Issue 699 remove autograd

[valentinsulzer]

Description

Remove autograd dependency. Also had to reformat the current functions and introduce a Heaviside symbol.

Fixes #699

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.

• 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 #723 into master will increase coverage by 0.03%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master     #723      +/-   ##
==========================================
+ Coverage    98.1%   98.13%   +0.03%     
==========================================
  Files         175      172       -3     
  Lines        9196     9188       -8     
==========================================
- Hits         9022     9017       -5     
+ Misses        174      171       -3

Impacted Files	Coverage Δ
pybamm/expression_tree/interpolant.py	100% <ø> (ø)	⬆️
pybamm/parameters/parameter_values.py	100% <100%> (ø)	⬆️
pybamm/spatial_methods/scikit_finite_element.py	97.95% <100%> (ø)	⬆️
...mm/expression_tree/operations/convert_to_casadi.py	100% <100%> (ø)	⬆️
pybamm/expression_tree/functions.py	100% <100%> (ø)	⬆️
pybamm/expression_tree/binary_operators.py	98.84% <100%> (+0.4%)	⬆️
pybamm/spatial_methods/finite_volume.py	96.97% <100%> (-0.01%)	⬇️
pybamm/expression_tree/operations/simplify.py	94.98% <100%> (ø)	⬆️
pybamm/discretisations/discretisation.py	99.71% <100%> (ø)	⬆️
...nterface/inverse_kinetics/inverse_butler_volmer.py	100% <100%> (ø)	⬆️
... and 1 more

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[rtimms]

this is all much cleaner, thanks @tinosulzer !

[rtimms]

typo: object

[rtimms]

does this work for things like diffusivity which we assume is a function of some of the variables, or just functions of time/parameters?

[valentinsulzer]

It should work with both. If something is assumed to be a function in the model then we can pass a scalar and it will always take that scalar value without changing the model. But the other way round (scalar to function) doesn't (can't) work, as you have to tell the model what the function depends on