import matplotlib.pyplot as plt
from kafe2 import XYContainer, XYFit, Plot
from kafe2.fit.tools import ContoursProfiler
# Construct a fit with data loaded from a yaml file. The model function is the default of f(x) = a * x + b
nonlinear_fit = XYFit(xy_data=XYContainer.from_file('x_errors.yml'))
# The x errors are much bigger than the y errors. This will cause a distortion of the likelihood function.
nonlinear_fit.add_error('x', 1.0)
nonlinear_fit.add_error('y', 0.1)
# Perform the fit.
nonlinear_fit.do_fit()
# Optional: Print out a report on the fit results on the console.
# Note the asymmetric_parameter_errors flag
nonlinear_fit.report(asymmetric_parameter_errors=True)
# Optional: Create a plot of the fit results using Plot.
# Note the asymmetric_parameter_errors flag
plot = Plot(nonlinear_fit)
plot.plot(fit_info=True, asymmetric_parameter_errors=True)
# Optional: Calculate a detailed representation of the profile likelihood
# Note how the actual chi2 profile differs from the parabolic approximation that you would expect with a linear fit.
profiler = ContoursProfiler(nonlinear_fit)
profiler.plot_profiles_contours_matrix(show_grid_for='all')
plt.show()
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)
# Optional: Create a contour plot for the exponential fit to show the parameter correlations.
cpf = ContoursProfiler(exponential_fit)
cpf.plot_profiles_contours_matrix(show_grid_for='contours')
# Show the fit results.
plt.show()
def expected_activity_per_day(x, Delta_t=5000, T_12_C14=5730):
# activity = number of radioactive decays
expected_initial_activity_per_day = expected_initial_num_c14_atoms * np.log(2) / (T_12_C14 * days_per_year)
total_years_since_death = Delta_t + current_year - x
return expected_initial_activity_per_day * np.exp(-np.log(2) * total_years_since_death / T_12_C14)
# This is where we tell the fit to assume a poisson distribution for our data.
xy_fit = XYFit(
xy_data=[years_of_death, measured_c14_activity],
model_function=expected_activity_per_day,
cost_function=XYCostFunction_NegLogLikelihood(data_point_distribution='poisson')
)
# The half life of carbon-14 is only known with a precision of +-40 years
xy_fit.add_parameter_constraint(name='T_12_C14', value=5730, uncertainty=40)
# Perform the fit
# Note that since for a Poisson distribution the data error is directly linked to the mean.
# Because of this fits can be performed without explicitly adding data errors.
xy_fit.do_fit()
# Optional: print out a report on the fit results on the console
xy_fit.report()
# Optional: create a plot of the fit results using Plot
xy_plot = Plot(xy_fit)
xy_plot.plot(fit_info=True)
plt.show()
def exponential(x, A0=1, tau=1):
return A0 * np.exp(-x/tau)
# define the data as simple Python lists
x = [8.018943e-01, 1.839664e+00, 1.941974e+00, 1.276013e+00, 2.839654e+00, 3.488302e+00, 3.775855e+00, 4.555187e+00,
4.477186e+00, 5.376026e+00]
xerr = 3.000000e-01
y = [2.650644e-01, 1.472682e-01, 8.077234e-02, 1.850181e-01, 5.326301e-02, 1.984233e-02, 1.866309e-02, 1.230001e-02,
9.694612e-03, 2.412357e-03]
yerr = [1.060258e-01, 5.890727e-02, 3.230893e-02, 7.400725e-02, 2.130520e-02, 7.936930e-03, 7.465238e-03, 4.920005e-03,
3.877845e-03, 9.649427e-04]
# create a fit object from the data arrays
fit = XYFit(xy_data=[x, y], model_function=exponential)
fit.add_error(axis='x', err_val=xerr) # add the x-error to the fit
fit.add_error(axis='y', err_val=yerr) # add the y-errors to the fit
fit.do_fit() # perform the fit
fit.report(asymmetric_parameter_errors=True) # print a report with asymmetric uncertainties
# Optional: create a plot
plot = Plot(fit)
plot.plot(asymmetric_parameter_errors=True, ratio=True) # add the ratio data/function and asymmetric errors
# Optional: create the contours profiler
cpf = ContoursProfiler(fit)
cpf.plot_profiles_contours_matrix() # plot the contour profile matrix for all parameters
plt.show()
# Constrain model parameters to measurements
fit.add_parameter_constraint(name='l', value=l, uncertainty=delta_l)
fit.add_parameter_constraint(name='r', value=r, uncertainty=delta_r)
fit.add_parameter_constraint(name='y_0',
value=y_0,
uncertainty=delta_y_0,
relative=True)
# Because the model function is oscillating the fit needs to be initialized with near guesses for unconstrained
# parameters in order to converge
g_initial = 9.81 # initial guess for g
c_initial = 0.01 # initial guess for c
fit.set_parameter_values(g=g_initial, c=c_initial)
# Optional: Set the initial values of the remaining parameters to correspond to their constraint values
# (this may help some minimization algorithms converge)
fit.set_parameter_values(y_0=y_0, l=l, r=r)
# Perform the fit
fit.do_fit()
# Optional: Print out a report on the fit results on the console.
fit.report()
# Optional: plot the fit results
plot = Plot(fit)
plot.plot(fit_info=True)
plt.show()
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()
# (Optional) plot the results
auxiliary_plot = Plot(auxiliary_fit)
auxiliary_plot.plot(fit_info=True)
# Step 2: perform the main fit
main_fit = XYFit(xy_data=[U, I], model_function=I_U_model)
# declare errors on U
main_fit.add_error(axis='x', err_val=sigU)
# declare errors on I
main_fit.add_error(axis='y', err_val=sigI)
# constrain the parameters
main_fit.add_matrix_parameter_constraint(
from kafe2 import XYContainer, XYFit, Plot import matplotlib.pyplot as plt # Create an XYContainer object to hold the xy data for the fit. xy_data = XYContainer(x_data=[1.0, 2.0, 3.0, 4.0], y_data=[2.3, 4.2, 7.5, 9.4]) # x_data and y_data are combined depending on their order. # The above translates to the points (1.0, 2.3), (2.0, 4.2), and (4.0, 9.4). # Important: Specify uncertainties for the data. xy_data.add_error(axis='x', err_val=0.1) xy_data.add_error(axis='y', err_val=0.4) # Create an XYFit object from the xy data container. # By default, a linear function f=a*x+b will be used as the model function. line_fit = XYFit(xy_data=xy_data) # Perform the fit: Find values for a and b that minimize the # difference between the model function and the data. line_fit.do_fit() # This will throw an exception if no errors were specified. # Optional: Print out a report on the fit results on the console. line_fit.report() # Optional: Create a plot of the fit results using Plot. plot = Plot(fit_objects=line_fit) # Create a kafe2 plot object. plot.plot() # Do the plot. # Show the fit result. plt.show()