Model Fitting

The fitting module is for actually performing fits to data using the previously defined fit models to estimate model parameters.

class experimentalis.fitting.FitModelResult(initial_guess_graph=None, initial_guess_residuals_graph=None, autofit_graph=None, autofit_residuals_graph=None, chi2=None, covariance_matrix=None)

Bases: object

A result structure for collecting and displaying fit results visually. Produced automatically after performing an autofit.

Variables:

  • initial_guess_graph (Image) – A plot of the model pre-optimization, using the initial parameter guesses (if provided).

  • initial_guess_residuals_graph (Image) – A plot of the residuals of the initial values.

  • autofit_graph (Image) – A plot of the model post-optimization.

  • autofit_residuals_graph (Image) – A plot of the post-optimization model residuals.

  • chi2 (float) – The goodness-of-fit of the model post-optimization.

autofit_graph = None
autofit_residuals_graph = None
chi2 = None
covariance_matrix = None
initial_guess_graph = None
initial_guess_residuals_graph = None
experimentalis.fitting.autofit(data, model, graphing_options)

Optimizes a model to fit a dataset (editing the model in-place), and plots the results to a FitModelResult object.

Parameters:

  • data (Dataset) – The dataset to fit to.

  • model (Model) – The model.

  • graphing_options (GraphingOptions) – The graphing options for plotting.

Returns:

The results of the optimization.

Return type:

FitModelResult

experimentalis.fitting.calculate_chi_squared(model, dataset)

Calculates the goodness-of-fit \(\chi^2\) for a given model post-fitting via the equation

\[\chi^2 = \frac{1}{N} \sum_{i=1}^{N} \left( \frac{y_i - f(x_i)}{dy} \right)^2\]

given model \(f\) and dataset \(D_i=(x_i,y_i)\).

Parameters:

  • model (Model) – The model post-optimization.

  • dataset (Dataset) – The dataset to compare against.

Returns:

The goodness-of-fit \(\chi^2\).

experimentalis.fitting.print_results(model, results, print_cov=False, units=None)

Prints the results of a fitting in a tabulated format, with the optional inclusion of the covariance matrix for the parameters.

Parameters:

  • model (Model) – The fit model, used to access the optimized parameters.

  • results (FitModelResults) – The results of the fitting. Used to access the covariance matrix and the goodness-of-fit.

  • print_cov (bool) – Whether or not to include the covariance matrix.

  • units (list[str]) – The (optional) ordered list of units for each parameter.