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

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

.. _sphx_glr_auto_examples_d_differential_geometry_plot_cartesian_gradient.py:


=================================
Gradient In Cartesian Coordinates
=================================

Calculate the gradient of a function in Cartesian coordinates.

.. GENERATED FROM PYTHON SOURCE LINES 9-23

In this example, we'll use the methods in the low-level :mod:`differential_geometry` to
compute the gradient of the function

.. math::

    f(x_1,x_2) = A\sin\left(\omega \left[x_1^2+x_2^2\right]\right).

In Cartesian coordinates, this is an extremely simple operation to compute directly:

.. math::

    \nabla_i f(x_1,x_2) = 2\omega x_i f(x_1,x_2).

To do this computationally, we need to perform the following operations:

.. GENERATED FROM PYTHON SOURCE LINES 23-46

.. code-block:: Python


    import matplotlib.pyplot as plt

    # Import necessary modules.
    import numpy as np

    from pymetric.differential_geometry.dense_ops import dense_gradient

    # Settings:
    A, omega = 1, 5
    cmap = "seismic"

    # Create the x and y grids.
    x, y = np.linspace(-1, 1, 500), np.linspace(-1, 1, 500)
    X, Y = np.meshgrid(x, y, indexing="ij")

    # Compute the field `Z`
    R = X**2 + Y**2
    Z = A * np.sin(omega * R)

    # Compute the gradient.
    gradZ = dense_gradient(Z, 0, 2, x, y)








.. GENERATED FROM PYTHON SOURCE LINES 47-48

With the gradient computed, we can plot the output. The result has a shape ``(500,500,2)``.

.. GENERATED FROM PYTHON SOURCE LINES 48-79

.. code-block:: Python


    fig, ax = plt.subplots(1, 3, figsize=(10, 4), sharex=True, sharey=True)

    ax[0].imshow(Z.T, extent=[-1, 1, -1, 1], cmap=cmap, vmin=-A, vmax=A)
    ax[1].imshow(
        gradZ[..., 0].T, extent=[-1, 1, -1, 1], cmap=cmap, vmin=-A * omega, vmax=A * omega
    )
    ax[2].imshow(
        gradZ[..., 1].T, extent=[-1, 1, -1, 1], cmap=cmap, vmin=-A * omega, vmax=A * omega
    )

    plt.colorbar(
        plt.cm.ScalarMappable(plt.Normalize(vmin=-A, vmax=A), cmap=cmap),
        ax=ax[0],
        orientation="horizontal",
        location="top",
    )
    plt.colorbar(
        plt.cm.ScalarMappable(plt.Normalize(vmin=-A * omega, vmax=A * omega), cmap=cmap),
        ax=ax[1],
        orientation="horizontal",
        location="top",
    )
    plt.colorbar(
        plt.cm.ScalarMappable(plt.Normalize(vmin=-A * omega, vmax=A * omega), cmap=cmap),
        ax=ax[2],
        orientation="horizontal",
        location="top",
    )

    plt.show()



.. image-sg:: /auto_examples/d_differential_geometry/images/sphx_glr_plot_cartesian_gradient_001.png
   :alt: plot cartesian gradient
   :srcset: /auto_examples/d_differential_geometry/images/sphx_glr_plot_cartesian_gradient_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.214 seconds)


.. _sphx_glr_download_auto_examples_d_differential_geometry_plot_cartesian_gradient.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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