Preserve residual shape in analytic JVPs

[ChrisRackauckas-Claude]

Ignore this PR until it has been reviewed by @ChrisRackauckas.

Summary

• reshape out-of-place analytic Jacobian-vector products to the residual shape, not the unknown shape
• cover a rectangular matrix-valued least-squares residual
• bump SciMLJacobianOperators from 0.1.16 to 0.1.17 for the bug-fix release

For a rectangular Jacobian, the product has one entry per residual. Reshaping it to size(u) only worked when residual and unknown shapes happened to match.

Verification

• NONLINEARSOLVE_TEST_GROUP=Core julia +1.10 --project=lib/SciMLJacobianOperators -e "using Pkg; Pkg.instantiate(); Pkg.test()"
  • Scalar Ops: 1248/1248
  • Inplace Problems: 864/864
  • Out-of-place Problems: 1250/1250
  • Copy with Tuple parameters: 11/11
• Runic 1.7 repository check: exit 0
• git diff --check upstream/master...HEAD: exit 0

This is the release prerequisite for #1062.

[ChrisRackauckas-Claude]

The root downgrade job failed in the pre-existing Broyden robustness lane, not in SciMLJacobianOperators: Generalized Rosenbrock function | alg #4 returned residual norm 4.4. The exact same failure is present on clean master run 29258191482 at commit 579761dd2; this PRs analytic-Jacobian test passed before that lane.

Per the repository instructions, I have queued a separate clean-master reproduce/bisect/fix audit rather than changing or silencing the robustness assertion here. All other #1063 checks remain under monitoring.

[ChrisRackauckas-Claude]

Prior-art check found that the clean-master downgrade failure is already fully audited in #1057: it reproduces the same generalized-Rosenbrock bad-Broyden case, bisects the first bad commit to 6a7687f542, and provides the focused triangular-solve fix with local Core/downstream verification. I will not duplicate that work. The later unrelated Brown bookkeeping behavior is already documented in #1056.

[ChrisRackauckas-Claude]

Owning-package CI is now green across the full matrix: SciMLJacobianOperators Core passed on Julia lts, current release, and prerelease; QA passed on current release; and the strict sublibrary downgrade job passed. Runic and spell checks are also green. The only completed red remains the exact clean-master Broyden failure already fixed by #1057.

[ChrisRackauckas-Claude]

Version-order note: draft #1060 independently uses SciMLJacobianOperators 0.1.16 (and NonlinearSolveFirstOrder 2.2.1). These are provisional next-version numbers, not interchangeable fixes. If #1060 merges first, this PR must rebase and become SciMLJacobianOperators 0.1.17, and dependent #1062 must raise its floor accordingly. If #1063/#1062 merge first, #1060 must take the later patch versions. No release should treat the shared provisional number as meaning both patches are present.

[ChrisRackauckas-Claude]

Post-#1060 rebase verification:

• Safely rebased onto merged master 41681c5e4 after fetching both remotes and confirming the feature remote still pointed to the sole agent-authored commit f7c5c29bc.
• Because Raise SciMLOperators public API floors and resolve cache ambiguity #1060 registered the previously provisional SciMLJacobianOperators 0.1.16 bump, this branch now correctly uses 0.1.17. The PR body has been updated accordingly.
• Exact Julia 1.10.11 SciMLJacobianOperators Core on rebased head af904522c passed: Scalar 1248/1248, in-place 864/864, out-of-place 1250/1250, tuple copy 11/11.
• Whole-repository Runic and git diff --check both exited 0.

The rewritten branch was pushed with an exact lease against verified old SHA f7c5c29bc; no contributor commit was overwritten.

[ChrisRackauckas-Claude]

Early CI classification for the two red downgrade jobs on rebased head af904522c:

• Root Downgrade Tests - Core stops before tests because the current downgrade action pins SciMLOperators = 1.22.0, while the in-tree NonlinearSolveQuasiNewton 1.14.1 now correctly requires SciMLOperators >= 1.24 after merged Raise SciMLOperators public API floors and resolve cache ambiguity #1060.
• downgrade-sublibraries / SimpleNonlinearSolve stops for the same reason: its generated manifest pins SciMLOperators = 1.22.0, while the in-tree NonlinearSolveBase 2.34.3 requires >= 1.24.

Both logs are resolver failures before any test starts. This is the already-audited shared julia-downgrade-compat path-source problem addressed by stacked upstream drafts #54 and #55, not a failure in the analytic-JVP change. The remaining checks are still running.

[ChrisRackauckas-Claude]

Additional rebased-head CI classification from the exact failed logs:

• NonlinearSolveBase [QA] has the sole ExplicitImports violation for FunctionWrappersWrappers.SingleCacheStorage; owning-package public-API draft FunctionWrappersWrappers.jl#70 is the prerequisite.
• Root Core on Julia current and pre reproduces the clean-master Broyden pair: generalized Rosenbrock alg Make iip a compile-time constant #4 has residual 4.3999999999999995 > 0.001, and Brown alg Make iip a compile-time constant #4 is an unexpected pass. The real solver regression is addressed by the focused alternatives Preserve triangular solves for Broyden Jacobian inversion #1057/Restore dense pinv fallback for inverse Jacobian init #1058; the environment-sensitive Brown bookkeeping is tracked in Brown bad-Broyden broken test is environment-sensitive #1056.
• Root Core on Julia LTS reproduces the same generalized-Rosenbrock residual (4.3999999999999995) without the Brown unexpected pass.

These failures are outside the SciMLJacobianOperators analytic-JVP diff and match the already-audited clean-master failures. No tests or broken-test bookkeeping were changed here.

[ChrisRackauckas-Claude]

The remaining rebased-head failure is root CUDA: both QuasiNewtonAlgorithm cases at test/gpu/cuda_tests__item1.jl:34 and :44 error with DimensionMismatch: array could not be broadcast to match destination (18 pass, 2 error). The job never enters the SciMLJacobianOperators analytic-JVP regression.

The same two line-level failures have been observed on the clean-master CUDA lane, so this is being kept out of the analytic-JVP diff and queued for the required separate reproduce/bisect/fix audit on the GPU runner. No CUDA test is skipped or weakened here.

[ChrisRackauckas-Claude]

The two newly completed macOS Core jobs match the same already-audited root Broyden regression:

• Julia current and prerelease each fail only Generalized Rosenbrock function | alg #4, with residual 4.3999999999999995 > 0.001 (94 pass, 1 fail, 20 existing broken).
• Both logs enter the root Broyden robustness suite after the owning SciMLJacobianOperators matrix has already passed; neither failure exercises this PR's analytic-JVP regression.

This is the same cross-platform clean-master failure addressed by focused draft #1057 (with #1058 as the alternative dense fallback), so no additional test change or duplicate audit is needed here.

[ChrisRackauckas-Claude]

The final macOS Core lane, Julia LTS, has now completed with the same sole generalized-Rosenbrock alg #4 residual (4.3999999999999995 > 0.001; 94 pass, 1 fail, 20 existing broken). Thus the full Linux/macOS × LTS/current/prerelease Core matrix is classified under the already-bisected #1057/#1058 Broyden work. The only remaining queued check is the independent SimpleNonlinearSolve CUDA sublibrary lane.

[ChrisRackauckas-Claude]

Terminal CI follow-up: the final queued SimpleNonlinearSolve CUDA lane passed, bringing the run to 82 successes, 3 skipped matrix placeholders, and 10 previously classified failures. Those failures remain the clean-master downgrade resolver, NonlinearSolveBase ExplicitImports, root CUDA (addressed separately by #1066), and generalized-Rosenbrock root Core failures. No analytic-JVP-specific failure appeared.