Label QRCompactWY.T as Triangular

[jiahao]

Fixes JuliaLang/LinearAlgebra.jl#122

This PR currently does fix the original issue, but in order to do so, I had to reorder the way things are loaded in LinAlg so that Triangular in triangular.jl was defined before QRCompactWY in factorization.jl. This now throws the ambiguity warning:

linalg.jl
Warning: New definition 
    A_mul_Bc could not show value of type Tuple at linalg/factorization.jl:370
is ambiguous with: 
    A_mul_Bc could not show value of type Tuple at linalg/triangular.jl:185.
To fix, define 
    A_mul_Bc could not show value of type Tuple
before the new definition.

when building Julia.

Would appreciate any help to resolve the warning.

[ViralBShah]

Rebased this on master.

[ViralBShah]

This warning looks a little puzzling. Cc: @JeffBezanson @andreasnoackjensen

Also, I wonder if it should be AbstractMatrix instead of AbstractArray for the overloaded multiplication with QR objects at line 370 of factorization.jl.

[JeffBezanson]

Fixed the warning, but still have this test failure:

exception on 2: ERROR: `QRCompactWYQ{S}` has no method matching QRCompactWYQ{S}(::Array{Float32,2}, ::Triangular{Float32,Array{Float32,2},:U,false})
 in getindex at linalg/factorization.jl:203
 in anonymous at no file:115
 in runtests at /home/jeff/src/julia2/julia/test/testdefs.jl:5
 in anonymous at multi.jl:847
 in run_work_thunk at multi.jl:613
 in anonymous at task.jl:847
while loading linalg1.jl, in expression starting on line 25

Should QRCompactWYQ.T also be Triangular?

[jiahao]

Should QRCompactWYQ.T also be Triangular?

Yes

[andreasnoack]

Is it enough to specify Triangular{S} when the type has four parameters? If yes, why? Regarding the AbstractArray, it might be because the signature predates the definition of AbstractVecOrMat.

[ViralBShah]

It should be ok to specify Triangular{S}, just like we often do only Array{T}. Good to know that we can replace the AbstractArray with AbstracVecOrMat.