Is there a library that allows einstein summation on dense, sparse, and LinearOperator type tensors

Question

Numpy's einsum only works with dense tensors.

Is there an alternative that also works with sparse tensors and linear operators?

For example, I might have a function f that computes matrix vector multiplications of the form $A^{-1}x$ for some matrix $A$. Numpy's einsum doesn't even allow

np.einsum('ij,j',A,x)

let alone

np.einsum('ijkl,mj->imkl',X,A)

The same operations also don't work when $A$ is a sparse matrix (let alone a general sparse tensor).

While the LinearOperator support is more of a convenience question, the support for sparse tensors is crucial to me.

Answer 1

See the list at Wikipedia and answers to Fast, lightweight C++ tensor library for dimension-agnostic code. Especially taco seems to fit your needs.