cholfact and bkfact fail for non-<:StridedMatrix types

[Sacha0]

Similar to #18970, cholfact and bkfact fail for matrices that are not subtypes of StridedMatrix. Contrast with qrfact, which succeeds for many more matrix types. (The difference seems to be that qrfact has a fallback that gracefully handles <:AbstractArrays more generally. Fixing this may be as simple as adding such ~five-line fallbacks for bkfact and cholfact.) Best!

julia> VERSION
v"0.6.0-dev.979"

julia> bkfact(SymTridiagonal(fill(2, 4), ones(3)))
ERROR: MethodError: no method matching bkfact(::SymTridiagonal{Float64})
Closest candidates are:
  bkfact(::Union{Hermitian{T,S},Symmetric{T,S}}) at linalg/symmetric.jl:183
  bkfact{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}}) at linalg/bunchkaufman.jl:72
  bkfact{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}}, ::Symbol) at linalg/bunchkaufman.jl:72
  ...

(Yes, LDLt would be better for [edit: positive- or quasi-definite] SymTridiagonals.) (Edited to include cholfact.)

[tkelman]

LDLt would be better for SymTridiagonal

Many indefinite cases won't necessarily admit a diagonal-D factorization, will they? Though I think once you need Bunch-Kaufman pivoting then you can't necessarily remain within a fixed number of subdiagonals unless you use the more recent banded retraction factorization, IIRC.

[Sacha0]

Many indefinite cases won't necessarily admit a diagonal-D factorization, will they? Though I think once you need Bunch-Kaufman pivoting then you can't necessarily remain within a fixed number of subdiagonals unless you use the more recent banded retraction factorization, IIRC.

Good point --- I had only the positive- and quasi-definite cases in mind. Best!