Sparse Arrays
=============

By swapping out in-memory numpy arrays with in-memory sparse arrays we can
reuse the blocked algorithms of Dask.array to achieve parallel and distributed
sparse arrays.

The blocked algorithms in Dask.array normally parallelize around in-memory
numpy arrays.  However, if another in-memory array library supports the NumPy
interface then it too can take advantage of dask.array's parallel algorithms.
In particular the `sparse <https://github.com/mrocklin/sparse/>`_ array library
satisfies a subset of the NumPy API and works well with, and is tested against,
Dask.array.

Example
-------

Say we have a dask.array with mostly zeros

.. code-block:: python

   x = da.random.random((100000, 100000), chunks=(1000, 1000))
   x[x < 0.95] = 0

We can convert each of these chunks of NumPy arrays into a sparse.COO array.

.. code-block:: python

   import sparse
   s = x.map_blocks(sparse.COO)

Now our array is composed not of many NumPy arrays, but rather of many
sparse arrays.  Semantically this does not change anything.  Operations that
work will work identically (assuming that the behavior of ``numpy`` and
``sparse`` are identical) but performance characteristics and storage costs may
change significantly

.. code-block:: python

   >>> s.sum(axis=0)[:100].compute()
   <COO: shape=(100,), dtype=float64, nnz=100>

   >>> _.todense()
   array([ 4803.06859272,  4913.94964525,  4877.13266438,  4860.7470773 ,
           4938.94446802,  4849.51326473,  4858.83977856,  4847.81468485,
           ... ])

Requirements
------------

Any in-memory library that copies the NumPy ndarray interface should work here.
The `sparse <https://github.com/mrocklin/sparse/>`_ library is a minimal
example.  In particular an in-memory library should implement at least the
following operations:

1.  Simple slicing with slices, lists, and elements (for slicing, rechunking,
    reshaping, etc).
2.  A ``concatenate`` function at the top level of the package (for assembling
    results)
3.  All ufuncs must support the full ufunc interface, including ``dtype=`` and
    ``out=`` parameters (even if they don't function properly)
4.  All reductions must support the full ``axis=`` and ``keepdims=`` keywords
    and behave like numpy in this respect
5.  The array class should follow the ``__array_priority__`` protocol and be
    prepared to respond to other arrays of lower priority.

The implementation of other operations like tensordot, reshape, transpose, etc.
should follow standard NumPy conventions regarding shape and dtype.  Not
implementing these is fine; the parallel dask.array will err at runtime if
these operations are attempted.


Mixed Arrays
------------

Dask.array supports mixing different kinds of in-memory arrays.  This relies
on the in-memory arrays knowing how to interact with each other when necessary.
When two arrays interact the functions from the array with the highest
``__array_priority__`` will take precedence (for example for concatenate,
tensordot, etc.).
