Efficient iteration for tensor dot product - alternatives to splatting

[Alex Williams]

I'm trying to code an efficient implementation of the n-mode tensor product. Basically, this amounts to taking a dot product between a vector (b) and the mode-n fibers of a higher-order Array. For example, the mode-3 product of a 4th order array is:

```

C[i,j,k] = dot(A[i,j,:,k], b)

```

After iterating over all (i,j,k). Doing this for any arbitrary `A` and `n` can be achieved by the function below. But I believe it is slower than necessary due to the use of the splatting operator (`...`). Any ideas for making this faster?

```julia

"""

    B = tensordot(A, b, n)

Multiply N-dimensional array A by vector b along mode n. For inputs

size(A) = (I_1,...,I_n,...,I_N), and length(x) = (I_n), the output is

a (N-1)-dimensional array with size(B) = (I_1,...,I_n-1,I_n+1,...,I_N)

formed by taking the vector dot product of b and the mode-n fibers

of B.

"""

function tensordot{T,N}(A::Array{T,N}, b::Vector{T}, n::Integer)

    I = size(A)

    @assert I[n] == length(b)

    D = I[setdiff(1:N,n)]

    K = [ 1:d for d in D ]

    # preallocate result

    

    C = Array(T,D...)

    # do multiplication

    for i in product(K...)

        C[i...] = dot(b, vec(A[i[1:(n-1)]...,:,i[n:end]...]))

    end

    return C

end

```

Thanks all,

-- Alex

[Tim Holy]

I'd try TensorOperations.jl or AxisAlgorithms.jl

Best,
--Tim