def plot_known(self):
r"""
TESTS::
sage: from ore_algebra import *
sage: from ore_algebra.analytic.function import DFiniteFunction
sage: DiffOps, x, Dx = DifferentialOperators()
sage: f = DFiniteFunction((x^2 + 1)*Dx^2 + 2*x*Dx, [0, 1])
sage: f(-10, 100) # long time
[-1.4711276743037345918528755717...]
sage: f.approx(5, post_transform=Dx) # long time
[0.038461538461538...]
sage: f.plot_known() # long time
Graphics object consisting of ... graphics primitives
"""
g = plot.Graphics()
for center, polys in self._polys.iteritems():
center, rad = self._disk(Point(center, self.dop))
xrange = (center - rad).mid(), (center + rad).mid()
for i, a in enumerate(polys):
# color palette copied from sage.plot.plot.plot
color = plot.Color((0.66666 + i * 0.61803) % 1,
1,
0.4,
space='hsl')
Balls = a.pol.base_ring()
g += plot.plot(lambda x: a.pol(Balls(x)).mid(),
xrange,
color=color)
g += plot.text(str(a.prec), (center, a.pol(center).mid()),
color=color)
for point, ini in self._inivecs.iteritems():
g += plot.point2d((point, 0), size=50)
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 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')