[WIP] entropic_partial_wasserstein_logscale: stable log-domain solver (rescue of #724)

[hinanohart]

Context

This is a rescue follow-up to PR #724 (and issue #723), both opened by @wzm2256 in March 2025. The original PR adds a numerically-stable entropic_partial_wasserstein_logscale to fix the NaN regime that #723 documents, but has been stuck CONFLICTING since 2025-09 — the author wrote in the PR body that they could not (a) build the docs locally (sphinx_rtd_theme missing) or (b) write pytest cases, and asked for help.

I hit the same NaN regime as a downstream user of entropic_partial_wasserstein, so this PR re-applies @wzm2256's function on top of current master and supplies the missing pieces.

Why a new PR rather than pushing to #724's branch

When PR #724 was opened, ot/partial.py was a single file. The maintainers later split it into the ot/partial/ package, so the diff between #724's branch and current master is now +2k / −13k lines of mostly unrelated movement. Re-applying just the new function on the new layout is cleaner than fighting that rebase.

If maintainers prefer to keep #724 as the canonical PR, I'm happy to close this and instead push these changes to that branch (write access permitting).

What's added (additive only; nothing removed)

• ot/partial/partial_solvers.py — entropic_partial_wasserstein_logscale function, identical algorithm to PR [WIP] Add a stablized function entropic_partial_wasserstein_logscale #724 re-applied on the current layout.
• ot/partial/__init__.py — export + __all__ entry.
• test/test_partial.py — 5 new test functions / 11 parametrised cases:
  • No NaN/Inf at small ε across [0.1, 0.05, 0.01, 5e-3, 1e-3, 5e-4] — reproduces issue entropic_partial_wasserstein not stable #723's failure mode and verifies the logscale solver stays finite.
  • Bit-for-bit agreement with the standard solver at large ε (atol=1e-10, rtol=1e-10) across [1.0, 10.0].
  • approaches_exact_at_small_reg — checks the plan-cost vs. exact partial-OT gap at reg=1e-3 (not just NaN-freeness; verifies mathematical correctness).
• examples/unbalanced-partial/plot_entropic_partial_wasserstein_logscale.py — Sphinx-Gallery example reproducing entropic_partial_wasserstein not stable #723's failure and showing the fix. Adapted from @wzm2256's compare_logscale_POT.py.
• docs/source/user_guide.rst — one-paragraph mention next to entropic_partial_wasserstein.
• RELEASES.md — one-line entry under 0.9.7.dev0, phrased as mitigation (the standard solver itself is unchanged; callers opt into the log-domain variant).

Local verification

• pytest test/test_partial.py -q → 19 passed (8 originals + 11 new parametrised cases).
• pytest test/ (full suite) → 1939 passed, 97 skipped, 6 xfailed — no regression outside partial.
• Example script runs end-to-end with MPLBACKEND=Agg. Standard solver returns NaN at reg ∈ {0.05, 0.01} on the 50×50 cost-scale-50 problem; logscale solver stays finite over the full sweep.
• git diff master -- ot/partial/partial_solvers.py shows exactly one hunk: the new function block. Nothing else drifts.

Co-authorship

Credit for the actual numerical work belongs to @wzm2256. If you'd prefer me to mark the commit Co-authored-by: wzm2256 <wzm2256@qq.com> and amend, I'm happy to — it just wasn't clear from the PR conventions here whether you prefer trailers or PR description acknowledgements.

cc @rflamary @cedricvincentcuaz — you both did master-merges on #724 earlier this year so it looked like a "we want this in" signal. Happy to do whatever's least friction here: this PR can be the canonical one, or I can close it and push to #724's branch.

The [WIP] prefix matches the original PR's convention and signals this is open for re-titling to [MRG] once you've had a look.