delta_fourier_transform_1d_1d

mdhelper.algorithm.accelerated.delta_fourier_transform_1d_1d(q: ndarray[float], r: ndarray[float]) → complex

Serial Numba-accelerated Fourier transform of a Dirac delta function involving two one-dimensional NumPy arrays \(\mathbf{q}\) and \(\mathbf{r}\), each with shape \((3,)\).

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

Parameters:

qnp.ndarray

First vector \(\mathbf{q}\).

Shape: \((3,)\).

rnp.ndarray

Second vector \(\mathbf{r}\).

Shape: \((3,)\).

Returns:

Fcomplex

Fourier transforms of the Dirac delta functions, \(\mathcal{F}[\delta(\mathbf{q}-\mathbf{r})]\).