Fix VR_FRM + noise_rate_prototype + adaptive SDE solver hang (#592)

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas.

Closes #592.

Summary

mul!(c::ExtendedJumpArray, A, u) only writes to c.u when size(A, 1) == length(c.u) (the noise rate matrix is sized for the original state, not the extended state). The adaptive LambaEM step (and other adaptive non-diagonal SDE solvers) reuses the same scratchpad ExtendedJumpArray and writes scalar error-estimate values into c.jump_u during the error calculation. On the next step's mul!, c.jump_u is left untouched — so the SDE solver reads back those stale values and adds them to the integrator state as if they were a noise contribution on the jump-rate-integral component. The result is that jump_u is driven to ±1e15 within a few steps, the VR_FRM continuous-callback condition (u.jump_u[idx]) never crosses zero, and no variable-rate jumps ever fire.

The MRE in the issue (hybrid CLE↔SSA birth-death with noise_rate_prototype = zeros(1, 2)) reproduces this: after the CLE→SSA callback fires, u gets pinned at the threshold (95.0) forever even though the SSA rates are non-zero, because the corresponding continuous callbacks for the variable-rate jumps never trigger.

Fix

Zero c.jump_u after the partial mul!. Semantically: when the noise matrix only addresses the c.u portion, the noise contribution to c.jump_u is exactly zero, and mul! has overwrite semantics, so the result should reflect that — not whatever happened to be in the scratchpad.

function LinearAlgebra.mul!(c::ExtendedJumpArray, A::AbstractVecOrMat, u::AbstractVector)
    Nu = length(c.u)
    if size(A, 1) == Nu
        mul!(c.u, A, u)
        fill!(c.jump_u, zero(eltype(c.jump_u)))   # <-- added
    elseif size(A, 1) == length(c)
        mul!(c.u, @view(A[1:Nu, :]), u)
        mul!(c.jump_u, @view(A[(Nu + 1):end, :]), u)
    else
        ...
    end
end

Tests

• test/extended_jump_array.jl: direct unit tests for both mul! branches.
• test/variable_rate.jl: regression test that reproduces the hybrid CLE→SSA scenario from Potential bug when switching from SDE to SSA using Callbacks #592 with noise_rate_prototype and LambaEM(adaptive=true). The test verifies jump_u stays bounded (the bug drove it past ±1e15 within a few steps) and that the post-switch SSA jumps actually fire.

Test plan

• CI green on Run Tests (InterfaceI / InterfaceII)
• CI green on Spell Check, Downgrade, Thread Safety Tests
• test/variable_rate.jl passes locally on Julia 1.11 with patched source
• test/extended_jump_array.jl passes locally on Julia 1.11 with patched source
• Manually verified the user's MRE from Potential bug when switching from SDE to SSA using Callbacks #592 now runs to completion and produces a trajectory that actually fires SSA jumps after the CLE→SSA switch (u decays from 95 → 17 over tspan = (0, 10) instead of getting pinned at 95)

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

CI summary:

• ✅ All test jobs pass: Tests (1, lts, pre × InterfaceI, InterfaceII, QA), GPU Tests, Spell Check
• ❌ build (Documentation) fails — but this is a pre-existing failure on master since 2026-05-11 (master run), not caused by this PR. The error is UndefVarError: \JumpProblem` not defined in `Main.__atexample__named__tut3`indocs/src/tutorials/jump_diffusion.md— likely a name collision after the DifferentialEquations 8.0 / ModelingToolkitBase / Catalyst bump (the error log explicitly hintsJumpProblem` is "also exported by ModelingToolkitBase (loaded but not imported in Main)" and "also exported by Catalyst").

Investigating the master docs failure separately.