[NDTensors] BlockSparseArrays prototype

[mtfishman]

Description

This is a prototype for a BlockSparseArray type based on the BlockArrays.jl interface. It is based on wrapping an elementwise sparse array (SparseArray, also introduced in this PR) which uses a dictionary-of-keys data storage, similar to the design of SparseArrayKit.jl.

It is fairly functional with just this amount of code, for example you can get and set elements and blocks and some basic linear algebra works (but isn't optimized for sparsity).

An interesting next step would be to define some tensor operations (perhaps using the interface defined in TensorOperations.jl), remove the type restriction on Tensor constraining the storage to TensorStorage, and see if we can get it working as an ITensor backend.

@kmp5VT I think this could be a good starting point to build off of for reworking the block sparse code. It already allows blocks with general types. The current BlockSparseArray type defined here can have blocks that are slices of a contiguous piece of data but also can be totally general AbstractArrays. If we add a DiagArray type and store them inside the blocks, it would cover our current use cases for the BlockSparse and DiagBlockSparse storage types. A more fully functional type that works with a contiguous data backend will probably require a slightly more sophisticated type, however, which stores an extra data field separate from the block structure, and the block structure stores SubArrays which are slices into that data.

[codecov-commenter]

Codecov Report

All modified lines are covered by tests ✅

Comparison is base (ea0f602) 85.41% compared to head (1864f14) 67.22%.

❗ Current head 1864f14 differs from pull request most recent head d9b7d97. Consider uploading reports for the commit d9b7d97 to get more accurate results

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Additional details and impacted files

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see 40 files with indirect coverage changes

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[emstoudenmire]

Nice that it's already up and running with so little code.

[mtfishman]

@kmp5VT I'm going to merge this so we can start using it.

You can already use it as an ITensor storage type, but many operations won't work (so far just getting and setting elements will work, but tensor contractions, additions, and decompositions will fail).