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ChrisRackauckas merged 2 commits into from
Jun 27, 2026
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Improve ForwardDiff sparse matrix specialization and add tests #1063

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914ce38
Share index vectors in ForwardDiff overload for sparse matrices
hersle Jun 27, 2026
a479f35
Test ForwardDiff overload for sparse matrices
hersle Jun 27, 2026
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4 changes: 2 additions & 2 deletions ext/LinearSolveForwardDiffExt.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -683,15 +683,15 @@ function partials_to_list(partial_matrix::SparseMatrixCSC)
V = ForwardDiff.valtype(T) # use type for concrete array below in empty-nz case (e.g. all-zero Jacobian at init)
return [
SparseMatrixCSC(
m, n, copy(partial_matrix.colptr), copy(partial_matrix.rowval),
m, n, partial_matrix.colptr, partial_matrix.rowval,
V[nz[i][k] for i in eachindex(nz)]
) for k in 1:p
]
end

function update_partials_list!(partial_matrix::SparseMatrixCSC, list_cache)
nz = nonzeros(partial_matrix)
if length(nz) != length(nonzeros(first(list_cache))) # TODO: more precise?
if length(nz) != length(nonzeros(first(list_cache)))
list_cache .= partials_to_list(partial_matrix) # sparsity pattern changed
else
for k in eachindex(list_cache)
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40 changes: 40 additions & 0 deletions test/Core/forwarddiff_overloads.jl
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Expand Up @@ -606,3 +606,43 @@ end
@test getfield(cache, :b_partials_valid)
@test ≈(x_p, new_A \ new_b, rtol = 1.0e-9)
end

@testset "Sparse matrices" begin
# Case 1: same number of nonzeros, same sparsity pattern, updated values
A1 = sparse([1, 2], [1, 2], [ForwardDiff.Dual(1.0, 10.0, 11.0), ForwardDiff.Dual(2.0, 20.0, 21.0)], 2, 2)
b = [1.0, 1.0]
prob = LinearProblem(A1, b)
cache = init(prob, KLUFactorization())
solve!(cache)
cache.A = A1
@test ≈(solve!(cache), Matrix(A1) \ b, rtol = 1.0e-9)

# Case 2: same number of nonzeros, but different positions
A2 = sparse([2, 1], [1, 2], [ForwardDiff.Dual(3.0, 30.0, 31.0), ForwardDiff.Dual(4.0, 40.0, 41.0)], 2, 2)
cache.A = A2
@test ≈(solve!(cache), Matrix(A2) \ b, rtol = 1.0e-9)

# Case 3: number of nonzeros increases
A3 = sparse([1, 2, 1], [1, 2, 2], [ForwardDiff.Dual(3.0, 30.0, 31.0), ForwardDiff.Dual(4.0, 40.0, 41.0), ForwardDiff.Dual(5.0, 50.0, 51.0)], 2, 2)
cache.A = A3
@test ≈(solve!(cache), Matrix(A3) \ b, rtol = 1.0e-9)

# Case 4: dual b (both A and b carry partials)
b_dual = [ForwardDiff.Dual(3.0, 1.0, 0.0), ForwardDiff.Dual(4.0, 0.0, 1.0)]
prob = LinearProblem(A1, b_dual)
cache = init(prob, KLUFactorization())
@test ≈(solve!(cache), Matrix(A1) \ b_dual, rtol = 1.0e-9)
b_dual2 = [ForwardDiff.Dual(5.0, 2.0, 0.0), ForwardDiff.Dual(6.0, 0.0, 2.0)]
cache.b = b_dual2
@test ≈(solve!(cache), Matrix(A1) \ b_dual2, rtol = 1.0e-9)

# Case 5: in-place mutation of A's nonzeros via setindex! (ODE solver pattern)
A = sparse([1, 2], [1, 2], [ForwardDiff.Dual(1.0, 10.0, 11.0), ForwardDiff.Dual(2.0, 20.0, 21.0)], 2, 2)
prob = LinearProblem(A, b)
cache = init(prob, KLUFactorization())
solve!(cache)
A[1, 1] = ForwardDiff.Dual(5.0, 50.0, 51.0)
A[2, 2] = ForwardDiff.Dual(6.0, 60.0, 61.0)
cache.A = A
@test ≈(solve!(cache), Matrix(A) \ b, rtol = 1.0e-9)
end
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