Error on tsvd(::Matrix{Double64})

[SamuelBadr]

Hey there,

would it be possible to support arbitrary types? As it stands this doesn't work:

julia> using TSVD

julia> using DoubleFloats

julia> a = rand(Double64, 4, 5)
4×5 Matrix{Double64}:
 0.04919379096293597  0.029652786425431454  0.027081051380154375  0.6350861122377742   0.5510473418841347
 0.733735967612336    0.6415795260533754    0.6656527330112074    0.6647302426142875   0.9267886977489933
 0.5170738341399638   0.9441092849553093    0.1405723138676932    0.41097554085638344  0.14776900362205803
 0.4750330510671744   0.8592283380698013    0.5907097170564828    0.12745449930369002  0.42578025724057467

julia> tsvd(a)
ERROR: SVD for lower triangular bidiagonal matrices isn't implemented yet.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:33
  [2] __svd!(B::LinearAlgebra.Bidiagonal{BigFloat, Vector{BigFloat}}, U::Matrix{BigFloat}, Vᴴ::Matrix{BigFloat}; tol::BigFloat, debug::Bool)
    @ GenericLinearAlgebra ~/.julia/packages/GenericLinearAlgebra/Bd8s0/src/svd.jl:196
  [3] _svd!(B::LinearAlgebra.Bidiagonal{BigFloat, Vector{BigFloat}}; tol::BigFloat, debug::Bool)
    @ GenericLinearAlgebra ~/.julia/packages/GenericLinearAlgebra/Bd8s0/src/svd.jl:232
  [4] #svd!#38
    @ ~/.julia/packages/GenericLinearAlgebra/Bd8s0/src/svd.jl:499 [inlined]
  [5] svd!
    @ ~/.julia/packages/GenericLinearAlgebra/Bd8s0/src/svd.jl:499 [inlined]
  [6] #svd#191
    @ /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/bidiag.jl:214 [inlined]
  [7] svd
    @ /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/bidiag.jl:214 [inlined]
  [8] biLanczos(A::Matrix{BigFloat}, nvals::Int64; maxiter::Int64, initvec::Vector{BigFloat}, tolconv::BigFloat, tolreorth::BigFloat, stepsize::Int64, debug::Bool)
    @ TSVD ~/.julia/packages/TSVD/q42gG/src/svd.jl:175
  [9] _tsvd(A::Matrix{BigFloat}, nvals::Int64; maxiter::Int64, initvec::Vector{BigFloat}, tolconv::BigFloat, tolreorth::BigFloat, stepsize::Int64, debug::Bool)
    @ TSVD ~/.julia/packages/TSVD/q42gG/src/svd.jl:236
 [10] #tsvd#7
    @ ~/.julia/packages/TSVD/q42gG/src/svd.jl:345 [inlined]
 [11] tsvd(A::Matrix{BigFloat}, nvals::Int64) (repeats 2 times)
    @ TSVD ~/.julia/packages/TSVD/q42gG/src/svd.jl:345
 [12] top-level scope
    @ REPL[6]:1

(The same thing happens with BigFloat, I just chose Double64 as an example because that's what I'd like to use.)

The error originates from GenericLinearAlgebra.jl because it expects an upper bidiagonal matrix and gets a lower one from TSVD.jl AFAICT. I'm not sure whether posting this issue in GenericLinearAlgebra.jl's repo would have been more appropriate.

Thanks in advance for any pointers!