## Simultaneous fit of two datasets

In this example we demonstrate how to fit two datasets simultaneously.

Suppose that we have a sample measured twice for two different incident angles. We are going to fit both datasets simultaneously to find the unknown sample parameters.

To do this, we define one dataset (a pair of real data and corresponding simulation builder) for the first incidence angle and another pair for the second incidence angle. We add both pairs to the FitObjective and run the fit as usual.

In the given script we simulate a dilute random assembly of hemi-ellipsoids on a substrate. The particle form factor has 3 parameters: radius_a and height are parameters to find, radius_b is fixed.

The custom PlotObserver class plots the fit for the two datasets every 10th iteration.

  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  #!/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.Detector2D(3*deg, 2*deg, n, n, 0, 1*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 = 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()): data = fit_objective.experimentalData(i_dataset) simul_data = fit_objective.simulationResult(i_dataset) chi2_map = fit_objective.relativeDifference(i_dataset) zmax = data.maxVal() plt.subplot(canvas[i_dataset*3]) bp.plot_simres(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 = 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() plt.show() 
auto/Examples/fit/scatter2d/multiple_datasets.py