Overview

This document assumes that the user is familiar with the numpy package and the Levenberg-Marquardt Algorithm.

Summary

The user provides one or more functions (models) and corresponding datasets to be fitted by their model by adjusting specified parameters to minimize the total \(\chi^2\) across all datasets.

A dataset consists of a multi-dimensional array of dependant values along with their uncertainties and one or more sets of independent variables. Each model is a function of the independent variables and some or all of the parameters. Each sub-array along the specified axes is independently fit by adjusting parameters.

A fit is optimized if the results of the model functions most closely match the dependant values provided. This produces an output array of fits. Each fit specifies the optimal parameter values and other information.

Fitter Class

The frankford.Fitter class is used in two steps:

  • The initializer is passed information about the parameters to be used in the fits and the model(s) (function(s)) that will be fitted to the data. This method creates the GPU code and loads it into the current context.

  • The fitter object is called with data about free parameters and datasets. This actually runs the code on the GPU and returns fit data. The fit data that is returned contains the optimal parameter values and other information.

class frankford.Fitter(parameters, models)

Represent a fit set.

__init__(parameters, models)

Setup an array of fits.

Parameters:
__call__(parameter_settings, datasets, *, returned_parameters=None, returned_uncertainties=(), returned_covar=(), block_size=256)

Execute an array of fits on the GPU and return the output array.

Parameters:

  • parameter_settings (dict of str to (frankford.FreeParameterSetting | frankford.FixedParameterSetting)) – settings for free and fixed parameters

  • returned_parameters (None | list of str, optional) – list of parameters to return, defaults to returning all parameters.

  • returned_uncertainties (list of str, optional) – list of parameter uncertainties to return, defaults to []

  • returned_covar (list of (str, str), optional) – list of parameter covariances to return, defaults to []

  • block_size (int, optional) – number of threads per block on GPU, defaults to 256

property ftol

Relative chi-square convergence criterium

Return type:

np.double

property xtol

Relative parameter convergence criterium

Return type:

np.double

property gtol

Orthogonality convergence criterium

Return type:

np.double

property stepfactor

Initial step bound

Return type:

np.double

property covtol

Range tolerance for covariance calculation

Return type:

np.double

property maxiter

Maximum number of iterations

Return type:

np.int64

property douserscale

Scale variables by user values?

Return type:

bool

property parameters

Loaded parameter

Return type:

dict of str to (frankford.FreeParameter | frankford.FixedParameter | frankford.TiedParameter)

property models

Loaded models

Return type:

dict of Any to callable