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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.10"
# dependencies = ["bornagain>=25,<26", "lmfit"]
# ///
"""
Basic real-life example of fitting specular data.
The sample consists of single Ni film on SiO2 substrate.
"""
from itertools import count
import math
import bornagain as ba
ba.require_versions("bornagain>=25,<26")
import os
from bornagain import deg, nm
import lmfit
import numpy as np
def load_data():
# By default, read data files from the script directory.
datadir = ba.data_dir(beside=__file__)
fname = os.path.join(datadir, "MLZ-TREFF-Ni58.txt")
q_angstrom, intensity = ba.read_columns(fname, usecols=(0, 1))
q = 10*q_angstrom
return q, intensity
def get_sample(P):
# Materials
material_Ni_58_color = (0.93, 0.48, 0.14)
material_Ni_58 = ba.SLDMaterial("Ni", material_Ni_58_color, 9.408e-06, 0)
sio2_color = (0.20, 0.55, 0.72)
sio2_mat = ba.SLDMaterial("SiO2", sio2_color, 2.0704e-06, 0)
# Layers and interfaces
transient = ba.TanhTransient()
Ni_autocorr = ba.SelfAffineFractalModel(P["sigma_Ni"], 0.7, 25*nm)
roughness_Ni = ba.Roughness(Ni_autocorr, transient)
sub_autocorr = ba.SelfAffineFractalModel(P["sigma_Substrate"], 0.7, 25*nm)
roughness_Substrate = ba.Roughness(sub_autocorr, transient)
layer_Ni = ba.Layer(material_Ni_58, P["thickness"], roughness_Ni)
substrate = ba.Layer(sio2_mat, roughness_Substrate)
sample = ba.Sample()
sample.addLayer(ba.Layer(ba.Vacuum()))
sample.addLayer(layer_Ni)
sample.addLayer(substrate)
return sample
def get_simulation(q_axis, P):
scan = ba.QzScan(q_axis)
# Finite resolution due to beam divergence
n_samples = 5
rel_sampling_width = 2.0
res_distr = ba.DistributionGaussian(0, 1, n_samples, rel_sampling_width)
wavelength = 0.473*nm
res_alpha = 0.006*deg
res_q = 4*math.pi*res_alpha/wavelength
scan.setAbsoluteQResolution(res_distr, res_q)
sample = get_sample(P)
simulation = ba.SpecularSimulation(scan, sample)
simulation.setBackground(ba.ConstantBackground(1e-4))
return simulation
if __name__ == '__main__':
q_axis, exp_values = load_data()
eps = np.finfo(float).tiny
log_exp_values = np.log10(np.maximum(eps, exp_values))
exp_data = ba.Datafield(ba.Frame(ba.ListScan("q_z (1/nm)", q_axis)),
exp_values.tolist())
# Fit progress display
fit_plotter = ba.FitPlotter(
ba.plot_specular,
context_data=exp_data,
ylabel="Intensity",
)
monitor = ba.FitMonitor(
fit_plotter,
ncols=1,
show_best=True,
max_fps=1,
printer=ba.Printer(every_nth=10),
live=True)
P = lmfit.Parameters()
P.add("thickness", value=75*nm, min=50*nm, max=100*nm)
P.add("sigma_Ni", value=1.505*nm, min=0.01*nm, max=3*nm)
P.add("sigma_Substrate", value=1.505*nm, min=0.01*nm, max=3*nm)
def residuals(P):
"""
Simulates, reports, and returns log-intensity residuals.
"""
sim_result = get_simulation(q_axis, P.valuesdict()).simulate()
sim_values = sim_result.intensities()
residuals = np.log10(np.maximum(eps, sim_values)) - log_exp_values
monitor.update(sim_result, P, residuals)
return residuals
# Stage 1: global search with differential evolution
n_generations = 5
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")
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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