Make SVD more general to accommodate graded arrays

[mtfishman]

@lkdvos this is still work in progress, but this should give you an idea for what I have in mind for generalizing the block sparse SVD function to accommodate graded arrays.

With the right overloads of eachblockaxis, mortar_axis, and similar_output for graded unit ranges/arrays, locally I'm able to preserve symmetry information.

To-do:

• Make the new interface functions public (?).
• Add tests.

[codecov]

Codecov Report

Attention: Patch coverage is 95.34884% with 2 lines in your changes missing coverage. Please review.

Project coverage is 75.23%. Comparing base (6c05eb9) to head (bf2a7a8).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/BlockArraysExtensions/blockedunitrange.jl	71.42%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #114      +/-   ##
==========================================
+ Coverage   75.15%   75.23%   +0.07%     
==========================================
  Files          29       29              
  Lines        1284     1296      +12     
==========================================
+ Hits          965      975      +10     
- Misses        319      321       +2     

Flag	Coverage Δ
docs	13.32% <0.00%> (-0.13%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ 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.

[mtfishman]

@lkdvos this is ready for review. I think it would be nice to merge this soon so then I can make a corresponding PR to GradedArrays.jl using these new customization points to fix ITensor/GradedArrays.jl#29 (though I know you are traveling so may not have time to review, I can make a draft PR to GradedArrays.jl in the meantime).

I think the main considerations are:

1. The names and arguments, I'm definitely open to suggestions.
2. Whether these are the right customization points.

[mtfishman]

You can see how this interface is used to account for abelian symmetries in ITensor/GradedArrays.jl#33.

[lkdvos]

I think this looks very clean in general, should be good to go?

[mtfishman]

I think this looks very clean in general, should be good to go?

Thanks, I think so, the main things I wanted feedback on are the names/interfaces of the new interface functions eachblockaxis, mortar_axis, and similar_output, since those are semi-public and act as the customization points for ITensor/GradedArrays.jl#33. If you're happy with those, I'm happy with those!

[lkdvos]

I don't think I can come up with anything better than eachblockaxis or mortar_axis. similar_output is a little non-descriptive maybe, and the semi-public state of that is an interesting problem. I don't think this is a major issue though, and I'm fine with keeping the name as is since I also can't come up with better alternatives

[mtfishman]

That's basically how I feel as well. Since it is semi-public we can always reassess as we go along (we'll have to make a breaking change to change it but it would be very minor since it will only be used by GradedArrays.jl for now).