Metadata-Version: 1.2
Name: NonlinearLeastSquares
Version: 2.0.2
Summary: A Python module for solving optimization problems with nonlinear least-squares
Home-page: https://engineering.purdue.edu/kak/distNonlinearLeastSquares/NonlinearLeastSquares-2.0.2.html
Author: Avinash Kak
Author-email: kak@purdue.edu
Maintainer: Avinash Kak
Maintainer-email: kak@purdue.edu
License: Python Software Foundation License
Download-URL: https://engineering.purdue.edu/kak/distNonlinearLeastSquares/NonlinearLeastSquares-2.0.2.tar.gz
Description:  
        
        Consult the module API page at 
        
              https://engineering.purdue.edu/kak/distNonlinearLeastSquares/NonlinearLeastSquares-2.0.2.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 two
        additional classes: **OptimizedSurfaceFit** and
        **ProjectiveCamera.**  
        
        The job of **OptimizedSurfaceFit** 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.  
        
        And the job of **ProjectiveCamera** is to demonstrate how
        nonlinear least-squares can be used for estimating scene
        structure from camera motion.  The underlying ideas is that
        you take multiple images of a scene with a camera ---
        something that you can simulate with **ProjectiveCamera**.
        You feed the pixels thus recorded into the
        NonlinearLeastSquares class to estimate the coordinates of
        the scene structure points and, when using uncalibrated
        cameras, to also estimate the extrinsic parameters of the
        camera at each of its positions.
        
        Starting with Version 2.0.0, the module includes code for
        the sparse-bundle-adjustment variant of the
        Levenberg-Marquardt algorithm.
        
        Typical usage syntax for invoking the domain-agnostic
        NonlinearLeastSquares through your own domain-specific class
        such as OptimizedSurfaceFit or ProjectiveCamera is shown below:
        
        ::
        
                optimizer =  NonlinearLeastSquares(                                            
                                 max_iterations = 200,
                                 delta_for_jacobian = 0.000001,
                                 delta_for_step_size = 0.0001,
                             )
            
                surface_fitter = OptimizedSurfaceFit(                                           
                                     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')  
        
        
                                               OR
        
        
                optimizer =  NonlinearLeastSquares.NonlinearLeastSquares(
                                                     max_iterations = 400,
                                                     delta_for_jacobian = 0.000001,
                                                     delta_for_step_size = 0.0001,
                             )
                
                camera = ProjectiveCamera.ProjectiveCamera(
                                     camera_type = 'projective',
                                     alpha_x = 1000.0,
                                     alpha_y = 1000.0,
                                     x0 = 300.0,
                                     y0 = 250.0,
                         )
                camera.initialize()
        
                world_points = camera.make_world_points_for_triangle()
                world_points_xformed = camera.apply_transformation_to_generic_world_points(world_points, ..... )
        
                ##  Now move the camera to different positions and orientations and then
        
                result = camera.get_scene_structure_from_camera_motion('lm')
        
                                               OR
        
                result = camera.get_scene_structure_from_camera_motion_with_bundle_adjustment()
        
                  
Keywords: gradient descent,nonlinear least-squares,optimization,bundle adjustment
Platform: All platforms
Classifier: Topic :: Scientific/Engineering :: Information Analysis
Classifier: Programming Language :: Python :: 3.8
