keepdims=True for xarray reductions

[shoyer]

For operations where arrays are aggregated but then combined, the keepdims=True option for NumPy aggregations is convenient.

We should consider supporting this in xarray as well. Aggregating a DataArray/Dataset with keepdims=True (or maybe keep_dims=True) would remove all original coordinates along aggregated dimensions and return a result with a dimension of size 1 without any coordinates, e.g.,

>>> array = xr.DataArray([1, 2, 3], dims='x', coords={'x': ['a', 'b', 'c']})
>>> array.mean(keepdims=True)
<xarray.DataArray (x: 1)>
array([2.])
Dimensions without coordinates: x

In case, array.mean(keepdims=True() is equivalent to array.mean().expand_dims('x') but in general this equivalent does not hold, because the location of the original dimension is lost.

Implementation-wise, we have two options:

1. Pass on keepdims=True to NumPy functions like numpy.mean(), or
2. Implement keepdims=True ourselves, in Variable.reduce().

I think I like option 2 a little better, because it places fewer requirements on aggregation functions. For example, functions like bottleneck.nanmean() don't accept a keepdims argument.

[seth-p]

I second this request.

The following may not be optimal, but seems to work for me as a keepdims=True version of reduce():

    def dim_preserving_reduce(self, func, dim=None, axis=None, label=None, keep_attrs=False, **kwargs):
        if axis is not None:
            dim = np.take(self._obj.dims, axis, mode='wrap')
        dims = dim if isinstance(dim, (list, tuple)) else [dim]
        dims_coords = {dim: [lab] for dim, lab in zip(dims, (label if isinstance(label, list) else [label]))}
        return self._obj.reduce(func, dim=dims, keep_attrs=keep_attrs, **kwargs). \
            expand_dims(dims, axis=[self._obj.dims.index(dim) for dim in dims]). \
            assign_coords(**dims_coords)

[aldanor]

Please!

It's really painful in some cases where keepdims option is not available, tons of unneeded boilerplate required to mimic the same thing.

[shoyer]

Pull requests would be very welcome here.