def exponential_model(x, A0=1., x0=5.):
# Our second model is a simple exponential function
# The kwargs in the function header specify parameter defaults.
return A0 * np.exp(x / x0)
# Read in the measurement data from a yaml file.
# For more information on reading/writing kafe2 objects from/to files see TODO
xy_data = XYContainer.from_file("data.yml")
# Create 2 XYFit objects with the same data but with different model functions
linear_fit = XYFit(xy_data=xy_data, model_function=linear_model)
exponential_fit = XYFit(xy_data=xy_data, model_function=exponential_model)
# Optional: Assign LaTeX strings to parameters and model functions.
linear_fit.assign_parameter_latex_names(a='a', b='b')
linear_fit.assign_model_function_latex_expression("{a}{x} + {b}")
exponential_fit.assign_parameter_latex_names(A0='A_0', x0='x_0')
exponential_fit.assign_model_function_latex_expression("{A0} e^{{{x}/{x0}}}")
# Perform the fits.
linear_fit.do_fit()
exponential_fit.do_fit()
# Optional: Print out a report on the result of each fit.
linear_fit.report()
exponential_fit.report()
# Optional: Create a plot of the fit results using Plot.
p = Plot(fit_objects=[linear_fit, exponential_fit], separate_figures=False)
p.plot(fit_info=True)
# -- Next, read the data from an external file
# load all data into numpy arrays
U, I, T = np.loadtxt('OhmsLawExperiment.dat', unpack=True) # data
sigU, sigI, sigT = 0.1, 0.1, 0.1 # uncertainties
T0 = 273.15 # 0 degrees C as absolute Temperature (in Kelvin)
T -= T0 # Measurements are in Kelvin, convert to °C
# -- Finally, go through the fitting procedure
# Step 1: perform an "auxiliary" fit to the T(U) data
auxiliary_fit = XYFit(xy_data=[U, T], model_function=empirical_T_U_model)
# (Optional): Assign names for models and parameters
auxiliary_fit.assign_parameter_latex_names(x='U', p2='p_2', p1='p_1', p0='p_0')
auxiliary_fit.assign_model_function_expression('{1}*{x}^2 + {2}*{x} + {3}')
auxiliary_fit.assign_model_function_latex_expression(
r'{1}\,{x}^2 + {2}\,{x} + {3}')
# declare errors on U
auxiliary_fit.add_error(axis='x', err_val=sigU)
# declare errors on T
auxiliary_fit.add_error(axis='y', err_val=sigT)
# perform the auxiliary fit
auxiliary_fit.do_fit()
# (Optional) print the results
auxiliary_fit.report()