psf_trigonometric

mdcraft.analysis.structure.psf_trigonometric(qrs1: ndarray[float], qrs2: ndarray[float]) → ndarray[float]

Computes the partial structure factors given two two-dimensional NumPy arrays, each containing \(\mathbf{q}\cdot\mathbf{r}\), using the trigonometric form.

\[\frac{NS_{\alpha\beta}(q)}{2-\delta_{\alpha\beta}} =\left\langle \sum_{j=1}^{N_\alpha}\cos{(\mathbf{q}\cdot\mathbf{r}_j)} \sum_{k=1}^{N_\beta}\cos{(\mathbf{q}\cdot\mathbf{r}_k)} +\sum_{j=1}^{N_\alpha}\sin{(\mathbf{q}\cdot\mathbf{r}_j)} \sum_{k=1}^{N_\beta}\sin{(\mathbf{q}\cdot\mathbf{r}_k)} \right\rangle\]

Parameters:

qrs1np.ndarray

First set of inner products \(\mathbf{q}\cdot\mathbf{r}_j\).

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

qrs2np.ndarray

Second set of inner products \(\mathbf{q}\cdot\mathbf{r}_k\).

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

Returns:

ssfnp.ndarray

Partial structure factors.

Shape: \((N_q,)\).