# Source code for aiida.orm.nodes.data.array.kpoints

```
# -*- coding: utf-8 -*-
###########################################################################
# Copyright (c), The AiiDA team. All rights reserved. #
# This file is part of the AiiDA code. #
# #
# The code is hosted on GitHub at https://github.com/aiidateam/aiida-core #
# For further information on the license, see the LICENSE.txt file #
# For further information please visit http://www.aiida.net #
###########################################################################
"""
Module of the KpointsData class, defining the AiiDA data type for storing
lists and meshes of k-points (i.e., points in the reciprocal space of a
periodic crystal structure).
"""
import numpy
from .array import ArrayData
__all__ = ('KpointsData',)
_DEFAULT_EPSILON_LENGTH = 1e-5
_DEFAULT_EPSILON_ANGLE = 1e-5
[docs]class KpointsData(ArrayData):
"""
Class to handle array of kpoints in the Brillouin zone. Provide methods to
generate either user-defined k-points or path of k-points along symmetry
lines.
Internally, all k-points are defined in terms of crystal (fractional)
coordinates.
Cell and lattice vector coordinates are in Angstroms, reciprocal lattice
vectors in Angstrom^-1 .
:note: The methods setting and using the Bravais lattice info assume the
PRIMITIVE unit cell is provided in input to the set_cell or
set_cell_from_structure methods.
"""
[docs] def get_description(self):
"""
Returns a string with infos retrieved from kpoints node's properties.
:param node:
:return: retstr
"""
try:
mesh = self.get_kpoints_mesh()
return 'Kpoints mesh: {}x{}x{} (+{:.1f},{:.1f},{:.1f})'.format(
mesh[0][0], mesh[0][1], mesh[0][2], mesh[1][0], mesh[1][1], mesh[1][2]
)
except AttributeError:
try:
return f'(Path of {len(self.get_kpoints())} kpts)'
except OSError:
return self.node_type
@property
def cell(self):
"""
The crystal unit cell. Rows are the crystal vectors in Angstroms.
:return: a 3x3 numpy.array
"""
return numpy.array(self.base.attributes.get('cell'))
@cell.setter
def cell(self, value):
"""
Set the crystal unit cell
:param value: a 3x3 list/tuple/array of numbers (units = Angstroms).
"""
self._set_cell(value)
[docs] def _set_cell(self, value):
"""
Validate if 'value' is a allowed crystal unit cell
:param value: something compatible with a 3x3 tuple of floats
"""
from aiida.common.exceptions import ModificationNotAllowed
from aiida.orm.nodes.data.structure import _get_valid_cell
if self.is_stored:
raise ModificationNotAllowed('KpointsData cannot be modified, it has already been stored')
the_cell = _get_valid_cell(value)
self.base.attributes.set('cell', the_cell)
@property
def pbc(self):
"""
The periodic boundary conditions along the vectors a1,a2,a3.
:return: a tuple of three booleans, each one tells if there are periodic
boundary conditions for the i-th real-space direction (i=1,2,3)
"""
# return copy.deepcopy(self._pbc)
return (self.base.attributes.get('pbc1'), self.base.attributes.get('pbc2'), self.base.attributes.get('pbc3'))
@pbc.setter
def pbc(self, value):
"""
Set the value of pbc, i.e. a tuple of three booleans, indicating if the
cell is periodic in the 1,2,3 crystal direction
"""
self._set_pbc(value)
[docs] def _set_pbc(self, value):
"""
validate the pbc, then store them
"""
from aiida.common.exceptions import ModificationNotAllowed
from aiida.orm.nodes.data.structure import get_valid_pbc
if self.is_stored:
raise ModificationNotAllowed('The KpointsData object cannot be modified, it has already been stored')
the_pbc = get_valid_pbc(value)
self.base.attributes.set('pbc1', the_pbc[0])
self.base.attributes.set('pbc2', the_pbc[1])
self.base.attributes.set('pbc3', the_pbc[2])
@property
def labels(self):
"""
Labels associated with the list of kpoints.
List of tuples with kpoint index and kpoint name: ``[(0,'G'),(13,'M'),...]``
"""
label_numbers = self.base.attributes.get('label_numbers', None)
labels = self.base.attributes.get('labels', None)
if labels is None or label_numbers is None:
return None
return list(zip(label_numbers, labels))
@labels.setter
def labels(self, value):
self._set_labels(value)
[docs] def _set_labels(self, value):
"""
set label names. Must pass in input a list like: ``[[0,'X'],[34,'L'],... ]``
"""
# check if kpoints were set
try:
self.get_kpoints()
except AttributeError:
raise AttributeError('Kpoints must be set before the labels')
if value is None:
value = []
try:
label_numbers = [int(i[0]) for i in value]
except ValueError:
raise ValueError('The input must contain an integer index, to map the labels into the kpoint list')
labels = [str(i[1]) for i in value]
if any(i > len(self.get_kpoints()) - 1 for i in label_numbers):
raise ValueError('Index of label exceeding the list of kpoints')
self.base.attributes.set('label_numbers', label_numbers)
self.base.attributes.set('labels', labels)
[docs] def _change_reference(self, kpoints, to_cartesian=True):
"""
Change reference system, from cartesian to crystal coordinates (units of b1,b2,b3) or viceversa.
:param kpoints: a list of (3) point coordinates
:return kpoints: a list of (3) point coordinates in the new reference
"""
if not isinstance(kpoints, numpy.ndarray):
raise ValueError('kpoints must be a numpy.array for method change_reference()')
try:
rec_cell = self.reciprocal_cell
except AttributeError:
# rec_cell = numpy.eye(3)
raise AttributeError('Cannot use cartesian coordinates without having defined a cell')
trec_cell = numpy.transpose(numpy.array(rec_cell))
if to_cartesian:
matrix = trec_cell
else:
matrix = numpy.linalg.inv(trec_cell)
# note: kpoints is a list Nx3, matrix is 3x3.
# hence, first transpose kpoints, then multiply, finally transpose it back
return numpy.transpose(numpy.dot(matrix, numpy.transpose(kpoints)))
[docs] def set_cell_from_structure(self, structuredata):
"""
Set a cell to be used for symmetry analysis from an AiiDA structure.
Inherits both the cell and the pbc's.
To set manually a cell, use "set_cell"
:param structuredata: an instance of StructureData
"""
from aiida.orm import StructureData
if not isinstance(structuredata, StructureData):
raise ValueError(
'An instance of StructureData should be passed to '
'the KpointsData, found instead {}'.format(structuredata.__class__)
)
cell = structuredata.cell
self.set_cell(cell, structuredata.pbc)
[docs] def set_cell(self, cell, pbc=None):
"""
Set a cell to be used for symmetry analysis.
To set a cell from an AiiDA structure, use "set_cell_from_structure".
:param cell: 3x3 matrix of cell vectors. Orientation: each row
represent a lattice vector. Units are Angstroms.
:param pbc: list of 3 booleans, True if in the nth crystal direction the
structure is periodic. Default = [True,True,True]
"""
self.cell = cell
if pbc is None:
pbc = [True, True, True]
self.pbc = pbc
@property
def reciprocal_cell(self):
"""
Compute reciprocal cell from the internally set cell.
:returns: reciprocal cell in units of 1/Angstrom with cell vectors stored as rows.
Use e.g. reciprocal_cell[0] to access the first reciprocal cell vector.
"""
the_cell = numpy.array(self.cell)
reciprocal_cell = 2. * numpy.pi * numpy.linalg.inv(the_cell).transpose()
return reciprocal_cell
[docs] def set_kpoints_mesh(self, mesh, offset=None):
"""
Set KpointsData to represent a uniformily spaced mesh of kpoints in the
Brillouin zone. This excludes the possibility of set/get kpoints
:param mesh: a list of three integers, representing the size of the
kpoint mesh along b1,b2,b3.
:param offset: (optional) a list of three floats between 0 and 1.
[0.,0.,0.] is Gamma centered mesh
[0.5,0.5,0.5] is half shifted
[1.,1.,1.] by periodicity should be equivalent to [0.,0.,0.]
Default = [0.,0.,0.].
"""
from aiida.common.exceptions import ModificationNotAllowed
# validate
try:
the_mesh = [int(i) for i in mesh]
if len(the_mesh) != 3:
raise ValueError
except (IndexError, ValueError, TypeError):
raise ValueError('The kpoint mesh must be a list of three integers')
if offset is None:
offset = [0., 0., 0.]
try:
the_offset = [float(i) for i in offset]
if len(the_offset) != 3:
raise ValueError
except (IndexError, ValueError, TypeError):
raise ValueError('The offset must be a list of three floats')
# check that there is no list of kpoints saved already
# I cannot have both of them at the same time
try:
_ = self.get_array('kpoints')
raise ModificationNotAllowed('KpointsData has already a kpoint-list stored')
except KeyError:
pass
# store
self.base.attributes.set('mesh', the_mesh)
self.base.attributes.set('offset', the_offset)
[docs] def get_kpoints_mesh(self, print_list=False):
"""
Get the mesh of kpoints.
:param print_list: default=False. If True, prints the mesh of kpoints as a list
:raise AttributeError: if no mesh has been set
:return mesh,offset: (if print_list=False) a list of 3 integers and a list of three
floats 0<x<1, representing the mesh and the offset of kpoints
:return kpoints: (if print_list = True) an explicit list of kpoints coordinates,
similar to what returned by get_kpoints()
"""
mesh = self.base.attributes.get('mesh')
offset = self.base.attributes.get('offset')
if not print_list:
return mesh, offset
kpoints = numpy.mgrid[0:mesh[0], 0:mesh[1], 0:mesh[2]]
kpoints = kpoints.reshape(3, -1).T
offset_kpoints = kpoints + numpy.array(offset)
offset_kpoints[:, 0] /= mesh[0]
offset_kpoints[:, 1] /= mesh[1]
offset_kpoints[:, 2] /= mesh[2]
return offset_kpoints
[docs] def set_kpoints_mesh_from_density(self, distance, offset=None, force_parity=False):
"""
Set a kpoints mesh using a kpoints density, expressed as the maximum
distance between adjacent points along a reciprocal axis
:param distance: distance (in 1/Angstrom) between adjacent
kpoints, i.e. the number of kpoints along each reciprocal
axis i is :math:`|b_i|/distance`
where :math:`|b_i|` is the norm of the reciprocal cell vector.
:param offset: (optional) a list of three floats between 0 and 1.
[0.,0.,0.] is Gamma centered mesh
[0.5,0.5,0.5] is half shifted
Default = [0.,0.,0.].
:param force_parity: (optional) if True, force each integer in the mesh
to be even (except for the non-periodic directions).
:note: a cell should be defined first.
:note: the number of kpoints along non-periodic axes is always 1.
"""
if offset is None:
offset = [0., 0., 0.]
try:
rec_cell = self.reciprocal_cell
except AttributeError:
# rec_cell = numpy.eye(3)
raise AttributeError('Cannot define a mesh from a density without having defined a cell')
# I first round to the fifth digit |b|/distance (to avoid that e.g.
# 3.00000001 becomes 4)
kpointsmesh = [
max(int(numpy.ceil(round(numpy.linalg.norm(b) / distance, 5))), 1) if pbc else 1
for pbc, b in zip(self.pbc, rec_cell)
]
if force_parity:
kpointsmesh = [k + (k % 2) if pbc else 1 for pbc, k in zip(self.pbc, kpointsmesh)]
self.set_kpoints_mesh(kpointsmesh, offset=offset)
@property
def _dimension(self):
"""
Dimensionality of the structure, found from its pbc (i.e. 1 if it's a 1D
structure, 2 if its 2D, 3 if it's 3D ...).
:return dimensionality: 0, 1, 2 or 3
:note: will return 3 if pbc has not been set beforehand
"""
try:
return sum(self.pbc)
except AttributeError:
return 3
[docs] def _validate_kpoints_weights(self, kpoints, weights):
"""
Validate the list of kpoints and of weights before storage.
Kpoints and weights must be convertible respectively to an array of
N x dimension and N floats
"""
kpoints = numpy.array(kpoints)
# I cannot just use `if not kpoints` because it's a numpy array and
# `not` of a numpy array does not work
if len(kpoints) == 0: # pylint: disable=len-as-condition
if self._dimension == 0:
# replace empty list by Gamma point
kpoints = numpy.array([[0., 0., 0.]])
else:
raise ValueError(
'empty kpoints list is valid only in zero dimension'
'; instead here with have {} dimensions'
''.format(self._dimension)
)
if len(kpoints.shape) <= 1:
# list of scalars is accepted only in the 0D and 1D cases
if self._dimension <= 1:
# replace by singletons
kpoints = kpoints.reshape(kpoints.shape[0], 1)
else:
raise ValueError(f'kpoints must be a list of lists in {self._dimension}D case')
if kpoints.dtype != numpy.dtype(float):
raise ValueError(f'kpoints must be an array of type floats. Found instead {kpoints.dtype}')
if kpoints.shape[1] < self._dimension:
raise ValueError(
'In a system which has {0} dimensions, kpoint need'
'more than {0} coordinates (found instead {1})'.format(self._dimension, kpoints.shape[1])
)
if weights is not None:
weights = numpy.array(weights)
if weights.shape[0] != kpoints.shape[0]:
raise ValueError(f'Found {weights.shape[0]} weights but {kpoints.shape[0]} kpoints')
if weights.dtype != numpy.dtype(float):
raise ValueError(f'weights must be an array of type floats. Found instead {weights.dtype}')
return kpoints, weights
[docs] def set_kpoints(self, kpoints, cartesian=False, labels=None, weights=None, fill_values=0):
"""
Set the list of kpoints. If a mesh has already been stored, raise a
ModificationNotAllowed
:param kpoints: a list of kpoints, each kpoint being a list of one, two
or three coordinates, depending on self.pbc: if structure is 1D
(only one True in self.pbc) one allows singletons or scalars for
each k-point, if it's 2D it can be a length-2 list, and in all
cases it can be a length-3 list.
Examples:
* [[0.,0.,0.],[0.1,0.1,0.1],...] for 1D, 2D or 3D
* [[0.,0.],[0.1,0.1,],...] for 1D or 2D
* [[0.],[0.1],...] for 1D
* [0., 0.1, ...] for 1D (list of scalars)
For 0D (all pbc are False), the list can be any of the above
or empty - then only Gamma point is set.
The value of k for the non-periodic dimension(s) is set by
fill_values
:param cartesian: if True, the coordinates given in input are treated
as in cartesian units. If False, the coordinates are crystal,
i.e. in units of b1,b2,b3. Default = False
:param labels: optional, the list of labels to be set for some of the
kpoints. See labels for more info
:param weights: optional, a list of floats with the weight associated
to the kpoint list
:param fill_values: scalar to be set to all
non-periodic dimensions (indicated by False in self.pbc), or list of
values for each of the non-periodic dimensions.
"""
from aiida.common.exceptions import ModificationNotAllowed
# check that it is a 'dim'x #kpoints dimensional array
the_kpoints, the_weights = self._validate_kpoints_weights(kpoints, weights)
# if k-points have less than 3 coordinates (low dimensionality), fill
# with constant values the non-periodic dimensions
if the_kpoints.shape[1] < 3:
if numpy.isscalar(fill_values):
# replace scalar by a list of 3-the_kpoints.shape[1] identical
# elements
fill_values = [fill_values] * (3 - the_kpoints.shape[1])
if len(fill_values) < 3 - the_kpoints.shape[1]:
raise ValueError(f'fill_values should be either a scalar or a length-{3 - the_kpoints.shape[1]} list')
else:
tmp_kpoints = numpy.zeros((the_kpoints.shape[0], 0))
i_kpts = 0
i_fill = 0
for idim in range(3):
# check periodic boundary condition of each of the 3 dimensions:
# - if it's a periodic one, fill with the k-points values
# defined in input
# - if it's non-periodic, fill with one of the values in
# fill_values
if self.pbc[idim]:
tmp_kpoints = numpy.hstack(
(tmp_kpoints, the_kpoints[:, i_kpts].reshape((the_kpoints.shape[0], 1)))
)
i_kpts += 1
else:
tmp_kpoints = numpy.hstack(
(tmp_kpoints, numpy.ones((the_kpoints.shape[0], 1)) * fill_values[i_fill])
)
i_fill += 1
the_kpoints = tmp_kpoints
# change reference and always store in crystal coords
if cartesian:
the_kpoints = self._change_reference(the_kpoints, to_cartesian=False)
# check that we did not saved a mesh already
if self.base.attributes.get('mesh', None) is not None:
raise ModificationNotAllowed('KpointsData has already a mesh stored')
# store
self.set_array('kpoints', the_kpoints)
if the_weights is not None:
self.set_array('weights', the_weights)
if labels is not None:
self.labels = labels
[docs] def get_kpoints(self, also_weights=False, cartesian=False):
"""
Return the list of kpoints
:param also_weights: if True, returns also the list of weights.
Default = False
:param cartesian: if True, returns points in cartesian coordinates,
otherwise, returns in crystal coordinates. Default = False.
"""
try:
kpoints = numpy.array(self.get_array('kpoints'))
except KeyError:
raise AttributeError('Before the get, first set a list of kpoints')
if cartesian:
kpoints = self._change_reference(kpoints, to_cartesian=True)
if also_weights:
try:
the_weights = self.get_array('weights')
except KeyError:
raise AttributeError('No weights were set')
weights = numpy.array(the_weights)
return kpoints, weights
return kpoints
```