Multiplication with triangular arrays of (static) arrays.

[mschauer]

I have problems with matrix multiplication by a triangular array of (static) arrays:

julia> L*Z
ERROR: No precise constructor for StaticArrays.SArray{Tuple{2},Float64,1,2} found. Length of input was 4.
Stacktrace:
 [1] copy!(::IndexLinear, ::Array{StaticArrays.SArray{Tuple{2},Float64,1,2},2}, ::IndexLinear, ::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) at ./abstractarray.jl:656
 [2] convert(::Type{LowerTriangular{StaticArrays.SArray{Tuple{2},Float64,1,2},S} where S<:(AbstractArray{T,2} where T)}, ::LowerTriangular{StaticArrays.SArray{Tuple{2,2},Float64,2,4},Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}}) at ./linalg/triangular.jl:26
 [3] *(::LowerTriangular{StaticArrays.SArray{Tuple{2,2},Float64,2,4},Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}}, ::Array{StaticArrays.SArray{Tuple{2},Float64,1,2},1}) at ./linalg/triangular.jl:1605

Here

julia> L
4×4 LowerTriangular{StaticArrays.SArray{Tuple{2,2},Float64,2,4},Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}}:
 [0.0952057 0.0; 0.0 0.0952057]            ⋅                       …          ⋅                 
 [-4.09297 0.0; 0.0 -4.09297]      [8.78973 0.0; 0.0 8.78973]                 ⋅                 
 [0.00972564 0.0; 0.0 0.00972564]  [0.0408945 0.0; 0.0 0.0408945]             ⋅                 
 [3.35741 0.0; 0.0 3.35741]        [-7.48714 0.0; 0.0 -7.48714]       [4.98334 0.0; 0.0 4.98334]

and Z is accordingly a 4-element Array{StaticArrays.SArray{Tuple{2},Float64,1,2},1}
Note that this works:

julia> full(L)*Z
4-element Array{StaticArrays.SArray{Tuple{2},Float64,1,2},1}:
 [-0.00945207, 0.000834093]
 [98.2233, -51.3031]       
 [0.463661, -0.241061]     
 [-133.872, 67.4155]       

and that chol! and naivesub! are already supported, so this should be supported perhaps as well.

[andreasnoack]

This is an interesting case. We are assuming that we can promote the elements of L and Z to the same type but that is of course not possible when the elements are matrices and vectors. We convert to a common element type more aggressively for the triangular multiplication code to avoid excessive specialization of _generic_matmatmul! but we'll have to be more careful. In short, the issue is

julia> A = fill(@SMatrix(ones(2,2)), 1, 1);

julia> x = fill(@SVector(ones(2)), 1);

julia> convert(AbstractMatrix{typeof(A[1,1]*x[1])}, A)
ERROR: No precise constructor for StaticArrays.SArray{Tuple{2},Float64,1,2} found. Length of input was 4.
Stacktrace:
 [1] copy!(::IndexLinear, ::Array{StaticArrays.SArray{Tuple{2},Float64,1,2},2}, ::IndexLinear, ::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) at ./abstractarray.jl:656
 [2] convert(::Type{AbstractArray{StaticArrays.SArray{Tuple{2},Float64,1,2},2}}, ::Array{StaticArrays.SArray{Tuple{2,2},Float64,2,4},2}) at ./abstractarray.jl:836

[jishnub]

This appears to be fixed on a recent master:

julia> A = fill(@SMatrix(ones(2,2)), 4, 4);

julia> L = LowerTriangular(A)
4×4 LowerTriangular{SMatrix{2, 2, Float64, 4}, Matrix{SMatrix{2, 2, Float64, 4}}}:
 [1.0 1.0; 1.0 1.0]          ⋅           …          ⋅         
 [1.0 1.0; 1.0 1.0]  [1.0 1.0; 1.0 1.0]             ⋅         
 [1.0 1.0; 1.0 1.0]  [1.0 1.0; 1.0 1.0]             ⋅         
 [1.0 1.0; 1.0 1.0]  [1.0 1.0; 1.0 1.0]     [1.0 1.0; 1.0 1.0]

julia> Z = fill(@SVector(ones(2)), 4)
4-element Vector{SVector{2, Float64}}:
 [1.0, 1.0]
 [1.0, 1.0]
 [1.0, 1.0]
 [1.0, 1.0]

julia> L * Z
4-element Vector{SVector{2, Float64}}:
 [2.0, 2.0]
 [4.0, 4.0]
 [6.0, 6.0]
 [8.0, 8.0]