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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.10"
# dependencies = ["bornagain>=25,<26", "scipy>=1.7"]
# ///
"""
SciPy differential evolution for BornAgain fits.
"""
import bornagain as ba
ba.require_versions("bornagain>=25,<26")
from bornagain import deg, nm
import numpy as np
import scipy.optimize
def get_sample(P):
"""
Spheres on a hexagonal lattice, parameterized for fitting.
"""
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)
particle = ba.Particle(particle_mat, ba.Sphere(P["radius"]))
lattice = ba.HexagonalLattice2D(P["length"], 0)
struct = ba.Crystal2D(particle, lattice)
struct.setDecayFunction(ba.Profile2DCauchy(100*nm, 100*nm, 0))
particle_layer = ba.Layer(ba.Vacuum())
particle_layer.deposit2D(struct)
sample = ba.Sample()
sample.addLayer(particle_layer)
sample.addLayer(ba.Layer(substrate_mat))
return sample
def get_simulation(P):
"""
GISAS simulation for the parameterized hexagonal lattice.
"""
n_pix = 100
beam = ba.Beam(1e8, 0.1*nm, 0.2*deg)
detector = ba.SphericalDetector(n_pix, -1*deg, 1*deg, n_pix, 0, 2*deg)
simulation = ba.ScatteringSimulation(beam, get_sample(P), detector)
return simulation
def fake_data():
"""
Noisy synthetic data for a known hexagonal lattice.
"""
P = {"radius": 5*nm, "length": 14*nm}
return get_simulation(P).simulate().noisy(0.1, 0.1)
def print_result(result, initial_objective):
"""
Prints selected fields of the SciPy OptimizeResult.
"""
radius, length = result.x
print(f"Success: {result.success}")
print(f"Message: {result.message}")
print(f"Initial objective: {initial_objective:.6g}")
print(f"Objective: {result.fun:.6g}")
print(f"Function evaluations: {result.nfev}")
print(f"radius: {radius:.6g}")
print(f"length: {length:.6g}")
if __name__ == '__main__':
# Generate synthetic data for the fit target.
data = fake_data()
flat_exp_values = data.intensities().ravel()
def scalar_objective(values):
"""
Runs a simulation and returns the sum of squared residuals.
"""
radius, length = values
parameters = {"radius": radius, "length": length}
simulation = get_simulation(parameters)
result = simulation.simulate()
flat_sim_values = result.intensities().ravel()
residuals = flat_sim_values - flat_exp_values
return np.sum(residuals*residuals)
# Define SciPy's initial candidate and bounds.
initial_values = np.array([4.5*nm, 13.5*nm])
bounds = [(4*nm, 6*nm), (13*nm, 15*nm)]
initial_objective = scalar_objective(initial_values)
# differential_evolution expects a scalar objective value.
result = scipy.optimize.differential_evolution(
scalar_objective,
bounds=bounds,
x0=initial_values,
maxiter=30,
popsize=6,
polish=True,
seed=0)
print_result(result, initial_objective)
radius, length = result.x
final_parameters = {"radius": radius, "length": length}
final_result = get_simulation(final_parameters).simulate()
ba.showSample3D(get_sample(final_parameters), sample_size=300*nm, seed=0)
ba.plot_datafield(final_result, unit_aspect=1)
ba.plt.show()
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