def plot(self, disks=False, **kwds):
gr = plot.point2d(self.dop._singularities(CC),
marker='*', color='red', **kwds)
gr += plot.line([z.iv().mid() for z in self.vert])
gr.set_aspect_ratio(1)
if disks:
for step in self:
z = step.start.iv().mid()
gr += plot.circle((z.real(), z.imag()),
step.start.dist_to_sing().lower(),
linestyle='dotted', color='red')
gr += plot.circle((z.real(), z.imag()),
step.length().lower(),
linestyle='dashed')
return gr
def plot(self, disks=False):
gr = plot.point2d(dop_singularities(self.dop, CC),
marker='*',
size=200,
color='red')
for step in self:
gr += step.plot()
gr.set_aspect_ratio(1)
if disks:
for step in self:
z = step.start.iv().mid()
gr += plot.circle((z.real(), z.imag()),
step.start.dist_to_sing().lower(),
linestyle='dotted',
color='red')
gr += plot.circle((z.real(), z.imag()),
step.length().lower(),
linestyle='dashed')
return gr
def circle_plot(self):
pts = []
pi = RR.pi()
for angle in self.angles:
angle = RR(angle) * pi
c = angle.cos()
s = angle.sin()
if abs(s) < 0.00000001:
pts.append((c, s))
else:
pts.extend([(c, s), (c, -s)])
P = points(pts, size=100) + circle((0, 0), 1, color='black')
P.axes(False)
P.set_aspect_ratio(1)
return encode_plot(P)
def circle_plot(self):
pts = []
pi = RR.pi()
for angle in self.angles:
angle = RR(angle)*pi
c = angle.cos()
s = angle.sin()
if abs(s) < 0.00000001:
pts.append((c,s))
else:
pts.extend([(c,s),(c,-s)])
P = points(pts,size=100) + circle((0,0),1,color='black')
P.axes(False)
P.set_aspect_ratio(1)
return encode_plot(P)
def circle_plot(self):
pts = []
pi = RR.pi()
for angle in self.angles:
angle = RR(angle) * pi
c = angle.cos()
s = angle.sin()
if abs(s) < 0.00000001:
pts.append((c, s))
else:
pts.extend([(c, s), (c, -s)])
P = circle((0, 0), 1, color="black", thickness=2.5)
P[0].set_zorder(-1)
P += points(pts, size=300, rgbcolor="darkblue")
P.axes(False)
P.set_aspect_ratio(1)
return encode_plot(P, pad=0, pad_inches=None, transparent=True, axes_pad=0.04)
def set_edges(self, **edge_options):
"""
Sets the edge (or arrow) plotting parameters for the GraphPlot object. This
function is called by the constructor but can also be called to make updates to
the vertex options of an existing GraphPlot object. Note that the changes are
cumulative.
EXAMPLES::
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: GP = g.graphplot(vertex_size=100, edge_labels=True, color_by_label=True, edge_style='dashed')
sage: GP.set_edges(edge_style='solid')
sage: GP.plot()
sage: GP.set_edges(edge_color='black')
sage: GP.plot()
sage: d = DiGraph({}, loops=True, multiedges=True, sparse=True)
sage: d.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: GP = d.graphplot(vertex_size=100, edge_labels=True, color_by_label=True, edge_style='dashed')
sage: GP.set_edges(edge_style='solid')
sage: GP.plot()
sage: GP.set_edges(edge_color='black')
sage: GP.plot()
TESTS::
sage: G = Graph("Fooba")
sage: G.show(edge_colors={'red':[(3,6),(2,5)]})
Verify that default edge labels are pretty close to being between the vertices
in some cases where they weren't due to truncating division (trac #10124)::
sage: test_graphs = graphs.FruchtGraph(), graphs.BullGraph()
sage: tol = 0.001
sage: for G in test_graphs:
... E=G.edges()
... for e0, e1, elab in E:
... G.set_edge_label(e0, e1, '%d %d' % (e0, e1))
... gp = G.graphplot(save_pos=True,edge_labels=True)
... vx = gp._plot_components['vertices'][0].xdata
... vy = gp._plot_components['vertices'][0].ydata
... for elab in gp._plot_components['edge_labels']:
... textobj = elab[0]
... x, y, s = textobj.x, textobj.y, textobj.string
... v0, v1 = map(int, s.split())
... vn = vector(((x-(vx[v0]+vx[v1])/2.),y-(vy[v0]+vy[v1])/2.)).norm()
... assert vn < tol
"""
for arg in edge_options:
self._options[arg] = edge_options[arg]
if 'edge_colors' in edge_options: self._options['color_by_label'] = False
# Handle base edge options: thickness, linestyle
eoptions={}
if 'edge_style' in self._options:
eoptions['linestyle'] = self._options['edge_style']
if 'thickness' in self._options:
eoptions['thickness'] = self._options['thickness']
# Set labels param to add labels on the fly
labels = False
if self._options['edge_labels']:
labels = True
self._plot_components['edge_labels'] = []
# Make dict collection of all edges (keep label and edge color)
edges_to_draw = {}
if self._options['color_by_label'] or isinstance(self._options['edge_colors'], dict):
if self._options['color_by_label']: edge_colors = self._graph._color_by_label()
else: edge_colors = self._options['edge_colors']
for color in edge_colors:
for edge in edge_colors[color]:
key = tuple(sorted([edge[0],edge[1]]))
if key == (edge[0],edge[1]): head = 1
else: head = 0
if len(edge) < 3:
label = self._graph.edge_label(edge[0],edge[1])
if isinstance(label, list):
if key in edges_to_draw:
edges_to_draw[key].append((label[-1], color, head))
else:
edges_to_draw[key] = [(label[-1], color, head)]
for i in range(len(label)-1):
edges_to_draw[key].append((label[-1], color, head))
else:
label = edge[2]
if key in edges_to_draw:
edges_to_draw[key].append((label, color, head))
else:
edges_to_draw[key] = [(label, color, head)]
# add unspecified edges in (default color black)
for edge in self._graph.edge_iterator():
key = tuple(sorted([edge[0],edge[1]]))
label = edge[2]
specified = False
if key in edges_to_draw:
for old_label, old_color, old_head in edges_to_draw[key]:
if label == old_label:
specified = True
break
if not specified:
if key == (edge[0],edge[1]): head = 1
else: head = 0
edges_to_draw[key] = [(label, 'black', head)]
else:
for edge in self._graph.edges(sort=True):
key = tuple(sorted([edge[0],edge[1]]))
if key == (edge[0],edge[1]): head = 1
else: head = 0
if key in edges_to_draw:
edges_to_draw[key].append((edge[2], self._options['edge_color'], head))
else:
edges_to_draw[key] = [(edge[2], self._options['edge_color'], head)]
if edges_to_draw:
self._plot_components['edges'] = []
else:
return
# Check for multi-edges or loops
if self._arcs or self._loops:
tmp = edges_to_draw.copy()
dist = self._options['dist']*2.
loop_size = self._options['loop_size']
max_dist = self._options['max_dist']
from sage.functions.all import sqrt
for (a,b) in tmp:
if a == b:
# Loops
distance = dist
local_labels = edges_to_draw.pop((a,b))
if len(local_labels)*dist > max_dist:
distance = float(max_dist)/len(local_labels)
curr_loop_size = loop_size
for i in range(len(local_labels)):
self._plot_components['edges'].append(circle((self._pos[a][0],self._pos[a][1]-curr_loop_size), curr_loop_size, rgbcolor=local_labels[i][1], **eoptions))
if labels:
self._plot_components['edge_labels'].append(text(local_labels[i][0], (self._pos[a][0], self._pos[a][1]-2*curr_loop_size)))
curr_loop_size += distance/4
elif len(edges_to_draw[(a,b)]) > 1:
# Multi-edge
local_labels = edges_to_draw.pop((a,b))
# Compute perpendicular bisector
p1 = self._pos[a]
p2 = self._pos[b]
M = ((p1[0]+p2[0])/2., (p1[1]+p2[1])/2.) # midpoint
if not p1[1] == p2[1]:
S = float(p1[0]-p2[0])/(p2[1]-p1[1]) # perp slope
y = lambda x : S*x-S*M[0]+M[1] # perp bisector line
# f,g are functions of distance d to determine x values
# on line y at d from point M
f = lambda d : sqrt(d**2/(1.+S**2)) + M[0]
g = lambda d : -sqrt(d**2/(1.+S**2)) + M[0]
odd_x = f
even_x = g
if p1[0] == p2[0]:
odd_y = lambda d : M[1]
even_y = odd_y
else:
odd_y = lambda x : y(f(x))
even_y = lambda x : y(g(x))
else:
odd_x = lambda d : M[0]
even_x = odd_x
odd_y = lambda d : M[1] + d
even_y = lambda d : M[1] - d
# We now have the control points for each bezier curve
# in terms of distance parameter d.
# Also note that the label for each edge should be drawn at d/2.
# (This is because we're using the perp bisectors).
distance = dist
if len(local_labels)*dist > max_dist:
distance = float(max_dist)/len(local_labels)
for i in range(len(local_labels)/2):
k = (i+1.0)*distance
if self._arcdigraph:
odd_start = self._polar_hack_for_multidigraph(p1, [odd_x(k),odd_y(k)], self._vertex_radius)[0]
odd_end = self._polar_hack_for_multidigraph([odd_x(k),odd_y(k)], p2, self._vertex_radius)[1]
even_start = self._polar_hack_for_multidigraph(p1, [even_x(k),even_y(k)], self._vertex_radius)[0]
even_end = self._polar_hack_for_multidigraph([even_x(k),even_y(k)], p2, self._vertex_radius)[1]
self._plot_components['edges'].append(arrow(path=[[odd_start,[odd_x(k),odd_y(k)],odd_end]], head=local_labels[2*i][2], zorder=1, rgbcolor=local_labels[2*i][1], **eoptions))
self._plot_components['edges'].append(arrow(path=[[even_start,[even_x(k),even_y(k)],even_end]], head=local_labels[2*i+1][2], zorder=1, rgbcolor=local_labels[2*i+1][1], **eoptions))
else:
self._plot_components['edges'].append(bezier_path([[p1,[odd_x(k),odd_y(k)],p2]],zorder=1, rgbcolor=local_labels[2*i][1], **eoptions))
self._plot_components['edges'].append(bezier_path([[p1,[even_x(k),even_y(k)],p2]],zorder=1, rgbcolor=local_labels[2*i+1][1], **eoptions))
if labels:
j = k/2.0
self._plot_components['edge_labels'].append(text(local_labels[2*i][0],[odd_x(j),odd_y(j)]))
self._plot_components['edge_labels'].append(text(local_labels[2*i+1][0],[even_x(j),even_y(j)]))
if len(local_labels)%2 == 1:
edges_to_draw[(a,b)] = [local_labels[-1]] # draw line for last odd
dir = self._graph.is_directed()
for (a,b) in edges_to_draw:
if self._arcdigraph:
C,D = self._polar_hack_for_multidigraph(self._pos[a], self._pos[b], self._vertex_radius)
self._plot_components['edges'].append(arrow(C,D, rgbcolor=edges_to_draw[(a,b)][0][1], head=edges_to_draw[(a,b)][0][2], **eoptions))
if labels:
self._plot_components['edge_labels'].append(text(str(edges_to_draw[(a,b)][0][0]),[(C[0]+D[0])/2., (C[1]+D[1])/2.]))
elif dir:
self._plot_components['edges'].append(arrow(self._pos[a],self._pos[b], rgbcolor=edges_to_draw[(a,b)][0][1], arrowshorten=self._arrowshorten, head=edges_to_draw[(a,b)][0][2], **eoptions))
else:
self._plot_components['edges'].append(line([self._pos[a],self._pos[b]], rgbcolor=edges_to_draw[(a,b)][0][1], **eoptions))
if labels and not self._arcdigraph:
self._plot_components['edge_labels'].append(text(str(edges_to_draw[(a,b)][0][0]),[(self._pos[a][0]+self._pos[b][0])/2., (self._pos[a][1]+self._pos[b][1])/2.]))
def set_vertices(self, **vertex_options):
"""
Sets the vertex plotting parameters for this GraphPlot. This function
is called by the constructor but can also be called to make updates to
the vertex options of an existing GraphPlot object. Note that the
changes are cumulative.
EXAMPLES::
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: GP = g.graphplot(vertex_size=100, edge_labels=True, color_by_label=True, edge_style='dashed')
sage: GP.set_vertices(talk=True)
sage: GP.plot()
sage: GP.set_vertices(vertex_colors='pink', vertex_shape='^')
sage: GP.plot()
"""
# Handle base vertex options
voptions = {}
for arg in vertex_options:
self._options[arg] = vertex_options[arg]
# First set defaults for styles
vertex_colors = None
if self._options['talk']:
voptions['markersize'] = 500
if self._options['partition'] is None:
vertex_colors = '#ffffff'
else:
voptions['markersize'] = self._options['vertex_size']
if 'vertex_colors' not in self._options or self._options['vertex_colors'] is None:
if self._options['partition'] is not None:
from sage.plot.colors import rainbow,rgbcolor
partition = self._options['partition']
l = len(partition)
R = rainbow(l)
vertex_colors = {}
for i in range(l):
vertex_colors[R[i]] = partition[i]
elif len(self._graph._boundary) != 0:
vertex_colors = {}
bdy_verts = []
int_verts = []
for v in self._graph.vertex_iterator():
if v in self._graph._boundary:
bdy_verts.append(v)
else:
int_verts.append(v)
vertex_colors['#fec7b8'] = int_verts
vertex_colors['#b3e8ff'] = bdy_verts
elif not vertex_colors:
vertex_colors='#fec7b8'
else:
vertex_colors = self._options['vertex_colors']
if 'vertex_shape' in self._options:
voptions['marker'] = self._options['vertex_shape']
if self._graph.is_directed():
self._vertex_radius = sqrt(voptions['markersize']/pi)
self._arrowshorten = 2*self._vertex_radius
if self._arcdigraph:
self._vertex_radius = sqrt(voptions['markersize']/(20500*pi))
voptions['zorder'] = 7
if not isinstance(vertex_colors, dict):
voptions['facecolor'] = vertex_colors
if self._arcdigraph:
self._plot_components['vertices'] = [circle(center,
self._vertex_radius, fill=True, facecolor=vertex_colors, clip=False)
for center in self._pos.values()]
else:
self._plot_components['vertices'] = scatter_plot(
self._pos.values(), clip=False, **voptions)
else:
# Color list must be ordered:
pos = []
colors = []
for i in vertex_colors:
pos += [self._pos[j] for j in vertex_colors[i]]
colors += [i]*len(vertex_colors[i])
# If all the vertices have not been assigned a color
if len(self._pos)!=len(pos):
from sage.plot.colors import rainbow,rgbcolor
vertex_colors_rgb=[rgbcolor(c) for c in vertex_colors]
for c in rainbow(len(vertex_colors)+1):
if rgbcolor(c) not in vertex_colors_rgb:
break
leftovers=[j for j in self._pos.values() if j not in pos]
pos+=leftovers
colors+=[c]*len(leftovers)
if self._arcdigraph:
self._plot_components['vertices'] = [circle(pos[i],
self._vertex_radius, fill=True, facecolor=colors[i], clip=False)
for i in range(len(pos))]
else:
self._plot_components['vertices'] = scatter_plot(pos,
facecolor=colors, clip=False, **voptions)
if self._options['vertex_labels']:
self._plot_components['vertex_labels'] = []
# TODO: allow text options
for v in self._nodelist:
self._plot_components['vertex_labels'].append(text(str(v),
self._pos[v], rgbcolor=(0,0,0), zorder=8))
def set_edges(self, **edge_options):
"""
Sets the edge (or arrow) plotting parameters for the GraphPlot object. This
function is called by the constructor but can also be called to make updates to
the vertex options of an existing GraphPlot object. Note that the changes are
cumulative.
EXAMPLES::
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: GP = g.graphplot(vertex_size=100, edge_labels=True, color_by_label=True, edge_style='dashed')
sage: GP.set_edges(edge_style='solid')
sage: GP.plot()
sage: GP.set_edges(edge_color='black')
sage: GP.plot()
sage: d = DiGraph({}, loops=True, multiedges=True, sparse=True)
sage: d.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: GP = d.graphplot(vertex_size=100, edge_labels=True, color_by_label=True, edge_style='dashed')
sage: GP.set_edges(edge_style='solid')
sage: GP.plot()
sage: GP.set_edges(edge_color='black')
sage: GP.plot()
TESTS::
sage: G = Graph("Fooba")
sage: G.show(edge_colors={'red':[(3,6),(2,5)]})
Verify that default edge labels are pretty close to being between the vertices
in some cases where they weren't due to truncating division (trac #10124)::
sage: test_graphs = graphs.FruchtGraph(), graphs.BullGraph()
sage: tol = 0.001
sage: for G in test_graphs:
... E=G.edges()
... for e0, e1, elab in E:
... G.set_edge_label(e0, e1, '%d %d' % (e0, e1))
... gp = G.graphplot(save_pos=True,edge_labels=True)
... vx = gp._plot_components['vertices'][0].xdata
... vy = gp._plot_components['vertices'][0].ydata
... for elab in gp._plot_components['edge_labels']:
... textobj = elab[0]
... x, y, s = textobj.x, textobj.y, textobj.string
... v0, v1 = map(int, s.split())
... vn = vector(((x-(vx[v0]+vx[v1])/2.),y-(vy[v0]+vy[v1])/2.)).norm()
... assert vn < tol
"""
for arg in edge_options:
self._options[arg] = edge_options[arg]
if 'edge_colors' in edge_options:
self._options['color_by_label'] = False
# Handle base edge options: thickness, linestyle
eoptions = {}
if 'edge_style' in self._options:
eoptions['linestyle'] = self._options['edge_style']
if 'thickness' in self._options:
eoptions['thickness'] = self._options['thickness']
# Set labels param to add labels on the fly
labels = False
if self._options['edge_labels']:
labels = True
self._plot_components['edge_labels'] = []
# Make dict collection of all edges (keep label and edge color)
edges_to_draw = {}
if self._options['color_by_label'] or isinstance(
self._options['edge_colors'], dict):
if self._options['color_by_label']:
edge_colors = self._graph._color_by_label()
else:
edge_colors = self._options['edge_colors']
for color in edge_colors:
for edge in edge_colors[color]:
key = tuple(sorted([edge[0], edge[1]]))
if key == (edge[0], edge[1]): head = 1
else: head = 0
if len(edge) < 3:
label = self._graph.edge_label(edge[0], edge[1])
if isinstance(label, list):
if key in edges_to_draw:
edges_to_draw[key].append(
(label[-1], color, head))
else:
edges_to_draw[key] = [(label[-1], color, head)]
for i in range(len(label) - 1):
edges_to_draw[key].append(
(label[-1], color, head))
else:
label = edge[2]
if key in edges_to_draw:
edges_to_draw[key].append((label, color, head))
else:
edges_to_draw[key] = [(label, color, head)]
# add unspecified edges in (default color black)
for edge in self._graph.edge_iterator():
key = tuple(sorted([edge[0], edge[1]]))
label = edge[2]
specified = False
if key in edges_to_draw:
for old_label, old_color, old_head in edges_to_draw[key]:
if label == old_label:
specified = True
break
if not specified:
if key == (edge[0], edge[1]): head = 1
else: head = 0
edges_to_draw[key] = [(label, 'black', head)]
else:
for edge in self._graph.edges(sort=True):
key = tuple(sorted([edge[0], edge[1]]))
if key == (edge[0], edge[1]): head = 1
else: head = 0
if key in edges_to_draw:
edges_to_draw[key].append(
(edge[2], self._options['edge_color'], head))
else:
edges_to_draw[key] = [(edge[2],
self._options['edge_color'], head)]
if edges_to_draw:
self._plot_components['edges'] = []
else:
return
# Check for multi-edges or loops
if self._arcs or self._loops:
tmp = edges_to_draw.copy()
dist = self._options['dist'] * 2.
loop_size = self._options['loop_size']
max_dist = self._options['max_dist']
from sage.functions.all import sqrt
for (a, b) in tmp:
if a == b:
# Loops
distance = dist
local_labels = edges_to_draw.pop((a, b))
if len(local_labels) * dist > max_dist:
distance = float(max_dist) / len(local_labels)
curr_loop_size = loop_size
for i in range(len(local_labels)):
self._plot_components['edges'].append(
circle((self._pos[a][0],
self._pos[a][1] - curr_loop_size),
curr_loop_size,
rgbcolor=local_labels[i][1],
**eoptions))
if labels:
self._plot_components['edge_labels'].append(
text(local_labels[i][0],
(self._pos[a][0],
self._pos[a][1] - 2 * curr_loop_size)))
curr_loop_size += distance / 4
elif len(edges_to_draw[(a, b)]) > 1:
# Multi-edge
local_labels = edges_to_draw.pop((a, b))
# Compute perpendicular bisector
p1 = self._pos[a]
p2 = self._pos[b]
M = (
(p1[0] + p2[0]) / 2., (p1[1] + p2[1]) / 2.) # midpoint
if not p1[1] == p2[1]:
S = float(p1[0] - p2[0]) / (p2[1] - p1[1]
) # perp slope
y = lambda x: S * x - S * M[0] + M[
1] # perp bisector line
# f,g are functions of distance d to determine x values
# on line y at d from point M
f = lambda d: sqrt(d**2 / (1. + S**2)) + M[0]
g = lambda d: -sqrt(d**2 / (1. + S**2)) + M[0]
odd_x = f
even_x = g
if p1[0] == p2[0]:
odd_y = lambda d: M[1]
even_y = odd_y
else:
odd_y = lambda x: y(f(x))
even_y = lambda x: y(g(x))
else:
odd_x = lambda d: M[0]
even_x = odd_x
odd_y = lambda d: M[1] + d
even_y = lambda d: M[1] - d
# We now have the control points for each bezier curve
# in terms of distance parameter d.
# Also note that the label for each edge should be drawn at d/2.
# (This is because we're using the perp bisectors).
distance = dist
if len(local_labels) * dist > max_dist:
distance = float(max_dist) / len(local_labels)
for i in range(len(local_labels) / 2):
k = (i + 1.0) * distance
if self._arcdigraph:
odd_start = self._polar_hack_for_multidigraph(
p1, [odd_x(k), odd_y(k)],
self._vertex_radius)[0]
odd_end = self._polar_hack_for_multidigraph(
[odd_x(k), odd_y(k)], p2,
self._vertex_radius)[1]
even_start = self._polar_hack_for_multidigraph(
p1, [even_x(k), even_y(k)],
self._vertex_radius)[0]
even_end = self._polar_hack_for_multidigraph(
[even_x(k), even_y(k)], p2,
self._vertex_radius)[1]
self._plot_components['edges'].append(
arrow(path=[[
odd_start, [odd_x(k), odd_y(k)], odd_end
]],
head=local_labels[2 * i][2],
zorder=1,
rgbcolor=local_labels[2 * i][1],
**eoptions))
self._plot_components['edges'].append(
arrow(path=[[
even_start, [even_x(k),
even_y(k)], even_end
]],
head=local_labels[2 * i + 1][2],
zorder=1,
rgbcolor=local_labels[2 * i + 1][1],
**eoptions))
else:
self._plot_components['edges'].append(
bezier_path(
[[p1, [odd_x(k), odd_y(k)], p2]],
zorder=1,
rgbcolor=local_labels[2 * i][1],
**eoptions))
self._plot_components['edges'].append(
bezier_path(
[[p1, [even_x(k), even_y(k)], p2]],
zorder=1,
rgbcolor=local_labels[2 * i + 1][1],
**eoptions))
if labels:
j = k / 2.0
self._plot_components['edge_labels'].append(
text(local_labels[2 * i][0],
[odd_x(j), odd_y(j)]))
self._plot_components['edge_labels'].append(
text(local_labels[2 * i + 1][0],
[even_x(j), even_y(j)]))
if len(local_labels) % 2 == 1:
edges_to_draw[(a, b)] = [local_labels[-1]
] # draw line for last odd
dir = self._graph.is_directed()
for (a, b) in edges_to_draw:
if self._arcdigraph:
C, D = self._polar_hack_for_multidigraph(
self._pos[a], self._pos[b], self._vertex_radius)
self._plot_components['edges'].append(
arrow(C,
D,
rgbcolor=edges_to_draw[(a, b)][0][1],
head=edges_to_draw[(a, b)][0][2],
**eoptions))
if labels:
self._plot_components['edge_labels'].append(
text(str(edges_to_draw[(a, b)][0][0]),
[(C[0] + D[0]) / 2., (C[1] + D[1]) / 2.]))
elif dir:
self._plot_components['edges'].append(
arrow(self._pos[a],
self._pos[b],
rgbcolor=edges_to_draw[(a, b)][0][1],
arrowshorten=self._arrowshorten,
head=edges_to_draw[(a, b)][0][2],
**eoptions))
else:
self._plot_components['edges'].append(
line([self._pos[a], self._pos[b]],
rgbcolor=edges_to_draw[(a, b)][0][1],
**eoptions))
if labels and not self._arcdigraph:
self._plot_components['edge_labels'].append(
text(str(edges_to_draw[(a, b)][0][0]),
[(self._pos[a][0] + self._pos[b][0]) / 2.,
(self._pos[a][1] + self._pos[b][1]) / 2.]))
def set_vertices(self, **vertex_options):
"""
Sets the vertex plotting parameters for this GraphPlot. This function
is called by the constructor but can also be called to make updates to
the vertex options of an existing GraphPlot object. Note that the
changes are cumulative.
EXAMPLES::
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: GP = g.graphplot(vertex_size=100, edge_labels=True, color_by_label=True, edge_style='dashed')
sage: GP.set_vertices(talk=True)
sage: GP.plot()
sage: GP.set_vertices(vertex_colors='pink', vertex_shape='^')
sage: GP.plot()
"""
# Handle base vertex options
voptions = {}
for arg in vertex_options:
self._options[arg] = vertex_options[arg]
# First set defaults for styles
vertex_colors = None
if self._options['talk']:
voptions['markersize'] = 500
if self._options['partition'] is None:
vertex_colors = '#ffffff'
else:
voptions['markersize'] = self._options['vertex_size']
if 'vertex_colors' not in self._options:
if self._options['partition'] is not None:
from sage.plot.colors import rainbow, rgbcolor
partition = self._options['partition']
l = len(partition)
R = rainbow(l)
vertex_colors = {}
for i in range(l):
vertex_colors[R[i]] = partition[i]
elif len(self._graph._boundary) != 0:
vertex_colors = {}
bdy_verts = []
int_verts = []
for v in self._graph.vertex_iterator():
if v in self._graph._boundary:
bdy_verts.append(v)
else:
int_verts.append(v)
vertex_colors['#fec7b8'] = int_verts
vertex_colors['#b3e8ff'] = bdy_verts
elif not vertex_colors:
vertex_colors = '#fec7b8'
else:
vertex_colors = self._options['vertex_colors']
if 'vertex_shape' in self._options:
voptions['marker'] = self._options['vertex_shape']
if self._graph.is_directed():
self._vertex_radius = sqrt(voptions['markersize'] / pi)
self._arrowshorten = 2 * self._vertex_radius
if self._arcdigraph:
self._vertex_radius = sqrt(voptions['markersize'] /
(20500 * pi))
voptions['zorder'] = 7
if not isinstance(vertex_colors, dict):
voptions['facecolor'] = vertex_colors
if self._arcdigraph:
self._plot_components['vertices'] = [
circle(center,
self._vertex_radius,
fill=True,
facecolor=vertex_colors,
clip=False) for center in self._pos.values()
]
else:
self._plot_components['vertices'] = scatter_plot(
self._pos.values(), clip=False, **voptions)
else:
# Color list must be ordered:
pos = []
colors = []
for i in vertex_colors:
pos += [self._pos[j] for j in vertex_colors[i]]
colors += [i] * len(vertex_colors[i])
# If all the vertices have not been assigned a color
if len(self._pos) != len(pos):
from sage.plot.colors import rainbow, rgbcolor
vertex_colors_rgb = [rgbcolor(c) for c in vertex_colors]
for c in rainbow(len(vertex_colors) + 1):
if rgbcolor(c) not in vertex_colors_rgb:
break
leftovers = [j for j in self._pos.values() if j not in pos]
pos += leftovers
colors += [c] * len(leftovers)
if self._arcdigraph:
self._plot_components['vertices'] = [
circle(pos[i],
self._vertex_radius,
fill=True,
facecolor=colors[i],
clip=False) for i in range(len(pos))
]
else:
self._plot_components['vertices'] = scatter_plot(
pos, facecolor=colors, clip=False, **voptions)
if self._options['vertex_labels']:
self._plot_components['vertex_labels'] = []
# TODO: allow text options
for v in self._nodelist:
self._plot_components['vertex_labels'].append(
text(str(v), self._pos[v], rgbcolor=(0, 0, 0), zorder=8))
def plot_heap(self):
r"""
Display the Hasse diagram of the heap of ``self``.
The Hasse diagram is rendered in the lattice `S \times \NN`, with
every element `i` in the poset drawn as a point labelled by its label
`s_i`. Every point is placed in the column for its label at a certain
level. The levels start at 0 and the level k of an element `i` is the
maximal number `k` such that the heap contains a chain `i_0\prec
i_1\prec ... \prec i_k` where `i_k=i`. See [Ste1996]_ and [GX2020]_.
OUTPUT: GraphicsObject
EXAMPLES::
sage: FC = CoxeterGroup(['B', 5]).fully_commutative_elements()
sage: FC([3,2,4,3,1]).plot_heap()
Graphics object consisting of 15 graphics primitives
.. PLOT::
:width: 400px
FC = CoxeterGroup(['B', 5]).fully_commutative_elements()
g = FC([3,2,4,3,1]).plot_heap()
sphinx_plot(g)
"""
import sage.plot.all as plot
m = self.parent().coxeter_group().coxeter_matrix()
letters = self.parent().coxeter_group().index_set()
graphics = []
h = self.heap()
levels = h.level_sets()
letters_at_level = [set(self[i] for i in level) for level in levels]
for (level_zero_index, members) in enumerate(levels):
level = level_zero_index + 1
for i in members:
x = self[i]
# Draw the node
graphics.append(
plot.circle((x, level),
0.1,
fill=True,
facecolor='white',
edgecolor='blue',
zorder=1))
graphics.append(
plot.text(str(x), (x, level), color='blue', zorder=2))
neighbors = {z for z in letters if m[x, z] >= 3}
for other in neighbors:
highest_level = max((j + 1 for j in range(level_zero_index)
if other in letters_at_level[j]),
default=None)
if highest_level:
graphics.append(
plot.line([(other, highest_level), (x, level)],
color='black',
zorder=0))
g = sum(graphics)
g.axes(False)
return g
