[antonsoo]

For an unbatched low-rank-plus-diagonal operator, inv_quad_logdet(y) validates an N-vector but then raises linalg.solve_triangular: The input tensor B must have at least 2 dimensions. The equivalent y[:, None] succeeds.

Normalize the accepted vector to one RHS column after validating its length. This preserves the existing output shapes for both reduce_inv_quad settings and leaves matrix/batched inputs unchanged.

Regression tests compare inverse quadratic forms, optional log determinants and root/diagonal/RHS gradients with an independent dense solve for both reduction settings. They also check exact vector/column equivalence and the existing invalid-length error.

Validation:

• Full suite: 5,049 tests pass on both PyTorch 2.0 CPU (Python 3.10) and PyTorch 2.14 CPU (Python 3.12).
• Recorded Diabetes-feature covariance workloads: all 64 vector cases fail before and complete afterward across CPU/CUDA, float32/64, sizes 32-128 and ranks 4/8. Values and gradients agree with dense PyTorch calculations; worst float32 relative error is 3.7e-6, float64 below 4.7e-15. Matrix-input controls are byte-identical across sources.
• Eight 15-step likelihood-training runs now complete and track independent dense Adam runs (worst float32 absolute trajectory difference 3.1e-4, final-parameter relative difference 4.8e-6). This does not assert bitwise optimizer-state parity or predictive improvement.
• Configured pre-commit hooks, full flake8 and warnings-as-errors Sphinx build pass.

This concerns LowRankRootAddedDiagLinearOperator; the diagonal-operator change in #140 does not resolve it.