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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.10"
# dependencies = ["bornagain>=25,<26", "lmfit"]
# ///
"""
Fitting example: two-stage global+local fitting.
Stage 1 uses differential evolution for a global search over a large
parameter space. Stage 2 uses a local least-squares method to refine the
result to a precise minimum. Both stages use the same residual vector and
the lmfit API.
"""
from itertools import count
from matplotlib import pyplot as plt
import bornagain as ba
ba.require_versions("bornagain>=25,<26")
from bornagain import deg, angstrom, nm, nm2
import lmfit
def get_sample(P):
"""
A sample with uncorrelated cylinders and pyramids on a substrate.
"""
radius = P["radius"]
height = P["height"]
substrate_color = (0.28, 0.57, 0.82)
substrate_mat = ba.RefractiveMaterial("Substrate", substrate_color, 6e-6, 2e-8)
particle_color = (0.86, 0.24, 0.18)
particle_mat = ba.RefractiveMaterial("Particle", particle_color, 6e-4, 2e-8)
ff = ba.Cylinder(radius, height)
particle = ba.Particle(particle_mat, ff)
vacuum_layer = ba.Layer(ba.Vacuum())
# Modest coverage keeps material averaging physical over the fit bounds.
vacuum_layer.deposit2D(ba.Dilute2D(1e-3/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.
"""
beam = ba.Beam(1e8, 1*angstrom, 0.2*deg)
n = 100
detector = ba.SphericalDetector(n, 0., 2*deg, n, 0., 2*deg)
simulation = ba.ScatteringSimulation(beam, get_sample(P), detector)
return simulation
def fake_data():
"""
Generating "real" data by adding noise to the simulated data.
"""
P = {'radius': 5*nm, 'height': 5*nm}
simulation = get_simulation(P)
result = simulation.simulate()
return result.noisy(0.3, 0.5)
def run_fitting():
data = fake_data()
flat_exp_values = data.intensities().ravel()
flat_exp_errors = data.errors().ravel()
P = lmfit.Parameters()
P.add("height", value=10*nm, min=0.01*nm, max=15*nm)
P.add("radius", value=10*nm, min=0.01*nm, max=15*nm)
def residuals(P):
"""
Returns residuals normalized by the synthetic data uncertainties.
"""
sim_values = get_simulation(P.valuesdict()).simulate().intensities()
flat_sim_values = sim_values.ravel()
return (flat_sim_values - flat_exp_values)/flat_exp_errors
# Stage 1: global search with differential evolution
n_generations = 20
generations = count(1)
def stop_callback(*_args, **_kwargs):
return next(generations) >= n_generations
de_result = lmfit.minimize(
residuals,
P,
method="differential_evolution",
callback=stop_callback, # stops the search after n_generations
popsize=15,
max_nfev=1000, # emergency evaluation cap
polish=False,
seed=42)
# Stage 2: local refinement seeded from global search result
result = lmfit.minimize(
residuals,
de_result.params,
method="leastsq")
print(lmfit.fit_report(result))
finalP = result.params.valuesdict()
ba.showSample3D(get_sample(finalP), sample_size=120*nm, seed=0)
if __name__ == '__main__':
run_fitting()
plt.show()
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