# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.
"""
This module provides classes to perform fitting of structures.
"""
import numpy as np
import itertools
import abc
from monty.json import MSONable
from pymatgen.core import PeriodicSite
from pymatgen.core.structure import Structure
from pymatgen.core.lattice import Lattice
from pymatgen.core.composition import Composition
from pymatgen.core.periodic_table import get_el_sp
from pymatgen.optimization.linear_assignment import LinearAssignment # type: ignore
from pymatgen.util.coord_cython import pbc_shortest_vectors, is_coord_subset_pbc # type: ignore
from pymatgen.util.coord import lattice_points_in_supercell
from pymatgen.analysis.defects.core import Interstitial, \
Defect, Vacancy, Substitution
__author__ = "William Davidson Richards, Stephen Dacek, Shyue Ping Ong"
__copyright__ = "Copyright 2011, The Materials Project"
__version__ = "1.0"
__maintainer__ = "William Davidson Richards"
__email__ = "wrichard@mit.edu"
__status__ = "Production"
__date__ = "Dec 3, 2012"
[docs]class AbstractComparator(MSONable, metaclass=abc.ABCMeta):
"""
Abstract Comparator class. A Comparator defines how sites are compared in
a structure.
"""
[docs] @abc.abstractmethod
def are_equal(self, sp1, sp2):
"""
Defines how the species of two sites are considered equal. For
example, one can consider sites to have the same species only when
the species are exactly the same, i.e., Fe2+ matches Fe2+ but not
Fe3+. Or one can define that only the element matters,
and all oxidation state information are ignored.
Args:
sp1: First species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
sp2: Second species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
Returns:
Boolean indicating whether species are considered equal.
"""
return
[docs] @abc.abstractmethod
def get_hash(self, composition):
"""
Defines a hash to group structures. This allows structures to be
grouped efficiently for comparison. The hash must be invariant under
supercell creation. (e.g. composition is not a good hash, but
fractional_composition might be). Reduced formula is not a good formula,
due to weird behavior with fractional occupancy.
Composition is used here instead of structure because for anonymous
matches it is much quicker to apply a substitution to a composition
object than a structure object.
Args:
composition (Composition): composition of the structure
Returns:
A hashable object. Examples can be string formulas, integers etc.
"""
return
[docs] @classmethod
def from_dict(cls, d):
"""
:param d: Dict representation
:return: Comparator.
"""
for trans_modules in ['structure_matcher']:
mod = __import__('pymatgen.analysis.' + trans_modules,
globals(), locals(), [d['@class']], 0)
if hasattr(mod, d['@class']):
trans = getattr(mod, d['@class'])
return trans()
raise ValueError("Invalid Comparator dict")
[docs] def as_dict(self):
"""
:return: MSONable dict
"""
return {"version": __version__, "@module": self.__class__.__module__,
"@class": self.__class__.__name__}
[docs]class SpeciesComparator(AbstractComparator):
"""
A Comparator that matches species exactly. The default used in
StructureMatcher.
"""
[docs] def are_equal(self, sp1, sp2):
"""
True if species are exactly the same, i.e., Fe2+ == Fe2+ but not Fe3+.
Args:
sp1: First species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
sp2: Second species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
Returns:
Boolean indicating whether species are equal.
"""
return sp1 == sp2
[docs] def get_hash(self, composition):
"""
Returns: Fractional composition
"""
return composition.fractional_composition
[docs]class SpinComparator(AbstractComparator):
"""
A Comparator that matches magnetic structures to their inverse spins.
This comparator is primarily used to filter magnetically ordered
structures with opposite spins, which are equivalent.
"""
[docs] def are_equal(self, sp1, sp2):
"""
True if species are exactly the same, i.e., Fe2+ == Fe2+ but not
Fe3+. and the spins are reversed. i.e., spin up maps to spin down,
and vice versa.
Args:
sp1: First species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
sp2: Second species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
Returns:
Boolean indicating whether species are equal.
"""
for s1 in sp1.keys():
spin1 = getattr(s1, "spin", 0)
oxi1 = getattr(s1, "oxi_state", 0)
for s2 in sp2.keys():
spin2 = getattr(s2, "spin", 0)
oxi2 = getattr(s2, "oxi_state", 0)
if (s1.symbol == s2.symbol and oxi1 == oxi2 and
spin2 == -spin1):
break
else:
return False
return True
[docs] def get_hash(self, composition):
"""
Returns: Fractional composition
"""
return composition.fractional_composition
[docs]class ElementComparator(AbstractComparator):
"""
A Comparator that matches elements. i.e. oxidation states are
ignored.
"""
[docs] def are_equal(self, sp1, sp2):
"""
True if element:amounts are exactly the same, i.e.,
oxidation state is not considered.
Args:
sp1: First species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
sp2: Second species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
Returns:
Boolean indicating whether species are the same based on element
and amounts.
"""
comp1 = Composition(sp1)
comp2 = Composition(sp2)
return comp1.get_el_amt_dict() == comp2.get_el_amt_dict()
[docs] def get_hash(self, composition):
"""
Returns: Fractional element composition
"""
return composition.element_composition.fractional_composition
[docs]class FrameworkComparator(AbstractComparator):
"""
A Comparator that matches sites, regardless of species.
"""
[docs] def are_equal(self, sp1, sp2):
"""
True if there are atoms on both sites.
Args:
sp1: First species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
sp2: Second species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
Returns:
True always
"""
return True
[docs] def get_hash(self, composition):
"""
No hash possible
"""
return 1
[docs]class OrderDisorderElementComparator(AbstractComparator):
"""
A Comparator that matches sites, given some overlap in the element
composition
"""
[docs] def are_equal(self, sp1, sp2):
"""
True if there is some overlap in composition between the species
Args:
sp1: First species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
sp2: Second species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
Returns:
True always
"""
set1 = set(sp1.elements)
set2 = set(sp2.elements)
return set1.issubset(set2) or set2.issubset(set1)
[docs] def get_hash(self, composition):
"""
Returns: Fractional composition
"""
return composition.fractional_composition
[docs]class OccupancyComparator(AbstractComparator):
"""
A Comparator that matches occupancies on sites,
irrespective of the species of those sites.
"""
[docs] def are_equal(self, sp1, sp2):
"""
Args:
sp1: First species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
sp2: Second species. A dict of {specie/element: amt} as per the
definition in Site and PeriodicSite.
Returns:
True if sets of occupancies (amt) are equal on both sites.
"""
set1 = set(sp1.element_composition.values())
set2 = set(sp2.element_composition.values())
if set1 == set2:
return True
else:
return False
[docs] def get_hash(self, composition):
"""
:param composition: Composition.
:return: 1. Difficult to define sensible hash
"""
return 1
[docs]class StructureMatcher(MSONable):
"""
Class to match structures by similarity.
Algorithm:
1. Given two structures: s1 and s2
2. Optional: Reduce to primitive cells.
3. If the number of sites do not match, return False
4. Reduce to s1 and s2 to Niggli Cells
5. Optional: Scale s1 and s2 to same volume.
6. Optional: Remove oxidation states associated with sites
7. Find all possible lattice vectors for s2 within shell of ltol.
8. For s1, translate an atom in the smallest set to the origin
9. For s2: find all valid lattices from permutations of the list
of lattice vectors (invalid if: det(Lattice Matrix) < half
volume of original s2 lattice)
10. For each valid lattice:
a. If the lattice angles of are within tolerance of s1,
basis change s2 into new lattice.
b. For each atom in the smallest set of s2:
i. Translate to origin and compare fractional sites in
structure within a fractional tolerance.
ii. If true:
ia. Convert both lattices to cartesian and place
both structures on an average lattice
ib. Compute and return the average and max rms
displacement between the two structures normalized
by the average free length per atom
if fit function called:
if normalized max rms displacement is less than
stol. Return True
if get_rms_dist function called:
if normalized average rms displacement is less
than the stored rms displacement, store and
continue. (This function will search all possible
lattices for the smallest average rms displacement
between the two structures)
"""
def __init__(self, ltol=0.2, stol=0.3, angle_tol=5, primitive_cell=True,
scale=True, attempt_supercell=False, allow_subset=False,
comparator=SpeciesComparator(), supercell_size='num_sites',
ignored_species=None):
"""
Args:
ltol (float): Fractional length tolerance. Default is 0.2.
stol (float): Site tolerance. Defined as the fraction of the
average free length per atom := ( V / Nsites ) ** (1/3)
Default is 0.3.
angle_tol (float): Angle tolerance in degrees. Default is 5 degrees.
primitive_cell (bool): If true: input structures will be reduced to
primitive cells prior to matching. Default to True.
scale (bool): Input structures are scaled to equivalent volume if
true; For exact matching, set to False.
attempt_supercell (bool): If set to True and number of sites in
cells differ after a primitive cell reduction (divisible by an
integer) attempts to generate a supercell transformation of the
smaller cell which is equivalent to the larger structure.
allow_subset (bool): Allow one structure to match to the subset of
another structure. Eg. Matching of an ordered structure onto a
disordered one, or matching a delithiated to a lithiated
structure. This option cannot be combined with
attempt_supercell, or with structure grouping.
comparator (Comparator): A comparator object implementing an equals
method that declares declaring equivalency of sites. Default is
SpeciesComparator, which implies rigid species
mapping, i.e., Fe2+ only matches Fe2+ and not Fe3+.
Other comparators are provided, e.g., ElementComparator which
matches only the elements and not the species.
The reason why a comparator object is used instead of
supplying a comparison function is that it is not possible to
pickle a function, which makes it otherwise difficult to use
StructureMatcher with Python's multiprocessing.
supercell_size (str or list): Method to use for determining the
size of a supercell (if applicable). Possible values are
num_sites, num_atoms, volume, or an element or list of elements
present in both structures.
ignored_species (list): A list of ions to be ignored in matching.
Useful for matching structures that have similar frameworks
except for certain ions, e.g., Li-ion intercalation frameworks.
This is more useful than allow_subset because it allows better
control over what species are ignored in the matching.
"""
self.ltol = ltol
self.stol = stol
self.angle_tol = angle_tol
self._comparator = comparator
self._primitive_cell = primitive_cell
self._scale = scale
self._supercell = attempt_supercell
self._supercell_size = supercell_size
self._subset = allow_subset
self._ignored_species = [] if ignored_species is None else \
ignored_species[:]
def _get_supercell_size(self, s1, s2):
"""
Returns the supercell size, and whether the supercell should
be applied to s1. If fu == 1, s1_supercell is returned as
true, to avoid ambiguity.
"""
if self._supercell_size == 'num_sites':
fu = s2.num_sites / s1.num_sites
elif self._supercell_size == 'num_atoms':
fu = s2.composition.num_atoms / s1.composition.num_atoms
elif self._supercell_size == 'volume':
fu = s2.volume / s1.volume
elif not isinstance(self._supercell_size, str):
s1comp, s2comp = 0, 0
for el in self._supercell_size:
el = get_el_sp(el)
s1comp += s1.composition[el]
s2comp += s2.composition[el]
fu = s2comp / s1comp
else:
el = get_el_sp(self._supercell_size)
if (el in s2.composition) and (el in s1.composition):
fu = s2.composition[el] / s1.composition[el]
else:
raise ValueError('Invalid argument for supercell_size.')
if fu < 2 / 3:
return int(round(1 / fu)), False
else:
return int(round(fu)), True
def _get_lattices(self, target_lattice, s, supercell_size=1):
"""
Yields lattices for s with lengths and angles close to the
lattice of target_s. If supercell_size is specified, the
returned lattice will have that number of primitive cells
in it
Args:
s, target_s: Structure objects
"""
lattices = s.lattice.find_all_mappings(
target_lattice, ltol=self.ltol, atol=self.angle_tol,
skip_rotation_matrix=True)
for l, _, scale_m in lattices:
if abs(abs(np.linalg.det(scale_m)) - supercell_size) < 0.5:
yield l, scale_m
def _get_supercells(self, struct1, struct2, fu, s1_supercell):
"""
Computes all supercells of one structure close to the lattice of the
other
if s1_supercell == True, it makes the supercells of struct1, otherwise
it makes them of s2
yields: s1, s2, supercell_matrix, average_lattice, supercell_matrix
"""
def av_lat(l1, l2):
params = (np.array(l1.parameters) +
np.array(l2.parameters)) / 2
return Lattice.from_parameters(*params)
def sc_generator(s1, s2):
s2_fc = np.array(s2.frac_coords)
if fu == 1:
cc = np.array(s1.cart_coords)
for l, sc_m in self._get_lattices(s2.lattice, s1, fu):
fc = l.get_fractional_coords(cc)
fc -= np.floor(fc)
yield fc, s2_fc, av_lat(l, s2.lattice), sc_m
else:
fc_init = np.array(s1.frac_coords)
for l, sc_m in self._get_lattices(s2.lattice, s1, fu):
fc = np.dot(fc_init, np.linalg.inv(sc_m))
lp = lattice_points_in_supercell(sc_m)
fc = (fc[:, None, :] + lp[None, :, :]).reshape((-1, 3))
fc -= np.floor(fc)
yield fc, s2_fc, av_lat(l, s2.lattice), sc_m
if s1_supercell:
for x in sc_generator(struct1, struct2):
yield x
else:
for x in sc_generator(struct2, struct1):
# reorder generator output so s1 is still first
yield x[1], x[0], x[2], x[3]
def _cmp_fstruct(self, s1, s2, frac_tol, mask):
"""
Returns true if a matching exists between s2 and s2
under frac_tol. s2 should be a subset of s1
"""
if len(s2) > len(s1):
raise ValueError("s1 must be larger than s2")
if mask.shape != (len(s2), len(s1)):
raise ValueError("mask has incorrect shape")
return is_coord_subset_pbc(s2, s1, frac_tol, mask)
def _cart_dists(self, s1, s2, avg_lattice, mask, normalization, lll_frac_tol=None):
"""
Finds a matching in cartesian space. Finds an additional
fractional translation vector to minimize RMS distance
Args:
s1, s2: numpy arrays of fractional coordinates. len(s1) >= len(s2)
avg_lattice: Lattice on which to calculate distances
mask: numpy array of booleans. mask[i, j] = True indicates
that s2[i] cannot be matched to s1[j]
normalization (float): inverse normalization length
Returns:
Distances from s2 to s1, normalized by (V/Natom) ^ 1/3
Fractional translation vector to apply to s2.
Mapping from s1 to s2, i.e. with numpy slicing, s1[mapping] => s2
"""
if len(s2) > len(s1):
raise ValueError("s1 must be larger than s2")
if mask.shape != (len(s2), len(s1)):
raise ValueError("mask has incorrect shape")
# vectors are from s2 to s1
vecs, d_2 = pbc_shortest_vectors(avg_lattice, s2, s1, mask,
return_d2=True,
lll_frac_tol=lll_frac_tol)
lin = LinearAssignment(d_2)
s = lin.solution
short_vecs = vecs[np.arange(len(s)), s]
translation = np.average(short_vecs, axis=0)
f_translation = avg_lattice.get_fractional_coords(translation)
new_d2 = np.sum((short_vecs - translation) ** 2, axis=-1)
return new_d2 ** 0.5 * normalization, f_translation, s
def _get_mask(self, struct1, struct2, fu, s1_supercell):
"""
Returns mask for matching struct2 to struct1. If struct1 has sites
a b c, and fu = 2, assumes supercells of struct2 will be ordered
aabbcc (rather than abcabc)
Returns:
mask, struct1 translation indices, struct2 translation index
"""
mask = np.zeros((len(struct2), len(struct1), fu), dtype=np.bool)
inner = []
for sp2, i in itertools.groupby(enumerate(struct2.species_and_occu),
key=lambda x: x[1]):
i = list(i)
inner.append((sp2, slice(i[0][0], i[-1][0] + 1)))
for sp1, j in itertools.groupby(enumerate(struct1.species_and_occu),
key=lambda x: x[1]):
j = list(j)
j = slice(j[0][0], j[-1][0] + 1)
for sp2, i in inner:
mask[i, j, :] = not self._comparator.are_equal(sp1, sp2)
if s1_supercell:
mask = mask.reshape((len(struct2), -1))
else:
# supercell is of struct2, roll fu axis back to preserve
# correct ordering
mask = np.rollaxis(mask, 2, 1)
mask = mask.reshape((-1, len(struct1)))
# find the best translation indices
i = np.argmax(np.sum(mask, axis=-1))
inds = np.where(np.invert(mask[i]))[0]
if s1_supercell:
# remove the symmetrically equivalent s1 indices
inds = inds[::fu]
return np.array(mask, dtype=np.int_), inds, i
[docs] def fit(self, struct1, struct2, symmetric=False):
"""
Fit two structures.
Args:
struct1 (Structure): 1st structure
struct2 (Structure): 2nd structure
symmetric (Bool): Defaults to False
If True, check the equality both ways.
This only impacts a small percentage of structures
Returns:
True or False.
"""
struct1, struct2 = self._process_species([struct1, struct2])
if not self._subset and self._comparator.get_hash(struct1.composition) \
!= self._comparator.get_hash(struct2.composition):
return None
if not symmetric:
struct1, struct2, fu, s1_supercell = self._preprocess(struct1, struct2)
match = self._match(struct1, struct2, fu, s1_supercell,
break_on_match=True)
if match is None:
return False
else:
return match[0] <= self.stol
else:
struct1, struct2, fu, s1_supercell = self._preprocess(struct1, struct2)
match1 = self._match(struct1, struct2, fu, s1_supercell,
break_on_match=True)
struct1, struct2 = struct2, struct1
struct1, struct2, fu, s1_supercell = self._preprocess(struct1, struct2)
match2 = self._match(struct1, struct2, fu, s1_supercell,
break_on_match=True)
if match1 is None or match2 is None:
return False
else:
return max(match1[0], match2[0]) <= self.stol
[docs] def get_rms_dist(self, struct1, struct2):
"""
Calculate RMS displacement between two structures
Args:
struct1 (Structure): 1st structure
struct2 (Structure): 2nd structure
Returns:
rms displacement normalized by (Vol / nsites) ** (1/3)
and maximum distance between paired sites. If no matching
lattice is found None is returned.
"""
struct1, struct2 = self._process_species([struct1, struct2])
struct1, struct2, fu, s1_supercell = self._preprocess(struct1, struct2)
match = self._match(struct1, struct2, fu, s1_supercell, use_rms=True,
break_on_match=False)
if match is None:
return None
else:
return match[0], max(match[1])
def _process_species(self, structures):
copied_structures = []
for s in structures:
# We need the copies to be actual Structure to work properly, not
# subclasses. So do type(s) == Structure.
ss = s.copy() if type(s) == Structure else \
Structure.from_sites(s)
if self._ignored_species:
ss.remove_species(self._ignored_species)
copied_structures.append(ss)
return copied_structures
def _preprocess(self, struct1, struct2, niggli=True):
"""
Rescales, finds the reduced structures (primitive and niggli),
and finds fu, the supercell size to make struct1 comparable to
s2
"""
struct1 = struct1.copy()
struct2 = struct2.copy()
if niggli:
struct1 = struct1.get_reduced_structure(reduction_algo="niggli")
struct2 = struct2.get_reduced_structure(reduction_algo="niggli")
# primitive cell transformation
if self._primitive_cell:
struct1 = struct1.get_primitive_structure()
struct2 = struct2.get_primitive_structure()
if self._supercell:
fu, s1_supercell = self._get_supercell_size(struct1, struct2)
else:
fu, s1_supercell = 1, True
mult = fu if s1_supercell else 1 / fu
# rescale lattice to same volume
if self._scale:
ratio = (struct2.volume / (struct1.volume * mult)) ** (1 / 6)
nl1 = Lattice(struct1.lattice.matrix * ratio)
struct1.lattice = nl1
nl2 = Lattice(struct2.lattice.matrix / ratio)
struct2.lattice = nl2
return struct1, struct2, fu, s1_supercell
def _match(self, struct1, struct2, fu, s1_supercell=True, use_rms=False,
break_on_match=False):
"""
Matches one struct onto the other
"""
ratio = fu if s1_supercell else 1 / fu
if len(struct1) * ratio >= len(struct2):
return self._strict_match(
struct1, struct2, fu, s1_supercell=s1_supercell,
break_on_match=break_on_match, use_rms=use_rms)
else:
return self._strict_match(
struct2, struct1, fu, s1_supercell=(not s1_supercell),
break_on_match=break_on_match, use_rms=use_rms)
def _strict_match(self, struct1, struct2, fu, s1_supercell=True,
use_rms=False, break_on_match=False):
"""
Matches struct2 onto struct1 (which should contain all sites in
struct2).
Args:
struct1, struct2 (Structure): structures to be matched
fu (int): size of supercell to create
s1_supercell (bool): whether to create the supercell of
struct1 (vs struct2)
use_rms (bool): whether to minimize the rms of the matching
break_on_match (bool): whether to stop search at first
valid match
"""
if fu < 1:
raise ValueError("fu cannot be less than 1")
mask, s1_t_inds, s2_t_ind = self._get_mask(struct1, struct2,
fu, s1_supercell)
if mask.shape[0] > mask.shape[1]:
raise ValueError('after supercell creation, struct1 must '
'have more sites than struct2')
# check that a valid mapping exists
if (not self._subset) and mask.shape[1] != mask.shape[0]:
return None
if LinearAssignment(mask).min_cost > 0:
return None
best_match = None
# loop over all lattices
for s1fc, s2fc, avg_l, sc_m in \
self._get_supercells(struct1, struct2, fu, s1_supercell):
# compute fractional tolerance
normalization = (len(s1fc) / avg_l.volume) ** (1 / 3)
inv_abc = np.array(avg_l.reciprocal_lattice.abc)
frac_tol = inv_abc * self.stol / (np.pi * normalization)
# loop over all translations
for s1i in s1_t_inds:
t = s1fc[s1i] - s2fc[s2_t_ind]
t_s2fc = s2fc + t
if self._cmp_fstruct(s1fc, t_s2fc, frac_tol, mask):
inv_lll_abc = np.array(avg_l.get_lll_reduced_lattice().reciprocal_lattice.abc)
lll_frac_tol = inv_lll_abc * self.stol / (np.pi * normalization)
dist, t_adj, mapping = self._cart_dists(
s1fc, t_s2fc, avg_l, mask, normalization, lll_frac_tol)
if use_rms:
val = np.linalg.norm(dist) / len(dist) ** 0.5
else:
val = max(dist)
if best_match is None or val < best_match[0]:
total_t = t + t_adj
total_t -= np.round(total_t)
best_match = val, dist, sc_m, total_t, mapping
if (break_on_match or val < 1e-5) and val < self.stol:
return best_match
if best_match and best_match[0] < self.stol:
return best_match
[docs] def group_structures(self, s_list, anonymous=False):
"""
Given a list of structures, use fit to group
them by structural equality.
Args:
s_list ([Structure]): List of structures to be grouped
anonymous (bool): Whether to use anonymous mode.
Returns:
A list of lists of matched structures
Assumption: if s1 == s2 but s1 != s3, than s2 and s3 will be put
in different groups without comparison.
"""
if self._subset:
raise ValueError("allow_subset cannot be used with"
" group_structures")
original_s_list = list(s_list)
s_list = self._process_species(s_list)
# Use structure hash to pre-group structures
if anonymous:
def c_hash(c):
return c.anonymized_formula
else:
c_hash = self._comparator.get_hash
def s_hash(s):
return c_hash(s[1].composition)
sorted_s_list = sorted(enumerate(s_list), key=s_hash)
all_groups = []
# For each pre-grouped list of structures, perform actual matching.
for k, g in itertools.groupby(sorted_s_list, key=s_hash):
unmatched = list(g)
while len(unmatched) > 0:
i, refs = unmatched.pop(0)
matches = [i]
if anonymous:
inds = filter(lambda i: self.fit_anonymous(refs,
unmatched[i][1]), list(range(len(unmatched))))
else:
inds = filter(lambda i: self.fit(refs, unmatched[i][1]),
list(range(len(unmatched))))
inds = list(inds)
matches.extend([unmatched[i][0] for i in inds])
unmatched = [unmatched[i] for i in range(len(unmatched))
if i not in inds]
all_groups.append([original_s_list[i] for i in matches])
return all_groups
[docs] def as_dict(self):
"""
:return: MSONable dict
"""
return {"version": __version__, "@module": self.__class__.__module__,
"@class": self.__class__.__name__,
"comparator": self._comparator.as_dict(),
"stol": self.stol,
"ltol": self.ltol,
"angle_tol": self.angle_tol,
"primitive_cell": self._primitive_cell,
"scale": self._scale,
"attempt_supercell": self._supercell,
"allow_subset": self._subset,
"supercell_size": self._supercell_size,
"ignored_species": self._ignored_species}
[docs] @classmethod
def from_dict(cls, d):
"""
:param d: Dict representation
:return: StructureMatcher
"""
return StructureMatcher(
ltol=d["ltol"], stol=d["stol"], angle_tol=d["angle_tol"],
primitive_cell=d["primitive_cell"], scale=d["scale"],
attempt_supercell=d["attempt_supercell"],
allow_subset=d["allow_subset"],
comparator=AbstractComparator.from_dict(d["comparator"]),
supercell_size=d["supercell_size"],
ignored_species=d["ignored_species"])
def _anonymous_match(self, struct1, struct2, fu, s1_supercell=True,
use_rms=False, break_on_match=False, single_match=False):
"""
Tries all permutations of matching struct1 to struct2.
Args:
struct1, struct2 (Structure): Preprocessed input structures
Returns:
List of (mapping, match)
"""
if not isinstance(self._comparator, SpeciesComparator):
raise ValueError('Anonymous fitting currently requires SpeciesComparator')
# check that species lists are comparable
sp1 = struct1.composition.elements
sp2 = struct2.composition.elements
if len(sp1) != len(sp2):
return None
ratio = fu if s1_supercell else 1 / fu
swapped = len(struct1) * ratio < len(struct2)
s1_comp = struct1.composition
s2_comp = struct2.composition
matches = []
for perm in itertools.permutations(sp2):
sp_mapping = dict(zip(sp1, perm))
# do quick check that compositions are compatible
mapped_comp = Composition({sp_mapping[k]: v
for k, v in s1_comp.items()})
if (not self._subset) and (
self._comparator.get_hash(mapped_comp) !=
self._comparator.get_hash(s2_comp)):
continue
mapped_struct = struct1.copy()
mapped_struct.replace_species(sp_mapping)
if swapped:
m = self._strict_match(struct2, mapped_struct, fu,
(not s1_supercell), use_rms,
break_on_match)
else:
m = self._strict_match(mapped_struct, struct2, fu, s1_supercell,
use_rms, break_on_match)
if m:
matches.append((sp_mapping, m))
if single_match:
break
return matches
[docs] def get_rms_anonymous(self, struct1, struct2):
"""
Performs an anonymous fitting, which allows distinct species in one
structure to map to another. E.g., to compare if the Li2O and Na2O
structures are similar.
Args:
struct1 (Structure): 1st structure
struct2 (Structure): 2nd structure
Returns:
(min_rms, min_mapping)
min_rms is the minimum rms distance, and min_mapping is the
corresponding minimal species mapping that would map
struct1 to struct2. (None, None) is returned if the minimax_rms
exceeds the threshold.
"""
struct1, struct2 = self._process_species([struct1, struct2])
struct1, struct2, fu, s1_supercell = self._preprocess(struct1, struct2)
matches = self._anonymous_match(struct1, struct2, fu, s1_supercell,
use_rms=True, break_on_match=False)
if matches:
best = sorted(matches, key=lambda x: x[1][0])[0]
return best[1][0], best[0]
else:
return None, None
[docs] def get_best_electronegativity_anonymous_mapping(self, struct1, struct2):
"""
Performs an anonymous fitting, which allows distinct species in one
structure to map to another. E.g., to compare if the Li2O and Na2O
structures are similar. If multiple substitutions are within tolerance
this will return the one which minimizes the difference in
electronegativity between the matches species.
Args:
struct1 (Structure): 1st structure
struct2 (Structure): 2nd structure
Returns:
min_mapping (Dict): Mapping of struct1 species to struct2 species
"""
struct1, struct2 = self._process_species([struct1, struct2])
struct1, struct2, fu, s1_supercell = self._preprocess(struct1, struct2)
matches = self._anonymous_match(struct1, struct2, fu, s1_supercell,
use_rms=True, break_on_match=True)
if matches:
min_X_diff = np.inf
for m in matches:
X_diff = 0
for k, v in m[0].items():
X_diff += struct1.composition[k] * (k.X - v.X) ** 2
if X_diff < min_X_diff:
min_X_diff = X_diff
best = m[0]
return best
[docs] def get_all_anonymous_mappings(self, struct1, struct2, niggli=True,
include_dist=False):
"""
Performs an anonymous fitting, which allows distinct species in one
structure to map to another. Returns a dictionary of species
substitutions that are within tolerance
Args:
struct1 (Structure): 1st structure
struct2 (Structure): 2nd structure
niggli (bool): Find niggli cell in preprocessing
include_dist (bool): Return the maximin distance with each mapping
Returns:
list of species mappings that map struct1 to struct2.
"""
struct1, struct2 = self._process_species([struct1, struct2])
struct1, struct2, fu, s1_supercell = self._preprocess(struct1, struct2,
niggli)
matches = self._anonymous_match(struct1, struct2, fu, s1_supercell,
break_on_match=not include_dist)
if matches:
if include_dist:
return [(m[0], m[1][0]) for m in matches]
else:
return [m[0] for m in matches]
[docs] def fit_anonymous(self, struct1, struct2, niggli=True):
"""
Performs an anonymous fitting, which allows distinct species in one
structure to map to another. E.g., to compare if the Li2O and Na2O
structures are similar.
Args:
struct1 (Structure): 1st structure
struct2 (Structure): 2nd structure
Returns:
True/False: Whether a species mapping can map struct1 to stuct2
"""
struct1, struct2 = self._process_species([struct1, struct2])
struct1, struct2, fu, s1_supercell = self._preprocess(struct1, struct2,
niggli)
matches = self._anonymous_match(struct1, struct2, fu, s1_supercell,
break_on_match=True, single_match=True)
if matches:
return True
else:
return False
[docs] def get_supercell_matrix(self, supercell, struct):
"""
Returns the matrix for transforming struct to supercell. This
can be used for very distorted 'supercells' where the primitive cell
is impossible to find
"""
if self._primitive_cell:
raise ValueError("get_supercell_matrix cannot be used with the "
"primitive cell option")
struct, supercell, fu, s1_supercell = self._preprocess(struct,
supercell, False)
if not s1_supercell:
raise ValueError("The non-supercell must be put onto the basis"
" of the supercell, not the other way around")
match = self._match(struct, supercell, fu, s1_supercell, use_rms=True,
break_on_match=False)
if match is None:
return None
return match[2]
[docs] def get_s2_like_s1(self, struct1, struct2, include_ignored_species=True):
"""
Performs transformations on struct2 to put it in a basis similar to
struct1 (without changing any of the inter-site distances)
Args:
struct1 (Structure): Reference structure
struct2 (Structure): Structure to transform.
include_ignored_species (bool): Defaults to True,
the ignored_species is also transformed to the struct1
lattice orientation, though obviously there is no direct
matching to existing sites.
Returns:
A structure object similar to struct1, obtained by making a
supercell, sorting, and translating struct2.
"""
s1, s2 = self._process_species([struct1, struct2])
trans = self.get_transformation(s1, s2)
if trans is None:
return None
sc, t, mapping = trans
sites = [site for site in s2]
# Append the ignored sites at the end.
sites.extend([site for site in struct2 if site not in s2])
temp = Structure.from_sites(sites)
temp.make_supercell(sc)
temp.translate_sites(list(range(len(temp))), t)
# translate sites to correct unit cell
for i, j in enumerate(mapping[:len(s1)]):
if j is not None:
vec = np.round(struct1[i].frac_coords - temp[j].frac_coords)
temp.translate_sites(j, vec, to_unit_cell=False)
sites = [temp.sites[i] for i in mapping if i is not None]
if include_ignored_species:
start = int(round(len(temp) / len(struct2) * len(s2)))
sites.extend(temp.sites[start:])
return Structure.from_sites(sites)
[docs] def get_mapping(self, superset, subset):
"""
Calculate the mapping from superset to subset.
Args:
superset (Structure): Structure containing at least the sites in
subset (within the structure matching tolerance)
subset (Structure): Structure containing some of the sites in
superset (within the structure matching tolerance)
Returns:
numpy array such that superset.sites[mapping] is within matching
tolerance of subset.sites or None if no such mapping is possible
"""
if self._supercell:
raise ValueError("cannot compute mapping to supercell")
if self._primitive_cell:
raise ValueError("cannot compute mapping with primitive cell "
"option")
if len(subset) > len(superset):
raise ValueError("subset is larger than superset")
superset, subset, _, _ = self._preprocess(superset, subset, True)
match = self._strict_match(superset, subset, 1, break_on_match=False)
if match is None or match[0] > self.stol:
return None
return match[4]
[docs]class PointDefectComparator(MSONable):
"""
A class that matches pymatgen Point Defect objects even if their
cartesian co-ordinates are different (compares sublattices for the defect)
NOTE: for defect complexes (more than a single defect),
this comparator will break.
"""
def __init__(self, check_charge=False, check_primitive_cell=False,
check_lattice_scale=False):
"""
Args:
check_charge (bool): Gives option to check
if charges are identical.
Default is False (different charged defects can be same)
check_primitive_cell (bool): Gives option to
compare different supercells of bulk_structure,
rather than directly compare supercell sizes
Default is False (requires bulk_structure in each defect to be same size)
check_lattice_scale (bool): Gives option to scale volumes of
structures to each other identical lattice constants.
Default is False (enforces same
lattice constants in both structures)
"""
self.check_charge = check_charge
self.check_primitive_cell = check_primitive_cell
self.check_lattice_scale = check_lattice_scale
[docs] def are_equal(self, d1, d2):
"""
Args:
d1: First defect. A pymatgen Defect object.
d2: Second defect. A pymatgen Defect object.
Returns:
True if defects are identical in type and sublattice.
"""
possible_defect_types = (Defect, Vacancy, Substitution, Interstitial)
if not isinstance(d1, possible_defect_types) or not isinstance(d2, possible_defect_types):
raise ValueError("Cannot use PointDefectComparator to"
" compare non-defect objects...")
if not isinstance(d1, d2.__class__):
return False
elif d1.site.specie != d2.site.specie:
return False
elif self.check_charge and (d1.charge != d2.charge):
return False
sm = StructureMatcher(ltol=0.01,
primitive_cell=self.check_primitive_cell,
scale=self.check_lattice_scale)
if not sm.fit(d1.bulk_structure, d2.bulk_structure):
return False
d1 = d1.copy()
d2 = d2.copy()
if self.check_primitive_cell or self.check_lattice_scale:
# if allowing for base structure volume or supercell modifications,
# then need to preprocess defect objects to allow for matching
d1_mod_bulk_structure, d2_mod_bulk_structure, _, _ = sm._preprocess(
d1.bulk_structure, d2.bulk_structure)
d1_defect_site = PeriodicSite(d1.site.specie, d1.site.coords,
d1_mod_bulk_structure.lattice,
to_unit_cell=True,
coords_are_cartesian=True)
d2_defect_site = PeriodicSite(d2.site.specie, d2.site.coords,
d2_mod_bulk_structure.lattice,
to_unit_cell=True,
coords_are_cartesian=True)
d1._structure = d1_mod_bulk_structure
d2._structure = d2_mod_bulk_structure
d1._defect_site = d1_defect_site
d2._defect_site = d2_defect_site
return sm.fit(d1.generate_defect_structure(),
d2.generate_defect_structure())