Implement vnorm for xarray with dask support

[deanpospisil]

Similarly to #723 I'd like to see if I can port vnorm from Dask into xarray. This a useful quick operation to have handy for linear models.
Previously as I work around I tried:
n = da.reduce(np.linalg.norm, ['shapes', 'x'] )
but it quickly explodes (eats up all ram) for large DaskArrays

[shoyer]

I would be OK adding a norm method, although I don't think there's a super strong need for it -- usually I've been happy writing expressions like (x ** 2).sum(['shapes', 'x']) ** 0.5 instead.

You would either need to implement this all in xarray, or preferably write da.linalg.norm in dask and use that take. Take a look at the scipy source code for this function -- I suspect you could port this almost directly to dask.

[deanpospisil]

Note I mis-typed vecnorm instead of vnorm previously.

I would be OK adding a norm method, although I don't think there's a super strong need for it -- usually I've been happy writing expressions like (x ** 2).sum(['shapes', 'x']) ** 0.5 instead.

When using large dask arrays that operation tended to fill up ram. I'm not sure why, but it made the dask objects very large, I don't have a good understanding of how those graphs are constructed so I was unable to track down the problem.

I tried out da.std(['shapes', 'x']) and it worked like a charm, but it felt a little silly rescaling it to get the norm.

You would either need to implement this all in xarray, or preferably write da.linalg.norm in dask and use that take. Take a look at the scipy source code for this function -- I suspect you could port this almost directly to dask.

dask has a vnorm,
http://dask.pydata.org/en/latest/array-api.html?highlight=norm#dask.array.core.Array.vnorm
which I am currently trying to make use of, using the very helpful:
ops._dask_or_eager_func('vnorm', n_array_args=1)
unfortunately numpy calls their norm norm as opposed to vnorm so I think I'll need to put in a switch depending on the array type before hitting _dask_or_eager_func

[shoyer]

Looks like it would be worth writing a cross-compatible vnorm in xarray/core/ops.py. Take a look at that module for examples of how we wrote custom wrapper -- this should be pretty straightforward

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