def plot_n_matrices_eigenvectors(self, n, side='right', color_index=0, draw_line=False):
r"""
INPUT:
- ``n`` -- integer, length
- ``side`` -- ``'left'`` or ``'right'``, drawing left or right
eigenvectors
- ``color_index`` -- 0 for first letter, -1 for last letter
- ``draw_line`` -- boolean
EXAMPLES::
sage: from slabbe.matrix_cocycle import cocycles
sage: ARP = cocycles.ARP()
sage: G = ARP.plot_n_matrices_eigenvectors(2)
"""
from sage.plot.graphics import Graphics
from sage.plot.point import point
from sage.plot.line import line
from sage.plot.text import text
from sage.plot.colors import hue
from sage.modules.free_module_element import vector
from matrices import M3to2
R = self.n_matrices_eigenvectors(n)
L = [(w, M3to2*(a/sum(a)), M3to2*(b/sum(b))) for (w,a,b) in R]
G = Graphics()
alphabet = self._language._alphabet
color_ = dict( (letter, hue(i/float(len(alphabet)))) for i,letter in
enumerate(alphabet))
for letter in alphabet:
L_filtered = [(w,p1,p2) for (w,p1,p2) in L if w[color_index] == letter]
words,rights,lefts = zip(*L_filtered)
if side == 'right':
G += point(rights, color=color_[letter], legend_label=letter)
elif side == 'left':
G += point(lefts, color=color_[letter], legend_label=letter)
else:
raise ValueError("side(=%s) should be left or right" % side)
if draw_line:
for (a,b) in L:
G += line([a,b], color='black', linestyle=":")
G += line([M3to2*vector(a) for a in [(1,0,0), (0,1,0), (0,0,1), (1,0,0)]])
title = "%s eigenvectors, colored by letter w[%s] of cylinder w" % (side, color_index)
G += text(title, (0.5, 1.05), axis_coords=True)
G.axes(False)
return G
def plot_n_matrices_eigenvectors(self, n, side='right', color_index=0, draw_line=False):
r"""
INPUT:
- ``n`` -- integer, length
- ``side`` -- ``'left'`` or ``'right'``, drawing left or right
eigenvectors
- ``color_index`` -- 0 for first letter, -1 for last letter
- ``draw_line`` -- boolean
EXAMPLES::
sage: from slabbe.matrix_cocycle import cocycles
sage: ARP = cocycles.ARP()
sage: G = ARP.plot_n_matrices_eigenvectors(2)
"""
from sage.plot.graphics import Graphics
from sage.plot.point import point
from sage.plot.line import line
from sage.plot.text import text
from sage.plot.colors import hue
from sage.modules.free_module_element import vector
from .matrices import M3to2
R = self.n_matrices_eigenvectors(n)
L = [(w, M3to2*(a/sum(a)), M3to2*(b/sum(b))) for (w,a,b) in R]
G = Graphics()
alphabet = self._language._alphabet
color_ = dict( (letter, hue(i/float(len(alphabet)))) for i,letter in
enumerate(alphabet))
for letter in alphabet:
L_filtered = [(w,p1,p2) for (w,p1,p2) in L if w[color_index] == letter]
words,rights,lefts = zip(*L_filtered)
if side == 'right':
G += point(rights, color=color_[letter], legend_label=letter)
elif side == 'left':
G += point(lefts, color=color_[letter], legend_label=letter)
else:
raise ValueError("side(=%s) should be left or right" % side)
if draw_line:
for (a,b) in L:
G += line([a,b], color='black', linestyle=":")
G += line([M3to2*vector(a) for a in [(1,0,0), (0,1,0), (0,0,1), (1,0,0)]])
title = "%s eigenvectors, colored by letter w[%s] of cylinder w" % (side, color_index)
G += text(title, (0.5, 1.05), axis_coords=True)
G.axes(False)
return G
def options(self):
"""
Return the dictionary of options for this graphics primitive.
By default this function verifies that the options are all
valid; if any aren't, then a verbose message is printed with level 0.
EXAMPLES::
sage: from sage.plot.primitive import GraphicPrimitive
sage: GraphicPrimitive({}).options()
{}
"""
from sage.plot.graphics import do_verify
from sage.plot.colors import hue
O = dict(self._options)
if do_verify:
A = self._allowed_options()
t = False
K = A.keys() + ['xmin', 'xmax', 'ymin', 'ymax', 'axes']
for k in O.keys():
if not k in K:
do_verify = False
verbose("WARNING: Ignoring option '%s'=%s"%(k,O[k]), level=0)
t = True
if t:
s = "\nThe allowed options for %s are:\n"%self
K.sort()
for k in K:
if A.has_key(k):
s += " %-15s%-60s\n"%(k,A[k])
verbose(s, level=0)
if 'hue' in O:
t = O['hue']
if not isinstance(t, (tuple,list)):
t = [t,1,1]
O['rgbcolor'] = hue(*t)
del O['hue']
return O
def options(self):
"""
Return the dictionary of options for this graphics primitive.
By default this function verifies that the options are all
valid; if any aren't, then a verbose message is printed with level 0.
EXAMPLES::
sage: from sage.plot.primitive import GraphicPrimitive
sage: GraphicPrimitive({}).options()
{}
"""
from sage.plot.plot import do_verify
from sage.plot.colors import hue
O = dict(self.__options)
if do_verify:
A = self._allowed_options()
t = False
K = A.keys() + ['xmin', 'xmax', 'ymin', 'ymax', 'axes']
for k in O.keys():
if not k in K:
do_verify = False
verbose("WARNING: Ignoring option '%s'=%s" % (k, O[k]),
level=0)
t = True
if t:
s = "\nThe allowed options for %s are:\n" % self
K.sort()
for k in K:
if A.has_key(k):
s += " %-15s%-60s\n" % (k, A[k])
verbose(s, level=0)
if 'hue' in O:
t = O['hue']
if not isinstance(t, (tuple, list)):
t = [t, 1, 1]
O['rgbcolor'] = hue(*t)
del O['hue']
return O
self._max = max(sw_z[0], nw_z[0], se_z[0], ne_z[0], mid_z[0])
# jump in and start building blocks
outer = self.plot_block(min_x, mid_x, max_x, min_y, mid_y, max_y, sw_z,
nw_z, se_z, ne_z, mid_z, 0)
# build the boundary triangles
self.triangulate(outer.left, outer.left_c)
self.triangulate(outer.top, outer.top_c)
self.triangulate(outer.right, outer.right_c)
self.triangulate(outer.bottom, outer.bottom_c)
zrange = self._max - self._min
if num_colors is not None and zrange != 0:
colors = triangle_factory.get_colors(
[hue(float(i / num_colors)) for i in range(num_colors)])
for o in self._objects:
vertices = o.get_vertices()
avg_z = (vertices[0][2] + vertices[1][2] + vertices[2][2]) / 3
o.set_color(colors[int(num_colors * (avg_z - self._min) /
zrange)])
def plot_block(self, min_x, mid_x, max_x, min_y, mid_y, max_y, sw_z, nw_z,
se_z, ne_z, mid_z, depth):
"""
Recursive triangulation function for plotting.
First six inputs are scalars, next 5 are 2-dimensional lists, and the depth argument
keeps track of the depth of recursion.
TESTS::
def __init__(self,
triangle_factory,
f,
min_x__max_x,
min_y__max_y,
g=None,
min_depth=4,
max_depth=8,
num_colors=None,
max_bend=.3):
"""
TESTS::
sage: from sage.plot.plot3d.tri_plot import TrianglePlot, TriangleFactory
sage: tf = TriangleFactory()
sage: t = TrianglePlot(tf, lambda x,y: x^2+y^2, (0, 1), (0, 1))
sage: t._f(1,1)
2
"""
(min_x, max_x) = min_x__max_x
(min_y, max_y) = min_y__max_y
self._triangle_factory = triangle_factory
self._f = f
self._g = g
self._min_depth = min_depth
self._max_depth = max_depth
self._max_bend = max_bend
self._objects = []
if min(max_x - min_x, max_y - min_y) == 0:
raise ValueError(
'Plot rectangle is really a line. Make sure min_x != max_x and min_y != max_y.'
)
self._num_colors = num_colors
if g is None:
def fcn(x, y):
return [self._f(x, y)]
else:
def fcn(x, y):
return [self._f(x, y), self._g(x, y)]
self._fcn = fcn
# generate the necessary data to kick-start the recursion
mid_x = (min_x + max_x) / 2
mid_y = (min_y + max_y) / 2
sw_z = fcn(min_x, min_y)
nw_z = fcn(min_x, max_y)
se_z = fcn(max_x, min_y)
ne_z = fcn(max_x, max_y)
mid_z = fcn(mid_x, mid_y)
self._min = min(sw_z[0], nw_z[0], se_z[0], ne_z[0], mid_z[0])
self._max = max(sw_z[0], nw_z[0], se_z[0], ne_z[0], mid_z[0])
# jump in and start building blocks
outer = self.plot_block(min_x, mid_x, max_x, min_y, mid_y, max_y, sw_z,
nw_z, se_z, ne_z, mid_z, 0)
# build the boundary triangles
self.triangulate(outer.left, outer.left_c)
self.triangulate(outer.top, outer.top_c)
self.triangulate(outer.right, outer.right_c)
self.triangulate(outer.bottom, outer.bottom_c)
zrange = self._max - self._min
if num_colors is not None and zrange != 0:
colors = triangle_factory.get_colors(
[hue(float(i / num_colors)) for i in range(num_colors)])
for o in self._objects:
vertices = o.get_vertices()
avg_z = (vertices[0][2] + vertices[1][2] + vertices[2][2]) / 3
o.set_color(colors[int(num_colors * (avg_z - self._min) /
zrange)])
self._min = min(sw_z[0], nw_z[0], se_z[0], ne_z[0], mid_z[0])
self._max = max(sw_z[0], nw_z[0], se_z[0], ne_z[0], mid_z[0])
# jump in and start building blocks
outer = self.plot_block(min_x, mid_x, max_x, min_y, mid_y, max_y, sw_z, nw_z, se_z, ne_z, mid_z, 0)
# build the boundary triangles
self.triangulate(outer.left, outer.left_c)
self.triangulate(outer.top, outer.top_c)
self.triangulate(outer.right, outer.right_c)
self.triangulate(outer.bottom, outer.bottom_c)
zrange = self._max - self._min
if num_colors is not None and zrange != 0:
colors = triangle_factory.get_colors([hue(float(i/num_colors)) for i in range(num_colors)])
for o in self._objects:
vertices = o.get_vertices()
avg_z = (vertices[0][2] + vertices[1][2] + vertices[2][2])/3
o.set_color(colors[int(num_colors * (avg_z - self._min) / zrange)])
def plot_block(self, min_x, mid_x, max_x, min_y, mid_y, max_y, sw_z, nw_z, se_z, ne_z, mid_z, depth):
"""
Recursive triangulation function for plotting.
First six inputs are scalars, next 5 are 2-dimensional lists, and the depth argument
keeps track of the depth of recursion.
TESTS::
sage: from sage.plot.plot3d.tri_plot import TrianglePlot, TriangleFactory
def __init__(self, triangle_factory, f, min_x__max_x, min_y__max_y, g = None,
min_depth=4, max_depth=8, num_colors = None, max_bend=.3):
"""
TESTS::
sage: from sage.plot.plot3d.tri_plot import TrianglePlot, TriangleFactory
sage: tf = TriangleFactory()
sage: t = TrianglePlot(tf, lambda x,y: x^2+y^2, (0, 1), (0, 1))
sage: t._f(1,1)
2
"""
(min_x, max_x) = min_x__max_x
(min_y, max_y) = min_y__max_y
self._triangle_factory = triangle_factory
self._f = f
self._g = g
self._min_depth = min_depth
self._max_depth = max_depth
self._max_bend = max_bend
self._objects = []
if min(max_x - min_x, max_y - min_y) == 0:
raise ValueError('Plot rectangle is really a line. Make sure min_x != max_x and min_y != max_y.')
self._num_colors = num_colors
if g is None:
def fcn(x,y):
return [self._f(x,y)]
else:
def fcn(x,y):
return [self._f(x,y), self._g(x,y)]
self._fcn = fcn
# generate the necessary data to kick-start the recursion
mid_x = (min_x + max_x)/2
mid_y = (min_y + max_y)/2
sw_z = fcn(min_x,min_y)
nw_z = fcn(min_x,max_y)
se_z = fcn(max_x,min_y)
ne_z = fcn(max_x,max_y)
mid_z = fcn(mid_x,mid_y)
self._min = min(sw_z[0], nw_z[0], se_z[0], ne_z[0], mid_z[0])
self._max = max(sw_z[0], nw_z[0], se_z[0], ne_z[0], mid_z[0])
# jump in and start building blocks
outer = self.plot_block(min_x, mid_x, max_x, min_y, mid_y, max_y, sw_z, nw_z, se_z, ne_z, mid_z, 0)
# build the boundary triangles
self.triangulate(outer.left, outer.left_c)
self.triangulate(outer.top, outer.top_c)
self.triangulate(outer.right, outer.right_c)
self.triangulate(outer.bottom, outer.bottom_c)
zrange = self._max - self._min
if num_colors is not None and zrange != 0:
colors = triangle_factory.get_colors([hue(float(i/num_colors)) for i in range(num_colors)])
for o in self._objects:
vertices = o.get_vertices()
avg_z = (vertices[0][2] + vertices[1][2] + vertices[2][2])/3
o.set_color(colors[int(num_colors * (avg_z - self._min) / zrange)])
