`omatcopy` much slower than `copy` in OMP loop

I'm trying to use cblas_domatcopy to transpose large row-major matrices.

I'm finding that the function is slower than a simple loop of cblas_dcopy calls parallelized with OpenMP (with number of threads set to number of logical cores, otherwise OMP loop is much slower).

Function cblas_domatcopy appears to be especially slower when the inputs have more columns than rows - in this sense, in a dcopy loop, there's also a large timing difference according to whether the copies are by rows of the input or of the output, and I'm guessing that perhaps omatcopy always follows the same order.

(code is provided at the end of this post)

• Timings in seconds on an intel 12700H, average of 7 runs:

  • Input size: 100,000 x 5x000
    • OpenBLAS cblas_domatcopy: 3.12
    • OpenMP dcopy loop: 2.38
    • MKL MKL_Domatcopy: 1.26
  • Input size: 5,000 x 100,000
    • OpenBLAS cblas_domatcopy: 3.74
    • OpenMP dcopy loop: 1.23
    • MKL MKL_Domatcopy: 1.27

• Timings in seconds on an amd ryzen 7840HS, average of 7 runs:

  • Input size: 100,000 x 5x000
    • OpenBLAS cblas_domatcopy: 0.922
    • OpenMP dcopy loop: 0.586
    • MKL MKL_Domatcopy: 0.560
  • Input size: 5,000 x 100,000
    • OpenBLAS cblas_domatcopy: 1.12
    • OpenMP dcopy loop: 0.402
    • MKL MKL_Domatcopy: 0.516

OpenBLAS version: 0.3.26, OpenMP variant.

Code that I'm using for the OMP dcopy loop:

void transpose_mat(const double *A, const int nrows, const int ncols, double *B, int nthreads)
{
    if (nrows >= ncols)
    {
        #pragma omp parallel for schedule(static) num_threads(nthreads)
        for (int row = 0; row < nrows; row++)
            cblas_dcopy(ncols, A + (size_t)row*(size_t)ncols, 1, B + row, nrows);
    }
    
    else
    {
        #pragma omp parallel for schedule(static) num_threads(nthreads
        for (int col = 0; col < ncols; col++)
            cblas_dcopy(nrows, A + col, ncols, B + (size_t)col*(size_t)nrows, 1);
    }
}

Start with the cblas_domatcopy entry point and reproduce the supplied benchmarks on the two matrix shapes using OpenBLAS 0.3.26's OpenMP variant. Compare its behavior with the provided OpenMP cblas_dcopy loops, especially the row-versus-column traversal, and consider the issue addressed when the performance difference is explained and the affected cases are improved or documented.