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Use accelerative_smith_iteration! in eig_trunc_pullback! #294

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Merged
leburgel merged 2 commits into from
Oct 3, 2026
Merged

Use accelerative_smith_iteration! in eig_trunc_pullback! #294

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f8a0cbe
Fix overflow in `eig_trunc_pullback!` and use `accelerative_smith_ite…
leburgel Oct 2, 2026
d0455b9
Remove superseded outer normalization
leburgel Oct 2, 2026
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34 changes: 6 additions & 28 deletions src/pullbacks/eig.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -161,36 +161,14 @@ function eig_trunc_pullback!(
Z = ViG * VᴴΔAV

# add contribution from orthogonal complement
AP = mul!(complex.(A), V * Dmat, ViG', -1, 1)
X₀ = iszerotangent(ΔV₊) ? AP' * Z : mul!(ΔV₊, AP', Z, 1, 1)
# build the adjoint of AP directly, since that is what the series is summed with
APᴴ = mul!(complex.(A'), ViG, (V * Dmat)', -1, 1)
X₀ = iszerotangent(ΔV₊) ? APᴴ * Z : mul!(ΔV₊, APᴴ, Z, 1, 1)
X₀ ./= D'
dabsmax = maximum(abs, D)
AP ./= dabsmax
D̄⁻¹ = dabsmax ./ conj.(D)
X₁ = rmul!(AP' * X₀, Diagonal(D̄⁻¹))
X₁ .+= X₀
Xₖ, Xₖ₊₁ = X₁, X₀
APₖ, APₖ₊₁ = AP * AP, AP
D̄⁻¹ₖ, D̄⁻¹ₖ₊₁ = D̄⁻¹ .^ 2, D̄⁻¹
for k in 1:maxiter
Xₖ₊₁ = rmul!(mul!(Xₖ₊₁, APₖ', Xₖ), Diagonal(D̄⁻¹ₖ))
if norm(Xₖ₊₁, Inf) < degeneracy_atol
break
end
Xₖ₊₁ .+= Xₖ
if k == maxiter
@warn "Sylvester iteration did not converge after $k iterations, final norm of X: $(norm(Xₖ₊₁, Inf)))"
break
end
D̄⁻¹ₖ₊₁ .= D̄⁻¹ₖ .^ 2
APₖ₊₁ = mul!(APₖ₊₁, APₖ, APₖ)
Xₖ, Xₖ₊₁ = Xₖ₊₁, Xₖ
APₖ, APₖ₊₁ = APₖ₊₁, APₖ
D̄⁻¹ₖ, D̄⁻¹ₖ₊₁ = D̄⁻¹ₖ₊₁, D̄⁻¹ₖ
end
Z .+= Xₖ
X = accelerative_smith_iteration!(X₀, similar(X₀), APᴴ, inv.(conj.(D)), degeneracy_atol, maxiter)
Z .+= X
if eltype(ΔA) <: Real
ΔAc = mul!(AP, Z, V') # recycle AP
ΔAc = mul!(APᴴ, Z, V') # recycle APᴴ
ΔA .+= real.(ΔAc)
else
ΔA = mul!(ΔA, Z, V', 1, 1)
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