#2229 default linear interp

[rtimms]

Description

Make the default interpolator linear.

Fixes #2229 #2017

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

[valentinsulzer]

why is "cubic" better than "cubic spline"? Cubic spline is used by scipy https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.CubicSpline.html

[rtimms]

I originally changed it as I was going to just pass kind=interpolator to interp1d, but you couldn't take the derivative of that so changed back to using CubicSpline. Then I left it as "cubic" for no real reason. You can just pass kind=interpolator to interp2d.

[valentinsulzer]

so the default when creating an interpolant is "linear", but the default when using data is "cubic"?

[rtimms]

Yeah, I didn't like doing this. I think it would be better to use "linear" all the time, but you can't take the derivative. We could switch to using InterpolatedUnivariateSpline for the 1D interpolation and just change the degree, then you can, but it's not smooth anyway.

[codecov]

Codecov Report

Merging #2258 (c17c3f9) into develop (b25ce8c) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff            @@
##           develop    #2258   +/-   ##
========================================
  Coverage    99.39%   99.39%           
========================================
  Files          364      364           
  Lines        19996    19999    +3     
========================================
+ Hits         19876    19879    +3     
  Misses         120      120           

Impacted Files	Coverage Δ
pybamm/parameters/parameter_values.py	99.45% <ø> (ø)
pybamm/expression_tree/interpolant.py	100.00% <100.00%> (ø)
...mm/expression_tree/operations/convert_to_casadi.py	100.00% <100.00%> (ø)

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