Rework of the original patch, rebased onto current master (0be95df).

The GPU DAE lane has recovered on master without this change. After the CUDA environment rework on the self-hosted runner, GPU: dae_tests.jl stands at 136 passed / 1 failed / 7 broken as of master run 30340807357 (Jul 28); the one remaining failure is Hairer4 [jac=CSC, mass=diag_cu], a different problem. So the earlier "fixes 100% GPU DAE failure" framing no longer applies, and #3922 should be closed or retitled to track the remaining Hairer4 case. What this PR still fixes is the access pattern.

get_differential_vars (lib/OrdinaryDiffEqCore/src/misc_utils.jl) checks the mass matrix with all(!iszero, mm) before its _isdiag branch. For a Diagonal that walks all n^2 positions, and every diagonal hit is a scalar getindex on the underlying vector, which is disallowed by default when that vector is a CuVector, and O(n^2) for a question the type answers in O(n). The fix adds a Diagonal dispatch that broadcasts over mm.diag, so the reduction is O(n) and stays on device. This is the same diagonal-only reduction find_algebraic_vars_eqs(::Diagonal) in the same file performs, though that one goes through diag(M) rather than the field.

CPU results are unchanged. Mixed, all-nonzero and all-zero diagonals return exactly what the old _isdiag path returned, including the reshape to size(u) for matrix-valued u, and all three are covered by new tests.

The access pattern itself is now tested on CPU: a Diagonal wrapping a vector type that errors on scalar getindex but supports whole-array broadcast, i.e. device-array semantics without a GPU. On master's code path that construction throws inside all(!iszero, mm); with this patch it returns the correct differential-vars mask.

One test adjustment was required. The Diagonal branch is statically resolvable, which fixes inference of solve for the two Rodas4 + ShampineCollocationInit cases at lib/OrdinaryDiffEqNonlinearSolve/test/mass_matrix_tests.jl:385/387. Those lines were @test_broken sol = @inferred solve(...), a form that errors with "Expression evaluated to non-Boolean" once @inferred succeeds, because the successful @inferred returns the solution object. Both lines now read @test (@inferred solve(...); true): green while inference holds, an error if it regresses. I checked the replacement form against master's code and it does error there, so it is not a rubber stamp. The Rosenbrock23 and Rodas5 lines are untouched and stay @test_broken; those two fail because solve itself throws CheckInitFailureError, which this change does not affect.

Also wires up show_errors(results) in the GPU DAE test entry point; it was defined but never called, so a failing case only ever logged a status glyph with no exception text. That file runs only on the self-hosted GPU lane.

Local verification on Julia 1.12.6, rebased on master:

• lib/OrdinaryDiffEqCore/test/algebraic_vars_detection_tests.jl: 22 passed / 0 failed (18 on master, so 4 new assertions).
• lib/OrdinaryDiffEqNonlinearSolve/test/mass_matrix_tests.jl: 227 passed / 0 failed / 0 errored / 40 broken. Master baseline on the same file is 225 passed / 42 broken; the two that flip are the Rodas4 lines above.
• lib/OrdinaryDiffEqBDF: dae_convergence_tests.jl 50/50, dae_initialization_tests.jl 38 passed / 2 broken (pre-existing).
• Runic 1.5.1 clean on all four changed files.

No GPU hardware here, so the CUDA path is covered by the CPU device-semantics guard test rather than on-device.

The red checks on this PR are inherited from master. format-check fails on lib/OrdinaryDiffEqCore/src/disco.jl, lib/OrdinaryDiffEqCore/src/integrators/controllers.jl and test/Integrators_I/disco_tests.jl, none of which this PR touches and all of which are dirty in a clean master checkout. The lib/OrdinaryDiffEqNonlinearSolve Core lane dies in linear_solver_tests.jl with UndefVarError: MatrixOperator before it ever reaches mass_matrix_tests.jl; the same failure is on master run 30610465511. Both need fixing separately.

AI Disclosure

Claude assisted with this work.