#644 set atol and rtol

[rtimms]

Description

Allows the user to set rtol and atol separately. For the defaults I've selected 1e-3 for rtol and 1e-6 for atol. This is the same as other solvers (e.g. scipy.integrate or MATLABs ODE15s) and provides a pretty significant speedup vs 1e-8 for both. I've also reduced the default number of points in x, as again this speed things up quite a bit. Both of these result in a RMS voltage error of around 1e-4 compared with the previous defaults, but the default DFN now runs in around 3 seconds vs 23 seconds (on my computer at least).

I think for most users, this kind of error is ok out of the box (the plots are indistinguishable), particularly if they are new users and just want to quickly run some examples. Users now have more control over both solver tolerances, so I think this is an ok compromise.

EDIT: I've decreased rtol to 1e-6 too. Seems like the thermal model and some other models didn't like rtol as low as 1e-3. Probably safer to have both set as 1e-6 so that the solvers don't immediately fall over when people add new physics.

Fixes #644

Type of change

Please delete options that are not relevant.

• 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

[valentinsulzer]

Looks good :)
Still think we need a better solution for examples vs results, making sure the right things are tested but without taking forever. Maybe separate repository is the solution

[valentinsulzer]

should this be else or just default behaviour?

[rtimms]

yeah probably should just be default.

I agree, I think a separate repository on pybamm-team with paper results and any undocumented (or poorly documented) examples would be good. Then make sure the examples that come as part of pybamm are actually really useful for learning how to use it/showcasing feature, rather than just a relatively random collection of scripts we make during development.

[codecov]

Codecov Report

❗ No coverage uploaded for pull request base (master@8afc8f9). Click here to learn what that means.
The diff coverage is 100%.

@@            Coverage Diff            @@
##             master     #645   +/-   ##
=========================================
  Coverage          ?   98.49%           
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  Files             ?      167           
  Lines             ?     8177           
  Branches          ?        0           
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  Hits              ?     8054           
  Misses            ?      123           
  Partials          ?        0

Impacted Files	Coverage Δ
...m/models/full_battery_models/base_battery_model.py	100% <ø> (ø)
...l_battery_models/lead_acid/base_lead_acid_model.py	100% <100%> (ø)
pybamm/solvers/dae_solver.py	99.21% <100%> (ø)
pybamm/solvers/scikits_ode_solver.py	98.21% <100%> (ø)
pybamm/solvers/base_solver.py	98.61% <100%> (ø)
pybamm/solvers/scipy_solver.py	100% <100%> (ø)
pybamm/solvers/scikits_dae_solver.py	97.67% <100%> (ø)
pybamm/solvers/ode_solver.py	100% <100%> (ø)

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