Speed up the eigensolver and the mean curvature flow

[m-reuter]

Speeds up two computations behind spectral sphere maps: the eigensolver and the mean curvature flow. tria_spherical_project gains from the faster flow right away. It keeps the strict eigensolver tolerance for now: a loose tolerance needs a few extra eigenpairs to avoid missing a repeated eigenvalue, so it goes into the follow-up PR that reworks the sphere map, together with tests.

Changes

• Solver.eigs has a new tol argument, passed to ARPACK. The default 0 keeps machine precision. Eigenfunctions used as coordinates need far less: with tol=1e-6, the eigensolve on a cortical surface (143k vertices) takes about half the time, and the first eigenvectors span the same space to 1e-8.
• tria_mean_curvature_flow factorizes only the system matrix of the first step. The matrix changes little between steps, so later steps are solved with conjugate gradients preconditioned by that factorization; a step that does not converge falls back to a direct solve. The result matches solving every step directly to about 1e-11, and the flow is 2 to 3 times faster on a cortical surface, for 3 as well as 30 steps. This works with both backends (use_cholmod).
• The SciPy minimum rises to 1.12, the first version where cg takes rtol.
• Code style CI: bibclean 1.0 replaced the bibclean-check command with bibclean check and added rules for page ranges and month names. The workflow uses the new command, the style extra requires bibclean>=1.0, and doc/references.bib is reformatted with bibclean fix.

Tests

A new test flows a cube surface for 8 steps and compares it with solving every step directly. It fails (difference 4e-4) when later steps reuse the first factorization without the conjugate gradient solve. The full suite passes with the current dependencies and with the minimum versions (numpy 1.23.2, SciPy 1.12.0).

[codecov]

Codecov Report

❌ Patch coverage is 78.26087% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 67.10%. Comparing base (54dca7e) to head (286226b).

Files with missing lines	Patch %	Lines
lapy/diffgeo.py	78.26%	4 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #128      +/-   ##
==========================================
+ Coverage   67.05%   67.10%   +0.04%     
==========================================
  Files          19       19              
  Lines        3573     3590      +17     
  Branches      460      464       +4     
==========================================
+ Hits         2396     2409      +13     
- Misses        994      998       +4     
  Partials      183      183              

Flag	Coverage Δ
unittests	67.10% <78.26%> (+0.04%)	⬆️

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[Copilot]

🟡 Changes recommended

Address the CG fallback reuse, thread eigensolver tolerance into the spectral sphere path, and tighten the regression assertion.

2 open issues

• Reuse fallback factorization across failed coordinate columns · New
• Thread configured tolerance through spectral sphere path · New

What changed in this PR

This pull request improves eigensolver and mean-curvature-flow performance while updating dependency and formatting tooling.

Changes:

• Adds configurable ARPACK tolerance support.
• Uses preconditioned CG and factorization reuse for curvature flow.
• Updates SciPy, bibclean, CI, bibliography, and regression tests.

File	Description
pyproject.toml	Raises SciPy and bibclean minimum versions.
lapy/​utils/​tests/​test_diffgeo.py	Adds curvature-flow accuracy coverage.
lapy/​solver.py	Adds the eigensolver tolerance parameter.
lapy/​diffgeo.py	Optimizes curvature-flow linear solves.
doc/​references.bib	Applies bibclean formatting.
.github/​workflows/​code-style.yml	Uses the new bibclean command.

_{Review effort: Lite}

[Copilot]

🔵 Needs a closer look

Add regression coverage confirming Solver.eigs forwards tol and preserves the default.

No open issues 🎉

2 resolved since last review

• Thread configured tolerance through spectral sphere path
• Reuse fallback factorization across failed coordinate columns

_{Review effort: Lite}