1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
|
#!/usr/bin/env python3
"""
Fitting example: simultaneous fit of two datasets
"""
import numpy as np
import matplotlib
from matplotlib import pyplot as plt
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.MultiLayer()
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 create_real_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()
# retrieving simulated data in the form of numpy array
real_data = result.array()
# spoiling simulated data with the noise to produce "real" data
noise_factor = 0.1
noisy = np.random.normal(real_data, noise_factor*np.sqrt(real_data))
noisy[noisy < 0.1] = 0.1
return noisy
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 = 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 i_dataset in range(0, fit_objective.fitObjectCount()):
real_data = fit_objective.experimentalData(i_dataset)
simul_data = fit_objective.simulationResult(i_dataset)
chi2_map = fit_objective.relativeDifference(i_dataset)
zmax = real_data.maxVal()
plt.subplot(canvas[i_dataset*3])
bp.plot_simres(real_data,
title="\"Real\" data - #" +
str(i_dataset + 1),
intensity_min=1,
intensity_max=zmax,
zlabel="")
plt.subplot(canvas[1 + i_dataset*3])
bp.plot_simres(simul_data,
title="Simulated data - #" +
str(i_dataset + 1),
intensity_min=1,
intensity_max=zmax,
zlabel="")
plt.subplot(canvas[2 + i_dataset*3])
bp.plot_simres(chi2_map,
title="Chi2 map - #" + str(i_dataset + 1),
intensity_min=0.001,
intensity_max=10,
zlabel="")
@staticmethod
def display_fit_parameters(fit_objective):
"""
Displays fit parameters, chi and iteration number.
"""
plt.title('Parameters')
plt.axis('off')
iteration_info = fit_objective.iterationInfo()
plt.text(
0.01, 0.85, "Iterations " +
'{:d}'.format(iteration_info.iterationCount()))
plt.text(0.01, 0.75,
"Chi2 " + '{:8.4f}'.format(iteration_info.chi2()))
for index, P in enumerate(iteration_info.parameters()):
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.
"""
plt.axis('off')
iteration_info = fit_objective.iterationInfo()
plt.text(
0.01, 0.95, "Iterations " +
'{:d}'.format(iteration_info.iterationCount()))
plt.text(0.01, 0.70,
"Chi2 " + '{:8.4f}'.format(iteration_info.chi2()))
for index, P in enumerate(iteration_info.parameters()):
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)
plt.subplot(canvas[6:])
self.plot_fit_parameters(fit_objective)
plt.draw()
plt.pause(0.01)
def run_fitting():
"""
main function to run fitting
"""
data1 = create_real_data(0.1*deg)
data2 = create_real_data(0.4*deg)
fit_objective = ba.FitObjective()
fit_objective.addSimulationAndData(simulation1, data1, 1)
fit_objective.addSimulationAndData(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()
plt.show()
|
