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 gen_reaction_matrices(model,
domain_enum,
sink,
validity_test):
"""
Returns generator yielding the sparse matrices for each reaction term.
Generator yielding the sparse matrices for the dp/dt term of each reaction,
matching the ordering implied by the ordering of the reaction propensity
functions and transtions in the model.
Arguments:
* ``domain_enum`` : :class:`StateEnum` instance enumerating the states
in the domain
* ``sink`` : boolean flag indicating if the reaction matrices should add
a 'sink' state used to accumulate probability that flows outside
of the domain. If sink is set to ``True``, the index of the sink state
is chosen to be ``domain_enum.size``
* ``validity_test`` : a function of the form
validity_test(state_array) -> bool_array
Returns a boolean array of flags corresponding to those states in
``state_array`` that are valid.
See: non_neg_states(state_array)
"""
mdl.validate_model(model)
if domain_enum.offset != 0:
raise NotImplementedError('non-zero domain_enum offset unsupported')
sink = bool(sink)
if sink:
sink_index = domain_enum.size
propensities = model.propensities
transitions = model.transitions
reactions = itertools.izip(propensities, transitions)
src_states = numpy.array(domain_enum.ordered_states)
src_indices = domain_enum.indices(src_states)
for (propensity, transition) in reactions:
# compute destination states for this transition
transition = numpy.asarray(transition)[:, numpy.newaxis]
dst_states = src_states + transition
# determine which states have destination states inside the
# truncated domain. these will be defined as the 'interior' states.
# conversely, 'exterior' states are those states of the truncated
# domain with destination states not in the domain.
interior = domain_enum.contains(dst_states)
exterior = numpy.logical_not(interior)
num_int_states = numpy.add.reduce(interior)
num_ext_states = numpy.add.reduce(exterior)
# these lists will be used to accumulate 'COO'-ordinate format
# sparse matrix data for this reaction.
data = []
rows = []
cols = []
# account for the sparse matrix data for the flux out of the
# interior states of the truncated domain
if num_int_states > 0:
int_src_states = numpy.array(src_states[:, interior])
int_src_indices = numpy.array(src_indices[interior])
int_dst_states = numpy.array(dst_states[:, interior])
int_dst_indices = domain_enum.indices(int_dst_states)
int_coefficients = compute_propensity(propensity,
int_src_states)
# flux out
data.append(-int_coefficients)
cols.append(int_src_indices)
rows.append(int_src_indices)
# flux in
data.append(int_coefficients)
cols.append(int_src_indices)
rows.append(int_dst_indices)
# account for the sparse matrix data for the flux out of the interior
# states of the truncated domain and into the sink state
if sink and (num_ext_states > 0):
valid = validity_test(dst_states[:, exterior])
num_valid_states = numpy.add.reduce(valid)
if num_valid_states > 0:
ext_src_indices = numpy.array(src_indices[exterior][valid])
ext_src_states = numpy.array(src_states[:, exterior][:, valid])
ext_coefficients = compute_propensity(propensity,
ext_src_states)
shape = numpy.shape(ext_src_indices)
ext_dst_indices = sink_index * numpy.ones(shape,
dtype = numpy.int)
# these terms account for the flux out of the truncated
# domain into the sink state
data.append(-ext_coefficients)
cols.append(ext_src_indices)
rows.append(ext_src_indices)
# these terms account for the flux in to the sink state
# from the truncated domain
data.append(ext_coefficients)
cols.append(ext_src_indices)
rows.append(ext_dst_indices)
matrix_size = domain_enum.size
if sink:
matrix_size += 1
matrix_shape = (matrix_size, )*2
if len(data) == 0:
reaction_matrix = scipy.sparse.csr_matrix(matrix_shape)
else:
# merge data, rows, cols
data = numpy.concatenate(data)
cols = numpy.concatenate(cols)
rows = numpy.concatenate(rows)
# create coo matrix
coo_data = (data, (rows, cols))
reaction_matrix = scipy.sparse.coo_matrix(coo_data, matrix_shape)
# convert to sparse csr format, then compress & optimise the storage
reaction_matrix = reaction_matrix.tocsr()
optimise_csr_matrix(reaction_matrix)
yield reaction_matrix
return
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