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#!/usr/bin/env python3
"""
Fitting example: fit along slices
"""
from matplotlib.colors import ListedColormap
from matplotlib import pyplot as plt
import bornagain as ba
from bornagain import ba_fit, ba_plot, deg, nm, nm2
import lmfit
import numpy as np
def get_sample(P):
"""
Uncorrelated cylinders on a substrate, parameterized for fitting.
"""
substrate_mat = ba.RefractiveMaterial(
"Substrate", (0.28, 0.57, 0.82), 6e-6, 2e-8)
particle_mat = ba.RefractiveMaterial(
"Particle", (0.86, 0.24, 0.18), 6e-4, 2e-8)
particle = ba.Particle(
particle_mat, ba.Cylinder(P["radius"], P["height"]))
particle_layer = ba.Layer(ba.Vacuum())
particle_layer.deposit2D(ba.Dilute2D(0.01/nm2, particle))
sample = ba.Sample()
sample.addLayer(particle_layer)
sample.addLayer(ba.Layer(substrate_mat))
return sample
def get_simulation(P):
"""
GISAS simulation for the parameterized cylinder sample.
"""
n = 100
beam = ba.Beam(1e8, 0.1*nm, 0.2*deg)
detector = ba.SphericalDetector(n, -1*deg, 1*deg, n, 0, 2*deg)
simulation = ba.ScatteringSimulation(beam, get_sample(P), detector)
simulation.options().setUseAvgMaterials(False)
return simulation
phi_slice_value = 0.0 # position of vertical slice in deg
alpha_slice_value = 0.2 # position of horizontal slice in deg
def closest_axis_index(axis, value):
width = (axis.max() - axis.min()) / axis.size()
centers = axis.min() + width*(np.arange(axis.size()) + 0.5)
return int(np.argmin(np.abs(centers - value)))
def get_masked_simulation(P):
"""
GISAS simulation with only one horizontal and one vertical slice active.
"""
n = 100
beam = ba.Beam(1e8, 0.1*nm, 0.2*deg)
sample = get_sample(P)
detector = ba.SphericalDetector(n, -1*deg, 1*deg, n, 0, 2*deg)
n_phi = detector.axis(0).size()
n_alpha = detector.axis(1).size()
mask = np.ones((n_alpha, n_phi), dtype=bool)
i_phi = closest_axis_index(detector.axis(0), phi_slice_value*deg)
i_alpha = closest_axis_index(detector.axis(1), alpha_slice_value*deg)
mask[:, i_phi] = False
mask[i_alpha, :] = False
detector.setMask(mask)
simulation = ba.ScatteringSimulation(beam, sample, detector)
simulation.options().setUseAvgMaterials(False)
return simulation
def fake_data():
"""
Generating "real" data by adding noise to the simulated data.
"""
# initial values which we will have to find later during the fit
P = {'radius': 5*nm, 'height': 10*nm}
simulation = get_simulation(P)
simulation.setBackground(ba.PoissonBackground(seed=0))
result = simulation.simulate()
return result.noisy(0.1, 0.1)
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()
@staticmethod
def slice_indices(data):
"""
Returns detector bin indices that correspond to the requested slices.
"""
i_phi = closest_axis_index(data.xAxis(), phi_slice_value*deg)
i_alpha = closest_axis_index(data.yAxis(), alpha_slice_value*deg)
return i_phi, i_alpha
@staticmethod
def x_slice(data, i_alpha):
"""
Returns horizontal slice values from plottable 2D data.
"""
return (np.asarray(data.xCenters()),
np.asarray(data.intensities()[i_alpha, :]))
@staticmethod
def y_slice(data, i_phi):
"""
Returns vertical slice values from plottable 2D data.
"""
return (np.asarray(data.yCenters()),
np.asarray(data.intensities()[:, i_phi]))
@staticmethod
def plot_data(data, mask_source, i_phi, i_alpha):
"""
Plot experimental data with the inactive mask area dimmed.
"""
data.setTitle("Experimental data")
ax = plt.gca()
image = ba_plot.plot_heatmap(data, with_cb=False)
masked = ~np.isfinite(mask_source.intensities())
overlay = np.ma.masked_where(~masked,
np.ones_like(masked, dtype=float))
base_image = ax.images[0]
ax.imshow(overlay,
origin='lower',
cmap=ListedColormap([(0.86, 0.86, 0.86, 0.58)]),
extent=base_image.get_extent(),
aspect=ax.get_aspect(),
interpolation='nearest',
zorder=2)
# line representing vertical slice
x_slice = data.xCenters()[i_phi]
y_slice = data.yCenters()[i_alpha]
plt.plot([x_slice, x_slice],
[data.yAxis().min(), data.yAxis().max()],
color='gray',
linestyle='-',
linewidth=1,
zorder=3)
# line representing horizontal slice
plt.plot([data.xAxis().min(), data.xAxis().max()],
[y_slice, y_slice],
color='gray',
linestyle='-',
linewidth=1,
zorder=3)
return image
@staticmethod
def plot_slices(slices, title):
"""
Plots vertical and horizontal projections.
"""
plt.yscale('log')
ymax = 1.0
for label, x_values, y_values in slices:
visible = np.isfinite(y_values) & (y_values > 0)
plt.plot(x_values[visible], y_values[visible], label=label)
plt.xlim(np.amin(x_values), np.amax(x_values))
if np.any(visible):
ymax = max(ymax, np.amax(y_values[visible]))
plt.ylim(1, max(10, ymax*10))
plt.legend(loc='upper right')
plt.title(title)
@staticmethod
def display_fit_parameters(P, iteration, chi2):
"""
Displays fit parameters, chi and iteration number.
"""
plt.title('Parameters')
plt.axis('off')
plt.text(
0.01, 0.85, "Iterations " +
'{:d}'.format(iteration))
plt.text(0.01, 0.75,
"Chi2 " + '{:8.4f}'.format(chi2))
for index, (name, val) in enumerate(P.valuesdict().items()):
plt.text(
0.01, 0.55 - index*0.1,
'{:30.30s}: {:6.3f}'.format(name, val))
def update(self, raw_data, simul_data, P, iteration, chi2):
"""
Callback to plot every n'th iteration.
"""
self.fig.clf()
i_phi, i_alpha = self.slice_indices(simul_data)
data = raw_data.plottableField()
masked_data = ba_plot.masked_datafield(raw_data, simul_data).plottableField()
simul_data = simul_data.plottableField()
phi_slice = data.xCenters()[i_phi]
alpha_slice = data.yCenters()[i_alpha]
canvas = self.fig.add_gridspec(2, 2)
canvas.update(left=0.07, right=0.96, bottom=0.08, top=0.93,
wspace=0.45, hspace=0.35)
# plot real data
plt.sca(self.fig.add_subplot(canvas[0, 0]))
data_image = self.plot_data(data, simul_data, i_phi, i_alpha)
# horizontal slices
slices = [("real", *self.x_slice(masked_data, i_alpha)),
("simul", *self.x_slice(simul_data, i_alpha))]
title = ("Horizontal slice at alpha =" +
'{:4.2f}'.format(alpha_slice))
plt.sca(self.fig.add_subplot(canvas[0, 1]))
self.plot_slices(slices, title)
# vertical slices
slices = [("real", *self.y_slice(masked_data, i_phi)),
("simul", *self.y_slice(simul_data, i_phi))]
title = "Vertical slice at phi =" + '{:4.2f}'.format(phi_slice)
plt.sca(self.fig.add_subplot(canvas[1, 0]))
self.plot_slices(slices, title)
# display fit parameters
plt.sca(self.fig.add_subplot(canvas[1, 1]))
self.display_fit_parameters(P, iteration, chi2)
ba_plot.add_colorbar(data_image, fig=self.fig, pad=0.012,
width=0.014, fontsize=12)
plt.draw()
plt.pause(0.01)
def run_fitting():
"""
main function to run fitting
"""
data = fake_data()
exp_values = data.intensities()
sim_result = None # latest simulation, shared with the plot callback
def residuals(P):
"""
Runs a simulation for given parameters P, and returns residuals
vector; masked (NaN) pixels contribute zero.
"""
nonlocal sim_result
sim_result = get_masked_simulation(P.valuesdict()).simulate()
return ba_fit.valid_pixel_residual(exp_values,
sim_result.intensities())
# creating custom observer which will draw fit progress
plotter = PlotObserver()
def plot_iteration(P, iteration, resid):
if iteration % 10 == 0 and sim_result is not None:
plotter.update(data, sim_result, P, iteration,
float(np.sum(resid*resid)))
P = lmfit.Parameters()
P.add("radius", 6.*nm, min=4, max=8)
P.add("height", 9.*nm, min=8, max=12)
result = lmfit.minimize(residuals, P, iter_cb=plot_iteration)
print(lmfit.fit_report(result))
finalP = result.params.valuesdict()
ba.showSample3D(get_sample(finalP), sample_size=120*nm, seed=0)
if __name__ == '__main__':
run_fitting()
plt.show()
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