Bunch-Kaufman doesn't support reverse-mode autodiff

[jpbrodrick89]

Describe the bug 🐞

Using Enzyme.autodiff(Reverse, ... on BunchKaufmanFactorization because A must be symmetric and enzyme tries to write to it. Even if I lazily tag it inside another function it still guards against this.

Expected behavior

I expected the Linear Solver Enzyme extension rules to apply the adjoint appropriately as it does in forward mode. Due to symmetry, the transpose solve for the cotangent should be the same as the standard solve.

grad_b = A^(-1) cotangent

I presume the problem comes with trying to compute the contagent with respect to the elements of A which would break symmetry but there should be a clever symmetry preserving way to do this.

Minimal Reproducible Example 👇

  using LinearAlgebra, LinearSolve, Enzyme

  A = Float64[4 1 0.5; 1 3 0.2; 0.5 0.2 2]
  b = Float64[1, 2, 3]

 function bk_solve(b)
      A = Symmetric(Float64[4 1 0.5; 1 3 0.2; 0.5 0.2 2])
      prob = LinearProblem(A, copy(b))
      sol = solve(prob, BunchKaufmanFactorization())
      return sum(sol.u)
  end

  b = Float64[1, 2, 3]

  # Forward works
  bk_solve(b)

  # Enzyme forward works
  Enzyme.autodiff(Forward, Const(bk_solve), Duplicated(copy(b), Float64[1, 0, 0]))

  # Enzyme reverse fails
  db = zero(b)
  Enzyme.autodiff(Reverse, Const(bk_solve), Active, Duplicated(copy(b), db))
  # ArgumentError: Cannot set a non-diagonal index in a symmetric matrix
  # at LinearSolveEnzymeExt.jl:143 (_sparse_outer_sub!)

**Error & Stacktrace ⚠️**

  ⎿  Error: Exit code 1
     Traceback (most recent call last):
       File "<string>", line 3, in <module>
         jl.seval('versioninfo()')
         ~~~~~~~~^^^^^^^^^^^^^^^^^
       File "/Users/jonathanbrodrick/.julia/packages/PythonCall/83z4q/src/JlWrap/module.jl", line 27, in seval
         return self._jl_callmethod($(pyjl_methodnum(pyjlmodule_seval)), expr)
                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
     juliacall.JuliaError: UndefVarError: `versioninfo` not defined in `Main`
     Stacktrace:
      [1] top-level scope
        @ none:1
      [2] eval
        @ ./boot.jl:430 [inlined]
      [3] eval
        @ ./Base.jl:130 [inlined]
      [4] pyjlmodule_seval(self::Module, expr::Py)
        @ PythonCall.JlWrap ~/.julia/packages/PythonCall/83z4q/src/JlWrap/module.jl:13
      [5] _pyjl_callmethod(f::Any, self_::Ptr{PythonCall.C.PyObject}, args_::Ptr{PythonCall.C.PyObject}, nargs::Int64)
        @ PythonCall.JlWrap ~/.julia/packages/PythonCall/83z4q/src/JlWrap/base.jl:65
      [6] _pyjl_callmethod(o::Ptr{PythonCall.C.PyObject}, args::Ptr{PythonCall.C.PyObject})
        @ PythonCall.JlWrap.Cjl ~/.julia/packages/PythonCall/83z4q/src/JlWrap/C.jl:63

Output of `using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)`

⎿  Status `~/pasteurcodes/tesseract-core/.venv/julia_env/Manifest.toml`
       [47edcb42] ADTypes v1.21.0
       [7d9f7c33] Accessors v0.1.44
       [79e6a3ab] Adapt v4.5.0
       [4fba245c] ArrayInterface v7.23.0
       [fa961155] CEnum v0.5.0
       [d360d2e6] ChainRulesCore v1.26.0
       [38540f10] CommonSolve v0.2.6
       [34da2185] Compat v4.18.1
       [a33af91c] CompositionsBase v0.1.2
       [2569d6c7] ConcreteStructs v0.2.3
       [992eb4ea] CondaPkg v0.2.34
       [187b0558] ConstructionBase v1.6.0
       [9a962f9c] DataAPI v1.16.0
       [e2d170a0] DataValueInterfaces v1.0.0
       [ffbed154] DocStringExtensions v0.9.5
       [4e289a0a] EnumX v1.0.7
       [7da242da] Enzyme v0.13.134
       [f151be2c] EnzymeCore v0.8.18
       [e2ba6199] ExprTools v0.1.10
       [55351af7] ExproniconLite v0.10.14
       [069b7b12] FunctionWrappers v1.1.3
       [77dc65aa] FunctionWrappersWrappers v0.1.3
       [46192b85] GPUArraysCore v0.2.0
       [61eb1bfa] GPUCompiler v1.8.2
       [3587e190] InverseFunctions v0.1.17
       [82899510] IteratorInterfaceExtensions v1.0.0
       [692b3bcd] JLLWrappers v1.7.1
       [682c06a0] JSON v1.4.0
       [ae98c720] Jieko v0.2.1
       [ba0b0d4f] Krylov v0.10.6
       [929cbde3] LLVM v9.4.6
       [7ed4a6bd] LinearSolve v3.68.0
       [e6f89c97] LoggingExtras v1.2.0
       [1914dd2f] MacroTools v0.5.16
       [0b3b1443] MicroMamba v0.1.15
       [2e0e35c7] Moshi v0.3.7
       [d8793406] ObjectFile v0.5.0
       [bac558e1] OrderedCollections v1.8.1
       [69de0a69] Parsers v2.8.3
       [fa939f87] Pidfile v1.3.0
       [d236fae5] PreallocationTools v1.2.0
     ⌅ [aea7be01] PrecompileTools v1.2.1
       [21216c6a] Preferences v1.5.2
       [6099a3de] PythonCall v0.9.31
       [3cdcf5f2] RecipesBase v1.3.4
       [731186ca] RecursiveArrayTools v3.48.0
       [189a3867] Reexport v1.2.2
       [ae029012] Requires v1.3.1
       [7e49a35a] RuntimeGeneratedFunctions v0.5.17
       [0bca4576] SciMLBase v2.152.1
       [a6db7da4] SciMLLogging v1.9.1
       [c0aeaf25] SciMLOperators v1.15.1
       [431bcebd] SciMLPublic v1.0.1
       [53ae85a6] SciMLStructures v1.10.0
       [6c6a2e73] Scratch v1.3.0
       [efcf1570] Setfield v1.1.2
       [1e83bf80] StaticArraysCore v1.4.4
       [10745b16] Statistics v1.11.1
       [53d494c1] StructIO v0.3.1
       [ec057cc2] StructUtils v2.7.1
       [2efcf032] SymbolicIndexingInterface v0.3.46
       [3783bdb8] TableTraits v1.0.1
       [bd369af6] Tables v1.12.1
       [e689c965] Tracy v0.1.6
       [e17b2a0c] UnsafePointers v1.0.0
       [7cc45869] Enzyme_jll v0.0.256+0
       [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
       [dad2f222] LLVMExtra_jll v0.0.38+0
       [ad6e5548] LibTracyClient_jll v0.13.1+0
       [856f044c] MKL_jll v2025.2.0+0
     ⌅ [458c3c95] OpenSSL_jll v3.0.16+0
       [f8abcde7] micromamba_jll v2.3.1+0
       [1317d2d5] oneTBB_jll v2022.0.0+1
       [4d7b5844] pixi_jll v0.41.3+0
       [0dad84c5] ArgTools v1.1.2
       [56f22d72] Artifacts v1.11.0
       [2a0f44e3] Base64 v1.11.0
       [ade2ca70] Dates v1.11.0
       [8ba89e20] Distributed v1.11.0
       [f43a241f] Downloads v1.6.0
       [7b1f6079] FileWatching v1.11.0
       [9fa8497b] Future v1.11.0
       [b77e0a4c] InteractiveUtils v1.11.0
       [4af54fe1] LazyArtifacts v1.11.0
       [b27032c2] LibCURL v0.6.4
       [76f85450] LibGit2 v1.11.0
       [8f399da3] Libdl v1.11.0
       [37e2e46d] LinearAlgebra v1.11.0
       [56ddb016] Logging v1.11.0
       [d6f4376e] Markdown v1.11.0
       [ca575930] NetworkOptions v1.2.0
       [44cfe95a] Pkg v1.11.0
       [de0858da] Printf v1.11.0
       [9a3f8284] Random v1.11.0
       [ea8e919c] SHA v0.7.0
       [9e88b42a] Serialization v1.11.0
       [6462fe0b] Sockets v1.11.0
       [2f01184e] SparseArrays v1.11.0
       [fa267f1f] TOML v1.0.3
       [a4e569a6] Tar v1.10.0
       [8dfed614] Test v1.11.0
       [cf7118a7] UUIDs v1.11.0
       [4ec0a83e] Unicode v1.11.0
       [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
       [deac9b47] LibCURL_jll v8.6.0+0
       [e37daf67] LibGit2_jll v1.7.2+0
       [29816b5a] LibSSH2_jll v1.11.0+1
       [c8ffd9c3] MbedTLS_jll v2.28.6+0
       [14a3606d] MozillaCACerts_jll v2023.12.12
       [4536629a] OpenBLAS_jll v0.3.27+1
       [bea87d4a] SuiteSparse_jll v7.7.0+0
       [83775a58] Zlib_jll v1.2.13+1
       [8e850b90] libblastrampoline_jll v5.11.0+0
       [8e850ede] nghttp2_jll v1.59.0+0
       [3f19e933] p7zip_jll v17.4.0+2
     Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

• Output of versioninfo()

  Julia Version 1.11.9
  Commit 53a02c0720c (2026-02-06 00:27 UTC)
  Platform Info:
    OS: macOS (arm64-apple-darwin24.0.0)
    CPU: 12 × Apple M2 Pro
    WORD_SIZE: 64
    LLVM: libLLVM-16.0.6 (ORCJIT, apple-m2)

  Key package versions:
  - Enzyme v0.13.134
  - EnzymeCore v0.8.18
  - LinearSolve v3.68.0
  - SciMLBase v2.152.1

Additional context

Add any other context about the problem here.