Refactor and update QR Op

[jessegrabowski]

Description

This PR updates the QRFull Op, adding static shape checking, infer_shape, and destroy_map. It also optimizes the perform method for the C backend, and tries to improve the gradient graph by checking static shapes (to avoid an ifelse).

I renamed it to QR, because I don't know what was Full about the old one. I also moved it from the numpy implementation to scipy, which gives us all the usual benefits (inplace, etc). I also went ahead and unpacked the scipy wrapper and used the LAPACK functions directly. This will give us better error handling (that is to say, none -- it should eventually return a matrix of NaN on failure) and some performance boost by caching workspace requirements.

Still a WIP, because it breaks everything by moving QR from nlinalg to slinalg. I thought about using this as an opportunity to finally eliminate this distinction and go to a more logical organization (linalg/decomposition/qr.py), but then decided against it for now. Needs discussion.

Related Issue

• Closes Add infer_shape method to QRFull #1511
• Related to #

Checklist

• Checked that the pre-commit linting/style checks pass
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks)
• If you are a pro: each commit corresponds to a relevant logical change

Type of change

• New feature / enhancement
• Bug fix
• Documentation
• Maintenance
• Other (please specify):

---

📚 Documentation preview 📚: https://pytensor--1518.org.readthedocs.build/en/1518/

[codecov]

Codecov Report

❌ Patch coverage is 49.75530% with 308 lines in your changes missing coverage. Please review.
✅ Project coverage is 81.45%. Comparing base (b9fc4f8) to head (112f6fd).
⚠️ Report is 132 commits behind head on main.

Files with missing lines	Patch %	Lines
...sor/link/numba/dispatch/linalg/decomposition/qr.py	19.41%	274 Missing ⚠️
pytensor/link/numba/dispatch/slinalg.py	63.41%	10 Missing and 5 partials ⚠️
pytensor/tensor/slinalg.py	93.58%	5 Missing and 7 partials ⚠️
pytensor/link/pytorch/dispatch/slinalg.py	77.77%	4 Missing ⚠️
pytensor/link/numba/dispatch/linalg/_LAPACK.py	85.00%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1518      +/-   ##
==========================================
- Coverage   81.85%   81.45%   -0.41%     
==========================================
  Files         230      232       +2     
  Lines       52522    53027     +505     
  Branches     9345     9422      +77     
==========================================
+ Hits        42992    43192     +200     
- Misses       7095     7390     +295     
- Partials     2435     2445      +10     

Files with missing lines	Coverage Δ
pytensor/link/jax/dispatch/nlinalg.py	93.47% <ø> (-0.76%)	⬇️
pytensor/link/jax/dispatch/slinalg.py	94.84% <100.00%> (+0.33%)	⬆️
pytensor/link/numba/dispatch/nlinalg.py	100.00% <ø> (ø)
pytensor/link/pytorch/dispatch/__init__.py	100.00% <100.00%> (ø)
pytensor/link/pytorch/dispatch/nlinalg.py	78.00% <ø> (+2.59%)	⬆️
pytensor/tensor/nlinalg.py	94.98% <ø> (-0.65%)	⬇️
pytensor/link/numba/dispatch/linalg/_LAPACK.py	79.78% <85.00%> (+0.49%)	⬆️
pytensor/link/pytorch/dispatch/slinalg.py	77.77% <77.77%> (ø)
pytensor/tensor/slinalg.py	93.41% <93.58%> (+0.01%)	⬆️
pytensor/link/numba/dispatch/slinalg.py	68.39% <63.41%> (-1.38%)	⬇️
... and 1 more

... and 9 files with indirect coverage changes

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[ricardoV94]

Do we need to worry about a not being F-contiguous like other lapack/blas stuff?

[ricardoV94]

I see, it's done in the lower level functions