Add Cholesky decomposition

[alewis]

We should support the Cholesky decomposition per https://numpy.org/doc/stable/reference/generated/numpy.linalg.cholesky.html#numpy.linalg.cholesky, adding a pivot argument in the same way as qr and svd.

[Dbhasin1]

Hello, can this issue be assigned to me?

[mganahl]

Sure thing!

[alewis]

Hi @Dbhasin1,

The function and tests first need to be added to the various backends, which live in tensornetwork/backends/blah. The first is the AbstractBackend, a base class that just throws NotImplementedError. The others all wrap functions from other numerical packages, the idea being to provide a means to quickly switch between these.

Inside the backend files you will see many other functions, such as qr. Our QR differs from e.g. NumPy's by the presence of a pivot argument that matricizes the input. Cholesky should have a similar mechanism.

Once added to the backends, the function should also be added to the tn.Tensor interface, which lives in tensornetwork/tensor.py with functions defined in tensornetwork/linalg/blah

[LuiGiovanni]

Hello there @alewis I'm interested in working on this issue has a PR been done? If not I would like to work on this.

[LuiGiovanni]

Hello, please ignore this PR I made a mistake, the changes implemented for the Cholesky decomposition will be from a different PR.

[LuiGiovanni]

Hello, I am sorry for the mess but #886 is the correct PR I was working on disregard #885 thank you.

[LuiGiovanni]

@alewis @mganahl I have added the NotImplementedError function and it's respective test and made a PR for you to review.

[alewis]

Looks good! Just a small fix.