Eigen decomposition fails with Measurements

[BambOoxX]

Hello, I have attempted to use GenericLinearAlgebra along with Measurements but that seems to fail in a fresh environment.
See JuliaPhysics/Measurements.jl#189 for first analysis by @giordano.

The environment

Status `D:\bamboo\AppData\Local\Temp\jl_hvNm0T\Project.toml`
  [14197337] GenericLinearAlgebra v0.3.18
  [eff96d63] Measurements v2.14.0

The example

] add Measurements GenericLinearAlgebra
using LinearAlgebra, GenericLinearAlgebra, Measurements
Ar = rand(10,10) .± rand(10,10)
Ai = rand(10,10) .± rand(10,10)
A = Ar + im * Ai
eigvals(Ar) # fails
eigvals(A) # fails

The reproduced stacktrace

julia> eigvals(Ar)
ERROR: MethodError: no method matching Float64(::Measurement{Float64})
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:265
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:900
  Float64(::Irrational{:SQRT_HALF})
   @ Random irrationals.jl:251
  ...

Stacktrace:
  [1] givensAlgorithm(f::Measurement{Float64}, g::Measurement{Float64})
    @ LinearAlgebra D:\bamboo\AppData\Local\Programs\Julia-1.11.5\share\julia\stdlib\v1.11\LinearAlgebra\src\givens.jl:80
  [2] givens(f::Measurement{Float64}, g::Measurement{Float64}, i1::Int64, i2::Int64)
    @ LinearAlgebra D:\bamboo\AppData\Local\Programs\Julia-1.11.5\share\julia\stdlib\v1.11\LinearAlgebra\src\givens.jl:292
  [3] doubleShiftQR!(HH::Matrix{…}, τ::LinearAlgebra.Rotation{…}, shiftTrace::Measurement{…}, shiftDeterminant::Measurement{…}, istart::Int64, iend::Int64)
    @ GenericLinearAlgebra D:\bamboo\.julia\packages\GenericLinearAlgebra\jlOvW\src\eigenGeneral.jl:241
  [4] _schur!(H::GenericLinearAlgebra.HessenbergFactorization{…}; tol::Float64, shiftmethod::Symbol, maxiter::Int64)
    @ GenericLinearAlgebra D:\bamboo\.julia\packages\GenericLinearAlgebra\jlOvW\src\eigenGeneral.jl:161
  [5] _schur!
    @ D:\bamboo\.julia\packages\GenericLinearAlgebra\jlOvW\src\eigenGeneral.jl:89 [inlined]
  [6] _schur!
    @ D:\bamboo\.julia\packages\GenericLinearAlgebra\jlOvW\src\eigenGeneral.jl:182 [inlined]
  [7] _eigvals!
    @ D:\bamboo\.julia\packages\GenericLinearAlgebra\jlOvW\src\eigenGeneral.jl:281 [inlined]
  [8] eigvals!(A::Matrix{Measurement{Float64}}; sortby::typeof(LinearAlgebra.eigsortby), kwargs::@Kwargs{})
    @ GenericLinearAlgebra D:\bamboo\.julia\packages\GenericLinearAlgebra\jlOvW\src\eigenGeneral.jl:294
  [9] eigvals!
    @ D:\bamboo\.julia\packages\GenericLinearAlgebra\jlOvW\src\eigenGeneral.jl:285 [inlined]
 [10] eigvals(A::Matrix{Measurement{Float64}}; kws::@Kwargs{})
    @ LinearAlgebra D:\bamboo\AppData\Local\Programs\Julia-1.11.5\share\julia\stdlib\v1.11\LinearAlgebra\src\eigen.jl:343
 [11] eigvals(A::Matrix{Measurement{Float64}})
    @ LinearAlgebra D:\bamboo\AppData\Local\Programs\Julia-1.11.5\share\julia\stdlib\v1.11\LinearAlgebra\src\eigen.jl:343
 [12] top-level scope
    @ REPL[12]:1
Some type information was truncated. Use `show(err)` to see complete types.

The problem seems to be that GenericLinearAlgebra forwards Measurements to LinearAlgebra instead of standard float types, but that is not really helpful to solve the problem :)

[andreasnoack]

The problem seems to be that GenericLinearAlgebra forwards Measurements to LinearAlgebra instead of standard float types, but that is not really helpful to solve the problem :)

I'm not following. What is the alternative to computing the Givens rotations between the Measurements? I believe the root cause is JuliaLang/julia@7fb758a#r167343271

[stevengj]

Probably https://github.com/JuliaLang/LinearAlgebra.jl/blob/7b21cabb1e81b719e93ab612937c0ded809fbe6e/src/givens.jl#L80 should be zeropar = zero(onepar)

[andreasnoack]

@BambOoxX would you be able to try out that change and open a PR to LinearAlgebra.jl if it works?

[BambOoxX]

Sorry for the late reply. I'll try.