Tridiagonal and UniformScaling are missing compatible operations

[ChrisRackauckas]

λ = 2
using LinearAlgebra # from the standard library, no install required
A = Tridiagonal(2:5,1:5,1:4)
A - λ*I

setindex! not defined for UnitRange{Int64}

Stacktrace:
 [1] error(::String, ::Type) at ./error.jl:42
 [2] error_if_canonical_setindex(::IndexLinear, ::UnitRange{Int64}, ::Int64) at ./abstractarray.jl:1006
 [3] setindex! at ./abstractarray.jl:997 [inlined]
 [4] setindex!(::Tridiagonal{Int64,UnitRange{Int64}}, ::Int64, ::Int64, ::Int64) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.0/LinearAlgebra/src/tridiag.jl:581
 [5] +(::Tridiagonal{Int64,UnitRange{Int64}}, ::UniformScaling{Int64}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.0/LinearAlgebra/src/uniformscaling.jl:117
 [6] -(::Tridiagonal{Int64,UnitRange{Int64}}, ::UniformScaling{Int64}) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.0/LinearAlgebra/src/uniformscaling.jl:96
 [7] top-level scope at In[48]:4

[mcognetta]

This seems to be due to the UnitRange rather than the structured matrix type.

julia> A = Tridiagonal(2:5,1:5,1:4)
5×5 Tridiagonal{Int64,UnitRange{Int64}}:
 1  1  ⋅  ⋅  ⋅
 2  2  2  ⋅  ⋅
 ⋅  3  3  3  ⋅
 ⋅  ⋅  4  4  4
 ⋅  ⋅  ⋅  5  5

julia> A-λ*I
ERROR: setindex! not defined for UnitRange{Int64}
Stacktrace:
 [1] error(::String, ::Type) at ./error.jl:42
 [2] error_if_canonical_setindex(::IndexLinear, ::UnitRange{Int64}, ::Int64) at ./abstractarray.jl:1006
 [3] setindex! at ./abstractarray.jl:997 [inlined]
 [4] setindex!(::Tridiagonal{Int64,UnitRange{Int64}}, ::Int64, ::Int64, ::Int64) at /home/mc/github/julia-dev/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/tridiag.jl:581
 [5] +(::Tridiagonal{Int64,UnitRange{Int64}}, ::UniformScaling{Int64}) at /home/mc/github/julia-dev/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/uniformscaling.jl:117
 [6] -(::Tridiagonal{Int64,UnitRange{Int64}}, ::UniformScaling{Int64}) at /home/mc/github/julia-dev/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/uniformscaling.jl:96
 [7] top-level scope at none:0

julia> B = Bidiagonal(1:5, 1:4, :U)
5×5 Bidiagonal{Int64,UnitRange{Int64}}:
 1  1  ⋅  ⋅  ⋅
 ⋅  2  2  ⋅  ⋅
 ⋅  ⋅  3  3  ⋅
 ⋅  ⋅  ⋅  4  4
 ⋅  ⋅  ⋅  ⋅  5

julia> B-λ*I
ERROR: setindex! not defined for UnitRange{Int64}
Stacktrace:
 [1] error(::String, ::Type) at ./error.jl:42
 [2] error_if_canonical_setindex(::IndexLinear, ::UnitRange{Int64}, ::Int64) at ./abstractarray.jl:1006
 [3] setindex! at ./abstractarray.jl:997 [inlined]
 [4] setindex!(::Bidiagonal{Int64,UnitRange{Int64}}, ::Int64, ::Int64, ::Int64) at /home/mc/github/julia-dev/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/bidiag.jl:125
 [5] +(::Bidiagonal{Int64,UnitRange{Int64}}, ::UniformScaling{Int64}) at /home/mc/github/julia-dev/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/uniformscaling.jl:117
 [6] -(::Bidiagonal{Int64,UnitRange{Int64}}, ::UniformScaling{Int64}) at /home/mc/github/julia-dev/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/uniformscaling.jl:96
 [7] top-level scope at none:0

julia> C = Bidiagonal(rand(5), rand(4), :U)
5×5 Bidiagonal{Float64,Array{Float64,1}}:
 0.687357  0.687688   ⋅         ⋅         ⋅      
  ⋅        0.52413   0.717214   ⋅         ⋅      
  ⋅         ⋅        0.875585  0.287643   ⋅      
  ⋅         ⋅         ⋅        0.67056   0.907939
  ⋅         ⋅         ⋅         ⋅        0.126001

julia> C-λ*I
5×5 Bidiagonal{Float64,Array{Float64,1}}:
 -1.31264   0.687688    ⋅          ⋅          ⋅      
   ⋅       -1.47587    0.717214    ⋅          ⋅      
   ⋅         ⋅        -1.12442    0.287643    ⋅      
   ⋅         ⋅          ⋅        -1.32944    0.907939
   ⋅         ⋅          ⋅          ⋅        -1.874

julia> D = Tridiagonal(rand(5,5))
5×5 Tridiagonal{Float64,Array{Float64,1}}:
 0.533607   0.98904    ⋅         ⋅         ⋅      
 0.0336893  0.952063  0.993883   ⋅         ⋅      
  ⋅         0.464622  0.406044  0.876364   ⋅      
  ⋅          ⋅        0.600339  0.8533    0.293575
  ⋅          ⋅         ⋅        0.205733  0.784922

julia> D-λ*I
5×5 Tridiagonal{Float64,Array{Float64,1}}:
 -1.46639     0.98904     ⋅          ⋅          ⋅      
  0.0336893  -1.04794    0.993883    ⋅          ⋅      
   ⋅          0.464622  -1.59396    0.876364    ⋅      
   ⋅           ⋅         0.600339  -1.1467     0.293575
   ⋅           ⋅          ⋅         0.205733  -1.21508

The fix is probably to promote UnitRange similarly to the following:

julia> D = Tridiagonal(rand(5,5))
5×5 Tridiagonal{Float64,Array{Float64,1}}:
 0.933716   0.971155   ⋅         ⋅         ⋅       
 0.0402409  0.811677  0.665386   ⋅         ⋅       
  ⋅         0.113584  0.272957  0.340441   ⋅       
  ⋅          ⋅        0.950946  0.877905  0.541269 
  ⋅          ⋅         ⋅        0.960005  0.0502889

julia> E = Tridiagonal(2:5,1:5,1:4)
5×5 Tridiagonal{Int64,UnitRange{Int64}}:
 1  1  ⋅  ⋅  ⋅
 2  2  2  ⋅  ⋅
 ⋅  3  3  3  ⋅
 ⋅  ⋅  4  4  4
 ⋅  ⋅  ⋅  5  5

julia> E+E
5×5 Tridiagonal{Int64,StepRange{Int64,Int64}}:
 2  2  ⋅   ⋅   ⋅
 4  4  4   ⋅   ⋅
 ⋅  6  6   6   ⋅
 ⋅  ⋅  8   8   8
 ⋅  ⋅  ⋅  10  10

julia> D+E
5×5 Tridiagonal{Float64,Array{Float64,1}}:
 1.93372  1.97115   ⋅        ⋅        ⋅     
 2.04024  2.81168  2.66539   ⋅        ⋅     
  ⋅       3.11358  3.27296  3.34044   ⋅     
  ⋅        ⋅       4.95095  4.8779   4.54127
  ⋅        ⋅        ⋅       5.96     5.05029

But it will have to be hardcoded (maybe?) since UniformScaling has no internal container type.

[ranocha]

Shall this be closed? The issue seems to be fixed on newer versions of Julia.

julia> versioninfo()
Julia Version 1.4.0-rc2.0
Commit b99ed72c95 (2020-02-24 16:51 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i7-8565U CPU @ 1.80GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-8.0.1 (ORCJIT, skylake)
Environment:
  JULIA_NUM_THREADS = 2

julia> λ = 2
2

julia> using LinearAlgebra # from the standard library, no install required

julia> A = Tridiagonal(2:5,1:5,1:4)
5×5 Tridiagonal{Int64,UnitRange{Int64}}:
 1  1  ⋅  ⋅  ⋅
 2  2  2  ⋅  ⋅
 ⋅  3  3  3  ⋅
 ⋅  ⋅  4  4  4
 ⋅  ⋅  ⋅  5  5

julia> A - λ*I
5×5 Tridiagonal{Int64,UnitRange{Int64}}:
 -1  1  ⋅  ⋅  ⋅
  2  0  2  ⋅  ⋅
  ⋅  3  1  3  ⋅
  ⋅  ⋅  4  2  4
  ⋅  ⋅  ⋅  5  3

[ChrisRackauckas]

It would probably be good to close with a test.

[ranocha]

Okay. I'll do that.