convert to banded matrix types from AbstractMatrixes

[jishnub]

After this, the following work:

julia> M = diagm(0=>1:4, -1=>1:3)
4×4 Matrix{Int64}:
 1  0  0  0
 1  2  0  0
 0  2  3  0
 0  0  3  4

julia> convert(Bidiagonal, M)
4×4 Bidiagonal{Int64, Vector{Int64}}:
 1  ⋅  ⋅  ⋅
 1  2  ⋅  ⋅
 ⋅  2  3  ⋅
 ⋅  ⋅  3  4

julia> convert(Tridiagonal, M)
4×4 Tridiagonal{Int64, Vector{Int64}}:
 1  0  ⋅  ⋅
 1  2  0  ⋅
 ⋅  2  3  0
 ⋅  ⋅  3  4

julia> M = diagm(0=>1:4, -1=>1:3, 1=>1:3)
4×4 Matrix{Int64}:
 1  1  0  0
 1  2  2  0
 0  2  3  3
 0  0  3  4

julia> convert(SymTridiagonal, M)
4×4 SymTridiagonal{Int64, Vector{Int64}}:
 1  1  ⋅  ⋅
 1  2  2  ⋅
 ⋅  2  3  3
 ⋅  ⋅  3  4

These parallel the analogous convert method for Diagonal that already exists. The method for Bidiagonal detects the zero band and automatically chooses the uplo accordingly. This fixes the currently broken behavior, where the uplo was not provided to the constructor:

julia> convert(Bidiagonal, M)
ERROR: MethodError: no method matching Bidiagonal(::Matrix{Int64})

[dkarrasch]

Does this work (in all cases) when the converted-to type has a different eltype? Like implicit eltype promotion?

[jishnub]

Should work now after generalizing the constructor.

julia> M = diagm(0=>fill(3,4), 1=>fill(3,3))
4×4 Matrix{Int64}:
 3  3  0  0
 0  3  3  0
 0  0  3  3
 0  0  0  3

julia> using FillArrays

julia> f = Fill(Int8(4), 3);

julia> convert(Bidiagonal{eltype(f)}, M)
4×4 Bidiagonal{Int8, Vector{Int8}}:
 3  3  ⋅  ⋅
 ⋅  3  3  ⋅
 ⋅  ⋅  3  3
 ⋅  ⋅  ⋅  3

julia> convert(Bidiagonal{eltype(f), typeof(f)}, M)
4×4 Bidiagonal{Int8, Fill{Int8, 1, Tuple{Base.OneTo{Int64}}}}:
 3  3  ⋅  ⋅
 ⋅  3  3  ⋅
 ⋅  ⋅  3  3
 ⋅  ⋅  ⋅  3

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 91.90%. Comparing base (b464203) to head (6f4b663).
Report is 17 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1212      +/-   ##
==========================================
+ Coverage   91.88%   91.90%   +0.01%     
==========================================
  Files          34       34              
  Lines       15374    15386      +12     
==========================================
+ Hits        14127    14141      +14     
+ Misses       1247     1245       -2     

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[jishnub]

Gentle bump