import numpy as np
from lattice_mc import lattice, lattice_site
from math import sqrt
import re
"""
Functions for constructing lattices.
"""
[docs]def square_lattice( a, b, spacing ):
"""
Generate a square lattice.
Args:
a (Int): Number of lattice repeat units along x.
b (Int): Number of lattice repeat units along y.
spacing (Float): Distance between lattice sites.
Returns:
(Lattice): The new lattice
Notes:
The returned lattice is 3D periodic, but all sites and edges lie in the xy plane.
"""
grid = np.array( list( range( 1, a * b + 1 ) ) ).reshape( a, b, order='F' )
it = np.nditer( grid, flags=['multi_index'] )
sites = []
while not it.finished:
x, y = it.multi_index
r = np.array( [ x * spacing, y * spacing, 0.0 ] )
neighbours = [ np.roll( grid, +1, axis=0 )[x,y],
np.roll( grid, -1, axis=0 )[x,y],
np.roll( grid, +1, axis=1 )[x,y],
np.roll( grid, -1, axis=1 )[x,y] ]
sites.append( lattice_site.Site( int( it[0] ), r, neighbours, 0.0, 'L' ) )
it.iternext()
return lattice.Lattice( sites, cell_lengths = np.array( [ a, b, 0.0 ] ) * spacing )
[docs]def honeycomb_lattice( a, b, spacing, alternating_sites=False ):
"""
Generate a honeycomb lattice.
Args:
a (Int): Number of lattice repeat units along x.
b (Int): Number of lattice repeat units along y.
spacing (Float): Distance between lattice sites.
alternating_sites (Bool, optional): Label alternating sites with 'A' and 'B'. Defaults to False.
Returns:
(Lattice): The new lattice
Notes:
The returned lattice is 3D periodic, but all sites and edges lie in the xy plane.
"""
if alternating_sites:
site_labels = [ 'A', 'B', 'A', 'B' ]
else:
site_labels = [ 'L', 'L', 'L', 'L' ]
unit_cell_lengths = np.array( [ sqrt(3), 3.0, 0.0 ] ) * spacing
cell_lengths = unit_cell_lengths * np.array( [ a, b, 1.0 ] )
grid = np.array( list( range( 1, int( a * b * 4 + 1 ) ) ) ).reshape( a, b, 4, order='C' )
sites = []
for i in range( a ):
for j in range( b ):
# site 1
r = np.array( [ i * sqrt(3) * spacing, j * 3 * spacing, 0.0 ] )
neighbours = [ grid[ i, j, 1 ],
np.roll( grid, +1, axis=0 )[ i, j, 1 ],
np.roll( grid, +1, axis=1 )[ i, j, 3 ] ]
sites.append( lattice_site.Site( grid[ i, j, 0 ], r, neighbours, 0.0, site_labels[0] ) )
# site 2
r = np.array( [ i * sqrt(3) * spacing + sqrt(3)/2 * spacing, ( j * 3 + 0.5 ) * spacing, 0.0 ] )
neighbours = [ grid[ i, j, 0 ],
grid[ i, j, 2 ],
np.roll( grid, -1, axis=0 )[ i, j, 0 ] ]
sites.append( lattice_site.Site( grid[ i, j, 1 ], r, neighbours, 0.0, site_labels[1] ) )
# site 3
r = np.array( [ i * sqrt(3) * spacing + sqrt(3)/2 * spacing, ( j * 3 + 1.5 ) * spacing, 0.0 ] )
neighbours = [ grid[ i, j, 1 ],
grid[ i, j, 3 ],
np.roll( grid, -1, axis=0 )[ i, j, 3 ] ]
sites.append( lattice_site.Site( grid[ i, j, 2 ], r, neighbours, 0.0, site_labels[2] ) )
# site 4
r = np.array( [ i * sqrt(3) * spacing, ( j * 3 + 2 ) * spacing, 0.0 ] )
neighbours = [ grid[ i, j, 2 ],
np.roll( grid, +1, axis=0 )[ i, j, 2 ],
np.roll( grid, -1, axis=1 )[ i, j, 0 ] ]
sites.append( lattice_site.Site( grid[ i, j, 3 ], r, neighbours, 0.0, site_labels[3] ) )
return lattice.Lattice( sites, cell_lengths=cell_lengths )
[docs]def cubic_lattice( a, b, c, spacing ):
"""
Generate a cubic lattice.
Args:
a (Int): Number of lattice repeat units along x.
b (Int): Number of lattice repeat units along y.
c (Int): Number of lattice repeat units along z.
spacing (Float): Distance between lattice sites.
Returns:
(Lattice): The new lattice
"""
grid = np.array( list( range( 1, a * b * c + 1 ) ) ).reshape( a, b, c, order='F' )
it = np.nditer( grid, flags=[ 'multi_index' ] )
sites = []
while not it.finished:
x, y, z = it.multi_index
r = np.array( [ x, y, z ] ) * spacing
neighbours = [ np.roll( grid, +1, axis=0 )[x,y,z],
np.roll( grid, -1, axis=0 )[x,y,z],
np.roll( grid, +1, axis=1 )[x,y,z],
np.roll( grid, -1, axis=1 )[x,y,z],
np.roll( grid, +1, axis=2 )[x,y,z],
np.roll( grid, -1, axis=2 )[x,y,z] ]
sites.append( lattice_site.Site( int( it[0] ), r, neighbours, 0.0, 'L' ) )
it.iternext()
return lattice.Lattice( sites, cell_lengths = np.array( [ a, b, c ] ) * spacing )
#def lattice_from_sites_file( site_file, cell_lengths ):
# sites = []
# with open( site_file ) as f:
# number_of_sites = int( f.readline() )
# for i in range( number_of_sites ):
# f.readline()
# number = int( f.readline().split()[1] )
# r = np.array( [ float( s ) for s in f.readline().split()[1:4] ] )
# f.readline() # ignore vertices
# neighbours = [ int( s ) for s in f.readline().split()[1:] ]
# label = f.readline().split()[1]
# sites.append( lattice_site.Site( number, r, neighbours, 0.0, label ) )
# return lattice.Lattice( sites, cell_lengths = np.array( cell_lengths ) )
[docs]def lattice_from_sites_file( site_file, cell_lengths ):
"""
Generate a lattice from a sites file.
Args:
site_file (Str): Filename for the file containing the site information.
cell_lengths (List(Float,Float,Float)): A list containing the [ x, y, z ] cell lengths.
Returns:
(Lattice): The new lattice
Notes:
| The site information file format is:
| <number_of_sites> (Int).
| Followed by blocks of data separated by double linebreaks; one block per site.
| site: <site number> (Int).
| centre: <x> <y> <z> (Float,Float,Float).
| neighbours: <list of site numbers of neighbouring sites> (List[Int]).
| label: <site group labal> (Str).
| energy: <site occupation energy> (Float).
| The energy is optional, and will be set to 0.0 if not included.
| Line order within each block is not meaningful.
| British and American English spellings for centre|center and neighbour|neighbor are accepted.
| An example file can be found in the examples directory.
"""
sites = []
site_re = re.compile( 'site:\s+([-+]?\d+)' )
r_re = re.compile( 'cent(?:er|re):\s+([-\d\.e]+)\s+([-\d\.e]+)\s+([-\d\.e]+)' )
r_neighbours = re.compile( 'neighbou{0,1}rs:((\s+[-+]?\d+)+)' )
r_label = re.compile( 'label:\s+(\S+)' )
r_energy = re.compile( 'energy:\s([-+\d\.]+)' )
with open( site_file ) as f:
filein = f.read().split("\n\n")
number_of_sites = int( filein[0] )
for i in range( number_of_sites ):
block = filein[ i+1 ]
number = int( site_re.findall( block )[0] )
r = np.array( [ float(s) for s in r_re.findall( block )[0] ] )
neighbours = [ int( s ) for s in r_neighbours.findall( block )[0][0].split() ]
label = r_label.findall( block )[0]
energy = r_energy.findall( block )
if energy:
energy = float( energy[0] )
else:
energy = 0.0
sites.append( lattice_site.Site( number, r, neighbours, energy, label ) )
return lattice.Lattice( sites, cell_lengths = np.array( cell_lengths ) )