Add Op corresponding to scipy.linalg.solve_discrete_are

[jessegrabowski]

Motivation for these changes

Move solve_discrete_are from pymc_experimental/statespace/pytensor_scipy.py to here.

I also did a few cleanups in tensor.slinalg.py:

• Removed unused helper function is_complex_obj
• Removed unused solvetriangular instance of SolveTriangular (the SolveTriangular Op is instead accessed through the solve_triangular wrapper function)
• Changed return type hint on Op wrapper functions from TensorVariable to Variable to appease the linter
• Added solve_discrete_lyapunov, solve_cotinuous_lyapunov, solve_discrete_are, and solve_triangular to __all__, so there are no more "hidden functions" in nlinalg

Implementation details

Op is just a wrapper around scipy.linalg.solve_discrete_are, with gradients taken from Kao and Hennequin (2020), https://arxiv.org/pdf/2011.11430.pdf

The use-case is solving matrix quadratic equations. It pops up in state space models (the steady state covariance matrix comes from the solution to such an equation). It can also be used to compute the policy function for Bellman equations with linear-quadratic loss function (also relevant to state space modeling).

Checklist

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Major / Breaking Changes

• ...

New features

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Bugfixes

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Documentation

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Maintenance

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[codecov-commenter]

Codecov Report

Merging #417 (d2d1c15) into main (d9b494d) will decrease coverage by 0.01%.
Report is 13 commits behind head on main.
The diff coverage is 100.00%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #417      +/-   ##
==========================================
- Coverage   80.78%   80.77%   -0.01%     
==========================================
  Files         156      156              
  Lines       45483    45571      +88     
  Branches    11139    11152      +13     
==========================================
+ Hits        36742    36812      +70     
- Misses       6532     6552      +20     
+ Partials     2209     2207       -2     

Files Changed	Coverage Δ
pytensor/tensor/slinalg.py	94.91% <100.00%> (+1.37%)	⬆️

... and 9 files with indirect coverage changes

[jessegrabowski]

Does the solve = Solve() here do anything? It's immediately shadowed by def solve in the next line.

[ricardoV94]

Does the solve = Solve() here do anything? It's immediately shadowed by def solve in the next line.

No. I guess it was left accidentally when the parametrized helper was implemented