Limits for inputs to functions

[valentinsulzer]

Could/should limits be specified by the BPX for inputs into functions? e.g. concentration between 0 and 3 molar, temperature between 10 and 40 Celsius. See pybamm-team/PyBaMM#989

[brosaplanella]

This ties into this PyBaMM issue

[ejfdickinson]

An alternative short-term route, that places this more in the hands of the user, would be to put a note in the specification that encourages regions of validity and means of extrapolation to be expressed explicitly in the functional form. So:

U =
    (x < 0.99)*(x > 0.01)*complicated_function(min(0.99,max(x,0.01))) +
    (x > 0.99)*upper_extrapolated_function(x) +
    (x < 0.01)*lower_extrapolated_function(x)