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Do you have in mind a way to compute the sum (LaTeX)
R_{i,j,k} = \sum_{l=0}^{2} J_{i,j,l+3k} v_{i,j,l}
obviously vectorised. This may sound like an equivalent of
c = np.einsum('ij(l + 3k),ijl->ijk', j, v)
where of course the notation 'ij(l + 3k),ijl->ijk' is not accepted by einsum.
I tri...