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annotate planemo/lib/python3.7/site-packages/networkx/generators/lattice.py @ 1:56ad4e20f292 draft

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"planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
author guerler
date Fri, 31 Jul 2020 00:32:28 -0400
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1 # -*- coding: utf-8 -*-
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2 # Copyright (C) 2004-2019 by
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3 # Aric Hagberg <hagberg@lanl.gov>
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4 # Dan Schult <dschult@colgate.edu>
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5 # Pieter Swart <swart@lanl.gov>
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6 # All rights reserved.
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7 # BSD license.
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8 #
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9 # Authors: Aric Hagberg (hagberg@lanl.gov)
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10 # Pieter Swart (swart@lanl.gov)
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11 # Joel Miller (jmiller@lanl.gov)
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12 # Dan Schult (dschult@lanl.gov)
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13 """Functions for generating grid graphs and lattices
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14
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15 The :func:`grid_2d_graph`, :func:`triangular_lattice_graph`, and
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16 :func:`hexagonal_lattice_graph` functions correspond to the three
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17 `regular tilings of the plane`_, the square, triangular, and hexagonal
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18 tilings, respectively. :func:`grid_graph` and :func:`hypercube_graph`
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19 are similar for arbitrary dimensions. Useful relevant discussion can
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20 be found about `Triangular Tiling`_, and `Square, Hex and Triangle Grids`_
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21
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22 .. _regular tilings of the plane: https://en.wikipedia.org/wiki/List_of_regular_polytopes_and_compounds#Euclidean_tilings
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23 .. _Square, Hex and Triangle Grids: http://www-cs-students.stanford.edu/~amitp/game-programming/grids/
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24 .. _Triangular Tiling: https://en.wikipedia.org/wiki/Triangular_tiling
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25
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26 """
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27
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28 from math import sqrt
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29
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30 from networkx.classes import Graph
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31 from networkx.classes import set_node_attributes
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32 from networkx.algorithms.minors import contracted_nodes
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33 from networkx.algorithms.operators.product import cartesian_product
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34 from networkx.exception import NetworkXError
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35 from networkx.relabel import relabel_nodes
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36 from networkx.utils import flatten
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37 from networkx.utils import nodes_or_number
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38 from networkx.utils import pairwise
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39 from networkx.generators.classic import cycle_graph
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40 from networkx.generators.classic import empty_graph
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41 from networkx.generators.classic import path_graph
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42
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43 __all__ = ['grid_2d_graph', 'grid_graph', 'hypercube_graph',
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44 'triangular_lattice_graph', 'hexagonal_lattice_graph']
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45
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46
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47 @nodes_or_number([0, 1])
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48 def grid_2d_graph(m, n, periodic=False, create_using=None):
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49 """Returns the two-dimensional grid graph.
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50
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51 The grid graph has each node connected to its four nearest neighbors.
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52
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53 Parameters
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54 ----------
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55 m, n : int or iterable container of nodes
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56 If an integer, nodes are from `range(n)`.
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57 If a container, elements become the coordinate of the nodes.
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58
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59 periodic : bool (default: False)
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60 If this is ``True`` the nodes on the grid boundaries are joined
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61 to the corresponding nodes on the opposite grid boundaries.
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62
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63 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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64 Graph type to create. If graph instance, then cleared before populated.
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65
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66 Returns
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67 -------
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68 NetworkX graph
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69 The (possibly periodic) grid graph of the specified dimensions.
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70
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71 """
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72 G = empty_graph(0, create_using)
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73 row_name, rows = m
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74 col_name, cols = n
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75 G.add_nodes_from((i, j) for i in rows for j in cols)
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76 G.add_edges_from(((i, j), (pi, j))
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77 for pi, i in pairwise(rows) for j in cols)
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78 G.add_edges_from(((i, j), (i, pj))
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79 for i in rows for pj, j in pairwise(cols))
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80 if periodic is True:
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81 if len(rows) > 2:
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82 first = rows[0]
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83 last = rows[-1]
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84 G.add_edges_from(((first, j), (last, j)) for j in cols)
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85 if len(cols) > 2:
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86 first = cols[0]
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87 last = cols[-1]
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88 G.add_edges_from(((i, first), (i, last)) for i in rows)
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89 # both directions for directed
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90 if G.is_directed():
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91 G.add_edges_from((v, u) for u, v in G.edges())
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92 return G
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93
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94
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95 def grid_graph(dim, periodic=False):
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96 """Returns the *n*-dimensional grid graph.
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97
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98 The dimension *n* is the length of the list `dim` and the size in
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99 each dimension is the value of the corresponding list element.
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100
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101 Parameters
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102 ----------
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103 dim : list or tuple of numbers or iterables of nodes
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104 'dim' is a tuple or list with, for each dimension, either a number
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105 that is the size of that dimension or an iterable of nodes for
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106 that dimension. The dimension of the grid_graph is the length
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107 of `dim`.
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108
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109 periodic : bool
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110 If `periodic is True` the nodes on the grid boundaries are joined
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111 to the corresponding nodes on the opposite grid boundaries.
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112
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113 Returns
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114 -------
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115 NetworkX graph
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116 The (possibly periodic) grid graph of the specified dimensions.
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117
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118 Examples
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119 --------
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120 To produce a 2 by 3 by 4 grid graph, a graph on 24 nodes:
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121
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122 >>> from networkx import grid_graph
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123 >>> G = grid_graph(dim=[2, 3, 4])
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124 >>> len(G)
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125 24
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126 >>> G = grid_graph(dim=[range(7, 9), range(3, 6)])
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127 >>> len(G)
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128 6
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129 """
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130 dlabel = "%s" % dim
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131 if not dim:
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132 return empty_graph(0)
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133
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134 func = cycle_graph if periodic else path_graph
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135 G = func(dim[0])
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136 for current_dim in dim[1:]:
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137 Gnew = func(current_dim)
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138 G = cartesian_product(Gnew, G)
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139 # graph G is done but has labels of the form (1, (2, (3, 1))) so relabel
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140 H = relabel_nodes(G, flatten)
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141 return H
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142
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143
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144 def hypercube_graph(n):
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145 """Returns the *n*-dimensional hypercube graph.
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146
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147 The nodes are the integers between 0 and ``2 ** n - 1``, inclusive.
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148
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149 For more information on the hypercube graph, see the Wikipedia
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150 article `Hypercube graph`_.
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151
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152 .. _Hypercube graph: https://en.wikipedia.org/wiki/Hypercube_graph
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153
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154 Parameters
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155 ----------
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156 n : int
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157 The dimension of the hypercube.
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158 The number of nodes in the graph will be ``2 ** n``.
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159
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160 Returns
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161 -------
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162 NetworkX graph
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163 The hypercube graph of dimension *n*.
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164 """
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165 dim = n * [2]
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166 G = grid_graph(dim)
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167 return G
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168
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169
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170 def triangular_lattice_graph(m, n, periodic=False, with_positions=True,
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171 create_using=None):
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172 r"""Returns the $m$ by $n$ triangular lattice graph.
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173
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174 The `triangular lattice graph`_ is a two-dimensional `grid graph`_ in
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175 which each square unit has a diagonal edge (each grid unit has a chord).
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176
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177 The returned graph has $m$ rows and $n$ columns of triangles. Rows and
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178 columns include both triangles pointing up and down. Rows form a strip
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179 of constant height. Columns form a series of diamond shapes, staggered
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180 with the columns on either side. Another way to state the size is that
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181 the nodes form a grid of `m+1` rows and `(n + 1) // 2` columns.
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182 The odd row nodes are shifted horizontally relative to the even rows.
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183
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184 Directed graph types have edges pointed up or right.
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185
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186 Positions of nodes are computed by default or `with_positions is True`.
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187 The position of each node (embedded in a euclidean plane) is stored in
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188 the graph using equilateral triangles with sidelength 1.
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189 The height between rows of nodes is thus $\sqrt(3)/2$.
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190 Nodes lie in the first quadrant with the node $(0, 0)$ at the origin.
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191
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192 .. _triangular lattice graph: http://mathworld.wolfram.com/TriangularGrid.html
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193 .. _grid graph: http://www-cs-students.stanford.edu/~amitp/game-programming/grids/
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194 .. _Triangular Tiling: https://en.wikipedia.org/wiki/Triangular_tiling
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195
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196 Parameters
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197 ----------
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198 m : int
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199 The number of rows in the lattice.
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200
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201 n : int
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202 The number of columns in the lattice.
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203
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204 periodic : bool (default: False)
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205 If True, join the boundary vertices of the grid using periodic
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206 boundary conditions. The join between boundaries is the final row
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207 and column of triangles. This means there is one row and one column
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208 fewer nodes for the periodic lattice. Periodic lattices require
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209 `m >= 3`, `n >= 5` and are allowed but misaligned if `m` or `n` are odd
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210
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211 with_positions : bool (default: True)
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212 Store the coordinates of each node in the graph node attribute 'pos'.
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213 The coordinates provide a lattice with equilateral triangles.
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214 Periodic positions shift the nodes vertically in a nonlinear way so
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215 the edges don't overlap so much.
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216
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217 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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218 Graph type to create. If graph instance, then cleared before populated.
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219
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220 Returns
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221 -------
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222 NetworkX graph
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223 The *m* by *n* triangular lattice graph.
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224 """
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225 H = empty_graph(0, create_using)
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226 if n == 0 or m == 0:
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227 return H
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228 if periodic:
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229 if n < 5 or m < 3:
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230 msg = "m > 2 and n > 4 required for periodic. m={}, n={}"
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231 raise NetworkXError(msg.format(m, n))
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232
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233 N = (n + 1) // 2 # number of nodes in row
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234 rows = range(m + 1)
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235 cols = range(N + 1)
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236 # Make grid
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237 H.add_edges_from(((i, j), (i + 1, j)) for j in rows for i in cols[:N])
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238 H.add_edges_from(((i, j), (i, j + 1)) for j in rows[:m] for i in cols)
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239 # add diagonals
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240 H.add_edges_from(((i, j), (i + 1, j + 1))
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241 for j in rows[1:m:2] for i in cols[:N])
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242 H.add_edges_from(((i + 1, j), (i, j + 1))
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243 for j in rows[:m:2] for i in cols[:N])
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244 # identify boundary nodes if periodic
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245 if periodic is True:
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246 for i in cols:
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247 H = contracted_nodes(H, (i, 0), (i, m))
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248 for j in rows[:m]:
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249 H = contracted_nodes(H, (0, j), (N, j))
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250 elif n % 2:
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251 # remove extra nodes
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252 H.remove_nodes_from(((N, j) for j in rows[1::2]))
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253
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254 # Add position node attributes
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255 if with_positions:
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256 ii = (i for i in cols for j in rows)
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257 jj = (j for i in cols for j in rows)
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258 xx = (0.5 * (j % 2) + i for i in cols for j in rows)
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259 h = sqrt(3) / 2
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260 if periodic:
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261 yy = (h * j + .01 * i * i for i in cols for j in rows)
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262 else:
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263 yy = (h * j for i in cols for j in rows)
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264 pos = {(i, j): (x, y) for i, j, x, y in zip(ii, jj, xx, yy)
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265 if (i, j) in H}
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266 set_node_attributes(H, pos, 'pos')
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267 return H
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268
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269
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270 def hexagonal_lattice_graph(m, n, periodic=False, with_positions=True,
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271 create_using=None):
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272 """Returns an `m` by `n` hexagonal lattice graph.
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273
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274 The *hexagonal lattice graph* is a graph whose nodes and edges are
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275 the `hexagonal tiling`_ of the plane.
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276
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277 The returned graph will have `m` rows and `n` columns of hexagons.
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278 `Odd numbered columns`_ are shifted up relative to even numbered columns.
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279
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280 Positions of nodes are computed by default or `with_positions is True`.
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281 Node positions creating the standard embedding in the plane
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282 with sidelength 1 and are stored in the node attribute 'pos'.
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283 `pos = nx.get_node_attributes(G, 'pos')` creates a dict ready for drawing.
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284
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285 .. _hexagonal tiling: https://en.wikipedia.org/wiki/Hexagonal_tiling
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286 .. _Odd numbered columns: http://www-cs-students.stanford.edu/~amitp/game-programming/grids/
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287
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288 Parameters
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289 ----------
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290 m : int
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291 The number of rows of hexagons in the lattice.
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292
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293 n : int
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294 The number of columns of hexagons in the lattice.
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295
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296 periodic : bool
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297 Whether to make a periodic grid by joining the boundary vertices.
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298 For this to work `n` must be odd and both `n > 1` and `m > 1`.
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299 The periodic connections create another row and column of hexagons
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300 so these graphs have fewer nodes as boundary nodes are identified.
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301
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302 with_positions : bool (default: True)
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303 Store the coordinates of each node in the graph node attribute 'pos'.
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304 The coordinates provide a lattice with vertical columns of hexagons
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305 offset to interleave and cover the plane.
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306 Periodic positions shift the nodes vertically in a nonlinear way so
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307 the edges don't overlap so much.
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308
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309 create_using : NetworkX graph constructor, optional (default=nx.Graph)
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310 Graph type to create. If graph instance, then cleared before populated.
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311 If graph is directed, edges will point up or right.
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312
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313 Returns
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314 -------
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315 NetworkX graph
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316 The *m* by *n* hexagonal lattice graph.
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317 """
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318 G = empty_graph(0, create_using)
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319 if m == 0 or n == 0:
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320 return G
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321 if periodic and (n % 2 == 1 or m < 2 or n < 2):
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322 msg = "periodic hexagonal lattice needs m > 1, n > 1 and even n"
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323 raise NetworkXError(msg)
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324
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325 M = 2 * m # twice as many nodes as hexagons vertically
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326 rows = range(M + 2)
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327 cols = range(n + 1)
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328 # make lattice
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329 col_edges = (((i, j), (i, j + 1)) for i in cols for j in rows[:M + 1])
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330 row_edges = (((i, j), (i + 1, j)) for i in cols[:n] for j in rows
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331 if i % 2 == j % 2)
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332 G.add_edges_from(col_edges)
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333 G.add_edges_from(row_edges)
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334 # Remove corner nodes with one edge
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335 G.remove_node((0, M + 1))
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336 G.remove_node((n, (M + 1) * (n % 2)))
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337
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338 # identify boundary nodes if periodic
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339 if periodic:
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340 for i in cols[:n]:
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341 G = contracted_nodes(G, (i, 0), (i, M))
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342 for i in cols[1:]:
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343 G = contracted_nodes(G, (i, 1), (i, M + 1))
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344 for j in rows[1:M]:
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345 G = contracted_nodes(G, (0, j), (n, j))
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346 G.remove_node((n, M))
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347
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348 # calc position in embedded space
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349 ii = (i for i in cols for j in rows)
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350 jj = (j for i in cols for j in rows)
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351 xx = (0.5 + i + i // 2 + (j % 2) * ((i % 2) - .5)
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352 for i in cols for j in rows)
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353 h = sqrt(3) / 2
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354 if periodic:
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355 yy = (h * j + .01 * i * i for i in cols for j in rows)
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356 else:
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357 yy = (h * j for i in cols for j in rows)
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358 # exclude nodes not in G
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359 pos = {(i, j): (x, y) for i, j, x, y in zip(ii, jj, xx, yy) if (i, j) in G}
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360 set_node_attributes(G, pos, 'pos')
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361 return G