import copy
import itertools
import multiprocessing as mp
import numbers
import sys
import warnings
import platform
import casadi
import numpy as np
import pybamm
from pybamm.expression_tree.binary_operators import _Heaviside
from pybamm import ParameterValues
[docs]
class BaseSolver:
"""Solve a discretised model.
Parameters
----------
method : str, optional
The method to use for integration, specific to each solver
rtol : float, optional
The relative tolerance for the solver (default is 1e-6).
atol : float, optional
The absolute tolerance for the solver (default is 1e-6).
root_method : str or pybamm algebraic solver class, optional
The method to use to find initial conditions (for DAE solvers).
If a solver class, must be an algebraic solver class.
If "casadi",
the solver uses casadi's Newton rootfinding algorithm to find initial
conditions. Otherwise, the solver uses 'scipy.optimize.root' with method
specified by 'root_method' (e.g. "lm", "hybr", ...)
root_tol : float, optional
The tolerance for the initial-condition solver (default is 1e-6).
extrap_tol : float, optional
The tolerance to assert whether extrapolation occurs or not. Default is 0.
output_variables : list[str], optional
List of variables to calculate and return. If none are specified then
the complete state vector is returned (can be very large) (default is [])
on_extrapolation : str, optional
What to do if the solver is extrapolating. Options are "warn", "error", or "ignore".
Default is "warn".
"""
def __init__(
self,
method=None,
rtol=1e-6,
atol=1e-6,
root_method=None,
root_tol=1e-6,
extrap_tol=None,
on_extrapolation=None,
output_variables=None,
):
self.method = method
self.rtol = rtol
self.atol = atol
self.root_tol = root_tol
self.root_method = root_method
self.extrap_tol = extrap_tol or -1e-10
self.output_variables = [] if output_variables is None else output_variables
self.on_extrapolation = on_extrapolation or "warn"
self._model_set_up = {}
# Defaults, can be overwritten by specific solver
self.name = "Base solver"
self._ode_solver = False
self._algebraic_solver = False
self._supports_interp = False
self.computed_var_fcns = {}
self._mp_context = self.get_platform_context(platform.system())
@property
def ode_solver(self):
return self._ode_solver
@property
def algebraic_solver(self):
return self._algebraic_solver
@property
def supports_interp(self):
return self._supports_interp
@property
def supports_parallel_solve(self):
return False
@property
def on_extrapolation(self):
return self._on_extrapolation
@on_extrapolation.setter
def on_extrapolation(self, value):
if value not in ["warn", "error", "ignore"]:
raise ValueError("on_extrapolation must be 'warn', 'raise', or 'ignore'")
self._on_extrapolation = value
@property
def root_method(self):
return self._root_method
@root_method.setter
def root_method(self, method):
if method == "casadi":
method = pybamm.CasadiAlgebraicSolver(self.root_tol)
elif isinstance(method, str):
method = pybamm.AlgebraicSolver(method, self.root_tol)
elif not (
method is None
or (
isinstance(method, pybamm.BaseSolver)
and method.algebraic_solver is True
)
):
raise pybamm.SolverError("Root method must be an algebraic solver")
self._root_method = method
[docs]
def copy(self):
"""Returns a copy of the solver"""
new_solver = copy.copy(self)
# clear _model_set_up
new_solver._model_set_up = {}
return new_solver
[docs]
def set_up(self, model, inputs=None, t_eval=None, ics_only=False):
"""Unpack model, perform checks, and calculate jacobian.
Parameters
----------
model : :class:`pybamm.BaseModel`
The model whose solution to calculate. Must have attributes rhs and
initial_conditions
inputs : dict, optional
Any input parameters to pass to the model when solving
t_eval : numeric type, optional
The times at which to stop the integration due to a discontinuity in time.
"""
inputs = inputs or {}
if ics_only:
pybamm.logger.info("Start solver set-up, initial_conditions only")
else:
pybamm.logger.info("Start solver set-up")
self._check_and_prepare_model_inplace(model, inputs, ics_only)
# set default calculate sensitivities on model
if not hasattr(model, "calculate_sensitivities"):
model.calculate_sensitivities = []
self._set_up_model_sensitivities_inplace(model, inputs)
vars_for_processing = self._get_vars_for_processing(model, inputs)
# Process initial conditions
initial_conditions, _, jacp_ic, _ = process(
model.concatenated_initial_conditions,
"initial_conditions",
vars_for_processing,
use_jacobian=False,
)
model.initial_conditions_eval = initial_conditions
model.jacp_initial_conditions_eval = jacp_ic
# set initial conditions
self._set_initial_conditions(model, 0.0, inputs)
if ics_only:
pybamm.logger.info("Finish solver set-up")
return
# Process rhs, algebraic, residual and event expressions
# and wrap in callables
rhs, jac_rhs, jacp_rhs, jac_rhs_action = process(
model.concatenated_rhs, "RHS", vars_for_processing
)
algebraic, jac_algebraic, jacp_algebraic, jac_algebraic_action = process(
model.concatenated_algebraic, "algebraic", vars_for_processing
)
# combine rhs and algebraic functions
if len(model.rhs) == 0:
rhs_algebraic = model.concatenated_algebraic
elif len(model.algebraic) == 0:
rhs_algebraic = model.concatenated_rhs
else:
rhs_algebraic = pybamm.NumpyConcatenation(
model.concatenated_rhs, model.concatenated_algebraic
)
(
rhs_algebraic,
jac_rhs_algebraic,
jacp_rhs_algebraic,
jac_rhs_algebraic_action,
) = process(rhs_algebraic, "rhs_algebraic", vars_for_processing)
(
casadi_switch_events,
terminate_events,
interpolant_extrapolation_events,
discontinuity_events,
) = self._set_up_events(model, t_eval, inputs, vars_for_processing)
# Add the solver attributes
model.rhs_eval = rhs
model.algebraic_eval = algebraic
model.rhs_algebraic_eval = rhs_algebraic
model.terminate_events_eval = terminate_events
model.discontinuity_events_eval = discontinuity_events
model.interpolant_extrapolation_events_eval = interpolant_extrapolation_events
model.jac_rhs_eval = jac_rhs
model.jac_rhs_action_eval = jac_rhs_action
model.jacp_rhs_eval = jacp_rhs
model.jac_algebraic_eval = jac_algebraic
model.jac_algebraic_action_eval = jac_algebraic_action
model.jacp_algebraic_eval = jacp_algebraic
model.jac_rhs_algebraic_eval = jac_rhs_algebraic
model.jac_rhs_algebraic_action_eval = jac_rhs_algebraic_action
model.jacp_rhs_algebraic_eval = jacp_rhs_algebraic
# Save CasADi functions for the CasADi solver
# Save CasADi functions for solvers that use CasADi
# Note: when we pass to casadi the ode part of the problem must be in
if isinstance(self.root_method, pybamm.CasadiAlgebraicSolver) or isinstance(
self, (pybamm.CasadiSolver, pybamm.CasadiAlgebraicSolver)
):
# can use DAE solver to solve model with algebraic equations only
if len(model.rhs) > 0:
t_casadi = vars_for_processing["t_casadi"]
y_casadi = vars_for_processing["y_casadi"]
p_casadi_stacked = vars_for_processing["p_casadi_stacked"]
mass_matrix_inv = casadi.MX(model.mass_matrix_inv.entries)
explicit_rhs = mass_matrix_inv @ rhs(
t_casadi, y_casadi, p_casadi_stacked
)
model.casadi_rhs = casadi.Function(
"rhs", [t_casadi, y_casadi, p_casadi_stacked], [explicit_rhs]
)
model.casadi_switch_events = casadi_switch_events
model.casadi_algebraic = algebraic
model.casadi_sensitivities = jacp_rhs_algebraic
model.casadi_sensitivities_rhs = jacp_rhs
model.casadi_sensitivities_algebraic = jacp_algebraic
if getattr(self.root_method, "algebraic_solver", False):
self.root_method.set_up_root_solver(model, inputs, t_eval)
# if output_variables specified then convert functions to casadi
# expressions for evaluation within the respective solver
self.computed_var_fcns = {}
self.computed_dvar_dy_fcns = {}
self.computed_dvar_dp_fcns = {}
for key in self.output_variables:
# ExplicitTimeIntegral's are not computed as part of the solver and
# do not need to be converted
if isinstance(model.variables_and_events[key], pybamm.ExplicitTimeIntegral):
continue
# Generate Casadi function to calculate variable and derivates
# to enable sensitivites to be computed within the solver
(
self.computed_var_fcns[key],
self.computed_dvar_dy_fcns[key],
self.computed_dvar_dp_fcns[key],
_,
) = process(
model.variables_and_events[key],
BaseSolver._wrangle_name(key),
vars_for_processing,
use_jacobian=True,
return_jacp_stacked=True,
)
pybamm.logger.info("Finish solver set-up")
def _set_initial_conditions(self, model, time, inputs):
# model should have been discretised or an error raised in Self._check_and_prepare_model_inplace
len_tot = model.len_rhs_and_alg
y_zero = np.zeros((len_tot, 1))
casadi_format = model.convert_to_format == "casadi"
if casadi_format:
# stack inputs
inputs_y0_ics = casadi.vertcat(*[x for x in inputs.values()])
else:
inputs_y0_ics = inputs
model.y0 = model.initial_conditions_eval(time, y_zero, inputs_y0_ics)
if model.jacp_initial_conditions_eval is None:
model.y0S = None
return
if casadi_format:
inputs_jacp_ics = inputs_y0_ics
else:
# we are calculating the derivative wrt the inputs
# so need to make sure we convert int -> float
# This is to satisfy JAX jacfwd function which requires
# float inputs
inputs_jacp_ics = {
key: float(value) if isinstance(value, int) else value
for key, value in inputs.items()
}
model.y0S = model.jacp_initial_conditions_eval(time, y_zero, inputs_jacp_ics)
@classmethod
def _wrangle_name(cls, name: str) -> str:
"""
Wrangle a function name to replace special characters
"""
replacements = [
(" ", "_"),
("[", ""),
("]", ""),
(".", "_"),
("-", "_"),
("(", ""),
(")", ""),
("%", "prc"),
(",", ""),
(".", ""),
]
name = "v_" + name.casefold()
for string, replacement in replacements:
name = name.replace(string, replacement)
return name
def _check_and_prepare_model_inplace(self, model, inputs, ics_only):
"""
Performs checks on the model and prepares it for solving.
"""
# Check model.algebraic for ode solvers
if self.ode_solver is True and len(model.algebraic) > 0:
raise pybamm.SolverError(
f"Cannot use ODE solver '{self.name}' to solve DAE model"
)
# Check model.rhs for algebraic solvers
if self._algebraic_solver is True and len(model.rhs) > 0:
raise pybamm.SolverError(
"""Cannot use algebraic solver to solve model with time derivatives"""
)
# casadi solver won't allow solving algebraic model so we have to raise an
# error here
if isinstance(self, pybamm.CasadiSolver) and len(model.rhs) == 0:
raise pybamm.SolverError(
"Cannot use CasadiSolver to solve algebraic model, "
"use CasadiAlgebraicSolver instead"
)
# Discretise model if it isn't already discretised
# This only works with purely 0D models, as otherwise the mesh and spatial
# method should be specified by the user
if model.is_discretised is False:
try:
disc = pybamm.Discretisation()
disc.process_model(model)
except pybamm.DiscretisationError as e:
raise pybamm.DiscretisationError(
"Cannot automatically discretise model, "
f"model should be discretised before solving ({e})"
) from e
if (
isinstance(self, (pybamm.CasadiSolver, pybamm.CasadiAlgebraicSolver))
) and model.convert_to_format != "casadi":
pybamm.logger.warning(
f"Converting {model.name} to CasADi for solving with CasADi solver"
)
model.convert_to_format = "casadi"
if (
isinstance(self.root_method, pybamm.CasadiAlgebraicSolver)
and model.convert_to_format != "casadi"
):
pybamm.logger.warning(
f"Converting {model.name} to CasADi for calculating ICs with CasADi"
)
model.convert_to_format = "casadi"
@staticmethod
def _get_vars_for_processing(model, inputs):
vars_for_processing = {
"model": model,
}
if model.convert_to_format != "casadi":
# Create Jacobian from concatenated rhs and algebraic
y = pybamm.StateVector(slice(0, model.len_rhs_and_alg))
# set up Jacobian object, for re-use of dict
jacobian = pybamm.Jacobian()
vars_for_processing.update({"y": y, "jacobian": jacobian})
return vars_for_processing
else:
# Convert model attributes to casadi
t_casadi = casadi.MX.sym("t")
# Create the symbolic state vectors
y_diff = casadi.MX.sym("y_diff", model.len_rhs)
y_alg = casadi.MX.sym("y_alg", model.len_alg)
y_casadi = casadi.vertcat(y_diff, y_alg)
p_casadi = {}
for name, value in inputs.items():
if isinstance(value, numbers.Number):
p_casadi[name] = casadi.MX.sym(name)
else:
p_casadi[name] = casadi.MX.sym(name, value.shape[0])
p_casadi_stacked = casadi.vertcat(*[p for p in p_casadi.values()])
vars_for_processing.update(
{
"t_casadi": t_casadi,
"y_diff": y_diff,
"y_alg": y_alg,
"y_casadi": y_casadi,
"p_casadi": p_casadi,
"p_casadi_stacked": p_casadi_stacked,
}
)
return vars_for_processing
@staticmethod
def _set_up_model_sensitivities_inplace(model, inputs):
"""
Set up model attributes related to sensitivities.
"""
has_mass_matrix = model.mass_matrix is not None
has_mass_matrix_inv = model.mass_matrix_inv is not None
if not has_mass_matrix:
return
model.mass_matrix = pybamm.Matrix(
model.mass_matrix.entries[: model.len_rhs_and_alg, : model.len_rhs_and_alg]
)
if has_mass_matrix_inv:
model.mass_matrix_inv = pybamm.Matrix(
model.mass_matrix_inv.entries[: model.len_rhs, : model.len_rhs]
)
def _set_up_events(self, model, t_eval, inputs, vars_for_processing):
# Check for heaviside and modulo functions in rhs and algebraic and add
# discontinuity events if these exist.
# Note: only checks for the case of t < X, t <= X, X < t, or X <= t,
# but also accounts for the fact that t might be dimensional
# Only do this for DAE models as ODE models can deal with discontinuities
# fine
if len(model.algebraic) > 0:
for symbol in itertools.chain(
model.concatenated_rhs.pre_order(),
model.concatenated_algebraic.pre_order(),
):
if isinstance(symbol, _Heaviside):
if symbol.right == pybamm.t:
expr = symbol.left
elif symbol.left == pybamm.t:
expr = symbol.right
else:
# Heaviside function does not contain pybamm.t as an argument.
# Do not create an event
continue # pragma: no cover
model.events.append(
pybamm.Event(
str(symbol),
expr,
pybamm.EventType.DISCONTINUITY,
)
)
elif isinstance(symbol, pybamm.Modulo) and symbol.left == pybamm.t:
expr = symbol.right
num_events = 200 if (t_eval is None) else (t_eval[-1] // expr.value)
for i in np.arange(num_events):
model.events.append(
pybamm.Event(
str(symbol),
expr * pybamm.Scalar(i + 1),
pybamm.EventType.DISCONTINUITY,
)
)
else:
continue
casadi_switch_events = []
terminate_events = []
interpolant_extrapolation_events = []
discontinuity_events = []
for n, event in enumerate(model.events):
if event.event_type == pybamm.EventType.DISCONTINUITY:
# discontinuity events are evaluated before the solver is called,
# so don't need to process them
discontinuity_events.append(event)
elif event.event_type == pybamm.EventType.SWITCH and (
isinstance(self, pybamm.CasadiSolver)
and self.mode == "fast with events"
and model.algebraic != {}
):
# Save some events to casadi_switch_events for the 'fast with
# events' mode of the casadi solver
# We only need to do this if the model is a DAE model
# see #1082
k = 20
# address numpy 1.25 deprecation warning: array should have
# ndim=0 before conversion
init_sign = float(
np.sign(event.evaluate(0, model.y0.full(), inputs=inputs)).item()
)
# We create a sigmoid for each event which will multiply the
# rhs. Doing * 2 - 1 ensures that when the event is crossed,
# the sigmoid is zero. Hence the rhs is zero and the solution
# stays constant for the rest of the simulation period
# We can then cut off the part after the event was crossed
event_sigmoid = (
pybamm.sigmoid(0, init_sign * event.expression, k) * 2 - 1
)
event_casadi = process(
event_sigmoid,
f"event_{n}",
vars_for_processing,
use_jacobian=False,
)[0]
# use the actual casadi object as this will go into the rhs
casadi_switch_events.append(event_casadi)
else:
# use the function call
event_call = process(
event.expression,
f"event_{n}",
vars_for_processing,
use_jacobian=False,
)[0]
if event.event_type == pybamm.EventType.TERMINATION:
terminate_events.append(event_call)
elif event.event_type == pybamm.EventType.INTERPOLANT_EXTRAPOLATION:
interpolant_extrapolation_events.append(event_call)
return (
casadi_switch_events,
terminate_events,
interpolant_extrapolation_events,
discontinuity_events,
)
def _set_consistent_initialization(self, model, time, inputs_dict):
"""
Set initialized states for the model. This is skipped if the solver is an
algebraic solver (since this would make the algebraic solver redundant), and if
the model doesn't have any algebraic equations (since there are no initial
conditions to be calculated in this case).
Parameters
----------
model : :class:`pybamm.BaseModel`
The model for which to calculate initial conditions.
time : numeric type
The time at which to calculate the initial conditions
inputs_dict : dict
Any input parameters to pass to the model when solving
update_rhs : bool
Whether to update the rhs. True for 'solve', False for 'step'.
"""
if self._algebraic_solver or model.len_alg == 0:
# Don't update model.y0
return
# Calculate consistent states for the algebraic equations
model.y0 = self.calculate_consistent_state(model, time, inputs_dict)
[docs]
def calculate_consistent_state(self, model, time=0, inputs=None):
"""
Calculate consistent state for the algebraic equations through
root-finding. model.y0 is used as the initial guess for rootfinding
Parameters
----------
model : :class:`pybamm.BaseModel`
The model for which to calculate initial conditions.
time : float
The time at which to calculate the initial conditions
inputs: dict, optional
Any input parameters to pass to the model when solving
Returns
-------
y0_consistent : array-like, same shape as y0_guess
Initial conditions that are consistent with the algebraic equations (roots
of the algebraic equations). If self.root_method == None then returns
model.y0.
"""
pybamm.logger.debug("Start calculating consistent states")
if self.root_method is None:
return model.y0
try:
root_sol = self.root_method._integrate(model, np.array([time]), inputs)
except pybamm.SolverError as e:
raise pybamm.SolverError(
f"Could not find consistent states: {e.args[0]}"
) from e
pybamm.logger.debug("Found consistent states")
self.check_extrapolation(root_sol, model.events)
y0 = root_sol.all_ys[0]
return y0
def _solve_process_calculate_sensitivities_arg(
inputs, model, calculate_sensitivities
):
# get a list-only version of calculate_sensitivities
if isinstance(calculate_sensitivities, bool):
if calculate_sensitivities:
calculate_sensitivities_list = [p for p in inputs.keys()]
else:
calculate_sensitivities_list = []
else:
calculate_sensitivities_list = calculate_sensitivities
calculate_sensitivities_list.sort()
if not hasattr(model, "calculate_sensitivities"):
model.calculate_sensitivities = []
# Check that calculate_sensitivites have not been updated
sensitivities_have_changed = (
calculate_sensitivities_list != model.calculate_sensitivities
)
# save sensitivity parameters so we can identify them later on
# (FYI: this is used in the Solution class)
model.calculate_sensitivities = calculate_sensitivities_list
return calculate_sensitivities_list, sensitivities_have_changed
[docs]
def solve(
self,
model,
t_eval=None,
inputs=None,
nproc=None,
calculate_sensitivities=False,
t_interp=None,
):
"""
Execute the solver setup and calculate the solution of the model at
specified times.
Parameters
----------
model : :class:`pybamm.BaseModel`
The model whose solution to calculate. Must have attributes rhs and
initial_conditions. All calls to solve must pass in the same model or
an error is raised
t_eval : None, list or ndarray, optional
The times (in seconds) at which to compute the solution. Defaults to None.
inputs : dict or list, optional
A dictionary or list of dictionaries describing any input parameters to
pass to the model when solving
nproc : int, optional
Number of processes to use when solving for more than one set of input
parameters. Defaults to value returned by "os.cpu_count()".
calculate_sensitivities : list of str or bool, optional
Whether the solver calculates sensitivities of all input parameters. Defaults to False.
If only a subset of sensitivities are required, can also pass a
list of input parameter names. **Limitations**: sensitivities are not calculated up to numerical tolerances
so are not guarenteed to be within the tolerances set by the solver, please raise an issue if you
require this functionality. Also, when using this feature with `pybamm.Experiment`, the sensitivities
do not take into account the movement of step-transitions wrt input parameters, so do not use this feature
if the timings of your experimental protocol change rapidly with respect to your input parameters.
t_interp : None, list or ndarray, optional
The times (in seconds) at which to interpolate the solution. Defaults to None.
Only valid for solvers that support intra-solve interpolation (`IDAKLUSolver`).
Returns
-------
:class:`pybamm.Solution` or list of :class:`pybamm.Solution` objects.
If type of `inputs` is `list`, return a list of corresponding
:class:`pybamm.Solution` objects.
Raises
------
:class:`pybamm.ModelError`
If an empty model is passed (`model.rhs = {}` and `model.algebraic={}` and
`model.variables = {}`)
:class:`RuntimeError`
If multiple calls to `solve` pass in different models
"""
pybamm.logger.info(f"Start solving {model.name} with {self.name}")
# Make sure model isn't empty
self._check_empty_model(model)
# t_eval can only be None if the solver is an algebraic solver. In that case
# set it to 0
if t_eval is None:
if self._algebraic_solver is False:
raise ValueError("t_eval cannot be None")
t_eval = np.array([0])
# If t_eval is provided as [t0, tf] return the solution at 100 points
elif isinstance(t_eval, list):
if len(t_eval) == 1 and self._algebraic_solver is True:
t_eval = np.array(t_eval)
elif len(t_eval) != 2:
raise pybamm.SolverError(
"'t_eval' can be provided as an array of times at which to "
"return the solution, or as a list [t0, tf] where t0 is the "
"initial time and tf is the final time, but has been provided "
f"as a list of length {len(t_eval)}."
)
elif not self.supports_interp:
t_eval = np.linspace(t_eval[0], t_eval[-1], 100)
# Make sure t_eval is monotonic
if (np.diff(t_eval) < 0).any():
raise pybamm.SolverError("t_eval must increase monotonically")
t_interp = self.process_t_interp(t_interp)
# Set up inputs
#
# Argument "inputs" can be either a list of input dicts or
# a single dict. The remaining of this function is only working
# with variable "input_list", which is a list of dictionaries.
# If "inputs" is a single dict, "inputs_list" is a list of only one dict.
inputs_list = inputs if isinstance(inputs, list) else [inputs]
model_inputs_list = [
self._set_up_model_inputs(model, inputs) for inputs in inputs_list
]
calculate_sensitivities_list, sensitivities_have_changed = (
BaseSolver._solve_process_calculate_sensitivities_arg(
model_inputs_list[0], model, calculate_sensitivities
)
)
# (Re-)calculate consistent initialization
# Assuming initial conditions do not depend on input parameters
# when len(inputs_list) > 1, only `model_inputs_list[0]`
# is passed to `_set_consistent_initialization`.
# See https://github.com/pybamm-team/PyBaMM/pull/1261
if len(model_inputs_list) > 1:
all_inputs_names = set(
itertools.chain.from_iterable(
[model_inputs.keys() for model_inputs in model_inputs_list]
)
)
if all_inputs_names:
initial_conditions_node_names = set(
[
it.name
for it in model.concatenated_initial_conditions.pre_order()
]
)
if all_inputs_names.issubset(initial_conditions_node_names):
raise pybamm.SolverError(
"Input parameters cannot appear in expression "
"for initial conditions."
)
# if any setup configuration has changed, we need to re-set up
if sensitivities_have_changed:
self._model_set_up.pop(model, None)
# CasadiSolver caches its integrators using model, so delete this too
if isinstance(self, pybamm.CasadiSolver):
self.integrators.pop(model, None)
# save sensitivity parameters so we can identify them later on
# (FYI: this is used in the Solution class)
model.calculate_sensitivities = calculate_sensitivities_list
# Set up (if not done already)
timer = pybamm.Timer()
# Set the initial conditions
if model not in self._model_set_up:
if len(self._model_set_up) > 0:
existing_model = next(iter(self._model_set_up))
raise RuntimeError(
"This solver has already been initialised for model "
f'"{existing_model.name}". Please create a separate '
"solver for this model"
)
# It is assumed that when len(inputs_list) > 1, model set
# up (initial condition, time-scale and length-scale) does
# not depend on input parameters. Therefore, only `model_inputs[0]`
# is passed to `set_up`.
# See https://github.com/pybamm-team/PyBaMM/pull/1261
self.set_up(model, model_inputs_list[0], t_eval)
self._model_set_up.update(
{model: {"initial conditions": model.concatenated_initial_conditions}}
)
elif (
self._model_set_up[model]["initial conditions"]
!= model.concatenated_initial_conditions
):
if self._algebraic_solver:
# For an algebraic solver, we don't need to set up the initial
# conditions function and we can just evaluate
# model.concatenated_initial_conditions
model.y0 = model.concatenated_initial_conditions.evaluate()
else:
# If the new initial conditions are different
# and cannot be evaluated directly, set up again
self.set_up(model, model_inputs_list[0], t_eval, ics_only=True)
self._model_set_up[model]["initial conditions"] = (
model.concatenated_initial_conditions
)
else:
# Set the standard initial conditions
self._set_initial_conditions(model, t_eval[0], model_inputs_list[0])
# Solve for the consistent initialization
self._set_consistent_initialization(model, t_eval[0], model_inputs_list[0])
set_up_time = timer.time()
timer.reset()
# Check initial conditions don't violate events
self._check_events_with_initialization(t_eval, model, model_inputs_list[0])
# Process discontinuities
(
start_indices,
end_indices,
t_eval,
) = self._get_discontinuity_start_end_indices(model, inputs, t_eval)
# Integrate separately over each time segment and accumulate into the solution
# object, restarting the solver at each discontinuity (and recalculating a
# consistent state afterwards if a DAE)
old_y0 = model.y0
solutions = None
for start_index, end_index in zip(start_indices, end_indices):
pybamm.logger.verbose(
f"Calling solver for {t_eval[start_index]} < t < {t_eval[end_index - 1]}"
)
if self.supports_parallel_solve:
# Jax and IDAKLU solver can accept a list of inputs
new_solutions = self._integrate(
model,
t_eval[start_index:end_index],
model_inputs_list,
t_interp,
)
else:
ninputs = len(model_inputs_list)
if ninputs == 1:
new_solution = self._integrate(
model,
t_eval[start_index:end_index],
model_inputs_list[0],
t_interp=t_interp,
)
new_solutions = [new_solution]
else:
with mp.get_context(self._mp_context).Pool(processes=nproc) as p:
new_solutions = p.starmap(
self._integrate,
zip(
[model] * ninputs,
[t_eval[start_index:end_index]] * ninputs,
model_inputs_list,
[t_interp] * ninputs,
),
)
p.close()
p.join()
# Setting the solve time for each segment.
# pybamm.Solution.__add__ assumes attribute solve_time.
solve_time = timer.time()
for sol in new_solutions:
sol.solve_time = solve_time
if start_index == start_indices[0]:
solutions = [sol for sol in new_solutions]
else:
for i, new_solution in enumerate(new_solutions):
solutions[i] = solutions[i] + new_solution
if solutions[0].termination != "final time":
break
if end_index != len(t_eval):
# setup for next integration subsection
last_state = solutions[0].y[:, -1]
# update y0 (for DAE solvers, this updates the initial guess for the
# rootfinder)
model.y0 = last_state
if len(model.algebraic) > 0:
model.y0 = self.calculate_consistent_state(
model, t_eval[end_index], model_inputs_list[0]
)
solve_time = timer.time()
for i, solution in enumerate(solutions):
# Check if extrapolation occurred
self.check_extrapolation(solution, model.events)
# Identify the event that caused termination and update the solution to
# include the event time and state
solutions[i], termination = self.get_termination_reason(
solution, model.events
)
# Assign times
solutions[i].set_up_time = set_up_time
# all solutions get the same solve time, but their integration time
# will be different (see https://github.com/pybamm-team/PyBaMM/pull/1261)
solutions[i].solve_time = solve_time
# Restore old y0
model.y0 = old_y0
# Report times
if len(solutions) == 1:
pybamm.logger.info(f"Finish solving {model.name} ({termination})")
pybamm.logger.info(
f"Set-up time: {solutions[0].set_up_time}, Solve time: {solutions[0].solve_time} (of which integration time: {solutions[0].integration_time}), "
f"Total time: {solutions[0].total_time}"
)
else:
pybamm.logger.info(f"Finish solving {model.name} for all inputs")
pybamm.logger.info(
f"Set-up time: {solutions[0].set_up_time}, Solve time: {solutions[0].solve_time}, Total time: {solutions[0].total_time}"
)
# Raise error if solutions[0] only contains one timestep (except for algebraic
# solvers, where we may only expect one time in the solution)
if (
self._algebraic_solver is False
and len(solutions[0].all_ts) == 1
and len(solutions[0].all_ts[0]) == 1
):
raise pybamm.SolverError(
"Solution time vector has length 1. "
"Check whether simulation terminated too early."
)
# Return solution(s)
if len(solutions) == 1:
return solutions[0]
else:
return solutions
@staticmethod
def _get_discontinuity_start_end_indices(model, inputs, t_eval):
if not model.discontinuity_events_eval:
pybamm.logger.verbose("No discontinuity events found")
return [0], [len(t_eval)], t_eval
# Calculate discontinuities
discontinuities = [
# Assuming that discontinuities do not depend on
# input parameters when len(input_list) > 1, only
# `inputs` is passed to `evaluate`.
# See https://github.com/pybamm-team/PyBaMM/pull/1261
event.expression.evaluate(inputs=inputs)
for event in model.discontinuity_events_eval
]
# make sure they are increasing in time
discontinuities = sorted(discontinuities)
# remove any identical discontinuities
discontinuities = [
v
for i, v in enumerate(discontinuities)
if (
i == len(discontinuities) - 1
or discontinuities[i] < discontinuities[i + 1]
)
and v > 0
]
# remove any discontinuities after end of t_eval
discontinuities = [v for v in discontinuities if v < t_eval[-1]]
pybamm.logger.verbose(f"Discontinuity events found at t = {discontinuities}")
if isinstance(inputs, list):
raise pybamm.SolverError(
"Cannot solve for a list of input parameters sets with discontinuities"
)
# insert time points around discontinuities in t_eval
# keep track of subsections to integrate by storing start and end indices
start_indices = [0]
end_indices = []
eps = sys.float_info.epsilon
for dtime in discontinuities:
dindex = np.searchsorted(t_eval, dtime, side="left")
end_indices.append(dindex + 1)
start_indices.append(dindex + 1)
if dtime * (1 - eps) < t_eval[dindex] < dtime * (1 + eps):
t_eval[dindex] *= 1 + eps
t_eval = np.insert(t_eval, dindex, dtime * (1 - eps))
else:
t_eval = np.insert(
t_eval, dindex, [dtime * (1 - eps), dtime * (1 + eps)]
)
end_indices.append(len(t_eval))
return start_indices, end_indices, t_eval
@staticmethod
def _check_events_with_initialization(t_eval, model, inputs_dict):
num_terminate_events = len(model.terminate_events_eval)
if num_terminate_events == 0:
return
if model.convert_to_format == "casadi":
inputs = casadi.vertcat(*[x for x in inputs_dict.values()])
events_eval = [None] * num_terminate_events
for idx, event in enumerate(model.terminate_events_eval):
if model.convert_to_format == "casadi":
event_eval = event(t_eval[0], model.y0, inputs)
elif model.convert_to_format in ["python", "jax"]:
event_eval = event(t=t_eval[0], y=model.y0, inputs=inputs_dict)
events_eval[idx] = event_eval
events_eval = np.array(events_eval)
if any(events_eval < 0):
# find the events that were triggered by initial conditions
termination_events = [
x for x in model.events if x.event_type == pybamm.EventType.TERMINATION
]
idxs = np.where(events_eval < 0)[0]
event_names = [termination_events[idx].name for idx in idxs]
raise pybamm.SolverError(
f"Events {event_names} are non-positive at initial conditions"
)
def _set_sens_initial_conditions_from(
self, solution: pybamm.Solution, model: pybamm.BaseModel
) -> tuple:
"""
A restricted version of BaseModel.set_initial_conditions_from that only extracts the
sensitivities from a solution object, and only for a model that has been descretised.
This is used when setting the initial conditions for a sensitivity model.
Parameters
----------
solution : :class:`pybamm.Solution`
The solution to use to initialize the model
model: :class:`pybamm.BaseModel`
The model whose sensitivities to set
Returns
-------
initial_conditions : tuple of ndarray
The initial conditions for the sensitivities, each element of the tuple
corresponds to an input parameter
"""
ninputs = len(model.calculate_sensitivities)
initial_conditions = tuple([] for _ in range(ninputs))
solution = solution.last_state
for var in model.initial_conditions:
final_state = solution[var.name]
final_state = final_state.sensitivities
final_state_eval = tuple(
final_state[key] for key in model.calculate_sensitivities
)
scale, reference = var.scale.value, var.reference.value
for i in range(ninputs):
scaled_final_state_eval = (final_state_eval[i] - reference) / scale
initial_conditions[i].append(scaled_final_state_eval)
# Also update the concatenated initial conditions if the model is already
# discretised
# Unpack slices for sorting
y_slices = {var: slce for var, slce in model.y_slices.items()}
slices = [y_slices[symbol][0] for symbol in model.initial_conditions.keys()]
# sort equations according to slices
concatenated_initial_conditions = [
casadi.vertcat(*[eq for _, eq in sorted(zip(slices, init))])
for init in initial_conditions
]
return concatenated_initial_conditions
def process_t_interp(self, t_interp):
# set a variable for this
no_interp = (not self.supports_interp) and (
t_interp is not None and len(t_interp) != 0
)
if no_interp:
warnings.warn(
f"Explicit interpolation times not implemented for {self.name}",
pybamm.SolverWarning,
stacklevel=2,
)
if no_interp or t_interp is None:
t_interp = np.empty(0)
return t_interp
[docs]
def step(
self,
old_solution,
model,
dt,
t_eval=None,
npts=None,
inputs=None,
save=True,
calculate_sensitivities=False,
t_interp=None,
):
"""
Step the solution of the model forward by a given time increment. The
first time this method is called it executes the necessary setup by
calling `self.set_up(model)`.
Parameters
----------
old_solution : :class:`pybamm.Solution` or None
The previous solution to be added to. If `None`, a new solution is created.
model : :class:`pybamm.BaseModel`
The model whose solution to calculate. Must have attributes rhs and
initial_conditions
dt : numeric type
The timestep (in seconds) over which to step the solution
t_eval : list or numpy.ndarray, optional
An array of times at which to stop the simulation and return the solution during the step
(Note: t_eval is the time measured from the start of the step, so should start at 0 and end at dt).
By default, the solution is returned at t0 and t0 + dt.
npts : deprecated
inputs : dict, optional
Any input parameters to pass to the model when solving
save : bool, optional
Save solution with all previous timesteps. Defaults to True.
calculate_sensitivities : list of str or bool, optional
Whether the solver calculates sensitivities of all input parameters. Defaults to False.
If only a subset of sensitivities are required, can also pass a
list of input parameter names. **Limitations**: sensitivities are not calculated up to numerical tolerances
so are not guarenteed to be within the tolerances set by the solver, please raise an issue if you
require this functionality. Also, when using this feature with `pybamm.Experiment`, the sensitivities
do not take into account the movement of step-transitions wrt input parameters, so do not use this feature
if the timings of your experimental protocol change rapidly with respect to your input parameters.
t_interp : None, list or ndarray, optional
The times (in seconds) at which to interpolate the solution. Defaults to None.
Only valid for solvers that support intra-solve interpolation (`IDAKLUSolver`).
Raises
------
:class:`pybamm.ModelError`
If an empty model is passed (`model.rhs = {}` and `model.algebraic = {}` and
`model.variables = {}`)
"""
if old_solution is None:
old_solution = pybamm.EmptySolution()
if not (
isinstance(old_solution, pybamm.EmptySolution)
or old_solution.termination == "final time"
or "[experiment]" in old_solution.termination
):
# Return same solution as an event has already been triggered
# With hack to allow stepping past experiment current / voltage cut-off
return old_solution
# Make sure model isn't empty
self._check_empty_model(model)
# Make sure dt is greater than zero
if dt <= 0:
raise pybamm.SolverError("Step time must be >0")
# Raise deprecation warning for npts and convert it to t_eval
if npts is not None:
warnings.warn(
"The 'npts' parameter is deprecated, use 't_eval' instead.",
DeprecationWarning,
stacklevel=2,
)
t_eval = np.linspace(0, dt, npts)
elif t_eval is None:
t_eval = np.array([0, dt])
elif t_eval[0] != 0 or t_eval[-1] != dt:
raise pybamm.SolverError(
"Elements inside array t_eval must lie in the closed interval 0 to dt"
)
else:
pass
t_interp = self.process_t_interp(t_interp)
t_start = old_solution.t[-1]
t_eval = t_start + t_eval
t_interp = t_start + t_interp
t_end = t_start + dt
if t_start == 0:
t_start_shifted = t_start
else:
# find the next largest floating point value for t_start
# to avoid repeated times in the solution
# from having the same time at the end of the previous step and
# the start of the next step
t_start_shifted = np.nextafter(t_start, np.inf)
t_eval[0] = t_start_shifted
if t_interp.size > 0 and t_interp[0] == t_start:
t_interp[0] = t_start_shifted
# Set timer
timer = pybamm.Timer()
# Set up inputs
model_inputs = self._set_up_model_inputs(model, inputs)
# process calculate_sensitivities argument
calculate_sensitivities_list, sensitivities_have_changed = (
BaseSolver._solve_process_calculate_sensitivities_arg(
model_inputs, model, calculate_sensitivities
)
)
first_step_this_model = model not in self._model_set_up
if first_step_this_model or sensitivities_have_changed:
if len(self._model_set_up) > 0:
existing_model = next(iter(self._model_set_up))
raise RuntimeError(
"This solver has already been initialised for model "
f'"{existing_model.name}". Please create a separate '
"solver for this model"
)
self.set_up(model, model_inputs)
self._model_set_up.update(
{model: {"initial conditions": model.concatenated_initial_conditions}}
)
if (
isinstance(old_solution, pybamm.EmptySolution)
and old_solution.termination is None
):
pybamm.logger.verbose(f"Start stepping {model.name} with {self.name}")
using_sensitivities = len(model.calculate_sensitivities) > 0
if isinstance(old_solution, pybamm.EmptySolution):
if not first_step_this_model:
# reset y0 to original initial conditions
self.set_up(model, model_inputs, ics_only=True)
elif old_solution.all_models[-1] == model:
last_state = old_solution.last_state
model.y0 = last_state.all_ys[0]
if using_sensitivities:
full_sens = last_state._all_sensitivities["all"][0]
model.y0S = tuple(full_sens[:, i] for i in range(full_sens.shape[1]))
else:
_, concatenated_initial_conditions = model.set_initial_conditions_from(
old_solution, return_type="ics"
)
model.y0 = concatenated_initial_conditions.evaluate(0, inputs=model_inputs)
if using_sensitivities:
model.y0S = self._set_sens_initial_conditions_from(old_solution, model)
set_up_time = timer.time()
# (Re-)calculate consistent initialization
self._set_consistent_initialization(model, t_start_shifted, model_inputs)
# Check consistent initialization doesn't violate events
self._check_events_with_initialization(t_eval, model, model_inputs)
# Step
pybamm.logger.verbose(f"Stepping for {t_start_shifted:.0f} < t < {t_end:.0f}")
timer.reset()
# API for _integrate is different for JaxSolver and IDAKLUSolver
if self.supports_parallel_solve:
solutions = self._integrate(model, t_eval, [model_inputs], t_interp)
solution = solutions[0]
else:
solution = self._integrate(model, t_eval, model_inputs, t_interp)
solution.solve_time = timer.time()
# Check if extrapolation occurred
self.check_extrapolation(solution, model.events)
# Identify the event that caused termination and update the solution to
# include the event time and state
solution, termination = self.get_termination_reason(solution, model.events)
# Assign setup time
solution.set_up_time = set_up_time
# Report times
pybamm.logger.verbose(f"Finish stepping {model.name} ({termination})")
pybamm.logger.verbose(
f"Set-up time: {solution.set_up_time}, Step time: {solution.solve_time} (of which integration time: {solution.integration_time}), "
f"Total time: {solution.total_time}"
)
# Return solution
if save is False:
return solution
else:
return old_solution + solution
[docs]
@staticmethod
def get_termination_reason(solution, events):
"""
Identify the cause for termination. In particular, if the solver terminated
due to an event, (try to) pinpoint which event was responsible. If an event
occurs the event time and state are added to the solution object.
Note that the current approach (evaluating all the events and then finding which
one is smallest at the final timestep) is pretty crude, but is the easiest one
that works for all the different solvers.
Parameters
----------
solution : :class:`pybamm.Solution`
The solution object
events : dict
Dictionary of events
"""
termination_events = [
x for x in events if x.event_type == pybamm.EventType.TERMINATION
]
if solution.termination == "final time":
return (
solution,
"the solver successfully reached the end of the integration interval",
)
# solution.termination == "event":
pybamm.logger.debug("Start post-processing events")
if solution.closest_event_idx is not None:
solution.termination = (
f"event: {termination_events[solution.closest_event_idx].name}"
)
else:
# Get final event value
final_event_values = {}
for event in termination_events:
final_event_values[event.name] = event.expression.evaluate(
solution.t_event,
solution.y_event,
inputs=solution.all_inputs[-1],
)
termination_event = min(final_event_values, key=final_event_values.get)
# Check that it's actually an event
if final_event_values[termination_event] > 0.1: # pragma: no cover
# Hard to test this
raise pybamm.SolverError(
"Could not determine which event was triggered "
"(possibly due to NaNs)"
)
# Add the event to the solution object
solution.termination = f"event: {termination_event}"
# Update t, y and inputs to include event time and state
# Note: if the final entry of t is equal to the event time we skip
# this (having duplicate entries causes an error later in ProcessedVariable)
if solution.t_event != solution.all_ts[-1][-1]:
event_sol = pybamm.Solution(
solution.t_event,
solution.y_event,
solution.all_models[-1],
solution.all_inputs[-1],
solution.t_event,
solution.y_event,
solution.termination,
variables_returned=solution.variables_returned,
)
event_sol.solve_time = 0
event_sol.integration_time = 0
solution = solution + event_sol
pybamm.logger.debug("Finish post-processing events")
return solution, solution.termination
def _check_empty_model(self, model):
# Make sure model isn't empty
if (
(len(model.rhs) == 0 and len(model.algebraic) == 0)
and model.concatenated_rhs is None
and model.concatenated_algebraic is None
and not isinstance(self, pybamm.DummySolver)
):
raise pybamm.ModelError(
"Cannot simulate an empty model, use `pybamm.DummySolver` instead"
)
def get_platform_context(self, system_type: str):
# Set context for parallel processing depending on the platform
if system_type.lower() in ["linux", "darwin"]:
return "fork"
return "spawn"
@staticmethod
def _set_up_model_inputs(model, inputs):
"""Set up input parameters"""
if inputs is None:
inputs = {}
else:
inputs = ParameterValues.check_parameter_values(inputs)
# Go through all input parameters that can be found in the model
# Only keep the ones that are actually used in the model
# If any of them are *not* provided by "inputs", raise an error
inputs_in_model = {}
for input_param in model.input_parameters:
name = input_param.name
if name not in inputs:
raise pybamm.SolverError(f"No value provided for input '{name}'")
inputs_in_model[name] = inputs[name]
inputs = inputs_in_model
ordered_inputs_names = list(inputs.keys())
ordered_inputs_names.sort()
ordered_inputs = {name: inputs[name] for name in ordered_inputs_names}
return ordered_inputs
def process(
symbol, name, vars_for_processing, use_jacobian=None, return_jacp_stacked=None
):
"""
Parameters
----------
symbol: :class:`pybamm.Symbol`
expression tree to convert
name: str
function evaluators created will have this base name
use_jacobian: bool, optional
whether to return Jacobian functions
return_jacp_stacked: bool, optional
returns Jacobian function wrt stacked parameters instead of jacp
Returns
-------
func: :class:`pybamm.EvaluatorPython` or
:class:`pybamm.EvaluatorJax` or
:class:`casadi.Function`
evaluator for the function $f(y, t, p)$ given by `symbol`
jac: :class:`pybamm.EvaluatorPython` or
:class:`pybamm.EvaluatorJaxJacobian` or
:class:`casadi.Function`
evaluator for the Jacobian $\\frac{\\partial f}{\\partial y}$
of the function given by `symbol`
jacp: :class:`pybamm.EvaluatorPython` or
:class:`pybamm.EvaluatorJaxSensitivities` or
:class:`casadi.Function`
evaluator for the parameter sensitivities
$\frac{\\partial f}{\\partial p}$
of the function given by `symbol`
jac_action: :class:`pybamm.EvaluatorPython` or
:class:`pybamm.EvaluatorJax` or
:class:`casadi.Function`
evaluator for product of the Jacobian with a vector $v$,
i.e. $\\frac{\\partial f}{\\partial y} * v$
"""
def report(string):
# don't log event conversion
if "event" not in string:
pybamm.logger.verbose(string)
model = vars_for_processing["model"]
if use_jacobian is None:
use_jacobian = model.use_jacobian
if model.convert_to_format == "jax":
report(f"Converting {name} to jax")
func = pybamm.EvaluatorJax(symbol)
jacp = None
if model.calculate_sensitivities:
report(
f"Calculating sensitivities for {name} with respect "
f"to parameters {model.calculate_sensitivities} using jax"
)
jacp = func.get_sensitivities()
if use_jacobian:
report(f"Calculating jacobian for {name} using jax")
jac = func.get_jacobian()
jac_action = func.get_jacobian_action()
else:
jac = None
jac_action = None
elif model.convert_to_format != "casadi":
y = vars_for_processing["y"]
jacobian = vars_for_processing["jacobian"]
if model.calculate_sensitivities:
raise pybamm.SolverError( # pragma: no cover
"Sensitivies are no longer supported for the python "
"evaluator. Please use `convert_to_format = 'casadi'`, or `jax` "
"to calculate sensitivities."
)
else:
jacp = None
if use_jacobian:
report(f"Calculating jacobian for {name}")
jac = jacobian.jac(symbol, y)
report(f"Converting jacobian for {name} to python")
jac = pybamm.EvaluatorPython(jac)
# cannot do jacobian action efficiently for now
jac_action = None
else:
jac = None
jac_action = None
report(f"Converting {name} to python")
func = pybamm.EvaluatorPython(symbol)
else:
t_casadi = vars_for_processing["t_casadi"]
y_casadi = vars_for_processing["y_casadi"]
p_casadi = vars_for_processing["p_casadi"]
p_casadi_stacked = vars_for_processing["p_casadi_stacked"]
# Process with CasADi
report(f"Converting {name} to CasADi")
casadi_expression = symbol.to_casadi(t_casadi, y_casadi, inputs=p_casadi)
# Add sensitivity vectors to the rhs and algebraic equations
jacp = None
if model.calculate_sensitivities:
report(
f"Calculating sensitivities for {name} with respect "
f"to parameters {model.calculate_sensitivities} using "
"CasADi"
)
# Compute derivate wrt p-stacked (can be passed to solver to
# compute sensitivities online)
if return_jacp_stacked:
jacp = casadi.Function(
f"d{name}_dp",
[t_casadi, y_casadi, p_casadi_stacked],
[casadi.jacobian(casadi_expression, p_casadi_stacked)],
)
else:
# WARNING, jacp for convert_to_format=casadi does not return a dict
# instead it returns multiple return values, one for each param
# TODO: would it be faster to do the jacobian wrt pS_casadi_stacked?
jacp = casadi.Function(
name + "_jacp",
[t_casadi, y_casadi, p_casadi_stacked],
[
casadi.densify(
casadi.jacobian(casadi_expression, p_casadi[pname])
)
for pname in model.calculate_sensitivities
],
)
if use_jacobian:
report(f"Calculating jacobian for {name} using CasADi")
jac_casadi = casadi.jacobian(casadi_expression, y_casadi)
jac = casadi.Function(
name + "_jac",
[t_casadi, y_casadi, p_casadi_stacked],
[jac_casadi],
)
v = casadi.MX.sym(
"v",
model.len_rhs_and_alg,
)
jac_action_casadi = casadi.densify(
casadi.jtimes(casadi_expression, y_casadi, v)
)
jac_action = casadi.Function(
name + "_jac_action",
[t_casadi, y_casadi, p_casadi_stacked, v],
[jac_action_casadi],
)
else:
jac = None
jac_action = None
func = casadi.Function(
name, [t_casadi, y_casadi, p_casadi_stacked], [casadi_expression]
)
return func, jac, jacp, jac_action
