delta_fourier_transform_sum

mdcraft.analysis.structure.delta_fourier_transform_sum(qs: ndarray[float], rs: ndarray[float]) → ndarray[complex]

Evaluates the Fourier transforms of Dirac delta functions involving all possible combinations of multiple one-dimensional NumPy arrays \(\mathbf{q}\) and \(\mathbf{r}\), each with shape \((3,)\), summed over all \(\mathbf{r}\).

\[\sum_\mathbf{r}\mathcal{F}[\delta(\mathbf{q}-\mathbf{r})] =\sum_\mathbf{r}\exp(i\mathbf{q}\cdot\mathbf{r})\]

Parameters:

qsnp.ndarray

Multiple vectors \(\mathbf{q}\).

Shape: \((N_q,\,3)\).

rsnp.ndarray

Multiple vectors \(\mathbf{r}\).

Shape: \((N_r,\,3)\).

Returns:

Fnp.ndarray

Fourier transforms of the Dirac delta functions, summed over all \(\mathbf{r}\).

Shape: \((N_q,)\).