Question : Finding the bandwidth of a matrix

[338rajesh]

I am trying to get the bandwidth of a matrix using BandedMatrices.jl in the following manner.

julia> using BandedMatrices

julia> A =  [
           2.0 5.0 5.0 0.0 0.0 0.0
           2.0 5.0 5.0 0.0 0.0 0.0
           2.0 5.0 5.0 0.0 0.0 0.0
           0.0 0.0 0.0 8.0 0.0 0.0
           0.0 0.0 0.0 0.0 8.0 0.0
           0.0 0.0 0.0 0.0 0.0 8.0];

julia> println(bandwidths(A))
(5, 5)

It is giving (5,5) while I am expecting (3,3).

Please let me know the right procedure for getting the bandwidth of a given matrix.

Thanks in advance.

[jishnub]

julia> using SparseArrays

julia> sparse(A)
6×6 SparseMatrixCSC{Float64, Int64} with 12 stored entries:
 2.0  5.0  5.0   ⋅    ⋅    ⋅ 
 2.0  5.0  5.0   ⋅    ⋅    ⋅ 
 2.0  5.0  5.0   ⋅    ⋅    ⋅ 
  ⋅    ⋅    ⋅   8.0   ⋅    ⋅ 
  ⋅    ⋅    ⋅    ⋅   8.0   ⋅ 
  ⋅    ⋅    ⋅    ⋅    ⋅   8.0

julia> sparse(A) |> bandwidths
(2, 2)

Why are you expecting (3,3) btw?

[338rajesh]

yeah, I agree it must be (2, 2) not (3,3).

It is working for SparseArray type but not with dense matrices as I have mentioned in the question.
I am not sure, if it is intentionally designed to work in that way for any advantage.

I confirm the same behavior with the new version of the package.

[dlfivefifty]

bandwidths should be “fast”. Checking every entry is an O(n^2) operation

[MikaelSlevinsky]

How can you get the bandwidths of a dense matrix without checking for the zeros?

[dlfivefifty]

bandwidths is about structural zeros not actual zeros. So you just assume it’s full

[MikaelSlevinsky]

Maybe it needs info in the docs because, for example, rank of a dense matrix is slow, based on svdvals, but it could have been "generically" full. Contrast that to rank of a LowRankMatrix which is fast and structural by the type.

[dlfivefifty]

If you make a PR to the docs I’ll merge it