Basic eig(h) forward rules

[kshyatt]

This doesn't yet handle the trunc cases at all, if anyone wants to take a swing please do feel free. I also had to turn off the forward mode test for complex numbers as there's a freedom in V that's hard to account for (see https://github.com/Jutho/KrylovKit.jl/blob/master/test/ad/eigsolve.jl).

[github-actions]

Your PR no longer requires formatting changes. Thank you for your contribution!

[kshyatt]

CUDA + Mooncake here probably needs #244

[codecov]

Codecov Report

❌ Patch coverage is 68.18182% with 21 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
...ixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl	0.00%	21 Missing ⚠️

Files with missing lines	Coverage Δ
...gebraKitMooncakeExt/MatrixAlgebraKitMooncakeExt.jl	67.07% <100.00%> (+1.01%)	⬆️
src/MatrixAlgebraKit.jl	100.00% <ø> (ø)
src/pushforwards/eig.jl	100.00% <100.00%> (ø)
src/pushforwards/eigh.jl	100.00% <100.00%> (ø)
...ixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl	0.00% <0.00%> (ø)

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[kshyatt]

This is getting hit with the eig related instability 😭

[lkdvos]

Overall looks good! would you like me to add some optimization comments, or prefer me not to?

[kshyatt]

Feel free to suggest optimizations anytime, I again did this inefficiently in order to keep things straight at first.

…

On Mon, Jun 8, 2026 at 9:31 PM Lukas Devos ***@***.***> wrote: ***@***.**** commented on this pull request. Overall looks good! would you like me to add some optimization comments, or prefer me not to? ------------------------------ In ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl <#245 (comment)> : > + A::Annotation{TA}, + arg::Annotation, alg::Const{<:MatrixAlgebraKit.AbstractAlgorithm}, - ) where {RT, TA} + ) where {TA, RT} ⬇️ Suggested change - A::Annotation{TA}, - arg::Annotation, - alg::Const{<:MatrixAlgebraKit.AbstractAlgorithm}, - ) where {RT, TA} - ) where {TA, RT} + A::Annotation, + arg::Annotation, +alg::Const{<:MatrixAlgebraKit.AbstractAlgorithm}, + ) where {RT} I don't think this is used here? — Reply to this email directly, view it on GitHub <#245?email_source=notifications&email_token=AAGKJYZXX3A6V4DCPPHV3HD464H7NA5CNFSNUABKM5UWIORPF5TWS5BNNB2WEL2QOVWGYUTFOF2WK43UKJSXM2LFO4XTINBVGA4DCMZQHA22M4TFMFZW63VGMF2XI2DPOKSWK5TFNZ2KYZTPN52GK4S7MNWGSY3L#pullrequestreview-4450813085>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAGKJY53IHDP3YZW5H3XWKT464H7NAVCNFSM6AAAAACZ3TI4G2VHI2DSMVQWIX3LMV43YUDVNRWFEZLROVSXG5CSMV3GSZLXHM2DINJQHAYTGMBYGU> . Triage notifications, keep track of coding agent tasks and review pull requests on the go with GitHub Mobile for iOS <https://github.com/notifications/mobile/ios/AAGKJY5EKLEPIRW3FBG6LTL464H7NA5CNFSNUABKM5UWIORPF5TWS5BNNB2WEL2QOVWGYUTFOF2WK43UKJSXM2LFO4XTINBVGA4DCMZQHA22M4TFMFZW63VGMF2XI2DPOKSWK5TFNZ2KUZTPN52GK4S7NFXXG> and Android <https://github.com/notifications/mobile/android/AAGKJY4TJ7STEA55IQIUUG3464H7NA5CNFSNUABKM5UWIORPF5TWS5BNNB2WEL2QOVWGYUTFOF2WK43UKJSXM2LFO4XTINBVGA4DCMZQHA22M4TFMFZW63VGMF2XI2DPOKSWK5TFNZ2K4ZTPN52GK4S7MFXGI4TPNFSA>. Download it today! You are receiving this because you authored the thread.Message ID: ***@***.***>

[lkdvos]

As a small question: do you know if the pushforwards are supposed to accumulate the results into the provided destinations, or simply writing them into it is enough?

I also noticed some slight inconsistencies in the variable names between the two pushforwards, it might be nice to make both somewhat follow the same scheme?

[lkdvos]

I think this is guaranteed by degeneracy_atol > 0