`batched_mul!` doesn't support arrays of dimension larger than 3

[ZhaoFancy]

Motivation and description

On the other hand, batch_mul supports.

Possible Implementation

No response

[AntonOresten]

I looked into this. Here's a possible implementation that reshapes the input arrays (referencing the same data):

function batched_mul!(C::AbstractArray{T,N}, A::AbstractArray{<:Any,N}, B::AbstractArray{<:Any,N},
        α::Number=one(T), β::Number=zero(T)) where {T,N}
    batch_size = size(C)[3:end]
    @assert batch_size == size(A)[3:end] "batch size has to be the same for arrays."
    @assert batch_size == size(B)[3:end] "batch size has to be the same for arrays."
    
    C2 = reshape(C, size(C,1), size(C,2), :)
    A2 = reshape(A, size(A,1), size(A,2), :)
    B2 = reshape(B, size(B,1), size(B,2), :)
    
    batched_mul!(C2, A2, B2, α, β)
    return C
end

julia> A = randn(30, 40, 30, 60);

julia> B = randn(40, 50, 30, 60);

julia> C = similar(A, 30, 50, 30, 60);

julia> @btime batched_mul(A, B);
  7.785 ms (101 allocations: 20.61 MiB)

julia> @btime batched_mul!(C, A, B);
  6.969 ms (98 allocations: 12.88 KiB)