Question

I’m fairly new to C, not having much need to anything faster than python for most of my research. However, it turns out that recent work I’ve been doing required the computation of fairly large vectors/matrices, and there therefore a C+MPI solution might be in order.

Mathematically speaking, the task is very simple. I have a lot of vectors of dimensionality ~40k and wish to compute the Kronecker Product of selected pairs of these vectors, and then sum these kronecker products.

The question is, how to do this efficiently? Is there anything wrong with the following structure of code, using for loops, or obtain the effect?

The function kron described below passes vectors A and B of lengths vector_size, and computes their kronecker product, which it stores in C, a vector_size*vector_size matrix.

void kron(int *A, int *B, int *C, int vector_size) {

    int i,j;

    for(i = 0; i < vector_size; i++) {
        for (j = 0; j < vector_size; j++) {
            C[i*vector_size+j] = A[i] * B[j];
        }
    }
    return;
}

This seems fine to me, and certainly (if I’ve not made some silly syntax error) produce the right result, but I have a sneaking suspicion that embedded for loops is not optimal. If there’s another way I should be going about this, please let me know. Suggestions welcome.

I thank you for you patience and any advice you may have. Once again, I’m very inexperienced with C, but Googling around has brought me little joy for this query.

Answer 1

For double-precision vectors (single-precision and complex are similar), you can use the BLAS routine DGER (rank-one update) or similar to do the products one-at-a-time, since they are all on vectors. How many vectors are you multiplying? Remember that adding a bunch of vector outer products (which you can treat the Kronecker products as) ends up as a matrix-matrix multiplication, which BLAS’s DGEMM can handle efficiently. You might need to write your own routines if you truly need integer operations, though.