Linear algebra support

Share we support linear algebra? Thank you for your hardworking, I’m so happy that we do not need to rember the damned “axis number” in normal situations. But sometime we should still use the functions of linear algebra like LUdepart or determinant.
Follow is the codes to explain some personal idea of new functions API. #code

>>>Adata = np.random.randn(4,4,7)
>>>A = DataArray(Adata, dims=('x','y','z')) 
>>>L, U = LUdepart(A, dims1='x',  dims2='y',newdims='a') 

#result

>>> L
DataArray(x:4, z:7, a: 4)
...
>>> U
DataArray(y:4, z:7, a: 4)
... 
>>>L@U == A
True

I think other essential linear algebra function in numpy can be wraped by this way so that we will can use their named axis version. Do you have any suggestions? Finally, thankyou again for your work.

[OriolAbril]

I have created a library for easier linear algebra (plus others) with xarray: https://xarray-einstats.readthedocs.io/en/latest/.

It currently has:

• wrappers for many numpy.linalg functions
• wrappers for scipy.stats distributions plus a few functions
• wrappers for einops functions
• a numba.guvectorize-decorated version of numpy.histogram for dataarrays

I have mostly added wrappers for things I personally use, also trying to not overlap with xr-scipy nor xarray-extras, so it might not make much sense as a group, but the modules are completely independent between them and could be reorganized into independent packages or merged into existing ones.

Feedback very welcome!

[OriolAbril]

Great, thanks for the offer 😄 I think I’ll start with a minimal repo back at ArviZ and see how much of that can be used more generally. I probably should have named the example above arviz_dot instead. I definitely want to be able to do arviz_dot(a, b) and have it work automatically because in most ArviZ cases we do have all the information we need for this to be possible. We’ll therefore definitely need a higher ArviZ layer, but I think an xarray-linalg would be a great base on which to build and we can keep both in different files/modules so it can be split easily.

I also commented here as I thought it was the most related issue, many of the functions I have in mind are related to linalg, but we’ll probably have some other functions too.