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#!/usr/bin/env python3
"""
Fitting example: two-stage global+local fitting.
Stage 1 uses scipy differential_evolution for a global search over large
parameter space. Stage 2 uses lmfit (Levenberg-Marquardt) to refine
the result to a precise minimum.
"""
from matplotlib import pyplot as plt
import bornagain as ba
from bornagain import ba_fitmonitor, deg, angstrom, nm, nm2
import lmfit
import scipy.optimize
def get_sample(P):
"""
A sample with uncorrelated cylinders and pyramids on a substrate.
"""
radius = P["radius"]
height = P["height"]
vacuum = ba.Vacuum()
material_substrate = ba.RefractiveMaterial("Substrate", 6e-6, 2e-8)
material_particle = ba.RefractiveMaterial("Particle", 6e-4, 2e-8)
ff = ba.Cylinder(radius, height)
particle = ba.Particle(material_particle, ff, ba.AlignAt_Bottom)
vacuum_layer = ba.Layer(vacuum)
vacuum_layer.deposit2D(ba.Dilute2D(0.01/nm2, particle))
substrate_layer = ba.Layer(material_substrate)
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)
simulation.options().setUseAvgMaterials(False)
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()
fit_objective = ba.FitObjective()
fit_objective.addFitPair(get_simulation, data, 1)
fit_objective.initPrint(30)
observer = ba_fitmonitor.PlotterGISAS()
fit_objective.initPlot(30, observer)
P_names = ["height", "radius"]
bounds = [(0.01, 30), (0.01, 30)]
# Stage 1: global search with differential evolution
def de_objective(x):
P = lmfit.Parameters()
for name, val in zip(P_names, x):
P.add(name, val)
return fit_objective.evaluate(P)
de_result = scipy.optimize.differential_evolution(
de_objective, bounds,
maxiter=3,
popsize=15,
seed=42)
# Stage 2: local refinement seeded from global search result
P = lmfit.Parameters()
for name, val, (lo, hi) in zip(P_names, de_result.x, bounds):
P.add(name, val, min=lo, max=hi)
result = lmfit.minimize(fit_objective.evaluate_residuals, P)
print(lmfit.fit_report(result))
if __name__ == '__main__':
run_fitting()
plt.show()
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