def main():
initial_copies = 20
m = model.create(propensities=[lambda x: initial_copies - x],
transitions=[(1, )],
shape=(initial_copies + 1, ),
initial_state=(0, ))
s = solver.create(model=m, sink=False)
r = recorder.create((('A->B', ), ))
time_steps = numpy.linspace(0.0, 3.0, 6)
for t in time_steps:
s.step(t)
r.write(t, s.y)
pylab.figure()
for t, d in zip(r['A->B'].times, r['A->B'].distributions):
marginal = d.to_dense(m.shape)
pylab.plot(marginal, label='t = %.1f' % t)
pylab.xlabel('Reaction count')
pylab.ylabel('Probability')
pylab.legend()
pylab.savefig('simple_plot.png')
def main():
initial_copies = 20
m = model.create(
propensities = [lambda x: initial_copies - x],
transitions = [(1, )],
shape = (initial_copies + 1, ),
initial_state = (0, )
)
s = solver.create(
model = m,
sink = False
)
r = recorder.create(
(('A->B', ), )
)
time_steps = numpy.linspace(0.0, 3.0, 6)
for t in time_steps:
s.step(t)
r.write(t, s.y)
pylab.figure()
for t, d in zip(r['A->B'].times, r['A->B'].distributions):
marginal = d.to_dense(m.shape)
pylab.plot(marginal, label = 't = %.1f' % t)
pylab.xlabel('Reaction count')
pylab.ylabel('Probability')
pylab.legend()
pylab.savefig('simple_plot.png')
def main():
"""
the complete example from the slides
"""
import numpy
from cmepy import solver, recorder, model
from cmepy.util import non_neg
s_0 = 50
e_0 = 10
s = lambda *x : x[0]
e = lambda *x : non_neg(e_0 - x[1])
c = lambda *x : x[1]
p = lambda *x : non_neg(s_0 - x[0] - x[1])
m = model.create(
species_counts = (s, e, c, p, ),
propensities = (
lambda *x : 0.01*s(*x)*e(*x),
lambda *x : 35.0*c(*x),
lambda *x : 30.0*c(*x),
),
transitions = (
(-1, 1),
(1, -1),
(0, -1)
),
shape = (s_0 + 1, min(s_0, e_0) + 1),
initial_state = (s_0, 0)
)
enzyme_solver = solver.create(
model = m,
sink = False
)
time_steps = numpy.linspace(0.0, 10.0, 101)
r = recorder.create(
(['S', 'E', 'C', 'P'], m.species_counts)
)
for t in time_steps:
enzyme_solver.step(t)
r.write(t, enzyme_solver.y)
recorder.display_plots(r)
def main():
"""
Solves the competing clonotypes model and plots results
"""
import pylab
from cmepy import solver, recorder
m = create_model()
s = solver.create(
model = m,
sink = True,
time_dependencies = create_time_dependencies()
)
r = recorder.create(
(m.species, m.species_counts)
)
t_final = 15.0
steps_per_time = 1
time_steps = numpy.linspace(0.0, t_final, int(steps_per_time*t_final) + 1)
for t in time_steps:
s.step(t)
p, p_sink = s.y
print 't : %.2f, truncation error : %.2g' % (t, p_sink)
r.write(t, p)
# display a series of contour plots of P(A, B; t) for varying t
measurement = r[('A', 'B')]
epsilon = 1.0e-5
for t, marginal in zip(measurement.times, measurement.distributions):
pylab.figure()
pylab.contourf(
marginal.compress(epsilon).to_dense(m.shape)
)
pylab.title('P(A, B; t = %.f)' % t)
pylab.ylabel('species A count')
pylab.xlabel('species B count')
pylab.show()
def main():
import numpy
from cmepy import solver, recorder, model
from cmepy.util import non_neg
s_0 = 50
e_0 = 10
s = lambda *x : x[0]
e = lambda *x : non_neg(e_0 - x[1])
c = lambda *x : x[1]
p = lambda *x : non_neg(s_0 - x[0] - x[1])
m = model.create(
species_counts = (s, e, c, p, ),
propensities = (
lambda *x : 0.01*s(*x)*e(*x),
lambda *x : 35.0*c(*x),
lambda *x : 30.0*c(*x),
),
transitions = (
(-1, 1),
(1, -1),
(0, -1)
),
shape = (s_0 + 1, min(s_0, e_0) + 1),
initial_state = (s_0, 0)
)
enzyme_solver = solver.create(
model = m,
sink = False
)
time_steps = numpy.linspace(0.0, 30.0, 101)
species = ['S', 'E', 'C', 'P']
r = recorder.create(
(species, m.species_counts)
)
for t in time_steps:
enzyme_solver.step(t)
r.write(t, enzyme_solver.y)
import pylab
species_colours = {
'S' : 'r',
'E' : 'k',
'C' : 'g',
'P' : 'b',
}
pylab.figure()
for var in species:
colour = species_colours[var]
measurement = r[var]
mu = numpy.reshape(numpy.array(measurement.expected_value), (-1, ))
sigma = numpy.array(measurement.standard_deviation)
mu_style = '-'+colour
mu_pm_sigma_style = '--'+colour
pylab.plot(measurement.times, mu, mu_style, label = var)
pylab.plot(measurement.times, mu + sigma, mu_pm_sigma_style)
pylab.plot(measurement.times, mu - sigma, mu_pm_sigma_style)
title_lines = (
'Enzymatic Reaction Species Counts:',
'expected values $\pm$ 1 standard deviation',
)
pylab.title('\n'.join(title_lines))
pylab.xlabel('time')
pylab.ylabel('species count')
pylab.legend()
pylab.show()
