# Cluster space¶

## ClusterSpace¶

class hiphive.ClusterSpace(prototype_structure, cutoffs, config=None, **kwargs)[source]

Primitive object for handling clusters and force constants of a structure.

Parameters: prototype_structure (ase.Atoms) – prototype structure; spglib will be used to find a suitable cell based on this structure. cutoffs (list or Cutoffs) – cutoff radii for different orders starting with second order config (Config object) – config object containing information on how the cluster space should be built, e.g. values for tolerances and if acoustic sum rules be enforced not config is given then kwargs can be used to specify (If) – acoustic_sum_rules (bool) – If True the aucostic sum rules will be enforced by constraining the parameters. symprec (float) – numerical precision that will be used for analyzing the symmetry (this parameter will be forwarded to spglib) length_scale (float) – This will be used as a normalization constant for the eigentensors

Examples

To instantiate a ClusterSpace object one has to specify a prototype structure and cutoff radii for each cluster order that should be included. For example the following snippet will set up a ClusterSpace object for a body-centered-cubic (BCC) structure including second order terms up to a distance of 5 A and third order terms up to a distance of 4 A.

>>> from ase.build import bulk
>>> prim = bulk('W')
>>> cs = ClusterSpace(prim, [5.0, 4.0])

acoustic_sum_rules

True if acoustic sum rules are enforced

Type: bool
atom_list

atoms inside the cutoff relative to the of the center cell

Type: BiMap
cluster_list

clusters possible within the cutoff

Type: BiMap
cutoffs

cutoffs used for constructing the cluster space

Type: Cutoffs
get_parameter_indices(order)[source]

Returns a list of the parameter indices associated with the requested order.

Parameters: order (int) – order for which to return the parameter indices list of parameter indices associated with the requested order list(int) ValueError – if the order is not included in the cluster space
length_scale

normalization constant of the force constants

Type: float
n_dofs

number of free parameters in the model

If the sum rules are not enforced the number of DOFs is the same as the total number of eigentensors in all orbits.

Type: int
orbit_data

detailed information for each orbit, e.g., cluster radius and atom types.

Type: list(dict)
orbits

orbits associated with the lattice structure.

Type: list(Orbit)
permutations

lookup for permutation references

Type: list(numpy.ndarray)
primitive_structure

structure of the lattice

Type: ase.Atoms
print_orbits()[source]

Prints a list of all orbits.

print_tables()[source]

Prints table data, i.e. information as a function of order and n-body for the clusterspace.

read()[source]

Reads a cluster space from file.

Parameters: f (str or file object) – name of input file (str) or stream to load from (file object)
rotation_matrices

symmetry elements (3x3 matrices) representing rotations

Type: list(numpy.ndarray)
spacegroup

space group of the lattice structure obtained from spglib

Type: str
symprec

symprec value used when constructing the cluster space

Type: float
translation_vectors

symmetry elements representing translations

Type: list(numpy.ndarray)
write(fileobj)[source]

Writes cluster space to file.

The instance is saved into a custom format based on tar-files. The resulting file will be a valid tar file and can be browsed by by a tar reader. The included objects are themself either pickles, npz or other tars.

Parameters: fileobj (str or file-like object) – If the input is a string a tar archive will be created in the current directory. Otherwise the input must be a valid file like object.
wyckoff_sites

wyckoff sites in the primitive cell

Type: list

## Cutoffs¶

class hiphive.cutoffs.CutoffMaximumBody(cutoff_list, max_nbody)[source]

Specify cutoff-list plus maximum body

Usefull when creating e.g. 6th order expansions but with only 3-body interactions.

Parameters: cutoff_list (list) – list of cutoffs for order 2, 3, etc. Must be in decresing order max_nbody (int) – No clusters containing more than max_nbody atoms will be generated
class hiphive.cutoffs.Cutoffs(cutoff_matrix)[source]

This class maintains information about the cutoff configuration, i.e. which clusters will be included (=”inside cutoff”). It also encapsulates functionality that is used e.g., during cluster space construction.

Here, n-body refers to number of atoms in a cluster. For example the cluster (0011) is a two-body cluster of fourth order and the cluster (123) is a three-body cluster of third order.

Parameters: cutoff_matrix (numpy.ndarray) – the matrix element ij provides to the cutoff for order i+2 and nbody j+2; elements with j>i will be ignored
cutoff_matrix

copy of cutoff matrix

Type: numpy.ndarray
get_cutoff(order, nbody)[source]

Returns cutoff for a given body and order.

Parameters: order (int) – nbody (int) – ValueError – if order is not in orders ValueError – if nbody is not in nbodies ValueError – if nbody is larger than order float
max_cutoff

maximum cutoff

Type: float
max_nbody

maximum body

Type: int
max_nbody_cutoff(nbody)[source]

Return maximum cutoff for a given body.

max_nbody_order(nbody)[source]

Returns maximum order for a given body

max_order

maximum order

Type: int
nbodies

allowed bodies

Type: list(int)
orders

allowed orders

Type: list(int)
read()[source]

Parameters: fileobj (file-like object) – input file to read from
write(fileobj)[source]

Writes instance to file.

Parameters: fileobj (file-like object) – file-like object to which the cutoffs will be written to
hiphive.cutoffs.estimate_maximum_cutoff(atoms, max_iter=11)[source]

Estimates the maximum possible cutoff given the atoms object

Parameters: atoms (ase.Atoms) – structure used for checking compatibility with cutoff max_iter (int) – number of iterations in binary search
hiphive.cutoffs.is_cutoff_allowed(atoms, cutoff)[source]

Checks if atoms is compatible with cutoff

Parameters: atoms (ase.Atoms) – structure used for checking compatibility with cutoff cutoff (float) – cutoff to be tested True if cutoff compatible with atoms object, else False bool