Verification records#
Recorded numerical evidence behind claims the user docs state qualitatively. These are lab-notebook entries: the numbers are from the referenced verification runs, and the corresponding automated tests are the living guarantee.
The three sampling transposes are Riemannian-compatible#
(Stated qualitatively in ../entries_apply_probe.md §4.) For the least-squares objective
f(X) = ½‖S(X) − b‖² on the fixed-rank manifold, with S each of the three sampling operations,
the matrix-free Riemannian gradient
g = op_transpose(r, …, sum_over_probes=True).orthogonal_gauge_projection() and the Gauss-Newton
Hessian H V = (𝒥ᵀ 𝒥 V) gauged were checked end-to-end at an orthogonal, minimal-rank frame:
operator |
adjoint |
gradient vs finite-diff along the retraction |
Gauss-Newton Hessian |
|---|---|---|---|
entries |
exact |
rel. err ~5e-8 |
symmetric ~5e-17, PSD |
apply |
exact |
rel. err ~3e-7 |
symmetric ~1e-12, PSD |
probe |
exact |
rel. err ~5e-7 |
symmetric ~3e-13, PSD |
The adjoint identity and gradient/Hessian checks are pinned by the fitting and manifold test
suites (tests/test_fitting.py, tests/test_manifold.py).