.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/extras/gradient.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

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

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

.. _sphx_glr_gallery_extras_gradient.py:


Gradient of array
==================

In this example, we calculate the gradient of a 2D array using finite difference methods.
We will explore different orders of derivatives and visualize their effects on the input array.

.. GENERATED FROM PYTHON SOURCE LINES 10-13

Importing required packages
---------------------------
Here we import the necessary libraries for numerical computations, rendering, and finite difference operations.

.. GENERATED FROM PYTHON SOURCE LINES 13-19

.. code-block:: Python


    import numpy as np
    from PyFinitDiff.finite_difference_2D import get_array_derivative, Boundaries
    import matplotlib.pyplot as plt
    from PyFinitDiff import BoundaryValue








.. GENERATED FROM PYTHON SOURCE LINES 20-23

Creating the input mesh
------------------------
We define a 2D Gaussian mesh using two 1D exponential arrays.

.. GENERATED FROM PYTHON SOURCE LINES 23-32

.. code-block:: Python


    idx = np.linspace(-5, 5, 100)
    x_array = np.exp(-idx**2)
    y_array = np.exp(-idx**2)

    y_array, x_array = np.meshgrid(x_array, y_array)

    mesh = x_array * y_array








.. GENERATED FROM PYTHON SOURCE LINES 33-36

Setting boundary conditions
---------------------------
Define boundary conditions for the gradient calculation. Here, we use 'none' for all boundaries.

.. GENERATED FROM PYTHON SOURCE LINES 36-39

.. code-block:: Python


    boundaries = Boundaries(top=BoundaryValue.NONE, bottom=BoundaryValue.NONE, left=BoundaryValue.NONE, right=BoundaryValue.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 40-43

Visualizing the gradient for different derivatives
---------------------------------------------------
We compute the gradient for first, second, and third derivatives and visualize them.

.. GENERATED FROM PYTHON SOURCE LINES 43-64

.. code-block:: Python



    figure, axes = plt.subplots(1, 3, figsize=(12, 4), constrained_layout=True)
    axes = axes.flatten()

    for ax, derivative in zip(axes, [1, 2, 3]):
        gradient = get_array_derivative(
            array=mesh,
            accuracy=6,
            derivative=derivative,
            x_derivative=True,
            y_derivative=True,
            boundaries=boundaries
        )

        image = ax.pcolormesh(gradient.real, shading='auto', cmap='viridis')
        ax.set_title(f'Derivative: {derivative}')
        ax.set_aspect('equal')
        plt.colorbar(image, ax=ax)

    plt.show()



.. image-sg:: /gallery/extras/images/sphx_glr_gradient_001.png
   :alt: Derivative: 1, Derivative: 2, Derivative: 3
   :srcset: /gallery/extras/images/sphx_glr_gradient_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 7.018 seconds)


.. _sphx_glr_download_gallery_extras_gradient.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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