PAOFLOW.utils.get_R_grid_fft#

Functions#

get_R_grid_fft(data_controller, nr1, nr2, nr3)

Build the real-space lattice grid for FFT-based Hamiltonian operations.

Module Contents#

PAOFLOW.utils.get_R_grid_fft.get_R_grid_fft(data_controller, nr1, nr2, nr3)[source]#

Build the real-space lattice grid for FFT-based Hamiltonian operations.

Parameters:

  • data_controller (DataController) – Object providing data_arrays. Required array: a_vectors (shape (3, 3)), the primitive lattice vectors in units of the lattice constant.

  • nr1 (int) – Number of grid points along the first lattice vector.

  • nr2 (int) – Number of grid points along the second lattice vector.

  • nr3 (int) – Number of grid points along the third lattice vector.

Returns:

Adds the following keys to data_controller.data_arrays:

  • R : np.ndarray, shape (nr1*nr2*nr3, 3) — Cartesian coordinates of each real-space grid point in units of the lattice constant, centred around the origin (i.e. components folded into \([-0.5, 0.5)\)).

  • Rfft : np.ndarray, shape (nr1, nr2, nr3, 3) — same vectors on the 3-D grid layout, used as multiplicative factors in the FFT gradient and curvature routines.

  • idx : np.ndarray, shape (nr1, nr2, nr3), int — linear index mapping the 3-D grid position to a row in R.

  • R_wght : np.ndarray, shape (nr1*nr2*nr3,) — uniform weights, all set to 1.0.

Return type:

None

Notes

Grid coordinates are generated in reduced (crystal) units as \((i/nr_1, j/nr_2, k/nr_3)\) and folded into \([-0.5, 0.5)\) by subtracting 1 when the component is \(\geq 0.5\). The Cartesian position is then

\[\mathbf{R}_{ijk} = \tilde{R}_x \, nr_1 \, \mathbf{a}_1 + \tilde{R}_y \, nr_2 \, \mathbf{a}_2 + \tilde{R}_z \, nr_3 \, \mathbf{a}_3\]

where \(\tilde{R}_{x,y,z}\) are the folded reduced coordinates and \(\mathbf{a}_{1,2,3}\) are the rows of a_vectors.