Fixed by #731.

I'm split on whether a function or method makes more sense (a.tensordot(b, dim='x') vs xr.tensordot(a, b, dim='x')). I would be OK with either, so yes, please do go ahead!

Also that einsum does seem pretty ideal. I'll see if I can get it running in dask, so we can port it over here.

I wasn't sure where the best place to put the def would be. Currently I have been running it from the xarray class: t = da1.tensordot( da2, 'shapes' ) Let me know if that seems alright, then I'll write some simple tests in test_dataarray for tensor dot. Maybe make my first pull request!

Looks like it can perform tensor dot for dask and straight xarrays! But apparently dask has not implemented tensordot with multiple axes arguments, and it also does not work performing a tensor dot between a dask xarray and an xarray. Neither of these cases worries me too much, hopefully they don't worry you.

``` python from xarray import align, DataArray

note: using private imports (e.g., from xarray.core) is definitely discouraged!

this is not guaranteed to work in future versions of xarray

from xarray.core.ops import _dask_or_eager_func

def tensordot(a, b, dims): if not (isinstance(a, DataArray) and isinstance(b, DataArray)): raise ValueError

a, b = align(a, b, join='inner', copy=False)

axes = (a.get_axis_num(dims), b.get_axis_num(dims))
f = _dask_or_eager_func('tensordot', n_array_args=2)
new_data = f(a.data, b.data, axes=axes)

if isinstance(dims, str):
    dims = [dims]

new_coords = a.coords.merge(b.coords).drop(dims)

#drop the dims you are performing the sum product over
new_dims = ([d for d in a.dims if d not in dims] +
            [d for d in b.dims if d not in dims])

return DataArray(new_data, new_coords, new_dims)

import xarray as xr import numpy as np

x_trans = np.linspace(-3,3,6) y_trans = np.linspace(-3,3,5) imgID = range(4) da = xr.DataArray( np.ones((6,5,4)), coords = [ x_trans, y_trans, imgID ], dims = ['x_trans', 'y_trans', 'imgID'] )

models = range(20) dm = xr.DataArray( np.ones(( 20 , 5, 4 )), coords = [ models, y_trans, imgID], dims = [ 'models', 'y_trans', 'imgID' ] )

xarray tensordot

proj_a = tensordot(da, dm, 'imgID')

dask xarray tensor dot

da = da.chunk() dm = dm.chunk() proj_b = tensordot(da, dm, 'imgID')

errors

multiple dims

proj_c = tensordot(da, dm, ['imgID', 'y_trans'])

mixed types

da = da.chunk() dm = dm.load() proj_d = tensordot(da, dm, 'imgID') ```

@shoyer - I thought your answer dominated mine, so I left yours as the only response. But yup, that form of einsum would be pretty nice...

@MaximilianR I do like einsum, but I'm not sure the API would be a good fit for xarray (we already have dimension names), and it also does not exist yet for dask (https://github.com/blaze/dask/issues/732).

That said, I suppose you could make an xarray version of einsum with syntax that looks more like tensordot with *args, e.g., einsum(a, b, c, dims=('x', 'y')).

Yes, this would be a nice addition!

I spent a little bit of a time futzing around with this to see if there is an elegant way to plug this into our existing dispatching system. The short of it is that the answer appears to be no -- we don't have any elegant equivalent to dask.array's generic atop method.

So, for now I would simply write a function specialized to DataArray objects. Something like the following (barely tested) is a starting point:

``` python from xarray import align, DataArray

note: using private imports (e.g., from xarray.core) is definitely discouraged!

this is not guaranteed to work in future versions of xarray

from xarray.core.ops import _dask_or_eager_func

def tensordot(a, b, dims): if not (isinstance(a, DataArray) and isinstance(b, DataArray)): raise ValueError

a, b = align(a, b, join='inner', copy=False)

axes = (a.get_axis_num(dims), b.get_axis_num(dims))
f = _dask_or_eager_func('tensordot', n_array_args=2)
new_data = f(a.data, b.data, axes=axes)

if isinstance(dims, basestring):
    dims = [dims]

new_coords = a.coords.merge(b.coords).drop(dims)

new_dims = ([d for d in a.dims if d not in dims] +
            [d for d in b.dims if d not in dims])

return DataArray(new_data, new_coords, new_dims)

```

This would be worth cleaning up so we could add it to the codebase (mostly documentation & tests).