import numpy as np
import random
import itertools
import sys
from lattice_mc import atom, jump, transitions, cluster
from lattice_mc.error import BlockedLatticeError
from collections import Counter
[docs]class Lattice:
"""
Lattice class
"""
def __init__( self, sites, cell_lengths ):
"""
Initialise a Lattice instance.
Args:
sites (List(Site)): List of sites contained in the lattice.
cell_lengths (np.array(x,y,z)): Vector of cell lengths for the simulation cell.
Returns:
None
"""
self.cell_lengths = cell_lengths
self.sites = sites
self.number_of_sites = len( self.sites )
self.site_labels = set( [ site.label for site in self.sites ] )
self.site_populations = Counter( [ site.label for site in self.sites ] )
self.enforce_periodic_boundary_conditions()
self.initialise_site_lookup_table()
self.nn_energy = False
self.cn_energies = False
self.site_energies = False
self.jump_lookup_table = False
for site in self.sites:
site.p_neighbours = [ self.site_with_id( i ) for i in site.neighbours ]
self.reset()
[docs] def enforce_periodic_boundary_conditions( self ):
"""
Ensure that all lattice sites are within the central periodic image of the simulation cell.
Sites that are outside the central simulation cell are mapped back into this cell.
Args:
None
Returns:
None
"""
for s in self.sites:
for i in range(3):
if s.r[i] < 0.0:
s.r[i] += self.cell_lengths[i]
if s.r[i] > self.cell_lengths[i]:
s.r[i] -= self.cell_lengths[i]
[docs] def reset( self ):
"""
Reset all time-dependent counters for this lattice and its constituent sites
Args:
None
Returns:
None
"""
self.time = 0.0
for site in self.sites:
site.time_occupied = 0.0
[docs] def initialise_site_lookup_table( self ):
"""
Create a lookup table allowing sites in this lattice to be queried using `self.site_lookup[n]` where `n` is the identifying site numbe.
Args:
None
Returns:
None
"""
self.site_lookup = {}
for site in self.sites:
self.site_lookup[ site.number ] = site
[docs] def site_with_id( self, number ):
"""
Select the site with a specific id number.
Args:
number (Int): The identifying number for a specific site.
Returns:
(Site): The site with id number equal to `number`
"""
return self.site_lookup[ number ]
[docs] def vacant_sites( self ):
"""
The set of sites not occupied by atoms.
Args:
None
Returns:
List(Site): List of sites that are vacant.
"""
return ( site for site in self.sites if not site.is_occupied )
[docs] def occupied_sites( self ):
"""
The set of sites occupied by atoms.
Args:
None
Returns:
List(Site): List of sites that are occupied.
"""
return ( site for site in self.sites if site.is_occupied )
[docs] def vacant_site_numbers( self ):
"""
List of site id numbers for all sites that are vacant.
Args:
None
Returns:
List(Int): List of site id numbers for vacant sites.
"""
return [ site.number for site in self.sites if not site.is_occupied ]
[docs] def occupied_site_numbers( self ):
"""
List of site id numbers for all sites that are occupied.
Args:
None
Returns:
List(Int): List of site id numbers for occupied sites.
"""
return [ site.number for site in self.sites if site.is_occupied ]
[docs] def potential_jumps( self ):
"""
All nearest-neighbour jumps not blocked by volume exclusion
(i.e. from occupied to neighbouring unoccupied sites).
Args:
None
Returns:
(List(Jump)): List of possible jumps.
"""
jumps = []
if self.number_of_occupied_sites <= self.number_of_sites / 2:
for occupied_site in self.occupied_sites():
unoccupied_neighbours = [ site for site in [ self.site_with_id( n ) for n in occupied_site.neighbours ] if not site.is_occupied ]
for vacant_site in unoccupied_neighbours:
jumps.append( jump.Jump( occupied_site, vacant_site, self.nn_energy, self.cn_energies, self.jump_lookup_table ) )
else:
for vacant_site in self.vacant_sites():
occupied_neighbours = [ site for site in [ self.site_with_id( n ) for n in vacant_site.neighbours ] if site.is_occupied ]
for occupied_site in occupied_neighbours:
jumps.append( jump.Jump( occupied_site, vacant_site, self.nn_energy, self.cn_energies, self.jump_lookup_table ) )
return jumps
[docs] def update( self, jump ):
"""
Update the lattice state by accepting a specific jump
Args:
jump (Jump): The jump that has been accepted.
Returns:
None.
"""
atom = jump.initial_site.atom
dr = jump.dr( self.cell_lengths )
#print( "atom {} jumped from site {} to site {}".format( atom.number, jump.initial_site.number, jump.final_site.number ) )
jump.final_site.occupation = atom.number
jump.final_site.atom = atom
jump.final_site.is_occupied = True
jump.initial_site.occupation = 0
jump.initial_site.atom = None
jump.initial_site.is_occupied = False
# TODO: updating atom counters could be contained in an atom.move_to( site ) method
atom.site = jump.final_site
atom.number_of_hops += 1
atom.dr += dr
atom.summed_dr2 += np.dot( dr, dr )
[docs] def populate_sites( self, number_of_atoms, selected_sites=None ):
"""
Populate the lattice sites with a specific number of atoms.
Args:
number_of_atoms (Int): The number of atoms to populate the lattice sites with.
selected_sites (:obj:List, optional): List of site labels if only some sites are to be occupied. Defaults to None.
Returns:
None
"""
if number_of_atoms > self.number_of_sites:
raise ValueError
if selected_sites:
atoms = [ atom.Atom( initial_site = site ) for site in random.sample( [ s for s in self.sites if s.label in selected_sites ], number_of_atoms ) ]
else:
atoms = [ atom.Atom( initial_site = site ) for site in random.sample( self.sites, number_of_atoms ) ]
self.number_of_occupied_sites = number_of_atoms
return atoms
[docs] def jump( self ):
"""
Select a jump at random from all potential jumps, then update the lattice state.
Args:
None
Returns:
None
"""
potential_jumps = self.potential_jumps()
if not potential_jumps:
raise BlockedLatticeError('No moves are possible in this lattice')
all_transitions = transitions.Transitions( self.potential_jumps() )
random_jump = all_transitions.random()
delta_t = all_transitions.time_to_jump()
self.time += delta_t
self.update_site_occupation_times( delta_t )
self.update( random_jump )
return( all_transitions.time_to_jump() )
[docs] def update_site_occupation_times( self, delta_t ):
"""
Increase the time occupied for all occupied sites by delta t
Args:
delta_t (Float): Timestep.
Returns:
None
"""
for site in self.occupied_sites():
site.time_occupied += delta_t
[docs] def site_occupation_statistics( self ):
"""
Average site occupation for each site type
Args:
None
Returns:
(Dict(Str:Float)): Dictionary of occupation statistics, e.g.::
{ 'A' : 2.5, 'B' : 25.3 }
"""
if self.time == 0.0:
return None
occupation_stats = { label : 0.0 for label in self.site_labels }
for site in self.sites:
occupation_stats[ site.label ] += site.time_occupied
for label in self.site_labels:
occupation_stats[ label ] /= self.time
return occupation_stats
[docs] def set_site_energies( self, energies ):
"""
Set the energies for every site in the lattice according to the site labels.
Args:
energies (Dict(Str:Float): Dictionary of energies for each site label, e.g.::
{ 'A' : 1.0, 'B', 0.0 }
Returns:
None
"""
self.site_energies = energies
for site_label in energies:
for site in self.sites:
if site.label == site_label:
site.energy = energies[ site_label ]
[docs] def set_nn_energy( self, delta_E ):
"""
Set the lattice nearest-neighbour energy.
Args:
delta_E (Float): The nearest-neighbour energy E_nn.
Returns:
None
"""
self.nn_energy = delta_E
[docs] def set_cn_energies( self, cn_energies ):
"""
Set the coordination number dependent energies for this lattice.
Args:
cn_energies (Dict(Str:Dict(Int:Float))): Dictionary of dictionaries specifying the coordination number dependent energies for each site type. e.g.::
{ 'A' : { 0 : 0.0, 1 : 1.0, 2 : 2.0 }, 'B' : { 0 : 0.0, 1 : 2.0 } }
Returns:
None
"""
for site in self.sites:
site.set_cn_occupation_energies( cn_energies[ site.label ] )
self.cn_energies = cn_energies
[docs] def site_coordination_numbers( self ):
"""
Returns a dictionary of the coordination numbers for each site label. e.g.::
{ 'A' : { 4 }, 'B' : { 2, 4 } }
Args:
none
Returns:
coordination_numbers (Dict(Str:Set(Int))): dictionary of coordination
numbers for each site label.
"""
coordination_numbers = {}
for l in self.site_labels:
coordination_numbers[ l ] = set( [ len( site.neighbours ) for site in self.sites if site.label is l ] )
return coordination_numbers
[docs] def max_site_coordination_numbers( self ):
"""
Returns a dictionary of the maximum coordination number for each site label.
e.g.::
{ 'A' : 4, 'B' : 4 }
Args:
none
Returns:
max_coordination_numbers (Dict(Str:Int)): dictionary of maxmimum coordination
number for each site label.
"""
return { l : max( c ) for l, c in self.site_coordination_numbers().items() }
[docs] def site_specific_coordination_numbers( self ):
"""
Returns a dictionary of coordination numbers for each site type.
Args:
None
Returns:
(Dict(Str:List(Int))) : Dictionary of coordination numbers for each site type, e.g.::
{ 'A' : [ 2, 4 ], 'B' : [ 2 ] }
"""
specific_coordination_numbers = {}
for site in self.sites:
specific_coordination_numbers[ site.label ] = site.site_specific_neighbours()
return specific_coordination_numbers
[docs] def connected_site_pairs( self ):
"""
Returns a dictionary of all connections between pair of sites (by site label).
e.g. for a linear lattice A-B-C will return::
{ 'A' : [ 'B' ], 'B' : [ 'A', 'C' ], 'C' : [ 'B' ] }
Args:
None
Returns:
site_connections (Dict{Str List[Str]}): A dictionary of neighbouring site types in the lattice.
"""
site_connections = {}
for initial_site in self.sites:
if not initial_site.label in site_connections:
site_connections[ initial_site.label ] = []
for final_site in initial_site.p_neighbours:
if final_site.label not in site_connections[ initial_site.label ]:
site_connections[ initial_site.label ].append( final_site.label )
return site_connections
[docs] def transmute_sites( self, old_site_label, new_site_label, n_sites_to_change ):
"""
Selects a random subset of sites with a specific label and gives them a different label.
Args:
old_site_label (String or List(String)): Site label(s) of the sites to be modified..
new_site_label (String): Site label to be applied to the modified sites.
n_sites_to_change (Int): Number of sites to modify.
Returns:
None
"""
selected_sites = self.select_sites( old_site_label )
for site in random.sample( selected_sites, n_sites_to_change ):
site.label = new_site_label
self.site_labels = set( [ site.label for site in self.sites ] )
[docs] def connected_sites( self, site_labels=None ):
"""
Searches the lattice to find sets of sites that are contiguously neighbouring.
Mutually exclusive sets of contiguous sites are returned as Cluster objects.
Args:
site_labels (:obj:(List(Str)|Set(Str)|Str), optional): Labels for sites to be considered in the search.
This can be a list::
[ 'A', 'B' ]
a set::
( 'A', 'B' )
or a string::
'A'.
Returns:
(List(Cluster)): List of Cluster objects for groups of contiguous sites.
"""
if site_labels:
selected_sites = self.select_sites( site_labels )
else:
selected_sites = self.sites
initial_clusters = [ cluster.Cluster( [ site ] ) for site in selected_sites ]
if site_labels:
blocking_sites = self.site_labels - set( site_labels )
for c in initial_clusters:
c.remove_sites_from_neighbours( blocking_sites )
final_clusters = []
while initial_clusters: # loop until initial_clusters is empty
this_cluster = initial_clusters.pop(0)
while this_cluster.neighbours:
neighbouring_clusters = [ c for c in initial_clusters if this_cluster.is_neighbouring( c ) ]
for nc in neighbouring_clusters:
initial_clusters.remove( nc )
this_cluster = this_cluster.merge( nc )
final_clusters.append( this_cluster )
return final_clusters
[docs] def select_sites( self, site_labels ):
"""
Selects sites in the lattice with specified labels.
Args:
site_labels (List(Str)|Set(Str)|Str): Labels of sites to select.
This can be a List [ 'A', 'B' ], a Set ( 'A', 'B' ), or a String 'A'.
Returns:
(List(Site)): List of sites with labels given by `site_labels`.
"""
if type( site_labels ) in ( list, set ):
selected_sites = [ s for s in self.sites if s.label in site_labels ]
elif type( site_labels ) is str:
selected_sites = [ s for s in self.sites if s.label is site_labels ]
else:
raise ValueError( str( site_labels ) )
return selected_sites
[docs] def detached_sites( self, site_labels=None ):
"""
Returns all sites in the lattice (optionally from the set of sites with specific labels)
that are not part of a percolating network.
This is determined from clusters of connected sites that do not wrap round to
themselves through a periodic boundary.
Args:
site_labels (String or List(String)): Lables of sites to be considered.
Returns:
(List(Site)): List of sites not in a periodic percolating network.
"""
clusters = self.connected_sites( site_labels=site_labels )
island_clusters = [ c for c in clusters if not any( c.is_periodically_contiguous() ) ]
return list( itertools.chain.from_iterable( ( c.sites for c in island_clusters ) ) )
[docs] def is_blocked( self ):
"""
Check whether there are any possible jumps.
Args:
None
Returns:
(Bool): True if there are no possible jumps. Otherwise returns False.
"""
if not self.potential_jumps():
return True
else:
return False