def main():
import numpy
from cmepy import domain
import cmepy.solver
import cmepy.recorder
max_s1_copies = 40
max_s2_copies = 100
m = create_model_gene_toggle(max_s1_copies, max_s2_copies)
# define domain states as union of two rectangular regions along the axes
a_shape = (max_s1_copies, 6)
b_shape = (10, max_s2_copies)
domain_states_a = set(domain.to_iter(domain.from_rect(a_shape)))
domain_states_b = set(domain.to_iter(domain.from_rect(b_shape)))
states = domain.from_iter(domain_states_a | domain_states_b)
solver = cmepy.solver.create(m, sink=True, domain_states=states)
recorder = cmepy.recorder.create((m.species, m.species_counts))
time_steps = numpy.linspace(0.0, 100.0, 101)
for t in time_steps:
solver.step(t)
p, p_sink = solver.y
print('t = {:.4}; p_sink = {:.4E}'.format(t, p_sink))
recorder.write(t, p)
cmepy.recorder.display_plots(recorder, title=m.name)
def test_rect_offset_domain(self):
shape = (4, 7, 3)
origin = (3, -2, 2)
states = domain.from_rect(shape, origin=origin)
vect_origin = numpy.asarray(origin)[:, numpy.newaxis]
goal_states = numpy.reshape(numpy.indices(shape), (len(shape), -1))
goal_states += vect_origin
assert_array_equal(states, goal_states)
def test_rect_offset_domain(self):
shape = (4, 7, 3)
origin = (3, -2, 2)
states = domain.from_rect(shape, origin=origin)
vect_origin = numpy.asarray(origin)[:, numpy.newaxis]
goal_states = numpy.reshape(numpy.indices(shape), (len(shape), -1))
goal_states += vect_origin
assert_array_equal(states, goal_states)
def main():
import numpy
from cmepy import domain
import cmepy.solver
import cmepy.recorder
max_s1_copies = 40
max_s2_copies = 100
m = create_model_gene_toggle(max_s1_copies, max_s2_copies)
# define domain states as union of two rectangular regions along the axes
a_shape = (max_s1_copies, 6)
b_shape = (10, max_s2_copies)
domain_states_a = set(domain.to_iter(domain.from_rect(a_shape)))
domain_states_b = set(domain.to_iter(domain.from_rect(b_shape)))
states = domain.from_iter(domain_states_a | domain_states_b)
solver = cmepy.solver.create(
m,
sink = True,
domain_states = states
)
recorder = cmepy.recorder.create(
(m.species,
m.species_counts)
)
time_steps = numpy.linspace(0.0, 100.0, 101)
for t in time_steps:
solver.step(t)
p, p_sink = solver.y
print 't = %g; p_sink = %g' % (t, p_sink)
recorder.write(t, p)
cmepy.recorder.display_plots(recorder,
title = m.name)
def to_dense(self, shape, origin=None):
"""
Returns dense version of distribution for given array shape and origin
"""
if origin is None:
origin = (0, ) * len(shape)
states = set(domain.to_iter(domain.from_rect(shape, origin=origin)))
states &= set(self.keys())
p_dense = numpy.zeros(shape, dtype=numpy.float)
origin = numpy.asarray(origin)
for state in states:
probability = self[state]
shifted_state = tuple(numpy.asarray(state) + origin)
p_dense[shifted_state] += probability
return p_dense
def to_dense(self, shape, origin=None):
"""
Returns dense version of distribution for given array shape and origin
"""
if origin is None:
origin = (0, )*len(shape)
states = set(domain.to_iter(domain.from_rect(shape, origin=origin)))
states &= set(self.iterkeys())
p_dense = numpy.zeros(shape, dtype=numpy.float)
origin = numpy.asarray(origin)
for state in states:
probability = self[state]
shifted_state = tuple(numpy.asarray(state) + origin)
p_dense[shifted_state] += probability
return p_dense
def test_rect_domain(self):
shape = (3, 1, 3, 8)
states = domain.from_rect(shape)
goal_states = numpy.reshape(numpy.indices(shape), (len(shape), -1))
assert_array_equal(states, goal_states)
def create(model, sink, p_0=None, t_0=None, sink_0=None, time_dependencies=None, domain_states=None):
"""
Returns a solver for the Chemical Master Equation of the given model.
arguments:
model : the CME model to solve
sink : If sink is True, the solver will include a 'sink' state used
to accumulate any probability that may flow outside the domain.
This can be used to measure the error in the solution due to
truncation of the domain. If sink is False, the solver will not
include a 'sink' state, and probability will be artificially
prevented from flowing outside of the domain.
p_0 : (optional) mapping from states in the domain to probabilities,
for the initial probability distribution. If not specified,
and the initial state of the state space is given by the model,
defaults to all probability concentrated at the initial state,
otherwise, a ValueError will be raised.
t_0 : (optional) initial time, defaults to 0.0
sink_0 : (optional) initial sink probability, defaults to 0.0
Only a valid argument if sink is set to True.
time_dependencies : (optional) By default, reaction propensities are
time independent. If specified, time_dependencies must be of the
form { s_1 : phi_1, ..., s_n : phi_n }, where each (s_j, phi_j)
item satisifes :
s_j : set of reaction indices
phi_j : phi_j(t) -> time dependent coefficient
The propensities of the reactions with indicies contained in s_j
will all be multiplied by the coefficient phi_j(t), at time t.
Reactions are indexed according to the ordering of the propensities
in the model.
The reaction index sets s_j must be *disjoint*. It is not necessary
for the union of the s_j to include all the reaction indices.
If a reaction's index is not contained in any s_j then the reaction
is treated as time-independent.
mapping of time dependent coefficient
functions keyed by subsets of reaction indices, with respect to the
ordering of reactions determined by the order of the propensity
functions inside the model. The propensities of the reactions
with indices included in each subset are multiplied by the time
dependent coefficient function. By default, no time dependent
coefficient functions are specified, that is, the CME has
time-independent propensities.
domain_states : (optional) array of states in the domain.
By default, generate the rectangular lattice of states defined by
the 'shape' entry of the model. A ValueError is raised if both
domain_states and 'shape' are unspecified.
"""
mdl.validate_model(model)
if sink_0 is not None:
if not sink:
raise ValueError("sink_0 may not be specified if sink is False")
sink_0 = float(sink_0)
else:
sink_0 = 0.0
# determine states in domain, then construct an enumeration of the
# domain states
if domain_states is None:
if mdl.SHAPE not in model:
lament = "if no states given, model must contain key '%s'"
raise KeyError(lament % mdl.SHAPE)
else:
domain_states = domain.from_rect(shape=model.shape)
domain_enum = state_enum.create(domain_states)
# determine p_0, then construct a dense representation with respect to
# the domain enumeration
initial_state = model.get(mdl.INITIAL_STATE, None)
if p_0 is None:
if initial_state is None:
lament = "if no p_0 given, model must contain key '%s'"
raise ValueError(lament % mdl.INITIAL_STATE)
else:
p_0 = {initial_state: 1.0}
if t_0 is None:
t_0 = 0.0
member_flags = domain_enum.contains(domain.from_iter(p_0))
if not numpy.logical_and.reduce(member_flags):
raise ValueError("support of p_0 is not a subset of domain_states")
# compute reaction matrices and use them to define differential equations
gen_matrices = cme_matrix.gen_reaction_matrices(model, domain_enum, sink, cme_matrix.non_neg_states)
reaction_matrices = list(gen_matrices)
dy_dt = cme_matrix.create_diff_eqs(reaction_matrices, phi=time_dependencies)
# construct and initialise solver
if sink:
cme_solver = ode_solver.Solver(dy_dt, y_0=(p_0, sink_0), t_0=t_0)
pack, unpack = create_packing_functions(domain_enum)
cme_solver.set_packing(pack, unpack, transform_dy_dt=False)
else:
pack = domain_enum.pack_distribution
unpack = domain_enum.unpack_distribution
cme_solver = ode_solver.Solver(dy_dt, y_0=p_0, t_0=t_0)
cme_solver.set_packing(pack, unpack, transform_dy_dt=False)
return cme_solver
def create(model,
sink,
p_0=None,
t_0=None,
sink_0=None,
time_dependencies=None,
domain_states=None,
solver=ode_solver.Solver,
outflow=False,
**solver_args):
"""
Returns a solver for the Chemical Master Equation of the given model.
arguments:
model : the CME model to solve
sink : If sink is True, the solver will include a 'sink' state used
to accumulate any probability that may flow outside the domain.
This can be used to measure the error in the solution due to
truncation of the domain. If sink is False, the solver will not
include a 'sink' state, and probability will be artificially
prevented from flowing outside of the domain.
p_0 : (optional) mapping from states in the domain to probabilities,
for the initial probability distribution. If not specified,
and the initial state of the state space is given by the model,
defaults to all probability concentrated at the initial state,
otherwise, a ValueError will be raised.
t_0 : (optional) initial time, defaults to 0.0
sink_0 : (optional) initial sink probability, defaults to 0.0
Only a valid argument if sink is set to True.
time_dependencies : (optional) By default, reaction propensities are
time independent. If specified, time_dependencies must be of the
form { s_1 : phi_1, ..., s_n : phi_n }, where each (s_j, phi_j)
item satisifes :
s_j : set of reaction indices
phi_j : phi_j(t) -> time dependent coefficient
The propensities of the reactions with indicies contained in s_j
will all be multiplied by the coefficient phi_j(t), at time t.
Reactions are indexed according to the ordering of the propensities
in the model.
The reaction index sets s_j must be *disjoint*. It is not necessary
for the union of the s_j to include all the reaction indices.
If a reaction's index is not contained in any s_j then the reaction
is treated as time-independent.
mapping of time dependent coefficient
functions keyed by subsets of reaction indices, with respect to the
ordering of reactions determined by the order of the propensity
functions inside the model. The propensities of the reactions
with indices included in each subset are multiplied by the time
dependent coefficient function. By default, no time dependent
coefficient functions are specified, that is, the CME has
time-independent propensities.
domain_states : (optional) array of states in the domain.
By default, generate the rectangular lattice of states defined by
the 'shape' entry of the model. A ValueError is raised if both
domain_states and 'shape' are unspecified.
"""
mdl.validate_model(model)
if sink and outflow:
raise ValueError('sink and outflow cannot be both True')
if sink_0 is not None:
if not sink:
raise ValueError('sink_0 may not be specified if sink is False')
sink_0 = float(sink_0)
else:
sink_0 = 0.0
# determine states in domain, then construct an enumeration of the
# domain states
if domain_states is None:
if mdl.SHAPE not in model:
lament = 'if no states given, model must contain key \'%s\''
raise KeyError(lament % mdl.SHAPE)
else:
domain_states = domain.from_rect(shape=model.shape)
domain_enum = state_enum.create(domain_states)
# determine p_0, then construct a dense representation with respect to
# the domain enumeration
initial_state = model.get(mdl.INITIAL_STATE, None)
if p_0 is None:
if initial_state is None:
lament = 'if no p_0 given, model must contain key \'%s\''
raise ValueError(lament % mdl.INITIAL_STATE)
else:
p_0 = {initial_state: 1.0}
if t_0 is None:
t_0 = 0.0
member_flags = domain_enum.contains(domain.from_iter(p_0))
if not numpy.logical_and.reduce(member_flags):
raise ValueError('support of p_0 is not a subset of domain_states')
# compute reaction matrices and use them to define differential equations
gen_matrices = cme_matrix.gen_reaction_matrices(model,
domain_enum,
sink,
cme_matrix.non_neg_states,
outflow=outflow)
reaction_matrices = list(gen_matrices)
dy_dt = cme_matrix.create_diff_eqs(reaction_matrices,
phi=time_dependencies)
if solver_args:
solver_args['reaction_matrices'] = reaction_matrices
# construct and initialise solver
if sink:
cme_solver = solver(dy_dt, y_0=(p_0, sink_0), t_0=t_0, **solver_args)
pack, unpack = create_packing_functions(domain_enum)
cme_solver.set_packing(pack, unpack, transform_dy_dt=False)
else:
pack = domain_enum.pack_distribution
unpack = domain_enum.unpack_distribution
cme_solver = solver(dy_dt, y_0=p_0, t_0=t_0, **solver_args)
cme_solver.set_packing(pack, unpack, transform_dy_dt=False)
return cme_solver
def test_rect_domain(self):
shape = (3, 1, 3, 8)
states = domain.from_rect(shape)
goal_states = numpy.reshape(numpy.indices(shape), (len(shape), -1))
assert_array_equal(states, goal_states)