Metadata-Version: 1.1
Name: NonlinearLeastSquares
Version: 1.0
Summary: A Python module for solving cost-function minimization problems with nonlinear leastsquares
Home-page: https://engineering.purdue.edu/kak/distNonlinearLeastSquares/NonlinearLeastSquares-1.0.html
Author: Avinash Kak
Author-email: kak@purdue.edu
License: Python Software Foundation License
Download-URL: https://engineering.purdue.edu/kak/distNonlinearLeastSquares/NonlinearLeastSquares-1.0.tar.gz#md5=5cb2c6a468777c61e351ace8da787552
Description:  
        
        Consult the module API page at 
        
              https://engineering.purdue.edu/kak/distNonlinearLeastSquares/NonlinearLeastSquares-1.0.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, the 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')                             
        
                  
Keywords: gradient descent,nonlinear least-squares,optimization
Platform: All platforms
Classifier: Topic :: Scientific/Engineering :: Information Analysis
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3.5
