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

    Click :ref:`here <sphx_glr_download_intro_summary-exercises_auto_examples_plot_optimize_lidar_data_fit.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_intro_summary-exercises_auto_examples_plot_optimize_lidar_data_fit.py:


The lidar system, data and fit (1 of 2 datasets)
================================================

Generate a chart of the data fitted by Gaussian curve




.. image:: /intro/summary-exercises/auto_examples/images/sphx_glr_plot_optimize_lidar_data_fit_001.png
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [ 2.70363341 27.82020742 15.47924562  3.05636228]




|


.. code-block:: python

    import numpy as np
    import matplotlib.pyplot as plt

    from scipy.optimize import leastsq


    def model(t, coeffs):
        return coeffs[0] + coeffs[1] * np.exp(- ((t-coeffs[2])/coeffs[3])**2)


    def residuals(coeffs, y, t):
        return y - model(t, coeffs)


    waveform_1 = np.load('waveform_1.npy')
    t = np.arange(len(waveform_1))

    x0 = np.array([3, 30, 15, 1], dtype=float)
    x, flag = leastsq(residuals, x0, args=(waveform_1, t))

    print(x)

    fig, ax = plt.subplots(figsize=(8, 6))
    plt.plot(t, waveform_1, t, model(t, x))
    plt.xlabel('Time [ns]')
    plt.ylabel('Amplitude [bins]')
    plt.legend(['Waveform', 'Model'])
    plt.show()

**Total running time of the script:** ( 0 minutes  0.063 seconds)


.. _sphx_glr_download_intro_summary-exercises_auto_examples_plot_optimize_lidar_data_fit.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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