add specialized methods for Triangular * Triangular

[kleinschmidt]

Adds specialized methods so that products of two AbstractTriangulars from SMatrixs results in another SMatrix (or a triangular, if both are upper/lower).

This partially fixes #508 because the AbstractMatrix converter for a Cholesky falls back on U'U, which now returns an SMatrix instead of a normal Matrix.

[kleinschmidt]

Also, when looking at the code it seems like a lot of the specialized *_mul_* methods for triangulars are dead code since they're not exported or used anywhere else in the package as far as I can tell. AFAIK coverage is still borked right now so there's no way to see if they're actually being tested but might be worth taking them out if they're not used?

[kleinschmidt]

I haven't done systematic benchmarking but this gives you the kind of performance gains you'd expect:

julia> @btime $U * $U
  299.686 ns (2 allocations: 176 bytes)
3×3 UpperTriangular{Float64,Array{Float64,2}}:
 0.00598455  0.0774304  0.14636   
  ⋅          0.336431   0.521002  
  ⋅           ⋅         0.00217786

julia> @btime $SU * $SU
  3.618 ns (0 allocations: 0 bytes)
3×3 UpperTriangular{Float64,SArray{Tuple{3,3},Float64,2,9}}:
 0.00598455  0.0774304  0.14636   
  ⋅          0.336431   0.521002  
  ⋅           ⋅         0.00217786

julia> @btime $U * $L
  290.427 ns (1 allocation: 160 bytes)
3×3 Array{Float64,2}:
 0.331205   0.402724  0.0182264 
 0.720176   1.04825   0.0387971 
 0.0376679  0.039958  0.00217786

julia> @btime $SU * $SL
  4.327 ns (0 allocations: 0 bytes)
3×3 SArray{Tuple{3,3},Float64,2,9}:
 0.331205   0.402724  0.0182264 
 0.720176   1.04825   0.0387971 
 0.0376679  0.039958  0.00217786

[andyferris]

Do you want a LineNumberNode? If not you could just do code = Expr(:block) instead.

[kleinschmidt]

I was just blindly copying the code from the rest of this file; I don't know enough to know whether I should have a preference one way or the other.

[andyferris]

OK... let's change them all to Expr(:block), then. You'll get a relevant line number from the final quote anyway.

[kleinschmidt]

I can do that but won't get to it until later today; feel free to make the change yourself in the mean time if you'd rather.

[andyferris]

Sweet :)

[kleinschmidt]

Should be good to go now, I've replaced all the quote ends in the triangular methods with Expr(:block)s