Would it be conceivable to implement an alternative form of coordinate index which is explicitly a linear coordinate axis, storing only a first point and a step (possibly a last point but that would obviously be redundant with the length of the dimension)

It would be possible to do that after the explicit index refactor is complete (see https://github.com/pydata/xarray/projects/1).

5692 already adds several Xarray methods like isel, sel, concat, stack, roll, rename, etc. to the new Xarray Index base class so that it will be possible to provide alternative indexes as Index sub-classes with custom implementations.

We could certainly add an Index.pad method.

Would it be conceivable to implement an alternative form of coordinate index which is explicitly a linear coordinate axis, storing only a first point and a step (possibly a last point but that would obviously be redundant with the length of the dimension). This would be trivial to pad via linear extrapolation and the pad function would just have to ask the coordinate to pad itself. This could also in principle extend to other coordinates like a periodic one etc., although I don't personally have a use for those. Coordinates that don't know how to handle being padded can use NaN as currently. I guess that this is one of the things that could be enabled by #1603?

My use case is in MRI reconstruction where we frequently have asymmetric datasets and need to pad them to be symmetric before an IFT. I am using xrft which is great but makes a fuss if the coordinates are not correctly linear and centred on the origin. The degree of asymmetry and the step size change from dataset to dataset, so it is not trivial to assemble the necessary new coordinate values for @fujiisoup's proposed solution.

@fujiisoup's suggestions looks good to me. PRs welcome!

I'm not sure whether to open a separate feature request or just tag onto this one. Please correct me.

pad is an awesome method. I've used it to easily support interpolating or extrapolating dataarrays that happen to have unitary dimensions, or to quickly support a constant value extrapolation in any dimension. However, to do this, I have to go in and change alter the coords myself since the same value is just repeated.

Would it be possible to add an option that effectively adds "epsilon" to the newly added kwarg?

Thanks for implementing this! This is a feature, that we will be using for sure! Mostly with indices of type 1 which, in many cases, can easily be extrapolated. Having this as a default or a switch to enable extrapolation where possible would help a lot!

How about passing an Index instead of just a simple integer to the pad method? ```python In [4]: da = xr.DataArray([0.5, 1.5, 2.5], dims=['x'], coords={'x': [0, 1, 2]})

In [5]: da
Out[5]: <xarray.DataArray (x: 3)> array([0.5, 1.5, 2.5]) Coordinates: * x (x) int64 0 1 2

In [8]: da.pad(x=([-1, -2], 0))
Out[8]: <xarray.DataArray (x: 5)> array([nan, nan, 0.5, 1.5, 2.5]) Coordinates: * x (x) int64 -1 -2 0 1 2 ```