NonlinearLeastSquares 1.1

A Python module for solving cost-function minimization problems with nonlinear leastsquares

Consult the module API page at

https://engineering.purdue.edu/kak/distNonlinearLeastSquares/NonlinearLeastSquares-1.1.html

for all information related to this module, including information regarding the latest changes to the code. The page at the URL shown above lists all of the module functionality you can invoke in your own code.

With regard to the basic purpose of this module, it provides a domain agnostic implementation of nonlinear least-squares algorithms (gradient-descent and Levenberg-Marquardt) for fitting a model to observed data. Typically, a model involves several parameters and each observed data element can be expressed as a function of those parameters plus noise. The goal of nonlinear least-squares is to estimate the best values for the parameters given all of the observed data. In order to illustrate how to use the NonlinearLeastSquares class, the module also comes with another class, OptimizeSurfaceFit, whose job is to fit the best surface to noisy height data over an XY-plane. The model in this case would be an analytical expression for the height surface and the goal of nonlinear least-squares would be to estimate the best values for the parameters in the model.

Typical usage syntax for invoking the domain-agnostic NonlinearLeastSquares through your own domain-specific class such as OptimizeSurfaceFit is shown below:

optimizer =  NonlinearLeastSquares(
                 max_iterations = 200,
                 delta_for_jacobian = 0.000001,
                 delta_for_step_size = 0.0001,
             )

surface_fitter = OptimizeSurfaceFit(
                     gen_data_synthetically = True,
                     datagen_functional = "7.8*(x - 0.5)**4 + 2.2*(y - 0.5)**2",
                     data_dimensions = (16,16),
                     how_much_noise_for_synthetic_data = 0.3,
                     model_functional = "a*(x-b)**4 + c*(y-d)**2",
                     initial_param_values = {'a':2.0, 'b':0.4, 'c':0.8, 'd':0.4},
                     display_needed = True,
                     debug = True,
                 )

surface_fitter.set_constructor_options_for_optimizer(optimizer)

result = surface_fitter.calculate_best_fitting_surface('lm')

or

result = surface_fitter.calculate_best_fitting_surface('gd')