Tensor Ring Decomposition #605
Description
Is your feature request related to a problem?
Does it worth to implement tensor ring method based on https://arxiv.org/pdf/[1606.05535]
Describe the solution you'd like
Use https://arxiv.org/pdf/[1606.05535] to implement a TR decomposition on NumPy backend (for the beginning, maybe other backends later)
Describe alternatives you've considered
Tensor Train, as I know is the foundation for tensor ring, haven't seen it implemented.
Rough example function:
def tensor_ring(tensor, rank, n_iter_max=10, tol=1e-5, verbose=False):
"""
Parameters
----------
tensor : ndarray
Input tensor of shape (I1,...,Id)
rank : int or list/tuple of ints
TR-rank. If int, all ranks are identical.
n_iter_max : int
tol : float
verbose : bool
Returns
-------
cores : list of d arrays
Each core[k] has shape (r_k, I_k, r_{k+1})
rank : tuple
Actual TR-rank used (r1,...,rd, r1)
"""