usage of `isposdef` leads to cryptic error when taking gradients

[Maximilian-Stefan-Ernst]

Not shure if this belongs here or to ChainRules, but taking the gradient of functions that use isposdef fails with ERROR: MethodError: no method matching iterate(::Nothing). See this MWE:

using Zygote, LinearAlgebra

# a is actually positive definite
a = rand(3,3); a = a*a'

# works fine
function f(x)
    return x
end

gradient(f, 1.0)

# errors
function f(x)
    isposdef(a)
    return x
end

gradient(f, 1.0)

ERROR: MethodError: no method matching iterate(::Nothing)
Closest candidates are:
  iterate(::Union{LinRange, StepRangeLen}) at /usr/share/julia/base/range.jl:826
  iterate(::Union{LinRange, StepRangeLen}, ::Integer) at /usr/share/julia/base/range.jl:826
  iterate(::T) where T<:Union{Base.KeySet{<:Any, <:Dict}, Base.ValueIterator{<:Dict}} at /usr/share/julia/base/dict.jl:695
  ...
Stacktrace:
  [1] indexed_iterate(I::Nothing, i::Int64)
    @ Base ./tuple.jl:92
  [2] chain_rrule_kw
    @ ~/.julia/packages/Zygote/DkIUK/src/compiler/chainrules.jl:229 [inlined]
  [3] macro expansion
    @ ~/.julia/packages/Zygote/DkIUK/src/compiler/interface2.jl:0 [inlined]
  [4] _pullback(::Zygote.Context, ::LinearAlgebra.var"#cholesky##kw", ::NamedTuple{(:check,), Tuple{Bool}}, ::typeof(cholesky), ::Hermitian{Float64, Matrix{Float64}})
    @ Zygote ~/.julia/packages/Zygote/DkIUK/src/compiler/interface2.jl:9
  [5] _pullback
    @ /usr/share/julia/stdlib/v1.7/LinearAlgebra/src/dense.jl:92 [inlined]
  [6] _pullback(ctx::Zygote.Context, f::typeof(isposdef), args::Matrix{Float64})
    @ Zygote ~/.julia/packages/Zygote/DkIUK/src/compiler/interface2.jl:0
  [7] _pullback
    @ ~/Downloads/test_zygote.jl:151 [inlined]
  [8] _pullback(ctx::Zygote.Context, f::typeof(f), args::Float64)
    @ Zygote ~/.julia/packages/Zygote/DkIUK/src/compiler/interface2.jl:0
  [9] _pullback(f::Function, args::Float64)
    @ Zygote ~/.julia/packages/Zygote/DkIUK/src/compiler/interface.jl:34
 [10] pullback(f::Function, args::Float64)
    @ Zygote ~/.julia/packages/Zygote/DkIUK/src/compiler/interface.jl:40
 [11] gradient(f::Function, args::Float64)
    @ Zygote ~/.julia/packages/Zygote/DkIUK/src/compiler/interface.jl:75
 [12] top-level scope
    @ ~/Downloads/test_zygote.jl:155

The problem seems to be calling isposdef and Hermitian, as this fails too:

function f(x)
    isposdef(cholesky(Hermitian(a); check = false))
    return x
end

gradient(f, 1.0)

But interestingly enough, this works just fine:

function f(x)
    isposdef(cholesky(Symmetric(a); check = false))
    return x
end

gradient(f, 1.0)

function f(x)
    Hermitian(a)
    return x
end

gradient(f, 1.0)

Version info:

Julia Version 1.7.3
Commit 742b9abb4d (2022-05-06 12:58 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i5-8265U CPU @ 1.60GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-12.0.1 (ORCJIT, skylake)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 1

Package versions:

  [082447d4] ChainRules v1.35.1
  [d360d2e6] ChainRulesCore v1.15.0
  [a93c6f00] DataFrames v1.3.4
  [31c24e10] Distributions v0.25.62
  [6a86dc24] FiniteDiff v2.12.1
  [f6369f11] ForwardDiff v0.10.30
  [d3d80556] LineSearches v7.1.1
  [d41bc354] NLSolversBase v7.8.2
  [76087f3c] NLopt v0.6.5
  [429524aa] Optim v1.7.0
  [08abe8d2] PrettyTables v1.3.1
  [2913bbd2] StatsBase v0.33.16
  [78862bba] StenoGraphs v0.2.0
  [0c5d862f] Symbolics v4.6.0
  [e88e6eb3] Zygote v0.6.40
  [8bb1440f] DelimitedFiles
  [4af54fe1] LazyArtifacts
  [37e2e46d] LinearAlgebra
  [44cfe95a] Pkg
  [9a3f8284] Random
  [2f01184e] SparseArrays
  [10745b16] Statistics

[ToucheSir]

I suspect a @non_differentiable isposdef(...) in ChainRules would be sufficient to resolve this. Certainly there's no point for AD to dig into that function.

[devmotion]

The cholesky(Hermitian(...)) issue should probably be fixed by #1114 on the master branch.

[ToucheSir]

At least on nightly, the test for logdet(cholesky(Hermitian(...))) is still failing: https://github.com/FluxML/Zygote.jl/runs/6971643805?check_suite_focus=true