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#!/usr/bin/env python3
"""
Fitting example: fit along slices
"""
from matplotlib import pyplot as plt
import bornagain as ba
from bornagain import deg, angstrom, nm, ba_plot
import model1_cylinders as model
phi_slice_value = 0.0 # position of vertical slice in deg
alpha_slice_value = 0.2 # position of horizontal slice in deg
def get_masked_simulation(params):
"""
Create and return GISAXS simulation with beam and detector defined
"""
simulation = model.get_simulation(params)
"""
At this point we mask all the detector and then unmask two areas
corresponding to the vertical and horizontal lines. This will make
simulation/fitting to be performed along slices only.
"""
simulation.maskAll()
simulation.addMask(ba.HorizontalLine(alpha_slice_value*deg), False)
simulation.addMask(ba.VerticalLine(phi_slice_value*deg), False)
return simulation
def create_real_data():
"""
Generating "real" data by adding noise to the simulated data.
"""
# initial values which we will have to find later during the fit
params = {'radius': 5*nm, 'height': 10*nm}
# retrieving simulated data in the form of numpy array
simulation = model.get_simulation(params)
simulation.setBackground(ba.PoissonBackground())
result = simulation.simulate()
return result.array()
class PlotObserver:
"""
Draws fit progress every nth iteration. Here we plot slices along real
and simulated images to see fit progress.
"""
def __init__(self):
self.fig = plt.figure(figsize=(10.25, 7.69))
self.fig.canvas.draw()
def __call__(self, fit_objective):
self.update(fit_objective)
@staticmethod
def plot_real_data(data):
"""
Plot experimental data as heatmap with horizontal/vertical lines
representing slices on top.
"""
plt.subplots_adjust(wspace=0.2, hspace=0.2)
ba_plot.plot_histogram(data, title="Experimental data")
# line representing vertical slice
plt.plot([phi_slice_value, phi_slice_value],
[data.yAxis().min(), data.yAxis().max()],
color='gray',
linestyle='-',
linewidth=1)
# line representing horizontal slice
plt.plot([data.xAxis().min(), data.xAxis().max()],
[alpha_slice_value, alpha_slice_value],
color='gray',
linestyle='-',
linewidth=1)
@staticmethod
def plot_slices(slices, title):
"""
Plots vertical and horizontal projections.
"""
plt.subplots_adjust(wspace=0.2, hspace=0.3)
plt.yscale('log')
for label, slice in slices:
plt.plot(slice.xAxis().binCenters(), slice.flatVector(), label=label)
plt.xlim(slice.xAxis().min(), slice.xAxis().max())
plt.ylim(1, slice.maxVal()*10)
plt.legend(loc='upper right')
plt.title(title)
@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, params in enumerate(iteration_info.parameters()):
plt.text(
0.01, 0.55 - index*0.1,
'{:30.30s}: {:6.3f}'.format(params.name(), params.value))
plt.tight_layout()
plt.draw()
plt.pause(0.01)
def update(self, fit_objective):
"""
Callback to access fit_objective on every n'th iteration.
"""
self.fig.clf()
real_data = fit_objective.experimentalData().datafield()
simul_data = fit_objective.simulationResult().datafield()
# plot real data
plt.subplot(2, 2, 1)
self.plot_real_data(real_data)
# horizontal slices
slices = [("real", real_data.xProjection(alpha_slice_value)),
("simul", simul_data.xProjection(alpha_slice_value))]
title = ("Horizontal slice at alpha =" +
'{:3.1f}'.format(alpha_slice_value))
plt.subplot(2, 2, 2)
self.plot_slices(slices, title)
# vertical slices
slices = [("real", real_data.yProjection(phi_slice_value)),
("simul", simul_data.yProjection(phi_slice_value))]
title = "Vertical slice at phi =" + '{:3.1f}'.format(
phi_slice_value)
plt.subplot(2, 2, 3)
self.plot_slices(slices, title)
# display fit parameters
plt.subplot(2, 2, 4)
self.display_fit_parameters(fit_objective)
def run_fitting():
"""
main function to run fitting
"""
real_data = create_real_data()
fit_objective = ba.FitObjective()
fit_objective.addSimulationAndData(get_masked_simulation, real_data, 1)
fit_objective.initPrint(10)
# creating custom observer which will draw fit progress
plotter = PlotObserver()
fit_objective.initPlot(10, plotter)
params = ba.Parameters()
params.add("radius", 6.*nm, min=4, max=8)
params.add("height", 9.*nm, min=8, max=12)
minimizer = ba.Minimizer()
result = minimizer.minimize(fit_objective.evaluate, params)
fit_objective.finalize(result)
if __name__ == '__main__':
run_fitting()
plt.show()
|
BornAgain
≻ 20
≻ Documentation ≻ Python scripting ≻ Fitting ≻ Advanced examples ≻ Fitting along slices
