text: #
  # Solution class
  #
  import casadi
  import numbers
  import numpy as np
  import pickle
  import pybamm
  import pandas as pd
  from scipy.io import savemat
  
  
  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.
      model : :class:`pybamm.BaseModel`
          The model that was used to calculate the solution
      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
  
      """
  
      def __init__(
          self,
          all_ts,
          all_ys,
          model,
          all_inputs,
          t_event=None,
          y_event=None,
          termination="final time",
      ):
          if not isinstance(all_ts, list):
              all_ts = [all_ts]
          if not isinstance(all_ys, list):
              all_ys = [all_ys]
          self.all_ts = all_ts
          self.all_ys = all_ys
  
          self._t_event = t_event
          self._y_event = y_event
          self._termination = termination
  
          # Set up inputs
          if not isinstance(all_inputs, list):
              for key, value in all_inputs.items():
                  if isinstance(value, numbers.Number):
                      all_inputs[key] = np.array([value])
              all_inputs = [all_inputs]
          self.all_inputs = all_inputs
          self.has_symbolic_inputs = any(
              isinstance(v, casadi.MX) for v in all_inputs[0].values()
          )
  
          # Set up model
          self._model = model
  
          # Copy the timescale_eval and lengthscale_evals if they exist
          if hasattr(model, "timescale_eval"):
              self.timescale_eval = model.timescale_eval
          else:
              self.timescale_eval = model.timescale.evaluate()
          # self.timescale_eval = model.timescale_eval
          if hasattr(model, "length_scales_eval"):
              self.length_scales_eval = model.length_scales_eval
          else:
              self.length_scales_eval = {
                  domain: scale.evaluate()
                  for domain, scale in model.length_scales.items()
              }
  
          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]
  
          # Solution now uses CasADi
          pybamm.citations.register("Andersson2019")
  
      @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()
              return self._y
  
      def set_y(self):
          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)
  
      @property
      def model(self):
          """Model used for solution"""
          return self._model
  
      @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
  
      @t_event.setter
      def t_event(self, value):
          """Updates the event time"""
          self._t_event = value
  
      @property
      def y_event(self):
          """Value of the solution at the time of the event"""
          return self._y_event
  
      @y_event.setter
      def y_event(self, value):
          """Updates the solution at the time of the event"""
          self._y_event = value
  
      @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 total_time(self):
          return self.set_up_time + self.solve_time
  
      def update(self, variables):
          """Add ProcessedVariables to the dictionary of variables in the solution"""
          # 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.model.variables[key], self)
  
              # Otherwise a standard ProcessedVariable is ok
              else:
                  var_pybamm = self.model.variables[key]
  
                  if key in self.model._variables_casadi:
                      var_casadi = self.model._variables_casadi[key]
                  else:
                      self._t_MX = casadi.MX.sym("t")
                      self._y_MX = casadi.MX.sym("y", self.all_ys[0].shape[0])
                      self._symbolic_inputs_dict = {
                          key: casadi.MX.sym("input", value.shape[0])
                          for key, value in self.all_inputs[0].items()
                      }
                      self._symbolic_inputs = casadi.vertcat(
                          *[p for p in self._symbolic_inputs_dict.values()]
                      )
  
                      # Convert variable to casadi
                      # Make all inputs symbolic first for converting to casadi
                      var_sym = var_pybamm.to_casadi(
                          self._t_MX, self._y_MX, inputs=self._symbolic_inputs_dict
                      )
  
                      var_casadi = casadi.Function(
                          "variable",
                          [self._t_MX, self._y_MX, self._symbolic_inputs],
                          [var_sym],
                      )
                      self.model._variables_casadi[key] = var_casadi
  
                  var = pybamm.ProcessedVariable(var_pybamm, var_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]
  
      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)
  
      def clear_casadi_attributes(self):
          """Remove casadi objects for pickling, will be computed again automatically"""
          self._t_MX = None
          self._y_MX = None
          self._symbolic_inputs = None
          self._symbolic_inputs_dict = None
  
      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)
  
      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 """
          # 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]
          ):
              return self.copy()
  
          # 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.model,
              self.all_inputs + other.all_inputs,
              self.t_event,
              self.y_event,
              self.termination,
          )
  
          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
  
          # 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
  
          # Set sub_solutions
          new_sol._sub_solutions = self.sub_solutions + other.sub_solutions
  
          return new_sol
  
      def copy(self):
          new_sol = Solution(
              self.all_ts,
              self.all_ys,
              self.model,
              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.solve_time = self.solve_time
          new_sol.integration_time = self.integration_time
          new_sol.set_up_time = self.set_up_time
  
          return new_sol
  