def draw_funddom_d(coset_reps,format="MP",z0=I):
r""" Draw a fundamental domain for self in the circle model
INPUT:
- ''format'' -- (default 'Disp') How to present the f.d.
= 'S' -- Display directly on the screen
- z0 -- (default I) the upper-half plane is mapped to the disk by z-->(z-z0)/(z-z0.conjugate())
EXAMPLES::
sage: G=MySubgroup(Gamma0(3))
sage: G._draw_funddom_d()
"""
# The fundamental domain consists of copies of the standard fundamental domain
pi=RR.pi()
from sage.plot.plot import (Graphics,line)
g=Graphics()
bdcirc=_circ_arc(0 ,2 *pi,0 ,1 ,1000 )
g=g+bdcirc
# Corners
x1=-RR(0.5) ; y1=RR(sqrt(3 )/2)
x2=RR(0.5) ; y2=RR(sqrt(3 )/2)
z_inf=1
l1 = _geodesic_between_two_points_d(x1,y1,x1,infinity)
l2 = _geodesic_between_two_points_d(x2,y2,x2,infinity)
c0 = _geodesic_between_two_points_d(x1,y1,x2,y2)
tri=c0+l1+l2
g=g+tri
for A in coset_reps:
[a,b,c,d]=A
if(a==1 and b==0 and c==0 and d==1 ):
continue
if(a<0 ):
a=-a; b=-b; c=-c; d=-1
if(c==0 ): # then this is easier
l1 = _geodesic_between_two_points_d(x1+b,y1,x1+b,infinity)
l2 = _geodesic_between_two_points_d(x2+b,y2,x2+b,infinity)
c0 = _geodesic_between_two_points_d(x1+b,y1,x2+b,y2)
# c0=line(L0); l1=line(L1); l2=line(L2); l3=line(L3)
tri=c0+l1+l2
g=g+tri
else:
den=(c*x1+d)**2 +c**2 *y1**2
x1_t=(a*c*(x1**2 +y1**2 )+(a*d+b*c)*x1+b*d)/den
y1_t=y1/den
den=(c*x2+d)**2 +c**2 *y2**2
x2_t=(a*c*(x2**2 +y2**2 )+(a*d+b*c)*x2+b*d)/den
y2_t=y2/den
inf_t=a/c
c0=_geodesic_between_two_points_d(x1_t,y1_t,x2_t,y2_t)
c1=_geodesic_between_two_points_d(x1_t,y1_t,inf_t,0.0 )
c2=_geodesic_between_two_points_d(x2_t,y2_t,inf_t,0.0 )
tri=c0+c1+c2
g=g+tri
g.xmax(1 )
g.ymax(1 )
g.xmin(-1 )
g.ymin(-1 )
g.set_aspect_ratio(1 )
return g
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
- pos -- an optional positioning dictionary
- layout -- what kind of layout to use, takes precedence over pos
- 'circular' -- plots the graph with vertices evenly distributed
on a circle
- 'spring' -- uses the traditional spring layout, using the
graph's current positions as initial positions
- 'tree' -- the (di)graph must be a tree. One can specify the root
of the tree using the keyword tree_root, otherwise a root
will be selected at random. Then the tree will be plotted in
levels, depending on minimum distance for the root.
- vertex_labels -- whether to print vertex labels
edge_labels -- whether to print edge labels. By default, False,
but if True, the result of str(l) is printed on the edge for
each label l. Labels equal to None are not printed (to set edge
labels, see set_edge_label).
- vertex_size -- size of vertices displayed
- vertex_shape -- the shape to draw the vertices (Not available for
multiedge digraphs.
- graph_border -- whether to include a box around the graph
- vertex_colors -- optional dictionary to specify vertex colors: each
key is a color recognizable by matplotlib, and each corresponding
entry is a list of vertices. If a vertex is not listed, it looks
invisible on the resulting plot (it doesn't get drawn).
- edge_colors -- a dictionary specifying edge colors: each key is a
color recognized by matplotlib, and each entry is a list of edges.
- partition -- a partition of the vertex set. if specified, plot will
show each cell in a different color. vertex_colors takes precedence.
- talk -- if true, prints large vertices with white backgrounds so that
labels are legible on slides
- iterations -- how many iterations of the spring layout algorithm to
go through, if applicable
- color_by_label -- if True, color edges by their labels
- heights -- if specified, this is a dictionary from a set of
floating point heights to a set of vertices
- edge_style -- keyword arguments passed into the
edge-drawing routine. This currently only works for
directed graphs, since we pass off the undirected graph to
networkx
- tree_root -- a vertex of the tree to be used as the root for
the layout="tree" option. If no root is specified, then one
is chosen at random. Ignored unless layout='tree'.
- tree_orientation -- "up" or "down" (default is "down").
If "up" (resp., "down"), then the root of the tree will
appear on the bottom (resp., top) and the tree will grow
upwards (resp. downwards). Ignored unless layout='tree'.
- save_pos -- save position computed during plotting
EXAMPLES::
sage: from sage.graphs.graph_plot import graphplot_options
sage: list(sorted(graphplot_options.iteritems()))
[('by_component', 'Whether to do the spring layout by connected component -- a boolean.'),
('color_by_label', 'Whether or not to color the edges by their label values.'),
('dim', 'The dimension of the layout -- 2 or 3.'),
('dist', 'The distance between multiedges.'),
('edge_color', 'The default color for edges.'),
('edge_colors', 'Dictionary of edge coloring.'),
('edge_labels', 'Whether or not to draw edge labels.'),
('edge_style', 'The linestyle of the edges-- one of "solid", "dashed", "dotted", dashdot".'),
('graph_border', 'Whether or not to draw a frame around the graph.'),
('heights', 'A dictionary mapping heights to the list of vertices at this height.'),
('iterations', 'The number of times to execute the spring layout algorithm.'),
('layout', 'A layout algorithm -- one of "acyclic", "circular", "ranked", "graphviz", "planar", "spring", or "tree".'),
('loop_size', 'The radius of the smallest loop.'),
('max_dist', 'The max distance range to allow multiedges.'),
('partition', 'A partition of the vertex set. (Draws each cell of vertices in a different color).'),
('pos', 'The position dictionary of vertices'),
('prog', 'Which graphviz layout program to use -- one of "circo", "dot", "fdp", "neato", or "twopi".'),
('save_pos', 'Whether or not to save the computed position for the graph.'),
('spring', 'Use spring layout to finalize the current layout.'),
('talk', 'Whether to display the vertices in talk mode (larger and white)'),
('tree_orientation', 'The direction of tree branches -- "up" or "down".'),
('tree_root', 'A vertex designation for drawing trees.'),
('vertex_colors', 'Dictionary of vertex coloring.'),
('vertex_labels', 'Whether or not to draw vertex labels.'),
('vertex_shape', 'The shape to draw the vertices, Currently unavailable for Multi-edged DiGraphs.'),
('vertex_size', 'The size to draw the vertices.')]
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []}, implementation='networkx' )
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
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: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
"""
G = Graphics()
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
G.set_axes_range(*(self._graph._layout_bounding_box(self._pos)))
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax-xmin)/10.0
dy = (ymax-ymin)/10.0
border = (line([( xmin - dx, ymin - dy), ( xmin - dx, ymax + dy ), ( xmax + dx, ymax + dy ), ( xmax + dx, ymin - dy ), ( xmin - dx, ymin - dy )], thickness=1.3))
border.axes_range(xmin = (xmin - dx), xmax = (xmax + dx), ymin = (ymin - dy), ymax = (ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
G._extra_kwds['axes_pad']=.05
return G
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
- pos -- an optional positioning dictionary
- layout -- what kind of layout to use, takes precedence over pos
- 'circular' -- plots the graph with vertices evenly distributed
on a circle
- 'spring' -- uses the traditional spring layout, using the
graph's current positions as initial positions
- 'tree' -- the (di)graph must be a tree. One can specify the root
of the tree using the keyword tree_root, otherwise a root
will be selected at random. Then the tree will be plotted in
levels, depending on minimum distance for the root.
- vertex_labels -- whether to print vertex labels
edge_labels -- whether to print edge labels. By default, False,
but if True, the result of str(l) is printed on the edge for
each label l. Labels equal to None are not printed (to set edge
labels, see set_edge_label).
- vertex_size -- size of vertices displayed
- vertex_shape -- the shape to draw the vertices (Not available for
multiedge digraphs.
- graph_border -- whether to include a box around the graph
- vertex_colors -- optional dictionary to specify vertex colors: each
key is a color recognizable by matplotlib, and each corresponding
entry is a list of vertices. If a vertex is not listed, it looks
invisible on the resulting plot (it doesn't get drawn).
- edge_colors -- a dictionary specifying edge colors: each key is a
color recognized by matplotlib, and each entry is a list of edges.
- partition -- a partition of the vertex set. if specified, plot will
show each cell in a different color. vertex_colors takes precedence.
- talk -- if true, prints large vertices with white backgrounds so that
labels are legible on slides
- iterations -- how many iterations of the spring layout algorithm to
go through, if applicable
- color_by_label -- if True, color edges by their labels
- heights -- if specified, this is a dictionary from a set of
floating point heights to a set of vertices
- edge_style -- keyword arguments passed into the
edge-drawing routine. This currently only works for
directed graphs, since we pass off the undirected graph to
networkx
- tree_root -- a vertex of the tree to be used as the root for
the layout="tree" option. If no root is specified, then one
is chosen at random. Ignored unless layout='tree'.
- tree_orientation -- "up" or "down" (default is "down").
If "up" (resp., "down"), then the root of the tree will
appear on the bottom (resp., top) and the tree will grow
upwards (resp. downwards). Ignored unless layout='tree'.
- save_pos -- save position computed during plotting
EXAMPLES::
sage: from sage.graphs.graph_plot import graphplot_options
sage: list(sorted(graphplot_options.iteritems()))
[('by_component', 'Whether to do the spring layout by connected component -- a boolean.'),
('color_by_label', 'Whether or not to color the edges by their label values.'),
('dim', 'The dimension of the layout -- 2 or 3.'),
('dist', 'The distance between multiedges.'),
('edge_color', 'The default color for edges.'),
('edge_colors', 'Dictionary of edge coloring.'),
('edge_labels', 'Whether or not to draw edge labels.'),
('edge_style', 'The linestyle of the edges-- one of "solid", "dashed", "dotted", dashdot".'),
('graph_border', 'Whether or not to draw a frame around the graph.'),
('heights', 'A dictionary mapping heights to the list of vertices at this height.'),
('iterations', 'The number of times to execute the spring layout algorithm.'),
('layout', 'A layout algorithm -- one of "acyclic", "circular", "ranked", "graphviz", "planar", "spring", or "tree".'),
('loop_size', 'The radius of the smallest loop.'),
('max_dist', 'The max distance range to allow multiedges.'),
('partition', 'A partition of the vertex set. (Draws each cell of vertices in a different color).'),
('pos', 'The position dictionary of vertices'),
('prog', 'Which graphviz layout program to use -- one of "circo", "dot", "fdp", "neato", or "twopi".'),
('save_pos', 'Whether or not to save the computed position for the graph.'),
('spring', 'Use spring layout to finalize the current layout.'),
('talk', 'Whether to display the vertices in talk mode (larger and white)'),
('tree_orientation', 'The direction of tree branches -- "up" or "down".'),
('tree_root', 'A vertex designation for drawing trees.'),
('vertex_colors', 'Dictionary of vertex coloring.'),
('vertex_labels', 'Whether or not to draw vertex labels.'),
('vertex_shape', 'The shape to draw the vertices, Currently unavailable for Multi-edged DiGraphs.'),
('vertex_size', 'The size to draw the vertices.')]
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []}, implementation='networkx' )
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
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: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
"""
G = Graphics()
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
G.set_axes_range(*(self._graph._layout_bounding_box(self._pos)))
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax - xmin) / 10.0
dy = (ymax - ymin) / 10.0
border = (line([(xmin - dx, ymin - dy), (xmin - dx, ymax + dy),
(xmax + dx, ymax + dy), (xmax + dx, ymin - dy),
(xmin - dx, ymin - dy)],
thickness=1.3))
border.axes_range(xmin=(xmin - dx),
xmax=(xmax + dx),
ymin=(ymin - dy),
ymax=(ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
G._extra_kwds['axes_pad'] = .05
return G
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
The options accepted by this method are to be found in the documentation
of the :mod:`sage.graphs.graph_plot` module, and the
:meth:`~sage.plot.graphics.Graphics.show` method.
.. NOTE::
See :mod:`the module's documentation <sage.graphs.graph_plot>` for
information on default values of this method.
We can specify some pretty precise plotting of familiar graphs::
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
Here are some more common graphs with typical options::
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
The options for plotting also work with directed graphs::
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []})
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
This example shows off the coloring of edges::
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
With the ``partition`` option, we can separate out same-color groups
of vertices::
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
Loops are also plotted correctly::
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
::
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
More options::
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
Graphics object consisting of 11 graphics primitives
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
We can plot multiple graphs::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
Graphics object consisting of 14 graphics primitives
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
Graphics object consisting of 14 graphics primitives
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
Graphics object consisting of 20 graphics primitives
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
The tree layout is also useful::
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
More examples::
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
Graphics object consisting of 34 graphics primitives
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: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
Graphics object consisting of 22 graphics primitives
The ``edge_style`` option may be provided in the short format too::
sage: g.graphplot(edge_labels=True, color_by_label=True, edge_style='--').plot()
Graphics object consisting of 22 graphics primitives
TESTS:
Make sure that show options work with plot also::
sage: g = Graph({})
sage: g.plot(title='empty graph', axes=True)
Graphics object consisting of 0 graphics primitives
Check for invalid inputs::
sage: p = graphs.PetersenGraph().plot(egabrag='garbage')
Traceback (most recent call last):
...
ValueError: Invalid input 'egabrag=garbage'
Make sure that no graphics primitive is clipped::
sage: tadpole = Graph({0:[0,1]}).plot()
sage: bbox = tadpole.get_minmax_data()
sage: for part in tadpole:
....: part_bbox = part.get_minmax_data()
....: assert bbox['xmin'] <= part_bbox['xmin'] <= part_bbox['xmax'] <= bbox['xmax']
....: assert bbox['ymin'] <= part_bbox['ymin'] <= part_bbox['ymax'] <= bbox['ymax']
"""
G = Graphics()
options = self._options.copy()
options.update(kwds)
G._set_extra_kwds(Graphics._extract_kwds_for_show(options))
# Check the arguments
for o in options:
if o not in graphplot_options and o not in G._extra_kwds:
raise ValueError("Invalid input '{}={}'".format(o, options[o]))
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax - xmin) / 10.0
dy = (ymax - ymin) / 10.0
border = (line([(xmin - dx, ymin - dy), (xmin - dx, ymax + dy),
(xmax + dx, ymax + dy), (xmax + dx, ymin - dy),
(xmin - dx, ymin - dy)],
thickness=1.3))
border.axes_range(xmin=(xmin - dx),
xmax=(xmax + dx),
ymin=(ymin - dy),
ymax=(ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
return G
def draw_funddom_d(coset_reps, format="MP", z0=I, verbose=0):
r""" Draw a fundamental domain for self in the circle model
INPUT:
- ''format'' -- (default 'Disp') How to present the f.d.
= 'S' -- Display directly on the screen
- z0 -- (default I) the upper-half plane is mapped to the disk by z-->(z-z0)/(z-z0.conjugate())
EXAMPLES::
sage: G=MySubgroup(Gamma0(3))
sage: G._draw_funddom_d()
"""
# The fundamental domain consists of copies of the standard fundamental domain
pi = RR.pi()
from sage.plot.plot import (Graphics, line)
g = Graphics()
bdcirc = _circ_arc(0, 2 * pi, 0, 1, 1000)
g = g + bdcirc
# Corners
x1 = -RR(0.5)
y1 = RR(sqrt(3) / 2)
x2 = RR(0.5)
y2 = RR(sqrt(3) / 2)
z_inf = 1
l1 = _geodesic_between_two_points_d(x1, y1, x1, infinity)
l2 = _geodesic_between_two_points_d(x2, y2, x2, infinity)
c0 = _geodesic_between_two_points_d(x1, y1, x2, y2)
tri = c0 + l1 + l2
g = g + tri
for A in coset_reps:
a, b, c, d = A
if a == 1 and b == 0 and c == 0 and d == 1:
continue
if a < 0:
a = -a
b = -b
c = -c
d = -d
if verbose > 0:
print "a,b,c,d=", a, b, c, d
if c == 0: # then this is easier
l1 = _geodesic_between_two_points_d(x1 + b, y1, x1 + b, infinity)
l2 = _geodesic_between_two_points_d(x2 + b, y2, x2 + b, infinity)
c0 = _geodesic_between_two_points_d(x1 + b, y1, x2 + b, y2)
# c0=line(L0); l1=line(L1); l2=line(L2); l3=line(L3)
tri = c0 + l1 + l2
g = g + tri
else:
den = (c * x1 + d)**2 + c**2 * y1**2
x1_t = (a * c * (x1**2 + y1**2) +
(a * d + b * c) * x1 + b * d) / den
y1_t = y1 / den
den = (c * x2 + d)**2 + c**2 * y2**2
x2_t = (a * c * (x2**2 + y2**2) +
(a * d + b * c) * x2 + b * d) / den
y2_t = y2 / den
inf_t = a / c
if verbose > 0:
print "x1_t=", x1_t
print "y1_t=", y1_t
print "x2_t=", x2_t
print "y2_t=", y2_t
print "inf_t=", inf_t
c0 = _geodesic_between_two_points_d(x1_t, y1_t, x2_t, y2_t)
c1 = _geodesic_between_two_points_d(x1_t, y1_t, inf_t, 1.0)
c2 = _geodesic_between_two_points_d(x2_t, y2_t, inf_t, 1.0)
tri = c0 + c1 + c2
g = g + tri
g.xmax(1)
g.ymax(1)
g.xmin(-1)
g.ymin(-1)
g.set_aspect_ratio(1)
return g
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
The options accepted by this method are to be found in the documentation
of the :mod:`sage.graphs.graph_plot` module, and the
:meth:`~sage.plot.graphics.Graphics.show` method.
.. NOTE::
See :mod:`the module's documentation <sage.graphs.graph_plot>` for
information on default values of this method.
We can specify some pretty precise plotting of familiar graphs::
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
Here are some more common graphs with typical options::
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
The options for plotting also work with directed graphs::
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []})
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
This example shows off the coloring of edges::
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
With the ``partition`` option, we can separate out same-color groups
of vertices::
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
Loops are also plotted correctly::
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
::
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
More options::
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
Graphics object consisting of 11 graphics primitives
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
We can plot multiple graphs::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
Graphics object consisting of 14 graphics primitives
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
Graphics object consisting of 14 graphics primitives
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
Graphics object consisting of 20 graphics primitives
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
The tree layout is also useful::
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
More examples::
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
Graphics object consisting of 34 graphics primitives
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: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
Graphics object consisting of 22 graphics primitives
The ``edge_style`` option may be provided in the short format too::
sage: g.graphplot(edge_labels=True, color_by_label=True, edge_style='--').plot()
Graphics object consisting of 22 graphics primitives
TESTS:
Make sure that show options work with plot also::
sage: g = Graph({})
sage: g.plot(title='empty graph', axes=True)
Graphics object consisting of 0 graphics primitives
Check for invalid inputs::
sage: p = graphs.PetersenGraph().plot(egabrag='garbage')
Traceback (most recent call last):
...
ValueError: Invalid input 'egabrag=garbage'
Make sure that no graphics primitive is clipped::
sage: tadpole = Graph({0:[0,1]}).plot()
sage: bbox = tadpole.get_minmax_data()
sage: for part in tadpole:
....: part_bbox = part.get_minmax_data()
....: assert bbox['xmin'] <= part_bbox['xmin'] <= part_bbox['xmax'] <= bbox['xmax']
....: assert bbox['ymin'] <= part_bbox['ymin'] <= part_bbox['ymax'] <= bbox['ymax']
"""
G = Graphics()
options = self._options.copy()
options.update(kwds)
G._set_extra_kwds(Graphics._extract_kwds_for_show(options))
# Check the arguments
for o in options:
if o not in graphplot_options and o not in G._extra_kwds:
raise ValueError("Invalid input '{}={}'".format(o, options[o]))
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax-xmin)/10.0
dy = (ymax-ymin)/10.0
border = (line([( xmin - dx, ymin - dy), ( xmin - dx, ymax + dy ), ( xmax + dx, ymax + dy ), ( xmax + dx, ymin - dy ), ( xmin - dx, ymin - dy )], thickness=1.3))
border.axes_range(xmin = (xmin - dx), xmax = (xmax + dx), ymin = (ymin - dy), ymax = (ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
return G
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
The options accepted by this method are to be found in the documentation
of module :mod:`sage.graphs.graph_plot`.
.. NOTE::
See :mod:`the module's documentation <sage.graphs.graph_plot>` for
information on default values of this method.
We can specify some pretty precise plotting of familiar graphs::
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
Here are some more common graphs with typical options::
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
The options for plotting also work with directed graphs::
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []}, implementation='networkx' )
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
This example shows off the coloring of edges::
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
With the ``partition`` option, we can separate out same-color groups
of vertices::
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
Loops are also plotted correctly::
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
::
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
More options::
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
We can plot multiple graphs::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
The tree layout is also useful::
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
More examples::
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
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: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
Wrong input (any input) :trac:`13891`::
sage: graphs.PetersenGraph().graphplot().plot(aertataert=346345345)
doctest:...: DeprecationWarning: This method takes no argument ! You may want to give it as an argument to graphplot instead.
See http://trac.sagemath.org/13891 for details.
<BLANKLINE>
"""
# This method takes NO input
# This has been added in early 2013. Remove it before my death, please.
if kwds:
from sage.misc.superseded import deprecation
deprecation(13891, "This method takes no argument ! You may want "
"to give it as an argument to graphplot instead.")
G = Graphics()
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
G.set_axes_range(*(self._graph._layout_bounding_box(self._pos)))
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax-xmin)/10.0
dy = (ymax-ymin)/10.0
border = (line([( xmin - dx, ymin - dy), ( xmin - dx, ymax + dy ), ( xmax + dx, ymax + dy ), ( xmax + dx, ymin - dy ), ( xmin - dx, ymin - dy )], thickness=1.3))
border.axes_range(xmin = (xmin - dx), xmax = (xmax + dx), ymin = (ymin - dy), ymax = (ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
G._extra_kwds['axes_pad']=.05
return G
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
The options accepted by this method are to be found in the documentation
of module :mod:`sage.graphs.graph_plot`.
.. NOTE::
See :mod:`the module's documentation <sage.graphs.graph_plot>` for
information on default values of this method.
We can specify some pretty precise plotting of familiar graphs::
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
Here are some more common graphs with typical options::
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
The options for plotting also work with directed graphs::
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []}, implementation='networkx' )
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
This example shows off the coloring of edges::
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
With the ``partition`` option, we can separate out same-color groups
of vertices::
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
Loops are also plotted correctly::
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
::
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
More options::
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
We can plot multiple graphs::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
The tree layout is also useful::
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
More examples::
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
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: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
Wrong input (any input) :trac:`13891`::
sage: graphs.PetersenGraph().graphplot().plot(aertataert=346345345)
doctest:...: DeprecationWarning: This method takes no argument ! You may want to give it as an argument to graphplot instead.
See http://trac.sagemath.org/13891 for details.
<BLANKLINE>
"""
# This method takes NO input
# This has been added in early 2013. Remove it before my death, please.
if kwds:
from sage.misc.superseded import deprecation
deprecation(
13891, "This method takes no argument ! You may want "
"to give it as an argument to graphplot instead.")
G = Graphics()
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
G.set_axes_range(*(self._graph._layout_bounding_box(self._pos)))
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax - xmin) / 10.0
dy = (ymax - ymin) / 10.0
border = (line([(xmin - dx, ymin - dy), (xmin - dx, ymax + dy),
(xmax + dx, ymax + dy), (xmax + dx, ymin - dy),
(xmin - dx, ymin - dy)],
thickness=1.3))
border.axes_range(xmin=(xmin - dx),
xmax=(xmax + dx),
ymin=(ymin - dy),
ymax=(ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
G._extra_kwds['axes_pad'] = .05
return G