added extraction/generation of diagonal/triangonal matrices to linalg

[asmushetzel]

Description

This add operators to the linalg namespace to

• extract a diagonal from a single or a batch of square matrices
• construct a single or a batch of square diagonal matrices
• extract a triangle from a single or a batch of square matrices
• construct a single or a batch of square triangular matrices

This operators are useful for various tasks when working with linear algebra. We have a specific use case already where batches of triangular matrices exist and the non-zero entries above/below some diagonal must be rearranged as 1-d tensors.

There are various variants of such diagonal/triangular matrix manipulation in numpy (tril/triu/diag/diagonal/diagflat) and also one already in MXNet (diag-operator). Unfortunately without real consistency. MXNet's current diag operator is consistent with numpy's diag. So it lacks any notion of batches of matrices which is a fundamental concept for all linalg-operators.

It doesn't seem to be useful to write the "one fits all" operator for all types of manipulation of diagonal/triangular matrix operations. So this PR rather provides a consistent mechanism that can be used in the context of "linalg"-namespace and supports the usual operations that people need when they do advanced linear algebra. In particular, it does support the same level of batched matrix support, the same data types, diagonal and triangular matrices and enough flexibility to deal also with diagonal/triangular matrices that are defined by other than the main diagonal.

Checklist

Essentials

Please feel free to remove inapplicable items for your PR.

• [ X] Changes are complete (i.e. I finished coding on this PR)
• [ X] All changes have test coverage:
• Unit tests are added for small changes to verify correctness (e.g. adding a new operator)
• Nightly tests are added for complicated/long-running ones (e.g. changing distributed kvstore)
• Build tests will be added for build configuration changes (e.g. adding a new build option with NCCL)
• [ X] Code is well-documented:
• For user-facing API changes, API doc string has been updated.
• For new C++ functions in header files, their functionalities and arguments are documented.
• For new examples, README.md is added to explain the what the example does, the source of the dataset, expected performance on test set and reference to the original paper if applicable
• Check the API doc at http:https://mxnet-ci-doc.s3-accelerate.dualstack.amazonaws.com/PR-$PR_ID/$BUILD_ID/index.html
• [X ] To the my best knowledge, examples are either not affected by this change, or have been fixed to be compatible with this change

[asmushetzel]

@mseeger you may be interested in these operators

[asmushetzel]

All checks passed except two and the latter ones apparently related to a connectivity issue where they tried to download some data from a different server. Not sure that I can do anything about this. Any advice?

[pinaraws]

@mxnet-label-bot add[pr-awaiting-review, Operator]

[szha]

@asmushetzel thanks for the contribution. Could you rebase the PR to the latest commit on master?

[asmushetzel]

rebased.

[asmushetzel]

Anything that I can help with to get this through?

[Roshrini]

@asmushetzel Thanks for working on this. @eric-haibin-lin @reminisce @apeforest @anirudh2290 Can you please help review this PR?

[roywei]

@eric-haibin-lin @reminisce @apeforest @anirudh2290 gentle ping for review. Thanks!