Bug in svdvals

[andreasvarga]

Although the matrix B1 below is generated in my opinion with the wrong bandwiths, the equality with B is still satisfied. However, the function svdvals fails on B1, with an obviously wrong error message.

julia> B = BandedMatrix(1=> 1:3,0=>zeros(4))
4×4 BandedMatrix{Float64} with bandwidths (0, 1):
 0.0  1.0   ⋅    ⋅
  ⋅   0.0  2.0   ⋅
  ⋅    ⋅   0.0  3.0
  ⋅    ⋅    ⋅   0.0

julia> B1 = BandedMatrix(1=> 1.:3.)
4×4 BandedMatrix{Float64} with bandwidths (-1, 1):
  ⋅   1.0   ⋅    ⋅
  ⋅    ⋅   2.0   ⋅
  ⋅    ⋅    ⋅   3.0
  ⋅    ⋅    ⋅    ⋅

julia> B == B1
true

julia> svdvals(B)
4-element Vector{Float64}:
 3.0
 2.0
 1.0
 0.0

julia> svdvals(B1)
 ** On entry to DGBBRD parameter number  5 had an illegal value
ERROR: ArgumentError: invalid argument #5 to LAPACK call
Stacktrace:
 [1] chklapackerror
   @ C:\Users\Andreas\.julia\juliaup\julia-1.11.4+0.x64.w64.mingw32\share\julia\stdlib\v1.11\LinearAlgebra\src\lapack.jl:38 [inlined]
 [2] gbbrd!(vect::Char, m::Int64, n::Int64, ncc::Int64, kl::Int64, ku::Int64, ab::Matrix{Float64}, d::Vector{Float64}, e::Vector{Float64}, Q::Matrix{Float64}, Pt::Matrix{Float64}, C::Matrix{Float64}, work::Vector{Float64})       
   @ BandedMatrices C:\Users\Andreas\.julia\packages\BandedMatrices\KJZ2p\src\lapack.jl:187
 [3] _bidiagonalize!(A::BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}}, M::BandedMatrices.BandedColumns{ArrayLayouts.DenseColumnMajor})
   @ BandedMatrices C:\Users\Andreas\.julia\packages\BandedMatrices\KJZ2p\src\banded\BandedMatrix.jl:828
 [4] bidiagonalize!
   @ C:\Users\Andreas\.julia\packages\BandedMatrices\KJZ2p\src\banded\BandedMatrix.jl:846 [inlined]
 [5] svdvals!
   @ C:\Users\Andreas\.julia\packages\BandedMatrices\KJZ2p\src\banded\BandedMatrix.jl:849 [inlined]
 [6] svdvals(A::BandedMatrix{Float64, Matrix{Float64}, Base.OneTo{Int64}})
   @ BandedMatrices C:\Users\Andreas\.julia\packages\BandedMatrices\KJZ2p\src\banded\BandedMatrix.jl:850
 [7] top-level scope
   @ REPL[72]:1

Moreover, for both cases the implementation of svdvals should recognize that the matrix is already bidiagonal, which obviously doesn't happen.