Source code for pymatgen.analysis.structure_matcher

# 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.
"""

from __future__ import division, unicode_literals

import six
from six.moves import filter
from six.moves import zip

import numpy as np
import itertools
import abc

from monty.json import MSONable
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
from pymatgen.util.coord_cython import pbc_shortest_vectors, is_coord_subset_pbc
from pymatgen.util.coord import lattice_points_in_supercell

__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(six.with_metaclass(abc.ABCMeta, MSONable)): """ 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): 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 {"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.element_composition.keys()) set2 = set(sp2.element_composition.keys()) if set1.intersection(set2): return True return False
[docs] def get_hash(self, composition): """" No hash possible """ return 1
[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): # 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) 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): Method to use for determining the size of a supercell (if applicable). Possible values are num_sites, num_atoms, volume, or an element 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. """ 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): 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 else: try: el = get_el_sp(self._supercell_size) fu = s2.composition[el] / s1.composition[el] except: 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.lengths_and_angles) + np.array(l2.lengths_and_angles)) / 2 return Lattice.from_lengths_and_angles(*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): """ Fit two structures. Args: struct1 (Structure): 1st structure struct2 (Structure): 2nd structure 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 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
[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.modify_lattice(nl1) nl2 = Lattice(struct2.lattice.matrix / ratio) struct2.modify_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): Wheher 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: c_hash = lambda c: c.anonymized_formula else: c_hash = self._comparator.get_hash s_hash = lambda s: 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 {"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}
[docs] @classmethod def from_dict(cls, d): return StructureMatcher( ltol=d["ltol"], stol=d["stol"], angle_tol=d["angle_tol"], primitive_cell=d["primitive_cell"], scale=d["scale"], comparator=AbstractComparator.from_dict(d["comparator"]))
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_transformation(self, struct1, struct2): """ Returns the supercell transformation, fractional translation vector, and a mapping to transform struct2 to be similar to struct1. Args: struct1 (Structure): Reference structure struct2 (Structure): Structure to transform. Returns: supercell (numpy.ndarray(3, 3)): supercell matrix vector (numpy.ndarray(3)): fractional translation vector mapping (list(int or None)): The first len(struct1) items of the mapping vector are the indices of struct1's corresponding sites in struct2 (or None if there is no corresponding site), and the other items are the remaining site indices of struct2. """ if self._primitive_cell: raise ValueError("get_transformation cannot be used with the " "primitive cell option") struct1, struct2 = self._process_species((struct1, struct2)) s1, s2, fu, s1_supercell = self._preprocess(struct1, struct2, False) ratio = fu if s1_supercell else 1/fu if s1_supercell and fu > 1: raise ValueError("Struct1 must be the supercell, " "not the other way around") if len(s1) * ratio >= len(s2): # s1 is superset match = self._strict_match(s1, s2, fu=fu, s1_supercell=False, use_rms=True, break_on_match=False) if match is None: return None # invert the mapping, since it needs to be from s1 to s2 mapping = [list(match[4]).index(i) if i in match[4] else None for i in range(len(s1))] return match[2], match[3], mapping else: # s2 is superset match = self._strict_match(s2, s1, fu=fu, s1_supercell=True, use_rms=True, break_on_match=False) if match is None: return None # add sites not included in the mapping not_included = list(range(len(s2) * fu)) for i in match[4]: not_included.remove(i) mapping = list(match[4]) + not_included return match[2], -match[3], mapping
[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]