lufact fails for Diagonal, Bidiagonal, and SymTridiagonal

[Sacha0]

lufact fails for Diagonal, Bidiagonal, and SymTridiagonal matrices. (I realize the former two are in factored form and LDLt is a better choice for SymTridiagonal.) Contrast with qrfact, which succeeds for all such types. (The difference seems to be that qrfact calls similar to construct necessary fully mutable containers, whereas lufact merely copies the input matrix. The fix may be as simple as replacing the copy with similar and an appropriate type computation.) Ref. #136. Best!

julia> VERSION
v"0.6.0-dev.979"

julia> lufact(Diagonal(ones(4)))
ERROR: MethodError: no method matching lufact!(::Diagonal{Float64}, ::Type{Val{true}})
Closest candidates are:
  lufact!{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64}}(::Union{Base.ReshapedArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2},SubArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2,A<:Union{Base.ReshapedArray{T,N,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray},I<:Tuple{Vararg{Union{Base.AbstractCartesianIndex,Colon,Int64,Range{Int64}},N}},L}}, ::Union{Type{Val{false}},Type{Val{true}}}) at linalg/lu.jl:16
  lufact!(::Union{Base.ReshapedArray{T,2,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray{T,2},SubArray{T,2,A<:Union{Base.ReshapedArray{T,N,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray},I<:Tuple{Vararg{Union{Base.AbstractCartesianIndex,Colon,Int64,Range{Int64}},N}},L}}, ::Union{Type{Val{false}},Type{Val{true}}}) at linalg/lu.jl:31
  lufact!{T}(::Tridiagonal{T}, ::Union{Type{Val{false}},Type{Val{true}}}) at linalg/lu.jl:261
 in lufact(::Diagonal{Float64}) at ./linalg/lu.jl:81

julia> lufact(Bidiagonal(fill(2, 4), ones(3), true))
ERROR: MethodError: no method matching lufact!(::Bidiagonal{Float64}, ::Type{Val{true}})
Closest candidates are:
  lufact!{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64}}(::Union{Base.ReshapedArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2},SubArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2,A<:Union{Base.ReshapedArray{T,N,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray},I<:Tuple{Vararg{Union{Base.AbstractCartesianIndex,Colon,Int64,Range{Int64}},N}},L}}, ::Union{Type{Val{false}},Type{Val{true}}}) at linalg/lu.jl:16
  lufact!(::Union{Base.ReshapedArray{T,2,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray{T,2},SubArray{T,2,A<:Union{Base.ReshapedArray{T,N,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray},I<:Tuple{Vararg{Union{Base.AbstractCartesianIndex,Colon,Int64,Range{Int64}},N}},L}}, ::Union{Type{Val{false}},Type{Val{true}}}) at linalg/lu.jl:31
  lufact!{T}(::Tridiagonal{T}, ::Union{Type{Val{false}},Type{Val{true}}}) at linalg/lu.jl:261
 in lufact(::Bidiagonal{Float64}) at ./linalg/lu.jl:81

julia> lufact(SymTridiagonal(fill(2, 4), ones(3)))
ERROR: MethodError: no method matching lufact!(::SymTridiagonal{Float64}, ::Type{Val{true}})
Closest candidates are:
  lufact!{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64}}(::Union{Base.ReshapedArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2},SubArray{T<:Union{Complex{Float32},Complex{Float64},Float32,Float64},2,A<:Union{Base.ReshapedArray{T,N,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray},I<:Tuple{Vararg{Union{Base.AbstractCartesianIndex,Colon,Int64,Range{Int64}},N}},L}}, ::Union{Type{Val{false}},Type{Val{true}}}) at linalg/lu.jl:16
  lufact!(::Union{Base.ReshapedArray{T,2,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray{T,2},SubArray{T,2,A<:Union{Base.ReshapedArray{T,N,A<:DenseArray,MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N}}},DenseArray},I<:Tuple{Vararg{Union{Base.AbstractCartesianIndex,Colon,Int64,Range{Int64}},N}},L}}, ::Union{Type{Val{false}},Type{Val{true}}}) at linalg/lu.jl:31
  lufact!{T}(::Tridiagonal{T}, ::Union{Type{Val{false}},Type{Val{true}}}) at linalg/lu.jl:261
 in lufact(::SymTridiagonal{Float64}) at ./linalg/lu.jl:81

[andyferris]

Also, the matrices in StaticArrays.jl fail for lufact. Besides the inconsistent use of similar, I'm also see a problem that the LU container won't accept a vector container other than Vector, which seems too specific (compare with Eig).

[andreasnoack]

For most of the problems mentioned here, I think that using similar would be sufficient. It wouldn't help for the problems that @andyferris mentions.