adamstone/datafit

Python package for fitting experimental data to mathematical models and analyzing parameter correlations.

datafit.py

This is a python implementation for fitting experimental data to mathematical models and analyzing the quality of fit. The fitting itself is performed by a Levenberg-Marquardt algorithm via the scipy.optimize.leastsq function, and the main role of this code is to facilitate viewing and analysis of the fitting results, including

Standard deviations of best-fit parameter values
Sum of squares of residuals
Parameter covariance matrix
Parameter correlation matrix
Parameter partial correlation matrix
Plotting of model against data
Plotting of fit residuals

The original code was written in the Sage mathematics environment (http://www.sagemath.org) during a graduate data analysis class in order to analyze a series of specific case studies, which are included in the repository along with some of the code adapted to a pure python implementation. Because it began as Sage worksheets, it retains some aspects of the Sage implementation such as the use of symbolic expressions to define model functions (via the sympy module).

In general, csv data is imported and the x and y columns selected using the get_data and get_xy functions. The model expression is defined symbolically, using the sympy.symbols method to initialize the variables and fitting parameters, and passed to a Model object. The x and y data are then passed to the find_fit method of the model along with a dictionary of initial guess values. If the fit is successful, an instance of the Fit class will be returned.

The Fit class includes summary, plot, and plot_residuals methods. The summary prints the best-fit parameter values as well as several outputs useful for analyzing the quality of fit. By default the partial correlation matrix is omitted, as it can become relatively slow to calculate as the number of parameters increases, but it can be requested by setting the partial_correlations keyword of the Model's find_fit call to True.

Dependencies

numpy, scipy, matplotlib, and sympy.