Issue 1082 casadi sensitivity

[valentinsulzer]

Description

Reformat casadi solver to allow sensitivities.
Sensitivity API will be reformatted in a subsequent PR.
Doesn't really fix issue #1082 so still leaving that open

Type of change

Please add a line in the relevant section of CHANGELOG.md to document the change (include PR #) - note reverse order of PR #s. If necessary, also add to the list of breaking changes.

• New feature (non-breaking change which adds functionality)
• Optimization (back-end change that speeds up the code)
• Bug fix (non-breaking change which fixes an issue)

Key checklist:

• No style issues: $ flake8
• All tests pass: $ python run-tests.py --unit
• The documentation builds: $ cd docs and then $ make clean; make html

You can run all three at once, using $ python run-tests.py --quick.

Further checks:

• Code is commented, particularly in hard-to-understand areas
• Tests added that prove fix is effective or that feature works

[codecov]

Codecov Report

Merging #1109 into develop will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff            @@
##           develop    #1109   +/-   ##
========================================
  Coverage    97.82%   97.82%           
========================================
  Files          245      245           
  Lines        13269    13273    +4     
========================================
+ Hits         12980    12984    +4     
  Misses         289      289           

Impacted Files	Coverage Δ
pybamm/simulation.py	96.81% <100.00%> (ø)
pybamm/solvers/base_solver.py	100.00% <100.00%> (ø)
pybamm/solvers/casadi_algebraic_solver.py	100.00% <100.00%> (ø)
pybamm/solvers/casadi_solver.py	100.00% <100.00%> (ø)
pybamm/solvers/processed_symbolic_variable.py	100.00% <100.00%> (ø)

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[martinjrobins]

thanks @tinosulzer, looks great. My main comment is that the sensitivities api is currently quite different between the jax and casadi solvers, and ProcessedSymbolicVariable is very casadi specific, but we've already noted that and the plan is to iterate on the api to make it consistent.

Do you know how the sensitivities behave in the presence of an event? particularly if the location of the event changes in response to the symbolic variable?

[valentinsulzer]

Yes, I'm reformatting the sensitivity API (getting rid of ProcessedSymbolicVariable) as part of #1100. Currently the model ignores events when doing sensitivity analysis. I can't think of a good way to handle events.