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add overview to module docs

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Valentin Boettcher 2023-03-23 10:38:15 -04:00
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bandfit/bandfit.py
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@ -1,3 +1,19 @@
"""
This module provides the functionality to fit the band structure of
the long range SSH model to an experimentally measured two dimensional
image.
It is taylored to the specific case where the parameters ``a`` and
``b`` are close to each other.
The data can be loaded with :any:`load_data`. To detect the band
structure :any:`detect_bands` can be used. The result can be
visualized with :any:`plot_data_with_bands`.
To obtain the parameters of the band structure :any:`fit_to_bands` is
used. It's result can be visualized with
:any:`plot_band_with_error_funnel`.
"""
import numpy as np import numpy as np
import scipy as sc import scipy as sc
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
@ -182,13 +198,19 @@ def plot_data_with_bands(data, bands):
""" """
Plot the measured band structure ``data`` together with the output Plot the measured band structure ``data`` together with the output
of :any:`detect_bands`. of :any:`detect_bands`.
:returns: Pyplot figure and axis objects.
""" """
plt.matshow(data) fig, ax = plt.subplots()
ax.matshow(data)
ks = np.arange(data.shape[1]) ks = np.arange(data.shape[1])
plt.errorbar(ks, bands[:, 0], yerr=bands[:, 2], color="white") ax.errorbar(ks, bands[:, 0], yerr=bands[:, 2], color="white")
plt.errorbar(ks, bands[:, 1], yerr=bands[:, 3], color="white") ax.errorbar(ks, bands[:, 1], yerr=bands[:, 3], color="white")
return fig, ax
def candidate(k, c, d, a, δb, k_scale, k_shift): def candidate(k, c, d, a, δb, k_scale, k_shift):
@ -330,23 +352,25 @@ def fit_to_bands(
return (final_params, σ) return (final_params, σ)
def plot_error_funnel(p, σ, ks=None): def plot_band_with_error_funnel(p, σ, ks=None):
""" """
Plot the band structure given the paramters ``p = (a, b, c, d)`` Plot the band structure given the paramters ``p = (a, b, c, d)``
and their uncertainties ``σ`` for monomentum vales ``ks``. and their uncertainties ``σ`` for monomentum vales ``ks``.
""" """
fig, ax = plt.subplots()
ks = ks or np.linspace(-np.pi, np.pi, 1000) ks = ks or np.linspace(-np.pi, np.pi, 1000)
params = np.random.multivariate_normal(p, np.diag(σ), 2000) params = np.random.multivariate_normal(p, np.diag(σ), 2000)
energies = [] energies = []
for param in params: for param in params:
energies.append(energy(ks, *param)) energies.append(energy(ks, *param))
# plt.plot(ks, energy(ks, *param), color="gray", alpha=0.1)
energies = np.array(energies) energies = np.array(energies)
σ_e = np.std(energies, axis=0) σ_e = np.std(energies, axis=0)
mean = energy(ks, *p) mean = energy(ks, *p)
plt.plot(ks, mean, linewidth=2)
plt.fill_between(ks, mean - σ_e, mean + σ_e, alpha=0.2)
return mean, mean - σ_e, mean + σ_e ax.plot(ks, mean, linewidth=2)
ax.fill_between(ks, mean - σ_e, mean + σ_e, alpha=0.2)
return fig, ax