Krylov: stop adaptive-path allocation thrash (expcache wipe + lanczos slice copy)

[ChrisRackauckas-Claude]

Summary

Removes the remaining per-step allocations from the adaptive Krylov path
(phiv_timestep! / expv_timestep! with adaptive_krylov), which the
exponential Rosenbrock integrators in OrdinaryDiffEq (Exp4/EPIRK/EXPRB) drive
every step. Two sources:

1. get_expcache! cache-wipe thrash. The exp-workspace store was reset with
   empty! once it held more than 16 distinct extended-matrix sizes. The
   adaptive path visits a bounded-but-varying set of subspace sizes as it adapts
   m; when that set exceeds 16, the wipe discarded still-hot workspaces and the
   entire working set (each workspace is 7 dense matrices + a LinearSolve.init)
   was reallocated periodically. Each workspace is O((m+p)^2) — tied to the
   subspace dimension, not the state size n — so keeping the seen sizes
   cached is cheap. Now evicts only the oldest entry (bound raised 16 → 64), so a
   repeat size is a hit instead of a reallocation.

2. lanczos! slice copy. copyto!(@diagview(H, 1), v[1:(end - 1)])
   materialized a fresh vector each call. @view makes it a view; source
   (sub-diagonal) and destination (super-diagonal) are disjoint, so the result is
   unchanged.

Measured effect

Per-step allocations via the step! interface on a 1D semilinear
reaction–diffusion ODEProblem, well warmed (adaptive Krylov has settling
transients + rare spikes, so this must be measured over a long window):

method / size	master	this PR
Exp4, N=512	~864 B/step	16 B/step (median 0)
EPIRK4s3B, N=512	~32.8 KB/step	~2.5 KB/step (median 0)

The quiet-state per-step allocation is now zero; the residual amortized cost
is the occasional genuinely-new subspace size (one unavoidable alloc_mem +
KrylovSubspace resize! when adaptive m reaches a new maximum).

Correctness

Final solutions are bit-identical to master (max|Δu| = 0 across
Exp4/EPIRK4s3A/EPIRK4s3B/EXPRB53s3 on a 50-step N=256 solve). Both changes are
semantics-preserving by construction (view vs. copy of disjoint memory; the
workspace store is scratch that is fully overwritten on each use, so which sizes
are cached never affects results).

Test

Adds a regression test: a size seen earlier must still be cached after >16
further distinct sizes are requested (the old wipe bound), and a cache hit must
not allocate. The Core suite passes locally.

Pairs with SciML/OrdinaryDiffEq.jl#3993 (the stepper-side @views slice fix);
together they take the exponential Rosenbrock steppers to zero quiet-state
per-step allocations.

---

Draft — please ignore until reviewed by @ChrisRackauckas.

🤖 Generated with Claude Code