"""
SBML Import
-----------
This module provides all necessary functionality to import a model specified
in the `Systems Biology Markup Language (SBML) <http://sbml.org/Main_Page>`_.
"""
import copy
import itertools as itt
import logging
import math
import os
import re
import warnings
import xml.etree.ElementTree as ET
from pathlib import Path
from typing import (
Any,
Callable,
Optional,
Union,
)
from collections.abc import Iterable, Sequence
import libsbml as sbml
import numpy as np
import sympy as sp
from sympy.logic.boolalg import BooleanFalse, BooleanTrue
from . import has_clibs
from .de_model import DEModel
from .constants import SymbolId
from .de_export import (
DEExporter,
)
from .de_model_components import symbol_to_type, Expression
from .sympy_utils import smart_is_zero_matrix, smart_multiply
from .import_utils import (
RESERVED_SYMBOLS,
_check_unsupported_functions,
_get_str_symbol_identifiers,
_parse_special_functions,
amici_time_symbol,
annotation_namespace,
generate_measurement_symbol,
generate_regularization_symbol,
noise_distribution_to_cost_function,
noise_distribution_to_observable_transformation,
sbml_time_symbol,
smart_subs,
smart_subs_dict,
symbol_with_assumptions,
toposort_symbols,
_default_simplify,
generate_flux_symbol,
)
from .logging import get_logger, log_execution_time, set_log_level
from .sbml_utils import SBMLException, _parse_logical_operators
from .splines import AbstractSpline
from sympy.matrices.dense import MutableDenseMatrix
SymbolicFormula = dict[sp.Symbol, sp.Expr]
default_symbols = {symbol: {} for symbol in SymbolId}
ConservationLaw = dict[str, Union[str, sp.Expr]]
logger = get_logger(__name__, logging.ERROR)
[docs]
class SbmlImporter:
"""
Class to generate AMICI C++ files for a model provided in the Systems
Biology Markup Language (SBML).
:ivar show_sbml_warnings:
indicates whether libSBML warnings should be
displayed
:ivar symbols:
dict carrying symbolic definitions
:ivar sbml_reader:
The libSBML sbml reader
.. warning::
Not storing this may result in a segfault.
:ivar sbml_doc:
document carrying the sbml definition
.. warning::
Not storing this may result in a segfault.
:ivar sbml:
SBML model to import
:ivar compartments:
dict of compartment ids and compartment volumes
:ivar stoichiometric_matrix:
stoichiometric matrix of the model
:ivar flux_vector:
reaction kinetic laws
:ivar flux_ids:
identifiers for elements of flux_vector
:ivar _local_symbols:
model symbols for sympy to consider during sympification
see `locals`argument in `sympy.sympify`
:ivar species_assignment_rules:
Assignment rules for species.
Key is symbolic identifier and value is assignment value
:ivar compartment_assignment_rules:
Assignment rules for compartments.
Key is symbolic identifier and value is assignment value
:ivar parameter_assignment_rules:
assignment rules for parameters, these parameters are not permissible
for sensitivity analysis
:ivar initial_assignments:
initial assignments for parameters, these parameters are not
permissible for sensitivity analysis
:ivar sbml_parser_settings:
sets behaviour of SBML Formula parsing
"""
[docs]
def __init__(
self,
sbml_source: Union[str, Path, sbml.Model],
show_sbml_warnings: bool = False,
from_file: bool = True,
discard_annotations: bool = False,
) -> None:
"""
Create a new Model instance.
:param sbml_source:
Either a path to SBML file where the model is specified,
or a model string as created by sbml.sbmlWriter(
).writeSBMLToString() or an instance of `libsbml.Model`.
:param show_sbml_warnings:
Indicates whether libSBML warnings should be displayed.
:param from_file:
Whether `sbml_source` is a file name (True, default), or an SBML
string
:param discard_annotations:
discard information contained in AMICI SBML annotations (debug).
"""
if isinstance(sbml_source, sbml.Model):
self.sbml_doc: sbml.Document = sbml_source.getSBMLDocument()
else:
self.sbml_reader: sbml.SBMLReader = sbml.SBMLReader()
if from_file:
sbml_doc = self.sbml_reader.readSBMLFromFile(str(sbml_source))
else:
sbml_doc = self.sbml_reader.readSBMLFromString(sbml_source)
self.sbml_doc = sbml_doc
self.show_sbml_warnings: bool = show_sbml_warnings
# process document
self._process_document()
self.sbml: sbml.Model = self.sbml_doc.getModel()
# Long and short names for model components
self.symbols: dict[SymbolId, dict[sp.Symbol, dict[str, Any]]] = {}
self._local_symbols: dict[str, Union[sp.Expr, sp.Function]] = {}
self.compartments: SymbolicFormula = {}
self.compartment_assignment_rules: SymbolicFormula = {}
self.species_assignment_rules: SymbolicFormula = {}
self.parameter_assignment_rules: SymbolicFormula = {}
self.initial_assignments: SymbolicFormula = {}
self.splines: list[AbstractSpline] = []
self._reset_symbols()
# https://sbml.org/software/libsbml/5.18.0/docs/formatted/python-api/classlibsbml_1_1_l3_parser_settings.html#ab30d7ed52ca24cbb842d0a7fed7f4bfd
# all defaults except disable unit parsing
self.sbml_parser_settings = sbml.L3ParserSettings()
self.sbml_parser_settings.setModel(self.sbml)
self.sbml_parser_settings.setParseUnits(sbml.L3P_NO_UNITS)
self._discard_annotations: bool = discard_annotations
@log_execution_time("loading SBML", logger)
def _process_document(self) -> None:
"""
Validate and simplify document.
"""
# Ensure we got a valid SBML model, otherwise further processing
# might lead to undefined results
log_execution_time("validating SBML", logger)(
self.sbml_doc.validateSBML
)()
_check_lib_sbml_errors(self.sbml_doc, self.show_sbml_warnings)
# Flatten "comp" model? Do that before any other converters are run
if any(
self.sbml_doc.getPlugin(i_plugin).getPackageName() == "comp"
for i_plugin in range(self.sbml_doc.getNumPlugins())
):
# see libsbml CompFlatteningConverter for options
conversion_properties = sbml.ConversionProperties()
conversion_properties.addOption("flatten comp", True)
conversion_properties.addOption("leave_ports", False)
conversion_properties.addOption("performValidation", False)
conversion_properties.addOption("abortIfUnflattenable", "none")
if (
log_execution_time("flattening hierarchical SBML", logger)(
self.sbml_doc.convert
)(conversion_properties)
!= sbml.LIBSBML_OPERATION_SUCCESS
):
raise SBMLException(
"Required SBML comp extension is currently not supported "
"and flattening the model failed."
)
# check the flattened model is still valid
log_execution_time("re-validating SBML", logger)(
self.sbml_doc.validateSBML
)()
_check_lib_sbml_errors(self.sbml_doc, self.show_sbml_warnings)
# apply several model simplifications that make our life substantially
# easier
if self.sbml_doc.getModel().getNumFunctionDefinitions():
convert_config = (
sbml.SBMLFunctionDefinitionConverter().getDefaultProperties()
)
log_execution_time("converting SBML functions", logger)(
self.sbml_doc.convert
)(convert_config)
convert_config = (
sbml.SBMLLocalParameterConverter().getDefaultProperties()
)
log_execution_time("converting SBML local parameters", logger)(
self.sbml_doc.convert
)(convert_config)
# If any of the above calls produces an error, this will be added to
# the SBMLError log in the sbml document. Thus, it is sufficient to
# check the error log just once after all conversion/validation calls.
_check_lib_sbml_errors(self.sbml_doc, self.show_sbml_warnings)
# need to reload the converted model
self.sbml = self.sbml_doc.getModel()
def _reset_symbols(self) -> None:
"""
Reset the symbols attribute to default values
"""
self.symbols = copy.deepcopy(default_symbols)
self._local_symbols = {}
[docs]
def sbml2amici(
self,
model_name: str,
output_dir: Union[str, Path] = None,
observables: dict[str, dict[str, str]] = None,
event_observables: dict[str, dict[str, str]] = None,
constant_parameters: Iterable[str] = None,
sigmas: dict[str, Union[str, float]] = None,
event_sigmas: dict[str, Union[str, float]] = None,
noise_distributions: dict[str, Union[str, Callable]] = None,
event_noise_distributions: dict[str, Union[str, Callable]] = None,
verbose: Union[int, bool] = logging.ERROR,
assume_pow_positivity: bool = False,
compiler: str = None,
allow_reinit_fixpar_initcond: bool = True,
compile: bool = True,
compute_conservation_laws: bool = True,
simplify: Optional[Callable] = _default_simplify,
cache_simplify: bool = False,
log_as_log10: bool = True,
generate_sensitivity_code: bool = True,
hardcode_symbols: Sequence[str] = None,
) -> None:
"""
Generate and compile AMICI C++ files for the model provided to the
constructor.
The resulting model can be imported as a regular Python module (if
`compile=True`), or used from Matlab or C++ as described in the
documentation of the respective AMICI interface.
Note that this generates model ODEs for changes in concentrations, not
amounts unless the `hasOnlySubstanceUnits` attribute has been
defined for a particular species.
Sensitivity analysis for local parameters is enabled by creating
global parameters ``_{reactionId}_{localParameterName}``.
:param model_name:
Name of the generated model package.
Note that in a given Python session, only one model with a given
name can be loaded at a time.
The generated Python extensions cannot be unloaded. Therefore,
make sure to choose a unique name for each model.
:param output_dir:
Directory where the generated model package will be stored.
:param observables:
Observables to be added to the model:
``dictionary( observableId:{'name':observableName
(optional), 'formula':formulaString)})``.
:param event_observables:
Event observables to be added to the model:
``dictionary( eventObservableId:{'name':eventObservableName
(optional), 'event':eventId, 'formula':formulaString)})``
:param constant_parameters:
list of SBML Ids identifying constant parameters
:param sigmas:
dictionary(observableId: sigma value or (existing) parameter name)
:param event_sigmas:
dictionary(eventObservableId: sigma value or (existing) parameter
name)
:param noise_distributions:
dictionary(observableId: noise type).
If nothing is passed for some observable id, a normal model is
assumed as default. Either pass a noise type identifier, or a
callable generating a custom noise string.
For noise identifiers, see
:func:`amici.import_utils.noise_distribution_to_cost_function`.
:param event_noise_distributions:
dictionary(eventObservableId: noise type).
If nothing is passed for some observable id, a normal model is
assumed as default. Either pass a noise type identifier, or a
callable generating a custom noise string.
For noise identifiers, see
:func:`amici.import_utils.noise_distribution_to_cost_function`.
:param verbose:
verbosity level for logging, ``True``/``False`` default to
``logging.Error``/``logging.DEBUG``
:param assume_pow_positivity:
if set to ``True``, a special pow function is
used to avoid problems with state variables that may become
negative due to numerical errors
:param compiler:
Absolute path to the compiler executable to be used to build the Python
extension, e.g. ``/usr/bin/clang``.
:param allow_reinit_fixpar_initcond:
see :class:`amici.de_export.ODEExporter`
:param compile:
If ``True``, compile the generated Python package,
if ``False``, just generate code.
:param compute_conservation_laws:
if set to ``True``, conservation laws are automatically computed
and applied such that the state-jacobian of the ODE
right-hand-side has full rank. This option should be set to
``True`` when using the Newton algorithm to compute steadystate
sensitivities.
Conservation laws for constant species are enabled by default.
Support for conservation laws for non-constant species is
experimental and may be enabled by setting an environment variable
``AMICI_EXPERIMENTAL_SBML_NONCONST_CLS`` to either ``demartino``
to use the algorithm proposed by De Martino et al. (2014)
https://doi.org/10.1371/journal.pone.0100750, or to any other value
to use the deterministic algorithm implemented in
``conserved_moieties2.py``. In some cases, the ``demartino`` may
run for a very long time. This has been observed for example in the
case of stoichiometric coefficients with many significant digits.
:param simplify:
see :attr:`amici.ODEModel._simplify`
:param cache_simplify:
see :meth:`amici.ODEModel.__init__`
:param log_as_log10:
If ``True``, log in the SBML model will be parsed as ``log10``
(default), if ``False``, log will be parsed as natural logarithm
``ln``.
:param generate_sensitivity_code:
If ``False``, the code required for sensitivity computation will
not be generated.
:param hardcode_symbols:
List of SBML entity IDs that are to be hardcoded in the generated model.
Their values cannot be changed anymore after model import.
Currently only parameters that are not targets of rules or
initial assignments are supported.
"""
set_log_level(logger, verbose)
ode_model = self._build_ode_model(
observables=observables,
event_observables=event_observables,
constant_parameters=constant_parameters,
sigmas=sigmas,
event_sigmas=event_sigmas,
noise_distributions=noise_distributions,
event_noise_distributions=event_noise_distributions,
verbose=verbose,
compute_conservation_laws=compute_conservation_laws,
simplify=simplify,
cache_simplify=cache_simplify,
log_as_log10=log_as_log10,
hardcode_symbols=hardcode_symbols,
)
exporter = DEExporter(
ode_model,
model_name=model_name,
outdir=output_dir,
verbose=verbose,
assume_pow_positivity=assume_pow_positivity,
compiler=compiler,
allow_reinit_fixpar_initcond=allow_reinit_fixpar_initcond,
generate_sensitivity_code=generate_sensitivity_code,
)
exporter.generate_model_code()
if compile:
if not has_clibs:
warnings.warn(
"AMICI C++ extensions have not been built. "
"Generated model code, but unable to compile."
)
exporter.compile_model()
def _build_ode_model(
self,
observables: dict[str, dict[str, str]] = None,
event_observables: dict[str, dict[str, str]] = None,
constant_parameters: Iterable[str] = None,
sigmas: dict[str, Union[str, float]] = None,
event_sigmas: dict[str, Union[str, float]] = None,
noise_distributions: dict[str, Union[str, Callable]] = None,
event_noise_distributions: dict[str, Union[str, Callable]] = None,
verbose: Union[int, bool] = logging.ERROR,
compute_conservation_laws: bool = True,
simplify: Optional[Callable] = _default_simplify,
cache_simplify: bool = False,
log_as_log10: bool = True,
hardcode_symbols: Sequence[str] = None,
) -> DEModel:
"""Generate an ODEModel from this SBML model.
See :py:func:`sbml2amici` for parameters.
"""
constant_parameters = (
list(constant_parameters) if constant_parameters else []
)
hardcode_symbols = set(hardcode_symbols) if hardcode_symbols else {}
if invalid := (set(constant_parameters) & set(hardcode_symbols)):
raise ValueError(
"The following parameters were selected as both constant "
f"and hard-coded which is not allowed: {invalid}"
)
if sigmas is None:
sigmas = {}
if event_sigmas is None:
event_sigmas = {}
if noise_distributions is None:
noise_distributions = {}
if event_noise_distributions is None:
event_noise_distributions = {}
self._reset_symbols()
self.sbml_parser_settings.setParseLog(
sbml.L3P_PARSE_LOG_AS_LOG10
if log_as_log10
else sbml.L3P_PARSE_LOG_AS_LN
)
self._process_sbml(
constant_parameters=constant_parameters,
hardcode_symbols=hardcode_symbols,
)
if (
self.symbols.get(SymbolId.EVENT, False)
or any(
x["value"].has(sp.Heaviside, sp.Piecewise)
for x in self.symbols[SymbolId.EXPRESSION].values()
)
or self.flux_vector.has(sp.Heaviside, sp.Piecewise)
):
if compute_conservation_laws:
logger.warning(
"Conservation laws are currently not supported for models "
"with events, piecewise or Heaviside functions, "
"and will be turned off."
)
compute_conservation_laws = False
self._process_observables(observables, sigmas, noise_distributions)
self._process_event_observables(
event_observables, event_sigmas, event_noise_distributions
)
self._replace_compartments_with_volumes()
self._clean_reserved_symbols()
self._process_time()
ode_model = DEModel(
verbose=verbose,
simplify=simplify,
cache_simplify=cache_simplify,
)
ode_model._has_quadratic_nllh = all(
llh["dist"]
in ["normal", "lin-normal", "log-normal", "log10-normal"]
for llh in self.symbols[SymbolId.LLHY].values()
)
# add splines as expressions to the model
# saved for later substituting into the fluxes
spline_subs = {}
for ispl, spl in enumerate(self.splines):
spline_expr = spl.ode_model_symbol(self)
spline_subs[spl.sbml_id] = spline_expr
ode_model.add_spline(spl, spline_expr)
# assemble fluxes and add them as expressions to the model
assert len(self.flux_ids) == len(self.flux_vector)
fluxes = [
generate_flux_symbol(ir, name=flux_id)
for ir, flux_id in enumerate(self.flux_ids)
]
# create dynamics without respecting conservation laws first
dxdt = smart_multiply(
self.stoichiometric_matrix, MutableDenseMatrix(fluxes)
)
# correct time derivatives for compartment changes
for ix, ((species_id, species), formula) in enumerate(
zip(self.symbols[SymbolId.SPECIES].items(), dxdt)
):
# rate rules and amount species don't need to be updated
if "dt" in species:
continue
if species["amount"]:
species["dt"] = formula
else:
species["dt"] = self._transform_dxdt_to_concentration(
species_id, formula
)
# create all basic components of the DE model and add them.
for symbol_name in self.symbols:
# transform dict of lists into a list of dicts
args = ["name", "identifier"]
if symbol_name == SymbolId.SPECIES:
args += ["dt", "init"]
elif symbol_name == SymbolId.ALGEBRAIC_STATE:
args += ["init"]
else:
args += ["value"]
if symbol_name == SymbolId.EVENT:
args += ["state_update", "initial_value"]
elif symbol_name == SymbolId.OBSERVABLE:
args += ["transformation"]
elif symbol_name == SymbolId.EVENT_OBSERVABLE:
args += ["event"]
comp_kwargs = [
{
"identifier": var_id,
**{k: v for k, v in var.items() if k in args},
}
for var_id, var in self.symbols[symbol_name].items()
]
for comp_kwarg in comp_kwargs:
ode_model.add_component(
symbol_to_type[symbol_name](**comp_kwarg)
)
# add fluxes as expressions, this needs to happen after base
# expressions from symbols have been parsed
for flux_id, flux in zip(fluxes, self.flux_vector):
# replace splines inside fluxes
flux = flux.subs(spline_subs)
ode_model.add_component(
Expression(identifier=flux_id, name=str(flux_id), value=flux)
)
if compute_conservation_laws:
self._process_conservation_laws(ode_model)
# fill in 'self._sym' based on prototypes and components in ode_model
ode_model.generate_basic_variables()
# substitute SBML-rateOf constructs
ode_model._process_sbml_rate_of()
return ode_model
@log_execution_time("importing SBML", logger)
def _process_sbml(
self,
constant_parameters: list[str] = None,
hardcode_symbols: Sequence[str] = None,
) -> None:
"""
Read parameters, species, reactions, and so on from SBML model
:param constant_parameters:
SBML Ids identifying constant parameters
:param hardcode_symbols:
Parameter IDs to be replaced by their values in the generated model.
"""
if not self._discard_annotations:
self._process_annotations()
self.check_support()
self._gather_locals(hardcode_symbols=hardcode_symbols)
self._process_parameters(
constant_parameters=constant_parameters,
hardcode_symbols=hardcode_symbols,
)
self._process_compartments()
self._process_species()
self._process_reactions()
self._process_rules()
self._process_events()
self._process_initial_assignments()
self._process_species_references()
[docs]
def check_support(self) -> None:
"""
Check whether all required SBML features are supported.
Also ensures that the SBML contains at least one reaction, or rate
rule, or assignment rule, to produce change in the system over time.
"""
# Check for required but unsupported SBML extensions
if (
self.sbml_doc.getLevel() != 3
and hasattr(self.sbml, "all_elements_from_plugins")
and self.sbml.all_elements_from_plugins.getSize()
):
raise SBMLException("SBML extensions are currently not supported!")
if self.sbml_doc.getLevel() == 3:
# the "required" attribute is only available in SBML Level 3
for i_plugin in range(self.sbml.getNumPlugins()):
plugin = self.sbml.getPlugin(i_plugin)
if (
self.sbml_doc.getPkgRequired(plugin.getPackageName())
is False
):
# if not "required", this has no impact on model
# simulation, and we can safely ignore it
if (
plugin.getPackageName() == "fbc"
and plugin.getListOfAllElements()
):
# fbc is labeled not-required, but in fact it is.
# we don't care about the extra attributes of core
# elements, such as fbc:chemicalFormula, but we can't
# do anything meaningful with fbc:objective or
# fbc:fluxBounds
raise SBMLException(
"The following fbc extension elements are "
"currently not supported: "
+ ", ".join(
list(map(str, plugin.getListOfAllElements()))
)
)
continue
# Check if there are extension elements. If not, we can safely
# ignore the enabled package
if plugin.getListOfAllElements():
raise SBMLException(
f"Required SBML extension {plugin.getPackageName()} "
f"is currently not supported!"
)
if any(
rule.isRate()
and not isinstance(
self.sbml.getElementBySId(rule.getVariable()),
(sbml.Compartment, sbml.Species, sbml.Parameter),
)
for rule in self.sbml.getListOfRules()
):
raise SBMLException(
"Rate rules are only supported for "
"species, compartments, and parameters."
)
if any(r.getFast() for r in self.sbml.getListOfReactions()):
raise SBMLException("Fast reactions are currently not supported!")
# Check events for unsupported functionality
self.check_event_support()
[docs]
def check_event_support(self) -> None:
"""
Check possible events in the model, as AMICI does currently not support
* delays in events
* priorities of events
* events fired at initial time
Furthermore, event triggers are optional (e.g., if an event is fired at
initial time, no trigger function is necessary).
In this case, warn that this event will have no effect.
"""
for event in self.sbml.getListOfEvents():
event_id = event.getId()
# Check for delays in events
delay = event.getDelay()
if delay is not None:
try:
delay_time = float(self._sympy_from_sbml_math(delay))
if delay_time != 0:
raise ValueError
# `TypeError` would be raised in the above `float(...)`
# if the delay is not a fixed time
except (TypeError, ValueError):
raise SBMLException(
"Events with execution delays are "
"currently not supported in AMICI."
)
# Check for priorities
if event.getPriority() is not None:
raise SBMLException(
f"Event {event_id} has a priority "
"specified. This is currently not "
"supported in AMICI."
)
# check trigger
trigger_sbml = event.getTrigger()
if trigger_sbml is None:
logger.warning(
f"Event {event_id} trigger has no trigger, "
"so will be skipped."
)
continue
if trigger_sbml.getMath() is None:
logger.warning(
f"Event {event_id} trigger has no trigger "
"expression, so a dummy trigger will be set."
)
if not trigger_sbml.getPersistent():
raise SBMLException(
f"Event {event_id} has a non-persistent trigger."
"This is currently not supported in AMICI."
)
@log_execution_time("gathering local SBML symbols", logger)
def _gather_locals(self, hardcode_symbols: Sequence[str] = None) -> None:
"""
Populate self.local_symbols with all model entities.
This is later used during sympifications to avoid sympy builtins
shadowing model entities as well as to avoid possibly costly
symbolic substitutions
"""
self._gather_base_locals(hardcode_symbols=hardcode_symbols)
self._gather_dependent_locals()
def _gather_base_locals(
self, hardcode_symbols: Sequence[str] = None
) -> None:
"""
Populate self.local_symbols with pure symbol definitions that do not
depend on any other symbol.
"""
special_symbols_and_funs = {
# oo is sympy infinity
"INF": sp.oo,
"NaN": sp.nan,
"rem": sp.Mod,
"time": sbml_time_symbol,
# SBML L3 explicitly defines this value, which is not equal
# to the most recent SI definition.
"avogadro": sp.Float(6.02214179e23),
"exponentiale": sp.E,
}
for s, v in special_symbols_and_funs.items():
self.add_local_symbol(s, v)
for c in itt.chain(
self.sbml.getListOfSpecies(),
self.sbml.getListOfParameters(),
self.sbml.getListOfCompartments(),
):
if not c.isSetId():
continue
if c.getId() in hardcode_symbols:
if c.getConstant() is not True:
# disallow anything that can be changed by rules/reaction/events
raise ValueError(
f"Cannot hardcode non-constant symbol `{c.getId()}`."
)
if self.sbml.getInitialAssignment(c.getId()):
raise NotImplementedError(
f"Cannot hardcode symbol `{c.getId()}` "
"that is an initial assignment target."
)
self.add_local_symbol(c.getId(), sp.Float(c.getValue()))
else:
self.add_local_symbol(c.getId(), _get_identifier_symbol(c))
for x_ref in _get_list_of_species_references(self.sbml):
if not x_ref.isSetId():
continue
if (
x_ref.isSetStoichiometry()
and not self.is_assignment_rule_target(x_ref)
):
value = sp.Float(x_ref.getStoichiometry())
else:
value = _get_identifier_symbol(x_ref)
ia_sym = self._get_element_initial_assignment(x_ref.getId())
if ia_sym is not None:
value = ia_sym
self.add_local_symbol(x_ref.getId(), value)
def _gather_dependent_locals(self):
"""
Populate self.local_symbols with symbol definitions that may depend on
other symbol definitions.
"""
for r in self.sbml.getListOfReactions():
if not r.isSetId():
continue
self.add_local_symbol(
r.getId(),
self._sympy_from_sbml_math(r.getKineticLaw() or sp.Float(0)),
)
[docs]
def add_local_symbol(self, key: str, value: sp.Expr):
"""
Add local symbols with some sanity checking for duplication which
would indicate redefinition of internals, which SBML permits,
but we don't.
:param key:
local symbol key
:param value:
local symbol value
"""
if key in self._local_symbols.keys():
raise SBMLException(
f"AMICI tried to add a local symbol {key} with value {value}, "
f"but {key} was already instantiated with "
f"{self._local_symbols[key]}. This means that there "
f"are multiple SBML elements with SId {key}, which is "
f"invalid SBML. This can be fixed by renaming "
f"the elements with SId {key}."
)
if key in {"True", "False", "true", "false", "pi"}:
raise SBMLException(
f"AMICI tried to add a local symbol {key} with value {value}, "
f"but {key} is a reserved symbol in AMICI. This can be fixed "
f"by renaming the element with SId {key}."
)
self._local_symbols[key] = value
@log_execution_time("processing SBML compartments", logger)
def _process_compartments(self) -> None:
"""
Get compartment information, stoichiometric matrix and fluxes from
SBML model.
"""
compartments = self.sbml.getListOfCompartments()
self.compartments = {}
for comp in compartments:
init = sp.Float(1.0)
if comp.isSetVolume():
init = self._sympy_from_sbml_math(comp.getVolume())
ia_sym = self._get_element_initial_assignment(comp.getId())
if ia_sym is not None:
init = ia_sym
self.compartments[_get_identifier_symbol(comp)] = init
@log_execution_time("processing SBML species", logger)
def _process_species(self) -> None:
"""
Get species information from SBML model.
"""
if self.sbml.isSetConversionFactor():
conversion_factor = symbol_with_assumptions(
self.sbml.getConversionFactor()
)
else:
conversion_factor = 1
for s in self.sbml.getListOfSpecies():
if self.is_assignment_rule_target(s):
continue
self.symbols[SymbolId.SPECIES][_get_identifier_symbol(s)] = {
"name": s.getName() if s.isSetName() else s.getId(),
"compartment": _get_species_compartment_symbol(s),
"constant": s.getConstant() or s.getBoundaryCondition(),
"amount": s.getHasOnlySubstanceUnits(),
"conversion_factor": symbol_with_assumptions(
s.getConversionFactor()
)
if s.isSetConversionFactor()
else conversion_factor,
"index": len(self.symbols[SymbolId.SPECIES]),
}
self._convert_event_assignment_parameter_targets_to_species()
self._process_species_initial()
self._process_rate_rules()
@log_execution_time("processing SBML species initials", logger)
def _process_species_initial(self):
"""
Extract initial values and initial assignments from species
"""
for species_variable in self.sbml.getListOfSpecies():
initial = get_species_initial(species_variable)
species_id = _get_identifier_symbol(species_variable)
# If species_id is a target of an AssignmentRule, species will be
# None, but we don't have to account for the initial definition
# of the species itself and SBML doesn't permit AssignmentRule
# targets to have InitialAssignments.
species = self.symbols[SymbolId.SPECIES].get(species_id, None)
ia_initial = self._get_element_initial_assignment(
species_variable.getId()
)
if ia_initial is not None:
initial = ia_initial
if species:
species["init"] = initial
# hide rateOf-arguments from toposort and the substitution below
all_rateof_dummies = []
for species in self.symbols[SymbolId.SPECIES].values():
species["init"], rateof_dummies = _rateof_to_dummy(species["init"])
all_rateof_dummies.append(rateof_dummies)
# don't assign this since they need to stay in order
sorted_species = toposort_symbols(
self.symbols[SymbolId.SPECIES], "init"
)
for species, rateof_dummies in zip(
self.symbols[SymbolId.SPECIES].values(), all_rateof_dummies
):
species["init"] = _dummy_to_rateof(
smart_subs_dict(species["init"], sorted_species, "init"),
rateof_dummies,
)
@log_execution_time("processing SBML rate rules", logger)
def _process_rate_rules(self):
"""
Process rate rules for species, compartments and parameters.
Compartments and parameters with rate rules are implemented as species.
Note that, in the case of species, rate rules may describe the change
in amount, not concentration, of a species.
"""
rules = self.sbml.getListOfRules()
# compartments with rules are replaced with constants in the relevant
# equations during the _replace_in_all_expressions call inside
# _process_rules
for rule in rules:
if rule.getTypeCode() != sbml.SBML_RATE_RULE:
continue
variable = symbol_with_assumptions(rule.getVariable())
formula = self._sympy_from_sbml_math(rule)
if formula is None:
continue
# Species rules are processed first, to avoid processing
# compartments twice (as compartments with rate rules are
# implemented as species).
ia_init = self._get_element_initial_assignment(rule.getVariable())
if variable in self.symbols[SymbolId.SPECIES]:
init = self.symbols[SymbolId.SPECIES][variable]["init"]
name = None
if variable in self.compartments:
init = self.compartments[variable]
name = str(variable)
del self.compartments[variable]
elif variable in self.symbols[SymbolId.PARAMETER]:
init = self._sympy_from_sbml_math(
self.symbols[SymbolId.PARAMETER][variable]["value"],
)
name = self.symbols[SymbolId.PARAMETER][variable]["name"]
del self.symbols[SymbolId.PARAMETER][variable]
# parameter with initial assignment, cannot use
# self.initial_assignments as it is not filled at this
# point
elif ia_init is not None:
init = ia_init
par = self.sbml.getElementBySId(rule.getVariable())
name = par.getName() if par.isSetName() else par.getId()
self.add_d_dt(formula, variable, init, name)
[docs]
def add_d_dt(
self,
d_dt: sp.Expr,
variable: sp.Symbol,
variable0: Union[float, sp.Expr],
name: str,
) -> None:
"""
Creates or modifies species, to implement rate rules for
compartments and species, respectively.
:param d_dt:
The rate rule (or, right-hand side of an ODE).
:param variable:
The subject of the rate rule.
:param variable0:
The initial value of the variable.
:param name:
Species name, only applicable if this function generates a new
species
"""
if variable in self.symbols[SymbolId.SPECIES]:
# only update dt if species was already generated
self.symbols[SymbolId.SPECIES][variable]["dt"] = d_dt
else:
# update initial values
for species_id, species in self.symbols[SymbolId.SPECIES].items():
variable0 = smart_subs(variable0, species_id, species["init"])
for species in self.symbols[SymbolId.SPECIES].values():
species["init"] = smart_subs(
species["init"], variable, variable0
)
# add compartment/parameter species
self.symbols[SymbolId.SPECIES][variable] = {
"name": name,
"init": variable0,
"amount": False,
"conversion_factor": 1.0,
"constant": False,
"index": len(self.symbols[SymbolId.SPECIES]),
"dt": d_dt,
}
@log_execution_time("processing SBML annotations", logger)
def _process_annotations(self) -> None:
"""
Process annotations that make modifications to the
SBML model and thus have to be run before everything else
"""
# Remove all parameters (and corresponding rules)
# for which amici:discard is set
parameter_ids_to_remove = []
for p in self.sbml.getListOfParameters():
annotation = p.getAnnotationString()
assert isinstance(annotation, str)
if len(annotation) != 0:
annotation = ET.fromstring(annotation)
for child in annotation:
if child.tag == f"{{{annotation_namespace}}}discard":
parameter_ids_to_remove.append(p.getIdAttribute())
for parameter_id in parameter_ids_to_remove:
# Remove corresponding rules
self.sbml.removeRuleByVariable(parameter_id)
# Remove parameter
self.sbml.removeParameter(parameter_id)
@log_execution_time("processing SBML parameters", logger)
def _process_parameters(
self,
constant_parameters: list[str] = None,
hardcode_symbols: Sequence[str] = None,
) -> None:
"""
Get parameter information from SBML model.
:param constant_parameters:
SBML Ids identifying constant parameters
"""
if constant_parameters is None:
constant_parameters = []
# Ensure specified constant parameters exist in the model
for parameter in constant_parameters:
if not self.sbml.getParameter(parameter):
raise KeyError(
"Cannot make %s a constant parameter: "
"Parameter does not exist." % parameter
)
# parameter ID => initial assignment sympy expression
par_id_to_ia = {
par.getId(): ia.subs(
{
BooleanTrue(): sp.Float(1.0),
BooleanFalse(): sp.Float(0.0),
}
).evalf()
for par in self.sbml.getListOfParameters()
if (ia := self._get_element_initial_assignment(par.getId()))
is not None
}
fixed_parameters = [
parameter
for parameter in self.sbml.getListOfParameters()
if parameter.getId() in constant_parameters
]
for parameter in fixed_parameters:
ia_math = par_id_to_ia.get(parameter.getId())
if (
(ia_math is not None and not ia_math.is_Number)
or self.is_assignment_rule_target(parameter)
or self.is_rate_rule_target(parameter)
):
raise SBMLException(
f"Cannot turn parameter {parameter.getId()} into a "
"constant/fixed parameter since it either has an "
"initial assignment or is the target of an assignment or "
"rate rule."
)
parameters = [
parameter
for parameter in self.sbml.getListOfParameters()
if parameter.getId() not in constant_parameters
and (
(ia_math := par_id_to_ia.get(parameter.getId())) is None
or ia_math.is_Number
)
and not self.is_assignment_rule_target(parameter)
and parameter.getId() not in hardcode_symbols
]
loop_settings = {
SymbolId.PARAMETER: {"var": parameters, "name": "parameter"},
SymbolId.FIXED_PARAMETER: {
"var": fixed_parameters,
"name": "fixed_parameter",
},
}
for partype, settings in loop_settings.items():
for par in settings["var"]:
self.symbols[partype][_get_identifier_symbol(par)] = {
"name": par.getName() if par.isSetName() else par.getId(),
"value": par_id_to_ia.get(
par.getId(), sp.Float(par.getValue())
),
}
# Parameters that need to be turned into expressions
# so far, this concerns parameters with symbolic initial assignments
# (those have been skipped above) that are not rate rule targets
for par in self.sbml.getListOfParameters():
if (
(ia := par_id_to_ia.get(par.getId())) is not None
and not ia.is_Number
and not self.is_rate_rule_target(par)
):
self.symbols[SymbolId.EXPRESSION][
_get_identifier_symbol(par)
] = {
"name": par.getName() if par.isSetName() else par.getId(),
"value": ia,
}
@log_execution_time("processing SBML reactions", logger)
def _process_reactions(self):
"""
Get reactions from SBML model.
"""
reactions = self.sbml.getListOfReactions()
# nr (number of reactions) should have a minimum length of 1. This is
# to ensure that, if there are no reactions, the stoichiometric matrix
# and flux vector multiply to a zero vector with dimensions (nx, 1).
nr = max(1, len(reactions))
nx = len(self.symbols[SymbolId.SPECIES])
# stoichiometric matrix
self.stoichiometric_matrix = sp.SparseMatrix(sp.zeros(nx, nr))
self.flux_vector = sp.zeros(nr, 1)
# Use reaction IDs as IDs for flux expressions (note that prior to SBML
# level 3 version 2 the ID attribute was not mandatory and may be
# unset)
self.flux_ids = [
f"flux_{reaction.getId()}"
if reaction.isSetId()
else f"flux_r{reaction_idx}"
for reaction_idx, reaction in enumerate(reactions)
] or ["flux_r0"]
reaction_ids = [
reaction.getId() for reaction in reactions if reaction.isSetId()
]
for reaction_index, reaction in enumerate(reactions):
for element_list, sign in [
(reaction.getListOfReactants(), -1),
(reaction.getListOfProducts(), 1),
]:
for element in element_list:
stoichiometry = self._get_element_stoichiometry(element)
sbml_species = self.sbml.getSpecies(element.getSpecies())
if self.is_assignment_rule_target(sbml_species):
continue
species_id = _get_identifier_symbol(sbml_species)
species = self.symbols[SymbolId.SPECIES][species_id]
if species["constant"]:
continue
# Division by species compartment size (to find the
# rate of change in species concentration) now occurs
# in the `dx_dt` method in "de_export.py", which also
# accounts for possibly variable compartments.
self.stoichiometric_matrix[
species["index"], reaction_index
] += sign * stoichiometry * species["conversion_factor"]
if reaction.isSetId():
sym_math = self._local_symbols[reaction.getId()]
else:
sym_math = self._sympy_from_sbml_math(
reaction.getKineticLaw() or sp.Float(0)
)
self.flux_vector[reaction_index] = sym_math.subs(
{
BooleanTrue(): sp.Float(1.0),
BooleanFalse(): sp.Float(0.0),
}
)
if any(
str(symbol) in reaction_ids
for symbol in self.flux_vector[reaction_index].free_symbols
):
raise SBMLException(
"Kinetic laws involving reaction ids are currently"
" not supported!"
)
@log_execution_time("processing SBML rules", logger)
def _process_rules(self) -> None:
"""
Process Rules defined in the SBML model.
"""
for rule in self.sbml.getListOfRules():
# rate rules are processed in _process_species
if rule.getTypeCode() == sbml.SBML_RATE_RULE:
continue
if rule.getTypeCode() == sbml.SBML_ALGEBRAIC_RULE:
if self.sbml_doc.getLevel() < 3:
# not interested in implementing level 2 boundary condition
# shenanigans, see test 01787 in the sbml testsuite
raise SBMLException(
"Algebraic rules are only supported in SBML L3+"
)
self._process_rule_algebraic(rule)
else:
self._process_rule_assignment(rule)
self.symbols[SymbolId.EXPRESSION] = toposort_symbols(
self.symbols[SymbolId.EXPRESSION], "value"
)
# expressions must not occur in definition of x0
for species in self.symbols[SymbolId.SPECIES].values():
species["init"] = self._make_initial(
smart_subs_dict(
species["init"], self.symbols[SymbolId.EXPRESSION], "value"
)
)
def _process_rule_algebraic(self, rule: sbml.AlgebraicRule):
formula = self._sympy_from_sbml_math(rule)
if formula is None:
return
free_variables = set()
# SBML L3V2 spec, p. 61:
# "Therefore, if an algebraic rule is introduced in a model,
# for at least one of the entities referenced in the rule’s
# math element the value of that entity must not be
# completely determined by other constructs in the model"
# find those elements:
for symbol in formula.free_symbols:
sbml_var = self.sbml.getElementBySId(str(symbol))
# This means that at least this entity must
# not have the attribute constant=“true”
if sbml_var.isSetConstant() and sbml_var.getConstant():
continue
# and there must also not be a rate rule or assignment
# rule for it
if self.is_assignment_rule_target(
sbml_var
) or self.is_rate_rule_target(sbml_var):
continue
# Furthermore, if the entity is a Species object, its value
# must not be determined by reactions, which means that it
# must either have the attribute boundaryCondition=“false”
# or else not be involved in any reaction at all.
is_species = isinstance(sbml_var, sbml.Species)
is_boundary_condition = (
is_species
and sbml_var.isSetBoundaryCondition()
and sbml_var.getBoundaryCondition()
)
is_involved_in_reaction = is_species and not smart_is_zero_matrix(
self.stoichiometric_matrix[
list(self.symbols[SymbolId.SPECIES].keys()).index(symbol),
:,
]
)
if (
is_species
and not is_boundary_condition
and is_involved_in_reaction
):
continue
free_variables.add(symbol)
# this should be guaranteed by sbml validation, so better check to make sure
# we don't mess anything up
assert len(free_variables) >= 1
self.symbols[SymbolId.ALGEBRAIC_EQUATION][
f"ae{len(self.symbols[SymbolId.ALGEBRAIC_EQUATION])}"
] = {"value": formula}
# remove the symbol from the original definition and add to
# algebraic symbols (if not already done)
for var in free_variables:
if var in self.symbols[SymbolId.FIXED_PARAMETER]:
raise SBMLException(
"There are algebraic rules that specify the "
f"value of {var}, which is also marked as "
"fixed parameter. This is currently not supported! "
f"If {var} is supposed to be a fixed parameter, "
"set its SBML attribute `constant` to True."
)
if var in self.symbols[SymbolId.ALGEBRAIC_STATE]:
continue
if var in self.compartments:
init = self.compartments[var]
symbol = {
"name": str(var),
"value": init,
}
symbol_id = "compartment"
var_ix = np.nan
del self.compartments[var]
else:
symbol_id, source_symbols = next(
(
(symbol_id, self.symbols[symbol_id])
for symbol_id in (SymbolId.PARAMETER, SymbolId.SPECIES)
if var in self.symbols[symbol_id]
),
)
var_ix = list(source_symbols.keys()).index(var)
symbol = source_symbols.pop(var)
# update symbol and adapt stoichiometric matrix
if symbol_id != SymbolId.SPECIES:
# parameters have numeric values so we can use Float here
symbol["init"] = sp.Float(symbol.pop("value"))
# if not a species, add a zeros row to the stoichiometric
# matrix
if (
isinstance(symbol["init"], float)
and np.isnan(symbol["init"])
) or (
isinstance(symbol["init"], sp.Number)
and symbol["init"] == sp.nan
):
# placeholder, needs to be determined in IC calculation
symbol["init"] = sp.Float(0.0)
self.stoichiometric_matrix = (
self.stoichiometric_matrix.row_insert(
self.stoichiometric_matrix.shape[0],
sp.SparseMatrix(
[[0] * self.stoichiometric_matrix.shape[1]]
),
)
)
elif var_ix != self.stoichiometric_matrix.shape[0] - 1:
# if not the last col, move it to the end
# as we reorder state variables
state_ordering = list(
range(
len(self.symbols[SymbolId.SPECIES])
+ len(self.symbols[SymbolId.ALGEBRAIC_STATE])
+ 1
)
)
state_ordering.append(state_ordering.pop(var_ix))
self.stoichiometric_matrix = self.stoichiometric_matrix[
state_ordering, :
]
self.symbols[SymbolId.ALGEBRAIC_STATE][var] = symbol
def _process_rule_assignment(self, rule: sbml.AssignmentRule):
sbml_var = self.sbml.getElementBySId(rule.getVariable())
sym_id = symbol_with_assumptions(rule.getVariable())
# Check whether this rule is a spline rule.
if not self._discard_annotations:
if rule.getTypeCode() == sbml.SBML_ASSIGNMENT_RULE:
annotation = AbstractSpline.get_annotation(rule)
if annotation is not None:
spline = AbstractSpline.from_annotation(
sym_id,
annotation,
locals_=self._local_symbols,
)
if (
spline.evaluate_at != amici_time_symbol
and spline.evaluate_at != sbml_time_symbol
):
raise NotImplementedError(
"AMICI at the moment does not support splines "
"whose evaluation point is not the model time."
)
self.splines.append(spline)
return
formula = self._sympy_from_sbml_math(rule)
if formula is None:
return
if isinstance(sbml_var, sbml.Species):
self.species_assignment_rules[sym_id] = formula
elif isinstance(sbml_var, sbml.Compartment):
self.compartment_assignment_rules[sym_id] = formula
self.compartments[sym_id] = formula
elif isinstance(sbml_var, sbml.Parameter):
self.parameter_assignment_rules[sym_id] = formula
self.symbols[SymbolId.EXPRESSION][sym_id] = {
"name": str(sym_id),
"value": formula,
}
def _process_time(self) -> None:
"""
Convert time_symbol into cpp variable.
"""
self._replace_in_all_expressions(sbml_time_symbol, amici_time_symbol)
def _convert_event_assignment_parameter_targets_to_species(self):
"""
Convert parameters that are targets of event assignments to species.
This is for the convenience of only implementing event assignments for
"species".
"""
parameter_targets = _collect_event_assignment_parameter_targets(
self.sbml
)
for parameter_target in parameter_targets:
# Parameter rate rules already exist as species.
if parameter_target in self.symbols[SymbolId.SPECIES]:
continue
if parameter_target in self.parameter_assignment_rules:
raise SBMLException(
"AMICI does not currently support models with SBML events "
"that affect parameters that are also the target of "
"assignment rules."
)
parameter_def = None
for symbol_id in {SymbolId.PARAMETER, SymbolId.FIXED_PARAMETER}:
if parameter_target in self.symbols[symbol_id]:
# `parameter_target` should only exist in one of the
# `symbol_id` dictionaries.
if parameter_def is not None:
raise AssertionError(
"Unexpected error. The parameter target of an "
"event assignment was processed twice."
)
parameter_def = self.symbols[symbol_id].pop(
parameter_target
)
if parameter_def is None:
# this happens for parameters that have initial assignments
# or are assignment rule targets
par = self.sbml.getElementBySId(str(parameter_target))
ia_init = self._get_element_initial_assignment(par.getId())
parameter_def = {
"name": par.getName() if par.isSetName() else par.getId(),
"value": sp.Float(par.getValue())
if ia_init is None
else ia_init,
}
# Fixed parameters are added as species such that they can be
# targets of events.
self.symbols[SymbolId.SPECIES][parameter_target] = {
"name": parameter_def["name"],
"init": parameter_def["value"],
# 'compartment': None, # can ignore for amounts
"constant": False,
"amount": True,
# 'conversion_factor': 1.0, # can be ignored
"index": len(self.symbols[SymbolId.SPECIES]),
"dt": sp.Float(0),
}
@log_execution_time("processing SBML events", logger)
def _process_events(self) -> None:
"""Process SBML events."""
events = self.sbml.getListOfEvents()
def get_empty_bolus_value() -> sp.Float:
"""
Used in the event update vector for species that are not affected
by the event.
"""
return sp.Symbol("AMICI_EMTPY_BOLUS")
# Used to update species concentrations when an event affects a
# compartment.
concentration_species_by_compartment = {
symbol_with_assumptions(c.getId()): []
for c in self.sbml.getListOfCompartments()
}
for species, species_def in self.symbols[SymbolId.SPECIES].items():
if (
# Species is a concentration
not species_def.get("amount", True)
and
# Species has a compartment
"compartment" in species_def
):
concentration_species_by_compartment[
species_def["compartment"]
].append(species)
for ievent, event in enumerate(events):
# get the event id (which is optional unfortunately)
event_id = event.getId()
if event_id is None or event_id == "":
event_id = f"event_{ievent}"
event_sym = sp.Symbol(event_id)
# get and parse the trigger function
trigger_sbml = event.getTrigger()
trigger_sym = self._sympy_from_sbml_math(trigger_sbml)
trigger = _parse_event_trigger(trigger_sym)
# Currently, all event assignment targets must exist in
# self.symbols[SymbolId.SPECIES]
state_vector = list(self.symbols[SymbolId.SPECIES].keys())
# parse the boluses / event assignments
bolus = [get_empty_bolus_value() for _ in state_vector]
event_assignments = event.getListOfEventAssignments()
compartment_event_assignments = set()
for event_assignment in event_assignments:
variable_sym = symbol_with_assumptions(
event_assignment.getVariable()
)
if event_assignment.getMath() is None:
# Ignore event assignments with no change in value.
continue
formula = self._sympy_from_sbml_math(event_assignment)
try:
# Try to find the species in the state vector.
index = state_vector.index(variable_sym)
bolus[index] = formula
except ValueError:
raise SBMLException(
"Could not process event assignment for "
f"{str(variable_sym)}. AMICI currently only allows "
"event assignments to species; parameters; or, "
"compartments with rate rules, at the moment."
)
try:
# Try working with the formula now to detect errors
# here instead of at multiple points downstream.
_ = formula - variable_sym
except TypeError:
raise SBMLException(
"Could not process event assignment for "
f"{str(variable_sym)}. AMICI only allows symbolic "
"expressions as event assignments."
)
if variable_sym in concentration_species_by_compartment:
compartment_event_assignments.add(variable_sym)
for (
comp,
assignment,
) in self.compartment_assignment_rules.items():
if variable_sym not in assignment.free_symbols:
continue
compartment_event_assignments.add(comp)
# Update the concentration of species with concentration units
# in compartments that were affected by the event assignments.
for compartment_sym in compartment_event_assignments:
for species_sym in concentration_species_by_compartment[
compartment_sym
]:
# If the species was not affected by an event assignment
# then the old value should be updated.
if (
bolus[state_vector.index(species_sym)]
== get_empty_bolus_value()
):
species_value = species_sym
# else the species was affected by an event assignment,
# hence the updated value should be updated further.
else:
species_value = bolus[state_vector.index(species_sym)]
# New species value is old amount / new volume.
bolus[state_vector.index(species_sym)] = (
species_value * compartment_sym / formula
)
# Subtract the current species value from each species with an
# update, as the bolus will be added on to the current species
# value during simulation.
for index in range(len(bolus)):
if bolus[index] != get_empty_bolus_value():
bolus[index] -= state_vector[index]
bolus[index] = bolus[index].subs(
get_empty_bolus_value(), sp.Float(0.0)
)
initial_value = (
trigger_sbml.getInitialValue()
if trigger_sbml is not None
else True
)
if self.symbols[SymbolId.ALGEBRAIC_EQUATION] and not initial_value:
# in principle this could be implemented, requires running
# IDACalcIc (in solver->setup) before check event initialization
# (in model->initialize), but at the time of writing this sounded
# like something that might break stuff in all kinds of other places
# (it might not, but this could be checked when someone actually
# needs the feature).
raise SBMLException(
"Events with initial values are not supported in models with"
" algebraic rules."
)
self.symbols[SymbolId.EVENT][event_sym] = {
"name": event_id,
"value": trigger,
"state_update": sp.MutableDenseMatrix(bolus),
"initial_value": initial_value,
}
@log_execution_time("processing SBML observables", logger)
def _process_observables(
self,
observables: Union[dict[str, dict[str, str]], None],
sigmas: dict[str, Union[str, float]],
noise_distributions: dict[str, str],
) -> None:
"""
Perform symbolic computations required for observable and objective
function evaluation.
:param observables:
dictionary(observableId: {'name':observableName
(optional), 'formula':formulaString)})
to be added to the model
:param sigmas:
dictionary(observableId: sigma value or (existing)
parameter name)
:param noise_distributions:
dictionary(observableId: noise type)
See :py:func:`sbml2amici`.
"""
_validate_observables(
observables, sigmas, noise_distributions, events=False
)
# add user-provided observables or make all species, and compartments
# with assignment rules, observable
if observables:
# gather local symbols before parsing observable and sigma formulas
for obs in observables.keys():
self.add_local_symbol(obs, symbol_with_assumptions(obs))
self.symbols[SymbolId.OBSERVABLE] = {
symbol_with_assumptions(obs): {
"name": definition.get("name", f"y{iobs}"),
"value": self._sympy_from_sbml_math(definition["formula"]),
"transformation": noise_distribution_to_observable_transformation(
noise_distributions.get(obs, "normal")
),
}
for iobs, (obs, definition) in enumerate(observables.items())
}
# check for nesting of observables (unsupported)
observable_syms = set(self.symbols[SymbolId.OBSERVABLE].keys())
for obs in self.symbols[SymbolId.OBSERVABLE].values():
if any(
sym in observable_syms for sym in obs["value"].free_symbols
):
raise ValueError(
"Nested observables are not supported, "
f"but observable `{obs['name']} = {obs['value']}` "
"references another observable."
)
elif observables is None:
self._generate_default_observables()
_check_symbol_nesting(
self.symbols[SymbolId.OBSERVABLE], "eventObservable"
)
self._process_log_likelihood(sigmas, noise_distributions)
@log_execution_time("processing SBML event observables", logger)
def _process_event_observables(
self,
event_observables: dict[str, dict[str, str]],
event_sigmas: dict[str, Union[str, float]],
event_noise_distributions: dict[str, str],
) -> None:
"""
Perform symbolic computations required for observable and objective
function evaluation.
:param event_observables:
See :py:func:`sbml2amici`.
:param event_sigmas:
See :py:func:`sbml2amici`.
:param event_noise_distributions:
See :py:func:`sbml2amici`.
"""
if event_observables is None:
return
_validate_observables(
event_observables,
event_sigmas,
event_noise_distributions,
events=True,
)
# gather local symbols before parsing observable and sigma formulas
for obs, definition in event_observables.items():
self.add_local_symbol(obs, symbol_with_assumptions(obs))
# check corresponding event exists
if (
sp.Symbol(definition["event"])
not in self.symbols[SymbolId.EVENT]
):
raise ValueError(
"Could not find an event with the event identifier "
f'{definition["event"]} for the event observable with name'
f'{definition["name"]}.'
)
self.symbols[SymbolId.EVENT_OBSERVABLE] = {
symbol_with_assumptions(obs): {
"name": definition.get("name", f"z{iobs}"),
"value": self._sympy_from_sbml_math(definition["formula"]),
"event": sp.Symbol(definition.get("event")),
"transformation": noise_distribution_to_observable_transformation(
event_noise_distributions.get(obs, "normal")
),
}
for iobs, (obs, definition) in enumerate(event_observables.items())
}
wrong_t = sp.Symbol("t")
for eo in self.symbols[SymbolId.EVENT_OBSERVABLE].values():
if eo["value"].has(wrong_t):
warnings.warn(
f'Event observable {eo["name"]} uses `t` in '
"it's formula which is not the time variable. "
"For the time variable, please use `time` "
"instead!"
)
# check for nesting of observables (unsupported)
_check_symbol_nesting(
self.symbols[SymbolId.EVENT_OBSERVABLE], "eventObservable"
)
self._process_log_likelihood(
event_sigmas, event_noise_distributions, events=True
)
self._process_log_likelihood(
event_sigmas,
event_noise_distributions,
events=True,
event_reg=True,
)
def _generate_default_observables(self):
"""
Generate default observables from species, compartments and
(initial) assignment rules.
"""
self.symbols[SymbolId.OBSERVABLE] = {
symbol_with_assumptions(f"y{state_id}"): {
"name": state["name"],
"value": state_id,
}
for state_id, state in {
**self.symbols[SymbolId.SPECIES],
**self.symbols[SymbolId.ALGEBRAIC_STATE],
}.items()
}
for variable, formula in itt.chain(
self.parameter_assignment_rules.items(),
self.initial_assignments.items(),
self.compartment_assignment_rules.items(),
self.species_assignment_rules.items(),
self.compartments.items(),
):
symbol = symbol_with_assumptions(f"y{variable}")
# Assignment rules take precedence over compartment volume
# definitions, so they need to be evaluated first.
# Species assignment rules always overwrite.
if (
symbol in self.symbols[SymbolId.OBSERVABLE]
and variable not in self.species_assignment_rules
):
continue
self.symbols[SymbolId.OBSERVABLE][symbol] = {
"name": str(variable),
"value": formula,
}
def _process_log_likelihood(
self,
sigmas: dict[str, Union[str, float]],
noise_distributions: dict[str, str],
events: bool = False,
event_reg: bool = False,
):
"""
Perform symbolic computations required for objective function
evaluation.
:param sigmas:
See :py:func:`SBMLImporter._process_observables`
:param noise_distributions:
See :py:func:`SBMLImporter._process_observables`
:param events:
indicates whether the passed definitions are for observables
(False) or for event observables (True).
:param event_reg:
indicates whether log-likelihood definitions should be processed
for event observable regularization (Jrz). If this is activated,
measurements are substituted by 0 and the observable by the
respective regularization symbol.
"""
if events:
if event_reg:
obs_symbol = SymbolId.EVENT_OBSERVABLE
sigma_symbol = SymbolId.SIGMAZ
llh_symbol = SymbolId.LLHRZ
else:
obs_symbol = SymbolId.EVENT_OBSERVABLE
sigma_symbol = SymbolId.SIGMAZ
llh_symbol = SymbolId.LLHZ
else:
assert not event_reg
obs_symbol = SymbolId.OBSERVABLE
sigma_symbol = SymbolId.SIGMAY
llh_symbol = SymbolId.LLHY
for obs_id, obs in self.symbols[obs_symbol].items():
obs["measurement_symbol"] = generate_measurement_symbol(obs_id)
if event_reg:
obs["reg_symbol"] = generate_regularization_symbol(obs_id)
if not event_reg:
self.symbols[sigma_symbol] = {
symbol_with_assumptions(f"sigma_{obs_id}"): {
"name": f'sigma_{obs["name"]}',
"value": self._sympy_from_sbml_math(
sigmas.get(str(obs_id), "1.0")
),
}
for obs_id, obs in self.symbols[obs_symbol].items()
}
self.symbols[llh_symbol] = {}
for (obs_id, obs), (sigma_id, sigma) in zip(
self.symbols[obs_symbol].items(),
self.symbols[sigma_symbol].items(),
):
symbol = symbol_with_assumptions(f"J{obs_id}")
dist = noise_distributions.get(str(obs_id), "normal")
cost_fun = noise_distribution_to_cost_function(dist)(obs_id)
value = sp.sympify(
cost_fun,
locals=dict(
zip(
_get_str_symbol_identifiers(obs_id),
(obs_id, obs["measurement_symbol"], sigma_id),
)
),
)
if event_reg:
value = value.subs(obs["measurement_symbol"], 0.0)
value = value.subs(obs_id, obs["reg_symbol"])
self.symbols[llh_symbol][symbol] = {
"name": f'J{obs["name"]}',
"value": value,
"dist": dist,
}
@log_execution_time("processing SBML initial assignments", logger)
def _process_initial_assignments(self):
"""
Accounts for initial assignments of parameters and species
references. Initial assignments for species and compartments are
processed in :py:func:`amici.SBMLImporter._process_initial_species` and
:py:func:`amici.SBMLImporter._process_compartments` respectively.
"""
for ia in self.sbml.getListOfInitialAssignments():
identifier = _get_identifier_symbol(ia)
if identifier in itt.chain(
self.symbols[SymbolId.SPECIES],
self.compartments,
self.symbols[SymbolId.EXPRESSION],
self.symbols[SymbolId.PARAMETER],
self.symbols[SymbolId.FIXED_PARAMETER],
):
continue
sym_math = self._get_element_initial_assignment(ia.getId())
if sym_math is None:
continue
sym_math = self._make_initial(
smart_subs_dict(
sym_math, self.symbols[SymbolId.EXPRESSION], "value"
)
)
self.initial_assignments[_get_identifier_symbol(ia)] = sym_math
# sort and flatten
self.initial_assignments = toposort_symbols(self.initial_assignments)
for ia_id, ia in self.initial_assignments.items():
self.initial_assignments[ia_id] = smart_subs_dict(
ia, self.initial_assignments
)
for identifier, sym_math in list(self.initial_assignments.items()):
self._replace_in_all_expressions(identifier, sym_math)
@log_execution_time("processing SBML species references", logger)
def _process_species_references(self):
"""
Replaces species references that define anything but stoichiometries.
Species references for stoichiometries are processed in
:py:func:`amici.SBMLImporter._process_reactions`.
"""
# doesnt look like there is a better way to get hold of those lists:
species_references = _get_list_of_species_references(self.sbml)
for species_reference in species_references:
if (
hasattr(species_reference, "getStoichiometryMath")
and species_reference.getStoichiometryMath() is not None
):
raise SBMLException(
"StoichiometryMath is currently not "
"supported for species references."
)
if species_reference.getId() == "":
continue
stoich = self._get_element_stoichiometry(species_reference)
self._replace_in_all_expressions(
_get_identifier_symbol(species_reference),
self._sympy_from_sbml_math(stoich),
)
def _make_initial(
self, sym_math: Union[sp.Expr, None, float]
) -> Union[sp.Expr, None, float]:
"""
Transforms an expression to its value at the initial time point by
replacing species by their initial values.
:param sym_math:
symbolic expression
:return:
transformed expression
"""
if not isinstance(sym_math, sp.Expr):
return sym_math
sym_math, rateof_to_dummy = _rateof_to_dummy(sym_math)
for species_id, species in self.symbols[SymbolId.SPECIES].items():
if "init" in species:
sym_math = smart_subs(sym_math, species_id, species["init"])
sym_math = smart_subs(sym_math, sbml_time_symbol, sp.Float(0))
sym_math = _dummy_to_rateof(sym_math, rateof_to_dummy)
return sym_math
def _process_conservation_laws(self, ode_model: DEModel) -> None:
"""
Find conservation laws in reactions and species.
:param ode_model:
:class:`DEModel` object with basic definitions
"""
conservation_laws = []
# Create conservation laws for constant species
species_solver = _add_conservation_for_constant_species(
ode_model, conservation_laws
)
# Non-constant species processed here
if (
"AMICI_EXPERIMENTAL_SBML_NONCONST_CLS" in os.environ
or "GITHUB_ACTIONS" in os.environ
):
species_solver = list(
set(
self._add_conservation_for_non_constant_species(
ode_model, conservation_laws
)
)
& set(species_solver)
)
# add algebraic variables to species_solver as they were ignored above
ndifferential = len(ode_model._differential_states)
nalgebraic = len(ode_model._algebraic_states)
species_solver.extend(
list(range(ndifferential, ndifferential + nalgebraic))
)
# Check, whether species_solver is empty now. As currently, AMICI
# cannot handle ODEs without species, CLs must be switched off in this
# case
if not len(species_solver):
conservation_laws = []
species_solver = list(range(ode_model.num_states_rdata()))
# prune out species from stoichiometry and
self.stoichiometric_matrix = self.stoichiometric_matrix[
species_solver, :
]
# add the found CLs to the ode_model
for cl in conservation_laws:
ode_model.add_conservation_law(**cl)
def _get_conservation_laws_demartino(
self,
ode_model: DEModel,
) -> list[tuple[int, list[int], list[float]]]:
"""Identify conservation laws based on algorithm by DeMartino et al.
(see conserved_moieties.py).
:param ode_model: Model for which to compute conserved quantities
:returns: List of one tuple per conservation law, each containing:
(0) the index of the (solver-)species to eliminate,
(1) (solver-)indices of all species engaged in the conserved
quantity (including the eliminated one)
(2) coefficients for the species in (1)
"""
from .conserved_quantities_demartino import (
compute_moiety_conservation_laws,
)
sm = self.stoichiometric_matrix[
: len(self.symbols[SymbolId.SPECIES]), :
]
try:
stoichiometric_list = [float(entry) for entry in sm.T.flat()]
except TypeError:
# Due to the numerical algorithm currently used to identify
# conserved quantities, we can't have symbols in the
# stoichiometric matrix
warnings.warn(
"Conservation laws for non-constant species in "
"combination with parameterized stoichiometric "
"coefficients are not currently supported "
"and will be turned off."
)
return []
if not _non_const_conservation_laws_supported(self.sbml):
return []
cls_state_idxs, cls_coefficients = compute_moiety_conservation_laws(
stoichiometric_list,
*sm.shape,
rng_seed=32,
species_names=[
str(x.get_id()) for x in ode_model._differential_states
],
)
# Sparsify conserved quantities
# ``compute_moiety_conservation_laws`` identifies conserved quantities
# with positive coefficients. The resulting system is, therefore,
# often non-sparse. This leads to circular dependencies in the
# state expressions of eliminated states. The identified conserved
# quantities are linearly independent. We can construct `A` as in
# `A * x0 = total_cl` and bring it to reduced row echelon form. The
# pivot species are the ones to be eliminated. The resulting state
# expressions are sparse and void of any circular dependencies.
A = sp.zeros(
len(cls_coefficients), len(ode_model._differential_states)
)
for i_cl, (cl, coefficients) in enumerate(
zip(cls_state_idxs, cls_coefficients)
):
for i, c in zip(cl, coefficients):
A[i_cl, i] = sp.Rational(c)
rref, pivots = A.rref()
raw_cls = []
for i_cl, target_state_model_idx in enumerate(pivots):
# collect values for species engaged in the current CL
state_idxs = [i for i, coeff in enumerate(rref[i_cl, :]) if coeff]
coefficients = [coeff for coeff in rref[i_cl, :] if coeff]
raw_cls.append(
(target_state_model_idx, state_idxs, coefficients),
)
return raw_cls
def _get_conservation_laws_rref(
self,
) -> list[tuple[int, list[int], list[float]]]:
"""Identify conservation laws based on left nullspace of the
stoichiometric matrix, computed through (numeric) Gaussian elimination
:returns: List of one tuple per conservation law, each containing:
(0) the index of the (solver-)species to eliminate,
(1) (solver-)indices of all species engaged in the conserved
quantity (including the eliminated one)
(2) coefficients for the species in (1)
"""
import numpy as np
from numpy.linalg import matrix_rank
from .conserved_quantities_rref import nullspace_by_rref, rref
try:
S = np.asarray(
self.stoichiometric_matrix[
: len(self.symbols[SymbolId.SPECIES]), :
],
dtype=float,
)
except TypeError:
# Due to the numerical algorithm currently used to identify
# conserved quantities, we can't have symbols in the
# stoichiometric matrix
warnings.warn(
"Conservation laws for non-constant species in "
"combination with parameterized stoichiometric "
"coefficients are not currently supported "
"and will be turned off."
)
return []
if not _non_const_conservation_laws_supported(self.sbml):
return []
# Determine rank via SVD
rank = matrix_rank(S) if S.shape[0] else 0
if rank == S.shape[0]:
return []
kernel = nullspace_by_rref(S.T)
# Check dimensions - due to numerical errors, nullspace_by_rref may
# fail in certain situations
if kernel.shape[0] != S.shape[0] - rank:
raise AssertionError(
"Failed to determine all conserved quantities "
f"(found {kernel.shape[0]}, expected {S.shape[0] - rank}). "
"Try another algorithm, disable detection of conservation "
"laws, or submit a bug report along with the model."
)
kernel = rref(kernel)
raw_cls = []
for row in kernel:
state_idxs = [i for i, coeff in enumerate(row) if coeff]
coefficients = [coeff for coeff in row if coeff]
raw_cls.append(
(state_idxs[0], state_idxs, coefficients),
)
return raw_cls
def _add_conservation_for_non_constant_species(
self, model: DEModel, conservation_laws: list[ConservationLaw]
) -> list[int]:
"""Add non-constant species to conservation laws
:param model:
ODEModel object with basic definitions
:param conservation_laws:
List of already known conservation laws
:returns:
List of species indices which later remain in the DE solver
"""
# indices of retained species
species_solver = list(range(len(model._differential_states)))
algorithm = os.environ.get("AMICI_EXPERIMENTAL_SBML_NONCONST_CLS", "")
if algorithm.lower() == "demartino":
raw_cls = self._get_conservation_laws_demartino(model)
else:
raw_cls = self._get_conservation_laws_rref()
if not raw_cls:
# no conservation laws identified
return species_solver
species_to_be_removed = {x[0] for x in raw_cls}
# keep new conservations laws separate until we know everything worked
new_conservation_laws = []
# previously removed constant species
eliminated_state_ids = {cl["state"] for cl in conservation_laws}
all_state_ids = [x.get_id() for x in model.states()]
all_compartment_sizes = []
for state_id in all_state_ids:
symbol = {
**self.symbols[SymbolId.SPECIES],
**self.symbols[SymbolId.ALGEBRAIC_STATE],
}[state_id]
if "amount" not in symbol:
continue # not a species
if symbol["amount"]:
compartment_size = sp.Integer(1)
else:
compartment_size = self.compartments[symbol["compartment"]]
all_compartment_sizes.append(compartment_size)
# iterate over list of conservation laws, create symbolic expressions,
for target_state_model_idx, state_idxs, coefficients in raw_cls:
if all_state_ids[target_state_model_idx] in eliminated_state_ids:
# constants state, already eliminated
continue
# collect values for species engaged in the current CL
state_ids = [all_state_ids[i_state] for i_state in state_idxs]
compartment_sizes = [all_compartment_sizes[i] for i in state_idxs]
target_state_id = all_state_ids[target_state_model_idx]
total_abundance = symbol_with_assumptions(f"tcl_{target_state_id}")
new_conservation_laws.append(
{
"state": target_state_id,
"total_abundance": total_abundance,
"coefficients": {
state_id: coeff * compartment
for state_id, coeff, compartment in zip(
state_ids, coefficients, compartment_sizes
)
},
}
)
species_to_be_removed.add(target_state_model_idx)
conservation_laws.extend(new_conservation_laws)
# list of species that are not determined by conservation laws
return [ix for ix in species_solver if ix not in species_to_be_removed]
def _replace_compartments_with_volumes(self):
"""
Replaces compartment symbols in expressions with their respective
(possibly variable) volumes.
"""
for comp, vol in self.compartments.items():
if (
comp in self.symbols[SymbolId.SPECIES]
or comp in self.symbols[SymbolId.ALGEBRAIC_STATE]
):
# for comps with rate rules volume is only initial
for state in {
**self.symbols[SymbolId.SPECIES],
**self.symbols[SymbolId.ALGEBRAIC_STATE],
}.values():
if isinstance(state["init"], sp.Expr):
state["init"] = smart_subs(state["init"], comp, vol)
continue
self._replace_in_all_expressions(comp, vol)
def _replace_in_all_expressions(
self, old: sp.Symbol, new: sp.Expr, replace_identifiers=False
) -> None:
"""
Replace 'old' by 'new' in all symbolic expressions.
:param old:
symbolic variables to be replaced
:param new:
replacement symbolic variables
"""
fields = [
"stoichiometric_matrix",
"flux_vector",
]
for field in fields:
if field in dir(self):
self.__setattr__(
field, smart_subs(self.__getattribute__(field), old, new)
)
dictfields = [
"compartment_assignment_rules",
"parameter_assignment_rules",
"initial_assignments",
]
for dictfield in dictfields:
d = getattr(self, dictfield)
# replace identifiers
if old in d and replace_identifiers:
d[new] = d[old]
del d[old]
if dictfield == "initial_assignments":
tmp_new = self._make_initial(new)
else:
tmp_new = new
# replace values
for k in d:
d[k] = smart_subs(d[k], old, tmp_new)
# replace in identifiers
if replace_identifiers:
for symbol in [
SymbolId.EXPRESSION,
SymbolId.SPECIES,
SymbolId.ALGEBRAIC_STATE,
]:
# completely recreate the dict to keep ordering consistent
if old not in self.symbols[symbol]:
continue
self.symbols[symbol] = {
smart_subs(k, old, new): v
for k, v in self.symbols[symbol].items()
}
for symbol in [
SymbolId.OBSERVABLE,
SymbolId.LLHY,
SymbolId.SIGMAY,
]:
if old not in self.symbols[symbol]:
continue
self.symbols[symbol][new] = self.symbols[symbol][old]
del self.symbols[symbol][old]
# replace in values
for symbol in [
SymbolId.OBSERVABLE,
SymbolId.LLHY,
SymbolId.LLHZ,
SymbolId.SIGMAY,
SymbolId.SIGMAZ,
SymbolId.EXPRESSION,
SymbolId.EVENT,
SymbolId.EVENT_OBSERVABLE,
SymbolId.ALGEBRAIC_EQUATION,
]:
for element in self.symbols[symbol].values():
element["value"] = smart_subs(element["value"], old, new)
# replace in event state updates (boluses)
if self.symbols.get(SymbolId.EVENT, False):
for event in self.symbols[SymbolId.EVENT].values():
for index in range(len(event["state_update"])):
event["state_update"][index] = smart_subs(
event["state_update"][index], old, new
)
for state in {
**self.symbols[SymbolId.SPECIES],
**self.symbols[SymbolId.ALGEBRAIC_STATE],
}.values():
state["init"] = smart_subs(
state["init"], old, self._make_initial(new)
)
if "dt" in state:
state["dt"] = smart_subs(state["dt"], old, new)
# Initial compartment volume may also be specified with an assignment
# rule (at the end of the _process_species method), hence needs to be
# processed here too.
self.compartments = {
smart_subs(c, old, new) if replace_identifiers else c: smart_subs(
v, old, self._make_initial(new)
)
for c, v in self.compartments.items()
}
# Substitute inside spline definitions
for spline in self.splines:
spline._replace_in_all_expressions(old, new)
def _clean_reserved_symbols(self) -> None:
"""
Remove all reserved symbols from self.symbols
"""
for sym in RESERVED_SYMBOLS:
old_symbol = symbol_with_assumptions(sym)
new_symbol = symbol_with_assumptions(f"amici_{sym}")
self._replace_in_all_expressions(
old_symbol, new_symbol, replace_identifiers=True
)
for symbols_ids, symbols in self.symbols.items():
if old_symbol in symbols:
# reconstitute the whole dict in order to keep the ordering
self.symbols[symbols_ids] = {
new_symbol if k is old_symbol else k: v
for k, v in symbols.items()
}
def _sympy_from_sbml_math(
self, var_or_math: [sbml.SBase, str]
) -> Union[sp.Expr, float, None]:
"""
Sympify Math of SBML variables with all sanity checks and
transformations
:param var_or_math:
SBML variable that has a getMath() function or math string
:return:
sympfified symbolic expression
"""
if isinstance(var_or_math, sbml.SBase):
math_string = sbml.formulaToL3StringWithSettings(
var_or_math.getMath(), self.sbml_parser_settings
)
ele_name = var_or_math.element_name
else:
math_string = var_or_math
ele_name = "string"
math_string = replace_logx(math_string)
try:
try:
formula = sp.sympify(
_parse_logical_operators(math_string),
locals=self._local_symbols,
)
except TypeError as err:
if str(err) == "BooleanAtom not allowed in this context.":
formula = sp.sympify(
_parse_logical_operators(math_string),
locals={
"true": sp.Float(1.0),
"false": sp.Float(0.0),
**self._local_symbols,
},
)
else:
raise
except (sp.SympifyError, TypeError, ZeroDivisionError) as err:
raise SBMLException(
f'{ele_name} "{math_string}" '
"contains an unsupported expression: "
f"{err}."
)
if isinstance(formula, sp.Expr):
formula = _parse_special_functions_sbml(formula)
_check_unsupported_functions_sbml(
formula, expression_type=ele_name
)
return formula
def _get_element_initial_assignment(
self, element_id: str
) -> Union[sp.Expr, None]:
"""
Extract value of sbml variable according to its initial assignment
:param element_id:
sbml variable name
:return:
"""
assignment = self.sbml.getInitialAssignment(element_id)
if assignment is None:
return None
sym = self._sympy_from_sbml_math(assignment)
# this is an initial assignment so we need to use
# initial conditions
sym = self._make_initial(sym)
return sym
def _get_element_stoichiometry(self, ele: sbml.SBase) -> sp.Expr:
"""
Computes the stoichiometry of a reactant or product of a reaction
:param ele:
reactant or product
:return:
symbolic variable that defines stoichiometry
"""
if ele.isSetId():
sym = self._get_element_initial_assignment(ele.getId())
if sym is not None:
return sym
if self.is_assignment_rule_target(ele):
return _get_identifier_symbol(ele)
if ele.isSetStoichiometry():
stoichiometry: float = ele.getStoichiometry()
return (
sp.Integer(stoichiometry)
if stoichiometry.is_integer()
else sp.Float(stoichiometry)
)
return sp.Integer(1)
[docs]
def is_assignment_rule_target(self, element: sbml.SBase) -> bool:
"""
Checks if an element has a valid assignment rule in the specified
model.
:param element:
SBML variable
:return:
boolean indicating truth of function name
"""
a = self.sbml.getAssignmentRuleByVariable(element.getId())
return a is not None and self._sympy_from_sbml_math(a) is not None
[docs]
def is_rate_rule_target(self, element: sbml.SBase) -> bool:
"""
Checks if an element has a valid assignment rule in the specified
model.
:param element:
SBML variable
:return:
boolean indicating truth of function name
"""
a = self.sbml.getRateRuleByVariable(element.getId())
return a is not None and self._sympy_from_sbml_math(a) is not None
def _transform_dxdt_to_concentration(
self, species_id: sp.Symbol, dxdt: sp.Expr
) -> sp.Expr:
"""
Produces the appropriate expression for the first derivative of a
species with respect to time, for species that reside in
compartments with a constant volume, or a volume that is defined by
an assignment or rate rule.
:param species_id:
The identifier of the species (generated in "sbml_import.py").
:param dxdt:
The element-wise product of the row in the stoichiometric
matrix that corresponds to the species (row x_index) and the
flux (kinetic laws) vector. Ignored in the case of rate rules.
"""
# The derivation of the below return expressions can be found in
# the documentation. They are found by rearranging
# $\frac{d}{dt} (vx) = Sw$ for $\frac{dx}{dt}$, where $v$ is the
# vector of species compartment volumes, $x$ is the vector of
# species concentrations, $S$ is the stoichiometric matrix, and $w$
# is the flux vector. The conditional below handles the cases of
# species in (i) compartments with a rate rule, (ii) compartments
# with an assignment rule, and (iii) compartments with a constant
# volume, respectively.
species = self.symbols[SymbolId.SPECIES][species_id]
comp = species["compartment"]
if comp in self.symbols[SymbolId.SPECIES]:
dv_dt = self.symbols[SymbolId.SPECIES][comp]["dt"]
xdot = (dxdt - dv_dt * species_id) / comp
return xdot
elif comp in self.compartment_assignment_rules:
v = self.compartment_assignment_rules[comp]
# we need to flatten out assignments in the compartment in
# order to ensure that we catch all species dependencies
v = smart_subs_dict(v, self.symbols[SymbolId.EXPRESSION], "value")
dv_dt = v.diff(amici_time_symbol)
# we may end up with a time derivative of the compartment
# volume due to parameter rate rules
comp_rate_vars = [
p
for p in v.free_symbols
if p in self.symbols[SymbolId.SPECIES]
]
for var in comp_rate_vars:
dv_dt += (
v.diff(var) * self.symbols[SymbolId.SPECIES][var]["dt"]
)
dv_dx = v.diff(species_id)
xdot = (dxdt - dv_dt * species_id) / (dv_dx * species_id + v)
return xdot
elif comp in self.symbols[SymbolId.ALGEBRAIC_STATE]:
raise SBMLException(
f"Species {species_id} is in a compartment {comp} that is"
f" defined by an algebraic equation. This is not"
f" supported."
)
else:
v = self.compartments[comp]
if v == 1.0:
return dxdt
return dxdt / v
def _check_lib_sbml_errors(
sbml_doc: sbml.SBMLDocument, show_warnings: bool = False
) -> None:
"""
Checks the error log in the current self.sbml_doc.
:param sbml_doc:
SBML document
:param show_warnings:
display SBML warnings
"""
num_warning = sbml_doc.getNumErrors(sbml.LIBSBML_SEV_WARNING)
num_error = sbml_doc.getNumErrors(sbml.LIBSBML_SEV_ERROR)
num_fatal = sbml_doc.getNumErrors(sbml.LIBSBML_SEV_FATAL)
if num_warning + num_error + num_fatal:
for i_error in range(sbml_doc.getNumErrors()):
error = sbml_doc.getError(i_error)
# we ignore any info messages for now
if error.getSeverity() >= sbml.LIBSBML_SEV_ERROR or (
show_warnings
and error.getSeverity() >= sbml.LIBSBML_SEV_WARNING
):
logger.error(
f"libSBML {error.getCategoryAsString()} "
f"({error.getSeverityAsString()}):"
f" {error.getMessage()}"
)
if num_error + num_fatal:
raise SBMLException(
"SBML Document failed to load (see error messages above)"
)
def _parse_event_trigger(trigger: sp.Expr) -> sp.Expr:
"""
Recursively translates a boolean trigger function into a real valued
root function
:param trigger:
:return: real valued root function expression
"""
# Events can be defined without trigger, i.e., the event will never fire.
# In this case, set a dummy trigger:
if trigger is None:
return sp.Float(1.0)
if trigger.is_Relational:
root = trigger.args[0] - trigger.args[1]
_check_unsupported_functions_sbml(root, "sympy.Expression")
# convert relational expressions into trigger functions
if isinstance(
trigger,
(sp.core.relational.LessThan, sp.core.relational.StrictLessThan),
):
# y < x or y <= x
return -root
if isinstance(
trigger,
(
sp.core.relational.GreaterThan,
sp.core.relational.StrictGreaterThan,
),
):
# y >= x or y > x
return root
# or(x,y): any of {x,y} is > 0: sp.Max(x, y)
if isinstance(trigger, sp.Or):
return sp.Max(*[_parse_event_trigger(arg) for arg in trigger.args])
# and(x,y): all out of {x,y} are > 0: sp.Min(x, y)
if isinstance(trigger, sp.And):
return sp.Min(*[_parse_event_trigger(arg) for arg in trigger.args])
raise SBMLException(
"AMICI can not parse piecewise/event trigger functions with argument "
f"{trigger}."
)
[docs]
def assignmentRules2observables(
sbml_model: sbml.Model, filter_function: Callable = lambda *_: True
):
"""
Turn assignment rules into observables.
:param sbml_model:
Model to operate on
:param filter_function:
Callback function taking assignment variable as input and returning
``True``/``False`` to indicate if the respective rule should be
turned into an observable.
:return:
A dictionary(observableId:{
'name': observableName,
'formula': formulaString
})
"""
observables = {}
for rule in sbml_model.getListOfRules():
if rule.getTypeCode() != sbml.SBML_ASSIGNMENT_RULE:
continue
parameter_id = rule.getVariable()
if (p := sbml_model.getParameter(parameter_id)) and filter_function(p):
observables[parameter_id] = {
"name": p.getName() if p.isSetName() else parameter_id,
"formula": sbml_model.getAssignmentRuleByVariable(
parameter_id
).getFormula(),
}
for parameter_id in observables:
sbml_model.removeRuleByVariable(parameter_id)
sbml_model.removeParameter(parameter_id)
return observables
def _add_conservation_for_constant_species(
ode_model: DEModel, conservation_laws: list[ConservationLaw]
) -> list[int]:
"""
Adds constant species to conservations laws
:param ode_model:
ODEModel object with basic definitions
:param conservation_laws:
List of already known conservation laws
:returns species_solver:
List of species indices which remain later in the DE solver
"""
# decide which species to keep in stoichiometry
species_solver = list(range(len(ode_model._differential_states)))
# iterate over species, find constant ones
for ix in reversed(range(len(ode_model._differential_states))):
if ode_model.state_is_constant(ix):
# dont use sym('x') here since conservation laws need to be
# added before symbols are generated
target_state = ode_model._differential_states[ix].get_id()
total_abundance = symbol_with_assumptions(f"tcl_{target_state}")
conservation_laws.append(
{
"state": target_state,
"total_abundance": total_abundance,
"coefficients": {target_state: 1.0},
}
)
# mark species to delete from stoichiometric matrix
species_solver.pop(ix)
return species_solver
def _get_species_compartment_symbol(species: sbml.Species) -> sp.Symbol:
"""
Generate compartment symbol for the compartment of a specific species.
This function will always return the same unique python object for a
given species name.
:param species:
sbml species
:return:
compartment symbol
"""
return symbol_with_assumptions(species.getCompartment())
def _get_identifier_symbol(var: sbml.SBase) -> sp.Symbol:
"""
Generate identifier symbol for a sbml variable.
This function will always return the same unique python object for a
given entity.
:param var:
sbml variable
:return:
identifier symbol
"""
return symbol_with_assumptions(var.getId())
[docs]
def get_species_initial(species: sbml.Species) -> sp.Expr:
"""
Extract the initial concentration from a given species
:param species:
species index
:return:
initial species concentration
"""
if species.isSetInitialConcentration():
conc = species.getInitialConcentration()
if species.getHasOnlySubstanceUnits():
return sp.Float(conc) * _get_species_compartment_symbol(species)
else:
return sp.Float(conc)
if species.isSetInitialAmount():
amt = species.getInitialAmount()
if math.isnan(amt):
return sp.Float(0.0)
if species.getHasOnlySubstanceUnits():
return sp.Float(amt)
else:
return sp.Float(amt) / _get_species_compartment_symbol(species)
return sp.Float(0.0)
def _get_list_of_species_references(
sbml_model: sbml.Model,
) -> list[sbml.SpeciesReference]:
"""
Extracts list of species references as SBML doesn't provide a native
function for this.
:param sbml_model:
SBML model instance
:return:
ListOfSpeciesReferences
"""
return [
reference
for reaction in sbml_model.getListOfReactions()
for reference in itt.chain(
reaction.getListOfReactants(),
reaction.getListOfProducts(),
reaction.getListOfModifiers(),
)
]
[docs]
def replace_logx(math_str: Union[str, float, None]) -> Union[str, float, None]:
"""
Replace logX(.) by log(., X) since sympy cannot parse the former
:param math_str:
string for sympification
:return:
sympifiable string
"""
if not isinstance(math_str, str):
return math_str
return re.sub(r"(^|\W)log(\d+)\(", r"\g<1>1/ln(\2)*ln(", math_str)
def _collect_event_assignment_parameter_targets(
sbml_model: sbml.Model,
) -> list[sp.Symbol]:
targets = []
sbml_parameters = sbml_model.getListOfParameters()
sbml_parameter_ids = [p.getId() for p in sbml_parameters]
for event in sbml_model.getListOfEvents():
for event_assignment in event.getListOfEventAssignments():
target_id = event_assignment.getVariable()
if target_id in sbml_parameter_ids:
targets.append(
_get_identifier_symbol(
sbml_parameters[sbml_parameter_ids.index(target_id)]
)
)
return targets
def _check_unsupported_functions_sbml(
sym: sp.Expr, expression_type: str, full_sym: Optional[sp.Expr] = None
):
try:
_check_unsupported_functions(sym, expression_type, full_sym)
except RuntimeError as err:
raise SBMLException(str(err))
def _parse_special_functions_sbml(
sym: sp.Expr, toplevel: bool = True
) -> sp.Expr:
try:
return _parse_special_functions(sym, toplevel)
except RuntimeError as err:
raise SBMLException(str(err))
def _validate_observables(
observables: Union[dict[str, dict[str, str]], None],
sigmas: dict[str, Union[str, float]],
noise_distributions: dict[str, str],
events: bool = False,
) -> None:
if observables is None or not observables:
return
# Ensure no non-existing observableIds have been specified
# (no problem here, but usually an upstream bug)
unknown_ids = set(sigmas.keys()) - set(observables.keys())
if unknown_ids:
raise ValueError(
f"Sigma provided for unknown "
f"{'eventO' if events else 'o'}bservableIds: "
f"{unknown_ids}."
)
# Ensure no non-existing observableIds have been specified
# (no problem here, but usually an upstream bug)
unknown_ids = set(noise_distributions.keys()) - set(observables.keys())
if unknown_ids:
raise ValueError(
f"Noise distribution provided for unknown "
f"{'eventO' if events else 'o'}bservableIds: "
f"{unknown_ids}."
)
def _check_symbol_nesting(
symbols: dict[sp.Symbol, dict[str, sp.Expr]], symbol_type: str
):
observable_syms = set(symbols.keys())
for obs in symbols.values():
if any(sym in observable_syms for sym in obs["value"].free_symbols):
raise ValueError(
"Nested observables are not supported, "
f"but {symbol_type} `{obs['name']} = {obs['value']}` "
"references another observable."
)
def _non_const_conservation_laws_supported(sbml_model: sbml.Model) -> bool:
"""Check whether non-constant conservation laws can be handled for the
given model."""
if any(
rule.getTypeCode() == sbml.SBML_RATE_RULE
for rule in sbml_model.getListOfRules()
):
# see SBML semantic test suite, case 33 for an example
warnings.warn(
"Conservation laws for non-constant species in "
"models with RateRules are currently not supported "
"and will be turned off."
)
return False
if any(
rule.getTypeCode() == sbml.SBML_ASSIGNMENT_RULE
and sbml_model.getSpecies(rule.getVariable())
for rule in sbml_model.getListOfRules()
):
warnings.warn(
"Conservation laws for non-constant species in "
"models with Species-AssignmentRules are currently not "
"supported and will be turned off."
)
return False
return True
def _rateof_to_dummy(sym_math):
"""Replace rateOf(...) by dummy variable
if `rateOf(some_species)` is used in an initial assignment, we don't want to substitute the species argument
by its initial value.
Usage:
sym_math, rateof_to_dummy = _rateof_to_dummy(sym_math)
[...substitute...]
sym_math = _dummy_to_rateof(sym_math, rateof_to_dummy)
"""
if rate_ofs := sym_math.find(sp.core.function.UndefinedFunction("rateOf")):
# replace by dummies to avoid species substitution
rateof_dummies = {
rate_of: sp.Dummy(f"Dummy_RateOf_{rate_of.args[0].name}")
for rate_of in rate_ofs
}
return sym_math.subs(rateof_dummies), rateof_dummies
return sym_math, {}
def _dummy_to_rateof(sym_math, rateof_dummies):
"""Back-substitution of dummies from `_rateof_to_dummy`"""
if rateof_dummies:
return sym_math.subs({v: k for k, v in rateof_dummies.items()})
return sym_math