Issue 580 processed variable

[valentinsulzer]

Description

Change ProcessedVariable to be able to plot variables as functions of t, x and z
This is still pretty hacky but seems to work ok for now.
We will need to think of a better way to do this at some point, perhaps by assigning some more attributes to the variables during discretisation (e.g. whether they depend on x, r or z)

Getting a codacy error with eval(...) but can't get ast.literal_eval(...) to work. How bad is it to use eval?

Fixes #580

Type of change

• New feature (non-breaking change which adds functionality)

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
• Any dependent changes have been merged and published in downstream modules

[codecov]

Codecov Report

Merging #581 into master will decrease coverage by 0.02%.
The diff coverage is 93.33%.

@@            Coverage Diff             @@
##           master     #581      +/-   ##
==========================================
- Coverage   98.24%   98.22%   -0.03%     
==========================================
  Files         151      151              
  Lines        7393     7418      +25     
==========================================
+ Hits         7263     7286      +23     
- Misses        130      132       +2

Impacted Files	Coverage Δ
pybamm/spatial_methods/spatial_method.py	92.06% <100%> (ø)	⬆️
pybamm/expression_tree/binary_operators.py	98.41% <100%> (ø)	⬆️
pybamm/discretisations/discretisation.py	97.64% <100%> (ø)	⬆️
pybamm/expression_tree/unary_operators.py	96.6% <100%> (+0.01%)	⬆️
pybamm/expression_tree/functions.py	99.31% <90%> (-0.69%)	⬇️
pybamm/expression_tree/parameter.py	95.34% <90%> (-1.71%)	⬇️
pybamm/processed_variable.py	94.65% <93.47%> (+0.14%)	⬆️

---

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[codecov]

Codecov Report

Merging #581 into master will increase coverage by 0.04%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master     #581      +/-   ##
==========================================
+ Coverage   98.54%   98.59%   +0.04%     
==========================================
  Files         169      169              
  Lines        8441     8450       +9     
==========================================
+ Hits         8318     8331      +13     
+ Misses        123      119       -4

Impacted Files	Coverage Δ
pybamm/expression_tree/concatenations.py	98.63% <ø> (+0.57%)	⬆️
pybamm/spatial_methods/spatial_method.py	95.65% <100%> (ø)	⬆️
pybamm/expression_tree/vector.py	100% <100%> (ø)	⬆️
pybamm/expression_tree/functions.py	100% <100%> (ø)	⬆️
pybamm/expression_tree/binary_operators.py	98.41% <100%> (-0.03%)	⬇️
pybamm/processed_variable.py	97.19% <100%> (+1.67%)	⬆️
pybamm/discretisations/discretisation.py	100% <100%> (ø)	⬆️
pybamm/expression_tree/symbol.py	97.65% <100%> (+0.07%)	⬆️
pybamm/expression_tree/parameter.py	97.14% <100%> (+0.08%)	⬆️
pybamm/expression_tree/matrix.py	100% <100%> (ø)	⬆️
... and 1 more

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[martinjrobins]

Thanks @tinosulzer, some queries below which should be dealt with first. I also don't think there is any documentation on what auxiliary_domains are? Is this part of Symbol, if so it should be described here: https://pybamm.readthedocs.io/en/latest/source/expression_tree/symbol.html

Would we need to assign some more attributes to the variables during discretisation? We have the domain/auxiliary_domain, perhaps there should be some logic somewhere that maps between domain/auxiliary_domain and a list of coordinates. Sounds like this should be in the mesh?

Regarding the eval's. They are a bit of a security hole, not that we are terribly concerned with security with modelling packages :) But I think you could get rid of them just using an if statement? So it might be worth doing this to get rid of the error.

[martinjrobins]

These changes look great, thanks @tinosulzer