[ChrisRackauckas-Claude]

Summary

Stacked on #1363 (needs Utils.normal_form_workspace / Utils.normal_form_jacobian!! in NonlinearSolveBaseSparseArraysExt).

Moré TrustRegion on sparse Jacobians rebuilt JᵀJ every Jacobian update through MaybeInplace's CSC __mul! (C .= A * B, ~239 KB/step on a 1000-dim tridiagonal Bratu problem). This PR builds the #1363 normal-form workspace once at MoreTrustRegionDescent init and calls Utils.normal_form_jacobian!! on each update, so the Gramian stays in-place on a fixed jac_prototype and falls back to the allocating product when an in-place jac! grows the pattern.

Before / after (JULIA_NUM_THREADS=1 taskset -c 120, 1000-dim sparse Bratu, TrustRegion()):

• warmed step! max @allocated: 239536 → 144 bytes
• @benchmark solve minimum: 11.60 ms / 2993176 B → 11.94 ms / 1796536 B (time within machine noise; solve memory −1.2 MB)
• iterates / residual / stats bitwise identical on fixed-pattern problems (nsteps=38, njacs=5, nfactors=77, nsolve=114)
• allocation regression: fails on unfixed code (239536 < 40000), passes with the fix
• growing-pattern jac! regression: unguarded fill leaves JᵀJ nnz=3 / wrong solve; guarded helper matches dense TR (maxerr=0)

Test-group tails

• GROUP=QA NonlinearSolveBase: QA | 20 20 50.1s … Testing NonlinearSolveBase tests passed
• GROUP=QA NonlinearSolveFirstOrder: QA | 20 20 56.5s … Testing NonlinearSolveFirstOrder tests passed
• GROUP=Core NonlinearSolveBase: Testing NonlinearSolveBase tests passed
• GROUP=Core NonlinearSolveFirstOrder: TrustRegion sparse normal-form | 8 8 12.6s … Testing NonlinearSolveFirstOrder tests passed

Not verified: full GROUP=All; GPU / non-CSC sparse layouts; banded/structured Jacobians on the Moré normal-form path; wall-time speedup beyond allocation (solve minima were noise-dominated on a loaded host).

Reviewer pushback: whether stacking on #1363 is the right merge order; whether the residual ≤144 B/@allocated noise bound (< 40000) is the right regression threshold.

Please ignore until reviewed by @ChrisRackauckas.

Risk assessment

Independent review: CHANGES addressed (reuse #1363 guarded helper; growing-pattern regression; Base QA)

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Review findings addressed

Commit fcb0adc responds to the Codex (gpt-6-astra) review and to the Devin review comment on this PR.

• Astra P2: the PR added new ExplicitImports all_qualified_accesses_are_public ignore entries. Fixed. normal_form_workspace and normal_form_jacobian!! now live in the top-level NonlinearSolveBase module instead of Utils, and are declared public next to requires_normal_form_jacobian. Their docstrings state the extension contract, and they are listed in docs/src/devdocs/internal_interfaces.md under "Normal-Form Jacobian". The SparseArrays extension extends the public names, and both ignore entries are removed. I ran Base GROUP=QA with the ignore entries removed:

  • before the move: QA | 19 1 20, with normal_form_jacobian!! is not public in NonlinearSolveBase.Utils and the same error for normal_form_workspace;
  • after the move: QA | 20 20.

• Devin: the new sparse path had no test of reinit! with a changed parameter. Fixed. sparsity_tests__item4.jl now runs init → solve! → reinit!(cache, u0; p = p₂) → solve! with linsolve = nothing and with KLUFactorization(). It asserts:

  • residual < 1e-8;
  • retcode and u equal (==) to a fresh solve(remake(prob; p = p₂));
  • J and JᵀJ are both still SparseMatrixCSC;
  • JᵀJ == transpose(J) * J.

  This is new coverage, not a bug fix: these tests also pass with the MoreTrustRegionDescent change reverted.

• Devin: merge order. No code change. This branch still carries Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363's commit (3cf0c9a), and this commit changes code that Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363 introduced. Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363 itself still has the two ignore entries. The options are: merge Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363 first and then merge master into this branch (this commit then removes the entries on top of it), or merge this PR alone, which makes Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363 redundant.

• Devin (non-blocking): the allocation bound was not derived from anything. The bound is tightened from < 40_000 to < 1000, the same as the sibling LM test, and the test now also asserts that cache.stats.njacs grows inside the measured window.

  • Measured per-step allocations: (144, 0, 0, 144, 0) with 2 new Jacobians on Julia 1.13.0, and (0, 0, 0, 0, 0) with 1 new Jacobian on 1.10.12.
  • With the MoreTrustRegionDescent change reverted to @bb cache.JᵀJ = transpose(J_) × J_, the test fails: Evaluated: 239536 < 1000.

• Devin (non-blocking): the top-of-file comment in item4 was retrospective. It now describes the property under test.

• Devin (non-blocking): the TrustRegion Bratu solves return Stalled / ShrinkThresholdExceeded with a residual of about 3e-11. Not changed. This is existing termination behaviour and also happens on the parent tree, so the new test asserts the residual rather than the retcode. It is worth a separate issue.

• Devin (non-blocking): the PR body's nfactors/nsolve counts differ from the reviewer's. Not changed. The counts depend on the Julia version, and the bitwise-identity claim was confirmed by the reviewer.

Not breaking. The commit adds two public names to NonlinearSolveBase, so its next release needs a minor version bump rather than a patch. No existing public name changes. Following the repository's practice of separate release PRs, I did not bump the version.

Verification (for fcb0adc)

All of these ran locally with JULIA_NUM_THREADS=4.

Test groups

• GROUP=Core NonlinearSolveBase (Julia 1.13.0): Testing NonlinearSolveBase tests passed.
• GROUP=Core NonlinearSolveFirstOrder (Julia 1.13.0): Sparse normal-form LevenbergMarquardt | 14 14, TrustRegion sparse normal-form | 21 21 … Testing NonlinearSolveFirstOrder tests passed.
• GROUP=QA NonlinearSolveBase: QA | 20 20 on 1.13.0, and QA | 18 18 on 1.10.12, where the public checks do not run.

Sparse test files on their own (item3 and item4)

• Julia 1.10.12: 14 14 and 21 21.
• Julia 1.13.0, with the MoreTrustRegionDescent change reverted: TrustRegion sparse normal-form | 18 1 19, failing at Evaluated: 239536 < 1000.

Docs and formatting

• Docs: I built only the new "Normal-Form Jacobian" @docs section, in a minimal Documenter build with NonlinearSolveBase and SparseArrays loaded. It had no errors, both docstrings rendered, and their @ref links resolved. I did not run the full docs/make.jl, which needs Sundials, SciPy, PETSc and the MTK tutorials, plus linkcheck.
• Runic --check on the changed .jl files: exit 0. typos on the changed files: exit 0.

Not verified: Julia pre, the full docs build, GPU paths, and downstream packages.

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Risk assessment (independent review, codex-cli gpt-6.1-sol, reviewed head fcb0adc)

• Risk: medium
• Blast radius: CSC normal-form Jacobian products shared by LevenbergMarquardt and Moré TrustRegion, including least-squares damping. Two additive public developer interfaces; no public API removal or incompatible behavior change, and no new dependency or license change.
• Evidence: Reviewed fcb0adc; head unchanged at the final check. Ran JULIA_DEPOT_PATH="$PWD/depot:~/.julia" JULIA_NUM_THREADS=4 JULIA_NUM_PRECOMPILE_TASKS=4 julia +release --project=env run-tests.jl on Julia 1.13.2: LM 14/14, TrustRegion 21/21, public extension access 3/3 passed. The driver includes the PR's item3/item4 tests in separate SafeTestsets, asserts both helpers are public, and runs ExplicitImports on the SparseArrays extension using exactly the existing repository qualified-access exclusions. This covers bitwise sparse products, rectangular matrices, changing patterns, allocation bounds, and reinit! with new parameters for default/KLU solvers. Initial and final CI checks both showed 18 pending, no failures: root https://github.com/SciML/NonlinearSolve.jl/actions/runs/38922327164 and sublibraries https://github.com/SciML/NonlinearSolve.jl/actions/runs/38922327037. Latest completed default-branch sublibrary CI passed: https://github.com/SciML/NonlinearSolve.jl/actions/runs/38812969499. Read default-branch root failure logs: both LTS jobs fail the existing PolyAlgorithm solve! inference test at core_tests__item3.jl:27, https://github.com/SciML/NonlinearSolve.jl/actions/runs/38812969394. No current-head failure exists to compare against it. Full Core/QA groups, LTS, docs build, downstreams, wall-time benchmarks, and an independent before-fix run were not performed in this review. git diff --check passed.
• Independent review: codex-cli 0.162.1 gpt-6.1-sol rated it medium, high confidence: targeted numerical, allocation, reinitialization and public-access checks pass; full CI is pending. Risk was assessed before reading the author's risk claims.
• Merge: needs human review — shared numerical kernel and new public extension interface; CI remains pending. No blocking code findings.

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[ChrisRackauckas]

🤖 Automated comment from an AI agent running as @ChrisRackauckas — not written or reviewed by Chris.

Independent review (Devin CLI 3000.11.3, model fusion-claude-opus-5-5-high-sidekick-swe-2-medium): CHANGES, risk low.

Full review

VERDICT: CHANGES
RISK: low

Scope: the PR is stacked. git diff origin/master...HEAD contains two commits: 3cf0c9a (PR #1363: the normal_form_jacobian!! kernel, the LM wiring, the QA ignore-list entries, and test item3) and bd7e750 (this PR's own change: the MoreTrustRegionDescent wiring plus test item4). I reviewed both, because merging #1366 into master brings in both. The TrustRegion change is numerically sound: I got bitwise-identical results to the parent commit on every fixed-pattern case I tried, and the allocation reduction is real. The verdict is CHANGES because of one AGENTS.md test-coverage rule and the merge order. I found no wrong results.

Blocking findings

1. AGENTS.md rule: the new sparse in-place path has no test of reinit! with a changed parameter (lib/NonlinearSolveFirstOrder/test/sparsity_tests__item4.jl).

   • The rule. AGENTS.md says: "Exercise parameter-changing reinitialization and preconditioning on these paths." The new JᵀJ_workspace is created once, in InternalAPI.init (more_trust_region.jl:1004-1011), and it is reused across reinit!. InternalAPI.reinit! (more_trust_region.jl:1081-1097) does not touch JᵀJ or the workspace. No test covers that lifecycle.
   • Confirmed by running: the behaviour is correct today. I ran scratch/probe.jl section 2: sparse Bratu (n=200), init, then solve!, then reinit!(cache, zeros(200); p = (λ = 3.0, …)), then solve!. Observed: Success, s2.u == fresh.u is true (max diff 0.0), J and JᵀJ are both still SparseMatrixCSC, and nonzeros(JᵀJ) == nonzeros(transpose(J)*J). So this is a missing test, not a bug.
   • Required change. Add to item4 a reinit!-with-new-p case on the sparse TrustRegion() path. It should assert:
     • bitwise equality with a fresh solve(remake(prob; p = p2));
     • that cache.descent_cache.JᵀJ isa SparseMatrixCSC.

   It also helps to cover an explicit square linsolve such as KLUFactorization(), which is the case where needs_square_A forces the normal form.

2. Merge order: this PR's diff includes all of Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363.

   • The state. Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363 (Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363) is still OPEN and unmerged. The base of Eliminate TrustRegion sparse per-step JᵀJ allocations #1366 is master, so merging Eliminate TrustRegion sparse per-step JᵀJ allocations #1366 first would silently merge Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363's kernel, LM change and QA edits under a TrustRegion title. That is two concerns in one PR, against CLAUDE.md "small focused PRs".
   • Required change. Merge Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363 first and rebase Eliminate TrustRegion sparse per-step JᵀJ allocations #1366 so that its diff is only bd7e750 (3 files, +109/−2). Alternatively, retarget its base to lm-iteration-alloc until Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363 lands.

Non-blocking findings

• The allocation threshold is not derived from anything (sparsity_tests__item4.jl:375, maximum(allocs) < 40_000).
  • Confirmed by running: per-step allocations measured over the 5-step window are [144, 0, 0, 144, 0] on the PR head versus [144, 0, 0, 263904, 263760] on its parent. So the test does fail without the fix; the sidekick-run of item4 on the parent got Evaluated: 263904 < 40000.
  • The bound is about 280× the observed residual. A partial regression (for example a new length-n buffer per Jacobian, about 8 KB) would pass. The sibling LM test (item3) uses < 1000; the same bound fits here.
  • Only 2 of the 5 measured steps form a new Jacobian (njacs delta = 2, measured). The test's ability to catch the regression therefore depends on the Moré radius scheme's accept/reject sequence. Asserting that cache.stats.njacs increased inside the window would make it robust.
• The growing-pattern test does exercise the fallback. Confirmed with scratch/probe_grow.jl:
  • nnz(J) goes 3 → 7 and nnz(JᵀJ) goes 3 → 9 at step 2;
  • JᵀJ stays the same object (the fallback writes in place) and matches transpose(J)*J exactly;
  • after the fallback, the next call takes the fast path with @allocated == 0.
  • I also tried a jac! that shrinks the pattern (dropzeros!), with the default linsolve and with KLU. Max diff to dense TrustRegion was 8.9e-16, the same as on the parent.
• The item4 Bratu solve returns ReturnCode.Stalled, which the test hides by checking only norm(sol.resid) < 1e-8. Observed on both head and parent (alloctest_solve => (Stalled, 38, 5, 75, 110)), and on n=300, λ=3 Bratu with the default, UMFPACK, NLsolve and Bastin schemes (KLU and Hei return ShrinkThresholdExceeded). This is pre-existing TrustRegion termination behaviour, not caused by this PR, but it is worth an issue.
• The PR body's stats don't match my run exactly. The body says nfactors=77, nsolve=114; I get nfactors=75, nsolve=110 on Julia 1.12.7, identically on head and parent. The body's "bitwise identical" claim holds; the exact counts are probably version-dependent.
• The comment at the top of item4 is slightly retrospective. It says "must not rebuild sparse JᵀJ through MaybeInplace's allocating CSC product" — that is, it describes the old implementation rather than the property under test. Minor.
• Pre-existing, unrelated: TrustRegion() on Float32 sparse Bratu (n=100) returns InternalLinearSolveFailed, identically on head and parent.
• Sibling work: PR Reuse the init-time Jacobian on the first Newton step (stacked on #1365) #1367 (Reuse the init-time Jacobian on the first Newton step (stacked on #1365) #1367) also edits damped_newton.jl, which is Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363's file. It will conflict with Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363, not with the TrustRegion commit. No other open PR touches more_trust_region.jl, the SparseArrays extension or utils.jl.
• Reading the kernel (NonlinearSolveBaseSparseArraysExt.jl:55-92):
  • The pattern guard is sound: per column, nfilled == length(nzrange(C,i)) and every stored row of C filled means the sets are equal.
  • On a mismatch, fill!(filled,false) resets state.
  • transpose! resizes Jᵀ storage when nnz(J) grows (I checked the SparseArrays 1.12 source).
  • Bitwise equality with transpose(J)*J is tested in item3 and held in every probe.

What I ran

All on Julia 1.12.7 (aarch64). Two environments: env_head (PR head) and env_base1363, which is the 3cf0c9a tree exported with git archive, so it is the parent of the TrustRegion commit.

• Formatting and spelling. julia +1.12 --project=@runic -m Runic --check on all changed files: exit 0. git diff origin/master...HEAD | typos -: exit 0.

• sparsity_tests.jl on head: Brusselator 5/5, Structured 16/16, LM normal-form 14/14, TrustRegion sparse normal-form 8/8.

• Item4 on the parent: 7 pass, 1 fail. The allocation test reports 263904 < 40000, so it fails without the fix and passes with it.

• scratch/probe.jl on head and parent. The outputs are identical except for allocations:

  • seven TrustRegion configurations (default, KLU, UMFPACK, KrylovJL_CG, and the Hei, NLsolve and Bastin schemes) on n=300 Bratu: bitwise-equal u hash and equal nsteps/njacs/nfactors;
  • the reinit! case;
  • a rectangular 99×50 sparse least-squares problem (matches dense QR TrustRegion to 1.3e-15);
  • the shrinking-pattern jac!;
  • Float32;
  • the per-step allocation trace. Every Jacobian-forming step allocates 263760 B on the parent and 0 B on head.

• scratch/probe_grow.jl on head: the fallback behaviour described above.

• Targeted existing TrustRegion tests on head, all passing:

  Test set	Passed
  rootfind items 8–13	1176, 2, 2, 6, 28, 27
  rootfind item 19	12
  misc item 3	11
  misc item 9	125
  misc item 10	24
  least_squares item 6, run in its own process	138/138
  least_squares item 7	16/16
  inference item 1	no failures reported

• One error I traced to my test setup, not the PR. The first combined run reported an error at the @inferred init check in least_squares item 6 (line 236). I traced it to Enzyme having been loaded earlier in the same session by misc item 3. With using Enzyme loaded first, scratch/probe_infer.jl is not inferred on either head or parent. Without Enzyme, it is inferred on both. In the real Core order, least_squares runs before misc.

• GROUP=QA for NonlinearSolveBase: 20/20 passed.

• git status in the checkout is clean afterwards, and no Julia processes are left running.

What I did not verify

• The full GROUP=Core/All suites, and GROUP=QA for NonlinearSolveFirstOrder (I relied on the targeted files above).
• Julia LTS (1.10) and pre-release.
• GPU and non-SparseMatrixCSC sparse types: these take the generic nothing workspace path, which I read but did not run.
• ForwardDiff through a sparse TrustRegion solve. My probe raised MethodError: Float64(::Dual) on both head and parent; it is probably a defect in how my probe built the problem, and I did not investigate.
• Wall-time performance.
• The LevenbergMarquardt half (Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363) beyond the shared kernel and its item3 test passing.

Links

• PR Eliminate TrustRegion sparse per-step JᵀJ allocations #1366: Eliminate TrustRegion sparse per-step JᵀJ allocations #1366
• PR Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363 (stacked base, open): Form sparse JᵀJ in place in DampedNewtonDescent (LM normal-form step! allocations) #1363
• PR Reuse the init-time Jacobian on the first Newton step (stacked on #1365) #1367 (touches damped_newton.jl): Reuse the init-time Jacobian on the first Newton step (stacked on #1365) #1367

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