Give each autogenerated options prefix a unique index

[pbrubeck]

AI-assisted: diagnosed and written with Claude Code. I have read and understood every change, and run the tests locally.

Goal

OptionsManager hands out a unique prefix to any object built without an
explicit options_prefix. Since #39 it does not: self.count += 1 reads the
class attribute and rebinds the result onto the instance, so
OptionsManager.count never leaves zero and every autogenerated prefix is
{default_prefix}0_.

>>> [OptionsManager({}, default_prefix="firedrake_").options_prefix for _ in range(3)]
['firedrake_0_', 'firedrake_0_', 'firedrake_0_']

Sharing a prefix means sharing a namespace in the global options database. A
manager built while another manager's options are inserted reads those options
back out as if a user had passed them on the command line, and the warning it
emits names them:

WARNING petsctools:options.py:524 Setting options using an autogenerated prefix 'firedrake_0_' is unsafe:
  firedrake_0_ksp_monitor
  firedrake_0_ksp_type
  firedrake_0_mat_type
  firedrake_0_mg_levels_pc_type
  firedrake_0_pc_type
  ...

After this PR the prefixes are firedrake_0_, firedrake_1_, firedrake_2_
again, and nothing is inherited.

What's in it

• petsctools/options.py: increment the counter on OptionsManager rather
  than on self, so the class attribute actually advances.
• tests/test_options.py: test_options_prefix now asserts that successive
  autogenerated prefixes differ. It fails on main and passes here.

OptionsManager.count keeps its meaning — the index the next autogenerated
prefix will use — so test_commandline_options, which reads it to predict that
prefix, is unaffected.

Why this matters downstream

Firedrake depends on petsctools @ git+https://github.com/firedrakeproject/petsctools.git@main,
unpinned. #39 merged at 11:32 UTC on 26 August; the next Firedrake CI run on
main, at 12:05 UTC, went red, and it has been red since:

Firedrake test	before #39	after #39
macro/test_macro_multigrid.py::test_macro_multigrid_biharmonic[HCT, HCT-red]	pass	fail
multigrid/test_snes_adapt.py::test_snes_adapt_sequence_with_adaptive_multigrid[1, 2]	pass	fail
regression/test_appctx_cleanup.py::test_appctx_cleanup	pass	fail
regression/test_stress_elements.py::test_stress_displacement_convergence[conforming, high-order]	pass	fail
regression/test_bddc.py::test_bddc_cellwise_fdm[cube-nprocs=1-True-E-3]	pass	fail

All of them fail the same way. A solver runs, and inside its residual
assembly Firedrake builds a second, unrelated solver — the mass solve behind
Mesh.cell_sizes, say. That inner solver takes the same firedrake_0_ prefix,
inherits the outer solver's -pc_type mg, and then dies trying to coarsen a
problem that has no mesh hierarchy of its own:

petsc4py.PETSc.Error: error code 101
[0] SNESSolve() ... [0] PCSetUp_MG() ... [0] DMCoarsen()
TypeError: Incompatible function spaces in Action

Notes for review

Checked against Firedrake by putting this checkout ahead of the installed
petsctools on PYTHONPATH: each of the tests above fails on main and passes
with this commit. tests/test_options.py passes in full (18 tests) and ruff
is clean.

The remaining red tests on Firedrake main — test_io_backward_compat and an
intermittent xdist worker segfault in test_assemble_baseform — predate #39 and
are untouched by this.

[connorjward]

Thanks but already fixed in #52

[pbrubeck]

Rebased onto main and resolved the conflict, as two commits:

1. Revert "Use class count, not instance (#52)" — clean revert, no conflict.
2. Give each autogenerated options prefix a unique index — the fix, on OptionsManager itself.

Net effect against main is type(self).count → OptionsManager.count, plus the test.

Why not type(self). It reads the inherited value but writes the incremented one onto the subclass, so each class walks a counter of its own and prefixes repeat across a hierarchy. OptionsManager is used as a mixin, so this is live for Firedrake — NonlinearVariationalSolver → LinearVariationalSolver → LinearSolver, and LinearEigensolver. Building three of each in turn against 729712d:

firedrake_1_ ['NVS']
firedrake_2_ ['LVS', 'NVS']                  <-- collision
firedrake_3_ ['LinearSolver', 'LVS', 'NVS']  <-- collision
firedrake_4_ ['LinearSolver', 'LVS']         <-- collision
firedrake_5_ ['LinearSolver']

The test now catches it. The version on the closed PR only built three managers of the same class, which is unique under type(self).count — it would have passed on main and guarded nothing. It now builds two subclasses and the base class in turn, and fails on either spelling of the bug.

Verified against Firedrake by putting this branch ahead of the installed petsctools on PYTHONPATH: test_macro_multigrid_biharmonic[HCT, HCT-red], test_appctx_cleanup, test_snes_adapt and test_stress_displacement_convergence all pass. tests/test_options.py passes in full (18) and ruff is clean.

AI-assisted: written with Claude Code.