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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.10"
# dependencies = ["bornagain>=25,<26", "lmfit"]
# ///
"""
Fitting example: simultaneous fit of two datasets
"""
import numpy as np
import bornagain as ba
ba.require_versions("bornagain>=25,<26")
from bornagain import deg, nm, nm2
import lmfit
def get_sample(P):
"""
A sample with uncorrelated cylinders and pyramids.
"""
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)
ff = ba.EllipsoidalSegment(
P["radius_a"], P["radius_b"], P["radius_c"], 0, P["radius_c"])
particle = ba.Particle(particle_mat, ff)
vacuum_layer = ba.Layer(ba.Vacuum())
vacuum_layer.deposit2D(ba.Dilute2D(0.01/nm2, particle))
substrate_layer = ba.Layer(substrate_mat)
sample = ba.Sample()
sample.addLayer(vacuum_layer)
sample.addLayer(substrate_layer)
return sample
def get_simulation(P):
"""
A GISAXS simulation with beam and detector defined.
"""
incident_angle = P["incident_angle"]
beam = ba.Beam(1e8, 0.1*nm, incident_angle)
n = 100
detector = ba.SphericalDetector(n, -1.5*deg, 1.5*deg, n, 0, 2*deg)
return ba.ScatteringSimulation(beam, get_sample(P), detector)
def simulation1(P):
return get_simulation(P | {"incident_angle": 0.1*deg})
def simulation2(P):
return get_simulation(P | {"incident_angle": 0.4*deg})
def fake_data(incident_alpha):
"""
Generating "real" data by adding noise to the simulated data.
"""
P = {
'radius_a': 5*nm,
'radius_b': 6*nm,
'radius_c': 8*nm,
"incident_angle": incident_alpha
}
simulation = get_simulation(P)
result = simulation.simulate()
return result.noisy(0.1, 0.1)
def get_plotters(exp_data, index):
"""
Creates the three fit-progress plotters for one dataset.
"""
norm = ba.intensity_norm(exp_data)
suffix = f" {index + 1}"
def plot_selected_simulation(simulations, ax=None, **plot_args):
"""
Plots this dataset's simulation from the shared result tuple.
"""
return ba.plot_heatmap(simulations[index], ax=ax, **plot_args)
def plot_selected_difference(simulations, ax=None, **plot_args):
"""
Plots this dataset's relative difference from the result tuple.
"""
return ba.plot_difference(
simulations[index], ax=ax, context_data=exp_data, **plot_args)
experiment_plotter = ba.FitPlotter(
ba.plot_experimental,
context_data=exp_data,
norm=norm,
with_cb=True,
title="Experimental" + suffix,
)
simulation_plotter = ba.FitPlotter(
plot_selected_simulation,
norm=norm,
with_cb=True,
title="Simulation" + suffix,
)
difference_plotter = ba.FitPlotter(
plot_selected_difference,
with_cb=True,
title="Relative difference" + suffix,
)
return [
experiment_plotter,
simulation_plotter,
difference_plotter,
]
if __name__ == '__main__':
exp_data1 = fake_data(0.1*deg)
exp_data2 = fake_data(0.4*deg)
flat_exp_values1 = exp_data1.intensities().ravel()
flat_exp_values2 = exp_data2.intensities().ravel()
# Fit progress display
monitor = ba.FitMonitor(
get_plotters(exp_data1, 0) + get_plotters(exp_data2, 1),
ncols=3,
show_best=True,
max_fps=1,
printer=ba.Printer(every_nth=10),
live=True)
def residuals(P):
"""
Simulates, reports, and returns both datasets' residuals.
"""
values = P.valuesdict()
sim1 = simulation1(values).simulate()
sim2 = simulation2(values).simulate()
flat_sim_values1 = sim1.intensities().ravel()
flat_sim_values2 = sim2.intensities().ravel()
residuals = np.concatenate([
flat_exp_values1 - flat_sim_values1,
flat_exp_values2 - flat_sim_values2,
])
monitor.update((sim1, sim2), P, residuals)
return residuals
P = lmfit.Parameters()
P.add("radius_a", value=4*nm, min=2*nm, max=10*nm)
P.add("radius_b", value=6*nm, vary=False)
P.add("radius_c", value=4*nm, min=2*nm, max=10*nm)
result = lmfit.minimize(residuals, P, method="leastsq")
finalP = result.params.valuesdict()
# Recompute and report the simulations 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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