Fix instability Jacobian diagnostic on in-place problems with an analytic Jacobian

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas.

Closes #4155

What changed and why

get_fresh_jacobian unconditionally delegated to the out-of-place calc_J, which calls f.jac(uprev, p, t). On an in-place problem with an analytic jac!(J, u, p, t) that throws, so the instability diagnostic replaced the retcode = Unstable report with a FunctionWrappersWrappers.NoFunctionWrapperFoundError. Mutable caches now route through calc_J! into a scratch copy of cache.J (constant caches keep using calc_J), preserving the existing njacs restore in both. Separately, the whole Jacobian-analysis block in log_numerical_instability is now guarded: this is best-effort reporting on an already-failed solve, so a failure there degrades to a Jacobian analysis unavailable: <reason> line and the instability warning still prints.

Branch check on Rosenbrock and BDF

The #rosenbrock branch keys off _get_W(integrator), i.e. integrator.W — that field is the SDE noise process, which is nothing for a pure ODE, not the W-matrix. So that branch never fires for an ODE solve and Rosenbrock caches (which do have cache.J) fall through to the get_fresh_jacobian branch. Rodas5P was therefore broken by this bug too, which the tests confirm below. The BDF branch (cache.nlsolver.cache.J) reads an existing matrix and was genuinely unaffected — FBDF passes before and after. I left the dead W.J branch alone rather than widening the diff; it looks like a separate latent bug worth its own issue.

Verification

Base: 9d23061 at the time of the reproduction, rebased onto 4cb8020. Julia 1.12.6.

Failing before (src/ changes stashed, tests kept)

$ git stash push -- lib/
$ julia +1.12 --project=. test/InterfaceIII/instability_diagnostics.jl

in-place analytic Jacobian: Error During Test at test/InterfaceIII/instability_diagnostics.jl:32
  Got exception outside of a @test
  No matching function wrapper was found!
Rodas5P reads its stored Jacobian: Error During Test at test/InterfaceIII/instability_diagnostics.jl:43
  Got exception outside of a @test
  No matching function wrapper was found!
diagnostic does not inflate njacs: Error During Test at test/InterfaceIII/instability_diagnostics.jl:51
  Got exception outside of a @test
  No matching function wrapper was found!
a failing diagnostic still reports the instability: Error During Test at test/InterfaceIII/instability_diagnostics.jl:60
  Got exception outside of a @test
  No matching function wrapper was found!
ERROR: LoadError: Some tests did not pass: 13 passed, 0 failed, 4 errored, 0 broken.

Test Summary:                                        | Pass  Error  Total   Time
Instability diagnostics                              |   13      4     17  49.6s
  full diagnostic without an analytic Jacobian       |    5             5  13.6s
  in-place analytic Jacobian                         |           1      1   7.8s
  out-of-place analytic Jacobian                     |    4             4   4.7s
  Rodas5P reads its stored Jacobian                  |           1      1   9.2s
  FBDF reads its stored Jacobian                     |    4             4   8.6s
  diagnostic does not inflate njacs                  |           1      1   3.2s
  a failing diagnostic still reports the instability |           1      1   1.7s

Passing after

$ git stash pop
$ julia +1.12 --project=. test/InterfaceIII/instability_diagnostics.jl

Test Summary:           | Pass  Total   Time
Instability diagnostics |   28     28  50.0s
exit=0

The guard alone, isolated

With the dispatch fix applied but the try/catch guard reverted, only the guard test fails — confirming the two parts are independently load-bearing:

$ julia +1.12 --project=. test/InterfaceIII/instability_diagnostics.jl

a failing diagnostic still reports the instability: Error During Test at test/InterfaceIII/instability_diagnostics.jl:60
  Got exception outside of a @test
  deliberate diagnostic failure
ERROR: LoadError: Some tests did not pass: 23 passed, 0 failed, 1 errored, 0 broken.

Test Summary:                                        | Pass  Error  Total   Time
  full diagnostic without an analytic Jacobian       |    5             5  10.2s
  in-place analytic Jacobian                         |    4             4   3.7s
  out-of-place analytic Jacobian                     |    4             4   3.4s
  diagnostic does not inflate njacs                  |    2             2   0.7s
  a failing diagnostic still reports the instability |           1      1   3.0s

The diagnostic still works

The no-analytic-Jacobian case still emits all three sections, and the in-place analytic-Jacobian case now emits the identical report instead of throwing:

┌ Warning: Verbosity toggle: dt_epsilon
│  At t=1.0000038457234066, dt was forced below floating point epsilon 2.220446049250313e-16. Aborting. ...
│
│ Diagnostics:
│
│ State Analysis:
│   u[1] = 2.185e+15 has grown >1e6× its initial value
│
│ Jacobian Analysis:
│   row(s) [1] have unusually large entries (e.g. J[1,1] = 2.942e+15), suggesting a singularity in those equation(s)
│   column(s) [1] have unusually large entries, suggesting those state component(s) are diverging
│
│ Error Analysis:
│   step error estimate EEst = 2.278 (a step is accepted when EEst <= 1)
│   largest contributors to EEst = internalnorm(atmp), ...
│     atmp[1] = 2.278, u[1] = 2.185e+15, uprev[1] = 1.471e+15
└ @ SciMLBase .../SciMLBase/YjW4D/src/integrator_interface.jl:1017
retcode = Unstable

Test groups, format, spelling

$ GROUP=InterfaceIII julia +1.12 --project -e 'using Pkg; Pkg.test()'
Test Summary:              | Pass  Total     Time
Derivative Utilities Tests |   11     11  3m54.5s
Test Summary: | Pass  Total   Time
stats Tests   |   14     14  48.1s
Test Summary:  | Pass  Total     Time
No Index Tests |   24     24  2m37.2s
Test Summary:               | Pass  Total     Time
Events + DAE addsteps Tests |    5      5  2m12.9s
Test Summary: | Pass  Broken  Total     Time
Units Tests   |   52       4     56  4m15.6s
Test Summary:                 | Pass  Total     Time
Instability Diagnostics Tests |   28     28  1m46.0s
Test Summary:     | Pass  Total     Time
DEVerbosity Tests |  156    156  1m45.0s
exit=0

$ GROUP=QA julia +1.12 --project -e 'using Pkg; Pkg.test()'
public API has docstrings: Test Failed at SciMLTesting.jl:1205
  Expression: isempty(undocumented)
   Evaluated: isempty([:SciMLBase, :SciMLLogging])
Test Summary:                           | Pass  Fail  Total   Time
Quality Assurance Tests                 |   87     1     88  14.9s
exit=1

Runic 1.5.1 and typos are clean on every touched file.

What I did NOT verify

• GPU, Downstream, ModelingToolkit, and ODEInterfaceRegression groups.
• The docs build — this PR adds no public API and no rendered docstring.
• The SDE path through StochasticDiffEq, where integrator.W is an actual noise process.
• Sparse and structured jac_prototypes through the new copy(cache.J) scratch. copy was chosen over similar/zero precisely to preserve sparsity structure, and calc_J! already runs prepare_sparse_jac! for CSC prototypes, but I have no test covering an unstable sparse-Jacobian solve.

Worth pushing back on

• copy(cache.J) allocates a fresh Jacobian on the failure path. Writing into cache.J directly would avoid it, since the cache is discarded immediately after; I chose the copy so the diagnostic has no side effect on solver state.
• The guard is a try/catch around _analyze_instability_jacobian only, rethrowing InterruptException. It does not wrap the state or error-estimate analysis.
• The W.J dead-branch finding above — I did not change it, but someone should decide whether it was meant to read the W-matrix.

The QA failure is pre-existing on master and unrelated to this PR. I reran GROUP=QA on a detached checkout of 4cb8020 with no changes and got the identical isempty([:SciMLBase, :SciMLLogging]) failure (87 passed, 1 failed, 16.4s). A separate agent is bisecting it.

Logging is added to [extras]/[targets] because Pkg.test's restricted LOAD_PATH does not expose unlisted stdlibs, and the new test uses Test.TestLogger + with_logger to capture the warning text.

[ChrisRackauckas-Claude]

CI note: PositiveIntegrators.jl/Downstream/1.10 fails in 20s with ERROR: LoadError: Unsatisfiable requirements detected for package OrdinaryDiffEqRosenbrock [43230ef6]. That is a resolver failure, not a test failure, and it is pre-existing — the same job is failure on the base commit 4cb8020:

$ gh api repos/SciML/OrdinaryDiffEq.jl/commits/4cb8020/check-runs --jq '.check_runs[] | select(.name|test("PositiveIntegrators")) | "\(.name) \(.conclusion)"'
PositiveIntegrators.jl/Downstream/1.10 failure

Nothing in this PR touches a compat bound. Format and spelling are green:

Runic / Runic Format Check                    pass  1m4s
runic-suggestions / Runic Suggestions         pass  1m1s
Spell Check with Typos / Spell Check with Typos  pass  6s

[ChrisRackauckas-Claude]

Second CI note. Every red check so far is pre-existing, none of it touches this change:

Check	Status here	Pre-existing?
PositiveIntegrators.jl/Downstream/1.10	fail (20s, resolver)	yes — failure on base 4cb8020
downgrade-sublibraries / test (lib/{OrdinaryDiffEqBDF,OrdinaryDiffEqFIRK,OrdinaryDiffEqExtrapolation,ImplicitDiscreteSolve})	fail	yes — all four are failure on base 4cb8020, alongside ~20 other downgrade jobs
tests / InterfaceV (julia lts)	fail	yes — Illegal conversion of a JLArray to a Ptr in getrf!; failure on #4176, #4158 and #4148 too

The GROUP=QA failure I reported locally (isempty([:SciMLBase, :SciMLLogging])) is also pre-existing and external: it is a SciMLTesting v2.6.1→v2.6.2 change, fixed upstream in SciML/SciMLTesting.jl#45 but not yet registered. Tracked in #4194.

Green so far and relevant to this PR: Runic, runic-suggestions, Spell Check, sublibrary-ci / lib/OrdinaryDiffEqCore / Julia lts / Tests - Core, tests / ModelingToolkit (julia lts). tests / InterfaceIII — the group carrying the new tests — is still running on all three Julia versions.

[ChrisRackauckas-Claude]

Third CI note — the group this PR actually changes is green on all three Julia versions:

tests / InterfaceIII (julia 1,   ubuntu-latest)  pass
tests / InterfaceIII (julia lts, ubuntu-latest)  pass
tests / InterfaceIII (julia pre, ubuntu-latest)  pass

Also green: Documentation / Build and Deploy Documentation, sublibrary-ci / lib/OrdinaryDiffEqDifferentiation [QA], sublibrary-ci / lib/OrdinaryDiffEqCore / Julia lts / Tests - Core, Runic, runic-suggestions, Spell Check, plus InterfaceI/II/IV, AlgConvergence_I/III, Regression_I, ModelingToolkit and Downstream.

Remaining reds, all verified pre-existing:

• ~25 downgrade-sublibraries jobs — the identical set is failure on base 4cb8020.

• tests / InterfaceV (1, lts, pre) — Illegal conversion of a JLArray to a Ptr in getrf!. failure on Make the ABM Threaded group test the working tree (fixes its precompile failure) #4176, NonlinearSolveAlg: forward precondition/postcondition into the implicit stage solve #4158, Fix adaptive Newmark error estimation, GA remake, and oop aliasing #4148.

• tests / Integrators_II (1, lts) — failure on Make the ABM Threaded group test the working tree (fixes its precompile failure) #4176, NonlinearSolveAlg: forward precondition/postcondition into the implicit stage solve #4158, Fix adaptive Newmark error estimation, GA remake, and oop aliasing #4148.

• tests / QA and most sublibrary-ci / … [QA] jobs — SciMLTesting v2.6.2 hasdoc change; fixed upstream in Exempt reexported external modules from the API docstring check SciMLTesting.jl#45, unregistered. See GROUP=QA red on master: SciMLTesting 2.6.2 flags reexported :SciMLBase/:SciMLLogging as undocumented #4194 and DelayDiffEq QA fails tstop ownership and SciMLBase API-doc checks #4182.

• sublibrary-ci / lib/OrdinaryDiffEqCore [QA] — a different failure: ExplicitImports NonPublicQualifiedAccessException on SciMLBase.has_mtk_sys (integrator_utils.jl:764) and SciMLBase.log_numerical_instability (:828). Neither line is added or removed by this diff — has_mtk_sys is even still at line 764, byte-identical to base:

  $ git diff 4cb8020..HEAD -- lib/OrdinaryDiffEqCore/src/integrators/integrator_utils.jl \
      | grep -E '^[+-].*(has_mtk_sys|log_numerical_instability)'
  (no output)
  

  The only change is the line number log_numerical_instability sits on, because this PR adds two helpers above it. Making those two names public in SciMLBase is the real fix and is out of scope here.

• PositiveIntegrators.jl/Downstream/1.10 — resolver failure, failure on base.

[ChrisRackauckas]

@Shreyas-Ekanathan