Utility functions:

This is an overview of various miscellaneous utility functions, useful for different purposes when doing calculations with vitrum.

apply_strain_to_structure(structure, deformations)

Apply strain(s) to input structure and return transformation(s) as list.

Parameters:

Name	Type	Description	Default
structure	.Structure	Input structure to apply strain to	required
deformations	list[.Deformation]	A list of deformations to apply independently to the input structure, in anticipation of performing an EOS fit. Deformations should be of the form of a 3x3 matrix, e.g., [[1.2, 0., 0.], [0., 1.2, 0.], [0., 0., 1.2]] or ((1.2, 0., 0.), (0., 1.2, 0.), (0., 0., 1.2))	required

Returns:

Name	Type	Description
list	list	A list of .TransformedStructure objects corresponding to the list of input deformations.

Source code in src/vitrum/utility.py

def apply_strain_to_structure(structure, deformations: list) -> list:
    """
    Apply strain(s) to input structure and return transformation(s) as list.

    Parameters:
        structure (.Structure): Input structure to apply strain to
        deformations (list[.Deformation]): A list of deformations to apply independently to the input
            structure, in anticipation of performing an EOS fit.
            Deformations should be of the form of a 3x3 matrix, e.g.,

            [[1.2, 0., 0.], [0., 1.2, 0.], [0., 0., 1.2]]

            or

            ((1.2, 0., 0.), (0., 1.2, 0.), (0., 0., 1.2))

    Returns:
        list: A list of .TransformedStructure objects corresponding to the
            list of input deformations.
    """
    transformations = []
    for deformation in deformations:
        # deform the structure
        ts = TransformedStructure(
            structure,
            transformations=[DeformStructureTransformation(deformation=deformation)],
        )
        transformations += [ts]
    return transformations

correct_atom_types(atoms_list, atom_to_type_map)

Correct the atom types in a list of Atoms objects.

Parameters:

Name	Type	Description	Default
atoms_list	list of Atoms objects	The list of Atoms objects to correct.	required
atom_to_type_map	dict	A dictionary mapping atomic numbers to atom types.	required

Returns:

Name	Type	Description
atoms_list	list of Atoms objects	The corrected list of Atoms objects.

Source code in src/vitrum/utility.py

def correct_atom_types(atoms_list, atom_to_type_map):
    """
    Correct the atom types in a list of Atoms objects.

    Parameters:
        atoms_list (list of Atoms objects): The list of Atoms objects to correct.
        atom_to_type_map (dict): A dictionary mapping atomic numbers to atom types.

    Returns:
        atoms_list (list of Atoms objects): The corrected list of Atoms objects.
    """
    #Check if atoms_list is a list of Atoms objects
    if not isinstance(atoms_list, list):
        atoms_list = [atoms_list]

    for atoms in atoms_list:
        corr_symbols = [atom_to_type_map[i] for i in atoms.get_atomic_numbers()]
        atoms.set_chemical_symbols(corr_symbols)

dimer_checker(atoms, bond_length=2.0, num_allowed=2)

Check for the presence of dimers (e.g., O2, N2, F2, Cl2, Br2, I2) in the structure.

Parameters:

Name	Type	Description	Default
atoms	Atoms	The ASE Atoms object to check.	required
bond_length	float	The cutoff distance to define a bond. Defaults to 2.0.	2.0
num_allowed	int	The maximum number of allowed dimers before returning True. Defaults to 2.	2

Returns:

Name	Type	Description
bool		True if the number of dimers exceeds num_allowed, False otherwise.

Source code in src/vitrum/utility.py

def dimer_checker(atoms, bond_length=2.0, num_allowed=2):
    """
    Check for the presence of dimers (e.g., O2, N2, F2, Cl2, Br2, I2) in the structure.

    Args:
        atoms (Atoms): The ASE Atoms object to check.
        bond_length (float, optional): The cutoff distance to define a bond. Defaults to 2.0.
        num_allowed (int, optional): The maximum number of allowed dimers before returning True. Defaults to 2.

    Returns:
        bool: True if the number of dimers exceeds `num_allowed`, False otherwise.
    """
    atoms.wrap()
    species = ["O", "N", "F", "Cl", "Br", "I"]
    for spec in species:
        if spec not in atoms.get_chemical_symbols():
            continue
        spec_atoms = atoms[np.array(atoms.get_chemical_symbols()) == spec]
        if len(spec_atoms) < 2:
            continue
        spec_positions = spec_atoms.get_positions()
        distances = np.linalg.norm(spec_positions[:, np.newaxis] - spec_positions, axis=-1)
        np.fill_diagonal(distances, np.inf)  # Ignore self-distances
        num_dimers = np.sum(distances < bond_length)
        if num_dimers > num_allowed:  # Adjust threshold as needed
            return True
    return False

find_min_after_peak(padf)

Find the index of the first local minimum after the first peak in a function. Useful for determining cutoffs from PDFs.

Parameters:

Name	Type	Description	Default
padf	ndarray	The probability density function or similar array.	required

Returns:

Name	Type	Description
int		The index of the minimum.

Source code in src/vitrum/utility.py

def find_min_after_peak(padf):
    """
    Find the index of the first local minimum after the first peak in a function.
    Useful for determining cutoffs from PDFs.

    Args:
        padf (np.ndarray): The probability density function or similar array.

    Returns:
        int: The index of the minimum.
    """
    mins = argrelextrema(padf, np.less_equal, order=4)[0]
    second_min = [i for ind, i in enumerate(mins) if i != ind][0]
    return second_min

get_LAMMPS_dump_timesteps(filename)

Retrieves the timesteps from a LAMMPS dump file.

Parameters:

Name	Type	Description	Default
filename	str	The path to the LAMMPS dump file.	required

Returns:

Type	Description
	List[int]: A list of timesteps extracted from the file.

Source code in src/vitrum/utility.py

def get_LAMMPS_dump_timesteps(filename: str):
    """
    Retrieves the timesteps from a LAMMPS dump file.

    Parameters:
        filename (str): The path to the LAMMPS dump file.

    Returns:
        List[int]: A list of timesteps extracted from the file.
    """
    with open(filename, encoding="utf-8") as f:
        timesteps = []
        lines = deque(f.readlines())
        if len(lines) == 0:
            return timesteps
        line = lines.popleft()
        while len(lines) > 0:
            if "ITEM: TIMESTEP" in line:
                line = lines.popleft()
                timesteps.append(int(line))
            else:
                line = lines.popleft()
    return timesteps

get_average_volume_convex_hull(composition, MP_API_KEY=None)

Get the average volume per atom from the convex hull on Materials Project.

Parameters:

Name	Type	Description	Default
composition	Composition	The composition to query.	required
MP_API_KEY	str	Materials Project API Key.	None

Returns:

Name	Type	Description
float		Average volume per atom.

Source code in src/vitrum/utility.py

def get_average_volume_convex_hull(composition, MP_API_KEY=None):
    """
    Get the average volume per atom from the convex hull on Materials Project.

    Args:
        composition (Composition): The composition to query.
        MP_API_KEY (str, optional): Materials Project API Key.

    Returns:
        float: Average volume per atom.
    """
    with MPRester(api_key=MP_API_KEY) as mpr:
        entries = mpr.get_entries_in_chemsys(
            elements=[str(el) for el in composition.elements],
            additional_criteria={"thermo_types": ["GGA_GGA+U"]},
        )
    pd = PhaseDiagram(entries)
    decomp = pd.get_decomposition(composition)
    volume = sum([d.structure.volume / d.composition.num_atoms * decomp[d] for d in decomp])
    return volume

get_dist(list, cell)

Calculate the pairwise distance matrix for atoms in a periodic simulation box.

Parameters:

Name	Type	Description	Default
list	ndarray	Atomic positions (N x 3).	required
cell	ndarray	Cell dimensions (3,). Assumes an orthorhombic cell.	required

Returns:

Type	Description
	np.ndarray: Symmetric distance matrix (N x N) containing distances between all atom pairs.

Source code in src/vitrum/utility.py

def get_dist(list, cell):
    """
    Calculate the pairwise distance matrix for atoms in a periodic simulation box.

    Args:
        list (np.ndarray): Atomic positions (N x 3).
        cell (np.ndarray): Cell dimensions (3,). Assumes an orthorhombic cell.

    Returns:
        np.ndarray: Symmetric distance matrix (N x N) containing distances between all atom pairs.
    """
    dim = [cell[0], cell[1], cell[2]]
    x_dif = np.abs(list[:, 0][np.newaxis, :] - list[:, 0][:, np.newaxis])
    y_dif = np.abs(list[:, 1][np.newaxis, :] - list[:, 1][:, np.newaxis])
    z_dif = np.abs(list[:, 2][np.newaxis, :] - list[:, 2][:, np.newaxis])
    x_dif = np.where(x_dif > 0.5 * dim[0], np.abs(x_dif - dim[0]), x_dif)
    y_dif = np.where(y_dif > 0.5 * dim[1], np.abs(y_dif - dim[1]), y_dif)
    z_dif = np.where(z_dif > 0.5 * dim[2], np.abs(z_dif - dim[2]), z_dif)
    return np.sqrt(x_dif**2 + y_dif**2 + z_dif**2)

get_dist_numba(pos, cell)

Calculate the distance matrix between atoms using Numba for performance.

Parameters:

Name	Type	Description	Default
pos	ndarray	Array of atomic positions (N x 3).	required
cell	ndarray	Cell dimensions (3,). Assumes an orthorhombic cell (lx, ly, lz).	required

Returns:

Type	Description
	np.ndarray: Symmetric distance matrix (N x N).

Source code in src/vitrum/utility.py

@njit(parallel=True)
def get_dist_numba(pos, cell):
    """
    Calculate the distance matrix between atoms using Numba for performance.

    Args:
        pos (np.ndarray): Array of atomic positions (N x 3).
        cell (np.ndarray): Cell dimensions (3,). Assumes an orthorhombic cell (lx, ly, lz).

    Returns:
        np.ndarray: Symmetric distance matrix (N x N).
    """
    n = pos.shape[0]
    # Initialize the output matrix
    dist_matrix = np.zeros((n, n))

    # Extract cell dimensions for faster access
    lx, ly, lz = cell[0], cell[1], cell[2]
    half_lx, half_ly, half_lz = lx / 2.0, ly / 2.0, lz / 2.0

    for i in prange(n):
        for j in range(i + 1, n):  # Only calculate the upper triangle
            dx = abs(pos[i, 0] - pos[j, 0])
            dy = abs(pos[i, 1] - pos[j, 1])
            dz = abs(pos[i, 2] - pos[j, 2])

            # Apply Periodic Boundary Conditions (Minimum Image Convention)
            if dx > half_lx: dx -= lx
            if dy > half_ly: dy -= ly
            if dz > half_lz: dz -= lz

            d = np.sqrt(dx**2 + dy**2 + dz**2)

            # Fill both symmetric entries
            dist_matrix[i, j] = d
            dist_matrix[j, i] = d

    return dist_matrix

get_high_low_displacement_index(initial_state, current_state, target_atom, percentage=0.25)

Calculates the indices of the atoms with the high and low displacements between an initial and current state.

Parameters:

Name	Type	Description	Default
initial_state	Atoms	The initial state of the system.	required
current_state	Atoms	The current state of the system.	required
target_atom	str or int	The chemical symbol or atomic number of the target atom.	required
percentage	float	The percentage of the highest and lowest displacements to consider. Defaults to 0.25.	0.25

Returns:

Name	Type	Description
list		A list of two elements, where the first element is the index of the atoms with the highest displacements and the second element is the index of the atoms with the lowest displacements.

Source code in src/vitrum/utility.py

def get_high_low_displacement_index(initial_state, current_state, target_atom, percentage=0.25):
    """
    Calculates the indices of the atoms with the high and low displacements between an initial and current state.

    Parameters:
        initial_state (Atoms): The initial state of the system.
        current_state (Atoms): The current state of the system.
        target_atom (str or int): The chemical symbol or atomic number of the target atom.
        percentage (float, optional): The percentage of the highest and lowest displacements to consider. Defaults to 0.25.

    Returns:
        list: A list of two elements, where the first element is the index of the atoms with the highest displacements
            and the second element is the index of the atoms with the lowest displacements.
    """
    index = np.where(initial_state.get_chemical_symbols() == target_atom)[0]
    initial_positions = initial_state.get_positions()[index]
    current_positions = current_state.get_positions()[index]
    displacements = initial_positions - current_positions
    displacements = np.sum(displacements**2, axis=1)
    ind = np.argsort(displacements)
    low_ind = index[ind[: int(len(ind) * percentage)]]
    high_ind = index[ind[int(len(ind) * percentage) :]]
    return [low_ind, high_ind]

get_random_packed(composition, target_atoms=100, min_distance=None, radii_scaling=1.0, volume_scaling=1.0, vol_per_atom_source='mp', datatype='ase', db_kwargs=None, density=None, seed=None, side_ratios=[1, 1, 1], **kwargs)

Generate a random packed structure based on the given composition.

Parameters:

Name	Type	Description	Default
composition	(str, dict or Composition)	The composition of the structure.	required
density	float	The target density of the structure (in g/cm^3). If not provided, the volume per atom is estimated using the Materials Project API.	None
target_atoms	int	The target number of atoms in the structure. Defaults to 100.	100
radii_scaling	float	Scaling factor for the covalent radii of the atoms. Defaults to 1.0.	1.0
volume_scaling	float	Scaling factor for the volume of the structure. Defaults to 1.0.	1.0
vol_per_atom_source	float or str	The source for the volume per atom. Can be a float value or one of the following strings: "mp" (Materials Project), "icsd" (Inorganic Crystal Structure Database), "density" (use provided density), "covalent_radius" (estimate from covalent radii), or "convex_hull" (estimate from convex hull). Defaults to "mp".	'mp'
datatype	str	The type of data to return. Can be "ase" for ASE format or "pymatgen" for pymatgen format. Defaults to "ase".	'ase'
db_kwargs	dict	Additional keyword arguments for database access. Defaults to None.	None
seed	int	The seed for random number generation. Defaults to 0.	None
side_ratios	list	The side ratios for the lattice. Defaults to [1, 1, 1].	[1, 1, 1]

Returns:

Name	Type	Description
data	Atoms or Structure	The generated random packed structure.

Source code in src/vitrum/utility.py

def get_random_packed(
    composition: str | dict | Composition,
    target_atoms: int = 100,
    min_distance: float | None = None,
    radii_scaling: float = 1.0,
    volume_scaling: float = 1.0,
    vol_per_atom_source: float | str = "mp",
    datatype: str = "ase",
    db_kwargs: dict | None = None,
    density: float | None = None,
    seed: int | None = None,
    side_ratios: list = [1, 1, 1],
    **kwargs,
):
    """
    Generate a random packed structure based on the given composition.

    Parameters:
        composition (str, dict or pymatgen.core.Composition): The composition of the structure.
        density (float, optional): The target density of the structure (in g/cm^3). If not provided, the volume per atom
                                   is estimated using the Materials Project API.
        target_atoms (int, optional): The target number of atoms in the structure. Defaults to 100.
        radii_scaling (float, optional): Scaling factor for the covalent radii of the atoms. Defaults to 1.0.
        volume_scaling (float, optional): Scaling factor for the volume of the structure. Defaults to 1.0.
        vol_per_atom_source (float or str, optional): The source for the volume per atom. Can be a float value or one of the following strings:
                                                    "mp" (Materials Project), "icsd" (Inorganic Crystal Structure Database),
                                                     "density" (use provided density), "covalent_radius" (estimate from covalent radii),
                                                     or "convex_hull" (estimate from convex hull). Defaults to "mp".
        datatype (str, optional): The type of data to return. Can be "ase" for ASE format or "pymatgen"
                                  for pymatgen format. Defaults to "ase".
        db_kwargs (dict, optional): Additional keyword arguments for database access. Defaults to None.
        seed (int, optional): The seed for random number generation. Defaults to 0.
        side_ratios (list, optional): The side ratios for the lattice. Defaults to [1, 1, 1].

    Returns:
        data (ase.Atoms or pymatgen.core.Structure): The generated random packed structure.
    """

    if isinstance(composition, str):
        composition = Composition(composition)
    elif isinstance(composition, dict):
        comp_string = "".join(mol * (int(composition[mol] * 10)) for mol in composition)
        composition = Composition(comp_string)
    elements, factor = composition.get_integer_formula_and_factor()
    integer_composition = Composition(elements)
    full_cell_composition = integer_composition * np.ceil(target_atoms / integer_composition.num_atoms)

    structure = {}
    for el in full_cell_composition:
        structure[str(el)] = int(full_cell_composition.element_composition.get(el))
    elements = sum([[i] * structure[i] for i in structure], [])
    np.random.seed(seed)

    cell_vol = get_volume(composition, structure, vol_per_atom_source, db_kwargs, density, **kwargs)

    cell_vol *= volume_scaling
    k = (cell_vol / (side_ratios[0] * side_ratios[1] * side_ratios[2])) ** (1 / 3)
    cell = np.array([side_ratios[0] * k, side_ratios[1] * k, side_ratios[2] * k])
    cell = np.diag(cell)

    radii = covalent_radii[symbols2numbers(elements)] * radii_scaling

    if min_distance:
        radii = np.maximum(radii, min_distance / 2)

    nat = len(elements)

    pos = np.random.rand(len(elements), 3) @ cell
    ats = Atoms(elements, cell=cell, pbc=True, positions=pos)
    skin = 0.0
    nl = NeighborList(radii, self_interaction=False, bothways=True, skin=skin)

    for it in range(500):
        nl.update(ats)
        pos = ats.get_positions()
        dx = np.zeros(pos.shape)
        dsum = 0
        for i in range(nat):
            indices, offsets = nl.get_neighbors(i)
            rs = pos[indices, :] + offsets @ cell - pos[i, :]
            # ds is the overlap
            ds = np.linalg.norm(rs, axis=1) - (radii[indices] + radii[i])
            if np.any(ds > 1.e-10):
                print('Assertion failed: ds <= 0')
                print(np.max(ds))
                quit()
            # sum overlaps 
            dsum += np.sum(ds) 
            ds -= skin
            # move atoms away from each other by overlap amount
            dx[i,:] = np.sum(rs / np.linalg.norm(rs, axis=1)[:, None] * ds[:, None], axis=0)
        # print(it, dsum, np.linalg.norm(dx))
        ats.set_positions(pos + dx)
        if dsum >= -1.e-5:
            break
    else:
        raise RuntimeError('Cell packing not converged')

    ats.wrap()
    if datatype == "pymatgen":
        structure = Structure(
            lattice=ats.get_cell(),
            species=ats.get_chemical_symbols(),
            coords=ats.get_scaled_positions(),
            to_unit_cell=True,
            coords_are_cartesian=False,
        )
    else:
        structure = ats
    return structure

get_volume(composition, structure, vol_per_atom_source='mp', db_kwargs=None, density=None, MP_API_KEY=None)

Get the volume of the cell based on the composition and various estimation methods.

Parameters:

Name	Type	Description	Default
composition	Union[Composition, str]	The composition of the material.	required
structure	dict	A dictionary mapping element symbols to their count in the structure.	required
vol_per_atom_source	Union[float, str]	Method to estimate volume per atom. Options: - "mp": Use Materials Project (requires API key). - "icsd": Use ICSD database (if available). - "density": Calculate from provided density. - "covalent_radius": Estimate from covalent radii. - "convex_hull": Estimate from convex hull on Materials Project. - float: Directly provide the volume per atom. Defaults to "mp".	'mp'
db_kwargs	dict	Keyword arguments for database queries. Defaults to None.	None
density	float	Density in g/cm^3. Required if vol_per_atom_source="density". Defaults to None.	None
MP_API_KEY	str	Materials Project API key. Defaults to None.	None

Returns:

Name	Type	Description
float		The calculated total volume of the cell in Angstrom^3.

Raises:

Type	Description
ValueError	If estimating from density but estimates fail, or if an unknown source is provided.

Source code in src/vitrum/utility.py

def get_volume(
    composition: Composition | str,
    structure: dict,
    vol_per_atom_source: float | str = "mp",
    db_kwargs: dict | None = None,
    density: float | None = None,
    MP_API_KEY: str | None = None,
):
    """
    Get the volume of the cell based on the composition and various estimation methods.

    Args:
        composition (Union[Composition, str]): The composition of the material.
        structure (dict): A dictionary mapping element symbols to their count in the structure.
        vol_per_atom_source (Union[float, str], optional): Method to estimate volume per atom.
            Options:
            - "mp": Use Materials Project (requires API key).
            - "icsd": Use ICSD database (if available).
            - "density": Calculate from provided density.
            - "covalent_radius": Estimate from covalent radii.
            - "convex_hull": Estimate from convex hull on Materials Project.
            - float: Directly provide the volume per atom.
            Defaults to "mp".
        db_kwargs (dict, optional): Keyword arguments for database queries. Defaults to None.
        density (float, optional): Density in g/cm^3. Required if vol_per_atom_source="density". Defaults to None.
        MP_API_KEY (str, optional): Materials Project API key. Defaults to None.

    Returns:
        float: The calculated total volume of the cell in Angstrom^3.

    Raises:
        ValueError: If estimating from density but estimates fail, or if an unknown source is provided.
    """

    struct_db = vol_per_atom_source.lower() if isinstance(vol_per_atom_source, str) else None
    db_kwargs = db_kwargs or ({"use_cached": True} if struct_db == "mp" else {})
    cell_vol = None

    if density:
        if not isinstance(density, (float, int)):
            raise ValueError("Density must be a float or int.")

        struct_db = "density"

    if isinstance(vol_per_atom_source, float | int):
        vol_per_atom = vol_per_atom_source

    elif struct_db == "mp":
        vol_per_atom = get_average_volume_from_mp(composition, **db_kwargs)

    elif struct_db == "icsd":
        vol_per_atom = get_average_volume_from_db_cached(composition, db_name="icsd", **db_kwargs)

    elif struct_db == "density":
        mass = np.sum([Atoms(f"{i}").get_masses()[0] * structure[i] for i in structure])
        cell_vol = ((mass / (6.0221 * (10**23))) / density) * (10**24)

    elif struct_db == "covalent_radius":
        all_radii = np.hstack(
            [np.repeat(covalent_radii[atomic_numbers[key]], structure[key]) for key in structure.keys()]
        )
        cell_vol = np.sum((4 / 3 * np.pi * all_radii**3)) * 3

    elif struct_db == "convex_hull":
        try:
            vol_per_atom = get_average_volume_convex_hull(composition, MP_API_KEY=MP_API_KEY)
        except MPRestError as e:
            raise ValueError(f"Could not retrieve volume from convex hull. Check your MP_API_KEY. Error: {e}")

    else:
        raise ValueError(f"Unknown volume per atom source: {vol_per_atom_source}.")

    if not cell_vol:
        cell_vol = vol_per_atom * sum(structure.values())

    return cell_vol

homogeniety_checker(atoms, grid_density, slide_steps=2, target_species='all', upper_bound=1.5, lower_bound=0.5, box_threshold=0.1, seperated_species_threshold=0.5)

Check the homogeneity of the atomic structure by analyzing atom density in grid boxes.

Parameters:

Name	Type	Description	Default
atoms	Atoms	The ASE Atoms object to analyze.	required
grid_density	tuple or list	Number of grid divisions in x, y, z directions (nx, ny, nz).	required
slide_steps	int	Number of steps to slide the grid for averaging. Defaults to 2.	2
target_species	str or list	Species to check. "all" checks all present species. Defaults to "all".	'all'
upper_bound	float	Multiplier for average density to consider a box over-dense. Defaults to 1.5.	1.5
lower_bound	float	Multiplier for average density to consider a box under-dense. Defaults to 0.5.	0.5
box_threshold	float	Fraction of boxes allowed to be out of bounds before flagging a species. Defaults to 0.1.	0.1
seperated_species_threshold	float	Fraction of species allowed to be phase separated before the structure is flagged. Defaults to 0.5.	0.5

Returns:

Name	Type	Description
bool		True if the structure is considered homogeneous, False otherwise.

Raises:

Type	Description
ValueError	If no species are found in the atoms object.

Source code in src/vitrum/utility.py

def homogeniety_checker(
    atoms,
    grid_density,
    slide_steps=2,
    target_species="all",
    upper_bound=1.5,
    lower_bound=0.5,
    box_threshold=0.1,
    seperated_species_threshold=0.5,
):
    """
    Check the homogeneity of the atomic structure by analyzing atom density in grid boxes.

    Args:
        atoms (Atoms): The ASE Atoms object to analyze.
        grid_density (tuple or list): Number of grid divisions in x, y, z directions (nx, ny, nz).
        slide_steps (int, optional): Number of steps to slide the grid for averaging. Defaults to 2.
        target_species (str or list, optional): Species to check. "all" checks all present species. Defaults to "all".
        upper_bound (float, optional): Multiplier for average density to consider a box over-dense. Defaults to 1.5.
        lower_bound (float, optional): Multiplier for average density to consider a box under-dense. Defaults to 0.5.
        box_threshold (float, optional): Fraction of boxes allowed to be out of bounds before flagging a species. Defaults to 0.1.
        seperated_species_threshold (float, optional): Fraction of species allowed to be phase separated before the structure is flagged. Defaults to 0.5.

    Returns:
        bool: True if the structure is considered homogeneous, False otherwise.

    Raises:
        ValueError: If no species are found in the atoms object.
    """
    atoms.wrap()
    species = np.unique(atoms.get_chemical_symbols()) if target_species == "all" else [target_species]

    if len(species) == 0:
        raise ValueError("No species found in the atoms object.")

    cell_lengths = np.array(atoms.get_cell()).diagonal()
    num_boxes = np.prod(grid_density)

    x_edges = np.linspace(0, cell_lengths[0], grid_density[0] + 1)
    y_edges = np.linspace(0, cell_lengths[1], grid_density[1] + 1)
    z_edges = np.linspace(0, cell_lengths[2], grid_density[2] + 1)

    slide_fractions = np.linspace(0, 1, slide_steps, endpoint=False)

    phase_seperated_species = 0

    for spec in species:
        spec_atoms = atoms[np.array(atoms.get_chemical_symbols()) == spec]
        num_atoms = len(spec_atoms)
        avg_atoms_per_box = num_atoms / num_boxes

        if avg_atoms_per_box < 2:
            continue

        positions = spec_atoms.get_positions()

        out_of_bounds_boxes = []
        for dx, dy, dz in product(slide_fractions, repeat=3):
            # Apply offset in each direction
            x_slide = x_edges + dx * (cell_lengths[0] / grid_density[0])
            y_slide = y_edges + dy * (cell_lengths[1] / grid_density[1])
            z_slide = z_edges + dz * (cell_lengths[2] / grid_density[2])

            x_slide[-1] = cell_lengths[0]
            y_slide[-1] = cell_lengths[1]
            z_slide[-1] = cell_lengths[2]

            x_idx = np.digitize(positions[:, 0], x_slide) - 1
            y_idx = np.digitize(positions[:, 1], y_slide) - 1
            z_idx = np.digitize(positions[:, 2], z_slide) - 1

            x_idx[x_idx == -1] = 2
            y_idx[y_idx == -1] = 2
            z_idx[z_idx == -1] = 2

            counts = np.zeros(grid_density, dtype=int)
            for xi, yi, zi in zip(x_idx, y_idx, z_idx):
                counts[xi, yi, zi] += 1

            too_low = counts < avg_atoms_per_box * lower_bound
            too_high = counts > avg_atoms_per_box * upper_bound
            out_of_bounds_boxes.append(np.sum(too_low | too_high))

        if np.sum(out_of_bounds_boxes) > num_boxes * slide_steps**3 * box_threshold:
            phase_seperated_species += 1

    if phase_seperated_species > seperated_species_threshold * len(species):
        return False
    else:
        return True

pdf(dist_list, volume, rrange=10, nbin=100)

Calculate the pair distribution function (PDF) of a list of distances.

Parameters:

Name	Type	Description	Default
dist_list	ndarray	A 2D numpy array of distances.	required
volume	float	The volume of the system.	required
rrange	float	The range of the PDF. Defaults to 10.	10
nbin	int	The number of bins. Defaults to 100.	100

Returns:

Name	Type	Description
xval	ndarray	The x values of the PDF.
pdf	ndarray	The PDF values.

Source code in src/vitrum/utility.py

def pdf(dist_list, volume, rrange=10, nbin=100):
    """
    Calculate the pair distribution function (PDF) of a list of distances.

    Parameters:
        dist_list (np.ndarray): A 2D numpy array of distances.
        volume (float): The volume of the system.
        rrange (float, optional): The range of the PDF. Defaults to 10.
        nbin (int, optional): The number of bins. Defaults to 100.

    Returns:
        xval (np.ndarray): The x values of the PDF.
        pdf (np.ndarray): The PDF values.
    """

    edges = np.linspace(0, rrange, nbin + 1)
    xval = (edges[1:] + edges[:-1]) / 2
    volbin = (4 / 3) * np.pi * (edges[1:] ** 3 - edges[:-1] ** 3)
    h, bin_edges = np.histogram(dist_list, bins=nbin, range=(0, rrange))
    h[0] = 0
    pdf = (h / volbin) / (dist_list.size / volume)
    return xval, pdf

r_chi(function_1, function_2, x_min=0, x_max=np.inf, steps=100)

Calculate the Wright coefficient (https://doi.org/10.1016/0022-3093(93)90232-M) between two functions

Parameters:

Name	Type	Description	Default
function_1	dict	Dictionary with keys 'x' and 'y' representing the first function, usually from simulations	required
function_2	dict	Dictionary with keys 'x' and 'y' representing the second function, usually from experimental meassurements.	required

Returns:

Name	Type	Description
rchi	float	Wright coefficient, a measure of similarity between the two functions.

Source code in src/vitrum/utility.py

def r_chi(function_1, function_2, x_min=0, x_max=np.inf, steps=100):
    """
    Calculate the Wright coefficient (https://doi.org/10.1016/0022-3093(93)90232-M) between two functions

    Parameters:
        function_1 (dict): Dictionary with keys 'x' and 'y' representing the first function, usually from simulations
        function_2 (dict): Dictionary with keys 'x' and 'y' representing the second function, usually from experimental meassurements.

    Returns:
        rchi (float): Wright coefficient, a measure of similarity between the two functions.
    """
    # Determine the overlapping x-range
    min_x_val = np.max([np.min(function_1["x"]), np.min(function_2["x"]), x_min])
    max_x_val = np.min([np.max(function_1["x"]), np.max(function_2["x"]), x_max])

    if min_x_val >= max_x_val:
        raise ValueError("No overlapping x-range between the two functions.")

    # Create common x-axis over the overlap region
    common_x = np.linspace(min_x_val, max_x_val, steps)

    # Interpolate both functions onto the common x-axis
    interp_f1 = interp1d(function_1["x"], function_1["y"], kind="linear", bounds_error=False, fill_value=0)
    interp_f2 = interp1d(function_2["x"], function_2["y"], kind="linear", bounds_error=False, fill_value=0)

    y1 = interp_f1(common_x)
    y2 = interp_f2(common_x)

    # Calculate the r-chi (Wright coefficient)
    numerator = np.sum((y1 - y2) ** 2)

    denominator = np.sum(y2**2)
    rchi = np.sqrt(numerator / denominator)

    return rchi, common_x, y1, y2

unwrap_trajectory(atoms_list)

Unwraps a list of Atoms objects to remove periodic boundary crossings.

Parameters:

Name	Type	Description	Default
atoms_list	list of Atoms objects	The list of Atoms objects to unwrap.	required

Returns:

Name	Type	Description
unwrapped_atoms_list	list of Atoms objects	The unwrapped list of Atoms objects.

Source code in src/vitrum/utility.py

def unwrap_trajectory(atoms_list):
    """
    Unwraps a list of Atoms objects to remove periodic boundary crossings.

    Parameters:
        atoms_list (list of Atoms objects): The list of Atoms objects to unwrap.

    Returns:
        unwrapped_atoms_list (list of Atoms objects): The unwrapped list of Atoms objects.
    """

    if not atoms_list or len(atoms_list) == 0:
        raise ValueError("The input atoms_list must be a non-empty list of ASE Atom objects.")
    cell = np.diagonal(atoms_list[0].get_cell())
    n_atoms = len(atoms_list[0])
    unwrapped_atoms_list = [atoms.copy() for atoms in atoms_list]

    crossings = np.zeros((n_atoms, 3))
    previous_positions = unwrapped_atoms_list[0].get_positions()
    for atoms in unwrapped_atoms_list:
        current_positions = atoms.get_positions()
        difference = current_positions - previous_positions
        crossings = crossings + np.floor_divide(difference + 0.5 * cell, cell).astype(int)
        previous_positions = current_positions
        new_positions = current_positions - cell * crossings
        atoms.set_positions(new_positions)
    return unwrapped_atoms_list