Auto nonstructural zeros: decide on filled values, deactivate when nothing is droppable

[ChrisRackauckas-Claude]

What

Two fixes to the NonstructuralZeros.Auto state machine. Both target the same failure: the sparse reduction latching into per-solve dropzeros that drops nothing.

1. Defer the activation decision when the starting matrix is entirely zero.
A cache is commonly initialized from a prototype — the intended sparsity pattern with values not filled in yet. An all-zero sample is indistinguishable from "100% nonstructural zeros", so Auto activated on it with an all-false mask. The first filled solve then flipped every entry, making activated == nstart_zeros unconditionally trip the non-persistence guard and set cache_union = false permanently. From then on every solve allocated a fresh dropzeros copy — while dropping nothing, because the matrix has no nonstructural zeros at all. Deferring to the first matrix that carries a nonzero decides on real values instead.

2. Deactivate once the union covers every stored entry.
The union only ever grows, so at that point no future matrix can have anything dropped — the reduction is provably dead weight, not just heuristically unpromising. This is also structure-preserving: reduced equals the full pattern exactly when this triggers, so the operand handed to the factorization keeps the structure it just had. Previously the only escape from a bloated union was "drop per solve forever", which is the wrong conclusion when nothing is droppable.

Effect

Prototype-initialized cache, n=200, nnz=598, KLUFactorization:

	before	after
alloc/solve	17.7 kB (nnz(reduced) == nnz(A))	0 B

The reduction is unchanged where it pays, and becomes reachable where it previously self-destructed:

case	init	after first filled solve	reduced_nnz	alloc/solve
genuine nonstructural zeros	active	active, union caching	359/598	0 B
prototype → zeros-heavy fill	pending	active, union caching	359/598	0 B
prototype → no droppable zeros	pending	inactive	—	0 B
filled at init, no zeros	inactive	inactive	—	0 B

Row 2 is the point: a prototype-initialized caller that should benefit now does. Before, that exact case activated on the all-zero prototype and latched into the degraded path.

Downstream

This removes a 30× sparse allocation gap in OrdinaryDiffEq's NonlinearSolveAlg (11.8 MB → 0.42 MB per solve, ~2.3× faster on a 32-state Brusselator), whose inner Jacobian buffer is exactly such a prototype — with no change needed on the OrdinaryDiffEq side.

Testing

Two regression testsets added to test/Core/nonstructural_zeros.jl (deferral + decide-on-fill in both directions; dead-weight deactivation with continued correct solves). Core group run locally.

Draft — please ignore until reviewed by @ChrisRackauckas.

🤖 Generated with Claude Code