#
# Solution class
#
import casadi
import numbers
import numpy as np
import pickle
import pybamm
import pandas as pd
from scipy.io import savemat
[docs]class Solution(object):
"""
Class containing the solution of, and various attributes associated with, a PyBaMM
model.
Parameters
----------
all_ts : :class:`numpy.array`, size (n,) (or list of these)
A one-dimensional array containing the times at which the solution is evaluated.
A list of times can be provided instead to initialize a solution with
sub-solutions.
all_ys : :class:`numpy.array`, size (m, n) (or list of these)
A two-dimensional array containing the values of the solution. y[i, :] is the
vector of solutions at time t[i].
A list of ys can be provided instead to initialize a solution with
sub-solutions.
all_models : :class:`pybamm.BaseModel`
The model that was used to calculate the solution.
A list of models can be provided instead to initialize a solution with
sub-solutions that have been calculated using those models.
all_inputs : dict (or list of these)
The inputs that were used to calculate the solution
A list of inputs can be provided instead to initialize a solution with
sub-solutions.
t_event : :class:`numpy.array`, size (1,)
A zero-dimensional array containing the time at which the event happens.
y_event : :class:`numpy.array`, size (m,)
A one-dimensional array containing the value of the solution at the time when
the event happens.
termination : str
String to indicate why the solution terminated
sensitivities: bool or dict
True if sensitivities included as the solution of the explicit forwards
equations. False if no sensitivities included/wanted. Dict if sensitivities are
provided as a dict of {parameter: sensitivities} pairs.
"""
def __init__(
self,
all_ts,
all_ys,
all_models,
all_inputs,
t_event=None,
y_event=None,
termination="final time",
sensitivities=False,
):
if not isinstance(all_ts, list):
all_ts = [all_ts]
if not isinstance(all_ys, list):
all_ys = [all_ys]
if not isinstance(all_models, list):
all_models = [all_models]
self._all_ts = all_ts
self._all_ys = all_ys
self._all_ys_and_sens = all_ys
self._all_models = all_models
# Set up inputs
if not isinstance(all_inputs, list):
all_inputs_copy = dict(all_inputs)
for key, value in all_inputs_copy.items():
if isinstance(value, numbers.Number):
all_inputs_copy[key] = np.array([value])
self.all_inputs = [all_inputs_copy]
else:
self.all_inputs = all_inputs
self.sensitivities = sensitivities
self._t_event = t_event
self._y_event = y_event
self._termination = termination
self.has_symbolic_inputs = any(
isinstance(v, casadi.MX) for v in self.all_inputs[0].values()
)
# Copy the timescale_eval and lengthscale_evals if they exist
if hasattr(all_models[0], "timescale_eval"):
self.timescale_eval = all_models[0].timescale_eval
else:
self.timescale_eval = all_models[0].timescale.evaluate()
if hasattr(all_models[0], "length_scales_eval"):
self.length_scales_eval = all_models[0].length_scales_eval
else:
self.length_scales_eval = {
domain: scale.evaluate()
for domain, scale in all_models[0].length_scales.items()
}
# Events
self._t_event = t_event
self._y_event = y_event
self._termination = termination
self.closest_event_idx = None
# Initialize times
self.set_up_time = None
self.solve_time = None
self.integration_time = None
# initiaize empty variables and data
self._variables = pybamm.FuzzyDict()
self.data = pybamm.FuzzyDict()
# Add self as sub-solution for compatibility with ProcessedVariable
self._sub_solutions = [self]
# initialize empty cycles
self._cycles = []
# Initialize empty summary variables
self._summary_variables = None
# Solution now uses CasADi
pybamm.citations.register("Andersson2019")
def extract_explicit_sensitivities(self):
# if we got here, we havn't set y yet
self.set_y()
# extract sensitivities from full y solution
self._y, self._sensitivities = self._extract_explicit_sensitivities(
self.all_models[0], self.y, self.t, self.all_inputs[0]
)
# make sure we remove all sensitivities from all_ys
for index, (model, ys, ts, inputs) in enumerate(
zip(self.all_models, self.all_ys, self.all_ts, self.all_inputs)
):
self._all_ys[index], _ = self._extract_explicit_sensitivities(
model, ys, ts, inputs
)
def _extract_explicit_sensitivities(self, model, y, t_eval, inputs):
"""
given a model and a solution y, extracts the sensitivities
Parameters
--------
model : :class:`pybamm.BaseModel`
A model that has been already setup by this base solver
y: ndarray
The solution of the full explicit sensitivity equations
t_eval: ndarray
The evaluation times
inputs: dict
parameter inputs
Returns
-------
y: ndarray
The solution of the ode/dae in model
sensitivities: dict of (string: ndarray)
A dictionary of parameter names, and the corresponding solution of
the sensitivity equations
"""
n_states = model.len_rhs_and_alg
n_rhs = model.len_rhs
n_alg = model.len_alg
# Get the point where the algebraic equations start
if model.len_rhs != 0:
n_p = model.len_rhs_sens // model.len_rhs
else:
n_p = model.len_alg_sens // model.len_alg
len_rhs_and_sens = model.len_rhs + model.len_rhs_sens
n_t = len(t_eval)
# y gets the part of the solution vector that correspond to the
# actual ODE/DAE solution
# save sensitivities as a dictionary
# first save the whole sensitivity matrix
# reshape using Fortran order to get the right array:
# t0_x0_p0, t0_x0_p1, ..., t0_x0_pn
# t0_x1_p0, t0_x1_p1, ..., t0_x1_pn
# ...
# t0_xn_p0, t0_xn_p1, ..., t0_xn_pn
# t1_x0_p0, t1_x0_p1, ..., t1_x0_pn
# t1_x1_p0, t1_x1_p1, ..., t1_x1_pn
# ...
# t1_xn_p0, t1_xn_p1, ..., t1_xn_pn
# ...
# tn_x0_p0, tn_x0_p1, ..., tn_x0_pn
# tn_x1_p0, tn_x1_p1, ..., tn_x1_pn
# ...
# tn_xn_p0, tn_xn_p1, ..., tn_xn_pn
# 1, Extract rhs and alg sensitivities and reshape into 3D matrices
# with shape (n_p, n_states, n_t)
if isinstance(y, casadi.DM):
y_full = y.full()
else:
y_full = y
ode_sens = y_full[n_rhs:len_rhs_and_sens, :].reshape(n_p, n_rhs, n_t)
alg_sens = y_full[len_rhs_and_sens + n_alg :, :].reshape(n_p, n_alg, n_t)
# 2. Concatenate into a single 3D matrix with shape (n_p, n_states, n_t)
# i.e. along first axis
full_sens_matrix = np.concatenate([ode_sens, alg_sens], axis=1)
# Transpose and reshape into a (n_states * n_t, n_p) matrix
full_sens_matrix = full_sens_matrix.transpose(2, 1, 0).reshape(
n_t * n_states, n_p
)
# Save the full sensitivity matrix
sensitivity = {"all": full_sens_matrix}
# also save the sensitivity wrt each parameter (read the columns of the
# sensitivity matrix)
start = 0
for name in model.calculate_sensitivities:
inp = inputs[name]
input_size = inp.shape[0]
end = start + input_size
sensitivity[name] = full_sens_matrix[:, start:end]
start = end
y_dae = np.vstack(
[
y[: model.len_rhs, :],
y[len_rhs_and_sens : len_rhs_and_sens + model.len_alg, :],
]
)
return y_dae, sensitivity
@property
def t(self):
"""Times at which the solution is evaluated"""
try:
return self._t
except AttributeError:
self.set_t()
return self._t
def set_t(self):
self._t = np.concatenate(self.all_ts)
if any(np.diff(self._t) <= 0):
raise ValueError("Solution time vector must be strictly increasing")
@property
def y(self):
"""Values of the solution"""
try:
return self._y
except AttributeError:
self.set_y()
# if y is evaluated before sensitivities then need to extract them
if isinstance(self._sensitivities, bool) and self._sensitivities:
self.extract_explicit_sensitivities()
return self._y
@property
def sensitivities(self):
"""Values of the sensitivities. Returns a dict of param_name: np_array"""
if isinstance(self._sensitivities, bool):
if self._sensitivities:
self.extract_explicit_sensitivities()
else:
self._sensitivities = {}
return self._sensitivities
@sensitivities.setter
def sensitivities(self, value):
"""Updates the sensitivity"""
# sensitivities must be a dict or bool
if not isinstance(value, (bool, dict)):
raise TypeError("sensitivities arg needs to be a bool or dict")
self._sensitivities = value
def set_y(self):
try:
if isinstance(self.all_ys[0], (casadi.DM, casadi.MX)):
self._y = casadi.horzcat(*self.all_ys)
else:
self._y = np.hstack(self.all_ys)
except ValueError:
raise pybamm.SolverError(
"The solution is made up from different models, so `y` cannot be "
"computed explicitly."
)
@property
def all_ts(self):
return self._all_ts
@property
def all_ys(self):
return self._all_ys
@property
def all_models(self):
"""Model(s) used for solution"""
return self._all_models
@property
def all_inputs_casadi(self):
try:
return self._all_inputs_casadi
except AttributeError:
self._all_inputs_casadi = [
casadi.vertcat(*inp.values()) for inp in self.all_inputs
]
return self._all_inputs_casadi
@property
def t_event(self):
"""Time at which the event happens"""
return self._t_event
@property
def y_event(self):
"""Value of the solution at the time of the event"""
return self._y_event
@property
def termination(self):
"""Reason for termination"""
return self._termination
@termination.setter
def termination(self, value):
"""Updates the reason for termination"""
self._termination = value
@property
def first_state(self):
"""
A Solution object that only contains the first state. This is faster to evaluate
than the full solution when only the first state is needed (e.g. to initialize
a model with the solution)
"""
try:
return self._first_state
except AttributeError:
new_sol = Solution(
self.all_ts[0][:1],
self.all_ys[0][:, :1],
self.all_models[:1],
self.all_inputs[:1],
None,
None,
"success",
)
new_sol._all_inputs_casadi = self.all_inputs_casadi[:1]
new_sol._sub_solutions = self.sub_solutions[:1]
new_sol.solve_time = 0
new_sol.integration_time = 0
new_sol.set_up_time = 0
self._first_state = new_sol
return self._first_state
@property
def last_state(self):
"""
A Solution object that only contains the final state. This is faster to evaluate
than the full solution when only the final state is needed (e.g. to initialize
a model with the solution)
"""
try:
return self._last_state
except AttributeError:
new_sol = Solution(
self.all_ts[-1][-1:],
self.all_ys[-1][:, -1:],
self.all_models[-1:],
self.all_inputs[-1:],
self.t_event,
self.y_event,
self.termination,
)
new_sol._all_inputs_casadi = self.all_inputs_casadi[-1:]
new_sol._sub_solutions = self.sub_solutions[-1:]
new_sol.solve_time = 0
new_sol.integration_time = 0
new_sol.set_up_time = 0
self._last_state = new_sol
return self._last_state
@property
def total_time(self):
return self.set_up_time + self.solve_time
@property
def cycles(self):
return self._cycles
@cycles.setter
def cycles(self, cycles):
self._cycles = cycles
@property
def summary_variables(self):
return self._summary_variables
def set_summary_variables(self, all_summary_variables):
summary_variables = {var: [] for var in all_summary_variables[0]}
for sum_vars in all_summary_variables:
for name, value in sum_vars.items():
summary_variables[name].append(value)
summary_variables["Cycle number"] = range(1, len(all_summary_variables) + 1)
self.all_summary_variables = all_summary_variables
self._summary_variables = pybamm.FuzzyDict(
{name: np.array(value) for name, value in summary_variables.items()}
)
[docs] def update(self, variables):
"""Add ProcessedVariables to the dictionary of variables in the solution"""
# make sure that sensitivities are extracted if required
if isinstance(self._sensitivities, bool) and self._sensitivities:
self.extract_explicit_sensitivities()
# Convert single entry to list
if isinstance(variables, str):
variables = [variables]
# Process
for key in variables:
pybamm.logger.debug("Post-processing {}".format(key))
# If there are symbolic inputs then we need to make a
# ProcessedSymbolicVariable
if self.has_symbolic_inputs is True:
var = pybamm.ProcessedSymbolicVariable(
self.all_models[0].variables[key], self
)
# Otherwise a standard ProcessedVariable is ok
else:
vars_pybamm = [model.variables[key] for model in self.all_models]
# Iterate through all models, some may be in the list several times and
# therefore only get set up once
vars_casadi = []
for model, ys, inputs, var_pybamm in zip(
self.all_models, self.all_ys, self.all_inputs, vars_pybamm
):
if key in model._variables_casadi:
var_casadi = model._variables_casadi[key]
else:
t_MX = casadi.MX.sym("t")
y_MX = casadi.MX.sym("y", ys.shape[0])
symbolic_inputs_dict = {
key: casadi.MX.sym("input", value.shape[0])
for key, value in inputs.items()
}
symbolic_inputs = casadi.vertcat(
*[p for p in symbolic_inputs_dict.values()]
)
# Convert variable to casadi
# Make all inputs symbolic first for converting to casadi
var_sym = var_pybamm.to_casadi(
t_MX, y_MX, inputs=symbolic_inputs_dict
)
var_casadi = casadi.Function(
"variable", [t_MX, y_MX, symbolic_inputs], [var_sym]
)
model._variables_casadi[key] = var_casadi
vars_casadi.append(var_casadi)
var = pybamm.ProcessedVariable(vars_pybamm, vars_casadi, self)
# Save variable and data
self._variables[key] = var
self.data[key] = var.data
def __getitem__(self, key):
"""Read a variable from the solution. Variables are created 'just in time', i.e.
only when they are called.
Parameters
----------
key : str
The name of the variable
Returns
-------
:class:`pybamm.ProcessedVariable`
A variable that can be evaluated at any time or spatial point. The
underlying data for this variable is available in its attribute ".data"
"""
# return it if it exists
if key in self._variables:
return self._variables[key]
else:
# otherwise create it, save it and then return it
self.update(key)
return self._variables[key]
[docs] def plot(self, output_variables=None, **kwargs):
"""
A method to quickly plot the outputs of the solution. Creates a
:class:`pybamm.QuickPlot` object (with keyword arguments 'kwargs') and
then calls :meth:`pybamm.QuickPlot.dynamic_plot`.
Parameters
----------
output_variables: list, optional
A list of the variables to plot.
**kwargs
Additional keyword arguments passed to
:meth:`pybamm.QuickPlot.dynamic_plot`.
For a list of all possible keyword arguments see :class:`pybamm.QuickPlot`.
"""
return pybamm.dynamic_plot(self, output_variables=output_variables, **kwargs)
[docs] def clear_casadi_attributes(self):
"""Remove casadi objects for pickling, will be computed again automatically"""
# t_MX = None
# y_MX = None
# symbolic_inputs = None
# symbolic_inputs_dict = None
pass
[docs] def save(self, filename):
"""Save the whole solution using pickle"""
# No warning here if len(self.data)==0 as solution can be loaded
# and used to process new variables
self.clear_casadi_attributes()
# Pickle
with open(filename, "wb") as f:
pickle.dump(self, f, pickle.HIGHEST_PROTOCOL)
[docs] def save_data(self, filename, variables=None, to_format="pickle", short_names=None):
"""
Save solution data only (raw arrays)
Parameters
----------
filename : str
The name of the file to save data to
variables : list, optional
List of variables to save. If None, saves all of the variables that have
been created so far
to_format : str, optional
The format to save to. Options are:
- 'pickle' (default): creates a pickle file with the data dictionary
- 'matlab': creates a .mat file, for loading in matlab
- 'csv': creates a csv file (0D variables only)
short_names : dict, optional
Dictionary of shortened names to use when saving. This may be necessary when
saving to MATLAB, since no spaces or special characters are allowed in
MATLAB variable names. Note that not all the variables need to be given
a short name.
"""
if variables is None:
# variables not explicitly provided -> save all variables that have been
# computed
data = self.data
else:
# otherwise, save only the variables specified
data = {}
for name in variables:
data[name] = self[name].data
if len(data) == 0:
raise ValueError(
"""
Solution does not have any data. Please provide a list of variables
to save.
"""
)
# Use any short names if provided
data_short_names = {}
short_names = short_names or {}
for name, var in data.items():
# change to short name if it exists
if name in short_names:
data_short_names[short_names[name]] = var
else:
data_short_names[name] = var
if to_format == "pickle":
with open(filename, "wb") as f:
pickle.dump(data_short_names, f, pickle.HIGHEST_PROTOCOL)
elif to_format == "matlab":
# Check all the variable names only contain a-z, A-Z or _ or numbers
for name in data_short_names.keys():
# Check the string only contains the following ASCII:
# a-z (97-122)
# A-Z (65-90)
# _ (95)
# 0-9 (48-57) but not in the first position
for i, s in enumerate(name):
if not (
97 <= ord(s) <= 122
or 65 <= ord(s) <= 90
or ord(s) == 95
or (i > 0 and 48 <= ord(s) <= 57)
):
raise ValueError(
"Invalid character '{}' found in '{}'. ".format(s, name)
+ "MATLAB variable names must only contain a-z, A-Z, _, "
"or 0-9 (except the first position). "
"Use the 'short_names' argument to pass an alternative "
"variable name, e.g. \n\n"
"\tsolution.save_data(filename, "
"['Electrolyte concentration'], to_format='matlab, "
"short_names={'Electrolyte concentration': 'c_e'})"
)
savemat(filename, data_short_names)
elif to_format == "csv":
for name, var in data_short_names.items():
if var.ndim >= 2:
raise ValueError(
"only 0D variables can be saved to csv, but '{}' is {}D".format(
name, var.ndim - 1
)
)
df = pd.DataFrame(data_short_names)
df.to_csv(filename, index=False)
else:
raise ValueError("format '{}' not recognised".format(to_format))
@property
def sub_solutions(self):
"""List of sub solutions that have been
concatenated to form the full solution"""
return self._sub_solutions
def __add__(self, other):
"""Adds two solutions together, e.g. when stepping"""
if not isinstance(other, Solution):
raise pybamm.SolverError(
"Only a Solution or None can be added to a Solution"
)
# Special case: new solution only has one timestep and it is already in the
# existing solution. In this case, return a copy of the existing solution
if (
len(other.all_ts) == 1
and len(other.all_ts[0]) == 1
and other.all_ts[0][0] == self.all_ts[-1][-1]
):
new_sol = self.copy()
# Update termination using the latter solution
new_sol._termination = other.termination
new_sol._t_event = other._t_event
new_sol._y_event = other._y_event
return new_sol
# Update list of sub-solutions
if other.all_ts[0][0] == self.all_ts[-1][-1]:
# Skip first time step if it is repeated
all_ts = self.all_ts + [other.all_ts[0][1:]] + other.all_ts[1:]
all_ys = self.all_ys + [other.all_ys[0][:, 1:]] + other.all_ys[1:]
else:
all_ts = self.all_ts + other.all_ts
all_ys = self.all_ys + other.all_ys
new_sol = Solution(
all_ts,
all_ys,
self.all_models + other.all_models,
self.all_inputs + other.all_inputs,
other.t_event,
other.y_event,
other.termination,
bool(self.sensitivities),
)
new_sol.closest_event_idx = other.closest_event_idx
new_sol._all_inputs_casadi = self.all_inputs_casadi + other.all_inputs_casadi
# Set solution time
new_sol.solve_time = self.solve_time + other.solve_time
new_sol.integration_time = self.integration_time + other.integration_time
# Set sub_solutions
new_sol._sub_solutions = self.sub_solutions + other.sub_solutions
return new_sol
def __radd__(self, other):
"""
Right-side adding with special handling for the case None + Solution (returns
Solution)
"""
if other is None:
return self.copy()
else:
raise pybamm.SolverError(
"Only a Solution or None can be added to a Solution"
)
def copy(self):
new_sol = self.__class__(
self.all_ts,
self.all_ys,
self.all_models,
self.all_inputs,
self.t_event,
self.y_event,
self.termination,
)
new_sol._all_inputs_casadi = self.all_inputs_casadi
new_sol._sub_solutions = self.sub_solutions
new_sol.closest_event_idx = self.closest_event_idx
new_sol.solve_time = self.solve_time
new_sol.integration_time = self.integration_time
new_sol.set_up_time = self.set_up_time
return new_sol
def make_cycle_solution(step_solutions, esoh_sim=None, save_this_cycle=True):
"""
Function to create a Solution for an entire cycle, and associated summary variables
Parameters
----------
step_solutions : list of :class:`Solution`
Step solutions that form the entire cycle
esoh_sim : :class:`pybamm.Simulation`, optional
A simulation, whose model should be a :class:`pybamm.lithium_ion.ElectrodeSOH`
model, which is used to calculate some of the summary variables. If `None`
(default) then only summary variables that do not require the eSOH calculation
are calculated. See [1] for more details on eSOH variables.
save_this_cycle : bool, optional
Whether to save the entire cycle variables or just the summary variables.
Default True
Returns
-------
cycle_solution : :class:`pybamm.Solution` or None
The Solution object for this cycle, or None (if save_this_cycle is False)
cycle_summary_variables : dict
Dictionary of summary variables for this cycle
References
----------
.. [1] Mohtat, P., Lee, S., Siegel, J. B., & Stefanopoulou, A. G. (2019). Towards
better estimability of electrode-specific state of health: Decoding the cell
expansion. Journal of Power Sources, 427, 101-111.
"""
sum_sols = step_solutions[0].copy()
for step_solution in step_solutions[1:]:
sum_sols = sum_sols + step_solution
cycle_solution = Solution(
sum_sols.all_ts,
sum_sols.all_ys,
sum_sols.all_models,
sum_sols.all_inputs,
sum_sols.t_event,
sum_sols.y_event,
sum_sols.termination,
)
cycle_solution._all_inputs_casadi = sum_sols.all_inputs_casadi
cycle_solution._sub_solutions = sum_sols.sub_solutions
cycle_solution.solve_time = sum_sols.solve_time
cycle_solution.integration_time = sum_sols.integration_time
cycle_solution.set_up_time = sum_sols.set_up_time
cycle_solution.steps = step_solutions
cycle_summary_variables = get_cycle_summary_variables(cycle_solution, esoh_sim)
cycle_first_state = cycle_solution.first_state
if save_this_cycle:
cycle_solution.cycle_summary_variables = cycle_summary_variables
else:
cycle_solution = None
return cycle_solution, cycle_summary_variables, cycle_first_state
def get_cycle_summary_variables(cycle_solution, esoh_sim):
model = cycle_solution.all_models[0]
cycle_summary_variables = pybamm.FuzzyDict({})
# Measured capacity variables
if "Discharge capacity [A.h]" in model.variables:
Q = cycle_solution["Discharge capacity [A.h]"].data
min_Q = np.min(Q)
max_Q = np.max(Q)
cycle_summary_variables.update(
{
"Minimum measured discharge capacity [A.h]": min_Q,
"Maximum measured discharge capacity [A.h]": max_Q,
"Measured capacity [A.h]": max_Q - min_Q,
}
)
# Degradation variables
degradation_variables = model.summary_variables
first_state = cycle_solution.first_state
last_state = cycle_solution.last_state
for var in degradation_variables:
data_first = first_state[var].data
data_last = last_state[var].data
cycle_summary_variables[var] = data_last[0]
var_lowercase = var[0].lower() + var[1:]
cycle_summary_variables["Change in " + var_lowercase] = (
data_last[0] - data_first[0]
)
# eSOH variables (full-cell lithium-ion model only, for now)
if (
esoh_sim is not None
and isinstance(model, pybamm.lithium_ion.BaseModel)
and model.half_cell is False
):
V_min = esoh_sim.parameter_values["Lower voltage cut-off [V]"]
V_max = esoh_sim.parameter_values["Upper voltage cut-off [V]"]
C_n = last_state["Negative electrode capacity [A.h]"].data[0]
C_p = last_state["Positive electrode capacity [A.h]"].data[0]
n_Li = last_state["Total lithium in particles [mol]"].data[0]
if esoh_sim.solution is not None:
# initialize with previous solution if it is available
esoh_sim.built_model.set_initial_conditions_from(esoh_sim.solution)
solver = None
else:
x_100_init = np.max(cycle_solution["Negative electrode SOC"].data)
# make sure x_0 > 0
C_init = np.minimum(0.95 * (C_n * x_100_init), max_Q - min_Q)
# Solve the esoh model and add outputs to the summary variables
# use CasadiAlgebraicSolver if there are interpolants
if isinstance(
esoh_sim.parameter_values["Negative electrode OCP [V]"], tuple
) or isinstance(
esoh_sim.parameter_values["Positive electrode OCP [V]"], tuple
):
solver = pybamm.CasadiAlgebraicSolver()
# Choose x_100_init so as not to violate the interpolation limits
if isinstance(
esoh_sim.parameter_values["Positive electrode OCP [V]"], tuple
):
y_100_min = np.min(
esoh_sim.parameter_values["Positive electrode OCP [V]"][1][:, 0]
)
x_100_max = (
n_Li * pybamm.constants.F.value / 3600 - y_100_min * C_p
) / C_n
x_100_init = np.minimum(x_100_init, 0.99 * x_100_max)
else:
solver = None
# Update initial conditions using the cycle solution
esoh_sim.build()
esoh_sim.built_model.set_initial_conditions_from(
{"x_100": x_100_init, "C": C_init}
)
inputs = {
"V_min": V_min,
"V_max": V_max,
"C_n": C_n,
"C_p": C_p,
"n_Li": n_Li,
}
try:
esoh_sol = esoh_sim.solve([0], inputs=inputs, solver=solver)
except pybamm.SolverError: # pragma: no cover
raise pybamm.SolverError(
"Could not solve for summary variables, run "
"`sim.solve(calc_esoh=False)` to skip this step"
)
for var in esoh_sim.built_model.variables:
cycle_summary_variables[var] = esoh_sol[var].data[0]
cycle_summary_variables["Capacity [A.h]"] = cycle_summary_variables["C"]
return cycle_summary_variables