`show` and `getindex` for matrix inversion between LowerTriangular and Bidiagonal never completes

[DanielVandH]

julia> using LazyBandedMatrices, FillArrays, Infinities, LazyArrays, ContinuumArrays

julia> using LazyBandedMatrices: Bidiagonal, LowerTriangular

julia> R = [Vcat(1.0, Zeros(∞)) LowerTriangular(Bidiagonal(Ones(∞), Ones(∞), :L))]; # without the Vcat, we get a method ambiguity bug instead

julia> R′ = Bidiagonal(Ones(∞), Ones(∞), :U);

julia> RR = R′ \ R; # it can be computed apparently, but once you show it..

julia> RR # never ends
\(ℵ₀×ℵ₀ Bidiagonal{Float64, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}} with indices OneToInf()×OneToInf(), hcat(vcat(Float64, ℵ₀-element Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}} with indices OneToInf()) with indices OneToInf(), ℵ₀×ℵ₀ LowerTriangular{Float64, Bidiagonal{Float64, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}} with indices OneToInf()×OneToInf()) with indices OneToInf()×OneToInf()) with indices OneToInf()×OneToInf():
Error showing value of type ApplyMatrix{Float64, typeof(\), Tuple{Bidiagonal{Float64, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}, ApplyArray{Float64, 2, typeof(hcat), Tuple{ApplyArray{Float64, 1, typeof(vcat), Tuple{Float64, Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}, LowerTriangular{Float64, Bidiagonal{Float64, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}}}}}}:
ERROR: InterruptException:
Stacktrace:
  [1] cache_filldata!(::LazyArrays.CachedArray{Float64, 2, Matrix{…}, Zeros{…}}, ::UnitRange{Int64}, ::Base.OneTo{Int64})
    @ LazyArrays C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\cache.jl:222
  [2] resizedata!(::ArrayLayouts.DenseColumnMajor, ::ArrayLayouts.ZerosLayout, ::LazyArrays.CachedArray{…}, ::Int64, ::Int64)
    @ LazyArrays C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\cache.jl:263
  [3] resizedata!
    @ C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\cache.jl:218 [inlined]
  [4] setindex!
    @ C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\cache.jl:82 [inlined]
  [5] Matrix{Float64}(A::Bidiagonal{Float64, Ones{Float64, 1, Tuple{…}}, Ones{Float64, 1, Tuple{…}}})
    @ LazyBandedMatrices C:\Users\User\.julia\packages\LazyBandedMatrices\59umZ\src\bidiag.jl:151
  [6] (Matrix)(A::Bidiagonal{Float64, Ones{Float64, 1, Tuple{…}}, Ones{Float64, 1, Tuple{…}}})
    @ LazyBandedMatrices C:\Users\User\.julia\packages\LazyBandedMatrices\59umZ\src\bidiag.jl:159
  [7] Array(A::Bidiagonal{Float64, Ones{Float64, 1, Tuple{…}}, Ones{Float64, 1, Tuple{…}}})
    @ LazyBandedMatrices C:\Users\User\.julia\packages\LazyBandedMatrices\59umZ\src\bidiag.jl:160
  [8] convert(::Type{Array}, a::Bidiagonal{Float64, Ones{Float64, 1, Tuple{…}}, Ones{Float64, 1, Tuple{…}}})
    @ Base .\array.jl:665
  [9] concretize(L::Bidiagonal{Float64, Ones{Float64, 1, Tuple{…}}, Ones{Float64, 1, Tuple{…}}})
    @ ArrayLayouts C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\ldiv.jl:52
 [10] concretize(L::Ldiv{ArrayLayouts.BidiagonalLayout{…}, LazyArrays.ApplyLayout{…}, Bidiagonal{…}, SubArray{…}})
    @ ArrayLayouts C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\ldiv.jl:53
 [11] _getindex(::Type{…}, L::Ldiv{…}, ::Tuple{…})
    @ ArrayLayouts C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\ldiv.jl:54
 [12] getindex(L::Ldiv{ArrayLayouts.BidiagonalLayout{…}, LazyArrays.ApplyLayout{…}, Bidiagonal{…}, SubArray{…}}, k::Int64)
    @ ArrayLayouts C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\ldiv.jl:51
 [13] getindex
    @ C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\linalg\inv.jl:103 [inlined]
 [14] getindex
    @ C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\lazyapplying.jl:254 [inlined]
 [15] getindex(L::ApplyMatrix{Float64, typeof(\), Tuple{Bidiagonal{…}, ApplyArray{…}}}, k::Int64, j::Int64)
    @ LazyArrays C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\linalg\inv.jl:180
 [16] isassigned(::ApplyMatrix{Float64, typeof(\), Tuple{Bidiagonal{…}, ApplyArray{…}}}, ::Int64, ::Int64)
    @ Base .\multidimensional.jl:1578
 [17] alignment(io::IOContext{…}, X::AbstractVecOrMat, rows::Vector{…}, cols::Vector{…}, cols_if_complete::Int64, cols_otherwise::Int64, sep::Int64, ncols::InfiniteCardinal{…})
    @ Base .\arrayshow.jl:68
 [18] _print_matrix(io::IOContext{…}, X::AbstractVecOrMat, pre::String, sep::String, post::String, hdots::String, vdots::String, ddots::String, hmod::Int64, vmod::Int64, rowsA::InfiniteArrays.InfUnitRange{…}, colsA::InfiniteArrays.InfUnitRange{…})
    @ Base .\arrayshow.jl:207
 [19] print_matrix(io::IOContext{…}, X::ApplyMatrix{…}, pre::String, sep::String, post::String, hdots::String, vdots::String, ddots::String, hmod::Int64, vmod::Int64)
    @ Base .\arrayshow.jl:171
 [20] print_matrix
    @ .\arrayshow.jl:171 [inlined]
 [21] print_array
    @ .\arrayshow.jl:358 [inlined]
 [22] show(io::IOContext{Base.TTY}, ::MIME{Symbol("text/plain")}, X::ApplyMatrix{Float64, typeof(\), Tuple{…}})
    @ Base .\arrayshow.jl:399
 [23] (::REPL.var"#55#56"{REPL.REPLDisplay{REPL.LineEditREPL}, MIME{Symbol("text/plain")}, Base.RefValue{Any}})(io::Any)
    @ REPL C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:273
 [24] with_repl_linfo(f::Any, repl::REPL.LineEditREPL)
    @ REPL C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:569
 [25] display(d::REPL.REPLDisplay, mime::MIME{Symbol("text/plain")}, x::Any)
    @ REPL C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:259
 [26] display
    @ C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:278 [inlined]
 [27] display(x::Any)
    @ Base.Multimedia .\multimedia.jl:340
 [28] #invokelatest#2
    @ .\essentials.jl:892 [inlined]
 [29] invokelatest
    @ .\essentials.jl:889 [inlined]
 [30] print_response(errio::IO, response::Any, show_value::Bool, have_color::Bool, specialdisplay::Union{…})
    @ REPL C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:315
 [31] (::REPL.var"#57#58"{REPL.LineEditREPL, Pair{Any, Bool}, Bool, Bool})(io::Any)
    @ REPL C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:284
 [32] with_repl_linfo(f::Any, repl::REPL.LineEditREPL)
    @ REPL C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:569
 [33] print_response(repl::REPL.AbstractREPL, response::Any, show_value::Bool, have_color::Bool)
    @ REPL C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:282
 [34] (::REPL.var"#do_respond#80"{…})(s::REPL.LineEdit.MIState, buf::Any, ok::Bool)
    @ REPL C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:911
 [35] #invokelatest#2
    @ .\essentials.jl:892 [inlined]
 [36] invokelatest
    @ .\essentials.jl:889 [inlined]
 [37] run_interface(terminal::REPL.Terminals.TextTerminal, m::REPL.LineEdit.ModalInterface, s::REPL.LineEdit.MIState)
    @ REPL.LineEdit C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\LineEdit.jl:2656
 [38] run_frontend(repl::REPL.LineEditREPL, backend::REPL.REPLBackendRef)
    @ REPL C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:1312
 [39] (::REPL.var"#62#68"{REPL.LineEditREPL, REPL.REPLBackendRef})()
    @ REPL C:\Users\User\.julia\juliaup\julia-1.10.3+0.x64.w64.mingw32\share\julia\stdlib\v1.10\REPL\src\REPL.jl:386
Some type information was truncated. Use `show(err)` to see complete types.

julia> RR[1, 1] # also can't access it
ERROR: InterruptException:
Stacktrace:
  [1] cache_filldata!(::LazyArrays.CachedArray{Float64, 2, Matrix{…}, Zeros{…}}, ::UnitRange{Int64}, ::Base.OneTo{Int64})
    @ LazyArrays C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\cache.jl:222
  [2] resizedata!(::ArrayLayouts.DenseColumnMajor, ::ArrayLayouts.ZerosLayout, ::LazyArrays.CachedArray{…}, ::Int64, ::Int64)
    @ LazyArrays C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\cache.jl:263
  [3] resizedata!
    @ C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\cache.jl:218 [inlined]
  [4] setindex!
    @ C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\cache.jl:82 [inlined]
  [5] Matrix{Float64}(A::Bidiagonal{Float64, Ones{Float64, 1, Tuple{…}}, Ones{Float64, 1, Tuple{…}}})
    @ LazyBandedMatrices C:\Users\User\.julia\packages\LazyBandedMatrices\59umZ\src\bidiag.jl:149
  [6] (Matrix)(A::Bidiagonal{Float64, Ones{Float64, 1, Tuple{…}}, Ones{Float64, 1, Tuple{…}}})
    @ LazyBandedMatrices C:\Users\User\.julia\packages\LazyBandedMatrices\59umZ\src\bidiag.jl:159
  [7] Array(A::Bidiagonal{Float64, Ones{Float64, 1, Tuple{…}}, Ones{Float64, 1, Tuple{…}}})
    @ LazyBandedMatrices C:\Users\User\.julia\packages\LazyBandedMatrices\59umZ\src\bidiag.jl:160
  [8] convert(::Type{Array}, a::Bidiagonal{Float64, Ones{Float64, 1, Tuple{…}}, Ones{Float64, 1, Tuple{…}}})
    @ Base .\array.jl:665
  [9] concretize(L::Bidiagonal{Float64, Ones{Float64, 1, Tuple{…}}, Ones{Float64, 1, Tuple{…}}})
    @ ArrayLayouts C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\ldiv.jl:52
 [10] concretize(L::Ldiv{ArrayLayouts.BidiagonalLayout{…}, LazyArrays.ApplyLayout{…}, Bidiagonal{…}, SubArray{…}})
    @ ArrayLayouts C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\ldiv.jl:53
 [11] _getindex(::Type{…}, L::Ldiv{…}, ::Tuple{…})
    @ ArrayLayouts C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\ldiv.jl:54
 [12] getindex(L::Ldiv{ArrayLayouts.BidiagonalLayout{…}, LazyArrays.ApplyLayout{…}, Bidiagonal{…}, SubArray{…}}, k::Int64)
    @ ArrayLayouts C:\Users\User\.julia\packages\ArrayLayouts\ccyJu\src\ldiv.jl:51
 [13] getindex
    @ C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\linalg\inv.jl:103 [inlined]
 [14] getindex
    @ C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\lazyapplying.jl:254 [inlined]
 [15] getindex(L::ApplyMatrix{Float64, typeof(\), Tuple{Bidiagonal{…}, ApplyArray{…}}}, k::Int64, j::Int64)
    @ LazyArrays C:\Users\User\.julia\packages\LazyArrays\JNdsG\src\linalg\inv.jl:180
 [16] top-level scope
    @ REPL[44]:1
Some type information was truncated. Use `show(err)` to see complete types.

[dlfivefifty]

This is implemented in InfiniteLinearAlgebra.jl:

julia> using InfiniteLinearAlgebra

julia> RR # never ends
\(ℵ₀×ℵ₀ Bidiagonal{Float64, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}} with indices OneToInf()×OneToInf(), hcat(vcat(Float64, ℵ₀-element Zeros{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}} with indices OneToInf()) with indices OneToInf(), ℵ₀×ℵ₀ LowerTriangular{Float64, Bidiagonal{Float64, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}, Ones{Float64, 1, Tuple{InfiniteArrays.OneToInf{Int64}}}}} with indices OneToInf()×OneToInf()) with indices OneToInf()×OneToInf()) with indices OneToInf()×OneToInf():
 1.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  …  
  ⋅   1.0  0.0  0.0  0.0  0.0  0.0  0.0     
  ⋅    ⋅   1.0  0.0  0.0  0.0  0.0  0.0     
  ⋅    ⋅    ⋅   1.0  0.0  0.0  0.0  0.0     
  ⋅    ⋅    ⋅    ⋅   1.0  0.0  0.0  0.0     
  ⋅    ⋅    ⋅    ⋅    ⋅   1.0  0.0  0.0  …  
  ⋅    ⋅    ⋅    ⋅    ⋅    ⋅   1.0  0.0     
  ⋅    ⋅    ⋅    ⋅    ⋅    ⋅    ⋅   1.0     
  ⋅    ⋅    ⋅    ⋅    ⋅    ⋅    ⋅    ⋅      
  ⋅    ⋅    ⋅    ⋅    ⋅    ⋅    ⋅    ⋅      
 ⋮                        ⋮              ⋱  

In the future this can be changed to extensions.