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/pymatgen/analysis/magnetism/analyzer.py

# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.

"""
This module provides some useful functions for dealing with magnetic Structures
(e.g. Structures with associated magmom tags).
"""

from __future__ import annotations

import logging
import os
import warnings
from collections import namedtuple
from enum import Enum, unique
from typing import Any

import numpy as np
from monty.serialization import loadfn
from scipy.signal import argrelextrema
from scipy.stats import gaussian_kde

from pymatgen.core.structure import DummySpecies, Element, Species, Structure
from pymatgen.electronic_structure.core import Magmom
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from pymatgen.symmetry.groups import SpaceGroup
from pymatgen.transformations.advanced_transformations import (
    MagOrderingTransformation,
    MagOrderParameterConstraint,
)
from pymatgen.transformations.standard_transformations import (
    AutoOxiStateDecorationTransformation,
)
from pymatgen.util.typing import VectorLike

__author__ = "Matthew Horton"
__copyright__ = "Copyright 2017, The Materials Project"
__version__ = "0.1"
__maintainer__ = "Matthew Horton"
__email__ = "mkhorton@lbl.gov"
__status__ = "Development"
__date__ = "Feb 2017"

MODULE_DIR = os.path.dirname(os.path.abspath(__file__))

try:
    DEFAULT_MAGMOMS = loadfn(os.path.join(MODULE_DIR, "default_magmoms.yaml"))
except Exception:
    warnings.warn("Could not load default_magmoms.yaml, falling back to VASPIncarBase.yaml")
    DEFAULT_MAGMOMS = loadfn(os.path.join(MODULE_DIR, "../../io/vasp/VASPIncarBase.yaml"))
    DEFAULT_MAGMOMS = DEFAULT_MAGMOMS["MAGMOM"]


@unique
class Ordering(Enum):
    """
    Enumeration defining possible magnetic orderings.
    """

    FM = "FM"  # Ferromagnetic
    AFM = "AFM"  # Antiferromagnetic
    FiM = "FiM"  # Ferrimagnetic
    NM = "NM"  # Non-magnetic
    Unknown = "Unknown"


@unique
class OverwriteMagmomMode(Enum):
    """
    Enumeration defining different modes for analyzer.
    """

    none = "none"
    respect_sign = "respect_sign"
    respect_zero = "respect_zeros"
    replace_all = "replace_all"
    normalize = "normalize"


class CollinearMagneticStructureAnalyzer:
    """
    A class which provides a few helpful methods to analyze
    collinear magnetic structures.
    """

    def __init__(
        self,
        structure: Structure,
        overwrite_magmom_mode: OverwriteMagmomMode | str = "none",
        round_magmoms: bool = False,
        detect_valences: bool = False,
        make_primitive: bool = True,
        default_magmoms: dict | None = None,
        set_net_positive: bool = True,
        threshold: float = 0.00,
        threshold_nonmag: float = 0.1,
    ):
        """
        If magnetic moments are not defined, moments will be
        taken either from default_magmoms.yaml (similar to the
        default magmoms in MPRelaxSet, with a few extra definitions)
        or from a specie:magmom dict provided by the default_magmoms
        kwarg.

        Input magmoms can be replaced using the 'overwrite_magmom_mode'
        kwarg. This can be:
        * "none" to do nothing,
        * "respect_sign" which will overwrite existing magmoms with
          those from default_magmoms but will keep sites with positive magmoms
          positive, negative magmoms negative and zero magmoms zero,
        * "respect_zeros", which will give a ferromagnetic structure
          (all positive magmoms from default_magmoms) but still keep sites with
          zero magmoms as zero,
        * "replace_all" which will try to guess initial magmoms for
          all sites in the structure irrespective of input structure
          (this is most suitable for an initial DFT calculation),
        * "replace_all_if_undefined" is the same as "replace_all" but only if
          no magmoms are defined in input structure, otherwise it will respect
          existing magmoms.
        * "normalize" will normalize magmoms to unity, but will respect sign
          (used for comparing orderings), magmoms < theshhold will be set to zero

        Args:
            structure: input Structure object
            overwrite_magmom_mode: "respect_sign", "respect_zeros", "replace_all",
                "replace_all_if_undefined", "normalize" (default "none")
            round_magmoms: will round input magmoms to
                specified number of decimal places if integer is supplied, if set
                to a float will try and group magmoms together using a kernel density
                estimator of provided width, and extracting peaks of the estimator
                detect_valences: if True, will attempt to assign valences
                to input structure
            make_primitive: if True, will transform to primitive
                magnetic cell
            default_magmoms: (optional) dict specifying default magmoms
            set_net_positive: if True, will change sign of magnetic
                moments such that the net magnetization is positive. Argument will be
                ignored if mode "respect_sign" is used.
            threshold: number (in Bohr magnetons) below which magmoms
                will be rounded to zero
            threshold_nonmag: number (in Bohr magneton)
                below which nonmagnetic ions (with no magmom specified
                in default_magmoms) will be rounded to zero
        """
        if default_magmoms:
            self.default_magmoms = default_magmoms
        else:
            self.default_magmoms = DEFAULT_MAGMOMS

        structure = structure.copy()

        # check for disorder
        if not structure.is_ordered:
            raise NotImplementedError("Not implemented for disordered structures, make ordered approximation first.")

        if detect_valences:
            trans = AutoOxiStateDecorationTransformation()
            try:
                structure = trans.apply_transformation(structure)
            except ValueError:
                warnings.warn(f"Could not assign valences for {structure.composition.reduced_formula}")

        # check to see if structure has magnetic moments
        # on site properties or species spin properties,
        # prioritize site properties

        has_magmoms = bool(structure.site_properties.get("magmom", False))

        has_spin = False
        for comp in structure.species_and_occu:
            for sp in comp:
                if getattr(sp, "spin", False):
                    has_spin = True

        # perform input sanitation ...
        # rest of class will assume magnetic moments
        # are stored on site properties:
        # this is somewhat arbitrary, arguments can
        # be made for both approaches

        if has_magmoms and has_spin:
            raise ValueError(
                "Structure contains magnetic moments on both "
                "magmom site properties and spin species "
                "properties. This is ambiguous. Remove one or "
                "the other."
            )
        if has_magmoms:
            if None in structure.site_properties["magmom"]:
                warnings.warn(
                    "Be careful with mixing types in your magmom "
                    "site properties. Any 'None' magmoms have been "
                    "replaced with zero."
                )
            magmoms = [m or 0 for m in structure.site_properties["magmom"]]
        elif has_spin:
            magmoms = [getattr(sp, "spin", 0) for sp in structure.species]
            structure.remove_spin()
        else:
            # no magmoms present, add zero magmoms for now
            magmoms = [0] * len(structure)
            # and overwrite magmoms with default magmoms later unless otherwise stated
            if overwrite_magmom_mode == "replace_all_if_undefined":
                overwrite_magmom_mode = "replace_all"

        # test to see if input structure has collinear magmoms
        self.is_collinear = Magmom.are_collinear(magmoms)

        if not self.is_collinear:
            warnings.warn(
                "This class is not designed to be used with "
                "non-collinear structures. If your structure is "
                "only slightly non-collinear (e.g. canted) may still "
                "give useful results, but use with caution."
            )

        # this is for collinear structures only, make sure magmoms
        # are all floats
        magmoms = list(map(float, magmoms))

        # set properties that should be done /before/ we process input magmoms
        self.total_magmoms = sum(magmoms)
        self.magnetization = sum(magmoms) / structure.volume

        # round magmoms on magnetic ions below threshold to zero
        # and on non magnetic ions below threshold_nonmag
        magmoms = [
            m
            if abs(m) > threshold and a.species_string in self.default_magmoms
            else m
            if abs(m) > threshold_nonmag and a.species_string not in self.default_magmoms
            else 0
            for (m, a) in zip(magmoms, structure.sites)
        ]

        # overwrite existing magmoms with default_magmoms
        if overwrite_magmom_mode not in (
            "none",
            "respect_sign",
            "respect_zeros",
            "replace_all",
            "replace_all_if_undefined",
            "normalize",
        ):
            raise ValueError("Unsupported mode.")

        for idx, site in enumerate(structure):
            if site.species_string in self.default_magmoms:
                # look for species first, e.g. Fe2+
                default_magmom = self.default_magmoms[site.species_string]
            elif isinstance(site.specie, Species) and str(site.specie.element) in self.default_magmoms:
                # look for element, e.g. Fe
                default_magmom = self.default_magmoms[str(site.specie.element)]
            else:
                default_magmom = 0

            # overwrite_magmom_mode = "respect_sign" will change magnitude of
            # existing moments only, and keep zero magmoms as
            # zero: it will keep the magnetic ordering intact

            if overwrite_magmom_mode == "respect_sign":
                set_net_positive = False
                if magmoms[idx] > 0:
                    magmoms[idx] = default_magmom
                elif magmoms[idx] < 0:
                    magmoms[idx] = -default_magmom

            # overwrite_magmom_mode = "respect_zeros" will give a ferromagnetic
            # structure but will keep zero magmoms as zero

            elif overwrite_magmom_mode == "respect_zeros":
                if magmoms[idx] != 0:
                    magmoms[idx] = default_magmom

            # overwrite_magmom_mode = "replace_all" will ignore input magmoms
            # and give a ferromagnetic structure with magnetic
            # moments on *all* atoms it thinks could be magnetic

            elif overwrite_magmom_mode == "replace_all":
                magmoms[idx] = default_magmom

            # overwrite_magmom_mode = "normalize" set magmoms magnitude to 1

            elif overwrite_magmom_mode == "normalize":
                if magmoms[idx] != 0:
                    magmoms[idx] = int(magmoms[idx] / abs(magmoms[idx]))

        # round magmoms, used to smooth out computational data
        magmoms = self._round_magmoms(magmoms, round_magmoms) if round_magmoms else magmoms  # type: ignore

        if set_net_positive:
            sign = np.sum(magmoms)
            if sign < 0:
                magmoms = [-x for x in magmoms]

        structure.add_site_property("magmom", magmoms)

        if make_primitive:
            structure = structure.get_primitive_structure(use_site_props=True)

        self.structure = structure

    @staticmethod
    def _round_magmoms(magmoms: VectorLike, round_magmoms_mode: int | float) -> np.ndarray:
        """If round_magmoms_mode is an integer, simply round to that number
        of decimal places, else if set to a float will try and round
        intelligently by grouping magmoms.
        """
        if isinstance(round_magmoms_mode, int):
            # simple rounding to number of decimal places
            magmoms = np.around(magmoms, decimals=round_magmoms_mode)

        elif isinstance(round_magmoms_mode, float):
            try:
                # get range of possible magmoms, pad by 50% just to be safe
                range_m = max([max(magmoms), abs(min(magmoms))]) * 1.5

                # construct kde, here "round_magmoms_mode" is the width of the kde
                kernel = gaussian_kde(magmoms, bw_method=round_magmoms_mode)

                # with a linearly spaced grid 1000x finer than width
                xgrid = np.linspace(-range_m, range_m, int(1000 * range_m / round_magmoms_mode))

                # and evaluate the kde on this grid, extracting the maxima of the kde peaks
                kernel_m = kernel.evaluate(xgrid)
                extrema = xgrid[argrelextrema(kernel_m, comparator=np.greater)]

                # round magmoms to these extrema
                magmoms = [extrema[(np.abs(extrema - m)).argmin()] for m in magmoms]

            except Exception as e:
                # TODO: typically a singular matrix warning, investigate this
                warnings.warn("Failed to round magmoms intelligently, falling back to simple rounding.")
                warnings.warn(str(e))

            # and finally round roughly to the number of significant figures in our kde width
            num_decimals = len(str(round_magmoms_mode).split(".")[1]) + 1
            magmoms = np.around(magmoms, decimals=num_decimals)

        return np.array(magmoms)

    def get_structure_with_spin(self) -> Structure:
        """Returns a Structure with species decorated with spin values instead
        of using magmom site properties.
        """
        structure = self.structure.copy()
        structure.add_spin_by_site(structure.site_properties["magmom"])
        structure.remove_site_property("magmom")

        return structure

    def get_structure_with_only_magnetic_atoms(self, make_primitive: bool = True) -> Structure:
        """Returns a Structure with only magnetic atoms present.

        Args:
          make_primitive: Whether to make structure primitive after
            removing non-magnetic atoms (Default value = True)

        Returns: Structure
        """
        sites = [site for site in self.structure if abs(site.properties["magmom"]) > 0]

        structure = Structure.from_sites(sites)

        if make_primitive:
            structure = structure.get_primitive_structure(use_site_props=True)

        return structure

    def get_nonmagnetic_structure(self, make_primitive: bool = True) -> Structure:
        """Returns a Structure without magnetic moments defined.

        Args:
          make_primitive: Whether to make structure primitive after
            removing magnetic information (Default value = True)

        Returns:
          Structure
        """
        structure = self.structure.copy()
        structure.remove_site_property("magmom")

        if make_primitive:
            structure = structure.get_primitive_structure()

        return structure

    def get_ferromagnetic_structure(self, make_primitive: bool = True) -> Structure:
        """Returns a Structure with all magnetic moments positive
        or zero.

        Args:
          make_primitive: Whether to make structure primitive after
            making all magnetic moments positive (Default value = True)

        Returns:
          Structure
        """
        structure = self.structure.copy()

        structure.add_site_property("magmom", [abs(m) for m in self.magmoms])

        if make_primitive:
            structure = structure.get_primitive_structure(use_site_props=True)

        return structure

    @property
    def is_magnetic(self) -> bool:
        """Convenience property, returns True if any non-zero magmoms present."""
        return any(map(abs, self.structure.site_properties["magmom"]))

    @property
    def magmoms(self) -> np.ndarray:
        """Convenience property, returns magmoms as a numpy array."""

        return np.array(self.structure.site_properties["magmom"])

    @property
    def types_of_magnetic_species(
        self,
    ) -> tuple[Element | Species | DummySpecies, ...]:
        """Equivalent to Structure.types_of_specie but only returns
        magnetic species.

        Returns: types of Species as a list
        """
        if self.number_of_magnetic_sites > 0:
            structure = self.get_structure_with_only_magnetic_atoms()
            return tuple(sorted(structure.types_of_species))
        return tuple()

    @property
    def types_of_magnetic_specie(
        self,
    ) -> tuple[Element | Species | DummySpecies, ...]:
        """
        Specie->Species rename. Used to maintain backwards compatibility.
        """
        return self.types_of_magnetic_species

    @property
    def magnetic_species_and_magmoms(self) -> dict[str, Any]:
        """Returns a dict of magnetic species and the magnitude of
        their associated magmoms. Will return a list if there are
        multiple magmoms per species.

        Returns: dict of magnetic species and magmoms
        """
        structure = self.get_ferromagnetic_structure()

        magtypes: dict = {str(site.specie): set() for site in structure if site.properties["magmom"] != 0}

        for site in structure:
            if site.properties["magmom"] != 0:
                magtypes[str(site.specie)].add(site.properties["magmom"])

        for sp, magmoms in magtypes.items():
            if len(magmoms) == 1:
                magtypes[sp] = magmoms.pop()
            else:
                magtypes[sp] = sorted(list(magmoms))

        return magtypes

    @property
    def number_of_magnetic_sites(self) -> int:
        """Number of magnetic sites present in structure."""
        return int(np.sum([abs(m) > 0 for m in self.magmoms]))

    def number_of_unique_magnetic_sites(self, symprec: float = 1e-3, angle_tolerance: float = 5) -> int:
        """
        Args:
          symprec: same as in SpacegroupAnalyzer (Default value = 1e-3)
          angle_tolerance: same as in SpacegroupAnalyzer (Default value = 5)

        Returns: Number of symmetrically-distinct magnetic sites present
        in structure.
        """
        structure = self.get_nonmagnetic_structure()

        sga = SpacegroupAnalyzer(structure, symprec=symprec, angle_tolerance=angle_tolerance)

        symm_structure = sga.get_symmetrized_structure()

        num_unique_mag_sites = 0

        for group_of_sites in symm_structure.equivalent_sites:
            if group_of_sites[0].specie in self.types_of_magnetic_species:
                num_unique_mag_sites += 1

        return num_unique_mag_sites

    @property
    def ordering(self) -> Ordering:
        """Applies heuristics to return a magnetic ordering for a collinear
        magnetic structure. Result is not guaranteed for correctness.

        Returns: Ordering Enum ('FiM' is used as the abbreviation for
        ferrimagnetic)
        """
        if not self.is_collinear:
            warnings.warn("Detecting ordering in non-collinear structures not yet implemented.")
            return Ordering.Unknown

        if "magmom" not in self.structure.site_properties:
            # maybe this was a non-spin-polarized calculation, or we've
            # lost the magnetic moment information
            return Ordering.Unknown

        magmoms = self.magmoms

        max_magmom = max(magmoms)

        total_magnetization = abs(sum(magmoms))

        is_potentially_ferromagnetic = np.all(magmoms >= 0) or np.all(magmoms <= 0)

        if total_magnetization > 0 and is_potentially_ferromagnetic:
            return Ordering.FM
        if total_magnetization > 0:
            return Ordering.FiM
        if max_magmom > 0:
            return Ordering.AFM
        return Ordering.NM

    def get_exchange_group_info(self, symprec: float = 1e-2, angle_tolerance: float = 5.0) -> tuple[str, int]:
        """Returns the information on the symmetry of the Hamiltonian
        describing the exchange energy of the system, taking into
        account relative direction of magnetic moments but not their
        absolute direction.

        This is not strictly accurate (e.g. some/many atoms will
        have zero magnetic moments), but defining symmetry this
        way is a useful way of keeping track of distinct magnetic
        orderings within pymatgen.

        Args:
          symprec: same as SpacegroupAnalyzer (Default value = 1e-2)
          angle_tolerance: same as SpacegroupAnalyzer (Default value = 5.0)

        Returns:
          spacegroup_symbol, international_number
        """
        structure = self.get_structure_with_spin()

        return structure.get_space_group_info(symprec=symprec, angle_tolerance=angle_tolerance)

    def matches_ordering(self, other: Structure) -> bool:
        """Compares the magnetic orderings of one structure with another.

        Args:
          other: Structure to compare

        Returns: True or False
        """
        a = CollinearMagneticStructureAnalyzer(
            self.structure, overwrite_magmom_mode="normalize"
        ).get_structure_with_spin()

        # sign of spins doesn't matter, so we're comparing both
        # positive and negative versions of the structure
        # this code is possibly redundant, but is included out of
        # an abundance of caution
        b_positive = CollinearMagneticStructureAnalyzer(other, overwrite_magmom_mode="normalize", make_primitive=False)

        b_negative = b_positive.structure.copy()
        b_negative.add_site_property("magmom", np.multiply(-1, b_negative.site_properties["magmom"]))

        b_negative = CollinearMagneticStructureAnalyzer(
            b_negative, overwrite_magmom_mode="normalize", make_primitive=False
        )

        b_positive = b_positive.get_structure_with_spin()
        b_negative = b_negative.get_structure_with_spin()

        return a.matches(b_positive) or a.matches(b_negative)

    def __str__(self):
        """
        Sorts a Structure (by fractional coordinate), and
        prints sites with magnetic information. This is
        useful over Structure.__str__ because sites are in
        a consistent order, which makes visual comparison between
        two identical Structures with different magnetic orderings
        easier.
        """
        frac_coords = self.structure.frac_coords
        sorted_indices = np.lexsort((frac_coords[:, 2], frac_coords[:, 1], frac_coords[:, 0]))
        s = Structure.from_sites([self.structure[idx] for idx in sorted_indices])

        # adapted from Structure.__repr__
        outs = ["Structure Summary", repr(s.lattice)]
        outs.append("Magmoms Sites")
        for site in s:
            if site.properties["magmom"] != 0:
                prefix = f"{site.properties['magmom']:+.2f}   "
            else:
                prefix = "        "
            outs.append(prefix + repr(site))
        return "\n".join(outs)


class MagneticStructureEnumerator:
    """Combines MagneticStructureAnalyzer and MagOrderingTransformation to
    automatically generate a set of transformations for a given structure
    and produce a list of plausible magnetic orderings.
    """

    available_strategies = (
        "ferromagnetic",
        "antiferromagnetic",
        "ferrimagnetic_by_motif",
        "ferrimagnetic_by_species",
        "antiferromagnetic_by_motif",
        "nonmagnetic",
    )

    def __init__(
        self,
        structure: Structure,
        default_magmoms: dict[str, float] | None = None,
        strategies: list[str]
        | tuple[str, ...] = (
            "ferromagnetic",
            "antiferromagnetic",
        ),
        automatic: bool = True,
        truncate_by_symmetry: bool = True,
        transformation_kwargs: dict | None = None,
    ):
        """
        This class will try generated different collinear
        magnetic orderings for a given input structure.

        If the input structure has magnetic moments defined, it
        is possible to use these as a hint as to which elements are
        magnetic, otherwise magnetic elements will be guessed
        (this can be changed using default_magmoms kwarg).

        Args:
            structure: input structure
            default_magmoms: (optional, defaults provided) dict of
                magnetic elements to their initial magnetic moments in µB, generally
                these are chosen to be high-spin since they can relax to a low-spin
                configuration during a DFT electronic configuration
            strategies: different ordering strategies to use, choose from:
                ferromagnetic, antiferromagnetic, antiferromagnetic_by_motif,
                ferrimagnetic_by_motif and ferrimagnetic_by_species (here, "motif",
                means to use a different ordering parameter for symmetry inequivalent
                sites)
            automatic: if True, will automatically choose sensible strategies
            truncate_by_symmetry: if True, will remove very unsymmetrical
                orderings that are likely physically implausible
            transformation_kwargs: keyword arguments to pass to
                MagOrderingTransformation, to change automatic cell size limits, etc.
        """
        self.logger = logging.getLogger(type(self).__name__)

        self.structure = structure

        # decides how to process input structure, which sites are magnetic
        self.default_magmoms = default_magmoms

        # different strategies to attempt, default is usually reasonable
        self.strategies = list(strategies)
        # and whether to automatically add strategies that may be appropriate
        self.automatic = automatic

        # and whether to discard low symmetry structures
        self.truncate_by_symmetry = truncate_by_symmetry

        # other settings
        self.num_orderings = 64
        self.max_unique_sites = 8

        # kwargs to pass to transformation (ultimately to enumlib)
        default_transformation_kwargs = {"check_ordered_symmetry": False, "timeout": 5}
        transformation_kwargs = transformation_kwargs or {}
        transformation_kwargs.update(default_transformation_kwargs)
        self.transformation_kwargs = transformation_kwargs

        # our magnetically ordered structures will be
        # stored here once generated and also store which
        # transformation created them, this is used for
        # book-keeping/user interest, and
        # is be a list of strings in ("fm", "afm",
        # "ferrimagnetic_by_species", "ferrimagnetic_by_motif",
        # "afm_by_motif", "input_structure")
        self.ordered_structures: list[Structure] = []
        self.ordered_structure_origins: list[str] = []

        formula = structure.composition.reduced_formula

        # to process disordered magnetic structures, first make an
        # ordered approximation
        if not structure.is_ordered:
            raise ValueError(f"Please obtain an ordered approximation of the input structure ({formula}).")

        # CollinearMagneticStructureAnalyzer is used throughout:
        # it can tell us whether the input is itself collinear (if not,
        # this workflow is not appropriate), and has many convenience
        # methods e.g. magnetic structure matching, etc.
        self.input_analyzer = CollinearMagneticStructureAnalyzer(
            structure, default_magmoms=default_magmoms, overwrite_magmom_mode="none"
        )

        # this workflow enumerates structures with different combinations
        # of up and down spin and does not include spin-orbit coupling:
        # if your input structure has vector magnetic moments, this
        # workflow is not appropriate
        if not self.input_analyzer.is_collinear:
            raise ValueError(f"Input structure ({formula}) is non-collinear.")

        self.sanitized_structure = self._sanitize_input_structure(structure)

        # we will first create a set of transformations
        # and then apply them to our input structure
        self.transformations = self._generate_transformations(self.sanitized_structure)
        self._generate_ordered_structures(self.sanitized_structure, self.transformations)

    @staticmethod
    def _sanitize_input_structure(input_structure: Structure) -> Structure:
        """Sanitize our input structure by removing magnetic information
        and making primitive.

        Args:
          input_structure: Structure

        Returns: Structure
        """
        input_structure = input_structure.copy()

        # remove any annotated spin
        input_structure.remove_spin()

        # sanitize input structure: first make primitive ...
        input_structure = input_structure.get_primitive_structure(use_site_props=False)

        # ... and strip out existing magmoms, which can cause conflicts
        # with later transformations otherwise since sites would end up
        # with both magmom site properties and Species spins defined
        if "magmom" in input_structure.site_properties:
            input_structure.remove_site_property("magmom")

        return input_structure

    def _generate_transformations(self, structure: Structure) -> dict[str, MagOrderingTransformation]:
        """The central problem with trying to enumerate magnetic orderings is
        that we have to enumerate orderings that might plausibly be magnetic
        ground states, while not enumerating orderings that are physically
        implausible. The problem is that it is not always obvious by e.g.
        symmetry arguments alone which orderings to prefer. Here, we use a
        variety of strategies (heuristics) to enumerate plausible orderings,
        and later discard any duplicates that might be found by multiple
        strategies. This approach is not ideal, but has been found to be
        relatively robust over a wide range of magnetic structures.

        Args:
          structure: A sanitized input structure (_sanitize_input_structure)
        Returns: A dict of a transformation class instance (values) and name of
        enumeration strategy (keys)

        Returns: dict of Transformations keyed by strategy
        """
        formula = structure.composition.reduced_formula
        transformations: dict[str, MagOrderingTransformation] = {}

        # analyzer is used to obtain information on sanitized input
        analyzer = CollinearMagneticStructureAnalyzer(
            structure,
            default_magmoms=self.default_magmoms,
            overwrite_magmom_mode="replace_all",
        )

        if not analyzer.is_magnetic:
            raise ValueError(
                "Not detected as magnetic, add a new default magmom for the element you believe may be magnetic?"
            )

        # now we can begin to generate our magnetic orderings
        self.logger.info(f"Generating magnetic orderings for {formula}")

        mag_species_spin = analyzer.magnetic_species_and_magmoms
        types_mag_species = sorted(
            analyzer.types_of_magnetic_species,
            key=lambda sp: analyzer.default_magmoms.get(str(sp), 0),
            reverse=True,
        )
        num_mag_sites = analyzer.number_of_magnetic_sites
        num_unique_sites = analyzer.number_of_unique_magnetic_sites()

        # enumerations become too slow as number of unique sites (and thus
        # permutations) increase, 8 is a soft limit, this can be increased
        # but do so with care
        if num_unique_sites > self.max_unique_sites:
            raise ValueError("Too many magnetic sites to sensibly perform enumeration.")

        # maximum cell size to consider: as a rule of thumb, if the primitive cell
        # contains a large number of magnetic sites, perhaps we only need to enumerate
        # within one cell, whereas on the other extreme if the primitive cell only
        # contains a single magnetic site, we have to create larger supercells
        if "max_cell_size" not in self.transformation_kwargs:
            # TODO: change to 8 / num_mag_sites ?
            self.transformation_kwargs["max_cell_size"] = max(1, int(4 / num_mag_sites))
        self.logger.info(f"Max cell size set to {self.transformation_kwargs['max_cell_size']}")

        # when enumerating ferrimagnetic structures, it's useful to detect
        # symmetrically distinct magnetic sites, since different
        # local environments can result in different magnetic order
        # (e.g. inverse spinels)
        # initially, this was done by co-ordination number, but is
        # now done by a full symmetry analysis
        sga = SpacegroupAnalyzer(structure)
        structure_sym = sga.get_symmetrized_structure()
        wyckoff = ["n/a"] * len(structure)
        for indices, symbol in zip(structure_sym.equivalent_indices, structure_sym.wyckoff_symbols):
            for index in indices:
                wyckoff[index] = symbol
        is_magnetic_sites = [site.specie in types_mag_species for site in structure]
        # we're not interested in sites that we don't think are magnetic,
        # set these symbols to None to filter them out later
        wyckoff = [
            symbol if is_magnetic_site else "n/a" for symbol, is_magnetic_site in zip(wyckoff, is_magnetic_sites)
        ]
        structure.add_site_property("wyckoff", wyckoff)
        wyckoff_symbols = set(wyckoff) - {"n/a"}

        # if user doesn't specifically request ferrimagnetic orderings,
        # we apply a heuristic as to whether to attempt them or not
        if self.automatic:
            if (
                "ferrimagnetic_by_motif" not in self.strategies
                and len(wyckoff_symbols) > 1
                and len(types_mag_species) == 1
            ):
                self.strategies += ["ferrimagnetic_by_motif"]

            if (
                "antiferromagnetic_by_motif" not in self.strategies
                and len(wyckoff_symbols) > 1
                and len(types_mag_species) == 1
            ):
                self.strategies += ["antiferromagnetic_by_motif"]

            if "ferrimagnetic_by_species" not in self.strategies and len(types_mag_species) > 1:
                self.strategies += ["ferrimagnetic_by_species"]

        # we start with a ferromagnetic ordering
        if "ferromagnetic" in self.strategies:
            # TODO: remove 0 spins !

            fm_structure = analyzer.get_ferromagnetic_structure()
            # store magmom as spin property, to be consistent with output from
            # other transformations
            fm_structure.add_spin_by_site(fm_structure.site_properties["magmom"])  # type: ignore[arg-type]
            fm_structure.remove_site_property("magmom")

            # we now have our first magnetic ordering...
            self.ordered_structures.append(fm_structure)
            self.ordered_structure_origins.append("fm")

        # we store constraint(s) for each strategy first,
        # and then use each to perform a transformation later
        all_constraints: dict[str, Any] = {}

        # ...to which we can add simple AFM cases first...
        if "antiferromagnetic" in self.strategies:
            constraint = MagOrderParameterConstraint(
                0.5,
                # TODO: update MagOrderParameterConstraint in
                # pymatgen to take types_mag_species directly
                species_constraints=list(map(str, types_mag_species)),
            )
            all_constraints["afm"] = [constraint]

            # allows for non-magnetic sublattices
            if len(types_mag_species) > 1:
                for sp in types_mag_species:
                    constraints = [MagOrderParameterConstraint(0.5, species_constraints=str(sp))]

                    all_constraints[f"afm_by_{sp}"] = constraints

        # ...and then we also try ferrimagnetic orderings by motif if a
        # single magnetic species is present...
        if "ferrimagnetic_by_motif" in self.strategies and len(wyckoff_symbols) > 1:
            # these orderings are AFM on one local environment, and FM on the rest
            for symbol in wyckoff_symbols:
                constraints = [
                    MagOrderParameterConstraint(0.5, site_constraint_name="wyckoff", site_constraints=symbol),
                    MagOrderParameterConstraint(
                        1.0,
                        site_constraint_name="wyckoff",
                        site_constraints=list(wyckoff_symbols - {symbol}),
                    ),
                ]

                all_constraints[f"ferri_by_motif_{symbol}"] = constraints

        # and also try ferrimagnetic when there are multiple magnetic species
        if "ferrimagnetic_by_species" in self.strategies:
            sp_list = [str(site.specie) for site in structure]
            num_sp = {sp: sp_list.count(str(sp)) for sp in types_mag_species}
            total_mag_sites = sum(num_sp.values())

            for sp in types_mag_species:
                # attempt via a global order parameter
                all_constraints[f"ferri_by_{sp}"] = num_sp[sp] / total_mag_sites

                # attempt via afm on sp, fm on remaining species

                constraints = [
                    MagOrderParameterConstraint(0.5, species_constraints=str(sp)),
                    MagOrderParameterConstraint(
                        1.0,
                        species_constraints=list(map(str, set(types_mag_species) - {sp})),
                    ),
                ]

                all_constraints[f"ferri_by_{sp}_afm"] = constraints

        # ...and finally, we can try orderings that are AFM on one local
        # environment, and non-magnetic on the rest -- this is less common
        # but unless explicitly attempted, these states are unlikely to be found
        if "antiferromagnetic_by_motif" in self.strategies:
            for symbol in wyckoff_symbols:
                constraints = [
                    MagOrderParameterConstraint(0.5, site_constraint_name="wyckoff", site_constraints=symbol)
                ]

                all_constraints[f"afm_by_motif_{symbol}"] = constraints

        # and now construct all our transformations for each strategy
        transformations = {}
        for name, constraints in all_constraints.items():
            trans = MagOrderingTransformation(
                mag_species_spin, order_parameter=constraints, **self.transformation_kwargs
            )

            transformations[name] = trans

        return transformations

    def _generate_ordered_structures(
        self,
        sanitized_input_structure: Structure,
        transformations: dict[str, MagOrderingTransformation],
    ):
        """Apply our input structure to our list of transformations and output a list
        of ordered structures that have been pruned for duplicates and for those
        with low symmetry (optional).

        Args:
            sanitized_input_structure: A sanitized input structure
            (_sanitize_input_structure)
            transformations: A dict of transformations (values) and name of
            enumeration strategy (key), the enumeration strategy name is just
            for record keeping

        Returns: None (sets self.ordered_structures
        and self.ordered_structures_origins instance variables)

        Returns: List of Structures
        """
        ordered_structures = self.ordered_structures
        ordered_structures_origins = self.ordered_structure_origins

        # utility function to combine outputs from several transformations
        def _add_structures(ordered_structures, ordered_structures_origins, structures_to_add, origin=""):
            """Transformations with return_ranked_list can return either
            just Structures or dicts (or sometimes lists!) -- until this
            is fixed, we use this function to concat structures given
            by the transformation.
            """
            if structures_to_add:
                if isinstance(structures_to_add, Structure):
                    structures_to_add = [structures_to_add]
                structures_to_add = [s["structure"] if isinstance(s, dict) else s for s in structures_to_add]
                # concatenation
                ordered_structures += structures_to_add
                ordered_structures_origins += [origin] * len(structures_to_add)
                self.logger.info(f"Adding {len(structures_to_add)} ordered structures: {origin}")

            return ordered_structures, ordered_structures_origins

        for origin, trans in self.transformations.items():
            structures_to_add = trans.apply_transformation(
                self.sanitized_structure, return_ranked_list=self.num_orderings
            )
            ordered_structures, ordered_structures_origins = _add_structures(
                ordered_structures,
                ordered_structures_origins,
                structures_to_add,
                origin=origin,
            )

        # in case we've introduced duplicates, let's remove them
        self.logger.info("Pruning duplicate structures.")
        structures_to_remove: list[int] = []
        for idx, ordered_structure in enumerate(ordered_structures):
            if idx not in structures_to_remove:
                duplicate_checker = CollinearMagneticStructureAnalyzer(ordered_structure, overwrite_magmom_mode="none")
                for check_idx, check_structure in enumerate(ordered_structures):
                    if check_idx not in structures_to_remove and check_idx != idx:
                        if duplicate_checker.matches_ordering(check_structure):
                            structures_to_remove.append(check_idx)

        if len(structures_to_remove) == 0:
            self.logger.info(f"Removing {len(structures_to_remove)} duplicate ordered structures")
            ordered_structures = [s for idx, s in enumerate(ordered_structures) if idx not in structures_to_remove]
            ordered_structures_origins = [
                o for idx, o in enumerate(ordered_structures_origins) if idx not in structures_to_remove
            ]

        # also remove low symmetry structures
        if self.truncate_by_symmetry:
            # by default, keep structures with 5 most symmetric space groups
            if not isinstance(self.truncate_by_symmetry, int):
                self.truncate_by_symmetry = 5

            self.logger.info("Pruning low symmetry structures.")

            # first get a list of symmetries present
            symmetry_int_numbers = [s.get_space_group_info()[1] for s in ordered_structures]

            # then count the number of symmetry operations for that space group
            num_sym_ops = [len(SpaceGroup.from_int_number(n).symmetry_ops) for n in symmetry_int_numbers]

            # find the largest values...
            max_symmetries = sorted(list(set(num_sym_ops)), reverse=True)

            # ...and decide which ones to keep
            if len(max_symmetries) > self.truncate_by_symmetry:
                max_symmetries = max_symmetries[0:5]
            structs_to_keep = [(idx, num) for idx, num in enumerate(num_sym_ops) if num in max_symmetries]

            # sort so that highest symmetry structs are first
            structs_to_keep = sorted(structs_to_keep, key=lambda x: (x[1], -x[0]), reverse=True)

            self.logger.info(
                f"Removing {len(ordered_structures) - len(structs_to_keep)} low symmetry ordered structures"
            )

            ordered_structures = [ordered_structures[i] for i, _ in structs_to_keep]
            ordered_structures_origins = [ordered_structures_origins[i] for i, _ in structs_to_keep]

            # and ensure fm is always at index 0
            fm_index = ordered_structures_origins.index("fm")
            ordered_structures.insert(0, ordered_structures.pop(fm_index))
            ordered_structures_origins.insert(0, ordered_structures_origins.pop(fm_index))

        # if our input structure isn't in our generated structures,
        # let's add it manually and also keep a note of which structure
        # is our input: this is mostly for book-keeping/benchmarking
        self.input_index = None
        self.input_origin = None
        if self.input_analyzer.ordering != Ordering.NM:
            matches = [self.input_analyzer.matches_ordering(s) for s in ordered_structures]
            if not any(matches):
                ordered_structures.append(self.input_analyzer.structure)
                ordered_structures_origins.append("input")
                self.logger.info("Input structure not present in enumerated structures, adding...")
            else:
                self.logger.info(f"Input structure was found in enumerated structures at index {matches.index(True)}")
                self.input_index = matches.index(True)
                self.input_origin = ordered_structures_origins[self.input_index]

        self.ordered_structures = ordered_structures
        self.ordered_structure_origins = ordered_structures_origins


MagneticDeformation = namedtuple("MagneticDeformation", "type deformation")


def magnetic_deformation(structure_A: Structure, structure_B: Structure) -> MagneticDeformation:
    """Calculates 'magnetic deformation proxy',
    a measure of deformation (norm of finite strain)
    between 'non-magnetic' (non-spin-polarized) and
    ferromagnetic structures.

    Adapted from Bocarsly et al. 2017,
    doi: 10.1021/acs.chemmater.6b04729

    Args:
      structure_A: Structure
      structure_B: Structure

    Returns: Magnetic deformation
    """

    # retrieve orderings of both input structures
    ordering_a = CollinearMagneticStructureAnalyzer(structure_A, overwrite_magmom_mode="none").ordering
    ordering_b = CollinearMagneticStructureAnalyzer(structure_B, overwrite_magmom_mode="none").ordering

    # get a type string, this is either 'NM-FM' for between non-magnetic
    # and ferromagnetic, as in Bocarsly paper, or e.g. 'FM-AFM'
    type_str = f"{ordering_a.value}-{ordering_b.value}"

    lattice_a = structure_A.lattice.matrix.T
    lattice_b = structure_B.lattice.matrix.T
    lattice_a_inv = np.linalg.inv(lattice_a)
    p = np.dot(lattice_a_inv, lattice_b)
    eta = 0.5 * (np.dot(p.T, p) - np.identity(3))
    w, v = np.linalg.eig(eta)
    deformation = 100 * (1.0 / 3.0) * np.sqrt(w[0] ** 2 + w[1] ** 2 + w[2] ** 2)

    return MagneticDeformation(deformation=deformation, type=type_str)

materialsproject / pymatgen / 4075885785

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