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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.10"
# dependencies = ["bornagain>=25,<26", "lmfit"]
# ///
"""
Fitting example: fit along slices
"""
import bornagain as ba
ba.require_versions("bornagain>=25,<26")
from bornagain import deg, nm, nm2
import lmfit
import numpy as np
def get_sample(P):
"""
Uncorrelated cylinders on a substrate, parameterized for fitting.
"""
substrate_color = (0.28, 0.57, 0.82)
particle_color = (0.86, 0.24, 0.18)
substrate_mat = ba.RefractiveMaterial("Substrate", substrate_color, 6e-6, 2e-8)
particle_mat = ba.RefractiveMaterial("Particle", particle_color, 6e-4, 2e-8)
particle = ba.Particle(particle_mat, ba.Cylinder(P["radius"], P["height"]))
particle_layer = ba.Layer(ba.Vacuum())
# Modest coverage keeps material averaging physical over the fit bounds.
particle_layer.deposit2D(ba.Dilute2D(1e-3/nm2, particle))
sample = ba.Sample()
sample.addLayer(particle_layer)
sample.addLayer(ba.Layer(substrate_mat))
return sample
def get_simulation(P):
"""
GISAS simulation for the parameterized cylinder sample.
"""
n = 101
beam = ba.Beam(1e8, 0.1*nm, 0.2*deg)
detector = ba.SphericalDetector(n, -1*deg, 1*deg, n, 0, 2*deg)
simulation = ba.ScatteringSimulation(beam, get_sample(P), detector)
return simulation
phi_slice_value = 0.0 # position of vertical slice in deg
alpha_slice_value = 0.2 # position of horizontal slice in deg
def closest_axis_index(axis, value):
centers = np.asarray(axis.binCenters())
return int(np.argmin(np.abs(centers - value)))
def data_slice(data, axis_index, fixed_index):
"""
Returns one horizontal or vertical detector slice as a 1D Datafield.
"""
data = data.plottableField()
values = (data.intensities()[fixed_index, :]
if axis_index == 0 else
data.intensities()[:, fixed_index])
axis = data.axis(axis_index)
scale = ba.ListScan(axis.axisLabel(), list(axis.binCenters()))
return ba.Datafield(ba.Frame(scale), values.tolist())
def slice_curves(experimental, simulated, axis_index, fixed_index):
"""
Returns measured and simulated Datafields for one detector slice.
"""
return [("Slice",
data_slice(experimental, axis_index, fixed_index),
data_slice(simulated, axis_index, fixed_index))]
def plot_slice(simulation, ax=None, *, context_data, axis_index, fixed_index,
title):
"""
Plots one measured and simulated detector slice.
"""
curves = slice_curves(
context_data, simulation, axis_index, fixed_index)
ba.plot_specular_curves(curves, ax=ax, ylabel="Intensity")
ax.set_title(title)
def get_masked_simulation(P):
"""
GISAS simulation with only one horizontal and one vertical slice active.
"""
n = 101
beam = ba.Beam(1e8, 0.1*nm, 0.2*deg)
sample = get_sample(P)
detector = ba.SphericalDetector(n, -1*deg, 1*deg, n, 0, 2*deg)
n_phi = detector.axis(0).size()
n_alpha = detector.axis(1).size()
mask = np.ones((n_alpha, n_phi), dtype=bool)
i_phi = closest_axis_index(detector.axis(0), phi_slice_value*deg)
i_alpha = closest_axis_index(detector.axis(1), alpha_slice_value*deg)
mask[:, i_phi] = False
mask[i_alpha, :] = False
detector.setMask(mask)
simulation = ba.ScatteringSimulation(beam, sample, detector)
return simulation
def fake_data():
"""
Generating "real" data by adding noise to the simulated data.
"""
# initial values which we will have to find later during the fit
P = {'radius': 5*nm, 'height': 10*nm}
simulation = get_simulation(P)
simulation.setBackground(ba.PoissonBackground(seed=0))
result = simulation.simulate()
return result.noisy(0.1, 0.1)
def get_plotters(exp_data):
"""
Creates the detector-map and slice plotters.
"""
i_phi = closest_axis_index(exp_data.axis(0), phi_slice_value*deg)
i_alpha = closest_axis_index(exp_data.axis(1), alpha_slice_value*deg)
norm = ba.intensity_norm(exp_data)
experiment_plotter = ba.FitPlotter(
ba.plot_masked_experimental,
context_data=exp_data,
norm=norm,
with_cb=True,
title="Experimental",
)
horizontal_slice_plotter = ba.FitPlotter(
plot_slice,
context_data=exp_data,
axis_index=0,
fixed_index=i_alpha,
title=f"Horizontal: alpha = {alpha_slice_value:g} deg",
)
vertical_slice_plotter = ba.FitPlotter(
plot_slice,
context_data=exp_data,
axis_index=1,
fixed_index=i_phi,
title=f"Vertical: phi = {phi_slice_value:g} deg",
)
return [
experiment_plotter,
horizontal_slice_plotter,
vertical_slice_plotter,
]
if __name__ == '__main__':
exp_data = fake_data()
exp_values = exp_data.intensities()
# Fit progress display
monitor = ba.FitMonitor(
get_plotters(exp_data),
ncols=2,
show_best=True,
max_fps=1,
printer=ba.Printer(every_nth=10),
live=True)
def residuals(P):
"""
Simulates and reports residuals; masked pixels contribute zero.
"""
sim_result = get_masked_simulation(P.valuesdict()).simulate()
residuals = ba.valid_pixel_residual(exp_values,
sim_result.intensities())
monitor.update(sim_result, P, residuals)
return residuals
P = lmfit.Parameters()
P.add("radius", value=6*nm, min=4*nm, max=8*nm)
P.add("height", value=9*nm, min=8*nm, max=12*nm)
result = lmfit.minimize(residuals, P, method="leastsq")
finalP = result.params.valuesdict()
# Recompute and report the simulation at the fitted parameters.
residuals(result.params)
# Render the just-reported evaluation as the final fit state.
monitor.render_final(result.params)
print(lmfit.fit_report(result))
ba.showSample3D(get_sample(finalP), sample_size=120*nm, seed=0)
ba.plt.show()
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