Decompose Tridiagonal Solve into core steps

[ricardoV94]

This PR builds on top of #1396, extending it to the tridiagonal case.

It also adds a rewrite for when extracting diagonals out a symbolically allocated diagonal matrix (via set_subtensor or AllocDiag after it gets inlined during specialization)

TODO:

• Numba implementation and exclusion from other backends rewrites

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[jessegrabowski]

Is this blocked by anything? Or just needs a bit of polishing to make mypy happy etc

[ricardoV94]

Needs a bit rework after the LU PR

[jessegrabowski]

Same here -- get_lapack_output_dtype_from_inputs?

[ricardoV94]

What do you mean? Is there such a helper? Google doesn't return anything

[jessegrabowski]

I meant make that function to hold the logic for making dummy arrays and getting the out_dtype form get_lapack_funcs

[jessegrabowski]

Approving now, idk if there's more you want to adjust but I'm happy

[codecov]

Codecov Report

Attention: Patch coverage is 72.55814% with 59 lines in your changes missing coverage. Please review.

Project coverage is 82.09%. Comparing base (d10f245) to head (4847344).
Report is 4 commits behind head on main.

Files with missing lines	Patch %	Lines
pytensor/tensor/_linalg/solve/tridiagonal.py	76.57%	20 Missing and 6 partials ⚠️
...or/link/numba/dispatch/linalg/solve/tridiagonal.py	41.46%	24 Missing ⚠️
pytensor/tensor/rewriting/subtensor.py	84.09%	3 Missing and 4 partials ⚠️
pytensor/tensor/_linalg/solve/rewriting.py	89.47%	0 Missing and 2 partials ⚠️

❌ Your patch status has failed because the patch coverage (72.55%) is below the target coverage (100.00%). You can increase the patch coverage or adjust the target coverage.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1382      +/-   ##
==========================================
- Coverage   82.12%   82.09%   -0.03%     
==========================================
  Files         211      212       +1     
  Lines       49757    49965     +208     
  Branches     8819     8858      +39     
==========================================
+ Hits        40862    41018     +156     
- Misses       6715     6757      +42     
- Partials     2180     2190      +10     

Files with missing lines	Coverage Δ
pytensor/compile/mode.py	84.72% <ø> (ø)
pytensor/tensor/subtensor.py	89.98% <ø> (ø)
pytensor/tensor/_linalg/solve/rewriting.py	93.49% <89.47%> (+1.04%)	⬆️
pytensor/tensor/rewriting/subtensor.py	89.81% <84.09%> (-0.34%)	⬇️
...or/link/numba/dispatch/linalg/solve/tridiagonal.py	55.39% <41.46%> (-2.86%)	⬇️
pytensor/tensor/_linalg/solve/tridiagonal.py	76.57% <76.57%> (ø)

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