Shift VCC test u0[4] off saveat-coincident event time#1448
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ChrisRackauckas merged 1 commit intoMay 21, 2026
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The "callback with linear affect" testset uses condition `u[3] - 10` which, combined with u[3](t) = u0[4]*t, puts the event at τ = 10/u0[4]. With the original u0[4] = 2.0, τ = 5.0 exactly — landing on the saveat=0.5 grid. At a saveat-coincident event time the cost is jump-discontinuous in u0[3] and u0[4]: the post-event state propagates to that saveat sample, and the Float64 rootfinder versus ForwardDiff's Dual rootfinder converge to opposite ULP sides of the saveat. Both compute valid one-sided derivatives of a discontinuous cost; rtol comparisons between them fail by design at that point. Verified via central finite differences (1/h blow-up on components 3 and 4 at u0[4]=2.0; clean 5+ digit agreement among FD, BS, GA at u0[4]=2.01 with τ ≈ 4.975). Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
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Please ignore until reviewed by @ChrisRackauckas.
Summary
In
test_vector_continuous_callback(test/callbacks/vector_continuous_callbacks.jl), shiftu0[4]from2.0to2.01so the "callback with linear affect" event (conditionu[3] = 10) lands at τ ≈ 4.975 instead of exactly 5.0 — off thesaveat = 0.5grid.At τ = saveat, the cost has a true jump discontinuity in
u0[3]andu0[4]: the post-affect state (u[4] ← -p[2]·u[4] = -1.8) propagates to the saveat-5.0 sample on one side of the corner and the pre-affect state (u[4] = 2.0) on the other. The Float64 forward rootfinder converges 1 ULP below 5.0; ForwardDiff's Dual rootfinder converges ~6 ULPs above. Both compute valid one-sided derivatives, butBS ≈ FD rtol=1e-5then compares opposite-side derivatives and fails by design — not an algorithmic bug.Verification
Central finite differences (
(L(+h) − L(−h)) / 2h) atu0 = [50, 0, 0, 2.0]:1/h— classic jump signature ([323, 1.70e5, 1.70e7]for h ∈ {1e-3, 1e-5, 1e-7})At
u0[4] = 2.01(τ ≈ 4.975, off-grid): FD ≈ BS ≈ GA ≈ CFD to 5–6 digits across all components.Full FD writeup in closed issue #1447.
Relationship to #1446
#1446 fixes a
MethodErrorin the VCC tracking constructor that masked these tests entirely. Once #1446 lands, the constructor works but this testset numerically fails at the corner. This PR is the right resolution for the numerical failure.The two PRs can land in either order — this one is a pure test-data tweak with no functional impact; #1446 is an
src/fix that's still correct without this change.Refs
Test plan
test/callbacks/vector_continuous_callbacks.jlpass on Julia 1.12.6 locally with this change applied on top of Use single-affect VCC constructor in _track_callback #1446