Uncatchable LAPACKexception in infinite Cholesky

[TSGut]

Related to JuliaApproximation/SemiclassicalOrthogonalPolynomials.jl#68, I have a workaround for the problem described therein but it relies on being able to tell when a matrix is not positive definite, the standard test for that is to just run Cholesky. The plan is to try cholesky raw, if it fails we can perturb a bit.

But:

When an infinite dimensional Cholesky decomposition fails (due to positive definiteness) it crashes in a strange uncatchable way. Here is an example:

julia> using ClassicalOrthogonalPolynomials

julia> P = Normalized(Legendre())
Normalized(Legendre())

julia> x = axes(P,1)
Inclusion(-1.0..1.0 (Chebyshev))

julia> W = Symmetric(P \ ((1.02 .-x).^300 .* P))
ℵ₀×ℵ₀ Symmetric{Float64, ClassicalOrthogonalPolynomials.Clenshaw{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Base.OneTo{Int64}}, true}, LazyArrays.BroadcastVector{Float64, typeof(inv), Tuple{LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{LazyArrays.ApplyArray{Float64, 1, typeof(vcat), Tuple{Float64, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyBandedMatrices.SymTridiagonal{Float64, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}} with indices OneToInf()×OneToInf():
  1.35259e89  -2.32708e89   2.96419e89  -3.43737e89   3.79437e89  -4.05639e89   4.2357e89   …  
 -2.32708e89   4.00384e89  -5.10048e89   5.91548e89  -6.53102e89   6.9836e89   -7.29428e89     
  2.96419e89  -5.10048e89   6.49866e89  -7.5391e89    8.32659e89  -8.90761e89   9.3089e89      
 -3.43737e89   5.91548e89  -7.5391e89    8.74967e89  -9.66882e89   1.03505e90  -1.08255e90     
  3.79437e89  -6.53102e89   8.32659e89  -9.66882e89   1.06922e90  -1.14563e90   1.1995e90      
 -4.05639e89   6.9836e89   -8.90761e89   1.03505e90  -1.14563e90   1.22887e90  -1.28838e90  …  
  4.2357e89   -7.29428e89   9.3089e89   -1.08255e90   1.1995e90   -1.28838e90   1.35292e90     
 -4.34104e89   7.47803e89  -9.54941e89   1.11157e90  -1.23319e90   1.32663e90  -1.39568e90     
  4.37975e89  -7.54744e89   9.64499e89  -1.1239e90    1.24865e90  -1.34564e90   1.41867e90     
  ⋮                                                                ⋮                        ⋱  

julia> U = try 
               cholesky(W).U
           catch
               1
           end
ℵ₀×ℵ₀ UpperTriangular{Float64, InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrices.BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, ClassicalOrthogonalPolynomials.Clenshaw{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Base.OneTo{Int64}}, true}, LazyArrays.BroadcastVector{Float64, typeof(inv), Tuple{LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{LazyArrays.ApplyArray{Float64, 1, typeof(vcat), Tuple{Float64, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyBandedMatrices.SymTridiagonal{Float64, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}}} with indices OneToInf()×OneToInf():
ERROR: LAPACKException(1)
Stacktrace:
  [1] chklapackerror
    @ ~/Documents/Backends/julia-1.8.2/share/julia/stdlib/v1.8/LinearAlgebra/src/lapack.jl:41 [inlined]
  [2] pbtrf!(uplo::Char, m::Int64, kd::Int64, A::SubArray{Float64, 2, Matrix{Float64}, Tuple{UnitRange{Int64}, UnitRange{Int64}}, false})
    @ BandedMatrices ~/.julia/packages/BandedMatrices/nTq9x/src/lapack.jl:215
  [3] banded_chol!(#unused#::BandedMatrices.BandedColumns{ArrayLayouts.DenseColumnMajor}, A::SubArray{Float64, 2, BandedMatrices.BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, Tuple{UnitRange{Int64}, UnitRange{Int64}}, false}, #unused#::Type{UpperTriangular})
    @ BandedMatrices ~/.julia/packages/BandedMatrices/nTq9x/src/symbanded/BandedCholesky.jl:4
  [4] banded_chol!
    @ ~/.julia/packages/BandedMatrices/nTq9x/src/symbanded/BandedCholesky.jl:68 [inlined]
  [5] partialcholesky!(F::InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrices.BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, ClassicalOrthogonalPolynomials.Clenshaw{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Base.OneTo{Int64}}, true}, LazyArrays.BroadcastVector{Float64, typeof(inv), Tuple{LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{LazyArrays.ApplyArray{Float64, 1, typeof(vcat), Tuple{Float64, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyBandedMatrices.SymTridiagonal{Float64, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}}, n::Int64)
    @ InfiniteLinearAlgebra ~/.julia/packages/InfiniteLinearAlgebra/bvY1F/src/infcholesky.jl:27
  [6] getindex
    @ ~/.julia/packages/InfiniteLinearAlgebra/bvY1F/src/infcholesky.jl:40 [inlined]
  [7] getindex
    @ ~/Documents/Backends/julia-1.8.2/share/julia/stdlib/v1.8/LinearAlgebra/src/triangular.jl:228 [inlined]
  [8] isassigned(::UpperTriangular{Float64, InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrices.BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, ClassicalOrthogonalPolynomials.Clenshaw{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Base.OneTo{Int64}}, true}, LazyArrays.BroadcastVector{Float64, typeof(inv), Tuple{LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{LazyArrays.ApplyArray{Float64, 1, typeof(vcat), Tuple{Float64, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyBandedMatrices.SymTridiagonal{Float64, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}}}, ::Int64, ::Int64)
    @ Base ./abstractarray.jl:565
  [9] alignment(io::IOContext{Base.TTY}, X::AbstractVecOrMat, rows::Vector{Int64}, cols::Vector{Int64}, cols_if_complete::Int64, cols_otherwise::Int64, sep::Int64, ncols::Infinities.InfiniteCardinal{0})
    @ Base ./arrayshow.jl:68
 [10] _print_matrix(io::IOContext{Base.TTY}, X::AbstractVecOrMat, pre::String, sep::String, post::String, hdots::String, vdots::String, ddots::String, hmod::Int64, vmod::Int64, rowsA::InfiniteArrays.InfUnitRange{Int64}, colsA::InfiniteArrays.InfUnitRange{Int64})
    @ Base ./arrayshow.jl:207
 [11] print_matrix(io::IOContext{Base.TTY}, X::UpperTriangular{Float64, InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrices.BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, ClassicalOrthogonalPolynomials.Clenshaw{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Base.OneTo{Int64}}, true}, LazyArrays.BroadcastVector{Float64, typeof(inv), Tuple{LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{LazyArrays.ApplyArray{Float64, 1, typeof(vcat), Tuple{Float64, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyBandedMatrices.SymTridiagonal{Float64, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}}}, pre::String, sep::String, post::String, hdots::String, vdots::String, ddots::String, hmod::Int64, vmod::Int64) (repeats 2 times)
    @ Base ./arrayshow.jl:171
 [12] print_array
    @ ./arrayshow.jl:358 [inlined]
 [13] show(io::IOContext{Base.TTY}, #unused#::MIME{Symbol("text/plain")}, X::UpperTriangular{Float64, InfiniteLinearAlgebra.AdaptiveCholeskyFactors{Float64, BandedMatrices.BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, ClassicalOrthogonalPolynomials.Clenshaw{Float64, SubArray{Float64, 1, Vector{Float64}, Tuple{Base.OneTo{Int64}}, true}, LazyArrays.BroadcastVector{Float64, typeof(inv), Tuple{LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{LazyArrays.ApplyArray{Float64, 1, typeof(vcat), Tuple{Float64, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}, LazyBandedMatrices.SymTridiagonal{Float64, FillArrays.Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(sqrt), Tuple{LazyArrays.BroadcastVector{Float64, typeof(*), Tuple{LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}, LazyArrays.BroadcastVector{Float64, typeof(/), Tuple{InfiniteArrays.InfStepRange{Float64, Float64}, InfiniteArrays.InfStepRange{Int64, Int64}}}}}}}}}}})
    @ Base ./arrayshow.jl:399
 [14] (::REPL.var"#43#44"{REPL.REPLDisplay{REPL.LineEditREPL}, MIME{Symbol("text/plain")}, Base.RefValue{Any}})(io::Any)
    @ REPL ~/Documents/Backends/julia-1.8.2/share/julia/stdlib/v1.8/REPL/src/REPL.jl:267
 [15] with_repl_linfo(f::Any, repl::REPL.LineEditREPL)
    @ REPL ~/Documents/Backends/julia-1.8.2/share/julia/stdlib/v1.8/REPL/src/REPL.jl:521
 [16] display(d::REPL.REPLDisplay, mime::MIME{Symbol("text/plain")}, x::Any)
    @ REPL ~/Documents/Backends/julia-1.8.2/share/julia/stdlib/v1.8/REPL/src/REPL.jl:260
 [17] display(d::REPL.REPLDisplay, x::Any)
    @ REPL ~/Documents/Backends/julia-1.8.2/share/julia/stdlib/v1.8/REPL/src/REPL.jl:272
 [18] display(x::Any)
    @ Base.Multimedia ./multimedia.jl:328
 [19] #invokelatest#2
    @ ./essentials.jl:729 [inlined]
 [20] invokelatest
    @ ./essentials.jl:726 [inlined]
 [21] (::VSCodeServer.var"#66#70"{Bool, Bool, Bool, Module, String, Int64, Int64, String, VSCodeServer.ReplRunCodeRequestParams})()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.38.2/scripts/packages/VSCodeServer/src/eval.jl:199
 [22] withpath(f::VSCodeServer.var"#66#70"{Bool, Bool, Bool, Module, String, Int64, Int64, String, VSCodeServer.ReplRunCodeRequestParams}, path::String)
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.38.2/scripts/packages/VSCodeServer/src/repl.jl:249
 [23] (::VSCodeServer.var"#65#69"{Bool, Bool, Bool, Module, String, Int64, Int64, String, VSCodeServer.ReplRunCodeRequestParams})()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.38.2/scripts/packages/VSCodeServer/src/eval.jl:155
 [24] hideprompt(f::VSCodeServer.var"#65#69"{Bool, Bool, Bool, Module, String, Int64, Int64, String, VSCodeServer.ReplRunCodeRequestParams})
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.38.2/scripts/packages/VSCodeServer/src/repl.jl:38
 [25] (::VSCodeServer.var"#64#68"{Bool, Bool, Bool, Module, String, Int64, Int64, String, VSCodeServer.ReplRunCodeRequestParams})()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.38.2/scripts/packages/VSCodeServer/src/eval.jl:126
 [26] with_logstate(f::Function, logstate::Any)
    @ Base.CoreLogging ./logging.jl:511
 [27] with_logger
    @ ./logging.jl:623 [inlined]
 [28] (::VSCodeServer.var"#63#67"{VSCodeServer.ReplRunCodeRequestParams})()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.38.2/scripts/packages/VSCodeServer/src/eval.jl:225
 [29] #invokelatest#2
    @ ./essentials.jl:729 [inlined]
 [30] invokelatest(::Any)
    @ Base ./essentials.jl:726
 [31] macro expansion
    @ ~/.vscode/extensions/julialang.language-julia-1.38.2/scripts/packages/VSCodeServer/src/eval.jl:34 [inlined]
 [32] (::VSCodeServer.var"#61#62")()
    @ VSCodeServer ./task.jl:484

julia> U = try 
               cholesky(Symmetric(W[1:100,1:100])).U
           catch
               1
           end
1

julia> 

It's strange because it looks to me like it doesn't realize an error occured and instead it loads the error into the cholesky factor. The finite dimensional case works.