text: #
  # Base battery model class
  #
  
  import pybamm
  
  
  class BatteryModelOptions(pybamm.FuzzyDict):
      """
      Attributes
      ----------
  
      options: dict
          A dictionary of options to be passed to the model. The options that can
          be set are listed below. Note that not all of the options are compatible with
          each other and with all of the models implemented in PyBaMM. Each option is
          optional and takes a default value if not provided.
          In general, the option provided must be a string, but there are some cases
          where a 2-tuple of strings can be provided instead to indicate a different
          option for the negative and positive electrodes.
  
              * "cell geometry" : str
                  Sets the geometry of the cell. Can be "pouch" (default) or
                  "arbitrary". The arbitrary geometry option solves a 1D electrochemical
                  model with prescribed cell volume and cross-sectional area, and
                  (if thermal effects are included) solves a lumped thermal model
                  with prescribed surface area for cooling.
              * "convection" : str
                  Whether to include the effects of convection in the model. Can be
                  "none" (default), "uniform transverse" or "full transverse".
                  Must be "none" for lithium-ion models.
              * "current collector" : str
                  Sets the current collector model to use. Can be "uniform" (default),
                  "potential pair" or "potential pair quite conductive".
              * "dimensionality" : int
                  Sets the dimension of the current collector problem. Can be 0
                  (default), 1 or 2.
              * "electrolyte conductivity" : str
                  Can be "default" (default), "full", "leading order", "composite" or
                  "integrated".
              * "external submodels" : list
                  A list of the submodels that you would like to supply an external
                  variable for instead of solving in PyBaMM. The entries of the lists
                  are strings that correspond to the submodel names in the keys
                  of `self.submodels`.
              * "hydrolysis" : str
                  Whether to include hydrolysis in the model. Only implemented for
                  lead-acid models. Can be "false" (default) or "true". If "true", then
                  "surface form" cannot be 'false'.
              * "lithium plating" : str, optional
                  Sets the model for lithium plating. Can be "none" (default),
                  "reversible" or "irreversible".
              * "loss of active material" : str
                  Sets the model for loss of active material. Can be "none" (default),
                  "stress-driven", or "reaction-driven".
                  A 2-tuple can be provided for different behaviour in negative and
                  positive electrodes.
              * "operating mode" : str
                  Sets the operating mode for the model. Can be "current" (default),
                  "voltage" or "power". Alternatively, the operating mode can be
                  controlled with an arbitrary function by passing the function directly
                  as the option. In this case the function must define the residual of
                  an algebraic equation. The applied current will be solved for such
                  that the algebraic constraint is satisfied.
              * "particle" : str
                  Sets the submodel to use to describe behaviour within the particle.
                  Can be "Fickian diffusion" (default), "uniform profile",
                  "quadratic profile", or "quartic profile".
              * "particle shape" : str
                  Sets the model shape of the electrode particles. This is used to
                  calculate the surface area to volume ratio. Can be "spherical"
                  (default), "user" or "no particles". For the "user" option the surface
                  area per unit volume can be passed as a parameter, and is therefore not
                  necessarily consistent with the particle shape.
              * "particle size" : str
                  Sets the model to include a single active particle size or a
                  distribution of sizes at any macroscale location. Can be "single"
                  (default) or "distribution". Option applies to both electrodes.
              * "particle mechanics" : str
                  Sets the model to account for mechanical effects such as particle
                  swelling and cracking. Can be "none" (default), "swelling only",
                  or "swelling and cracking".
                  A 2-tuple can be provided for different behaviour in negative and
                  positive electrodes.
              * "SEI" : str
                  Set the SEI submodel to be used. Options are:
  
                  - "none": :class:`pybamm.sei.NoSEI` (no SEI growth)
                  - "constant": :class:`pybamm.sei.Constant` (constant SEI thickness)
                  - "reaction limited": :class:`pybamm.sei.ReactionLimited`
                  - "solvent-diffusion limited":\
                      :class:`pybamm.sei.SolventDiffusionLimited`
                  - "electron-migration limited": \
                      :class:`pybamm.sei.ElectronMigrationLimited`
                  - "interstitial-diffusion limited": \
                      :class:`pybamm.sei.InterstitialDiffusionLimited`
                  - "ec reaction limited": \
                      :class:`pybamm.sei.EcReactionLimited`
              * "SEI film resistance" : str
                  Set the submodel for additional term in the overpotential due to SEI.
                  The default value is "none" if the "SEI" option is "none", and
                  "distributed" otherwise. This is because the "distributed" model is more
                  complex than the model with no additional resistance, which adds
                  unnecessary complexity if there is no SEI in the first place
  
                  - "none": no additional resistance\
  
                      .. math::
                          \\eta_r = \\frac{F}{RT} * (\\phi_s - \\phi_e - U)
  
                  - "distributed": properly included additional resistance term\
  
                      .. math::
                          \\eta_r = \\frac{F}{RT}
                          * (\\phi_s - \\phi_e - U - R_{sei} * L_{sei} * j)
  
                  - "average": constant additional resistance term (approximation to the \
                      true model). This model can give similar results to the \
                      "distributed" case without needing to make j an algebraic state\
  
                      .. math::
                          \\eta_r = \\frac{F}{RT}
                          * (\\phi_s - \\phi_e - U - R_{sei} * L_{sei} * \\frac{I}{aL})
              * "SEI porosity change" : str
                  Whether to include porosity change due to SEI formation, can be "false"
                  (default) or "true".
              * "surface form" : str
                  Whether to use the surface formulation of the problem. Can be "false"
                  (default), "differential" or "algebraic".
              * "thermal" : str
                  Sets the thermal model to use. Can be "isothermal" (default), "lumped",
                  "x-lumped", or "x-full".
              * "total interfacial current density as a state" : str
                  Whether to make a state for the total interfacial current density and
                  solve an algebraic equation for it. Default is "false", unless "SEI film
                  resistance" is distributed in which case it is automatically set to
                  "true".
              * "working electrode": str
                  Which electrode(s) intercalates and which is counter. If "both"
                  (default), the model is a standard battery. Otherwise can be "negative"
                  or "positive" to indicate a half-cell model.
  
      **Extends:** :class:`dict`
      """
  
      def __init__(self, extra_options):
          self.possible_options = {
              "cell geometry": ["arbitrary", "pouch"],
              "convection": ["none", "uniform transverse", "full transverse"],
              "current collector": [
                  "uniform",
                  "potential pair",
                  "potential pair quite conductive",
              ],
              "dimensionality": [0, 1, 2],
              "electrolyte conductivity": [
                  "default",
                  "full",
                  "leading order",
                  "composite",
                  "integrated",
              ],
              "hydrolysis": ["true", "false"],
              "lithium plating": ["none", "reversible", "irreversible"],
              "lithium plating porosity change": ["true", "false"],
              "loss of active material": ["none", "stress-driven", "reaction-driven"],
              "operating mode": ["current", "voltage", "power", "CCCV"],
              "particle": [
                  "Fickian diffusion",
                  "fast diffusion",
                  "uniform profile",
                  "quadratic profile",
                  "quartic profile",
              ],
              "particle mechanics": ["none", "swelling only", "swelling and cracking"],
              "particle shape": ["spherical", "user", "no particles"],
              "particle size": ["single", "distribution"],
              "SEI": [
                  "none",
                  "constant",
                  "reaction limited",
                  "solvent-diffusion limited",
                  "electron-migration limited",
                  "interstitial-diffusion limited",
                  "ec reaction limited",
              ],
              "SEI film resistance": ["none", "distributed", "average"],
              "SEI porosity change": ["true", "false"],
              "surface form": ["false", "differential", "algebraic"],
              "thermal": ["isothermal", "lumped", "x-lumped", "x-full"],
              "total interfacial current density as a state": ["true", "false"],
              "working electrode": ["both", "negative", "positive"],
          }
  
          default_options = {
              "cell geometry": "none",
              "convection": "none",
              "current collector": "uniform",
              "dimensionality": 0,
              "electrolyte conductivity": "default",
              "external submodels": [],
              "hydrolysis": "false",
              "lithium plating": "none",
              "lithium plating porosity change": "false",
              "loss of active material": "none",
              "operating mode": "current",
              "particle": "Fickian diffusion",
              "particle mechanics": "none",
              "particle shape": "spherical",
              "particle size": "single",
              "SEI": "none",
              "SEI porosity change": "false",
              "surface form": "false",
              "thermal": "isothermal",
              "total interfacial current density as a state": "false",
              "working electrode": "both",
          }
  
          # Change the default for cell geometry based on which thermal option is provided
          extra_options = extra_options or {}
          # return "none" if option not given
          thermal_option = extra_options.get("thermal", "none")
          if thermal_option in ["none", "isothermal", "lumped"]:
              default_options["cell geometry"] = "arbitrary"
          else:
              default_options["cell geometry"] = "pouch"
          # The "cell geometry" option will still be overridden by extra_options if
          # provided
  
          # Change the default for SEI film resistance based on which SEI option is
          # provided
          # return "none" if option not given
          sei_option = extra_options.get("SEI", "none")
          if sei_option == "none":
              default_options["SEI film resistance"] = "none"
          else:
              default_options["SEI film resistance"] = "distributed"
          # The "SEI film resistance" option will still be overridden by extra_options if
          # provided
  
          # Change the default for swelling based on which LAM option is
          # provided
          # return "none" if option not given
          lam_option = extra_options.get("loss of active material", "none")
          if "stress-driven" in lam_option:
              default_options["particle mechanics"] = "swelling only"
          else:
              default_options["particle mechanics"] = "none"
          # The "SEI film resistance" option will still be overridden by extra_options if
          # provided
  
          options = pybamm.FuzzyDict(default_options)
          # any extra options overwrite the default options
          for name, opt in extra_options.items():
              if name in default_options:
                  options[name] = opt
              else:
                  if name == "particle cracking":
                      raise pybamm.OptionError(
                          "The 'particle cracking' option has been renamed. "
                          "Use 'particle mechanics' instead."
                      )
                  else:
                      raise pybamm.OptionError(
                          "Option '{}' not recognised. Best matches are {}".format(
                              name, options.get_best_matches(name)
                          )
                      )
  
          # If "SEI film resistance" is "distributed" then "total interfacial current
          # density as a state" must be "true"
          if options["SEI film resistance"] == "distributed":
              options["total interfacial current density as a state"] = "true"
              # Check that extra_options did not try to provide a clashing option
              if (
                  extra_options.get("total interfacial current density as a state")
                  == "false"
              ):
                  raise pybamm.OptionError(
                      "If 'sei film resistance' is 'distributed' then 'total interfacial "
                      "current density as a state' must be 'true'"
                  )
  
          # Options not yet compatible with particle-size distributions
          if options["particle size"] == "distribution":
              if options["SEI"] != "none":
                  raise NotImplementedError(
                      "SEI submodels do not yet support particle-size distributions."
                  )
              if options["lithium plating"] != "none":
                  raise NotImplementedError(
                      "Lithium plating submodels do not yet support particle-size "
                      "distributions."
                  )
              if options["particle mechanics"] != "none":
                  raise NotImplementedError(
                      "Particle mechanics submodels do not yet support particle-size"
                      " distributions."
                  )
              if options["particle shape"] != "spherical":
                  raise NotImplementedError(
                      "Particle shape must be 'spherical' for particle-size distributions"
                      " submodels."
                  )
              if options["thermal"] == "x-full":
                  raise NotImplementedError(
                      "X-full thermal submodels do not yet support particle-size"
                      " distributions."
                  )
  
          # Some standard checks to make sure options are compatible
          if options["SEI porosity change"] in [True, False]:
              raise pybamm.OptionError(
                  "SEI porosity change must now be given in string format "
                  "('true' or 'false')"
              )
  
          if options["dimensionality"] == 0:
              if options["current collector"] not in ["uniform"]:
                  raise pybamm.OptionError(
                      "current collector model must be uniform in 0D model"
                  )
              if options["convection"] == "full transverse":
                  raise pybamm.OptionError(
                      "cannot have transverse convection in 0D model"
                  )
  
          if options["particle"] == "fast diffusion":
              raise NotImplementedError(
                  "The 'fast diffusion' option has been renamed. "
                  "Use 'uniform profile' instead."
              )
  
          for option, value in options.items():
              if option == "external submodels" or option == "working electrode":
                  pass
              else:
                  if isinstance(value, str) or option in [
                      "dimensionality",
                      "operating mode",
                  ]:  # some options don't take strings
                      value = (value,)
                  else:
                      if not (
                          (
                              option
                              in [
                                  "loss of active material",
                                  "particle mechanics",
                                  "particle",
                              ]
                              and isinstance(value, tuple)
                              and len(value) == 2
                          )
                      ):
                          # more possible options that can take 2-tuples to be added
                          # as they come
                          raise pybamm.OptionError(
                              f"\n'{value}' is not recognized in option '{option}'. "
                              "Values must be strings or (in some cases) "
                              "2-tuples of strings"
                          )
                  for val in value:
                      if val not in self.possible_options[option]:
                          if not (option == "operating mode" and callable(val)):
                              raise pybamm.OptionError(
                                  f"\n'{val}' is not recognized in option '{option}'. "
                                  f"Possible values are {self.possible_options[option]}"
                              )
  
          super().__init__(options.items())
  
      def print_options(self):
          """
          Print the possible options with the ones currently selected
          """
          for key, value in self.items():
              if key in self.possible_options.keys():
                  print(f"{key!r}: {value!r} (possible: {self.possible_options[key]!r})")
              else:
                  print(f"{key!r}: {value!r}")
  
      def print_detailed_options(self):
          """
          Print the docstring for Options
          """
          print(self.__doc__)
  
  
  class BaseBatteryModel(pybamm.BaseModel):
      """
      Base model class with some default settings and required variables
      **Extends:** :class:`pybamm.BaseModel`
      """
  
      def __init__(self, options=None, name="Unnamed battery model"):
          super().__init__(name)
          self.options = options
          self.submodels = {}
          self._built = False
          self._built_fundamental_and_external = False
  
      @property
      def default_geometry(self):
          return pybamm.battery_geometry(
              options=self.options,
              current_collector_dimension=self.options["dimensionality"],
          )
  
      @property
      def default_var_pts(self):
          var = pybamm.standard_spatial_vars
          base_var_pts = {
              var.x_n: 20,
              var.x_s: 20,
              var.x_p: 20,
              var.r_n: 30,
              var.r_p: 30,
              var.y: 10,
              var.z: 10,
              var.R_n: 30,
              var.R_p: 30,
          }
          # Reduce the default points for 2D current collectors
          if self.options["dimensionality"] == 2:
              base_var_pts.update({var.x_n: 10, var.x_s: 10, var.x_p: 10})
          return base_var_pts
  
      @property
      def default_submesh_types(self):
          base_submeshes = {
              "negative electrode": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
              "separator": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
              "positive electrode": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
              "negative particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
              "positive particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
              "negative particle size": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
              "positive particle size": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
          }
          if self.options["dimensionality"] == 0:
              base_submeshes["current collector"] = pybamm.MeshGenerator(pybamm.SubMesh0D)
          elif self.options["dimensionality"] == 1:
              base_submeshes["current collector"] = pybamm.MeshGenerator(
                  pybamm.Uniform1DSubMesh
              )
          elif self.options["dimensionality"] == 2:
              base_submeshes["current collector"] = pybamm.MeshGenerator(
                  pybamm.ScikitUniform2DSubMesh
              )
          return base_submeshes
  
      @property
      def default_spatial_methods(self):
          base_spatial_methods = {
              "macroscale": pybamm.FiniteVolume(),
              "negative particle": pybamm.FiniteVolume(),
              "positive particle": pybamm.FiniteVolume(),
              "negative particle size": pybamm.FiniteVolume(),
              "positive particle size": pybamm.FiniteVolume(),
          }
          if self.options["dimensionality"] == 0:
              # 0D submesh - use base spatial method
              base_spatial_methods[
                  "current collector"
              ] = pybamm.ZeroDimensionalSpatialMethod()
          elif self.options["dimensionality"] == 1:
              base_spatial_methods["current collector"] = pybamm.FiniteVolume()
          elif self.options["dimensionality"] == 2:
              base_spatial_methods["current collector"] = pybamm.ScikitFiniteElement()
          return base_spatial_methods
  
      @property
      def options(self):
          return self._options
  
      @options.setter
      def options(self, extra_options):
          options = BatteryModelOptions(extra_options)
  
          # Options that are incompatible with models
          if isinstance(self, pybamm.lithium_ion.BaseModel):
              if options["convection"] != "none":
                  raise pybamm.OptionError(
                      "convection not implemented for lithium-ion models"
                  )
              if (
                  options["thermal"] in ["x-lumped", "x-full"]
                  and options["cell geometry"] != "pouch"
              ):
                  raise pybamm.OptionError(
                      options["thermal"] + " model must have pouch geometry."
                  )
          if isinstance(self, pybamm.lead_acid.BaseModel):
              if options["thermal"] != "isothermal" and options["dimensionality"] != 0:
                  raise pybamm.OptionError(
                      "Lead-acid models can only have thermal "
                      "effects if dimensionality is 0."
                  )
              if options["SEI"] != "none" or options["SEI film resistance"] != "none":
                  raise pybamm.OptionError("Lead-acid models cannot have SEI formation")
              if options["lithium plating"] != "none":
                  raise pybamm.OptionError("Lead-acid models cannot have lithium plating")
  
          if (
              isinstance(self, (pybamm.lead_acid.LOQS, pybamm.lead_acid.Composite))
              and options["surface form"] == "false"
              and options["hydrolysis"] == "true"
          ):
              raise pybamm.OptionError(
                  """must use surface formulation to solve {!s} with hydrolysis
                      """.format(
                      self
                  )
              )
  
          self._options = options
  
      def set_standard_output_variables(self):
          # Time
          self.variables.update(
              {
                  "Time": pybamm.t,
                  "Time [s]": pybamm.t * self.timescale,
                  "Time [min]": pybamm.t * self.timescale / 60,
                  "Time [h]": pybamm.t * self.timescale / 3600,
              }
          )
  
          # Spatial
          var = pybamm.standard_spatial_vars
          L_x = self.param.L_x
          L_z = self.param.L_z
          self.variables.update(
              {
                  "x": var.x,
                  "x [m]": var.x * L_x,
                  "x_n": var.x_n,
                  "x_n [m]": var.x_n * L_x,
                  "x_s": var.x_s,
                  "x_s [m]": var.x_s * L_x,
                  "x_p": var.x_p,
                  "x_p [m]": var.x_p * L_x,
              }
          )
          if self.options["dimensionality"] == 1:
              self.variables.update({"z": var.z, "z [m]": var.z * L_z})
          elif self.options["dimensionality"] == 2:
              # Note: both y and z are scaled with L_z
              self.variables.update(
                  {"y": var.y, "y [m]": var.y * L_z, "z": var.z, "z [m]": var.z * L_z}
              )
  
          # Initialize "total reaction" variables
          # These will get populated by the "get_coupled_variables" methods, and then used
          # later by "set_rhs" or "set_algebraic", which ensures that we always have
          # added all the necessary variables by the time the sum is used
          self.variables.update(
              {
                  "Sum of electrolyte reaction source terms": 0,
                  "Sum of positive electrode electrolyte reaction source terms": 0,
                  "Sum of x-averaged positive electrode "
                  "electrolyte reaction source terms": 0,
                  "Sum of interfacial current densities": 0,
                  "Sum of positive electrode interfacial current densities": 0,
                  "Sum of x-averaged positive electrode interfacial current densities": 0,
              }
          )
          if not self.half_cell:
              self.variables.update(
                  {
                      "Sum of negative electrode electrolyte reaction source terms": 0,
                      "Sum of x-averaged negative electrode "
                      "electrolyte reaction source terms": 0,
                      "Sum of negative electrode interfacial current densities": 0,
                      "Sum of x-averaged negative electrode interfacial current densities"
                      "": 0,
                  }
              )
  
      def build_fundamental_and_external(self):
          # Get the fundamental variables
          for submodel_name, submodel in self.submodels.items():
              pybamm.logger.debug(
                  "Getting fundamental variables for {} submodel ({})".format(
                      submodel_name, self.name
                  )
              )
              self.variables.update(submodel.get_fundamental_variables())
  
          # Set the submodels that are external
          for sub in self.options["external submodels"]:
              self.submodels[sub].external = True
  
          # Set any external variables
          self.external_variables = []
          for submodel_name, submodel in self.submodels.items():
              pybamm.logger.debug(
                  "Getting external variables for {} submodel ({})".format(
                      submodel_name, self.name
                  )
              )
              external_variables = submodel.get_external_variables()
  
              self.external_variables += external_variables
  
          self._built_fundamental_and_external = True
  
      def build_coupled_variables(self):
          # Note: pybamm will try to get the coupled variables for the submodels in the
          # order they are set by the user. If this fails for a particular submodel,
          # return to it later and try again. If setting coupled variables fails and
          # there are no more submodels to try, raise an error.
          submodels = list(self.submodels.keys())
          count = 0
          # For this part the FuzzyDict of variables is briefly converted back into a
          # normal dictionary for speed with KeyErrors
          self._variables = dict(self._variables)
          while len(submodels) > 0:
              count += 1
              for submodel_name, submodel in self.submodels.items():
                  if submodel_name in submodels:
                      pybamm.logger.debug(
                          "Getting coupled variables for {} submodel ({})".format(
                              submodel_name, self.name
                          )
                      )
                      try:
                          self.variables.update(
                              submodel.get_coupled_variables(self.variables)
                          )
                          submodels.remove(submodel_name)
                      except KeyError as key:
                          if len(submodels) == 1 or count == 100:
                              # no more submodels to try
                              raise pybamm.ModelError(
                                  "Missing variable for submodel '{}': {}.\n".format(
                                      submodel_name, key
                                  )
                                  + "Check the selected "
                                  "submodels provide all of the required variables."
                              )
                          else:
                              # try setting coupled variables on next loop through
                              pybamm.logger.debug(
                                  "Can't find {}, trying other submodels first".format(
                                      key
                                  )
                              )
          # Convert variables back into FuzzyDict
          self._variables = pybamm.FuzzyDict(self._variables)
  
      def build_model_equations(self):
          # Set model equations
          for submodel_name, submodel in self.submodels.items():
              if submodel.external is False:
                  pybamm.logger.verbose(
                      "Setting rhs for {} submodel ({})".format(submodel_name, self.name)
                  )
  
                  submodel.set_rhs(self.variables)
                  pybamm.logger.verbose(
                      "Setting algebraic for {} submodel ({})".format(
                          submodel_name, self.name
                      )
                  )
  
                  submodel.set_algebraic(self.variables)
                  pybamm.logger.verbose(
                      "Setting boundary conditions for {} submodel ({})".format(
                          submodel_name, self.name
                      )
                  )
  
                  submodel.set_boundary_conditions(self.variables)
                  pybamm.logger.verbose(
                      "Setting initial conditions for {} submodel ({})".format(
                          submodel_name, self.name
                      )
                  )
                  submodel.set_initial_conditions(self.variables)
                  submodel.set_events(self.variables)
                  pybamm.logger.verbose(
                      "Updating {} submodel ({})".format(submodel_name, self.name)
                  )
                  self.update(submodel)
                  self.check_no_repeated_keys()
  
      def build_model(self):
  
          # Check if already built
          if self._built:
              raise pybamm.ModelError(
                  """Model already built. If you are adding a new submodel, try using
                  `model.update` instead."""
              )
  
          pybamm.logger.info("Start building {}".format(self.name))
  
          if self._built_fundamental_and_external is False:
              self.build_fundamental_and_external()
  
          self.build_coupled_variables()
  
          self.build_model_equations()
  
          pybamm.logger.debug("Setting voltage variables ({})".format(self.name))
          self.set_voltage_variables()
  
          pybamm.logger.debug("Setting SoC variables ({})".format(self.name))
          self.set_soc_variables()
  
          pybamm.logger.debug("Setting degradation variables ({})".format(self.name))
          self.set_degradation_variables()
          self.set_summary_variables()
  
          # Massive hack for consistent delta_phi = phi_s - phi_e with SPMe
          # This needs to be corrected
          if isinstance(self, pybamm.lithium_ion.SPMe):
              for domain in ["Negative", "Positive"]:
                  phi_s = self.variables[domain + " electrode potential"]
                  phi_e = self.variables[domain + " electrolyte potential"]
                  delta_phi = phi_s - phi_e
                  s = self.submodels[domain.lower() + " interface"]
                  var = s._get_standard_surface_potential_difference_variables(delta_phi)
                  self.variables.update(var)
  
          self._built = True
          pybamm.logger.info("Finish building {}".format(self.name))
  
      def new_empty_copy(self):
          """See :meth:`pybamm.BaseModel.new_empty_copy()`"""
          new_model = self.__class__(name=self.name, options=self.options)
          new_model.use_jacobian = self.use_jacobian
          new_model.convert_to_format = self.convert_to_format
          new_model.timescale = self.timescale
          new_model.length_scales = self.length_scales
          return new_model
  
      @property
      def summary_variables(self):
          return self._summary_variables
  
      @summary_variables.setter
      def summary_variables(self, value):
          """
          Set summary variables
  
          Parameters
          ----------
          value : list of strings
              Names of the summary variables. Must all be in self.variables.
          """
          for var in value:
              if var not in self.variables:
                  raise KeyError(
                      f"No cycling variable defined for summary variable '{var}'"
                  )
          self._summary_variables = value
  
      def set_summary_variables(self):
          self._summary_variables = []
  
      def set_external_circuit_submodel(self):
          """
          Define how the external circuit defines the boundary conditions for the model,
          e.g. (not necessarily constant-) current, voltage, etc
          """
          if self.options["operating mode"] == "current":
              self.submodels["external circuit"] = pybamm.external_circuit.CurrentControl(
                  self.param
              )
          elif self.options["operating mode"] == "voltage":
              self.submodels[
                  "external circuit"
              ] = pybamm.external_circuit.VoltageFunctionControl(self.param)
          elif self.options["operating mode"] == "power":
              self.submodels[
                  "external circuit"
              ] = pybamm.external_circuit.PowerFunctionControl(self.param)
          elif self.options["operating mode"] == "CCCV":
              self.submodels[
                  "external circuit"
              ] = pybamm.external_circuit.CCCVFunctionControl(self.param)
          elif callable(self.options["operating mode"]):
              self.submodels[
                  "external circuit"
              ] = pybamm.external_circuit.FunctionControl(
                  self.param, self.options["operating mode"]
              )
  
      def set_tortuosity_submodels(self):
          self.submodels["electrolyte tortuosity"] = pybamm.tortuosity.Bruggeman(
              self.param, "Electrolyte", self.options
          )
          self.submodels["electrode tortuosity"] = pybamm.tortuosity.Bruggeman(
              self.param, "Electrode", self.options
          )
  
      def set_thermal_submodel(self):
  
          if self.options["thermal"] == "isothermal":
              thermal_submodel = pybamm.thermal.isothermal.Isothermal(
                  self.param, self.options
              )
  
          elif self.options["thermal"] == "lumped":
              thermal_submodel = pybamm.thermal.Lumped(
                  self.param,
                  cc_dimension=self.options["dimensionality"],
                  geometry=self.options["cell geometry"],
              )
  
          elif self.options["thermal"] == "x-lumped":
              if self.options["dimensionality"] == 0:
                  # With 0D current collectors x-lumped is equivalent to lumped pouch
                  thermal_submodel = pybamm.thermal.Lumped(self.param, geometry="pouch")
              elif self.options["dimensionality"] == 1:
                  thermal_submodel = pybamm.thermal.pouch_cell.CurrentCollector1D(
                      self.param
                  )
              elif self.options["dimensionality"] == 2:
                  thermal_submodel = pybamm.thermal.pouch_cell.CurrentCollector2D(
                      self.param
                  )
  
          elif self.options["thermal"] == "x-full":
              if self.options["dimensionality"] == 0:
                  thermal_submodel = pybamm.thermal.OneDimensionalX(self.param)
              elif self.options["dimensionality"] == 1:
                  raise NotImplementedError(
                      """X-full thermal submodels do not
                  yet support 1D current collectors"""
                  )
              elif self.options["dimensionality"] == 2:
                  raise NotImplementedError(
                      """X-full thermal submodels do
                      not yet support 2D current collectors"""
                  )
  
          self.submodels["thermal"] = thermal_submodel
  
      def set_current_collector_submodel(self):
  
          if self.options["current collector"] in ["uniform"]:
              submodel = pybamm.current_collector.Uniform(self.param)
          elif self.options["current collector"] == "potential pair":
              if self.options["dimensionality"] == 1:
                  submodel = pybamm.current_collector.PotentialPair1plus1D(self.param)
              elif self.options["dimensionality"] == 2:
                  submodel = pybamm.current_collector.PotentialPair2plus1D(self.param)
          self.submodels["current collector"] = submodel
  
      def set_voltage_variables(self):
  
          ocp_n = self.variables["Negative electrode open circuit potential"]
          ocp_p = self.variables["Positive electrode open circuit potential"]
          ocp_n_av = self.variables[
              "X-averaged negative electrode open circuit potential"
          ]
          ocp_p_av = self.variables[
              "X-averaged positive electrode open circuit potential"
          ]
  
          ocp_n_dim = self.variables["Negative electrode open circuit potential [V]"]
          ocp_p_dim = self.variables["Positive electrode open circuit potential [V]"]
          ocp_n_av_dim = self.variables[
              "X-averaged negative electrode open circuit potential [V]"
          ]
          ocp_p_av_dim = self.variables[
              "X-averaged positive electrode open circuit potential [V]"
          ]
  
          ocp_n_left = pybamm.boundary_value(ocp_n, "left")
          ocp_n_left_dim = pybamm.boundary_value(ocp_n_dim, "left")
          ocp_p_right = pybamm.boundary_value(ocp_p, "right")
          ocp_p_right_dim = pybamm.boundary_value(ocp_p_dim, "right")
  
          ocv_av = ocp_p_av - ocp_n_av
          ocv_av_dim = ocp_p_av_dim - ocp_n_av_dim
          ocv = ocp_p_right - ocp_n_left
          ocv_dim = ocp_p_right_dim - ocp_n_left_dim
  
          # overpotentials
          if self.half_cell:
              eta_r_n_av = self.variables[
                  "Lithium metal interface reaction overpotential"
              ]
              eta_r_n_av_dim = self.variables[
                  "Lithium metal interface reaction overpotential [V]"
              ]
          else:
              eta_r_n_av = self.variables[
                  "X-averaged negative electrode reaction overpotential"
              ]
              eta_r_n_av_dim = self.variables[
                  "X-averaged negative electrode reaction overpotential [V]"
              ]
          eta_r_p_av = self.variables[
              "X-averaged positive electrode reaction overpotential"
          ]
          eta_r_p_av_dim = self.variables[
              "X-averaged positive electrode reaction overpotential [V]"
          ]
  
          delta_phi_s_n_av = self.variables["X-averaged negative electrode ohmic losses"]
          delta_phi_s_n_av_dim = self.variables[
              "X-averaged negative electrode ohmic losses [V]"
          ]
          delta_phi_s_p_av = self.variables["X-averaged positive electrode ohmic losses"]
          delta_phi_s_p_av_dim = self.variables[
              "X-averaged positive electrode ohmic losses [V]"
          ]
  
          delta_phi_s_av = delta_phi_s_p_av - delta_phi_s_n_av
          delta_phi_s_av_dim = delta_phi_s_p_av_dim - delta_phi_s_n_av_dim
  
          eta_r_av = eta_r_p_av - eta_r_n_av
          eta_r_av_dim = eta_r_p_av_dim - eta_r_n_av_dim
  
          # SEI film overpotential
          if self.half_cell:
              eta_sei_av = self.variables["SEI film overpotential"]
              eta_sei_av_dim = self.variables["SEI film overpotential [V]"]
          else:
              eta_sei_av = self.variables["X-averaged SEI film overpotential"]
              eta_sei_av_dim = self.variables["X-averaged SEI film overpotential [V]"]
  
          # TODO: add current collector losses to the voltage in 3D
  
          self.variables.update(
              {
                  "X-averaged open circuit voltage": ocv_av,
                  "Measured open circuit voltage": ocv,
                  "X-averaged open circuit voltage [V]": ocv_av_dim,
                  "Measured open circuit voltage [V]": ocv_dim,
                  "X-averaged reaction overpotential": eta_r_av,
                  "X-averaged reaction overpotential [V]": eta_r_av_dim,
                  "X-averaged SEI film overpotential": eta_sei_av,
                  "X-averaged SEI film overpotential [V]": eta_sei_av_dim,
                  "X-averaged solid phase ohmic losses": delta_phi_s_av,
                  "X-averaged solid phase ohmic losses [V]": delta_phi_s_av_dim,
              }
          )
  
          # Battery-wide variables
          V = self.variables["Terminal voltage"]
          V_dim = self.variables["Terminal voltage [V]"]
          eta_e_av_dim = self.variables["X-averaged electrolyte ohmic losses [V]"]
          eta_c_av_dim = self.variables["X-averaged concentration overpotential [V]"]
          num_cells = pybamm.Parameter(
              "Number of cells connected in series to make a battery"
          )
          self.variables.update(
              {
                  "X-averaged battery open circuit voltage [V]": ocv_av_dim * num_cells,
                  "Measured battery open circuit voltage [V]": ocv_dim * num_cells,
                  "X-averaged battery reaction overpotential [V]": eta_r_av_dim
                  * num_cells,
                  "X-averaged battery solid phase ohmic losses [V]": delta_phi_s_av_dim
                  * num_cells,
                  "X-averaged battery electrolyte ohmic losses [V]": eta_e_av_dim
                  * num_cells,
                  "X-averaged battery concentration overpotential [V]": eta_c_av_dim
                  * num_cells,
                  "Battery voltage [V]": V_dim * num_cells,
              }
          )
          # Variables for calculating the equivalent circuit model (ECM) resistance
          # Need to compare OCV to initial value to capture this as an overpotential
          ocv_init = self.param.U_p_init - self.param.U_n_init
          ocv_init_dim = (
              self.param.U_p_ref
              - self.param.U_n_ref
              + self.param.potential_scale * ocv_init
          )
          eta_ocv = ocv - ocv_init
          eta_ocv_dim = ocv_dim - ocv_init_dim
          # Current collector current density for working out euiqvalent resistance
          # based on Ohm's Law
          i_cc = self.variables["Current collector current density"]
          i_cc_dim = self.variables["Current collector current density [A.m-2]"]
          # ECM overvoltage is OCV minus terminal voltage
          v_ecm = ocv - V
          v_ecm_dim = ocv_dim - V_dim
          # Current collector area for turning resistivity into resistance
          A_cc = self.param.A_cc
  
          # Hack to avoid division by zero if i_cc is exactly zero
          # If i_cc is zero, i_cc_not_zero becomes 1. But multiplying by sign(i_cc) makes
          # the local resistance 'zero' (really, it's not defined when i_cc is zero)
          i_cc_not_zero = ((i_cc > 0) + (i_cc < 0)) * i_cc + (i_cc >= 0) * (i_cc <= 0)
          i_cc_dim_not_zero = ((i_cc_dim > 0) + (i_cc_dim < 0)) * i_cc_dim + (
              i_cc_dim >= 0
          ) * (i_cc_dim <= 0)
  
          self.variables.update(
              {
                  "Change in measured open circuit voltage": eta_ocv,
                  "Change in measured open circuit voltage [V]": eta_ocv_dim,
                  "Local ECM resistance": pybamm.sign(i_cc)
                  * v_ecm
                  / (i_cc_not_zero * A_cc),
                  "Local ECM resistance [Ohm]": pybamm.sign(i_cc)
                  * v_ecm_dim
                  / (i_cc_dim_not_zero * A_cc),
              }
          )
  
          # Cut-off voltage
          self.events.append(
              pybamm.Event(
                  "Minimum voltage",
                  V - self.param.voltage_low_cut,
                  pybamm.EventType.TERMINATION,
              )
          )
          self.events.append(
              pybamm.Event(
                  "Maximum voltage",
                  V - self.param.voltage_high_cut,
                  pybamm.EventType.TERMINATION,
              )
          )
  
          # Cut-off open-circuit voltage (for event switch with casadi 'fast with events'
          # mode)
          # A tolerance of ~1 is sufficiently small since the dimensionless voltage is
          # scaled with the thermal voltage (0.025V) and hence has a range of around 60
          tol = 5
          self.events.append(
              pybamm.Event(
                  "Minimum voltage switch",
                  V - (self.param.voltage_low_cut - tol),
                  pybamm.EventType.SWITCH,
              )
          )
          self.events.append(
              pybamm.Event(
                  "Maximum voltage switch",
                  V - (self.param.voltage_high_cut + tol),
                  pybamm.EventType.SWITCH,
              )
          )
  
          # Power
          I_dim = self.variables["Current [A]"]
          self.variables.update({"Terminal power [W]": I_dim * V_dim})
  
      def set_degradation_variables(self):
          """
          Set variables that quantify degradation.
          This function is overriden by the base battery models
          """
          pass
  
      def set_soc_variables(self):
          """
          Set variables relating to the state of charge.
          This function is overriden by the base battery models
          """
          pass
  
      def process_parameters_and_discretise(self, symbol, parameter_values, disc):
          """
          Process parameters and discretise a symbol using supplied parameter values
          and discretisation. Note: care should be taken if using spatial operators
          on dimensional symbols. Operators in pybamm are written in non-dimensional
          form, so may need to be scaled by the appropriate length scale. It is
          recommended to use this method on non-dimensional symbols.
  
          Parameters
          ----------
          symbol : :class:`pybamm.Symbol`
              Symbol to be processed
          parameter_values : :class:`pybamm.ParameterValues`
              The parameter values to use during processing
          disc : :class:`pybamm.Discretisation`
              The discrisation to use
  
          Returns
          -------
          :class:`pybamm.Symbol`
              Processed symbol
          """
          # Set y slices
          if disc.y_slices == {}:
              variables = list(self.rhs.keys()) + list(self.algebraic.keys())
              disc.set_variable_slices(variables)
  
          # Set boundary conditions (also requires setting parameter values)
          if disc.bcs == {}:
              self.boundary_conditions = parameter_values.process_boundary_conditions(
                  self
              )
              disc.bcs = disc.process_boundary_conditions(self)
  
          # Process
          param_symbol = parameter_values.process_symbol(symbol)
          disc_symbol = disc.process_symbol(param_symbol)
  
          return disc_symbol
  