init_crystal.py

# @Author:  Felix Kramer
# @Date:   2021-05-22T13:11:37+02:00
# @Email:  kramer@mpi-cbg.de
# @Project: go-with-the-flow
# @Last modified by:    Felix Kramer
# @Last modified time: 2021-05-23T15:14:10+02:00
# @License: MIT
import networkx as nx
import numpy as np

# not finalized! todo: implement peridoc cell definition
# construct a non-trivial, periodic 3d embedding
def init_graph_from_crystal(crystal_type,periods):

    choose_constructor_option={ 'default': networkx_simple, 'simple': networkx_simple, 'chain': networkx_chain,'bcc': networkx_bcc,'fcc': networkx_fcc,'diamond': networkx_diamond,'laves':networkx_laves}

    if crystal_type in choose_constructor_option:
            crystal=choose_constructor_option[crystal_type](periods)

    else :
        print('Warning, crystal type unknown, set default: simple')
        crystal=choose_constructor_option['default'](1)

    return crystal.G

class networkx_crystal():

    def __init__(self):
        self.dict_cells={  }
        self.G=nx.Graph()
        self.lattice_constant=1
        self.translation_length=1

    # construct one of the following crystal topologies
    def lattice_translation(self,t,T):

        D=nx.Graph()
        for n in T.nodes():
            D.add_node(tuple(n+t),pos=T.nodes[n]['pos']+t)

        return D

    def periodic_cell_structure(self,cell,num_periods):

        DL=nx.Graph()

        if type(num_periods) is not int :
            periods=[range(num_periods[0]),range(num_periods[1]),range(num_periods[2])]
        else:
            periods=[range(num_periods),range(num_periods),range(num_periods)]
        for i in periods[0]:
            for j in periods[1]:
                for k in periods[2]:
                    TD=self.lattice_translation(self.translation_length*np.array([i,j,k]),cell)
                    DL.add_nodes_from(TD.nodes(data=True))
                    self.dict_cells[(i,j,k)]=list(TD.nodes())

        list_n=np.array(list(DL.nodes()))
        for i,n in enumerate(list_n[:-1]):
            for m in list_n[(i+1):]:
                dist=np.linalg.norm(DL.nodes[tuple(n)]['pos']-DL.nodes[tuple(m)]['pos'])
                if dist==self.lattice_constant:
                    DL.add_edge(tuple(n),tuple(m),slope=(DL.nodes[tuple(n)]['pos'],DL.nodes[tuple(m)]['pos']))

        dict_nodes={}
        for idx_n,n in enumerate(DL.nodes()):
            self.G.add_node(idx_n,pos=DL.nodes[n]['pos'])
            dict_nodes.update({n:idx_n})
        for idx_e,e in enumerate(DL.edges()):
            self.G.add_edge(dict_nodes[e[0]],dict_nodes[e[1]],slope=(DL.nodes[e[0]]['pos'],DL.nodes[e[1]]['pos']))

        self.dict_cubes={}
        dict_aux={}
        for i,k in enumerate(self.dict_cells.keys()):
            dict_aux[i]=[ dict_nodes[n] for n in self.dict_cells[k] ]
        for i,k in enumerate(dict_aux.keys()):
            self.dict_cubes[k]=nx.Graph()
            n_list=list(dict_aux[k])
            for u in n_list[:-1]:
                for v in n_list[1:]:
                    if self.G.has_edge(u,v):
                        self.dict_cubes[k].add_edge(u,v)

# 3D
class networkx_simple(networkx_crystal,object):


    def __init__(self, num_periods):

        super(networkx_simple,self).__init__()
        self.lattice_constant=1.
        self.translation_length=1.
        self.simple_cubic_lattice(num_periods)

    #construct full triangulated hex grid as skeleton
    def simple_unit_cell(self):

        D=nx.Graph()
        for i in [0,1]:
            for j in [0,1]:
                for k in [0,1]:
                    D.add_node(tuple((i,j,k)),pos=np.array([i,j,k]))

        return D

    def simple_cubic_lattice(self,num_periods):

        D=self.simple_unit_cell()
        self.periodic_cell_structure(D,num_periods)

class networkx_chain(networkx_crystal,object):

    def __init__(self, num_periods):

        super(networkx_chain,self).__init__()
        self.simple_chain(num_periods)

    def simple_chain(self,num_periods):

        #construct single box
        for i in range(num_periods):
          self.G.add_node(i, pos=np.array([i,0,0]))
        for i in range(num_periods-1):
          self.G.add_edge(i+1,i, slope=(self.G.nodes[i+1]['pos'],self.G.nodes[i]['pos']))

class networkx_bcc(networkx_crystal,object):

    def __init__(self, num_periods):
        super(networkx_bcc,self).__init__()
        self.lattice_constant=np.sqrt(3.)/2.
        self.translation_length=1.
        self.simple_bcc_lattice( num_periods)

    def bcc_unit_cell(self):

        D=nx.Graph()
        for i in [0,1]:
            for j in [0,1]:
                for k in [0,1]:
                    D.add_node(tuple((i,j,k)),pos=np.array([i,j,k]))
        D.add_node(tuple((0.5,0.5,0.5)),pos=np.array([0.5,0.5,0.5]))
        return D

    def simple_bcc_lattice(self,n):

        #construct single box

        D=self.bcc_unit_cell()
        self.periodic_cell_structure(D,n)

class networkx_fcc(networkx_crystal,object):

    def __init__(self, num_periods):
        super(networkx_fcc,self).__init__()
        self.lattice_constant=np.sqrt(2.)/2.
        self.translation_length=1.
        self.simple_fcc_lattice( num_periods)

    def fcc_unit_cell(self):

        D=nx.Graph()
        for i in [0,1]:
            for j in [0,1]:
                for k in [0,1]:
                    D.add_node(tuple((i,j,k)),pos=np.array([i,j,k]))
        for i in [0.,1.]:
            D.add_node(tuple((0.5,i,0.5)),pos=np.array([0.5,i,0.5]))
        for i in [0.,1.]:
            D.add_node(tuple((0.5,0.5,i)),pos=np.array([0.5,0.5,i]))
        for i in [0.,1.]:
            D.add_node(tuple((i,0.5,0.5)),pos=np.array([i,0.5,0.5]))

        return D

    def simple_fcc_lattice(self,n):

        D=self.fcc_unit_cell()
        self.periodic_cell_structure(D,n,lattice_constant,translation_length)

class networkx_diamond(networkx_crystal,object):

    def __init__(self, num_periods):
        super(networkx_diamond,self).__init__()
        self.lattice_constant=np.sqrt(3.)/2.
        self.translation_length=2.
        self.diamond_lattice(num_periods)

    def diamond_unit_cell(self):

        D=nx.Graph()
        T=[nx.Graph() for i in range(4)]
        T[0].add_node((0,0,0),pos=np.array([0,0,0]))
        T[0].add_node((1,1,0),pos=np.array([1,1,0]))
        T[0].add_node((1,0,1),pos=np.array([1,0,1]))
        T[0].add_node((0,1,1),pos=np.array([0,1,1]))
        T[0].add_node((0.5,0.5,0.5),pos=np.array([0.5,0.5,0.5]))
        translation=[np.array([1,1,0]),np.array([1,0,1]),np.array([0,1,1])]
        for i,t in enumerate(translation):
            for n in T[0].nodes():
                T[i+1].add_node(tuple(n+t),pos=T[0].nodes[n]['pos']+t)
        for t in T:
            D.add_nodes_from(t.nodes(data=True))

        return D

    def diamond_lattice(self,num_periods):

        D=self.diamond_unit_cell()
        self.periodic_cell_structure(D,num_periods)

class networkx_laves(networkx_crystal,object):

    def __init__(self, num_periods):
        super(networkx_laves,self).__init__()
        self.lattice_constant=2.
        self.laves_lattice(num_periods)

    def laves_lattice(self,num_periods):

        #construct single box
        counter=0
        G_aux=nx.Graph()
        # periods=range(-num_periods,num_periods)
        # periods=range(num_periods)
        if type(num_periods) is not int :
            periods=[range(num_periods[0]),range(num_periods[1]),range(num_periods[2])]
        else:
            periods=[range(num_periods),range(num_periods),range(num_periods)]

        fundamental_points=[[0,0,0],[1,1,0],[1,2,1],[0,3,1],[2,2,2],[3,3,2],[3,0,3],[2,1,3]]
        for l,fp in enumerate(fundamental_points):
            for i in periods[0]:
                for j in periods[1]:
                    for k in periods[2]:

                        pos_n=np.add(fp,[4.*i,4.*j,4.*k])
                        G_aux.add_node(tuple(pos_n),pos=pos_n)

        list_nodes=list(G_aux.nodes())
        self.G=nx.Graph()
        H=nx.Graph()
        points_G=[G_aux.nodes[n]['pos'] for i,n in enumerate(G_aux.nodes()) ]
        for i,n in enumerate(G_aux.nodes()) :

              H.add_node(n,pos=G_aux.nodes[n]['pos'])
        for i,n in enumerate(list_nodes[:-1]):
              for j,m in enumerate(list_nodes[(i+1):]):

                      v=np.subtract(n,m)
                      dist=np.dot(v,v)
                      if dist==self.lattice_constant:
                          H.add_edge(n,m,slope=(G_aux.nodes[n]['pos'],G_aux.nodes[m]['pos']))

        dict_nodes={}
        for idx_n,n in enumerate(H.nodes()):
          self.G.add_node(idx_n,pos=H.nodes[n]['pos'])
          dict_nodes.update({n:idx_n})
        for idx_e,e in enumerate(H.edges()):
          self.G.add_edge(dict_nodes[e[0]],dict_nodes[e[1]],slope=(H.nodes[e[0]]['pos'],H.nodes[e[1]]['pos']))

class networkx_trigonal_stack(networkx_crystal,object):

    def __init__(self, tiling_factor):
        super(networkx_trigonal_stack,self).__init__()
        self.triangulated_hexagon_stack(tiling_factor)
    #define crosslinking procedure between the generated single-layers
    def crosslink_stacks(self):

      for i,n in enumerate(self.G.nodes()):
          self.G.nodes[n]['label']=i
      if self.stacks > 1 :
          labels_n = nx.get_node_attributes(self.G,'label')
          sorted_label_n_list=sorted(labels_n ,key=labels_n.__getitem__)
          # for n in nx.nodes(self.G):
          for n in sorted_label_n_list:
              if n[2]!=self.stacks-1:

                  p1=self.G.nodes[(n[0],n[1],n[2])]['pos']
                  p2=self.G.nodes[(n[0],n[1],n[2]+1)]['pos']
                  self.G.add_edge((n[0],n[1],n[2]),(n[0],n[1],n[2]+1),slope=(p1,p2))

    # auxillary function, construct triangulated hex grid upper and lower wings
    def construct_spine_stack(self,z,n):
        self.spine = 2*(n-1)
        # self.spine=2*n
        self.G.add_node((0,0,z),pos=(0.,0.,z))

      # for m in range(self.spine-1):
        for m in range(self.spine):

            self.G.add_node((m+1,0,z),pos=((m+1),0.,z))
            self.G.add_edge((m,0,z),(m+1,0,z),slope=(self.G.nodes[(m,0,z)]['pos'],self.G.nodes[(m+1,0,z)]['pos']))

    def construct_wing_stack(self,z,a,n):
        for m in range(n-1):
            #m-th floor
            floor_m_nodes=self.spine-(m+1)
      # for m in range(n):
      #     #m-th floor
      #     floor_m_nodes=self.spine-(m+2)
            self.G.add_node((0,a*(m+1),z),pos=((m+1)/2.,a*(np.sqrt(3.)/2.)*(m+1),z))
            self.G.add_edge((0,a*(m+1),z),(0,a*m,z),slope=(self.G.nodes[(0,a*(m+1),z)]['pos'],self.G.nodes[(0,a*m,z)]['pos']))
            self.G.add_edge((0,a*(m+1),z),(1,a*m,z),slope=(self.G.nodes[(0,a*(m+1),z)]['pos'],self.G.nodes[(1,a*m,z)]['pos']))

            for p in range(floor_m_nodes):
              #add 3-junctions
                self.G.add_node((p+1,a*(m+1),z),pos=(((p+1)+(m+1)/2.),a*(np.sqrt(3.)/2.)*(m+1),z))
                self.G.add_edge((p+1,a*(m+1),z),(p+1,a*m,z),slope=(self.G.nodes[(p+1,a*(m+1),z)]['pos'],self.G.nodes[(p+1,a*m,z)]['pos']))
                self.G.add_edge((p+1,a*(m+1),z),(p+2,a*m,z),slope=(self.G.nodes[(p+1,a*(m+1),z)]['pos'],self.G.nodes[(p+2,a*m,z)]['pos']))
                self.G.add_edge((p+1,a*(m+1),z),(p,a*(m+1),z),slope=(self.G.nodes[(p+1,a*(m+1),z)]['pos'],self.G.nodes[(p,a*(m+1),z)]['pos']))

    #construct full triangulated hex grids as skeleton of a stacked structure
    def triangulated_hexagon_stack(self,stack,n):


      self.stacks=stack
      for z in range(self.stacks):

          #construct spine for different levels of lobule
          self.construct_spine_stack(z,n)

          #construct lower/upper halfspace
          self.construct_wing_stack( z,-1, n)
          self.construct_wing_stack( z, 1, n)

      self.crosslink_stacks()

# 2D
class networkx_square(networkx_crystal,object):

    def __init__(self, tiling_factor):
        super(networkx_square,self).__init__()
        self.square_grid( tiling_factor)

    def square_grid(self, tiling_factor):

        a=range(0,tiling_factor+1)

        for x in a:
            for y in a:
                self.G.add_node((x,y),pos=(x,y,0))

        list_n=list(self.G.nodes())
        dict_d={}
        threshold=1.
        for idx_n,n in enumerate(list_n[:-1]):
            for m in list_n[idx_n+1:]:
                dict_d[(n,m)]=np.linalg.norm(np.array(self.G.nodes[n]['pos'])-np.array(self.G.nodes[m]['pos']))
        for nm in dict_d:
            if dict_d[nm] <= threshold:
                self.G.add_edge(*nm,slope=[self.G.nodes[nm[0]]['pos'],self.G.nodes[nm[1]]['pos']])

class networkx_trigonal_planar(networkx_crystal,object):

    def __init__(self, tiling_factor):
        super(networkx_trigonal_planar,self).__init__()
        self.triangulated_hexagon_lattice(tiling_factor)
    #I) construct and define one-layer hex
    # auxillary function, construct triangulated hex grid upper and lower wings
    def construct_wing(self,a,n):

      for m in range(n-1):
          #m-th floor
          floor_m_nodes = self.spine - (m+1)
          self.G.add_node((0,a*(m+1)),pos=np.array([(m+1)/2.,a*(np.sqrt(3.)/2.)*(m+1)]))
          self.G.add_edge((0,a*(m+1)),(0,a*m),slope=(self.G.nodes[(0,a*(m+1))]['pos'],self.G.nodes[(0,a*m)]['pos']))
          self.G.add_edge((0,a*(m+1)),(1,a*m),slope=(self.G.nodes[(0,a*(m+1))]['pos'],self.G.nodes[(1,a*m)]['pos']))

          for p in range(floor_m_nodes):
              #add 3-junctions
              self.G.add_node((p+1,a*(m+1)),pos=np.array([((p+1)+(m+1)/2.),a*(np.sqrt(3.)/2.)*(m+1)]))
              self.G.add_edge((p+1,a*(m+1)),(p+1,a*m),slope=(self.G.nodes[(p+1,a*(m+1))]['pos'],self.G.nodes[(p+1,a*m)]['pos']))
              self.G.add_edge((p+1,a*(m+1)),(p+2,a*m),slope=(self.G.nodes[(p+1,a*(m+1))]['pos'],self.G.nodes[(p+2,a*m)]['pos']))
              self.G.add_edge((p+1,a*(m+1)),(p,a*(m+1)),slope=(self.G.nodes[(p+1,a*(m+1))]['pos'],self.G.nodes[(p,a*(m+1))]['pos']))

    #construct full triangulated hex grid as skeleton
    def triangulated_hexagon_lattice(self,n):

      #construct spine
      self.spine = 2*(n-1)
      self.G.add_node((0,0),pos=np.array([0.,0.]), label=self.count_n())

      for m in range(self.spine):

          self.G.add_node((m+1,0),pos=np.array([(m+1)*self.l,0.]),label=self.count_n())
          self.G.add_edge((m,0),(m+1,0),slope=(self.G.nodes[(m,0)]['pos'],self.G.nodes[(m+1,0)]['pos']))

      #construct lower/upper halfspace
      self.construct_wing(-1,n)
      self.construct_wing( 1,n)

class networkx_hexagonal(networkx_crystal,object):

        def __init__(self,tiling_factor,periodic=False):
            super(networkx_hexagonal,self).__init__()
            self.hexagonal_grid(tiling_factor,periodic)
        def hexagonal_grid(self, *args):

            tiling_factor,periodic_bool=args

            m=2*tiling_factor+1
            n=2*tiling_factor
            self.G=nx.hexagonal_lattice_graph(m, n, periodic=periodic_bool, with_positions=True)
            for n in self.G.nodes():
                self.G.nodes[n]['pos']=np.array(self.G.nodes[n]['pos'])
            for e in self.G.edges():
                self.G.edges[e]['slope']=[self.G.nodes[e[0]]['pos'],self.G.nodes[e[1]]['pos']]