            eligible_tags = tags if self.tags is None else self.tags

            indices = {}
            for tag in np.unique(tags):
                hits = np.where(tags == tag)[0]
                if len(hits) > 1 and tag in eligible_tags:
                    indices[tag] = hits

            n_rot = int(np.ceil(len(indices) * self.fraction))
            chosen_tags = np.random.choice(list(indices.keys()), size=n_rot,
                                           replace=False)

            too_close = True
            count = 0
            maxcount = 10000
            while too_close and count < maxcount:
                newpos = np.copy(pos)
                for tag in chosen_tags:
                    p = np.copy(newpos[indices[tag]])
                    cop = np.mean(p, axis=0)

                    if len(p) == 2:
                        line = (p[1] - p[0]) / np.linalg.norm(p[1] - p[0])
                        while True:
                            axis = np.random.random(3)
                            axis /= np.linalg.norm(axis)
                            a = np.arccos(np.dot(axis, line))
                            if np.pi / 4 < a < np.pi * 3 / 4:
                                break
                    else:
                        axis = np.random.random(3)
                        axis /= np.linalg.norm(axis)

                    angle = self.min_angle
                    angle += 2 * (np.pi - self.min_angle) * np.random.random()

                    m = get_rotation_matrix(axis, angle)
                    newpos[indices[tag]] = np.dot(m, (p - cop).T).T + cop

                mutant.set_positions(newpos)
                mutant.wrap()
                too_close = atoms_too_close(mutant, self.blmin, use_tags=True)
                count += 1

                if not too_close and self.test_dist_to_slab:
                    too_close = atoms_too_close_two_sets(slab, mutant, self.blmin)

            if count == maxcount:
                mutant = None
            else:
                mutant = slab + mutant

            return mutant

    class RattleRotationalMutation(CombinationMutation):
        """ Combination of RattleMutation and RotationalMutation.

        Parameters:

        rattlemutation: OffspringCreator instance
                        A mutation that rattles atoms.

        rotationalmutation: OffspringCreator instance
                            A mutation that rotates moieties.
        """

        def __init__(self, rattlemutation, rotationalmutation, verbose=False):
            super(RattleRotationalMutation, self).__init__(rattlemutation,
                                                           rotationalmutation,
                                                           verbose=verbose)
            self.descriptor = 'rattlerotational'

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