Vectorize a part of a huge matrix in C++

Question

I have a large matrix, side-length is about $n\geq 1000$. I need to do element-wise multiplication of this matrix with another matrix many, many times. I make this process by:

1. Vectorizing (through armadillo) this matrix, i.e., flattening it in a single array.
2. Splitting this array over many cores. Each core will take a part of this matrix and do its multiplication.

Now I realized that for Mathematical reasons, I only need the upper-triangular part of this matrix. How can I vectorize only the upper-triangular part and discard the other components of the matrix? Simply looping is not that good. Do I have any other options?

My matrices are Armadillo complex matrices of arma::cx_mat. And my current vectorization function is:

typedef double Real;
typedef std::vector<std::complex<Real> > VecType;
arma::cx_mat myMatrix;
//fill my matrix...
VecType  vectorizedMatrix = arma::conv_to<VecType>::from(myMatrix);

I find std::vector very useful, because I do element-wise multiplication very efficiently using standard algorithms with std::transform(), which is best optimized (AFAIK).

Answer 1

So I invented my own solution. Critique, suggestions are highly appreciated.

I learned that elements are stored in a matrix as column-major. So I assumed that using std::copy() with an iterator over a single column will just give consecutive elements, hence better speed.

Here's my solution:

template <typename T>
std::vector<T> vectorizeMatrix_upperTriangular_columnMajor(const arma::Mat<T>& mat)
{
    std::vector<T> output((mat.n_cols*(mat.n_cols-1))/2);
    typename arma::Mat<T>::const_iterator it = mat.begin() + mat.n_rows; //iterator at rows to skip in every step, starts at second column
    long toSkipInVec = 0;
    for(int i = 1; i < mat.n_cols; i++) //Starts with 1 to skip the diagonal
    {
        std::copy(it, it + i, output.begin() + toSkipInVec);
        toSkipInVec += i;
        it += mat.n_rows;
    }
    return output;
}