[BradyPlanden]

Description

IDAKLU already collects SUNDIALS' integrator counters, but only prints them under print_stats. This PR returns them with every solution from the pybammsolvers binding and exposes them as Solution.solver_statistics, a pybamm.SolverStatistics dataclass (steps, linear-solver setups, nonlinear iterations, nonlinear failures, error-test failures). Counts accumulate across t_eval breakpoints, are kept per input set, and are summed when solutions combine (+, stepping, experiments), so solver work can be asserted in tests and tracked in benchmarks without parsing stdout.

A multi-input solve used to split the input sets into equal static blocks per thread, plus a serial remainder on the calling thread. A heterogeneous sweep, such as a current sweep whose high currents stop early on a voltage cut-off, then waited on its slowest block. Sets are now handed out one at a time from a shared counter. The calling thread, which holds the GIL, always takes set 0, so its diagnostics still stream live. A failing set no longer hides the others: the error names every set that failed (input set 2: ...; input set 5: ...).

For pybammsolvers maintainers: pybamm now reads solution.stats unconditionally, so this bumps pybammsolvers to 0.10.0 and pins pybammsolvers>=0.10.0,<0.11.0. pybammsolvers-v0.10.0 has to be released before a pybamm release that contains this PR. #5783 (IDAS sensitivity scales) makes the identical version bump.

• IDAKLUStats travels through SolutionData to Solution and is bound as idaklu.SolverStats. Statistics are saved on every solve, not only under print_stats. The BBD preconditioner's counter is read only when that preconditioner is in use; with preconditioner="none" SUNDIALS read it out of the model's own data, which also fixes a garbage value in print_stats.
• IDAKLUSolverGroup runs #pragma omp parallel num_threads(team) over a std::atomic counter, rather than schedule(dynamic), which the macOS wheels' libomp and MSVC do not support. It still solves every set when the runtime starts fewer threads than asked (OMP_THREAD_LIMIT, nested regions). A Python exception such as KeyboardInterrupt stops new sets being taken, while an integrator failure is recorded against its set and the sweep continues.
• StandaloneAlgebraicSystem owns its residual and Jacobian as unique_ptr<Expression>, with the CasADi constructor delegating to the Expression one, and Expression gains a virtual destructor.
• IDAKLUSolver accepts a per-state atol as a list, tuple or array, so it survives a to_config/from_config round trip, and rejects one of the wrong width, booleans and non-real values with a SolverError.
• SolverStatistics is documented in the API reference. Solutions pickled before this change still load.

This is one of the backend-neutral pre-flight PRs split out of the Rust execution engine (#5732). It has no Rust dependency. It overlaps #5783 (IDAS sensitivity scales) in IDAKLUSolverGroup.cpp and the IDAKLU tests, so whichever lands second needs a rebase.

Type of change

Add an entry under # [Unreleased] in CHANGELOG.md, in one of ## Breaking changes, ## Deprecated, ## Features, or ## Bug fixes (include PR number; breaking and deprecation entries need a one-line migration note). Internal-only PRs — refactor, docs, CI, tests — can skip this. See RELEASE.md for the full policy.

Important checks:

Please confirm the following before marking the PR as ready for review:

• No style issues: nox -s pre-commit
• All tests pass: nox -s tests
• The documentation builds: nox -s doctests
• Code is commented for hard-to-understand areas
• Tests added that prove fix is effective or that feature works

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.09%. Comparing base (0ef15f2) to head (a5d4fd3).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #5782   +/-   ##
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  Coverage   98.08%   98.09%           
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  Files         346      346           
  Lines       35275    35323   +48     
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+ Hits        34599    34649   +50     
+ Misses        676      674    -2     

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[martinjrobins]

thanks @BradyPlanden, looks great, minor suggestions below and (possible) missing stats on adding two solutions

[github-actions]

Bencher Report

Project	PyBaMM
Branch	a2/idaklu-stats-scheduling
Testbed	bare-metal

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[martinjrobins]

looks great, thanks @BradyPlanden

[BradyPlanden]

Found a few regressions on a second pass + incremented pybammsolvers version to avoid a broken pybamm release. Could you re-review @martinjrobins