Replace `inverse_additive_relationships` with `pedigree_inverse_relationship`

Similar to #895, depends on #891

The inverse additive relationship matrix (ARM) is a sparse matrix which shouldn’t require the full (dense) kinship matrix to be calculated in advance. The inverse ARM can be calculated from the same subset of parental kinships used to calculate the inbreeding coefficient in #891 and this should result in a similar speed up as seen in that PR. Currently inverse_additive_relationships returns the inverse ARM as a dense matrix, but ideally this would (optionally?) be returned as a sparse matrix. How do others feel about picking up pydata/sparse as a dependency?

[timothymillar]

Thanks, that’s a useful reference. AFAICT the scipy.sparse array classes still have issues integrating with dask/xarray. I think it’s probably best to stick to dense arrays for now and revisit sparse encodings later if/when there’s a clear performance benefit.

[tomwhite]

I recall @tomwhite trying out sparse library options when he was working on scanpy: scverse/scanpy#921 (comment). He might have some thoughts?

My main thought is that it’s not always obvious how to best get chunking and sparsity to play well together.

As the referenced issue shows, there were some performance issues with pydata sparse, so I ended up writing my own wrapper class. However, since then sparse array classes (in contrast to sparse matrices) have been added to scipy, so I would suggest we use those (assuming everything is 2D).