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20120516a.py
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20120516a.py
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"""
Show that Jukes-Cantor identity slope plots can cross twice.
"""
from StringIO import StringIO
import string
import math
import numpy as np
import Form
import FormOut
import tikz
import latexutil
import iterutils
import mrate
import bezier
import JC69
def get_form():
"""
@return: the body of a form
"""
form_objects = [
Form.Float('plot_width', 'plot width in tikz units',
'9', low_exclusive=0, high_exclusive=20),
Form.Float('plot_height', 'plot height in tikz units',
'6', low_exclusive=0, high_exclusive=20),
Form.Float('t_max', 'max time',
'5', low_exclusive=0),
Form.Integer('a_N', 'first state cardinality', 4, low=2),
Form.Integer('b_N', 'second state cardinality', 16, low=2),
Form.Float('a_mu', 'first randomization rate',
'1.2', low_exclusive=0),
Form.Float('b_mu', 'second randomization rate',
'1.0', low_exclusive=0),
Form.TikzFormat()]
return form_objects
def get_form_out():
return FormOut.Tikz()
def get_tikz_bezier(bchunks):
"""
@param bchunks: a sequence of 2d bezier chunks
@return: multiline bezier text
"""
lines = []
# draw everything except for the last point of the last chunk
for b in bchunks:
pts = [tikz.point_to_tikz(p) for p in b.get_points()[:-1]]
lines.append('%s .. controls %s and %s ..' % tuple(pts))
# draw the last point of the last chunk
lines.append('%s;' % tikz.point_to_tikz(bchunks[-1].p3))
return '\n'.join(lines)
def get_seg(pta, ptb):
return '%s -- %s' % (tikz.point_to_tikz(pta), tikz.point_to_tikz(ptb))
def get_segment(pta, ptb):
return get_seg(pta, ptb) + ';'
def get_tikz_body(fs):
out = StringIO()
# define user variables
plot_width = fs.plot_width
plot_height = fs.plot_height
timescale = fs.t_max
# create the function objects
f_a = JC69.IdentitySlopeInformation(fs.a_mu, fs.a_N)
f_b = JC69.IdentitySlopeInformation(fs.b_mu, fs.b_N)
# Define some times for evaluation of the curve.
times = [timescale*2**-i for i in range(10)]
# define some more intermediate values
ymax = max(f_a(min(times)), f_b(min(times))) * 1.2
plotscale = np.array((plot_width / timescale, plot_height / ymax))
origin = (0, 0)
# draw the boundary of the plot
print >> out, r'\draw[color=gray] %s %s {%s} %s;' % (
tikz.point_to_tikz(origin),
'edge node[color=black,below]',
'$t$',
tikz.point_to_tikz((plot_width, 0)))
print >> out, r'\draw[color=gray] ' + get_segment(
origin, (0, plot_height))
# draw the bezier curves hitting the right knots
for f in (f_a, f_b):
bchunks = []
for a, b in iterutils.pairwise(sorted(times)):
pta = np.array((a, f(a)))
ptb = np.array((b, f(b)))
dta = np.array((1, f.deriv(a)))
dtb = np.array((1, f.deriv(b)))
bchunk = bezier.create_bchunk_hermite(
a, b,
pta * plotscale, ptb * plotscale,
dta * plotscale, dtb * plotscale)
bchunks.append(bchunk)
print >> out, r'\draw[color=gray] ' + get_tikz_bezier(bchunks)
# draw filled black dots at some intersections
dot_points = [origin]
dot_points.append((0, f_a(0)))
dot_points.append((0, f_b(0)))
for p in dot_points:
print >> out, r'\fill[color=black,inner sep=0pt]',
print >> out, tikz.point_to_tikz(np.array(p) * plotscale),
print >> out, 'circle (1pt);'
# draw some text annotations
pt_txt_pairs = [
((0, 0), '0'),
]
for i, (pt, txt) in enumerate(pt_txt_pairs):
print >> out, r'\node[anchor=east] (%s) at %s {%s};' % (
'ylabel%d' % i,
tikz.point_to_tikz(pt),
txt)
#
return out.getvalue().rstrip()
def get_response_content(fs):
"""
@param fs: a FieldStorage object containing the cgi arguments
@return: the response
"""
tikz_body = get_tikz_body(fs)
tikzpicture = tikz.get_picture(tikz_body, 'auto')
return tikz.get_response(tikzpicture, fs.tikzformat)