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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.10"
# dependencies = ["bornagain>=25,<26", "lmfit"]
# ///
"""
Basic GISAS 2D fitting example.
Fake experimental data are generated from a known sample model.
"""
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):
"""
Dilute cylinders on a substrate, parameterized for GISAS 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)
cylinder_ff = ba.Cylinder(P["cylinder_radius"], P["cylinder_height"])
particle = ba.Particle(particle_mat, cylinder_ff)
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 with fitted beam intensity and background.
"""
beam = ba.Beam(10**P["lg_intensity"], 0.1*nm, 0.2*deg)
detector = ba.SphericalDetector(100, -1.5*deg, 1.5*deg, 100, 0, 3*deg)
simulation = ba.ScatteringSimulation(beam, get_sample(P), detector)
simulation.setBackground(ba.ConstantBackground(10**P["lg_background"]))
return simulation
def get_plotters(exp_data):
"""
Creates the fit-progress plotters.
"""
norm = ba.intensity_norm(exp_data)
experiment_plotter = ba.FitPlotter(
ba.plot_experimental,
measured=exp_data,
norm=norm,
with_cb=True,
title="Experimental",
)
simulation_plotter = ba.FitPlotter(
ba.plot_heatmap,
norm=norm,
with_cb=True,
title="Simulation",
)
difference_plotter = ba.FitPlotter(
ba.plot_difference,
measured=exp_data,
with_cb=True,
title="Relative difference",
)
return [
experiment_plotter,
simulation_plotter,
difference_plotter,
]
if __name__ == '__main__':
fake_params = {
"lg_intensity": 5,
"lg_background": 1,
"cylinder_height": 5.*nm,
"cylinder_radius": 5.*nm,
}
exp_data = get_simulation(fake_params).simulate()
flat_exp_values = exp_data.intensities().ravel()
# 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, reports, and returns the residual vector.
"""
sim_result = get_simulation(P.valuesdict()).simulate()
flat_sim_values = sim_result.intensities().ravel()
residuals = flat_exp_values - flat_sim_values
monitor.update(sim_result, P, residuals)
return residuals
P = lmfit.Parameters()
P.add("lg_intensity", value=4.3, min=0, max=15) # (dimensionless)
P.add("lg_background", value=2.0, min=-2, max=10) # (dimensionless)
P.add("cylinder_height", value=8*nm, min=0.01*nm)
P.add("cylinder_radius", value=3.5*nm, min=0.01*nm, max=8*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("Fit completed.")
print(lmfit.fit_report(result))
ba.showSample3D(get_sample(finalP), sample_size=120*nm, seed=0)
ba.plt.show()
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