Fit
[1]:
import nexus as nx
import numpy as np
import matplotlib.pyplot as plt
data = np.loadtxt('example_spectrum.txt')
velocity_experiment = data[:,0]
intensity_experiment = data[:,1]
plt.plot(velocity_experiment, intensity_experiment)
plt.xlabel('velocity (mm/s)')
plt.ylabel('intensity')
plt.show()
[2]:
site = nx.Hyperfine(magnetic_field = nx.Var(value = 31, min = 25, max = 35, fit = True, id = "magnetic field"),
isotropic = True
)
layer_Fe = nx.Layer(id = "Fe",
material = nx.Material.Template(nx.lib.material.Fe),
thickness = 3000, # in nanometer
roughness = 100, # in nanometer
)
layer_Fe.material.hyperfine_sites = [site]
sample = nx.Sample(layers = [layer_Fe])
beam = nx.Beam()
beam.Unpolarized()
exp = nx.Experiment(beam = beam,
objects = [sample],
isotope = nx.moessbauer.Fe57
)
[3]:
spectrum = nx.MoessbauerSpectrum(exp,
velocity = velocity_experiment, # the measured detuning points
intensity_data = intensity_experiment, # the intensity data to be fit
)
# calculate the intensity from the assumed model
# the data are returned by the function
intensity = spectrum.Calculate()
#%matplotlib qt
plt.plot(velocity_experiment, intensity_experiment)
plt.plot(velocity_experiment, intensity)
plt.xlabel('velocity (mm/s)')
plt.ylabel('intensity')
plt.show()
[4]:
spectrum.Plot(velocity = True)
[5]:
# create a fit object with a list of measurments to be fit.
fit = nx.Fit(measurements = [spectrum])
# run the fit
fit.Evaluate()
Run Fit instance with id:
Starting fit with 1 measurement data set(s) and 3 fit parameter(s):
no. | id | initial value | min | max
0 | ES scaling | 2634.1 | 1e-16 | 263410
1 | ES backgr | 256.611 | 0 | 25661.1
2 | magnetic field | 31 | 25 | 35
Using 0 equality constraint(s) on parameter(s):
Using 0 inequality constraint(s).
Calling ceres solver with fit method LevMar
Ceres Solver Report: Iterations: 18, Initial cost: 6.134841e+02, Final cost: 2.135170e+01, Termination: CONVERGENCE
Gradient error analysis.
Fit performed with algorithm:
LevMar
Error analysis:
Gradient
Using 3 fit parameter(s):
no. | id | fit value | +/- std dev | initial value | min | max
0 | ES scaling | 3000.59 | 20.6781 | 2634.1 | 1e-16 | 263410
1 | ES backgr | 0 | 17.6848 | 256.611 | 0 | 25661.1
2 | magnetic field | 33.013 | 0.00655823 | 31 | 25 | 35
Values at boundaries:
ES backgr at LOWER boundary: 0
Correlation matrix:
no. | 0 1 2
-----|---------------------------
0 | 1.000 -1.000 0.000
1 | -1.000 1.000 -0.000
2 | 0.000 -0.000 1.000
Using 0 equality constraint(s) on parameter(s):
and 0 inequality constraint(s).
Total cost = 2.134e-02
cost for each FitMeasurement is:
no. | id | cost | %
0 | | 2.134e-02 | 100.000
Fit instance with id "" finished.
[6]:
# now the Var.values are the fitted values.
# print the fitted value
print(site.magnetic_field.value)
# and plot the data
#%matplotlib qt
plt.plot(velocity_experiment, intensity_experiment, label = 'data') # the 'measured' data
plt.plot(velocity_experiment, spectrum.result , label = 'fit model') # our assumed model
plt.legend()
plt.xlabel('velocity (mm/s)')
plt.ylabel('intensity')
plt.show()
33.01300799151598
[7]:
spectrum.Plot(velocity = True, residuals=True, datacolor='black',
theorycolor='r', theorywidth=2, datalinestyle='none', datamarker='+',
datamarkersize=2, datafillstyle='full', legend=True,
errors= False)
[8]:
# we set all fit parameters back to their inital values to start with the same conditions.
# there is a special method for this
fit.SetInitialVars()
print(site.magnetic_field.value)
# change the method in the fit.options
fit.options.method = "PagmoDiffEvol"
# because we want ot apply a global fit method we have to provide a range for the intensity scaling value
# spectrum.scaling = nx.Var(value = 1, min = 0, max = 1e4, fit = True, id = "scaling factor")
fit.Evaluate()
# and plot the data
plt.plot(velocity_experiment, intensity_experiment, label = 'data') # the 'measured' data
plt.plot(velocity_experiment, spectrum.result , label = 'fit model') # our fit model
plt.legend()
plt.xlabel('velocity (mm/s)')
plt.ylabel('intensity')
plt.show()
spectrum.Plot(velocity =True)
31.0
Run Fit instance with id:
Starting fit with 1 measurement data set(s) and 3 fit parameter(s):
no. | id | initial value | min | max
0 | ES scaling | 2634.1 | 1e-16 | 263410
1 | ES backgr | 256.611 | 0 | 25661.1
2 | magnetic field | 31 | 25 | 35
Using 0 equality constraint(s) on parameter(s):
Using 0 inequality constraint(s).
Calling Pagmo solver with fit method PagmoDiffEvol
population: 40
iterations: 100
cost = 2.132043e+01
Calling ceres solver with fit method LevMar
Ceres Solver Report: Iterations: 1, Initial cost: 2.132043e+01, Final cost: 2.132043e+01, Termination: CONVERGENCE
Gradient error analysis.
Fit performed with algorithm:
PagmoDiffEvol
Local algorithm:
LevMar
Error analysis:
Gradient
Using 3 fit parameter(s):
no. | id | fit value | +/- std dev | initial value | min | max
0 | ES scaling | 2996.17 | 20.6616 | 2634.1 | 1e-16 | 263410
1 | ES backgr | 3.21932 | 17.6706 | 256.611 | 0 | 25661.1
2 | magnetic field | 33.0128 | 0.00656268 | 31 | 25 | 35
Values at boundaries:
Correlation matrix:
no. | 0 1 2
-----|---------------------------
0 | 1.000 -1.000 0.000
1 | -1.000 1.000 -0.000
2 | 0.000 -0.000 1.000
Using 0 equality constraint(s) on parameter(s):
and 0 inequality constraint(s).
Total cost = 2.131e-02
cost for each FitMeasurement is:
no. | id | cost | %
0 | | 2.131e-02 | 100.000
Fit instance with id "" finished.
