"""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."""
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
[docs]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()}}
[docs]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': {}}
[docs]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] + ', ...]'
[docs]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')
[docs]def FixBondLength(a1, a2):
"""Fix distance between atoms with indices a1 and a2."""
return FixBondLengths([(a1, a2)])
[docs]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')
[docs]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
[docs]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
[docs]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
[docs]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
[docs] @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.row_stack(aa[:, i]))
txx = aa[:, self.n] * np.row_stack(aa[:, self.n])
tyy = aa[:, self.n + 1] * np.row_stack(aa[:, self.n + 1])
tzz = aa[:, self.n + 2] * np.row_stack(aa[:, self.n + 2])
rxx = aa[:, self.n + 3] * np.row_stack(aa[:, self.n + 3])
ryy = aa[:, self.n + 4] * np.row_stack(aa[:, self.n + 4])
rzz = aa[:, self.n + 5] * np.row_stack(aa[:, self.n + 5])
T = txx + tyy + tzz + rxx + ryy + rzz
for vec in hh:
T += vec
ff = np.dot(T, np.row_stack(ff))
forces[:, :] -= np.dot(T, np.row_stack(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)
[docs]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
[docs]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}}
[docs]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)