Data inspection and selection

Use these guides when you must prepare a cut or spectrum from measured coordinate ranges, follow a path through momentum space, or compare several slices.

Polygon masking

See Polygon masking to calculate a polygon from lattice parameters, apply it to a constant energy surface, and reproduce the result in Figure Composer.

Averaging a cut or spectrum over coordinate ranges

Prepare an energy-momentum cut by cropping its displayed coordinates and averaging over a finite ky window:

import erlab

cut = data.qsel(
    kx=slice(-0.3, 0.3),
    ky=0.3,
    ky_width=0.06,
    eV=slice(-0.25, 0.05),
)

To prepare a local EDC around one point in the momentum plane, average all points inside a radius stated in the same momentum units:

edc = data.qsel.around(0.06, kx=0.52, ky=0.3)

(Source code)

If the energy range is already selected, use qsel.mean to keep the mean energy as a scalar coordinate:

energy_window = data.sel(eV=slice(-0.025, 0.025))
constant_energy_map = energy_window.qsel.mean("eV")

Check the selected coordinate bounds and the number of averaged points before using the result. Use First notebook for the basic qsel sequence. A coordinate slice crops the data. A width averages the selected points. Interpolation estimates values on a new grid.

Extracting data along a momentum path

Define the path vertices in the coordinates of momentum_data, then select a step size in the same inverse-length units. This example follows Γ–M–K–Γ for the hexagonal model used by erlab.io.exampledata.generate_data():

import numpy as np

import erlab.analysis as era

lattice_constant = 6.97
high_symmetry_vertices = {
    "kx": [
        0.0,
        2 * np.pi / (np.sqrt(3) * lattice_constant),
        2 * np.pi / (np.sqrt(3) * lattice_constant),
        0.0,
    ],
    "ky": [0.0, 0.0, 2 * np.pi / (3 * lattice_constant), 0.0],
}
high_symmetry_cut = era.interpolate.slice_along_path(
    momentum_data,
    vertices=high_symmetry_vertices,
    step_size=0.005,
)

The figure below shows the Γ–M–K–Γ path on a constant energy surface and the interpolated energy–momentum cut. See high-symmetry cuts for the Python plotting code and Figure Composer steps.

(Source code)

The result uses path as the interpolation dimension and retains kx and ky as coordinates along that path. Confirm that the vertices follow the intended reciprocal- space trajectory before interpreting the result.

See erlab.analysis.interpolate.slice_along_path() for closed paths, dimension selection, and explicit sampling points.

Comparing slices from multidimensional data

Use erlab.plotting.plot_slices() to select and plot several coordinate values. Plot independent and shared intensity limits when you must choose between feature visibility and direct intensity comparison:

import matplotlib.pyplot as plt
import erlab.plotting as eplt

energies = [-0.4, -0.2, 0.0]
fig, axes = plt.subplots(
    2,
    3,
    figsize=(6.4, 4.0),
    layout="compressed",
    sharex=True,
    sharey=True,
)

for row in axes:
    eplt.plot_slices(
        [data],
        eV=energies,
        eV_width=0.05,
        axes=row,
        axis="image",
        gamma=0.5,
        annotate=False,
        cmap="Greys",
    )
    eplt.label_subplot_properties(row, values={"Eb": energies})

eplt.unify_clim(axes[1])
eplt.clean_labels(axes)
axes[0, 0].set_title("Independent intensity limits", loc="left")
axes[1, 0].set_title("Shared intensity limits", loc="left")

(Source code)

eV_width averages each slice over the stated energy width. Remove it when nearest- coordinate selection is required. The first row retains the automatic limit of each slice. erlab.plotting.unify_clim() applies one range to the second row. Use the shared range when intensity differences between slices must remain visible. Use independent limits when only feature positions must be compared and each panel needs its own contrast.

See erlab.plotting.plot_slices() for layout and normalization arguments.