def plot_generators(self):
r"""
Plot ray generators.
Ray generators must be specified during construction or using
:meth:`set_rays` before calling this method.
OUTPUT:
- a plot.
EXAMPLES::
sage: from sage.geometry.toric_plotter import ToricPlotter
sage: tp = ToricPlotter(dict(), 2, [(3,4)])
sage: print tp.plot_generators()
Graphics object consisting of 1 graphics primitive
"""
generators = self.generators
result = Graphics()
if not generators or not self.show_generators:
return result
colors = color_list(self.generator_color, len(generators))
d = self.dimension
extra_options = self.extra_options
origin = self.origin
thickness = self.generator_thickness
zorder = self.generator_zorder
for generator, ray, color in zip(generators, self.rays, colors):
if ray.norm() < generator.norm():
result += line([origin, ray],
color=color,
thickness=thickness,
zorder=zorder,
**extra_options)
else:
# This should not be the case, but as of 4.6 plotting
# functions are inconsistent and arrows behave very
# different compared to lines.
if d <= 2:
result += arrow(origin,
generator,
color=color,
width=thickness,
arrowsize=thickness + 1,
zorder=zorder,
**extra_options)
else:
result += line([origin, generator],
arrow_head=True,
color=color,
thickness=thickness,
zorder=zorder,
**extra_options)
return result
def plot_generators(self):
r"""
Plot ray generators.
Ray generators must be specified during construction or using
:meth:`set_rays` before calling this method.
OUTPUT:
- a plot.
EXAMPLES::
sage: from sage.geometry.toric_plotter import ToricPlotter
sage: tp = ToricPlotter(dict(), 2, [(3,4)])
sage: print tp.plot_generators()
Graphics object consisting of 1 graphics primitive
"""
generators = self.generators
result = Graphics()
if not generators or not self.show_generators:
return result
colors = color_list(self.generator_color, len(generators))
d = self.dimension
extra_options = self.extra_options
origin = self.origin
thickness = self.generator_thickness
zorder = self.generator_zorder
for generator, ray, color in zip(generators, self.rays, colors):
if ray.norm() < generator.norm():
result += line([origin, ray], color=color, thickness=thickness, zorder=zorder, **extra_options)
else:
# This should not be the case, but as of 4.6 plotting
# functions are inconsistent and arrows behave very
# different compared to lines.
if d <= 2:
result += arrow(
origin,
generator,
color=color,
width=thickness,
arrowsize=thickness + 1,
zorder=zorder,
**extra_options
)
else:
result += line(
[origin, generator],
arrow_head=True,
color=color,
thickness=thickness,
zorder=zorder,
**extra_options
)
return result
def plot_rays(self):
r"""
Plot rays and their labels.
Ray generators must be specified during construction or using
:meth:`set_rays` before calling this method.
OUTPUT:
- a plot.
EXAMPLES::
sage: from sage.geometry.toric_plotter import ToricPlotter
sage: tp = ToricPlotter(dict(), 2, [(3,4)])
sage: tp.plot_rays()
Graphics object consisting of 2 graphics primitives
"""
result = Graphics()
rays = self.rays
if not rays or not self.show_rays:
return result
extra_options = self.extra_options
origin = self.origin
colors = color_list(self.ray_color, len(rays))
thickness = self.ray_thickness
zorder = self.ray_zorder
for end, color in zip(rays, colors):
result += line([origin, end],
color=color, thickness=thickness,
zorder=zorder, **extra_options)
result += self.plot_ray_labels()
return result
def plot_rays(self):
r"""
Plot rays and their labels.
Ray generators must be specified during construction or using
:meth:`set_rays` before calling this method.
OUTPUT:
- a plot.
EXAMPLES::
sage: from sage.geometry.toric_plotter import ToricPlotter
sage: tp = ToricPlotter(dict(), 2, [(3,4)])
sage: print tp.plot_rays()
Graphics object consisting of 2 graphics primitives
"""
result = Graphics()
rays = self.rays
if not rays or not self.show_rays:
return result
extra_options = self.extra_options
origin = self.origin
colors = color_list(self.ray_color, len(rays))
thickness = self.ray_thickness
zorder = self.ray_zorder
for end, color in zip(rays, colors):
result += line([origin, end],
color=color,
thickness=thickness,
zorder=zorder,
**extra_options)
result += self.plot_ray_labels()
return result
def newton_plot(self):
S = [QQ(s) for s in self.polygon_slopes]
C = Counter(S)
pts = [(0, 0)]
x = y = 0
for s in sorted(C):
c = C[s]
x += c
y += c * s
pts.append((x, y))
L = Graphics()
L += line([(0, 0), (0, y + 0.2)], color="grey")
for i in range(1, y + 1):
L += line([(0, i), (0.06, i)], color="grey")
for i in range(1, C[0]):
L += line([(i, 0), (i, 0.06)], color="grey")
for i in range(len(pts) - 1):
P = pts[i]
Q = pts[i + 1]
for x in range(P[0], Q[0] + 1):
L += line(
[(x, P[1]),
(x, P[1] + (x - P[0]) * (Q[1] - P[1]) / (Q[0] - P[0]))],
color="grey",
)
for y in range(P[1], Q[1]):
L += line(
[(P[0] + (y - P[1]) * (Q[0] - P[0]) / (Q[1] - P[1]), y),
(Q[0], y)],
color="grey",
)
L += line(pts, thickness=2)
L.axes(False)
L.set_aspect_ratio(1)
return encode_plot(L, pad=0, pad_inches=0, bbox_inches="tight")
def newton_plot(self):
S = [QQ(s) for s in self.slopes]
C = Counter(S)
pts = [(0,0)]
x = y = 0
for s in sorted(C):
c = C[s]
x += c
y += c*s
pts.append((x,y))
L = Graphics()
L += line([(0,0),(0,y+0.2)],color="grey")
for i in range(1,y+1):
L += line([(0,i),(0.06,i)],color="grey")
for i in range(1,C[0]):
L += line([(i,0),(i,0.06)],color="grey")
for i in range(len(pts)-1):
P = pts[i]
Q = pts[i+1]
for x in range(P[0],Q[0]+1):
L += line([(x,P[1]),(x,P[1] + (x-P[0])*(Q[1]-P[1])/(Q[0]-P[0]))],color="grey")
for y in range(P[1],Q[1]):
L += line([(P[0] + (y-P[1])*(Q[0]-P[0])/(Q[1]-P[1]),y),(Q[0],y)],color="grey")
L += line(pts, thickness = 2)
L.axes(False)
L.set_aspect_ratio(1)
return encode_plot(L, pad=0, pad_inches=0, bbox_inches='tight')
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):
"""
Plot the points of the sequence.
Elements of the sequence are assumed to be real or from a
finite field, with a real indexing set ``I = range(len(self))``.
EXAMPLES::
sage: I = range(3)
sage: A = [ZZ(i^2)+1 for i in I]
sage: s = IndexedSequence(A,I)
sage: P = s.plot()
sage: show(P) # Not tested
"""
# elements must be coercible into RR
I = self.index_object()
S = self.list()
return line([[RR(I[i]),RR(S[i])] for i in range(len(I)-1)])
def plot(self):
"""
Plot the points of the sequence.
Elements of the sequence are assumed to be real or from a
finite field, with a real indexing set ``I = range(len(self))``.
EXAMPLES::
sage: I = range(3)
sage: A = [ZZ(i^2)+1 for i in I]
sage: s = IndexedSequence(A,I)
sage: P = s.plot()
sage: show(P) # Not tested
"""
# elements must be coercible into RR
I = self.index_object()
S = self.list()
return line([[RR(I[i]),RR(S[i])] for i in range(len(I)-1)])
def plot(self):
"""
Plots the points of the sequence, whose elements are assumed
to be real or from a finite field, with a real indexing set I
= range(len(self)).
EXAMPLES:
sage: I = range(3)
sage: A = [ZZ(i^2)+1 for i in I]
sage: s = IndexedSequence(A,I)
sage: P = s.plot()
Now type show(P) to view this in a browser.
"""
F = self.base_ring() ## elements must be coercible into RR
I = self.index_object()
N = len(I)
S = self.list()
P = line([[RR(I[i]),RR(S[i])] for i in range(N-1)])
return P
def plot(self):
"""
Plots the points of the sequence, whose elements are assumed
to be real or from a finite field, with a real indexing set I
= range(len(self)).
EXAMPLES:
sage: I = range(3)
sage: A = [ZZ(i^2)+1 for i in I]
sage: s = IndexedSequence(A,I)
sage: P = s.plot()
Now type show(P) to view this in a browser.
"""
F = self.base_ring() ## elements must be coercible into RR
I = self.index_object()
N = len(I)
S = self.list()
P = line([[RR(I[i]),RR(S[i])] for i in range(N-1)])
return P
def plot(self, xmin=None, xmax=None, **kwds):
"""
Special fast plot method for spike functions.
EXAMPLES::
sage: S = spike_function([(-1,1),(1,40)])
sage: P = plot(S)
sage: P[0]
Line defined by 8 points
"""
v = []
xmin, xmax = self._ranges(xmin, xmax)
x = xmin
eps = self.eps
while x < xmax:
y, i = self._eval(x)
v.append((x, y))
if i != -1:
x0 = self.support[i] + eps
v.extend([(x0, y), (x0, 0)])
if i + 1 < len(self.support):
x = self.support[i + 1] - eps
v.append((x, 0))
else:
x = xmax
v.append((xmax, 0))
else:
new_x = None
for j in range(len(self.support)):
if self.support[j] - eps > x:
new_x = self.support[j] - eps
break
if new_x is None:
new_x = xmax
v.append((new_x, 0))
x = new_x
L = line(v, **kwds)
L.xmin(xmin - 1)
L.xmax(xmax)
return L
def plot(self, xmin=None, xmax=None, **kwds):
"""
Special fast plot method for spike functions.
EXAMPLES::
sage: S = spike_function([(-1,1),(1,40)])
sage: P = plot(S)
sage: P[0]
Line defined by 8 points
"""
v = []
xmin, xmax = self._ranges(xmin, xmax)
x = xmin
eps = self.eps
while x < xmax:
y, i = self._eval(x)
v.append((x, y))
if i != -1:
x0 = self.support[i] + eps
v.extend([(x0, y), (x0, 0)])
if i + 1 < len(self.support):
x = self.support[i + 1] - eps
v.append((x, 0))
else:
x = xmax
v.append((xmax, 0))
else:
new_x = None
for j in range(len(self.support)):
if self.support[j] - eps > x:
new_x = self.support[j] - eps
break
if new_x is None:
new_x = xmax
v.append((new_x, 0))
x = new_x
L = line(v, **kwds)
L.xmin(xmin - 1)
L.xmax(xmax)
return L
def plot_bounds(dop, ini=None, pt=None, eps=None, **kwds):
r"""
EXAMPLES::
sage: from ore_algebra import *
sage: from ore_algebra.analytic.naive_sum import *
sage: Dops, x, Dx = DifferentialOperators()
sage: plot_bounds(Dx - 1, [CBF(1)], CBF(i)/2, RBF(1e-20))
Graphics object consisting of 5 graphics primitives
sage: plot_bounds(x*Dx^3 + 2*Dx^2 + x*Dx, eps=1e-8)
Graphics object consisting of 5 graphics primitives
sage: dop = x*Dx^2 + Dx + x
sage: plot_bounds(dop, eps=1e-8,
....: ini=LogSeriesInitialValues(0, {0: (1, 0)}, dop))
Graphics object consisting of 5 graphics primitives
sage: dop = ((x^2 + 10*x + 50)*Dx^10 + (5/9*x^2 + 50/9*x + 155/9)*Dx^9
....: + (-10/3*x^2 - 100/3*x - 190/3)*Dx^8 + (30*x^2 + 300*x + 815)*Dx^7
....: + (145*x^2 + 1445*x + 3605)*Dx^6 + (5/2*x^2 + 25*x + 115/2)*Dx^5
....: + (20*x^2 + 395/2*x + 1975/4)*Dx^4 + (-5*x^2 - 50*x - 130)*Dx^3
....: + (5/4*x^2 + 25/2*x + 105/4)*Dx^2 + (-20*x^2 - 195*x - 480)*Dx
....: + 5*x - 10)
sage: plot_bounds(dop, pol_part_len=4, bound_inverse="solve", eps=1e-10) # long time
Graphics object consisting of 5 graphics primitives
"""
import sage.plot.all as plot
from sage.all import VectorSpace, QQ, RIF
from ore_algebra.analytic.bounds import abs_min_nonzero_root
if ini is None:
ini = _random_ini(dop)
if pt is None:
rad = abs_min_nonzero_root(dop.leading_coefficient())
pt = QQ(2) if rad == infinity else RIF(rad/2).simplest_rational()
if eps is None:
eps = RBF(1e-50)
logger.info("point: %s", pt)
logger.info("initial values: %s", ini)
recd = []
maj = bounds.DiffOpBound(dop, max_effort=0, **kwds)
series_sum(dop, ini, pt, eps, stride=1, record_bounds_in=recd, maj=maj)
ref_sum = recd[-1][1][0].add_error(recd[-1][2])
recd[-1:] = []
# Note: this won't work well when the errors get close to the double
# precision underflow threshold.
err = [(psum[0]-ref_sum).abs() for n, psum, _ in recd]
large = float(1e200) # plot() is not robust to large values
error_plot_upper = plot.line(
[(n, v.upper()) for (n, v) in enumerate(err)
if abs(float(v.upper())) < large],
color="lightgray", scale="semilogy")
error_plot = plot.line(
[(n, v.lower()) for (n, v) in enumerate(err)
if abs(float(v.lower())) < large],
color="black", scale="semilogy")
bound_plot_lower = plot.line(
[(n, bound.lower()) for n, _, bound in recd
if abs(float(bound.lower())) < large],
color="lightblue", scale="semilogy")
bound_plot = plot.line(
[(n, bound.upper()) for n, _, bound in recd
if abs(float(bound.upper())) < large],
color="blue", scale="semilogy")
title = repr(dop) + " @ x=" + repr(pt)
title = title if len(title) < 80 else title[:77]+"..."
myplot = error_plot_upper + error_plot + bound_plot_lower + bound_plot
ymax = myplot.ymax()
if ymax < float('inf'):
txt = plot.text(title, (myplot.xmax(), ymax),
horizontal_alignment='right', vertical_alignment='top')
myplot += txt
return myplot
def plot(self, cell_colors=None, **kwds):
"""
Return a graphical representation for 2-dimensional Voronoi diagrams.
INPUT:
- ``cell_colors`` -- (default: ``None``) provide the colors for the cells, either as
dictionary. Randomly colored cells are provided with ``None``.
- ``**kwds`` -- optional keyword parameters, passed on as arguments for
plot().
OUTPUT:
A graphics object.
EXAMPLES::
sage: P = [[0.671, 0.650], [0.258, 0.767], [0.562, 0.406], [0.254, 0.709], [0.493, 0.879]]
sage: V = VoronoiDiagram(P); S=V.plot()
sage: show(S, xmin=0, xmax=1, ymin=0, ymax=1, aspect_ratio=1, axes=false)
sage: S=V.plot(cell_colors={0:'red', 1:'blue', 2:'green', 3:'white', 4:'yellow'})
sage: show(S, xmin=0, xmax=1, ymin=0, ymax=1, aspect_ratio=1, axes=false)
sage: S=V.plot(cell_colors=['red','blue','red','white', 'white'])
sage: show(S, xmin=0, xmax=1, ymin=0, ymax=1, aspect_ratio=1, axes=false)
sage: S=V.plot(cell_colors='something else')
Traceback (most recent call last):
...
AssertionError: 'cell_colors' must be a list or a dictionary
Trying to plot a Voronoi diagram of dimension other than 2 gives an
error::
sage: VoronoiDiagram([[1, 2, 3], [6, 5, 4]]).plot()
Traceback (most recent call last):
...
NotImplementedError: Plotting of 3-dimensional Voronoi diagrams not
implemented
"""
if self.ambient_dim() == 2:
S = line([])
if cell_colors is None:
from random import shuffle
cell_colors = rainbow(self._n)
shuffle(cell_colors)
else:
if not (isinstance(cell_colors, list) or (isinstance(cell_colors, dict))):
raise AssertionError("'cell_colors' must be a list or a dictionary")
for i, p in enumerate(self._P):
col = cell_colors[i]
S += (self.regions()[p]).render_solid(color=col, zorder=1)
S += point(p, color=col, pointsize=10, zorder=3)
S += point(p, color='black', pointsize=20, zorder=2)
return plot(S, **kwds)
raise NotImplementedError('Plotting of ' + str(self.ambient_dim()) +
'-dimensional Voronoi diagrams not' +
' implemented')
def geomrep(M1, B1=None, lineorders1=None, pd=None, sp=False):
"""
Return a sage graphics object containing geometric representation of
matroid M1.
INPUT:
- ``M1`` -- A matroid.
- ``B1`` -- (optional) A list of elements in ``M1.groundset()`` that
correspond to a basis of ``M1`` and will be placed as vertices of the
triangle in the geometric representation of ``M1``.
- ``lineorders1`` -- (optional) A list of ordered lists of elements of
``M1.grondset()`` such that if a line in geometric representation is
setwise same as any of these then points contained will be traversed in
that order thus overriding internal order deciding heuristic.
- ``pd`` - (optional) A dictionary mapping ground set elements to their
(x,y) positions.
- ``sp`` -- (optional) If True, a positioning dictionary and line orders
will be placed in ``M._cached_info``.
OUTPUT:
A sage graphics object of type <class 'sage.plot.graphics.Graphics'> that
corresponds to the geometric representation of the matroid.
EXAMPLES::
sage: from sage.matroids import matroids_plot_helpers
sage: M=matroids.named_matroids.P7()
sage: G=matroids_plot_helpers.geomrep(M)
sage: G.show(xmin=-2, xmax=3, ymin=-2, ymax=3)
sage: M=matroids.named_matroids.P7()
sage: G=matroids_plot_helpers.geomrep(M,lineorders1=[['f','e','d']])
sage: G.show(xmin=-2, xmax=3, ymin=-2, ymax=3)
.. NOTE::
This method does NOT do any checks.
"""
G = Graphics()
# create lists of loops and parallel elements and simplify given matroid
[M, L, P] = slp(M1, pos_dict=pd, B=B1)
if B1 is None:
B1 = list(M.basis())
M._cached_info = M1._cached_info
if M.rank() == 0:
limits = None
loops = L
looptext = ", ".join([str(l) for l in loops])
rectx = -1
recty = -1
rectw = 0.5 + 0.4*len(loops) + 0.5 # controlled based on len(loops)
recth = 0.6
G += polygon2d([[rectx, recty], [rectx, recty+recth],
[rectx+rectw, recty+recth], [rectx+rectw, recty]],
color='black', fill=False, thickness=4)
G += text(looptext, (rectx+0.5, recty+0.3), color='black',
fontsize=13)
G += point((rectx+0.2, recty+0.3), color=Color('#BDBDBD'), size=300,
zorder=2)
G += text('Loop(s)', (rectx+0.5+0.4*len(loops)+0.1, recty+0.3),
fontsize=13, color='black')
limits = tracklims(limits, [rectx, rectx+rectw], [recty, recty+recth])
G.axes(False)
G.axes_range(xmin=limits[0]-0.5, xmax=limits[1]+0.5,
ymin=limits[2]-0.5, ymax=limits[3]+0.5)
return G
elif M.rank() == 1:
if M._cached_info is not None and \
'plot_positions' in M._cached_info.keys() and \
M._cached_info['plot_positions'] is not None:
pts = M._cached_info['plot_positions']
else:
pts = {}
gnd = sorted(M.groundset())
pts[gnd[0]] = (1, float(2)/3)
G += point((1, float(2)/3), size=300, color=Color('#BDBDBD'), zorder=2)
pt = [1, float(2)/3]
if len(P) == 0:
G += text(gnd[0], (float(pt[0]), float(pt[1])), color='black',
fontsize=13)
pts2 = pts
# track limits [xmin,xmax,ymin,ymax]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
elif M.rank() == 2:
nB1 = list(set(list(M.groundset())) - set(B1))
bline = []
for j in nB1:
if M.is_dependent([j, B1[0], B1[1]]):
bline.append(j)
interval = len(bline)+1
if M._cached_info is not None and \
'plot_positions' in M._cached_info.keys() and \
M._cached_info['plot_positions'] is not None:
pts2 = M._cached_info['plot_positions']
else:
pts2 = {}
pts2[B1[0]] = (0, 0)
pts2[B1[1]] = (2, 0)
lpt = list(pts2[B1[0]])
rpt = list(pts2[B1[1]])
for k in range(len(bline)):
cc = (float(1)/interval)*(k+1)
pts2[bline[k]] = (cc*lpt[0]+(1-cc)*rpt[0],
cc*lpt[1]+(1-cc)*rpt[1])
if sp is True:
M._cached_info['plot_positions'] = pts2
# track limits [xmin,xmax,ymin,ymax]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
bline.extend(B1)
ptsx, ptsy, x_i, y_i = createline(pts2, bline, lineorders1)
lims = tracklims(lims, x_i, y_i)
G += line(zip(x_i, y_i), color='black', thickness=3, zorder=1)
pels = [p for p in pts2.keys() if any([M1.rank([p, q]) == 1
for q in P])]
allpts = [list(pts2[i]) for i in M.groundset()]
xpts = [float(k[0]) for k in allpts]
ypts = [float(k[1]) for k in allpts]
G += points(zip(xpts, ypts), color=Color('#BDBDBD'), size=300,
zorder=2)
for i in pts2:
if i not in pels:
pt = list(pts2[i])
G += text(i, (float(pt[0]), float(pt[1])), color='black',
fontsize=13)
else:
if M._cached_info is None or \
'plot_positions' not in M._cached_info.keys() or \
M._cached_info['plot_positions'] is None:
(pts, trilines,
nontripts, curvedlines) = it(M1, B1,
list(set(M.groundset())-set(B1)),
list(set(L) | set(P)))
pts2 = addnontripts([B1[0], B1[1], B1[2]], nontripts, pts)
trilines.extend(curvedlines)
else:
pts2 = M._cached_info['plot_positions']
trilines = [list(set(list(x)).difference(L | P))
for x in M1.flats(2)
if len(list(x)) >= 3]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
j = 0
for ll in trilines:
if len(ll) >= 3:
ptsx, ptsy, x_i, y_i = createline(pts2, ll, lineorders1)
lims = tracklims(lims, x_i, y_i)
G += line(zip(x_i, y_i), color='black', thickness=3, zorder=1)
pels = [p for p in pts2.keys() if any([M1.rank([p, q]) == 1
for q in P])]
allpts = [list(pts2[i]) for i in M.groundset()]
xpts = [float(k[0]) for k in allpts]
ypts = [float(k[1]) for k in allpts]
G += points(zip(xpts, ypts), color=Color('#BDBDBD'), size=300,
zorder=2)
for i in pts2:
if i not in pels:
pt = list(pts2[i])
G += text(i, (float(pt[0]), float(pt[1])), color='black',
fontsize=13)
if sp is True:
M1._cached_info['plot_positions'] = pts2
M1._cached_info['plot_lineorders'] = lineorders1
# deal with loops and parallel elements
G, lims = addlp(M1, M, L, P, pts2, G, lims)
G.axes(False)
G.axes_range(xmin=lims[0]-0.5, xmax=lims[1]+0.5, ymin=lims[2]-0.5,
ymax=lims[3]+0.5)
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 geomrep(M1, B1=None, lineorders1=None, pd=None, sp=False):
"""
Return a sage graphics object containing geometric representation of
matroid M1.
INPUT:
- ``M1`` -- A matroid.
- ``B1`` -- (optional) A list of elements in ``M1.groundset()`` that
correspond to a basis of ``M1`` and will be placed as vertices of the
triangle in the geometric representation of ``M1``.
- ``lineorders1`` -- (optional) A list of ordered lists of elements of
``M1.grondset()`` such that if a line in geometric representation is
setwise same as any of these then points contained will be traversed in
that order thus overriding internal order deciding heuristic.
- ``pd`` - (optional) A dictionary mapping ground set elements to their
(x,y) positions.
- ``sp`` -- (optional) If True, a positioning dictionary and line orders
will be placed in ``M._cached_info``.
OUTPUT:
A sage graphics object of type <class 'sage.plot.graphics.Graphics'> that
corresponds to the geometric representation of the matroid.
EXAMPLES::
sage: from sage.matroids import matroids_plot_helpers
sage: M=matroids.named_matroids.P7()
sage: G=matroids_plot_helpers.geomrep(M)
sage: G.show(xmin=-2, xmax=3, ymin=-2, ymax=3)
sage: M=matroids.named_matroids.P7()
sage: G=matroids_plot_helpers.geomrep(M,lineorders1=[['f','e','d']])
sage: G.show(xmin=-2, xmax=3, ymin=-2, ymax=3)
.. NOTE::
This method does NOT do any checks.
"""
G = Graphics()
# create lists of loops and parallel elements and simplify given matroid
[M, L, P] = slp(M1, pos_dict=pd, B=B1)
if B1 is None:
B1 = list(M.basis())
M._cached_info = M1._cached_info
if M.rank() == 0:
limits = None
loops = L
looptext = ", ".join([str(l) for l in loops])
rectx = -1
recty = -1
rectw = 0.5 + 0.4 * len(loops) + 0.5 # controlled based on len(loops)
recth = 0.6
G += polygon2d(
[[rectx, recty], [rectx, recty + recth],
[rectx + rectw, recty + recth], [rectx + rectw, recty]],
color='black',
fill=False,
thickness=4)
G += text(looptext, (rectx + 0.5, recty + 0.3),
color='black',
fontsize=13)
G += point((rectx + 0.2, recty + 0.3),
color=Color('#BDBDBD'),
size=300,
zorder=2)
G += text('Loop(s)',
(rectx + 0.5 + 0.4 * len(loops) + 0.1, recty + 0.3),
fontsize=13,
color='black')
limits = tracklims(limits, [rectx, rectx + rectw],
[recty, recty + recth])
G.axes(False)
G.axes_range(xmin=limits[0] - 0.5,
xmax=limits[1] + 0.5,
ymin=limits[2] - 0.5,
ymax=limits[3] + 0.5)
return G
elif M.rank() == 1:
if M._cached_info is not None and \
'plot_positions' in M._cached_info.keys() and \
M._cached_info['plot_positions'] is not None:
pts = M._cached_info['plot_positions']
else:
pts = {}
gnd = sorted(M.groundset())
pts[gnd[0]] = (1, float(2) / 3)
G += point((1, float(2) / 3),
size=300,
color=Color('#BDBDBD'),
zorder=2)
pt = [1, float(2) / 3]
if len(P) == 0:
G += text(gnd[0], (float(pt[0]), float(pt[1])),
color='black',
fontsize=13)
pts2 = pts
# track limits [xmin,xmax,ymin,ymax]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
elif M.rank() == 2:
nB1 = list(set(list(M.groundset())) - set(B1))
bline = []
for j in nB1:
if M.is_dependent([j, B1[0], B1[1]]):
bline.append(j)
interval = len(bline) + 1
if M._cached_info is not None and \
'plot_positions' in M._cached_info.keys() and \
M._cached_info['plot_positions'] is not None:
pts2 = M._cached_info['plot_positions']
else:
pts2 = {}
pts2[B1[0]] = (0, 0)
pts2[B1[1]] = (2, 0)
lpt = list(pts2[B1[0]])
rpt = list(pts2[B1[1]])
for k in range(len(bline)):
cc = (float(1) / interval) * (k + 1)
pts2[bline[k]] = (cc * lpt[0] + (1 - cc) * rpt[0],
cc * lpt[1] + (1 - cc) * rpt[1])
if sp is True:
M._cached_info['plot_positions'] = pts2
# track limits [xmin,xmax,ymin,ymax]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
bline.extend(B1)
ptsx, ptsy, x_i, y_i = createline(pts2, bline, lineorders1)
lims = tracklims(lims, x_i, y_i)
G += line(zip(x_i, y_i), color='black', thickness=3, zorder=1)
pels = [
p for p in pts2.keys() if any([M1.rank([p, q]) == 1 for q in P])
]
allpts = [list(pts2[i]) for i in M.groundset()]
xpts = [float(k[0]) for k in allpts]
ypts = [float(k[1]) for k in allpts]
G += points(zip(xpts, ypts),
color=Color('#BDBDBD'),
size=300,
zorder=2)
for i in pts2:
if i not in pels:
pt = list(pts2[i])
G += text(i, (float(pt[0]), float(pt[1])),
color='black',
fontsize=13)
else:
if M._cached_info is None or \
'plot_positions' not in M._cached_info.keys() or \
M._cached_info['plot_positions'] is None:
(pts, trilines, nontripts,
curvedlines) = it(M1, B1, list(set(M.groundset()) - set(B1)),
list(set(L) | set(P)))
pts2 = addnontripts([B1[0], B1[1], B1[2]], nontripts, pts)
trilines.extend(curvedlines)
else:
pts2 = M._cached_info['plot_positions']
trilines = [
list(set(list(x)).difference(L | P)) for x in M1.flats(2)
if len(list(x)) >= 3
]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
j = 0
for ll in trilines:
if len(ll) >= 3:
ptsx, ptsy, x_i, y_i = createline(pts2, ll, lineorders1)
lims = tracklims(lims, x_i, y_i)
G += line(zip(x_i, y_i), color='black', thickness=3, zorder=1)
pels = [
p for p in pts2.keys() if any([M1.rank([p, q]) == 1 for q in P])
]
allpts = [list(pts2[i]) for i in M.groundset()]
xpts = [float(k[0]) for k in allpts]
ypts = [float(k[1]) for k in allpts]
G += points(zip(xpts, ypts),
color=Color('#BDBDBD'),
size=300,
zorder=2)
for i in pts2:
if i not in pels:
pt = list(pts2[i])
G += text(i, (float(pt[0]), float(pt[1])),
color='black',
fontsize=13)
if sp is True:
M1._cached_info['plot_positions'] = pts2
M1._cached_info['plot_lineorders'] = lineorders1
# deal with loops and parallel elements
G, lims = addlp(M1, M, L, P, pts2, G, lims)
G.axes(False)
G.axes_range(xmin=lims[0] - 0.5,
xmax=lims[1] + 0.5,
ymin=lims[2] - 0.5,
ymax=lims[3] + 0.5)
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_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
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, cell_colors=None, **kwds):
"""
Return a graphical representation for 2-dimensional Voronoi diagrams.
INPUT:
- ``cell_colors`` -- (default: ``None``) provide the colors for the cells, either as
dictionary. Randomly colored cells are provided with ``None``.
- ``**kwds`` -- optional keyword parameters, passed on as arguments for
plot().
OUTPUT:
A graphics object.
EXAMPLES::
sage: P = [[0.671, 0.650], [0.258, 0.767], [0.562, 0.406], [0.254, 0.709], [0.493, 0.879]]
sage: V = VoronoiDiagram(P); S=V.plot()
sage: show(S, xmin=0, xmax=1, ymin=0, ymax=1, aspect_ratio=1, axes=false)
sage: S=V.plot(cell_colors={0:'red', 1:'blue', 2:'green', 3:'white', 4:'yellow'})
sage: show(S, xmin=0, xmax=1, ymin=0, ymax=1, aspect_ratio=1, axes=false)
sage: S=V.plot(cell_colors=['red','blue','red','white', 'white'])
sage: show(S, xmin=0, xmax=1, ymin=0, ymax=1, aspect_ratio=1, axes=false)
sage: S=V.plot(cell_colors='something else')
Traceback (most recent call last):
...
AssertionError: 'cell_colors' must be a list or a dictionary
Trying to plot a Voronoi diagram of dimension other than 2 gives an
error::
sage: VoronoiDiagram([[1, 2, 3], [6, 5, 4]]).plot()
Traceback (most recent call last):
...
NotImplementedError: Plotting of 3-dimensional Voronoi diagrams not
implemented
"""
if self.ambient_dim() == 2:
S = line([])
if cell_colors is None:
from random import shuffle
cell_colors = rainbow(self._n)
shuffle(cell_colors)
else:
if not (isinstance(cell_colors, list) or (isinstance(cell_colors, dict))):
raise AssertionError("'cell_colors' must be a list or a dictionary")
for i, p in enumerate(self._P):
col = cell_colors[i]
S += (self.regions()[p]).render_solid(color=col, zorder=1)
S += point(p, color=col, pointsize=10, zorder=3)
S += point(p, color='black', pointsize=20, zorder=2)
return plot(S, **kwds)
raise NotImplementedError('Plotting of ' + str(self.ambient_dim()) +
'-dimensional Voronoi diagrams not' +
' implemented')
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_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 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:
- 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 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
