Example codes
==============

Python example for fitting a concave ellipsoid height map:

.. code-block:: python

    import numpy as np
    import xmf

    # 1. Define lateral coordinates
    x_range = 200e-3 
    y_range = 20e-3 
    x_num = 201 
    y_num = 21 

    x1d = np.linspace(-x_range/2, x_range/2, x_num) 
    y1d = np.linspace(-y_range/2, y_range/2, y_num) 
    x2d, y2d = np.meshgrid(x1d, y1d)

    # 2. Set mirror parameters
    # 2.1. Shape parameters
    abs_p = 30 
    abs_q = 0.3
    theta = 30e-3 

    # 2.2. Pose parameters
    x_i = -1e-3 
    y_i = -2e-4 
    z_i = 3e-7 
    alpha = 2e-6 
    beta = 1e-5 
    gamma = 0.5e-3 

    # 2.3. True parameters as dictionary
    true_params_dict = {
        'p': abs_p,
        'q': abs_q,
        'theta': theta,
        'x_i': x_i,
        'y_i': y_i,
        'z_i': z_i,
        'alpha': alpha,
        'beta': beta,
        'gamma': gamma
    }

    # 3. Set measurement noise
    height_measurement_noise_std = 0.5e-9
    slope_measurement_noise_std = 100e-9

    # 4. Demonstarte the fitting 
    # 4.1. Set input parameters as dictionary
    input_params_dict = {
        'p': abs_p,
        'q': abs_q,
        'theta': theta
    }

    # 4.2. Set the tolerance dictionary
    tol_dict = {
        'p': 0,
        'q': 0,
        'theta': 0
    }

    # 4.3. Generate the surface
    z2d = xmf.generate_2d_curved_surface_height(xmf.standard_concave_ellipsoid_height, x2d, y2d, abs_p, abs_q, theta, x_i, y_i, z_i, alpha, beta, gamma) 
    # 4.4. Adding noise to mimic the measured data
    z2d_measured = z2d + np.random.randn(z2d.shape[0], z2d.shape[1])*height_measurement_noise_std 
    # 4.5. Fit the surface shape
    z2d_res, z2d_fit, opt_params_dict, opt_params_ci_dict, _ = xmf.fit_concave_ellipsoid_height(x2d, y2d, z2d_measured, input_params_dict, tol_dict) 
    # 4.6. Show fitting results
    xmf.fig_show_2d_fitting_map(x2d, y2d, z2d_measured, z2d_fit, z2d_res, true_params_dict, opt_params_dict, opt_params_ci_dict,'Concave Ellipsoid') 


MATLAB example for fitting a concave elliptic cylinder height map:

.. code-block:: matlab
   
    % 1. Define lateral coordinates
    x_range = 200e-3;
    y_range = 20e-3;
    x_num = 201;
    y_num = 21;
    x1d = linspace(-x_range/2, x_range/2, x_num);
    y1d = linspace(-y_range/2, y_range/2, y_num);
    [x2d, y2d] = meshgrid(x1d, y1d);

    % 2. Set mirror parameters
    % 2.1. Shape parameters
    abs_p = 30;
    abs_q = 0.3;
    theta = 30e-3;

    % 2.2. Pose parameters
    x_i = -1e-3;
    y_i = -2e-4;
    z_i = 3e-7;
    alpha = 2e-6;
    beta = 1e-5;
    gamma = 0.5e-3;

    % 2.3. True parameters as structure
    true_params_struct.p = abs_p;
    true_params_struct.q = abs_q;
    true_params_struct.theta = theta;
    true_params_struct.x_i = x_i;
    true_params_struct.y_i = y_i;
    true_params_struct.z_i = z_i;
    true_params_struct.alpha = alpha;
    true_params_struct.beta = beta;
    true_params_struct.gamma = gamma;

    % 3. Set measurement noise
    height_measurement_noise_std = 0.5e-9;
    slope_measurement_noise_std = 100e-9;

    % 4. Demonstarte the fitting 
    % 4.1. Set input parameters as structure
    input_params_struct.p = abs_p;
    input_params_struct.q = abs_q;
    input_params_struct.theta = theta;

    % 4.2. Set the optimization flag structure
    opt_struct.p = false;
    opt_struct.q = false;
    opt_struct.theta = false;

    % 4.3. Generate the surface
    z2d = generate_2d_cylinder_height(@standard_concave_elliptic_cylinder_height, x2d, y2d, abs_p, abs_q, theta, x_i, z_i, alpha, beta, gamma);
    % 4.4. Adding noise to mimic the measured data
    z2d_measured = z2d + randn(size(z2d))*height_measurement_noise_std;
    % 4.5. Fit the surface shape
    [z2d_res, z2d_fit, opt_params_struct, opt_params_ci_struct] = fit_concave_elliptic_cylinder_height(x2d, y2d, z2d_measured, input_params_struct, opt_struct);
    % 4.6. Show fitting results
    fig_show_2d_fitting_map(x1d, y1d, z2d_measured, z2d_fit, z2d_res, true_params_struct, opt_params_struct, opt_params_ci_struct, 'Concave Elliptic Cylinder');