Add `conv(::StaticVector, ::StaticVector)`

[dlfivefifty]

This is a missing function, though I'm not sure how useful it is in a general setting.

[dlfivefifty]

Here's a quick-and-dirty implementation:

@generated function conv(x::SVector{N}, y::SVector{M}) where {N,M}
    NM = N+M-1
    quote
        convert(SVector{$NM}, DSP.conv(Vector(x), Vector(y)))
    end
end

[andyferris]

What is conv?

[andyferris]

OK, it's a convolution from DSP.jl.

Note that StaticArrays has zero dependencies and will probably remain that way. I'd suggest have DSP inherit from StaticArrays instead. When we sort out offset arrays, I can see such convolutions being potentially faster if one kernel is small by using static arrays (you can unroll one of the loops).

[dlfivefifty]

conv is equivalent to multiplication by a lower-triangular Toeplitz (constant diagonal) matrix, so probably just creating a Toeplitz SMatrix and multiplying will be close to optimally efficient.

My application is fairly narrow (calculating block sizes of the Kronecker product of block vectors) and the Q&D implementation suffices. I agree it's not worth adding a dependency. But if it's of use beyond this it might be worth putting somewhere.

[andyferris]

Right. This is where all the special structured arrays from LinearAlgebra and elsewhere need to be designed to be composable with other array types. In theory, I shouldn’t need to make a static toeplitz matrix if the usual toeplitz matrix can wrap a static vector for the values instead of a normal vector.

[dlfivefifty]

That’s in my plan for ToeplitzMatrices.jl but first in needs a major redesign https://github.com/JuliaMatrices/ToeplitzMatrices.jl/issues/36

[c42f]

This seems a bit specialized for StaticArrays so I think I'll close this.

It might be interesting to have some package implement conv between an SVector and a normal Vector via direct summation rather than the fft. But I think it would be most natural for DSP to depend on StaticArrays if that's desired. Or to use / create another package which does general stenciling operations.