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#!/usr/bin/env python3
"""
Fitting example: simultaneous fit of two datasets
"""
import numpy as np
import matplotlib
import bornagain as ba
from bornagain import ba_plot as bp, deg, nm
def get_sample(P):
"""
A sample with uncorrelated cylinders and pyramids.
"""
radius_a = P["radius_a"]
radius_b = P["radius_b"]
height = P["height"]
vacuum = ba.RefractiveMaterial("Vacuum", 0, 0)
material_substrate = ba.RefractiveMaterial("Substrate", 6e-6, 2e-8)
material_particle = ba.RefractiveMaterial("Particle", 6e-4, 2e-8)
formfactor = ba.HemiEllipsoid(radius_a, radius_b, height)
particle = ba.Particle(material_particle, formfactor)
layout = ba.ParticleLayout()
layout.addParticle(particle)
vacuum_layer = ba.Layer(vacuum)
vacuum_layer.addLayout(layout)
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.
"""
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):
P["incident_angle"] = 0.1*deg
return get_simulation(P)
def simulation2(P):
P["incident_angle"] = 0.4*deg
return get_simulation(P)
def fake_data(incident_alpha):
"""
Generating "real" data by adding noise to the simulated data.
"""
P = {
'radius_a': 5*nm,
'radius_b': 6*nm,
'height': 8*nm,
"incident_angle": incident_alpha
}
simulation = get_simulation(P)
result = simulation.simulate()
return result.noisy(0.1, 0.1)
class PlotObserver():
"""
Draws fit progress every nth iteration. Real data, simulated data
and chi2 map will be shown for both datasets.
"""
def __init__(self):
self.fig = bp.plt.figure(figsize=(12.8, 10.24))
self.fig.canvas.draw()
def __call__(self, fit_objective):
self.update(fit_objective)
@staticmethod
def plot_dataset(fit_objective, canvas):
for j in range(0, fit_objective.nPairs()):
data = fit_objective.experimentalData(j)
simul_data = fit_objective.simulationResult(j)
chi2_map = fit_objective.relativeDifference(j)
zmax = data.maxVal()
bp.plt.subplot(canvas[j*3])
bp.plot_simres(data,
title="\"Real\" data - #" +
str(j + 1),
intensity_min=1,
intensity_max=zmax,
zlabel="")
bp.plt.subplot(canvas[1 + j*3])
bp.plot_simres(simul_data,
title="Simulated data - #" +
str(j + 1),
intensity_min=1,
intensity_max=zmax,
zlabel="")
bp.plt.subplot(canvas[2 + j*3])
bp.plot_simres(chi2_map,
title="Chi2 map - #" + str(j + 1),
intensity_min=0.001,
intensity_max=10,
zlabel="")
@staticmethod
def display_fit_parameters(fit_objective):
"""
Displays fit parameters, chi and iteration number.
"""
bp.plt.title('Parameters')
bp.plt.axis('off')
iteration_info = fit_objective.iterationInfo()
bp.plt.text(
0.01, 0.85, "Iterations " +
'{:d}'.format(iteration_info.iterationCount()))
bp.plt.text(0.01, 0.75,
"Chi2 " + '{:8.4f}'.format(iteration_info.chi2()))
for index, P in enumerate(iteration_info.parameters()):
bp.plt.text(
0.01, 0.55 - index*0.1,
'{:30.30s}: {:6.3f}'.format(P.name(), P.value))
@staticmethod
def plot_fit_parameters(fit_objective):
"""
Displays fit parameters, chi and iteration number.
"""
bp.plt.axis('off')
iteration_info = fit_objective.iterationInfo()
bp.plt.text(
0.01, 0.95, "Iterations " +
'{:d}'.format(iteration_info.iterationCount()))
bp.plt.text(0.01, 0.70,
"Chi2 " + '{:8.4f}'.format(iteration_info.chi2()))
for index, P in enumerate(iteration_info.parameters()):
bp.plt.text(
0.01, 0.30 - index*0.3,
'{:30.30s}: {:6.3f}'.format(P.name(), P.value))
def update(self, fit_objective):
self.fig.clf()
# we divide figure to have 3x3 subplots, with two first rows occupying
# most of the space
canvas = matplotlib.gridspec.GridSpec(3,
3,
width_ratios=[1, 1, 1],
height_ratios=[4, 4, 1])
canvas.update(left=0.05, right=0.95, hspace=0.5, wspace=0.2)
self.plot_dataset(fit_objective, canvas)
bp.plt.subplot(canvas[6:])
self.plot_fit_parameters(fit_objective)
bp.plt.draw()
bp.plt.pause(0.01)
def run_fitting():
"""
main function to run fitting
"""
data1 = fake_data(0.1*deg)
data2 = fake_data(0.4*deg)
fit_objective = ba.FitObjective()
fit_objective.addFitPair(simulation1, data1, 1)
fit_objective.addFitPair(simulation2, data2, 1)
fit_objective.initPrint(10)
# creating custom observer which will draw fit progress
plotter = PlotObserver()
fit_objective.initPlot(10, plotter.update)
P = ba.Parameters()
P.add("radius_a", 4.*nm, min=2, max=10)
P.add("radius_b", 6.*nm, vary=False)
P.add("height", 4.*nm, min=2, max=10)
minimizer = ba.Minimizer()
result = minimizer.minimize(fit_objective.evaluate, P)
fit_objective.finalize(result)
if __name__ == '__main__':
run_fitting()
bp.plt.show()
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