|
| 1 | +""" |
| 2 | +Format Mathics objects |
| 3 | +""" |
| 4 | + |
| 5 | +import random |
| 6 | +import networkx as nx |
| 7 | + |
| 8 | + |
| 9 | +def format_output(obj, expr, format=None): |
| 10 | + if format is None: |
| 11 | + format = obj.format |
| 12 | + |
| 13 | + if isinstance(format, dict): |
| 14 | + return dict((k, obj.format_output(expr, f)) for k, f in format.items()) |
| 15 | + |
| 16 | + from mathics.core.expression import Expression, BoxError |
| 17 | + |
| 18 | + expr_type = expr.get_head_name() |
| 19 | + if expr_type == "System`MathMLForm": |
| 20 | + format = "xml" |
| 21 | + leaves = expr.get_leaves() |
| 22 | + if len(leaves) == 1: |
| 23 | + expr = leaves[0] |
| 24 | + elif expr_type == "System`TeXForm": |
| 25 | + format = "tex" |
| 26 | + leaves = expr.get_leaves() |
| 27 | + if len(leaves) == 1: |
| 28 | + expr = leaves[0] |
| 29 | + elif expr_type == "System`Graphics": |
| 30 | + result = Expression("StandardForm", expr).format(obj, "System`MathMLForm") |
| 31 | + ml_str = result.leaves[0].leaves[0] |
| 32 | + # FIXME: not quite right. Need to parse out strings |
| 33 | + display_svg(str(ml_str)) |
| 34 | + |
| 35 | + if format == "text": |
| 36 | + result = expr.format(obj, "System`OutputForm") |
| 37 | + elif format == "xml": |
| 38 | + result = Expression("StandardForm", expr).format(obj, "System`MathMLForm") |
| 39 | + elif format == "tex": |
| 40 | + result = Expression("StandardForm", expr).format(obj, "System`TeXForm") |
| 41 | + elif format == "unformatted": |
| 42 | + if str(expr) == "-Graph-": |
| 43 | + return format_graph(expr.G) |
| 44 | + else: |
| 45 | + result = expr.format(obj, "System`OutputForm") |
| 46 | + else: |
| 47 | + raise ValueError |
| 48 | + |
| 49 | + try: |
| 50 | + boxes = result.boxes_to_text(evaluation=obj) |
| 51 | + except BoxError: |
| 52 | + boxes = None |
| 53 | + if not hasattr(obj, "seen_box_error"): |
| 54 | + obj.seen_box_error = True |
| 55 | + obj.message( |
| 56 | + "General", "notboxes", Expression("FullForm", result).evaluate(obj) |
| 57 | + ) |
| 58 | + return boxes |
| 59 | + |
| 60 | + |
| 61 | +def hierarchy_pos( |
| 62 | + G, root=None, width=1.0, vert_gap=0.2, vert_loc=0, leaf_vs_root_factor=0.5 |
| 63 | +): |
| 64 | + |
| 65 | + """From EoN (Epidemics on Networks): a fast, flexible Python package |
| 66 | + for simulation, analytic approximation, and analysis of epidemics |
| 67 | + on networks |
| 68 | + https://joss.theoj.org/papers/10.21105/joss.01731 |
| 69 | +
|
| 70 | + If the graph is a tree this will return the positions to plot this in a |
| 71 | + hierarchical layout. |
| 72 | +
|
| 73 | + Based on Joel's answer at https://stackoverflow.com/a/29597209/2966723, |
| 74 | + but with some modifications. |
| 75 | +
|
| 76 | + We include this because it may be useful for plotting transmission trees, |
| 77 | + and there is currently no networkx equivalent (though it may be coming soon). |
| 78 | +
|
| 79 | + There are two basic approaches we think of to allocate the horizontal |
| 80 | + location of a node. |
| 81 | +
|
| 82 | + - Top down: we allocate horizontal space to a node. Then its ``k`` |
| 83 | + descendants split up that horizontal space equally. This tends to result |
| 84 | + in overlapping nodes when some have many descendants. |
| 85 | + - Bottom up: we allocate horizontal space to each leaf node. A node at a |
| 86 | + higher level gets the entire space allocated to its descendant leaves. |
| 87 | + Based on this, leaf nodes at higher levels get the same space as leaf |
| 88 | + nodes very deep in the tree. |
| 89 | +
|
| 90 | + We use use both of these approaches simultaneously with ``leaf_vs_root_factor`` |
| 91 | + determining how much of the horizontal space is based on the bottom up |
| 92 | + or top down approaches. ``0`` gives pure bottom up, while 1 gives pure top |
| 93 | + down. |
| 94 | +
|
| 95 | +
|
| 96 | + :Arguments: |
| 97 | +
|
| 98 | + **G** the graph (must be a tree) |
| 99 | +
|
| 100 | + **root** the root node of the tree |
| 101 | + - if the tree is directed and this is not given, the root will be found and used |
| 102 | + - if the tree is directed and this is given, then the positions will be |
| 103 | + just for the descendants of this node. |
| 104 | + - if the tree is undirected and not given, then a random choice will be used. |
| 105 | +
|
| 106 | + **width** horizontal space allocated for this branch - avoids overlap with other branches |
| 107 | +
|
| 108 | + **vert_gap** gap between levels of hierarchy |
| 109 | +
|
| 110 | + **vert_loc** vertical location of root |
| 111 | +
|
| 112 | + **leaf_vs_root_factor** |
| 113 | +
|
| 114 | + xcenter: horizontal location of root |
| 115 | +
|
| 116 | + """ |
| 117 | + if not nx.is_tree(G): |
| 118 | + raise TypeError("cannot use hierarchy_pos on a graph that is not a tree") |
| 119 | + |
| 120 | + if root is None: |
| 121 | + if isinstance(G, nx.DiGraph): |
| 122 | + root = next( |
| 123 | + iter(nx.topological_sort(G)) |
| 124 | + ) # allows back compatibility with nx version 1.11 |
| 125 | + else: |
| 126 | + root = random.choice(list(G.nodes)) |
| 127 | + |
| 128 | + def _hierarchy_pos( |
| 129 | + G, |
| 130 | + root, |
| 131 | + leftmost, |
| 132 | + width, |
| 133 | + leafdx=0.2, |
| 134 | + vert_gap=0.2, |
| 135 | + vert_loc=0, |
| 136 | + xcenter=0.5, |
| 137 | + rootpos=None, |
| 138 | + leafpos=None, |
| 139 | + parent=None, |
| 140 | + ): |
| 141 | + """ |
| 142 | + see hierarchy_pos docstring for most arguments |
| 143 | +
|
| 144 | + pos: a dict saying where all nodes go if they have been assigned |
| 145 | + parent: parent of this branch. - only affects it if non-directed |
| 146 | +
|
| 147 | + """ |
| 148 | + |
| 149 | + if rootpos is None: |
| 150 | + rootpos = {root: (xcenter, vert_loc)} |
| 151 | + else: |
| 152 | + rootpos[root] = (xcenter, vert_loc) |
| 153 | + if leafpos is None: |
| 154 | + leafpos = {} |
| 155 | + children = list(G.neighbors(root)) |
| 156 | + leaf_count = 0 |
| 157 | + if not isinstance(G, nx.DiGraph) and parent is not None: |
| 158 | + children.remove(parent) |
| 159 | + if len(children) != 0: |
| 160 | + rootdx = width / len(children) |
| 161 | + nextx = xcenter - width / 2 - rootdx / 2 |
| 162 | + for child in children: |
| 163 | + nextx += rootdx |
| 164 | + rootpos, leafpos, newleaves = _hierarchy_pos( |
| 165 | + G, |
| 166 | + child, |
| 167 | + leftmost + leaf_count * leafdx, |
| 168 | + width=rootdx, |
| 169 | + leafdx=leafdx, |
| 170 | + vert_gap=vert_gap, |
| 171 | + vert_loc=vert_loc - vert_gap, |
| 172 | + xcenter=nextx, |
| 173 | + rootpos=rootpos, |
| 174 | + leafpos=leafpos, |
| 175 | + parent=root, |
| 176 | + ) |
| 177 | + leaf_count += newleaves |
| 178 | + |
| 179 | + leftmostchild = min((x for x, y in [leafpos[child] for child in children])) |
| 180 | + rightmostchild = max((x for x, y in [leafpos[child] for child in children])) |
| 181 | + leafpos[root] = ((leftmostchild + rightmostchild) / 2, vert_loc) |
| 182 | + else: |
| 183 | + leaf_count = 1 |
| 184 | + leafpos[root] = (leftmost, vert_loc) |
| 185 | + # pos[root] = (leftmost + (leaf_count-1)*dx/2., vert_loc) |
| 186 | + # print(leaf_count) |
| 187 | + return rootpos, leafpos, leaf_count |
| 188 | + |
| 189 | + xcenter = width / 2.0 |
| 190 | + if isinstance(G, nx.DiGraph): |
| 191 | + leafcount = len( |
| 192 | + [node for node in nx.descendants(G, root) if G.out_degree(node) == 0] |
| 193 | + ) |
| 194 | + elif isinstance(G, nx.Graph): |
| 195 | + leafcount = len( |
| 196 | + [ |
| 197 | + node |
| 198 | + for node in nx.node_connected_component(G, root) |
| 199 | + if G.degree(node) == 1 and node != root |
| 200 | + ] |
| 201 | + ) |
| 202 | + rootpos, leafpos, leaf_count = _hierarchy_pos( |
| 203 | + G, |
| 204 | + root, |
| 205 | + 0, |
| 206 | + width, |
| 207 | + leafdx=width * 1.0 / leafcount, |
| 208 | + vert_gap=vert_gap, |
| 209 | + vert_loc=vert_loc, |
| 210 | + xcenter=xcenter, |
| 211 | + ) |
| 212 | + pos = {} |
| 213 | + for node in rootpos: |
| 214 | + pos[node] = ( |
| 215 | + leaf_vs_root_factor * leafpos[node][0] |
| 216 | + + (1 - leaf_vs_root_factor) * rootpos[node][0], |
| 217 | + leafpos[node][1], |
| 218 | + ) |
| 219 | + # pos = {node:(leaf_vs_root_factor*x1+(1-leaf_vs_root_factor)*x2, y1) for ((x1,y1), (x2,y2)) in (leafpos[node], rootpos[node]) for node in rootpos} |
| 220 | + xmax = max(x for x, y in pos.values()) |
| 221 | + y_list = {} |
| 222 | + for node in pos: |
| 223 | + x, y = pos[node] = (pos[node][0] * width / xmax, pos[node][1]) |
| 224 | + y_list[y] = y_list.get(y, set([])) |
| 225 | + y_list[y].add(x) |
| 226 | + |
| 227 | + min_sep = xmax |
| 228 | + for y in y_list.keys(): |
| 229 | + x_list = sorted(y_list[y]) |
| 230 | + n = len(x_list) - 1 |
| 231 | + if n <= 0: |
| 232 | + continue |
| 233 | + min_sep = min([x_list[i + 1] - x_list[i] for i in range(n)] + [min_sep]) |
| 234 | + return pos, min_sep |
| 235 | + |
| 236 | + |
| 237 | +node_size = 300 # this is networkx's default size |
| 238 | + |
| 239 | + |
| 240 | +def tree_layout(G): |
| 241 | + global node_size |
| 242 | + root = G.root if hasattr(G, "root") else None |
| 243 | + pos, min_sep = hierarchy_pos(G, root=root) |
| 244 | + node_size = min_sep * 2000 |
| 245 | + return pos |
| 246 | + |
| 247 | + |
| 248 | +NETWORKX_LAYOUTS = { |
| 249 | + "circular": nx.circular_layout, |
| 250 | + "multipartite": nx.multipartite_layout, |
| 251 | + "planar": nx.planar_layout, |
| 252 | + "random": nx.random_layout, |
| 253 | + "shell": nx.shell_layout, |
| 254 | + "spectral": nx.spectral_layout, |
| 255 | + "spring": nx.spring_layout, |
| 256 | + "tree": tree_layout, |
| 257 | +} |
| 258 | + |
| 259 | + |
| 260 | +def format_graph(G): |
| 261 | + """ |
| 262 | + Format a Graph |
| 263 | + """ |
| 264 | + # FIXME handle graphviz as well |
| 265 | + import matplotlib.pyplot as plt |
| 266 | + |
| 267 | + global node_size |
| 268 | + node_size = 300 # This is networkx's default |
| 269 | + |
| 270 | + graph_layout = G.graph_layout if hasattr(G, "graph_layout") else None |
| 271 | + vertex_labeling = G.vertex_labeling if hasattr(G, "vertex_labeling") else False |
| 272 | + if vertex_labeling: |
| 273 | + vertex_labeling = vertex_labeling.to_python() or False |
| 274 | + |
| 275 | + if hasattr(G, "title") and G.title.get_string_value(): |
| 276 | + fig, ax = plt.subplots() # Create a figure and an axes |
| 277 | + ax.set_title(G.title.get_string_value()) |
| 278 | + |
| 279 | + if graph_layout: |
| 280 | + if not isinstance(graph_layout, str): |
| 281 | + graph_layout = graph_layout.get_string_value() |
| 282 | + layout_fn = NETWORKX_LAYOUTS.get(graph_layout, None) |
| 283 | + else: |
| 284 | + layout_fn = None |
| 285 | + |
| 286 | + if layout_fn: |
| 287 | + nx.draw(G, pos=layout_fn(G), with_labels=vertex_labeling, node_size=node_size) |
| 288 | + else: |
| 289 | + nx.draw_shell(G, with_labels=vertex_labeling, node_size=node_size) |
| 290 | + plt.show() |
| 291 | + return None |
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