Only parameterize and discretize variables when they are called by solution[variable_name]

[valentinsulzer]

Currently, we only evaluate a variable the first time it is called by by solution[variable_name] (here)

The motivation is that evaluating every single variable is slow and unnecessary if we're not going to evaluate the variables.
We could go further with this and only process (set parameters, discretize) when it is called. Most of the model processing time is spent processing variables, so this would speed up model processing a lot.

This would require storing the ParameterValues and Discretisation objects as attributes of the processed model, which I think @martinjrobins said wasn't ideal, but would it be worth it?

Implementing this should be quite straightforward:

• remove variable processing (looping over the model.variables dict) in ParameterValues and Discretisation classes
• store ParameterValues and Discretisation as attributes of the processed model at the end of the process_model function in each of these classes
• in Solution.update, replace

vars_pybamm = [
       model.variables_and_events[key] for model in self.all_models
]

with something like

vars_pybamm = []
for model in self.all_models:
    var_processed_param = model.parameter_values.process_symbol(model.variables_and_events[key])
    var_processed_disc = model.disc.process_symbol(var_processed_param)
    vars_pybamm.append(var_processed_disc)

[valentinsulzer]

Rough timings:
parameterization with variables: .107s
parameterization without variables: .08s

disc with variables: .208s
disc without variables: .09s

In total the script takes .7s, of which 20% is spent processing variables (some of which are then never used!)