abtem.magnetism.pauli

Module Contents

Functions

apply_A_xy_dot_nabla_xy	Compute the action of the operator $A_{xy} cdot nabla_{xy}$ on the wave functions using the central difference gradient.
central_difference_gradient_cbc	Compute the gradient of a 2D array using central differences with constant boundary conditions and Numba.
central_difference_gradient_pbc	Compute the gradient of a 2D array using central differences with periodic boundary conditions and Numba.

API

abtem.magnetism.pauli.apply_A_xy_dot_nabla_xy(...)

Compute the action of the operator $A_{xy} cdot nabla_{xy}$ on the wave functions using the central difference gradient.

Parameters:

• A (ndarray) – Vector field of shape (2, N, M) representing the operator A.

• wave_functions (ndarray) – Array of shape (…, N, M) representing the wave functions.

• sampling (two floats) – Spacing between points in the x and y directions.

Returns:

result – Result of the operation $A cdot nabla_{xy} psi$.

Return type:

ndarray

abtem.magnetism.pauli.central_difference_gradient_cbc(...)

Compute the gradient of a 2D array using central differences with constant boundary conditions and Numba.

Parameters:

• X (ndarray) – Array of shape (…, N, M) where the last two dimensions are the 2D grid.

• dx (float) – Spacing between points in the x direction.

• dy (float) – Spacing between points in the y direction.

Returns:

• grad_x (numpy.ndarray) – Gradient of X with respect to x.

• grad_y (numpy.ndarray) – Gradient of X with respect to y.

abtem.magnetism.pauli.central_difference_gradient_pbc(...)

Compute the gradient of a 2D array using central differences with periodic boundary conditions and Numba.

Parameters:

• X (ndarray) – Array of shape (…, N, M) where the last two dimensions are the 2D grid.

• dx (float) – Spacing between points in the x direction.

• dy (float) – Spacing between points in the y direction.

Returns:

• grad_x (numpy.ndarray) – Gradient of X with respect to x.

• grad_y (numpy.ndarray) – Gradient of X with respect to y.