Preserve coord in reductions that select an element

[jl-wynen]

Some reductions (max, min, median, etc.) select one element along a dimension. It is possible to retain coordinates along that dimension by also selecting the corresponding element. Currently, we simply remove all coords along a reduced dim. But if we changed this, we would get sort of combined max and argmax, etc. operations. I don't know of a cocnrete use case, it's just something that came to my mind.

E.g.

da = sc.DataArray(
    sc.array(dims=['x'], values=[3, 5, 1, 2]),
    coords={'x': sc.array(dims=['x'], values=[1, 2, 3, 4])}
)
da.max()

returns

da = sc.DataArray(
    sc.scalar(5),
    coords={'x': sc.scalar(2)}
)

[SimonHeybrock]

Would you convert to an unaligned coord, such that you can still to da - da.max()?

[SimonHeybrock]

Have you thought about the cost? This would probably be significantly more expensive to implement?

[jl-wynen]

Would you convert to an unaligned coord, such that you can still to da - da.max()?

Yes, I'd think so. This is akin to indexing into an element where we also preserve the coord.

Have you thought about the cost? This would probably be significantly more expensive to implement?

Not in detail. But if we implement it as argmax, etc., it shouldn't be much more expensive. It would be something like

i = argmax(da.data, dim)
res = da[dim, i]

[SimonHeybrock]

One could make it on opt-in keyword arg?

[jl-wynen]

Possibly.

I need to correct my initial list of functions where this can be used: median may return the average of two elements if there is an even number. So it actually cannot return a coord.