# fmt: off """Constraints""" from typing import Sequence from warnings import warn import numpy as np from ase import Atoms from ase.filters import ExpCellFilter as ExpCellFilterOld from ase.filters import Filter as FilterOld from ase.filters import StrainFilter as StrainFilterOld from ase.filters import UnitCellFilter as UnitCellFilterOld from ase.geometry import ( conditional_find_mic, find_mic, get_angles, get_angles_derivatives, get_dihedrals, get_dihedrals_derivatives, get_distances_derivatives, wrap_positions, ) from ase.spacegroup.symmetrize import ( prep_symmetry, refine_symmetry, symmetrize_rank1, symmetrize_rank2, ) from ase.stress import full_3x3_to_voigt_6_stress, voigt_6_to_full_3x3_stress from ase.utils import deprecated from ase.utils.parsemath import eval_expression __all__ = [ 'FixCartesian', 'FixBondLength', 'FixedMode', 'FixAtoms', 'FixScaled', 'FixCom', 'FixSubsetCom', 'FixedPlane', 'FixConstraint', 'FixedLine', 'FixBondLengths', 'FixLinearTriatomic', 'FixInternals', 'Hookean', 'ExternalForce', 'MirrorForce', 'MirrorTorque', 'FixScaledParametricRelations', 'FixCartesianParametricRelations', 'FixSymmetry'] def dict2constraint(dct): if dct['name'] not in __all__: raise ValueError return globals()[dct['name']](**dct['kwargs']) def slice2enlist(s, n): """Convert a slice object into a list of (new, old) tuples.""" if isinstance(s, slice): return enumerate(range(*s.indices(n))) return enumerate(s) def constrained_indices(atoms, only_include=None): """Returns a list of indices for the atoms that are constrained by a constraint that is applied. By setting only_include to a specific type of constraint you can make it only look for that given constraint. """ indices = [] for constraint in atoms.constraints: if only_include is not None: if not isinstance(constraint, only_include): continue indices.extend(np.array(constraint.get_indices())) return np.array(np.unique(indices)) class FixConstraint: """Base class for classes that fix one or more atoms in some way.""" def index_shuffle(self, atoms: Atoms, ind): """Change the indices. When the ordering of the atoms in the Atoms object changes, this method can be called to shuffle the indices of the constraints. ind -- List or tuple of indices. """ raise NotImplementedError def repeat(self, m: int, n: int): """ basic method to multiply by m, needs to know the length of the underlying atoms object for the assignment of multiplied constraints to work. """ msg = ("Repeat is not compatible with your atoms' constraints." ' Use atoms.set_constraint() before calling repeat to ' 'remove your constraints.') raise NotImplementedError(msg) def get_removed_dof(self, atoms: Atoms): """Get number of removed degrees of freedom due to constraint.""" raise NotImplementedError def adjust_positions(self, atoms: Atoms, new): """Adjust positions.""" def adjust_momenta(self, atoms: Atoms, momenta): """Adjust momenta.""" # The default is in identical manner to forces. # TODO: The default is however not always reasonable. self.adjust_forces(atoms, momenta) def adjust_forces(self, atoms: Atoms, forces): """Adjust forces.""" def copy(self): """Copy constraint.""" return dict2constraint(self.todict().copy()) def todict(self): """Convert constraint to dictionary.""" class IndexedConstraint(FixConstraint): def __init__(self, indices=None, mask=None): """Constrain chosen atoms. Parameters ---------- indices : sequence of int Indices for those atoms that should be constrained. mask : sequence of bool One boolean per atom indicating if the atom should be constrained or not. """ if mask is not None: if indices is not None: raise ValueError('Use only one of "indices" and "mask".') indices = mask indices = np.atleast_1d(indices) if np.ndim(indices) > 1: raise ValueError('indices has wrong amount of dimensions. ' f'Got {np.ndim(indices)}, expected ndim <= 1') if indices.dtype == bool: indices = np.arange(len(indices))[indices] elif len(indices) == 0: indices = np.empty(0, dtype=int) elif not np.issubdtype(indices.dtype, np.integer): raise ValueError('Indices must be integers or boolean mask, ' f'not dtype={indices.dtype}') if len(set(indices)) < len(indices): raise ValueError( 'The indices array contains duplicates. ' 'Perhaps you want to specify a mask instead, but ' 'forgot the mask= keyword.') self.index = indices def index_shuffle(self, atoms, ind): # See docstring of superclass index = [] # Resolve negative indices: actual_indices = set(np.arange(len(atoms))[self.index]) for new, old in slice2enlist(ind, len(atoms)): if old in actual_indices: index.append(new) if len(index) == 0: raise IndexError('All indices in FixAtoms not part of slice') self.index = np.asarray(index, int) # XXX make immutable def get_indices(self): return self.index.copy() def repeat(self, m, n): i0 = 0 natoms = 0 if isinstance(m, int): m = (m, m, m) index_new = [] for _ in range(m[2]): for _ in range(m[1]): for _ in range(m[0]): i1 = i0 + n index_new += [i + natoms for i in self.index] i0 = i1 natoms += n self.index = np.asarray(index_new, int) # XXX make immutable return self def delete_atoms(self, indices, natoms): """Removes atoms from the index array, if present. Required for removing atoms with existing constraint. """ i = np.zeros(natoms, int) - 1 new = np.delete(np.arange(natoms), indices) i[new] = np.arange(len(new)) index = i[self.index] self.index = index[index >= 0] # XXX make immutable if len(self.index) == 0: return None return self class FixAtoms(IndexedConstraint): """Fix chosen atoms. Examples -------- Fix all Copper atoms: >>> from ase.build import bulk >>> atoms = bulk('Cu', 'fcc', a=3.6) >>> mask = (atoms.symbols == 'Cu') >>> c = FixAtoms(mask=mask) >>> atoms.set_constraint(c) Fix all atoms with z-coordinate less than 1.0 Angstrom: >>> c = FixAtoms(mask=atoms.positions[:, 2] < 1.0) >>> atoms.set_constraint(c) """ def get_removed_dof(self, atoms): return 3 * len(self.index) def adjust_positions(self, atoms, new): new[self.index] = atoms.positions[self.index] def adjust_forces(self, atoms, forces): forces[self.index] = 0.0 def __repr__(self): clsname = type(self).__name__ indices = ints2string(self.index) return f'{clsname}(indices={indices})' def todict(self): return {'name': 'FixAtoms', 'kwargs': {'indices': self.index.tolist()}} class FixCom(FixConstraint): """Constraint class for fixing the center of mass.""" index = slice(None) # all atoms def get_removed_dof(self, atoms): return 3 def adjust_positions(self, atoms, new): masses = atoms.get_masses()[self.index] old_cm = atoms.get_center_of_mass(indices=self.index) new_cm = masses @ new[self.index] / masses.sum() diff = old_cm - new_cm new += diff def adjust_momenta(self, atoms, momenta): """Adjust momenta so that the center-of-mass velocity is zero.""" masses = atoms.get_masses()[self.index] velocity_com = momenta[self.index].sum(axis=0) / masses.sum() momenta[self.index] -= masses[:, None] * velocity_com def adjust_forces(self, atoms, forces): # Eqs. (3) and (7) in https://doi.org/10.1021/jp9722824 masses = atoms.get_masses()[self.index] lmd = masses @ forces[self.index] / sum(masses**2) forces[self.index] -= masses[:, None] * lmd def todict(self): return {'name': 'FixCom', 'kwargs': {}} class FixSubsetCom(FixCom, IndexedConstraint): """Constraint class for fixing the center of mass of a subset of atoms.""" def __init__(self, indices): super().__init__(indices=indices) def todict(self): return {'name': self.__class__.__name__, 'kwargs': {'indices': self.index.tolist()}} def ints2string(x, threshold=None): """Convert ndarray of ints to string.""" if threshold is None or len(x) <= threshold: return str(x.tolist()) return str(x[:threshold].tolist())[:-1] + ', ...]' class FixBondLengths(FixConstraint): maxiter = 500 def __init__(self, pairs, tolerance=1e-13, bondlengths=None, iterations=None): """iterations: Ignored""" self.pairs = np.asarray(pairs) self.tolerance = tolerance self.bondlengths = bondlengths def get_removed_dof(self, atoms): return len(self.pairs) def adjust_positions(self, atoms, new): old = atoms.positions masses = atoms.get_masses() if self.bondlengths is None: self.bondlengths = self.initialize_bond_lengths(atoms) for i in range(self.maxiter): converged = True for j, ab in enumerate(self.pairs): a = ab[0] b = ab[1] cd = self.bondlengths[j] r0 = old[a] - old[b] d0, _ = find_mic(r0, atoms.cell, atoms.pbc) d1 = new[a] - new[b] - r0 + d0 m = 1 / (1 / masses[a] + 1 / masses[b]) x = 0.5 * (cd**2 - np.dot(d1, d1)) / np.dot(d0, d1) if abs(x) > self.tolerance: new[a] += x * m / masses[a] * d0 new[b] -= x * m / masses[b] * d0 converged = False if converged: break else: raise RuntimeError('Did not converge') def adjust_momenta(self, atoms, p): old = atoms.positions masses = atoms.get_masses() if self.bondlengths is None: self.bondlengths = self.initialize_bond_lengths(atoms) for i in range(self.maxiter): converged = True for j, ab in enumerate(self.pairs): a = ab[0] b = ab[1] cd = self.bondlengths[j] d = old[a] - old[b] d, _ = find_mic(d, atoms.cell, atoms.pbc) dv = p[a] / masses[a] - p[b] / masses[b] m = 1 / (1 / masses[a] + 1 / masses[b]) x = -np.dot(dv, d) / cd**2 if abs(x) > self.tolerance: p[a] += x * m * d p[b] -= x * m * d converged = False if converged: break else: raise RuntimeError('Did not converge') def adjust_forces(self, atoms, forces): self.constraint_forces = -forces self.adjust_momenta(atoms, forces) self.constraint_forces += forces def initialize_bond_lengths(self, atoms): bondlengths = np.zeros(len(self.pairs)) for i, ab in enumerate(self.pairs): bondlengths[i] = atoms.get_distance(ab[0], ab[1], mic=True) return bondlengths def get_indices(self): return np.unique(self.pairs.ravel()) def todict(self): return {'name': 'FixBondLengths', 'kwargs': {'pairs': self.pairs.tolist(), 'tolerance': self.tolerance}} def index_shuffle(self, atoms, ind): """Shuffle the indices of the two atoms in this constraint""" map = np.zeros(len(atoms), int) map[ind] = 1 n = map.sum() map[:] = -1 map[ind] = range(n) pairs = map[self.pairs] self.pairs = pairs[(pairs != -1).all(1)] if len(self.pairs) == 0: raise IndexError('Constraint not part of slice') def FixBondLength(a1, a2): """Fix distance between atoms with indices a1 and a2.""" return FixBondLengths([(a1, a2)]) class FixLinearTriatomic(FixConstraint): """Holonomic constraints for rigid linear triatomic molecules.""" def __init__(self, triples): """Apply RATTLE-type bond constraints between outer atoms n and m and linear vectorial constraints to the position of central atoms o to fix the geometry of linear triatomic molecules of the type: n--o--m Parameters: triples: list Indices of the atoms forming the linear molecules to constrain as triples. Sequence should be (n, o, m) or (m, o, n). When using these constraints in molecular dynamics or structure optimizations, atomic forces need to be redistributed within a triple. The function redistribute_forces_optimization implements the redistribution of forces for structure optimization, while the function redistribute_forces_md implements the redistribution for molecular dynamics. References: Ciccotti et al. Molecular Physics 47 (1982) :doi:`10.1080/00268978200100942` """ self.triples = np.asarray(triples) if self.triples.shape[1] != 3: raise ValueError('"triples" has wrong size') self.bondlengths = None def get_removed_dof(self, atoms): return 4 * len(self.triples) @property def n_ind(self): return self.triples[:, 0] @property def m_ind(self): return self.triples[:, 2] @property def o_ind(self): return self.triples[:, 1] def initialize(self, atoms): masses = atoms.get_masses() self.mass_n, self.mass_m, self.mass_o = self.get_slices(masses) self.bondlengths = self.initialize_bond_lengths(atoms) self.bondlengths_nm = self.bondlengths.sum(axis=1) C1 = self.bondlengths[:, ::-1] / self.bondlengths_nm[:, None] C2 = (C1[:, 0] ** 2 * self.mass_o * self.mass_m + C1[:, 1] ** 2 * self.mass_n * self.mass_o + self.mass_n * self.mass_m) C2 = C1 / C2[:, None] C3 = self.mass_n * C1[:, 1] - self.mass_m * C1[:, 0] C3 = C2 * self.mass_o[:, None] * C3[:, None] C3[:, 1] *= -1 C3 = (C3 + 1) / np.vstack((self.mass_n, self.mass_m)).T C4 = (C1[:, 0]**2 + C1[:, 1]**2 + 1) C4 = C1 / C4[:, None] self.C1 = C1 self.C2 = C2 self.C3 = C3 self.C4 = C4 def adjust_positions(self, atoms, new): old = atoms.positions new_n, new_m, new_o = self.get_slices(new) if self.bondlengths is None: self.initialize(atoms) r0 = old[self.n_ind] - old[self.m_ind] d0, _ = find_mic(r0, atoms.cell, atoms.pbc) d1 = new_n - new_m - r0 + d0 a = np.einsum('ij,ij->i', d0, d0) b = np.einsum('ij,ij->i', d1, d0) c = np.einsum('ij,ij->i', d1, d1) - self.bondlengths_nm ** 2 g = (b - (b**2 - a * c)**0.5) / (a * self.C3.sum(axis=1)) g = g[:, None] * self.C3 new_n -= g[:, 0, None] * d0 new_m += g[:, 1, None] * d0 if np.allclose(d0, r0): new_o = (self.C1[:, 0, None] * new_n + self.C1[:, 1, None] * new_m) else: v1, _ = find_mic(new_n, atoms.cell, atoms.pbc) v2, _ = find_mic(new_m, atoms.cell, atoms.pbc) rb = self.C1[:, 0, None] * v1 + self.C1[:, 1, None] * v2 new_o = wrap_positions(rb, atoms.cell, atoms.pbc) self.set_slices(new_n, new_m, new_o, new) def adjust_momenta(self, atoms, p): old = atoms.positions p_n, p_m, p_o = self.get_slices(p) if self.bondlengths is None: self.initialize(atoms) mass_nn = self.mass_n[:, None] mass_mm = self.mass_m[:, None] mass_oo = self.mass_o[:, None] d = old[self.n_ind] - old[self.m_ind] d, _ = find_mic(d, atoms.cell, atoms.pbc) dv = p_n / mass_nn - p_m / mass_mm k = np.einsum('ij,ij->i', dv, d) / self.bondlengths_nm ** 2 k = self.C3 / (self.C3.sum(axis=1)[:, None]) * k[:, None] p_n -= k[:, 0, None] * mass_nn * d p_m += k[:, 1, None] * mass_mm * d p_o = (mass_oo * (self.C1[:, 0, None] * p_n / mass_nn + self.C1[:, 1, None] * p_m / mass_mm)) self.set_slices(p_n, p_m, p_o, p) def adjust_forces(self, atoms, forces): if self.bondlengths is None: self.initialize(atoms) A = self.C4 * np.diff(self.C1) A[:, 0] *= -1 A -= 1 B = np.diff(self.C4) / (A.sum(axis=1))[:, None] A /= (A.sum(axis=1))[:, None] self.constraint_forces = -forces old = atoms.positions fr_n, fr_m, fr_o = self.redistribute_forces_optimization(forces) d = old[self.n_ind] - old[self.m_ind] d, _ = find_mic(d, atoms.cell, atoms.pbc) df = fr_n - fr_m k = -np.einsum('ij,ij->i', df, d) / self.bondlengths_nm ** 2 forces[self.n_ind] = fr_n + k[:, None] * d * A[:, 0, None] forces[self.m_ind] = fr_m - k[:, None] * d * A[:, 1, None] forces[self.o_ind] = fr_o + k[:, None] * d * B self.constraint_forces += forces def redistribute_forces_optimization(self, forces): """Redistribute forces within a triple when performing structure optimizations. The redistributed forces needs to be further adjusted using the appropriate Lagrange multipliers as implemented in adjust_forces.""" forces_n, forces_m, forces_o = self.get_slices(forces) C1_1 = self.C1[:, 0, None] C1_2 = self.C1[:, 1, None] C4_1 = self.C4[:, 0, None] C4_2 = self.C4[:, 1, None] fr_n = ((1 - C4_1 * C1_1) * forces_n - C4_1 * (C1_2 * forces_m - forces_o)) fr_m = ((1 - C4_2 * C1_2) * forces_m - C4_2 * (C1_1 * forces_n - forces_o)) fr_o = ((1 - 1 / (C1_1**2 + C1_2**2 + 1)) * forces_o + C4_1 * forces_n + C4_2 * forces_m) return fr_n, fr_m, fr_o def redistribute_forces_md(self, atoms, forces, rand=False): """Redistribute forces within a triple when performing molecular dynamics. When rand=True, use the equations for random force terms, as used e.g. by Langevin dynamics, otherwise apply the standard equations for deterministic forces (see Ciccotti et al. Molecular Physics 47 (1982)).""" if self.bondlengths is None: self.initialize(atoms) forces_n, forces_m, forces_o = self.get_slices(forces) C1_1 = self.C1[:, 0, None] C1_2 = self.C1[:, 1, None] C2_1 = self.C2[:, 0, None] C2_2 = self.C2[:, 1, None] mass_nn = self.mass_n[:, None] mass_mm = self.mass_m[:, None] mass_oo = self.mass_o[:, None] if rand: mr1 = (mass_mm / mass_nn) ** 0.5 mr2 = (mass_oo / mass_nn) ** 0.5 mr3 = (mass_nn / mass_mm) ** 0.5 mr4 = (mass_oo / mass_mm) ** 0.5 else: mr1 = 1.0 mr2 = 1.0 mr3 = 1.0 mr4 = 1.0 fr_n = ((1 - C1_1 * C2_1 * mass_oo * mass_mm) * forces_n - C2_1 * (C1_2 * mr1 * mass_oo * mass_nn * forces_m - mr2 * mass_mm * mass_nn * forces_o)) fr_m = ((1 - C1_2 * C2_2 * mass_oo * mass_nn) * forces_m - C2_2 * (C1_1 * mr3 * mass_oo * mass_mm * forces_n - mr4 * mass_mm * mass_nn * forces_o)) self.set_slices(fr_n, fr_m, 0.0, forces) def get_slices(self, a): a_n = a[self.n_ind] a_m = a[self.m_ind] a_o = a[self.o_ind] return a_n, a_m, a_o def set_slices(self, a_n, a_m, a_o, a): a[self.n_ind] = a_n a[self.m_ind] = a_m a[self.o_ind] = a_o def initialize_bond_lengths(self, atoms): bondlengths = np.zeros((len(self.triples), 2)) for i in range(len(self.triples)): bondlengths[i, 0] = atoms.get_distance(self.n_ind[i], self.o_ind[i], mic=True) bondlengths[i, 1] = atoms.get_distance(self.o_ind[i], self.m_ind[i], mic=True) return bondlengths def get_indices(self): return np.unique(self.triples.ravel()) def todict(self): return {'name': 'FixLinearTriatomic', 'kwargs': {'triples': self.triples.tolist()}} def index_shuffle(self, atoms, ind): """Shuffle the indices of the three atoms in this constraint""" map = np.zeros(len(atoms), int) map[ind] = 1 n = map.sum() map[:] = -1 map[ind] = range(n) triples = map[self.triples] self.triples = triples[(triples != -1).all(1)] if len(self.triples) == 0: raise IndexError('Constraint not part of slice') class FixedMode(FixConstraint): """Constrain atoms to move along directions orthogonal to a given mode only. Initialize with a mode, such as one produced by ase.vibrations.Vibrations.get_mode().""" def __init__(self, mode): mode = np.asarray(mode) self.mode = (mode / np.sqrt((mode**2).sum())).reshape(-1) def get_removed_dof(self, atoms): return len(atoms) def adjust_positions(self, atoms, newpositions): newpositions = newpositions.ravel() oldpositions = atoms.positions.ravel() step = newpositions - oldpositions newpositions -= self.mode * np.dot(step, self.mode) def adjust_forces(self, atoms, forces): forces = forces.ravel() forces -= self.mode * np.dot(forces, self.mode) def index_shuffle(self, atoms, ind): eps = 1e-12 mode = self.mode.reshape(-1, 3) excluded = np.ones(len(mode), dtype=bool) excluded[ind] = False if (abs(mode[excluded]) > eps).any(): raise IndexError('All nonzero parts of mode not in slice') self.mode = mode[ind].ravel() def get_indices(self): # This function will never properly work because it works on all # atoms and it has no idea how to tell how many atoms it is # attached to. If it is being used, surely the user knows # everything is being constrained. return [] def todict(self): return {'name': 'FixedMode', 'kwargs': {'mode': self.mode.tolist()}} def __repr__(self): return f'FixedMode({self.mode.tolist()})' def _normalize(direction): if np.shape(direction) != (3,): raise ValueError("len(direction) is {len(direction)}. Has to be 3") direction = np.asarray(direction) / np.linalg.norm(direction) return direction class FixedPlane(IndexedConstraint): """ Constraint object for fixing chosen atoms to only move in a plane. The plane is defined by its normal vector *direction* """ def __init__(self, indices, direction): """Constrain chosen atoms. Parameters ---------- indices : int or list of int Index or indices for atoms that should be constrained direction : list of 3 int Direction of the normal vector Examples -------- Fix all Copper atoms to only move in the yz-plane: >>> from ase.build import bulk >>> from ase.constraints import FixedPlane >>> atoms = bulk('Cu', 'fcc', a=3.6) >>> c = FixedPlane( ... indices=[atom.index for atom in atoms if atom.symbol == 'Cu'], ... direction=[1, 0, 0], ... ) >>> atoms.set_constraint(c) or constrain a single atom with the index 0 to move in the xy-plane: >>> c = FixedPlane(indices=0, direction=[0, 0, 1]) >>> atoms.set_constraint(c) """ super().__init__(indices=indices) self.dir = _normalize(direction) def adjust_positions(self, atoms, newpositions): step = newpositions[self.index] - atoms.positions[self.index] newpositions[self.index] -= _projection(step, self.dir) def adjust_forces(self, atoms, forces): forces[self.index] -= _projection(forces[self.index], self.dir) def get_removed_dof(self, atoms): return len(self.index) def todict(self): return { 'name': 'FixedPlane', 'kwargs': {'indices': self.index.tolist(), 'direction': self.dir.tolist()} } def __repr__(self): return f'FixedPlane(indices={self.index}, {self.dir.tolist()})' def _projection(vectors, direction): dotprods = vectors @ direction projection = direction[None, :] * dotprods[:, None] return projection class FixedLine(IndexedConstraint): """ Constrain an atom index or a list of atom indices to move on a line only. The line is defined by its vector *direction* """ def __init__(self, indices, direction): """Constrain chosen atoms. Parameters ---------- indices : int or list of int Index or indices for atoms that should be constrained direction : list of 3 int Direction of the vector defining the line Examples -------- Fix all Copper atoms to only move in the x-direction: >>> from ase.constraints import FixedLine >>> c = FixedLine( ... indices=[atom.index for atom in atoms if atom.symbol == 'Cu'], ... direction=[1, 0, 0], ... ) >>> atoms.set_constraint(c) or constrain a single atom with the index 0 to move in the z-direction: >>> c = FixedLine(indices=0, direction=[0, 0, 1]) >>> atoms.set_constraint(c) """ super().__init__(indices) self.dir = _normalize(direction) def adjust_positions(self, atoms, newpositions): step = newpositions[self.index] - atoms.positions[self.index] projection = _projection(step, self.dir) newpositions[self.index] = atoms.positions[self.index] + projection def adjust_forces(self, atoms, forces): forces[self.index] = _projection(forces[self.index], self.dir) def get_removed_dof(self, atoms): return 2 * len(self.index) def __repr__(self): return f'FixedLine(indices={self.index}, {self.dir.tolist()})' def todict(self): return { 'name': 'FixedLine', 'kwargs': {'indices': self.index.tolist(), 'direction': self.dir.tolist()} } class FixCartesian(IndexedConstraint): """Fix atoms in the directions of the cartesian coordinates. Parameters ---------- a : Sequence[int] Indices of atoms to be fixed. mask : tuple[bool, bool, bool], default: (True, True, True) Cartesian directions to be fixed. (False: unfixed, True: fixed) """ def __init__(self, a, mask=(True, True, True)): super().__init__(indices=a) self.mask = np.asarray(mask, bool) def get_removed_dof(self, atoms: Atoms): return self.mask.sum() * len(self.index) def adjust_positions(self, atoms: Atoms, new): new[self.index] = np.where( self.mask[None, :], atoms.positions[self.index], new[self.index], ) def adjust_forces(self, atoms: Atoms, forces): forces[self.index] *= ~self.mask[None, :] def todict(self): return {'name': 'FixCartesian', 'kwargs': {'a': self.index.tolist(), 'mask': self.mask.tolist()}} def __repr__(self): name = type(self).__name__ return f'{name}(indices={self.index.tolist()}, {self.mask.tolist()})' class FixScaled(IndexedConstraint): """Fix atoms in the directions of the unit vectors. Parameters ---------- a : Sequence[int] Indices of atoms to be fixed. mask : tuple[bool, bool, bool], default: (True, True, True) Cell directions to be fixed. (False: unfixed, True: fixed) """ def __init__(self, a, mask=(True, True, True), cell=None): # XXX The unused cell keyword is there for compatibility # with old trajectory files. super().__init__(indices=a) self.mask = np.asarray(mask, bool) def get_removed_dof(self, atoms: Atoms): return self.mask.sum() * len(self.index) def adjust_positions(self, atoms: Atoms, new): cell = atoms.cell scaled_old = cell.scaled_positions(atoms.positions[self.index]) scaled_new = cell.scaled_positions(new[self.index]) scaled_new[:, self.mask] = scaled_old[:, self.mask] new[self.index] = cell.cartesian_positions(scaled_new) def adjust_forces(self, atoms: Atoms, forces): # Forces are covariant to the coordinate transformation, # use the inverse transformations cell = atoms.cell scaled_forces = cell.cartesian_positions(forces[self.index]) scaled_forces *= -(self.mask - 1) forces[self.index] = cell.scaled_positions(scaled_forces) def todict(self): return {'name': 'FixScaled', 'kwargs': {'a': self.index.tolist(), 'mask': self.mask.tolist()}} def __repr__(self): name = type(self).__name__ return f'{name}(indices={self.index.tolist()}, {self.mask.tolist()})' # TODO: Better interface might be to use dictionaries in place of very # nested lists/tuples class FixInternals(FixConstraint): """Constraint object for fixing multiple internal coordinates. Allows fixing bonds, angles, dihedrals as well as linear combinations of bonds (bondcombos). Please provide angular units in degrees using `angles_deg` and `dihedrals_deg`. Fixing planar angles is not supported at the moment. """ def __init__(self, bonds=None, angles=None, dihedrals=None, angles_deg=None, dihedrals_deg=None, bondcombos=None, mic=False, epsilon=1.e-7): """ A constrained internal coordinate is defined as a nested list: '[value, [atom indices]]'. The constraint is initialized with a list of constrained internal coordinates, i.e. '[[value, [atom indices]], ...]'. If 'value' is None, the current value of the coordinate is constrained. Parameters ---------- bonds: nested python list, optional List with targetvalue and atom indices defining the fixed bonds, i.e. [[targetvalue, [index0, index1]], ...] angles_deg: nested python list, optional List with targetvalue and atom indices defining the fixedangles, i.e. [[targetvalue, [index0, index1, index3]], ...] dihedrals_deg: nested python list, optional List with targetvalue and atom indices defining the fixed dihedrals, i.e. [[targetvalue, [index0, index1, index3]], ...] bondcombos: nested python list, optional List with targetvalue, atom indices and linear coefficient defining the fixed linear combination of bonds, i.e. [[targetvalue, [[index0, index1, coefficient_for_bond], [index1, index2, coefficient_for_bond]]], ...] mic: bool, optional, default: False Minimum image convention. epsilon: float, optional, default: 1e-7 Convergence criterion. """ warn_msg = 'Please specify {} in degrees using the {} argument.' if angles: warn(warn_msg.format('angles', 'angle_deg'), FutureWarning) angles = np.asarray(angles) angles[:, 0] = angles[:, 0] / np.pi * 180 angles = angles.tolist() else: angles = angles_deg if dihedrals: warn(warn_msg.format('dihedrals', 'dihedrals_deg'), FutureWarning) dihedrals = np.asarray(dihedrals) dihedrals[:, 0] = dihedrals[:, 0] / np.pi * 180 dihedrals = dihedrals.tolist() else: dihedrals = dihedrals_deg self.bonds = bonds or [] self.angles = angles or [] self.dihedrals = dihedrals or [] self.bondcombos = bondcombos or [] self.mic = mic self.epsilon = epsilon self.n = (len(self.bonds) + len(self.angles) + len(self.dihedrals) + len(self.bondcombos)) # Initialize these at run-time: self.constraints = [] self.initialized = False def get_removed_dof(self, atoms): return self.n def initialize(self, atoms): if self.initialized: return masses = np.repeat(atoms.get_masses(), 3) cell = None pbc = None if self.mic: cell = atoms.cell pbc = atoms.pbc self.constraints = [] for data, ConstrClass in [(self.bonds, self.FixBondLengthAlt), (self.angles, self.FixAngle), (self.dihedrals, self.FixDihedral), (self.bondcombos, self.FixBondCombo)]: for datum in data: targetvalue = datum[0] if targetvalue is None: # set to current value targetvalue = ConstrClass.get_value(atoms, datum[1], self.mic) constr = ConstrClass(targetvalue, datum[1], masses, cell, pbc) self.constraints.append(constr) self.initialized = True @staticmethod def get_bondcombo(atoms, indices, mic=False): """Convenience function to return the value of the bondcombo coordinate (linear combination of bond lengths) for the given Atoms object 'atoms'. Example: Get the current value of the linear combination of two bond lengths defined as `bondcombo = [[0, 1, 1.0], [2, 3, -1.0]]`.""" c = sum(df[2] * atoms.get_distance(*df[:2], mic=mic) for df in indices) return c def get_subconstraint(self, atoms, definition): """Get pointer to a specific subconstraint. Identification by its definition via indices (and coefficients).""" self.initialize(atoms) for subconstr in self.constraints: if isinstance(definition[0], Sequence): # Combo constraint defin = [d + [c] for d, c in zip(subconstr.indices, subconstr.coefs)] if defin == definition: return subconstr else: # identify primitive constraints by their indices if subconstr.indices == [definition]: return subconstr raise ValueError('Given `definition` not found on Atoms object.') def shuffle_definitions(self, shuffle_dic, internal_type): dfns = [] # definitions for dfn in internal_type: # e.g. for bond in self.bonds append = True new_dfn = [dfn[0], list(dfn[1])] for old in dfn[1]: if old in shuffle_dic: new_dfn[1][dfn[1].index(old)] = shuffle_dic[old] else: append = False break if append: dfns.append(new_dfn) return dfns def shuffle_combos(self, shuffle_dic, internal_type): dfns = [] # definitions for dfn in internal_type: # i.e. for bondcombo in self.bondcombos append = True all_indices = [idx[0:-1] for idx in dfn[1]] new_dfn = [dfn[0], list(dfn[1])] for i, indices in enumerate(all_indices): for old in indices: if old in shuffle_dic: new_dfn[1][i][indices.index(old)] = shuffle_dic[old] else: append = False break if not append: break if append: dfns.append(new_dfn) return dfns def index_shuffle(self, atoms, ind): # See docstring of superclass self.initialize(atoms) shuffle_dic = dict(slice2enlist(ind, len(atoms))) shuffle_dic = {old: new for new, old in shuffle_dic.items()} self.bonds = self.shuffle_definitions(shuffle_dic, self.bonds) self.angles = self.shuffle_definitions(shuffle_dic, self.angles) self.dihedrals = self.shuffle_definitions(shuffle_dic, self.dihedrals) self.bondcombos = self.shuffle_combos(shuffle_dic, self.bondcombos) self.initialized = False self.initialize(atoms) if len(self.constraints) == 0: raise IndexError('Constraint not part of slice') def get_indices(self): cons = [] for dfn in self.bonds + self.dihedrals + self.angles: cons.extend(dfn[1]) for dfn in self.bondcombos: for partial_dfn in dfn[1]: cons.extend(partial_dfn[0:-1]) # last index is the coefficient return list(set(cons)) def todict(self): return {'name': 'FixInternals', 'kwargs': {'bonds': self.bonds, 'angles_deg': self.angles, 'dihedrals_deg': self.dihedrals, 'bondcombos': self.bondcombos, 'mic': self.mic, 'epsilon': self.epsilon}} def adjust_positions(self, atoms, newpos): self.initialize(atoms) for constraint in self.constraints: constraint.setup_jacobian(atoms.positions) for _ in range(50): maxerr = 0.0 for constraint in self.constraints: constraint.adjust_positions(atoms.positions, newpos) maxerr = max(abs(constraint.sigma), maxerr) if maxerr < self.epsilon: return msg = 'FixInternals.adjust_positions did not converge.' if any(constr.targetvalue > 175. or constr.targetvalue < 5. for constr in self.constraints if isinstance(constr, self.FixAngle)): msg += (' This may be caused by an almost planar angle.' ' Support for planar angles would require the' ' implementation of ghost, i.e. dummy, atoms.' ' See issue #868.') raise ValueError(msg) def adjust_forces(self, atoms, forces): """Project out translations and rotations and all other constraints""" self.initialize(atoms) positions = atoms.positions N = len(forces) list2_constraints = list(np.zeros((6, N, 3))) tx, ty, tz, rx, ry, rz = list2_constraints list_constraints = [r.ravel() for r in list2_constraints] tx[:, 0] = 1.0 ty[:, 1] = 1.0 tz[:, 2] = 1.0 ff = forces.ravel() # Calculate the center of mass center = positions.sum(axis=0) / N rx[:, 1] = -(positions[:, 2] - center[2]) rx[:, 2] = positions[:, 1] - center[1] ry[:, 0] = positions[:, 2] - center[2] ry[:, 2] = -(positions[:, 0] - center[0]) rz[:, 0] = -(positions[:, 1] - center[1]) rz[:, 1] = positions[:, 0] - center[0] # Normalizing transl., rotat. constraints for r in list2_constraints: r /= np.linalg.norm(r.ravel()) # Add all angle, etc. constraint vectors for constraint in self.constraints: constraint.setup_jacobian(positions) constraint.adjust_forces(positions, forces) list_constraints.insert(0, constraint.jacobian) # QR DECOMPOSITION - GRAM SCHMIDT list_constraints = [r.ravel() for r in list_constraints] aa = np.column_stack(list_constraints) (aa, _bb) = np.linalg.qr(aa) # Projection hh = [] for i, constraint in enumerate(self.constraints): hh.append(aa[:, i] * np.vstack(aa[:, i])) txx = aa[:, self.n] * np.vstack(aa[:, self.n]) tyy = aa[:, self.n + 1] * np.vstack(aa[:, self.n + 1]) tzz = aa[:, self.n + 2] * np.vstack(aa[:, self.n + 2]) rxx = aa[:, self.n + 3] * np.vstack(aa[:, self.n + 3]) ryy = aa[:, self.n + 4] * np.vstack(aa[:, self.n + 4]) rzz = aa[:, self.n + 5] * np.vstack(aa[:, self.n + 5]) T = txx + tyy + tzz + rxx + ryy + rzz for vec in hh: T += vec ff = np.dot(T, np.vstack(ff)) forces[:, :] -= np.dot(T, np.vstack(ff)).reshape(-1, 3) def __repr__(self): constraints = [repr(constr) for constr in self.constraints] return f'FixInternals(_copy_init={constraints}, epsilon={self.epsilon})' # Classes for internal use in FixInternals class FixInternalsBase: """Base class for subclasses of FixInternals.""" def __init__(self, targetvalue, indices, masses, cell, pbc): self.targetvalue = targetvalue # constant target value self.indices = [defin[0:-1] for defin in indices] # indices, defs self.coefs = np.asarray([defin[-1] for defin in indices]) self.masses = masses self.jacobian = [] # geometric Jacobian matrix, Wilson B-matrix self.sigma = 1. # difference between current and target value self.projected_force = None # helps optimizers scan along constr. self.cell = cell self.pbc = pbc def finalize_jacobian(self, pos, n_internals, n, derivs): """Populate jacobian with derivatives for `n_internals` defined internals. n = 2 (bonds), 3 (angles), 4 (dihedrals).""" jacobian = np.zeros((n_internals, *pos.shape)) for i, idx in enumerate(self.indices): for j in range(n): jacobian[i, idx[j]] = derivs[i, j] jacobian = jacobian.reshape((n_internals, 3 * len(pos))) return self.coefs @ jacobian def finalize_positions(self, newpos): jacobian = self.jacobian / self.masses lamda = -self.sigma / (jacobian @ self.get_jacobian(newpos)) dnewpos = lamda * jacobian newpos += dnewpos.reshape(newpos.shape) def adjust_forces(self, positions, forces): self.projected_forces = ((self.jacobian @ forces.ravel()) * self.jacobian) self.jacobian /= np.linalg.norm(self.jacobian) class FixBondCombo(FixInternalsBase): """Constraint subobject for fixing linear combination of bond lengths within FixInternals. sum_i( coef_i * bond_length_i ) = constant """ def get_jacobian(self, pos): bondvectors = [pos[k] - pos[h] for h, k in self.indices] derivs = get_distances_derivatives(bondvectors, cell=self.cell, pbc=self.pbc) return self.finalize_jacobian(pos, len(bondvectors), 2, derivs) def setup_jacobian(self, pos): self.jacobian = self.get_jacobian(pos) def adjust_positions(self, oldpos, newpos): bondvectors = [newpos[k] - newpos[h] for h, k in self.indices] (_, ), (dists, ) = conditional_find_mic([bondvectors], cell=self.cell, pbc=self.pbc) value = self.coefs @ dists self.sigma = value - self.targetvalue self.finalize_positions(newpos) @staticmethod def get_value(atoms, indices, mic): return FixInternals.get_bondcombo(atoms, indices, mic) def __repr__(self): return (f'FixBondCombo({self.targetvalue}, {self.indices}, ' '{self.coefs})') class FixBondLengthAlt(FixBondCombo): """Constraint subobject for fixing bond length within FixInternals. Fix distance between atoms with indices a1, a2.""" def __init__(self, targetvalue, indices, masses, cell, pbc): if targetvalue <= 0.: raise ZeroDivisionError('Invalid targetvalue for fixed bond') indices = [list(indices) + [1.]] # bond definition with coef 1. super().__init__(targetvalue, indices, masses, cell=cell, pbc=pbc) @staticmethod def get_value(atoms, indices, mic): return atoms.get_distance(*indices, mic=mic) def __repr__(self): return f'FixBondLengthAlt({self.targetvalue}, {self.indices})' class FixAngle(FixInternalsBase): """Constraint subobject for fixing an angle within FixInternals. Convergence is potentially problematic for angles very close to 0 or 180 degrees as there is a singularity in the Cartesian derivative. Fixing planar angles is therefore not supported at the moment. """ def __init__(self, targetvalue, indices, masses, cell, pbc): """Fix atom movement to construct a constant angle.""" if targetvalue <= 0. or targetvalue >= 180.: raise ZeroDivisionError('Invalid targetvalue for fixed angle') indices = [list(indices) + [1.]] # angle definition with coef 1. super().__init__(targetvalue, indices, masses, cell=cell, pbc=pbc) def gather_vectors(self, pos): v0 = [pos[h] - pos[k] for h, k, l in self.indices] v1 = [pos[l] - pos[k] for h, k, l in self.indices] return v0, v1 def get_jacobian(self, pos): v0, v1 = self.gather_vectors(pos) derivs = get_angles_derivatives(v0, v1, cell=self.cell, pbc=self.pbc) return self.finalize_jacobian(pos, len(v0), 3, derivs) def setup_jacobian(self, pos): self.jacobian = self.get_jacobian(pos) def adjust_positions(self, oldpos, newpos): v0, v1 = self.gather_vectors(newpos) value = get_angles(v0, v1, cell=self.cell, pbc=self.pbc) self.sigma = value - self.targetvalue self.finalize_positions(newpos) @staticmethod def get_value(atoms, indices, mic): return atoms.get_angle(*indices, mic=mic) def __repr__(self): return f'FixAngle({self.targetvalue}, {self.indices})' class FixDihedral(FixInternalsBase): """Constraint subobject for fixing a dihedral angle within FixInternals. A dihedral becomes undefined when at least one of the inner two angles becomes planar. Make sure to avoid this situation. """ def __init__(self, targetvalue, indices, masses, cell, pbc): indices = [list(indices) + [1.]] # dihedral def. with coef 1. super().__init__(targetvalue, indices, masses, cell=cell, pbc=pbc) def gather_vectors(self, pos): v0 = [pos[k] - pos[h] for h, k, l, m in self.indices] v1 = [pos[l] - pos[k] for h, k, l, m in self.indices] v2 = [pos[m] - pos[l] for h, k, l, m in self.indices] return v0, v1, v2 def get_jacobian(self, pos): v0, v1, v2 = self.gather_vectors(pos) derivs = get_dihedrals_derivatives(v0, v1, v2, cell=self.cell, pbc=self.pbc) return self.finalize_jacobian(pos, len(v0), 4, derivs) def setup_jacobian(self, pos): self.jacobian = self.get_jacobian(pos) def adjust_positions(self, oldpos, newpos): v0, v1, v2 = self.gather_vectors(newpos) value = get_dihedrals(v0, v1, v2, cell=self.cell, pbc=self.pbc) # apply minimum dihedral difference 'convention': (diff <= 180) self.sigma = (value - self.targetvalue + 180) % 360 - 180 self.finalize_positions(newpos) @staticmethod def get_value(atoms, indices, mic): return atoms.get_dihedral(*indices, mic=mic) def __repr__(self): return f'FixDihedral({self.targetvalue}, {self.indices})' class FixParametricRelations(FixConstraint): def __init__( self, indices, Jacobian, const_shift, params=None, eps=1e-12, use_cell=False, ): """Constrains the degrees of freedom to act in a reduced parameter space defined by the Jacobian These constraints are based off the work in: https://arxiv.org/abs/1908.01610 The constraints linearly maps the full 3N degrees of freedom, where N is number of active lattice vectors/atoms onto a reduced subset of M free parameters, where M <= 3*N. The Jacobian matrix and constant shift vector map the full set of degrees of freedom onto the reduced parameter space. Currently the constraint is set up to handle either atomic positions or lattice vectors at one time, but not both. To do both simply add a two constraints for each set. This is done to keep the mathematics behind the operations separate. It would be possible to extend these constraints to allow non-linear transformations if functionality to update the Jacobian at each position update was included. This would require passing an update function evaluate it every time adjust_positions is callled. This is currently NOT supported, and there are no plans to implement it in the future. Args: indices (list of int): indices of the constrained atoms (if not None or empty then cell_indices must be None or Empty) Jacobian (np.ndarray(shape=(3*len(indices), len(params)))): The Jacobian describing the parameter space transformation const_shift (np.ndarray(shape=(3*len(indices)))): A vector describing the constant term in the transformation not accounted for in the Jacobian params (list of str): parameters used in the parametric representation if None a list is generated based on the shape of the Jacobian eps (float): a small number to compare the similarity of numbers and set the precision used to generate the constraint expressions use_cell (bool): if True then act on the cell object """ self.indices = np.array(indices) self.Jacobian = np.array(Jacobian) self.const_shift = np.array(const_shift) assert self.const_shift.shape[0] == 3 * len(self.indices) assert self.Jacobian.shape[0] == 3 * len(self.indices) self.eps = eps self.use_cell = use_cell if params is None: params = [] if self.Jacobian.shape[1] > 0: int_fmt_str = "{:0" + \ str(int(np.ceil(np.log10(self.Jacobian.shape[1])))) + "d}" for param_ind in range(self.Jacobian.shape[1]): params.append("param_" + int_fmt_str.format(param_ind)) else: assert len(params) == self.Jacobian.shape[-1] self.params = params self.Jacobian_inv = np.linalg.inv( self.Jacobian.T @ self.Jacobian) @ self.Jacobian.T @classmethod def from_expressions(cls, indices, params, expressions, eps=1e-12, use_cell=False): """Converts the expressions into a Jacobian Matrix/const_shift vector and constructs a FixParametricRelations constraint The expressions must be a list like object of size 3*N and elements must be ordered as: [n_0,i; n_0,j; n_0,k; n_1,i; n_1,j; .... ; n_N-1,i; n_N-1,j; n_N-1,k], where i, j, and k are the first, second and third component of the atomic position/lattice vector. Currently only linear operations are allowed to be included in the expressions so only terms like: - const * param_0 - sqrt[const] * param_1 - const * param_0 +/- const * param_1 +/- ... +/- const * param_M where const is any real number and param_0, param_1, ..., param_M are the parameters passed in params, are allowed. For example, fractional atomic position constraints for wurtzite are: params = ["z1", "z2"] expressions = [ "1.0/3.0", "2.0/3.0", "z1", "2.0/3.0", "1.0/3.0", "0.5 + z1", "1.0/3.0", "2.0/3.0", "z2", "2.0/3.0", "1.0/3.0", "0.5 + z2", ] For diamond are: params = [] expressions = [ "0.0", "0.0", "0.0", "0.25", "0.25", "0.25", ], and for stannite are params=["x4", "z4"] expressions = [ "0.0", "0.0", "0.0", "0.0", "0.5", "0.5", "0.75", "0.25", "0.5", "0.25", "0.75", "0.5", "x4 + z4", "x4 + z4", "2*x4", "x4 - z4", "x4 - z4", "-2*x4", "0.0", "-1.0 * (x4 + z4)", "x4 - z4", "0.0", "x4 - z4", "-1.0 * (x4 + z4)", ] Args: indices (list of int): indices of the constrained atoms (if not None or empty then cell_indices must be None or Empty) params (list of str): parameters used in the parametric representation expressions (list of str): expressions used to convert from the parametric to the real space representation eps (float): a small number to compare the similarity of numbers and set the precision used to generate the constraint expressions use_cell (bool): if True then act on the cell object Returns: cls( indices, Jacobian generated from expressions, const_shift generated from expressions, params, eps-12, use_cell, ) """ Jacobian = np.zeros((3 * len(indices), len(params))) const_shift = np.zeros(3 * len(indices)) for expr_ind, expression in enumerate(expressions): expression = expression.strip() # Convert subtraction to addition expression = expression.replace("-", "+(-1.0)*") if expression[0] == "+": expression = expression[1:] elif expression[:2] == "(+": expression = "(" + expression[2:] # Explicitly add leading zeros so when replacing param_1 with 0.0 # param_11 does not become 0.01 int_fmt_str = "{:0" + \ str(int(np.ceil(np.log10(len(params) + 1)))) + "d}" param_dct = {} param_map = {} # Construct a standardized param template for A/B filling for param_ind, param in enumerate(params): param_str = "param_" + int_fmt_str.format(param_ind) param_map[param] = param_str param_dct[param_str] = 0.0 # Replace the parameters according to the map # Sort by string length (long to short) to prevent cases like x11 # becoming f"{param_map["x1"]}1" for param in sorted(params, key=lambda s: -1.0 * len(s)): expression = expression.replace(param, param_map[param]) # Partial linearity check for express_sec in expression.split("+"): in_sec = [param in express_sec for param in param_dct] n_params_in_sec = len(np.where(np.array(in_sec))[0]) if n_params_in_sec > 1: raise ValueError( "FixParametricRelations expressions must be linear.") const_shift[expr_ind] = float( eval_expression(expression, param_dct)) for param_ind in range(len(params)): param_str = "param_" + int_fmt_str.format(param_ind) if param_str not in expression: Jacobian[expr_ind, param_ind] = 0.0 continue param_dct[param_str] = 1.0 test_1 = float(eval_expression(expression, param_dct)) test_1 -= const_shift[expr_ind] Jacobian[expr_ind, param_ind] = test_1 param_dct[param_str] = 2.0 test_2 = float(eval_expression(expression, param_dct)) test_2 -= const_shift[expr_ind] if abs(test_2 / test_1 - 2.0) > eps: raise ValueError( "FixParametricRelations expressions must be linear.") param_dct[param_str] = 0.0 args = [ indices, Jacobian, const_shift, params, eps, use_cell, ] if cls is FixScaledParametricRelations: args = args[:-1] return cls(*args) @property def expressions(self): """Generate the expressions represented by the current self.Jacobian and self.const_shift objects""" expressions = [] per = int(round(-1 * np.log10(self.eps))) fmt_str = "{:." + str(per + 1) + "g}" for index, shift_val in enumerate(self.const_shift): exp = "" if np.all(np.abs(self.Jacobian[index]) < self.eps) or np.abs( shift_val) > self.eps: exp += fmt_str.format(shift_val) param_exp = "" for param_index, jacob_val in enumerate(self.Jacobian[index]): abs_jacob_val = np.round(np.abs(jacob_val), per + 1) if abs_jacob_val < self.eps: continue param = self.params[param_index] if param_exp or exp: if jacob_val > -1.0 * self.eps: param_exp += " + " else: param_exp += " - " elif (not exp) and (not param_exp) and ( jacob_val < -1.0 * self.eps): param_exp += "-" if np.abs(abs_jacob_val - 1.0) <= self.eps: param_exp += f"{param:s}" else: param_exp += (fmt_str + "*{:s}").format(abs_jacob_val, param) exp += param_exp expressions.append(exp) return np.array(expressions).reshape((-1, 3)) def todict(self): """Create a dictionary representation of the constraint""" return { "name": type(self).__name__, "kwargs": { "indices": self.indices, "params": self.params, "Jacobian": self.Jacobian, "const_shift": self.const_shift, "eps": self.eps, "use_cell": self.use_cell, } } def __repr__(self): """The str representation of the constraint""" if len(self.indices) > 1: indices_str = "[{:d}, ..., {:d}]".format( self.indices[0], self.indices[-1]) else: indices_str = f"[{self.indices[0]:d}]" if len(self.params) > 1: params_str = "[{:s}, ..., {:s}]".format( self.params[0], self.params[-1]) elif len(self.params) == 1: params_str = f"[{self.params[0]:s}]" else: params_str = "[]" return '{:s}({:s}, {:s}, ..., {:e})'.format( type(self).__name__, indices_str, params_str, self.eps ) class FixScaledParametricRelations(FixParametricRelations): def __init__( self, indices, Jacobian, const_shift, params=None, eps=1e-12, ): """The fractional coordinate version of FixParametricRelations All arguments are the same, but since this is for fractional coordinates use_cell is false""" super().__init__( indices, Jacobian, const_shift, params, eps, False, ) def adjust_contravariant(self, cell, vecs, B): """Adjust the values of a set of vectors that are contravariant with the unit transformation""" scaled = cell.scaled_positions(vecs).flatten() scaled = self.Jacobian_inv @ (scaled - B) scaled = ((self.Jacobian @ scaled) + B).reshape((-1, 3)) return cell.cartesian_positions(scaled) def adjust_positions(self, atoms, positions): """Adjust positions of the atoms to match the constraints""" positions[self.indices] = self.adjust_contravariant( atoms.cell, positions[self.indices], self.const_shift, ) positions[self.indices] = self.adjust_B( atoms.cell, positions[self.indices]) def adjust_B(self, cell, positions): """Wraps the positions back to the unit cell and adjust B to keep track of this change""" fractional = cell.scaled_positions(positions) wrapped_fractional = (fractional % 1.0) % 1.0 self.const_shift += np.round(wrapped_fractional - fractional).flatten() return cell.cartesian_positions(wrapped_fractional) def adjust_momenta(self, atoms, momenta): """Adjust momenta of the atoms to match the constraints""" momenta[self.indices] = self.adjust_contravariant( atoms.cell, momenta[self.indices], np.zeros(self.const_shift.shape), ) def adjust_forces(self, atoms, forces): """Adjust forces of the atoms to match the constraints""" # Forces are coavarient to the coordinate transformation, use the # inverse transformations cart2frac_jacob = np.zeros(2 * (3 * len(atoms),)) for i_atom in range(len(atoms)): cart2frac_jacob[3 * i_atom:3 * (i_atom + 1), 3 * i_atom:3 * (i_atom + 1)] = atoms.cell.T jacobian = cart2frac_jacob @ self.Jacobian jacobian_inv = np.linalg.inv(jacobian.T @ jacobian) @ jacobian.T reduced_forces = jacobian.T @ forces.flatten() forces[self.indices] = (jacobian_inv.T @ reduced_forces).reshape(-1, 3) def todict(self): """Create a dictionary representation of the constraint""" dct = super().todict() del dct["kwargs"]["use_cell"] return dct class FixCartesianParametricRelations(FixParametricRelations): def __init__( self, indices, Jacobian, const_shift, params=None, eps=1e-12, use_cell=False, ): """The Cartesian coordinate version of FixParametricRelations""" super().__init__( indices, Jacobian, const_shift, params, eps, use_cell, ) def adjust_contravariant(self, vecs, B): """Adjust the values of a set of vectors that are contravariant with the unit transformation""" vecs = self.Jacobian_inv @ (vecs.flatten() - B) vecs = ((self.Jacobian @ vecs) + B).reshape((-1, 3)) return vecs def adjust_positions(self, atoms, positions): """Adjust positions of the atoms to match the constraints""" if self.use_cell: return positions[self.indices] = self.adjust_contravariant( positions[self.indices], self.const_shift, ) def adjust_momenta(self, atoms, momenta): """Adjust momenta of the atoms to match the constraints""" if self.use_cell: return momenta[self.indices] = self.adjust_contravariant( momenta[self.indices], np.zeros(self.const_shift.shape), ) def adjust_forces(self, atoms, forces): """Adjust forces of the atoms to match the constraints""" if self.use_cell: return forces_reduced = self.Jacobian.T @ forces[self.indices].flatten() forces[self.indices] = (self.Jacobian_inv.T @ forces_reduced).reshape(-1, 3) def adjust_cell(self, atoms, cell): """Adjust the cell of the atoms to match the constraints""" if not self.use_cell: return cell[self.indices] = self.adjust_contravariant( cell[self.indices], np.zeros(self.const_shift.shape), ) def adjust_stress(self, atoms, stress): """Adjust the stress of the atoms to match the constraints""" if not self.use_cell: return stress_3x3 = voigt_6_to_full_3x3_stress(stress) stress_reduced = self.Jacobian.T @ stress_3x3[self.indices].flatten() stress_3x3[self.indices] = ( self.Jacobian_inv.T @ stress_reduced).reshape(-1, 3) stress[:] = full_3x3_to_voigt_6_stress(stress_3x3) class Hookean(FixConstraint): """Applies a Hookean restorative force between a pair of atoms, an atom and a point, or an atom and a plane.""" def __init__(self, a1, a2, k, rt=None): """Forces two atoms to stay close together by applying no force if they are below a threshold length, rt, and applying a Hookean restorative force when the distance between them exceeds rt. Can also be used to tether an atom to a fixed point in space or to a distance above a plane. a1 : int Index of atom 1 a2 : one of three options 1) index of atom 2 2) a fixed point in cartesian space to which to tether a1 3) a plane given as (A, B, C, D) in A x + B y + C z + D = 0. k : float Hooke's law (spring) constant to apply when distance exceeds threshold_length. Units of eV A^-2. rt : float The threshold length below which there is no force. The length is 1) between two atoms, 2) between atom and point. This argument is not supplied in case 3. Units of A. If a plane is specified, the Hooke's law force is applied if the atom is on the normal side of the plane. For instance, the plane with (A, B, C, D) = (0, 0, 1, -7) defines a plane in the xy plane with a z intercept of +7 and a normal vector pointing in the +z direction. If the atom has z > 7, then a downward force would be applied of k * (atom.z - 7). The same plane with the normal vector pointing in the -z direction would be given by (A, B, C, D) = (0, 0, -1, 7). References: Andrew A. Peterson, Topics in Catalysis volume 57, pages40–53 (2014) https://link.springer.com/article/10.1007%2Fs11244-013-0161-8 """ if isinstance(a2, int): self._type = 'two atoms' self.indices = [a1, a2] elif len(a2) == 3: self._type = 'point' self.index = a1 self.origin = np.array(a2) elif len(a2) == 4: self._type = 'plane' self.index = a1 self.plane = a2 else: raise RuntimeError('Unknown type for a2') self.threshold = rt self.spring = k def get_removed_dof(self, atoms): return 0 def todict(self): dct = {'name': 'Hookean'} dct['kwargs'] = {'rt': self.threshold, 'k': self.spring} if self._type == 'two atoms': dct['kwargs']['a1'] = self.indices[0] dct['kwargs']['a2'] = self.indices[1] elif self._type == 'point': dct['kwargs']['a1'] = self.index dct['kwargs']['a2'] = self.origin elif self._type == 'plane': dct['kwargs']['a1'] = self.index dct['kwargs']['a2'] = self.plane else: raise NotImplementedError(f'Bad type: {self._type}') return dct def adjust_positions(self, atoms, newpositions): pass def adjust_momenta(self, atoms, momenta): pass def adjust_forces(self, atoms, forces): positions = atoms.positions if self._type == 'plane': A, B, C, D = self.plane x, y, z = positions[self.index] d = ((A * x + B * y + C * z + D) / np.sqrt(A**2 + B**2 + C**2)) if d < 0: return magnitude = self.spring * d direction = - np.array((A, B, C)) / np.linalg.norm((A, B, C)) forces[self.index] += direction * magnitude return if self._type == 'two atoms': p1, p2 = positions[self.indices] elif self._type == 'point': p1 = positions[self.index] p2 = self.origin displace, _ = find_mic(p2 - p1, atoms.cell, atoms.pbc) bondlength = np.linalg.norm(displace) if bondlength > self.threshold: magnitude = self.spring * (bondlength - self.threshold) direction = displace / np.linalg.norm(displace) if self._type == 'two atoms': forces[self.indices[0]] += direction * magnitude forces[self.indices[1]] -= direction * magnitude else: forces[self.index] += direction * magnitude def adjust_potential_energy(self, atoms): """Returns the difference to the potential energy due to an active constraint. (That is, the quantity returned is to be added to the potential energy.)""" positions = atoms.positions if self._type == 'plane': A, B, C, D = self.plane x, y, z = positions[self.index] d = ((A * x + B * y + C * z + D) / np.sqrt(A**2 + B**2 + C**2)) if d > 0: return 0.5 * self.spring * d**2 else: return 0. if self._type == 'two atoms': p1, p2 = positions[self.indices] elif self._type == 'point': p1 = positions[self.index] p2 = self.origin displace, _ = find_mic(p2 - p1, atoms.cell, atoms.pbc) bondlength = np.linalg.norm(displace) if bondlength > self.threshold: return 0.5 * self.spring * (bondlength - self.threshold)**2 else: return 0. def get_indices(self): if self._type == 'two atoms': return self.indices elif self._type == 'point': return self.index elif self._type == 'plane': return self.index def index_shuffle(self, atoms, ind): # See docstring of superclass if self._type == 'two atoms': newa = [-1, -1] # Signal error for new, old in slice2enlist(ind, len(atoms)): for i, a in enumerate(self.indices): if old == a: newa[i] = new if newa[0] == -1 or newa[1] == -1: raise IndexError('Constraint not part of slice') self.indices = newa elif (self._type == 'point') or (self._type == 'plane'): newa = -1 # Signal error for new, old in slice2enlist(ind, len(atoms)): if old == self.index: newa = new break if newa == -1: raise IndexError('Constraint not part of slice') self.index = newa def __repr__(self): if self._type == 'two atoms': return 'Hookean(%d, %d)' % tuple(self.indices) elif self._type == 'point': return 'Hookean(%d) to cartesian' % self.index else: return 'Hookean(%d) to plane' % self.index class ExternalForce(FixConstraint): """Constraint object for pulling two atoms apart by an external force. You can combine this constraint for example with FixBondLength but make sure that *ExternalForce* comes first in the list if there are overlaps between atom1-2 and atom3-4: >>> from ase.build import bulk >>> atoms = bulk('Cu', 'fcc', a=3.6) >>> atom1, atom2, atom3, atom4 = atoms[:4] >>> fext = 1.0 >>> con1 = ExternalForce(atom1, atom2, f_ext) >>> con2 = FixBondLength(atom3, atom4) >>> atoms.set_constraint([con1, con2]) see ase/test/external_force.py""" def __init__(self, a1, a2, f_ext): self.indices = [a1, a2] self.external_force = f_ext def get_removed_dof(self, atoms): return 0 def adjust_positions(self, atoms, new): pass def adjust_forces(self, atoms, forces): dist = np.subtract.reduce(atoms.positions[self.indices]) force = self.external_force * dist / np.linalg.norm(dist) forces[self.indices] += (force, -force) def adjust_potential_energy(self, atoms): dist = np.subtract.reduce(atoms.positions[self.indices]) return -np.linalg.norm(dist) * self.external_force def index_shuffle(self, atoms, ind): """Shuffle the indices of the two atoms in this constraint""" newa = [-1, -1] # Signal error for new, old in slice2enlist(ind, len(atoms)): for i, a in enumerate(self.indices): if old == a: newa[i] = new if newa[0] == -1 or newa[1] == -1: raise IndexError('Constraint not part of slice') self.indices = newa def __repr__(self): return 'ExternalForce(%d, %d, %f)' % (self.indices[0], self.indices[1], self.external_force) def todict(self): return {'name': 'ExternalForce', 'kwargs': {'a1': self.indices[0], 'a2': self.indices[1], 'f_ext': self.external_force}} class MirrorForce(FixConstraint): """Constraint object for mirroring the force between two atoms. This class is designed to find a transition state with the help of a single optimization. It can be used if the transition state belongs to a bond breaking reaction. First the given bond length will be fixed until all other degrees of freedom are optimized, then the forces of the two atoms will be mirrored to find the transition state. The mirror plane is perpendicular to the connecting line of the atoms. Transition states in dependence of the force can be obtained by stretching the molecule and fixing its total length with *FixBondLength* or by using *ExternalForce* during the optimization with *MirrorForce*. Parameters ---------- a1: int First atom index. a2: int Second atom index. max_dist: float Upper limit of the bond length interval where the transition state can be found. min_dist: float Lower limit of the bond length interval where the transition state can be found. fmax: float Maximum force used for the optimization. Notes ----- You can combine this constraint for example with FixBondLength but make sure that *MirrorForce* comes first in the list if there are overlaps between atom1-2 and atom3-4: >>> from ase.build import bulk >>> atoms = bulk('Cu', 'fcc', a=3.6) >>> atom1, atom2, atom3, atom4 = atoms[:4] >>> con1 = MirrorForce(atom1, atom2) >>> con2 = FixBondLength(atom3, atom4) >>> atoms.set_constraint([con1, con2]) """ def __init__(self, a1, a2, max_dist=2.5, min_dist=1., fmax=0.1): self.indices = [a1, a2] self.min_dist = min_dist self.max_dist = max_dist self.fmax = fmax def adjust_positions(self, atoms, new): pass def adjust_forces(self, atoms, forces): dist = np.subtract.reduce(atoms.positions[self.indices]) d = np.linalg.norm(dist) if (d < self.min_dist) or (d > self.max_dist): # Stop structure optimization forces[:] *= 0 return dist /= d df = np.subtract.reduce(forces[self.indices]) f = df.dot(dist) con_saved = atoms.constraints try: con = [con for con in con_saved if not isinstance(con, MirrorForce)] atoms.set_constraint(con) forces_copy = atoms.get_forces() finally: atoms.set_constraint(con_saved) df1 = -1 / 2. * f * dist forces_copy[self.indices] += (df1, -df1) # Check if forces would be converged if the bond with mirrored forces # would also be fixed if (forces_copy**2).sum(axis=1).max() < self.fmax**2: factor = 1. else: factor = 0. df1 = -(1 + factor) / 2. * f * dist forces[self.indices] += (df1, -df1) def index_shuffle(self, atoms, ind): """Shuffle the indices of the two atoms in this constraint """ newa = [-1, -1] # Signal error for new, old in slice2enlist(ind, len(atoms)): for i, a in enumerate(self.indices): if old == a: newa[i] = new if newa[0] == -1 or newa[1] == -1: raise IndexError('Constraint not part of slice') self.indices = newa def __repr__(self): return 'MirrorForce(%d, %d, %f, %f, %f)' % ( self.indices[0], self.indices[1], self.max_dist, self.min_dist, self.fmax) def todict(self): return {'name': 'MirrorForce', 'kwargs': {'a1': self.indices[0], 'a2': self.indices[1], 'max_dist': self.max_dist, 'min_dist': self.min_dist, 'fmax': self.fmax}} class MirrorTorque(FixConstraint): """Constraint object for mirroring the torque acting on a dihedral angle defined by four atoms. This class is designed to find a transition state with the help of a single optimization. It can be used if the transition state belongs to a cis-trans-isomerization with a change of dihedral angle. First the given dihedral angle will be fixed until all other degrees of freedom are optimized, then the torque acting on the dihedral angle will be mirrored to find the transition state. Transition states in dependence of the force can be obtained by stretching the molecule and fixing its total length with *FixBondLength* or by using *ExternalForce* during the optimization with *MirrorTorque*. This constraint can be used to find transition states of cis-trans-isomerization. a1 a4 | | a2 __ a3 Parameters ---------- a1: int First atom index. a2: int Second atom index. a3: int Third atom index. a4: int Fourth atom index. max_angle: float Upper limit of the dihedral angle interval where the transition state can be found. min_angle: float Lower limit of the dihedral angle interval where the transition state can be found. fmax: float Maximum force used for the optimization. Notes ----- You can combine this constraint for example with FixBondLength but make sure that *MirrorTorque* comes first in the list if there are overlaps between atom1-4 and atom5-6: >>> from ase.build import bulk >>> atoms = bulk('Cu', 'fcc', a=3.6) >>> atom1, atom2, atom3, atom4, atom5, atom6 = atoms[:6] >>> con1 = MirrorTorque(atom1, atom2, atom3, atom4) >>> con2 = FixBondLength(atom5, atom6) >>> atoms.set_constraint([con1, con2]) """ def __init__(self, a1, a2, a3, a4, max_angle=2 * np.pi, min_angle=0., fmax=0.1): self.indices = [a1, a2, a3, a4] self.min_angle = min_angle self.max_angle = max_angle self.fmax = fmax def adjust_positions(self, atoms, new): pass def adjust_forces(self, atoms, forces): angle = atoms.get_dihedral(self.indices[0], self.indices[1], self.indices[2], self.indices[3]) angle *= np.pi / 180. if (angle < self.min_angle) or (angle > self.max_angle): # Stop structure optimization forces[:] *= 0 return p = atoms.positions[self.indices] f = forces[self.indices] f0 = (f[1] + f[2]) / 2. ff = f - f0 p0 = (p[2] + p[1]) / 2. m0 = np.cross(p[1] - p0, ff[1]) / (p[1] - p0).dot(p[1] - p0) fff = ff - np.cross(m0, p - p0) d1 = np.cross(np.cross(p[1] - p0, p[0] - p[1]), p[1] - p0) / \ (p[1] - p0).dot(p[1] - p0) d2 = np.cross(np.cross(p[2] - p0, p[3] - p[2]), p[2] - p0) / \ (p[2] - p0).dot(p[2] - p0) omegap1 = (np.cross(d1, fff[0]) / d1.dot(d1)).dot(p[1] - p0) / \ np.linalg.norm(p[1] - p0) omegap2 = (np.cross(d2, fff[3]) / d2.dot(d2)).dot(p[2] - p0) / \ np.linalg.norm(p[2] - p0) omegap = omegap1 + omegap2 con_saved = atoms.constraints try: con = [con for con in con_saved if not isinstance(con, MirrorTorque)] atoms.set_constraint(con) forces_copy = atoms.get_forces() finally: atoms.set_constraint(con_saved) df1 = -1 / 2. * omegap * np.cross(p[1] - p0, d1) / \ np.linalg.norm(p[1] - p0) df2 = -1 / 2. * omegap * np.cross(p[2] - p0, d2) / \ np.linalg.norm(p[2] - p0) forces_copy[self.indices] += (df1, [0., 0., 0.], [0., 0., 0.], df2) # Check if forces would be converged if the dihedral angle with # mirrored torque would also be fixed if (forces_copy**2).sum(axis=1).max() < self.fmax**2: factor = 1. else: factor = 0. df1 = -(1 + factor) / 2. * omegap * np.cross(p[1] - p0, d1) / \ np.linalg.norm(p[1] - p0) df2 = -(1 + factor) / 2. * omegap * np.cross(p[2] - p0, d2) / \ np.linalg.norm(p[2] - p0) forces[self.indices] += (df1, [0., 0., 0.], [0., 0., 0.], df2) def index_shuffle(self, atoms, ind): # See docstring of superclass indices = [] for new, old in slice2enlist(ind, len(atoms)): if old in self.indices: indices.append(new) if len(indices) == 0: raise IndexError('All indices in MirrorTorque not part of slice') self.indices = np.asarray(indices, int) def __repr__(self): return 'MirrorTorque(%d, %d, %d, %d, %f, %f, %f)' % ( self.indices[0], self.indices[1], self.indices[2], self.indices[3], self.max_angle, self.min_angle, self.fmax) def todict(self): return {'name': 'MirrorTorque', 'kwargs': {'a1': self.indices[0], 'a2': self.indices[1], 'a3': self.indices[2], 'a4': self.indices[3], 'max_angle': self.max_angle, 'min_angle': self.min_angle, 'fmax': self.fmax}} class FixSymmetry(FixConstraint): """ Constraint to preserve spacegroup symmetry during optimisation. Requires spglib package to be available. """ def __init__(self, atoms, symprec=0.01, adjust_positions=True, adjust_cell=True, verbose=False): self.atoms = atoms.copy() self.symprec = symprec self.verbose = verbose refine_symmetry(atoms, symprec, self.verbose) # refine initial symmetry sym = prep_symmetry(atoms, symprec, self.verbose) self.rotations, self.translations, self.symm_map = sym self.do_adjust_positions = adjust_positions self.do_adjust_cell = adjust_cell def adjust_cell(self, atoms, cell): if not self.do_adjust_cell: return # stress should definitely be symmetrized as a rank 2 tensor # UnitCellFilter uses deformation gradient as cell DOF with steps # dF = stress.F^-T quantity that should be symmetrized is therefore dF . # F^T assume prev F = I, so just symmetrize dF cur_cell = atoms.get_cell() cur_cell_inv = atoms.cell.reciprocal().T # F defined such that cell = cur_cell . F^T # assume prev F = I, so dF = F - I delta_deform_grad = np.dot(cur_cell_inv, cell).T - np.eye(3) # symmetrization doesn't work properly with large steps, since # it depends on current cell, and cell is being changed by deformation # gradient max_delta_deform_grad = np.max(np.abs(delta_deform_grad)) if max_delta_deform_grad > 0.25: raise RuntimeError('FixSymmetry adjust_cell does not work properly' ' with large deformation gradient step {} > 0.25' .format(max_delta_deform_grad)) elif max_delta_deform_grad > 0.15: warn('FixSymmetry adjust_cell may be ill behaved with large ' 'deformation gradient step {}'.format(max_delta_deform_grad)) symmetrized_delta_deform_grad = symmetrize_rank2(cur_cell, cur_cell_inv, delta_deform_grad, self.rotations) cell[:] = np.dot(cur_cell, (symmetrized_delta_deform_grad + np.eye(3)).T) def adjust_positions(self, atoms, new): if not self.do_adjust_positions: return # symmetrize changes in position as rank 1 tensors step = new - atoms.positions symmetrized_step = symmetrize_rank1(atoms.get_cell(), atoms.cell.reciprocal().T, step, self.rotations, self.translations, self.symm_map) new[:] = atoms.positions + symmetrized_step def adjust_forces(self, atoms, forces): # symmetrize forces as rank 1 tensors # print('adjusting forces') forces[:] = symmetrize_rank1(atoms.get_cell(), atoms.cell.reciprocal().T, forces, self.rotations, self.translations, self.symm_map) def adjust_stress(self, atoms, stress): # symmetrize stress as rank 2 tensor raw_stress = voigt_6_to_full_3x3_stress(stress) symmetrized_stress = symmetrize_rank2(atoms.get_cell(), atoms.cell.reciprocal().T, raw_stress, self.rotations) stress[:] = full_3x3_to_voigt_6_stress(symmetrized_stress) def index_shuffle(self, atoms, ind): if len(atoms) != len(ind) or len(set(ind)) != len(ind): raise RuntimeError("FixSymmetry can only accomodate atom" " permutions, and len(Atoms) == {} " "!= len(ind) == {} or ind has duplicates" .format(len(atoms), len(ind))) ind_reversed = np.zeros((len(ind)), dtype=int) ind_reversed[ind] = range(len(ind)) new_symm_map = [] for sm in self.symm_map: new_sm = np.array([-1] * len(atoms)) for at_i in range(len(ind)): new_sm[ind_reversed[at_i]] = ind_reversed[sm[at_i]] new_symm_map.append(new_sm) self.symm_map = new_symm_map def todict(self): return { 'name': 'FixSymmetry', 'kwargs': { 'atoms': self.atoms, 'symprec': self.symprec, 'adjust_positions': self.do_adjust_positions, 'adjust_cell': self.do_adjust_cell, 'verbose': self.verbose, }, } class Filter(FilterOld): @deprecated('Import Filter from ase.filters') def __init__(self, *args, **kwargs): """ .. deprecated:: 3.23.0 Import ``Filter`` from :mod:`ase.filters` """ super().__init__(*args, **kwargs) class StrainFilter(StrainFilterOld): @deprecated('Import StrainFilter from ase.filters') def __init__(self, *args, **kwargs): """ .. deprecated:: 3.23.0 Import ``StrainFilter`` from :mod:`ase.filters` """ super().__init__(*args, **kwargs) class UnitCellFilter(UnitCellFilterOld): @deprecated('Import UnitCellFilter from ase.filters') def __init__(self, *args, **kwargs): """ .. deprecated:: 3.23.0 Import ``UnitCellFilter`` from :mod:`ase.filters` """ super().__init__(*args, **kwargs) class ExpCellFilter(ExpCellFilterOld): @deprecated('Import ExpCellFilter from ase.filters') def __init__(self, *args, **kwargs): """ .. deprecated:: 3.23.0 Import ``ExpCellFilter`` from :mod:`ase.filters` or use :class:`~ase.filters.FrechetCellFilter` for better convergence w.r.t. cell variables """ super().__init__(*args, **kwargs)