WIP: Support Hessenberg matrices

[jiahao]

This is a woefully incomplete stub toward supporting Hessenberg matrices (upper/lower triangular matrices with an extra nonzero sub/super-diagonal) in Julia.

Currently the only thing implemented is a LAPACK.hsein wrapper, which needs to be tested.

[andreasnoack]

Maybe we wan't to think of the Hessenberg matrix type together with a SymTridiagonalFactorization type (or maybe even a Factorization{SymTridiagonal}). Right now we have a Hessenberg factorization and a SymTridiagonal matrix type.

[jiahao]

Yes, I think we'll want both.

Ref: JuliaLang/LinearAlgebra.jl#99

[vtjnash]

Current status of this PR seems to be given by JuliaLang/LinearAlgebra.jl#99:

tkelman commented on Aug 11, 2015

Not really, the current Hessenberg is a QR-related factorization type. #7965 implements a little more of the lapack bindings for a Hessenberg matrix type, but is about a year out of date.

edit: amazingly there's apparently no conflict there, but it needs tests and updating for #8734 and probably a few other changes.

[andreasnoack]

This is from before the migration to standard libraries to it can't really be rebased so it would be easier to start over.