xarray-einstats
Stats, linear algebra and einops for xarray
⚠️ Caution: This project is still in a very early development stage
Installation
To install, run
(.venv) $ pip install xarray-einstats
Overview
As stated in their website:
xarray makes working with multi-dimensional labeled arrays simple, efficient and fun!
The code is often more verbose, but it is generally because it is clearer and thus less error prone and intuitive. Here are some examples of such trade-off:
| numpy | xarray |
|---|---|
a[2, 5] |
da.sel(drug="paracetamol", subject=5) |
a.mean(axis=(0, 1)) |
da.mean(dim=("chain", "draw")) |
| `` | `` |
In some other cases however, using xarray can result in overly verbose code that often also becomes less clear. xarray-einstats provides wrappers around some numpy and scipy functions (mostly numpy.linalg and scipy.stats) and around einops with an api and features adapted to xarray.
%
Data for examples
The examples in this overview page use the DataArrays from the Dataset below (stored as ds variable) to illustrate xarray-einstats features:
Dimensions: (dim_plot: 50, chain: 4, draw: 500, team: 6)
Coordinates:
* chain (chain) int64 0 1 2 3
* draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499
* team (team) object 'Wales' 'France' 'Ireland' ... 'Italy' 'England'
Dimensions without coordinates: dim_plot
Data variables:
x_plot (dim_plot) float64 0.0 0.2041 0.4082 0.6122 ... 9.592 9.796 10.0
atts (chain, draw, team) float64 0.1063 -0.01913 ... -0.2911 0.2029
sd_att (draw) float64 0.272 0.2685 0.2593 0.2612 ... 0.4112 0.2117 0.3401
Stats
xarray-einstats provides two wrapper classes {class}xarray_einstats.XrContinuousRV and {class}xarray_einstats.XrDiscreteRV that can be used to wrap any distribution in {mod}scipy.stats so they accept {class}~xarray.DataArray as inputs.
We can evaluate the logpdf using inputs that wouldn't align if using numpy in a couple lines:
norm_dist = xarray_einstats.XrContinuousRV(scipy.stats.norm)
norm_dist.logpdf(ds["x_plot"], ds["atts"], ds["sd_att"])
which returns:
array([[[[ 3.06470249e-01, 3.80373065e-01, 2.56575936e-01,
...
-4.41658154e+02, -4.57599982e+02, -4.14709280e+02]]]])
Coordinates:
* chain (chain) int64 0 1 2 3
* draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499
* team (team) object 'Wales' 'France' 'Ireland' ... 'Italy' 'England'
Dimensions without coordinates: dim_plot
einops
only rearrange wrapped for now
einops uses a convenient notation inspired in Einstein notation to specify operations on multidimensional arrays. It uses spaces as a delimiter between dimensions, parenthesis to indicate splitting or stacking of dimensions and -> to separate between input and output dim specification. einstats uses an adapted notation then translates to einops and calls {func}xarray.apply_ufunc under the hood.
Why change the notation? There are three main reasons, each concerning one of the elements respectively: ->, space as delimiter and parenthesis:
- In xarray dimensions are already labeled. In many cases, the left side in the einops notation is only used to label the dimensions. In fact, 5/7 examples in https://einops.rocks/api/rearrange/ fall in this category. This is not necessary when working with xarray objects.
- In xarray dimension names can be any {term}
xarray:hashable.xarray-einstatsonly supports strings as dimension names, but the space can't be used as delimiter. - In xarray dimensions are labeled and the order doesn't matter. This might seem the same as the first reason but it is not. When splitting or stacking dimensions you need (and want) the names of both parent and children dimensions. In some cases, for example stacking, we can autogenerate a default name, but in general you'll want to give a name to the new dimension. After all, dimension order in xarray doesn't matter and there isn't much to be done without knowing the dimension names.
xarray-einstats uses two separate arguments, one for the input pattern (optional) and another for the output pattern. Each is a list of dimensions (strings) or dimension operations (lists or dictionaries). Some examples:
We can combine the chain and draw dimensions and name the resulting dimension sample using a list with a single dictionary. The team dimension is not present in the pattern and is not modified.
rearrange(ds.atts, [{"sample": ("chain", "draw")}])
Out:
array([[ 0.10632395, 0.1538294 , 0.17806237, ..., 0.16744257,
0.14927569, 0.21803568],
...,
[ 0.30447644, 0.22650416, 0.25523419, ..., 0.28405435,
0.29232681, 0.20286656]])
Coordinates:
* team (team) object 'Wales' 'France' 'Ireland' ... 'Italy' 'England'
Dimensions without coordinates: sample
Note that following xarray convention, new dimensions and dimensions on which we operated are moved to the end. This only matters when you access the underlying array with .values or .data and you can always transpose using {meth}xarray.Dataset.transpose, but it can matter. You can change the pattern to enforce the output dimension order:
rearrange(ds.atts, [{"sample": ("chain", "draw")}, "team"])
Out:
array([[ 0.10632395, -0.01912607, 0.13671159, -0.06754783, -0.46083807,
0.30447644],
...,
[ 0.21803568, -0.11394285, 0.09447937, -0.11032643, -0.29111234,
0.20286656]])
Coordinates:
* team (team) object 'Wales' 'France' 'Ireland' ... 'Italy' 'England'
Dimensions without coordinates: sample
Now to a more complicated pattern. We will split the chain and draw dimension, then combine those split dimensions between them.
rearrange(
ds.atts,
# combine split chain and team dims between them
# here we don't use a dict so the new dimensions get a default name
out_dims=[("chain1", "team1"), ("team2", "chain2")],
# use dicts to specify which dimensions to split, here we *need* to use a dict
in_dims=[{"chain": ("chain1", "chain2")}, {"team": ("team1", "team2")}],
# set the lengths of split dimensions as kwargs
chain1=2, chain2=2, team1=2, team2=3
)
Out:
array([[[ 1.06323952e-01, 2.47005252e-01, -1.91260714e-02,
-2.55769582e-02, 1.36711590e-01, 1.23165119e-01],
...
[-2.76616968e-02, -1.10326428e-01, -3.99582340e-01,
-2.91112341e-01, 1.90714405e-01, 2.02866563e-01]]])
Coordinates:
* draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499
Dimensions without coordinates: chain1,team1, team2,chain2
More einops examples at {ref}einops
Linear Algebra
Still missing in the package
There is no one size fits all solution, but knowing the function we are wrapping we can easily make the code more concise and clear. Without xarray-einstats, to invert a batch of matrices stored in a 4d array you have to do:
inv = xarray.apply_ufunc( # output is a 4d labeled array
numpy.linalg.inv,
batch_of_matrices, # input is a 4d labeled array
input_core_dims=[["matrix_dim", "matrix_dim_bis"]],
output_core_dims=[["matrix_dim", "matrix_dim_bis"]]
)
to calculate it's norm instead, it becomes:
norm = xarray.apply_ufunc( # output is a 2d labeled array
numpy.linalg.norm,
batch_of_matrices, # input is a 4d labeled array
input_core_dims=[["matrix_dim", "matrix_dim_bis"]],
)
With xarray-einstats, those operations become:
inv = xarray_einstats.inv(batch_of_matrices, dim=("matrix_dim", "matrix_dim_bis"))
norm = xarray_einstats.norm(batch_of_matrices, dim=("matrix_dim", "matrix_dim_bis"))
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