Generalize istriu/istril to accept a band index

[jishnub]

Currently, only istriu(S) and istril(S) are specialized for sparse matrices, and this PR generalizes these to accept the band index k. This improves performance:

julia> S = sparse(1:4000, 1:4000, 1:4000);

julia> @btime istriu($S, -1);
  20.941 ms (0 allocations: 0 bytes) # main
  5.660 μs (0 allocations: 0 bytes) # this PR

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 84.07%. Comparing base (780c4de) to head (598da1f).
⚠️ Report is 30 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #590   +/-   ##
=======================================
  Coverage   84.07%   84.07%           
=======================================
  Files          12       12           
  Lines        9188     9188           
=======================================
  Hits         7725     7725           
  Misses       1463     1463           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[dkarrasch]

Nice!

[jonas-schulze]

It seems that Julia 1.12 is the first version to ship this. It would be nice to have this in the current LTS. What do you think?

[ViralBShah]

Since LTS and older releases can strictly only have bugfixes and no new features or capabilities, I do not think backporting to LTS will be feasible.

I believe this should already be on 1.12 - but it would be good to confirm with a Julia RC if that is indeed the case. If not, we should mark it for backport to 1.12.

[jonas-schulze]

Since LTS and older releases can strictly only have bugfixes and [no] new features or capabilities, I do not think backporting to LTS will be feasible.

I would argue this causes a performance bug of isdiag(::SparseMatrixCSC).

I believe this should already be on 1.12 - but it would be good to confirm with a Julia RC if that is indeed the case. If not, we should mark it for backport to 1.12.

It is present in 1.12.0-rc1.

[ViralBShah]

That's getting a little cute to get it in. I think it is small and simple enough that we can try.

[jishnub]

I don't think performance improvements are backported unless it's to fix a regression.