Support Everything that XArray Expects

[mrocklin]

bolt-project/bolt#58

• single argument ufuncs (sin, exp, etc.) and ufunc like functions (pd.isnull, notnull, astype, around, isclose)
• broadcasting binary operations (e.g., ndarray arithmetic)
• three argument version of where (preferably with broadcasting)
• aggregation methods
  • max/min/sum/prod
  • argmax/argmin/std/var
  • nan-skipping aggregations (e.g., nanmin, nanmax, nanprod, nansum)
• indexing with integer arrays, booleans, slices, None
• transpose
• indexing:
  • basic indexing (int/slice)
  • outer indexing for a single array
  • outer indexing (int, slice and 1d integer arrays separately applied to each axis)
  • vectorized indexing (integer arrays with broadcasting, like NumPy)
• broadcast_to (NumPy 1.10)
• concatenate and stack (NumPy 1.10)

[shoyer]

I updated the check-list (apparently I'm an "Owner" for pydata) to drop "insert/fancy indexing" and add a three-item checklist for indexing instead.

[hameerabbasi]

Do we have partial XArray compatibility or does XArray fail with sparse arrays outright?

[shoyer]

@hameerabbasi Not yet, see pydata/xarray#1375. But sparse is close enough that it might be worth trying soon.

From a usability perspective, the most helpful additional feature would be nan-skipping aggregations. I know sparse will probably rarely be used with NaNs, but xarray's aggregation methods default to skipna=True so this would be valuable for consistency.

In addition to the direct uses, xarray uses where and outer/vectorized indexing internally primarily for alignment with join='outer' (e.g., in concat or merge). This sort of alignment would require making sparse arrays dense, unless they have a fill value of NaN rather than 0. So these operations are less essential than they might otherwise seem.

[hameerabbasi]

I just tested with your example code, NaN-skipping aggregations use ufuncs with reduce, so they should already be supported in theory.

>>> class A(np.ndarray):
...     def __array_ufunc__(self, *args, **kwargs):
...         print('ufunc', args, kwargs)
...         
>>> np.nansum(np.arange(5).view(A))
ufunc (<ufunc 'add'>, 'reduce', A([0, 1, 2, 3, 4])) {'axis': None, 'dtype': None, 'keepdims': False}

Although I have absolutely now idea how to discern that this was NaN skipping from the args/kwargs.

[hameerabbasi]

Ah, it was a dtype issue.

>>> np.nansum(np.arange(5, dtype=np.float).view(A))
ufunc (<ufunc 'isnan'>, '__call__', A([0., 1., 2., 3., 4.])) {}
ufunc (<ufunc 'add'>, 'reduce', A([0., 1., 2., 3., 4.])) {'axis': None, 'dtype': None, 'keepdims': False}

So we're good to go on those already. :-)

Edit: Concrete example:

>>> ar = sparse.DOK((2, 2))
>>> ar[1, 1] = np.nan
>>> s = sparse.COO(ar)
>>> np.nansum(s)
0.0

[mrocklin]

FWIW this is a great demonstration of the value of NumPy's use of protocols. It would be great if we could get an alternative ndarray implementation, sparse, to work with a complex downstream user of NumPy code, XArray, without either library having to explicitly know about the other. cc @njsmith

[hameerabbasi]

I was also considering sparse arrays with different fill values. However, some operations (such as dot) blow up in complexity, and on others, it's fairly easy to support.

[shoyer]

NumPy's nan-aggregations work, but only by converting sparse arrays into numpy arrays, inside np.lib.nanfunctions._replace_nan:

import numpy as np
import sparse

class NoncoercibleCOO(sparse.COO):
  def __array__(self, *args, **kwargs):
    raise Exception('cannot convert to numpy')
  
ar = sparse.DOK((2, 2))
ar[1, 1] = np.nan
s = NoncoercibleCOO(ar)
np.nansum(s)

This results in:

---------------------------------------------------------------------------
Exception                                 Traceback (most recent call last)
<ipython-input-13-481c3bc38f6d> in <module>()
      9 ar[1, 1] = np.nan
     10 s = NoncoercibleCOO(ar)
---> 11 np.nansum(s)

/usr/local/lib/python3.6/dist-packages/numpy/lib/nanfunctions.py in nansum(a, axis, dtype, out, keepdims)
    579 
    580     """
--> 581     a, mask = _replace_nan(a, 0)
    582     return np.sum(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims)
    583 

/usr/local/lib/python3.6/dist-packages/numpy/lib/nanfunctions.py in _replace_nan(a, val)
     62 
     63     """
---> 64     a = np.array(a, subok=True, copy=True)
     65 
     66     if a.dtype == np.object_:

<ipython-input-13-481c3bc38f6d> in __array__(self, *args, **kwargs)
      4 class NoncoercibleCOO(sparse.COO):
      5   def __array__(self, *args, **kwargs):
----> 6     raise Exception('cannot convert to numpy')
      7 
      8 ar = sparse.DOK((2, 2))

Exception: cannot convert to numpy

So this really isn't a good solution yet :).

You might actually view this as the flip side of implementing protocols (like __array__): you get default implementations, but they aren't always good ones and it's not always obvious when that's the case.

[mrocklin]

Is this already reported upstream in NumPy?

[njsmith]

Hmm. So for this what we really want is something like: implement nansum using which=, and make reductions support which=?

[shoyer]

I was also considering sparse arrays with different fill values. However, some operations (such as dot) blow up in complexity, and on others, it's fairly easy to support.

I think this could be quite interesting indeed. NaN (which pandas's SparseArray uses) is the most obvious other default value to support. Even dot could be make to work if you make a nan-skipping version (nandot, nanmatmul?).

Is this already reported upstream in NumPy?

I don't know if this really qualifies as a bug, so much as an unintended consequence. I think the easiest fix would be to replace np.copyto() in _replace_nan with a protocol dispatching version of the three argument variant of np.where().

[hameerabbasi]

A simpler option would be to add skipnan= in ufunc reduce and accumulate methods.

Edit: And reduceat.

Edit: Or maybe in ufuncs themselves. ufunc(NaN, NaN) = NaN, otherwise, return the non-NaN item.