.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples\example_01_fit_concave_ellipsoid_with_tol.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_01_fit_concave_ellipsoid_with_tol.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_example_01_fit_concave_ellipsoid_with_tol.py:


Example 01: Fit concave ellipsoid
=================================

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

.. GENERATED FROM PYTHON SOURCE LINES 8-76



.. image-sg:: /auto_examples/images/sphx_glr_example_01_fit_concave_ellipsoid_with_tol_001.png
   :alt: Concave Ellipsoid, Fitting, Residual
   :srcset: /auto_examples/images/sphx_glr_example_01_fit_concave_ellipsoid_with_tol_001.png
   :class: sphx-glr-single-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 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') 


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

   **Total running time of the script:** (0 minutes 0.527 seconds)


.. _sphx_glr_download_auto_examples_example_01_fit_concave_ellipsoid_with_tol.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: example_01_fit_concave_ellipsoid_with_tol.ipynb <example_01_fit_concave_ellipsoid_with_tol.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: example_01_fit_concave_ellipsoid_with_tol.py <example_01_fit_concave_ellipsoid_with_tol.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: example_01_fit_concave_ellipsoid_with_tol.zip <example_01_fit_concave_ellipsoid_with_tol.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_