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|
#!/usr/bin/env python3
"""
This fitting and simulation example demonstrates how to replicate
the fitting example "Magnetically Dead Layers in Spinel Films"
given at the Nist website:
https://www.nist.gov/ncnr/magnetically-dead-layers-spinel-films
For simplicity, here we only reproduce the first part of that
demonstration without the magnetically dead layer.
"""
# import boranagain
import bornagain as ba
from bornagain import deg, angstrom, nm
import numpy
import matplotlib.pyplot as plt
# import more libs needed for data processing
from re import match, DOTALL
from sys import argv
from io import BytesIO
from urllib.request import urlopen
from zipfile import ZipFile
from os.path import isfile
# q-range on which the simulation and fitting are to be performed
qmin = 0.05997
qmax = 1.96
# number of points on which the computed result is plotted
scan_size = 1500
# The SLD of the substrate is kept constant
sldMao = (5.377e-06, 0)
# constant to convert between magnetization and magnetic SLD
RhoMconst = 2.910429812376859e-12
####################################################################
# Create Sample and Simulation #
####################################################################
def get_sample(params):
"""
construct the sample with the given parameters
"""
magnetizationMagnitude = params["rhoM_Mafo"]*1e-6/RhoMconst
angle = 0
magnetizationVector = ba.kvector_t(
magnetizationMagnitude*numpy.sin(angle*deg),
magnetizationMagnitude*numpy.cos(angle*deg), 0)
mat_vacuum = ba.MaterialBySLD("Vacuum", 0, 0)
mat_layer = ba.MaterialBySLD("(Mg,Al,Fe)3O4", params["rho_Mafo"]*1e-6,
0, magnetizationVector)
mat_substrate = ba.MaterialBySLD("MgAl2O4", *sldMao)
ambient_layer = ba.Layer(mat_vacuum)
layer = ba.Layer(mat_layer, params["t_Mafo"]*angstrom)
substrate_layer = ba.Layer(mat_substrate)
r_Mafo = ba.LayerRoughness()
r_Mafo.setSigma(params["r_Mafo"]*angstrom)
r_substrate = ba.LayerRoughness()
r_substrate.setSigma(params["r_Mao"]*angstrom)
multi_layer = ba.MultiLayer()
multi_layer.addLayer(ambient_layer)
multi_layer.addLayerWithTopRoughness(layer, r_Mafo)
multi_layer.addLayerWithTopRoughness(substrate_layer, r_substrate)
return multi_layer
def get_simulation(q_axis, parameters, polarization, analyzer):
"""
Returns a simulation object.
Polarization, analyzer and resolution are set
from given parameters
"""
simulation = ba.SpecularSimulation()
q_axis = q_axis + parameters["q_offset"]
scan = ba.QSpecScan(q_axis)
dq = parameters["q_res"]*q_axis
n_sig = 4.0
n_samples = 25
distr = ba.RangedDistributionGaussian(n_samples, n_sig)
scan.setAbsoluteQResolution(distr, parameters["q_res"])
simulation.beam().setPolarization(polarization)
simulation.setAnalyzerProperties(analyzer, 1, 0.5)
simulation.setScan(scan)
return simulation
def run_simulation(q_axis, fitParams, *, polarization, analyzer):
"""
Run a simulation on the given q-axis, where the sample is constructed
with the given parameters.
Vectors for polarization and analyzer need to be provided
"""
parameters = dict(fitParams, **fixedParams)
sample = get_sample(parameters)
simulation = get_simulation(q_axis, parameters, polarization, analyzer)
simulation.setSample(sample)
simulation.runSimulation()
return simulation
def qr(result):
"""
Returns two arrays that hold the q-values as well as the
reflectivity from a given simulation result
"""
q = numpy.array(result.result().axis(ba.Axes.QSPACE))
r = numpy.array(result.result().array(ba.Axes.QSPACE))
return q, r
####################################################################
# Plot Handling #
####################################################################
def plot(qs, rs, exps, labels, filename):
"""
Plot the simulated result together with the experimental data
"""
fig = plt.figure()
ax = fig.add_subplot(111)
for q, r, exp, l in zip(qs, rs, exps, labels):
ax.errorbar(exp[0],
exp[1],
xerr=exp[3],
yerr=exp[2],
fmt='.',
markersize=0.75,
linewidth=0.5)
ax.plot(q, r, label=l)
ax.set_yscale('log')
plt.legend()
plt.xlabel("Q [nm${}^{-1}$]")
plt.ylabel("R")
plt.tight_layout()
plt.savefig(filename)
def plotSpinAsymmetry(data_pp, data_mm, q, r_pp, r_mm, filename):
"""
Plot the simulated spin asymmetry as well its
experimental counterpart with errorbars
"""
# compute the errorbars of the spin asymmetry
delta = numpy.sqrt(4 * (data_pp[1]**2 * data_mm[2]**2 + \
data_mm[1]**2 * data_pp[2]**2 ) /
( data_pp[1] + data_mm[1] )**4 )
fig = plt.figure()
ax = fig.add_subplot(111)
ax.errorbar(data_pp[0],
(data_pp[1] - data_mm[1])/(data_pp[1] + data_mm[1]),
xerr=data_pp[3],
yerr=delta,
fmt='.',
markersize=0.75,
linewidth=0.5)
ax.plot(q, (r_pp - r_mm)/(r_pp + r_mm))
plt.gca().set_ylim((-0.3, 0.5))
plt.xlabel("Q [nm${}^{-1}$]")
plt.ylabel("Spin asymmetry")
plt.tight_layout()
plt.savefig(filename)
####################################################################
# Data Handling #
####################################################################
def normalizeData(data):
"""
Removes duplicate q values from the input data,
normalizes it such that the maximum of the reflectivity is
unity and rescales the q-axis to inverse nm
"""
r0 = numpy.where(data[0] - numpy.roll(data[0], 1) == 0)
data = numpy.delete(data, r0, 1)
data[0] = data[0]/angstrom
data[3] = data[3]/angstrom
norm = numpy.max(data[1])
data[1] = data[1]/norm
data[2] = data[2]/norm
so = numpy.argsort(data[0])
data = data[:, so]
return data
def filterData(data, qmin, qmax):
minIndex = numpy.argmin(numpy.abs(data[0] - qmin))
maxIndex = numpy.argmin(numpy.abs(data[0] - qmax))
return data[:, minIndex:maxIndex + 1]
def get_Experimental_data(qmin, qmax):
input_Data = downloadAndExtractData()
data_pp = normalizeData(input_Data[0])
data_mm = normalizeData(input_Data[1])
return (filterData(data_pp, qmin,
qmax), filterData(data_mm, qmin, qmax))
def downloadAndExtractData():
url = "https://www.nist.gov/document/spinelfilmzip"
if not isfile("spinelfilm.zip"):
downloadfile = urlopen(url)
with open("spinelfilm.zip", 'wb') as outfile:
outfile.write(downloadfile.read())
zipfile = ZipFile("spinelfilm.zip")
rawdata = zipfile.open("MAFO_Saturated.refl").read().decode("utf-8")
table_pp = match(
r'.*# "polarization": "\+\+"\n#.*?\n# "units".*?\n(.*?)#.*',
rawdata, DOTALL).group(1)
table_mm = match(
r'.*# "polarization": "\-\-"\n#.*?\n# "units".*?\n(.*?)#.*',
rawdata, DOTALL).group(1)
data_pp = numpy.genfromtxt(BytesIO(table_pp.encode()), unpack=True)
data_mm = numpy.genfromtxt(BytesIO(table_mm.encode()), unpack=True)
return (data_pp, data_mm)
####################################################################
# Fit Function #
####################################################################
def run_fit_ba(q_axis, r_data, r_uncertainty, simulationFactory,
startParams):
fit_objective = ba.FitObjective()
fit_objective.setObjectiveMetric("chi2")
fit_objective.addSimulationAndData(
lambda params: simulationFactory[0](q_axis[0], params), r_data[0],
r_uncertainty[0], 1)
fit_objective.addSimulationAndData(
lambda params: simulationFactory[1](q_axis[1], params), r_data[1],
r_uncertainty[1], 1)
fit_objective.initPrint(10)
params = ba.Parameters()
for name, p in startParams.items():
params.add(name, p[0], min=p[1], max=p[2])
minimizer = ba.Minimizer()
result = minimizer.minimize(fit_objective.evaluate, params)
fit_objective.finalize(result)
return {r.name(): r.value for r in result.parameters()}
####################################################################
# Main Function #
####################################################################
if __name__ == '__main__':
if len(argv) > 1 and argv[1] == "fit":
fixedParams = {
# parameters can be moved here to keep them fixed
}
fixedParams = {d: v[0] for d, v in fixedParams.items()}
startParams = {
# own starting values
"q_res": (0, 0, 0.1),
"q_offset": (0, -0.002, 0.002),
"rho_Mafo": (6.3649, 2, 7),
"rhoM_Mafo": (0, 0, 2),
"t_Mafo": (150, 60, 180),
"r_Mao": (1, 0, 12),
"r_Mafo": (1, 0, 12),
}
fit = True
else:
startParams = {}
fixedParams = {
# parameters from our own fit run
'q_res': 0.010542945012551425,
'q_offset': 7.971243487467318e-05,
'rho_Mafo': 6.370140108715461,
'rhoM_Mafo': 0.27399566816062926,
't_Mafo': 137.46913056084736,
'r_Mao': 8.60487712674644,
'r_Mafo': 3.7844265311293483
}
fit = False
paramsInitial = {d: v[0] for d, v in startParams.items()}
def run_Simulation_pp(qzs, params):
return run_simulation(qzs,
params,
polarization=ba.kvector_t(0, 1, 0),
analyzer=ba.kvector_t(0, 1, 0))
def run_Simulation_mm(qzs, params):
return run_simulation(qzs,
params,
polarization=ba.kvector_t(0, -1, 0),
analyzer=ba.kvector_t(0, -1, 0))
qzs = numpy.linspace(qmin, qmax, scan_size)
q_pp, r_pp = qr(run_Simulation_pp(qzs, paramsInitial))
q_mm, r_mm = qr(run_Simulation_mm(qzs, paramsInitial))
data_pp, data_mm = get_Experimental_data(qmin, qmax)
plot([q_pp, q_mm], [r_pp, r_mm], [data_pp, data_mm], ["$++$", "$--$"],
f'MAFO_Saturated_initial.pdf')
plotSpinAsymmetry(data_pp, data_mm, qzs, r_pp, r_mm,
"MAFO_Saturated_spin_asymmetry_initial.pdf")
if fit:
fitResult = run_fit_ba([data_pp[0], data_mm[0]],
[data_pp[1], data_mm[1]],
[data_pp[2], data_mm[2]],
[run_Simulation_pp, run_Simulation_mm],
startParams)
print("Fit Result:")
print(fitResult)
q_pp, r_pp = qr(run_Simulation_pp(qzs, fitResult))
q_mm, r_mm = qr(run_Simulation_mm(qzs, fitResult))
plot([q_pp, q_mm], [r_pp, r_mm], [data_pp, data_mm],
["$++$", "$--$"], f'MAFO_Saturated_fit.pdf')
plotSpinAsymmetry(data_pp, data_mm, qzs, r_pp, r_mm,
"MAFO_Saturated_spin_asymmetry_fit.pdf")
|
BornAgain
≻ 1.19
≻ Documentation ≻ Python scripting ≻ Fitting ≻ Extended examples ≻ Spin asymmetry fit example
