generic_matvecmul fails for some non-scalar element type and adjoint combinations

[JasonPries]

Here is a super stripped down MWE.

In the example below, I would expect M'*x to return a Vector{Float64} equivalent to [2.0]. But it looks like the fact that the matrix elements themselves should be adjoint is lost somewhere along the way to generic_matvecmul, which attempts straight multiplication of two vectors, rather than taking their inner product.

julia> M = [[[1.0]];;]
1×1 Matrix{Vector{Float64}}:
 [1.0]

julia> x = [[[2.0]];]
1-element Vector{Vector{Float64}}:
 [2.0]

julia> M'*x
ERROR: MethodError: no method matching *(::Vector{Float64}, ::Vector{Float64})
Closest candidates are:
  *(::Any, ::Any, ::Any, ::Any...) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/base/operators.jl:655
  *(::StridedMatrix{T}, ::StridedVector{S}) where {T<:Union{Float32, Float64, ComplexF32, ComplexF64}, S<:Real} at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:44
  *(::StridedVecOrMat, ::Adjoint{<:Any, <:LinearAlgebra.LQPackedQ}) at /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/lq.jl:266
  ...
Stacktrace:
 [1] generic_matvecmul!(C::Vector{Union{}}, tA::Char, A::Matrix{Vector{Float64}}, B::Vector{Vector{Float64}}, _add::LinearAlgebra.MulAddMul{true, true, Bool, Bool})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:745
 [2] mul!
   @ /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:129 [inlined]
 [3] mul!
   @ /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:275 [inlined]
 [4] *(adjA::Adjoint{Adjoint{Float64, Vector{Float64}}, Matrix{Vector{Float64}}}, x::Vector{Vector{Float64}})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:113
 [5] top-level scope
   @ REPL[152]:1

In contrast, these three other similar operations, seem to work correctly:

julia> M'*M
1×1 Matrix{Float64}:
 1.0

julia> x'*x
4.0

julia> N = [[[1.0]'];;]
1×1 Matrix{Adjoint{Float64, Vector{Float64}}}:
 [1.0;;]

julia> N*x
1-element Vector{Float64}:
 2.0

julia> versioninfo()
Julia Version 1.7.2
Commit bf53498635 (2022-02-06 15:21 UTC)
Platform Info:
  OS: macOS (x86_64-apple-darwin19.5.0)
  CPU: Intel(R) Core(TM) i7-9750H CPU @ 2.60GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-12.0.1 (ORCJIT, skylake)

[KristofferC]

#26008 (comment) is the same issue I think. I made a halfhearted try to fix it in #42715 but it seems that PR is incomplete.