Route duals-in-b PureKLU solves to a native LinearCache (uses PureKLU 1.1 mixed ldiv!)#1069
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ChrisRackauckas merged 6 commits intoJun 30, 2026
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A factorization is a linear operator, so `K \ Dual(v, p₁…p_N) = Dual(K\v, K\p₁ … K\p_N)`.
PureKLU stores its L/U in the factor element type, so a `KLUFactorization{<:AbstractFloat}`
can backsolve a Dual right-hand side by solving the primal value and each partial column
in one multi-RHS `klu_solve!`, then repacking — without ever promoting `A` to a Dual.
This keeps the factorization in fast Float64 arithmetic and lets the duals ride only
through the back-substitution, which is the single-solve analogue of the split path's
per-partial back-solves. It makes `solve(LinearProblem(A_float64, b_dual), PureKLU)` work
natively (previously a MethodError on `ldiv!(::KLUFactorization{Float64}, ::Vector{<:Dual})`).
The factor eltype is constrained to `AbstractFloat` so it never collides with PureKLU's
own `ldiv!(::KLUFactorization{Tv}, ::VecOrMat{Tv})` on the dual-factor path — a `Dual` is
`<: Real` but not `<: AbstractFloat`, so the dual-factor case stays with PureKLU's method.
Adds a correctness test (value + every partial column matches the dense Dual solve, factor
stays Float64) for chunk sizes 1/2/3.
Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
With the mixed-type `ldiv!` (primal KLU factor against a Dual RHS) in place, a `DualBLinearProblem` (duals only in b, A primal) no longer needs the split DualLinearCache machinery: it can be solved on a plain `LinearCache` whose factorization stays in Float64, with the duals carried through the back-solve. Add an `init(::DualBLinearProblem, ::PureKLUFactorization)` opt-out that returns `__init(prob, alg)` directly. This is type-stable — dispatch is purely on the problem subtype (b-dual / A-plain) and the alg type, so `init` always returns a `LinearCache` for this method (verified with `@inferred`), unlike the reverted value-based opt-out in SciML#1041-era code. It is also simpler than the split path and gets correct factorization reuse across b-only `reinit!`s for free, which the split path's `reinit!` does not (it unconditionally marks the inner cache fresh, forcing a refactorization even when only b changed). Scope: only PureKLU is routed, since it is the only sparse factorization with the mixed `ldiv!`. A-dual and mixed A/b problems are untouched and still take the split path. Adds routing + type-stability + correctness tests. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
The mixed-type `ldiv!` (primal KLU factor backsolving a Dual RHS) belongs in PureKLU, which owns `KLUFactorization` — it is the analogue of PureKLU's existing real-factor / Complex-RHS `ldiv!`, avoids type piracy here, and there it is non-allocating (the real `n × (N+1)` RHS reuses a buffer on the factorization). See SciML/PureKLU.jl#67. This drops the stop-gap `ldiv!` (and the `PureKLU` import) from this extension and bumps the PureKLU [compat] to 1.1, which provides it. The duals-in-b routing (`init(::DualBLinearProblem, ::PureKLUFactorization)` -> native `LinearCache`) is unchanged and now relies on PureKLU's `ldiv!`. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
ChrisRackauckas-Claude
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…solves The duals-in-b routing needs the primal-factor/Dual-RHS `ldiv!` from PureKLU 1.1.0 (SciML/PureKLU.jl#67), which is not yet registered. Add a temporary `[sources]` entry pointing at the PR branch so `PureKLU = "1.1"` resolves in CI (Julia >= 1.11; ignored on older Julia). To be removed once PureKLU 1.1.0 is in the General registry. Verified locally: a fresh resolve with this `[sources]` pulls PureKLU v1.1.0. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
PureKLU 1.1.0 (with the primal-factor/Dual-RHS `ldiv!`, SciML/PureKLU.jl#67) is in the General registry, so the `PureKLU = "1.1"` compat resolves directly. Remove the temporary `[sources]` override that pointed at the PR branch. Verified: forwarddiff_overloads.jl passes end-to-end against the registered PureKLU 1.1.0. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
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DualBLinearProblem's A slot is `Union{Number, AbstractArray}`, which a
Dual-eltype A also matches, so `DualLinearProblem <: DualBLinearProblem`.
The b-only PureKLU opt-out introduced in #1069 is more specific in the alg
argument than the general dual-path `init`, so both-Dual PureKLU problems
were routed to a plain `LinearCache` and `solve!` then failed with a
FieldError on `dual_linear_cache` (test/Core/forwarddiff_overloads.jl
"PureKLU direct dual path reuses inner LinearCache"). Add a more-specific
`DualLinearProblem` method restoring the direct dual path; the mixed-type
ldiv! only covers primal A.
Claude-Session: https://claude.ai/code/session_01EYp371jx6LurezUDhKcYRh
Co-authored-by: ChrisRackauckas-Claude <accounts@chrisrackauckas.com>
Co-authored-by: Claude Fable 5 <noreply@anthropic.com>
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The repo-wide Runic Format Check fails on main because this file landed unformatted in aabf007 (SciML#1069); format it here alongside the dispatch fix for the same commit's fallout. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com> Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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The repo-wide Runic Format Check fails on main because this file landed unformatted in aabf007 (SciML#1069); format it here alongside the dispatch fix for the same commit's fallout. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com> Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Adds native handling of duals-only-in-
bPureKLU solves: aDualBLinearProblem(A primal, b dual) is routed to a plainLinearCacheand solved with PureKLU's primal-factor / Dual-RHSldiv!, instead of the splitDualLinearCache. Came out of the #1064 / #1065 discussion (cc @hersle).Depends on PureKLU 1.1.0 (SciML/PureKLU.jl#67), now merged and registered — the
PureKLU = "1.1"compat resolves directly.What's here
init(::DualBLinearProblem, ::PureKLUFactorization) = __init(prob, alg)— routes duals-in-bto a nativeLinearCache. Type-stable: dispatch is purely on the problem subtype (A primal / b dual) + alg type, soinitalways returns aLinearCachehere (verified with@inferred). This sidesteps theUnion{LinearCache, DualLinearCache}instability that caused the value-based opt-out to be reverted (commit25f159c), because the subtype already encodes "A primal, b dual." Scope is narrow: only PureKLU; A-dual and mixed-A/b problems still take the split path.Plus a
PureKLU[compat]bump to1.1.Scope note (this does NOT fix #1064 by itself)
#1064 is an A-dual problem (the Rosenbrock
Wcarries duals). This PR only covers the b-dual case, so it is additive, not a replacement for the A-dual fix (#1066). The two cover different cells:Why it's worth it
reinit!s for free. The split path'sreinit!unconditionally setslinear_cache.isfresh = true, so it refactorizes even when onlybchanged. For a fixed operator with a varying dual RHS (cache reused), the native path is 5–15× faster on higher-fill matrices for that reason. (WhenAchanges every step, both refactorize and it's a tie — a simplification + fixed-A win, not a claim of being fundamentally faster than split.)n×(N+1)real RHS buffer lives on the PureKLU factorization (PureKLU#67,@allocated == 0).Verification (Julia 1.12, Linux)
test/Core/forwarddiff_overloads.jlpasses end-to-end against registered PureKLU 1.1.0; integration testset 12/12 (correctness through the publicsolve, routing returnsLinearCache,@inferredtype-stability).Runic --checkclean.Please ignore until reviewed by @ChrisRackauckas.
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