No method `eigen(::Tridiagonal)`

[carstenbauer]

julia> using LinearAlgebra

julia> eigen(Tridiagonal(rand(10,10)))
ERROR: MethodError: no method matching eigen(::Tridiagonal{Float64,Array{Float64,1}})
Closest candidates are:
  eigen(::AbstractArray{TA,2}, ::AbstractArray{TB,2}) where {TA, TB} at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.0\LinearAlgebra\src\eigen.jl:382
  eigen(::SymTridiagonal{T,V} where V<:AbstractArray{T,1}) where T at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.0\LinearAlgebra\src\tridiag.jl:201
  eigen(::SymTridiagonal{T,V} where V<:AbstractArray{T,1}, ::UnitRange) where T at C:\cygwin\home\Administrator\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.0\LinearAlgebra\src\tridiag.jl:205

Shouldn't this either fallback to a generic method (my opinion) or error in a more meaningful way?

Similar to #551

[andreasnoack]

You typically only end up with a Tridiagonal if you really try to and have good reasons to do so. It's when you want to exploit an efficient solver which in this case will be \. There is no specialized tridiagonal eigensolver (except that the matrix is already in lower Hessenberg form) so a no method error is not that unreasonable. Silenty converting to Array is an option but might give the false impression that there is an efficient solver.

I think that in Julia, no methods errors is something you'd have to live with. The alternative is to add fallback methods telling that the method isn't implemented which is exactly what a no method error is. Of course, the error message could then be made more informative but 1) it is quite a few custom error messages we'd have to add and 2) it can be difficult to know exactly what to propose as an alternative if the error is defined for an abstract type.

How did you end up with the Tridiagonal?

[stevengj]

It would be reasonable to convert this to a Hessenberg type and then solve it that way, if only we had an eigensolver for Hessenberg matrices (#31738 #858). It would be faster than converting it to a dense matrix and calling eigen.

[ViralBShah]

➜  ~ julia
               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.11.3 (2025-01-21)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

julia> using LinearAlgebra

julia> eigen(Tridiagonal(rand(10,10)))

Eigen{Float64, Float64, Matrix{Float64}, Vector{Float64}}
values:
10-element Vector{Float64}:
 -0.5518968596743832
 -0.530301321282996
 -0.100459759939088
  0.17837510842068138
  0.2842060884884628
  0.5319629461684828
  0.5957947711540806
  0.9184112242520165
  1.2991892571485828
  1.6595411992292717
vectors:
10×10 Matrix{Float64}:
  0.000937616   0.00236401  -0.00348234  …   0.0144229   -1.38976e-5
 -0.00240747   -0.00597689   0.00607527      0.0116428   -2.03494e-5
  0.0554076     0.133839    -0.060162        0.30587     -0.000763249
 -0.165293     -0.390756     0.0965035       0.669069    -0.00246959
  0.216023      0.49941     -0.0660451       0.643308    -0.00357256
 -0.128964     -0.187647    -0.387867    …   0.178159    -0.0153713
  0.260969      0.0508932    0.891013        0.107119    -0.128394
 -0.495117      0.374369    -0.122943       -0.0193758   -0.742977
  0.667883     -0.544524    -0.0533278      -0.0307796   -0.643742
 -0.383394      0.324784     0.142661       -0.00795698  -0.129776