ENH: Add array_api support for generalized eigenvalue decomposition (…

[V-bot5123]

As discussed in the issue thread, this PR introduces hardware acceleration (TPU/GPU) for the _smart_ged solver used by CSP, SPoC, and SSD.

Per @larsoner's suggestion, rather than hardcoding PyTorch/XLA or CuPy, this implementation leverages the Array API Standard (array_namespace). This dynamically routes the computation to whatever hardware the user provides, while maintaining a seamless zero-dependency fallback to scipy for standard NumPy users.

🧠 Logical & Architectural Changes
Array API Detection (_ged.py): The _smart_ged function now detects if the incoming matrices S and R support the Array API standard. If they do (e.g. PyTorch Tensors, JAX arrays), we use their native hardware-accelerated linear algebra operations.
Tensor Preservation (base.py): Modified _GEDTransformer.fit to use xp.stack(covs) instead of np.stack(covs). Previously, if a user passed hardware-accelerated tensors into the cov_callable, np.stack would force them back onto the CPU as NumPy arrays before they ever reached the eigensolver. They are now preserved on the device.
📐 Mathematical Changes
Because scipy.linalg.eigh(S, R) natively supports the Generalized Eigenvalue Problem (S * v = lambda * R * v), but most hardware accelerators (like torch.linalg.eigh) only support the Standard Eigenvalue Problem (C * y = lambda * y), we mathematically rewrote the solver to run on hardware accelerators via a Cholesky decomposition.

When a hardware tensor is detected, the code performs the following sequence to solve it natively on the accelerator:

Cholesky Decomposition: We decompose the positive-definite matrix R into a lower triangular matrix L such that R = L * L.T
Standardization: We construct a standard symmetric matrix C = L_inv * S * L_inv.T
Hardware Eigensolve: We solve C * y = lambda * y natively on the TPU/GPU.
Eigenvector Recovery: We transform back to original space using v = L_inv.T * y (prompted Gemini till want satisfied with the formalized way of presenting the text)

[larsoner]

Any AI tools used here (see disclosure policy here)?