Usage

Installation

To use magpack, first install it using pip:

(.venv)$ pip install magpack

Examples

magpack contains tools for:

• loading and saving data in formats such as .mat, .ovf and .vtk (magpack.io)

• performing vector operations (magpack.vectorop, see Vector Operations section)

• calculating and evaluating scalar and vector field rotations (magpack.rotations, see Rotations section)

• removing image distortions, coloring complex arrays (e.g. Fourier transforms) and evaluating image resolutions using Fourier shell correlation (magpack.image_utils)

Vector Operations

magpack provides vector operations that help analyse both simulations and reconstructions. The convention used here is such that index 0 corresponds to vector components, such that a vector field \(\vec{m} = (m_x,\,m_y,\,m_z)\) is created by combining the three constituent scalar fields os shape (nx, ny, nz)

vector_field = np.stack([mx, my, mz])

thus the vector_field variable will have shape (3, nx, ny, nz). Operations that are not specific to 3D, (e.g. curl) are generalized for M-component fields for N-dimensions (M, N1, N2, ..., Nn)

Some of the available operations include:

• Gradient, \(\nabla f\) magpack.vectorop.scalar_gradient()

• Divergence, \(\mathbf{\nabla} \cdot \mathbf{v}\) magpack.vectorop.divergence()

• Curl, \(\mathbf{\nabla} \times \mathbf{v}\) magpack.vectorop.curl()

• Laplacian, \(\nabla^2 \times f\) magpack.vectorop.scalar_laplacian()

• Vector Laplacian, \(\mathbf{\nabla} \mathbf{v}\) magpack.vectorop.vector_laplacian()

• Vorticity, \(\frac{1}{8\pi}\epsilon_{abc}\epsilon_{ijk}m_{i}\partial_{b}m_{j}\partial_{c}m_{k}\) magpack.vectorop.vorticity()

Rotations

magpack.rotations provides functions for rotating scalar and vector fields. It can also be used to calculate rotation matrices for different 3D imaging geometries such as tomography and laminography. For arbitrary rotation operations, the function magpack.rotations.eul2rot() can be used.

In tomographic imaging (assuming the incident beam is along the z axis), the sample is first tilted and then rotated from 0° to 180° about an axis perpendicular to the propagation of the beam. A sequence of rotation matrices describing this operation can be obtained using either of the two functions

angles = np.linspace(0, 179, 180)
rot = magpack.rotations.tomo_rot(angles, 30)
rot_eul = magpack.rotations.eul2rot('yz', angles, 30)

Both functions return the same matrices, but magpack.rotations.eul2rot() allows for more control over the order of operations and axes. The convention employed here, using the example yz, is such that the tilting (z rotation by 30°) is performed first, followed by the y rotation (from 0° to 179°). This is similar to matrix multiplication \(\mathbf{R}_y(\theta) \mathbf{R}_z(\phi) \vec{m}\) where \(\vec{m}\) represents a vector field.