BornAgain ≻ 20 ≻ Documentation ≻ Python scripting ≻ Fitting ≻ Extended examples ≻ Considering uncertainties

Taking uncertainties into account

In this example we are demonstrating how to allow for uncertainties during a Reflectometry fitting job. The sample to fit consists of twenty Titanium-Nickel bilayers. Assuming that all Titanium layers have the same thickness, the goal is to find that thickness.

The reference data was generated with GENX, setting the thickness of the Ti layers equal to 3 nm.

This example follows closely the tutorial on Fitting reflectometry data. The main points to focus on here are the following:

  • Added artificial uncertainties to the data being fitted
  • Use of the the $RQ^4$ view for plotting
  • Use of $\chi^2$ with $L_1$ normalization as the objective metric
  • Setting a genetic algorithm as the minimizer
Fitting with uncertainties plot. Notice the $RQ^4$ scale of the Intensity axis

Fitting with uncertainties plot. Notice the $RQ^4$ scale of the Intensity axis

 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

#!/usr/bin/env python3
"""
Example demonstrates how to fit specular data.
Our sample represents twenty interchanging layers of Ti and Ni. We will fit
thicknesses of all Ti layers, assuming them being equal.

Reference data was generated with GENX for ti layers' thicknesses equal to 3 nm

This example uses exactly the same data as in FitSpecularBasics. However this
time we will add artificial uncertainties and use RQ^4 view.
Besides we will set Chi squared with L1-normalization as the objective metric
and use genetic algorithm as the minimizer.
"""

import os
import numpy as np
from matplotlib import pyplot as plt
import bornagain as ba
from bornagain import ba_fitmonitor

import FitSpecularBasics as fsb


def run_fitting():
    """
    Setup simulation and fit
    """

    real_data = fsb.get_real_data_values()
    # setting artificial uncertainties (uncertainty sigma equals a half
    # of experimental data value)
    uncertainties = real_data*0.5

    fit_objective = ba.FitObjective()
    fit_objective.addSimulationAndData(fsb.get_simulation, real_data,
                                       uncertainties)

    plot_observer = ba_fitmonitor.PlotterSpecular(units=ba.Coords_RQ4)
    fit_objective.initPrint(10)
    fit_objective.initPlot(10, plot_observer)
    fit_objective.setObjectiveMetric("Chi2", "L1")

    params = ba.Parameters()
    params.add("ti_thickness",
               50*ba.angstrom,
               min=10*ba.angstrom,
               max=60*ba.angstrom)

    minimizer = ba.Minimizer()
    minimizer.setMinimizer("Genetic", "", "MaxIterations=40;PopSize=10")
    result = minimizer.minimize(fit_objective.evaluate, params)

    fit_objective.finalize(result)


if __name__ == '__main__':
    datadir = os.getenv('BA_EXAMPLE_DATA_DIR', '')
    data_fname = os.path.join(datadir, "genx_interchanging_layers.dat.gz")
    fsb.get_real_data(data_fname)
    run_fitting()
    plt.show()
Examples/fit/specular/FitWithUncertainties.py

Data to be fitted: Examples/data/genx_interchanging_layers.dat.gz