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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples\example_04_fit_concave_elliptic_cylinder_with_opt.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_example_04_fit_concave_elliptic_cylinder_with_opt.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_example_04_fit_concave_elliptic_cylinder_with_opt.py:


Example 04: Fit concave elliptic cylinder 
=========================================

This example shows how to fit a concave elliptic cylinder to simulated data using the XMF library.

.. GENERATED FROM PYTHON SOURCE LINES 7-85



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/images/sphx_glr_example_04_fit_concave_elliptic_cylinder_with_opt_001.png
         :alt: Concave Elliptic Cylinder
         :srcset: /auto_examples/images/sphx_glr_example_04_fit_concave_elliptic_cylinder_with_opt_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_example_04_fit_concave_elliptic_cylinder_with_opt_002.png
         :alt: Concave Elliptic Cylinder
         :srcset: /auto_examples/images/sphx_glr_example_04_fit_concave_elliptic_cylinder_with_opt_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_example_04_fit_concave_elliptic_cylinder_with_opt_003.png
         :alt: Concave Elliptic Cylinder, Fitting, Residual
         :srcset: /auto_examples/images/sphx_glr_example_04_fit_concave_elliptic_cylinder_with_opt_003.png
         :class: sphx-glr-multi-img





.. 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 optimization flag dictionary
    opt_dict = {
        'p': False,
        'q': False,
        'theta': False
    }

    # Concave Elliptic Cylinder 

    # Slope profile
    sx1d = xmf.generate_1d_slope(xmf.standard_concave_elliptic_cylinder_xslope, x1d, abs_p, abs_q, theta, x_i, beta) 
    sx1d_measured = sx1d + np.random.randn(sx1d.shape[0])*slope_measurement_noise_std 
    sx1d_res, sx1d_fit, opt_params_dict, opt_params_ci_dict, _ = xmf.fit_concave_ellipse_slope(x1d, sx1d_measured, input_params_dict, opt_dict) 
    xmf.fig_show_1d_fitting_slope(x1d, sx1d_measured, sx1d_fit, sx1d_res, true_params_dict, opt_params_dict, opt_params_ci_dict, 'Concave Elliptic Cylinder') 

    # Height profile
    z1d = xmf.generate_1d_height(xmf.standard_concave_elliptic_cylinder_height, x1d, abs_p, abs_q, theta, x_i, z_i, beta) 
    z1d_measured = z1d + np.random.randn(z1d.shape[0])*height_measurement_noise_std 
    z1d_res, z1d_fit, opt_params_dict, opt_params_ci_dict, _ = xmf.fit_concave_ellipse_height(x1d, z1d_measured, input_params_dict, opt_dict) 
    xmf.fig_show_1d_fitting_height(x1d, z1d_measured, z1d_fit, z1d_res, true_params_dict, opt_params_dict, opt_params_ci_dict, 'Concave Elliptic Cylinder') 

    # Height map
    z2d = xmf.generate_2d_cylinder_height(xmf.standard_concave_elliptic_cylinder_height, x2d, y2d, abs_p, abs_q, theta, x_i, z_i, alpha, beta, gamma) 
    z2d_measured = z2d + np.random.randn(z2d.shape[0], z2d.shape[1])*height_measurement_noise_std 
    z2d_res, z2d_fit, opt_params_dict, opt_params_ci_dict, _ = xmf.fit_concave_elliptic_cylinder_height(x2d, y2d, z2d_measured, input_params_dict, opt_dict) 
    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 Elliptic Cylinder') 

.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.830 seconds)


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