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

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

.. _sphx_glr_auto_examples_c_fields_plot_elem_wise_diff.py:


==========================================
Elementwise Partial Derivative (2D Cosine)
==========================================

This example demonstrates how to compute the **elementwise partial derivatives**
of a scalar field in a Cartesian coordinate system using PyMetric’s high-level
:class:`~fields.base.DenseField` interface.

We define a scalar field of the form:

.. math::

    f(x, y) = \cos(3x)\sin(4y)

We then compute and visualize:

- The original scalar field
- The partial derivative with respect to :math:`x`
- The partial derivative with respect to :math:`y`

This is useful for verifying numerical derivative accuracy in simple geometries.

Dependencies
------------
- :class:`~fields.base.DenseField`
- :class:`~grids.core.UniformGrid`
- :class:`~coordinates.coordinate_systems.CartesianCoordinateSystem2D`

.. GENERATED FROM PYTHON SOURCE LINES 30-33

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np








.. GENERATED FROM PYTHON SOURCE LINES 34-35

Import required modules

.. GENERATED FROM PYTHON SOURCE LINES 35-37

.. code-block:: Python

    from pymetric import CartesianCoordinateSystem2D, DenseField, UniformGrid








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Setup the coordinate system and uniform grid
--------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 40-46

.. code-block:: Python

    cs = CartesianCoordinateSystem2D()

    # Define bounding box and resolution
    bbox = [[-2, -2], [2, 2]]
    grid = UniformGrid(cs, bbox, [100, 100], center="cell")








.. GENERATED FROM PYTHON SOURCE LINES 47-50

Define the scalar field on the grid
-----------------------------------
We define f(x, y) = cos(3x) * sin(4y)

.. GENERATED FROM PYTHON SOURCE LINES 50-57

.. code-block:: Python

    field: DenseField = DenseField.from_function(
        lambda x, y: np.cos(3 * x) * np.sin(4 * y), grid, axes=["x", "y"]
    )

    # Extract mesh for plotting
    X, Y = field.grid.compute_domain_mesh(axes=["x", "y"])








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Plot the original scalar field
------------------------------

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.. code-block:: Python

    plt.figure(figsize=(6, 5))
    plt.pcolormesh(X, Y, field[...], shading="auto", cmap="viridis")
    plt.title(r"$f(x, y) = \cos(3x)\sin(4y)$")
    plt.xlabel("x")
    plt.ylabel("y")
    plt.colorbar(label="Field Value")
    plt.tight_layout()
    plt.show()




.. image-sg:: /auto_examples/c_fields/images/sphx_glr_plot_elem_wise_diff_001.png
   :alt: $f(x, y) = \cos(3x)\sin(4y)$
   :srcset: /auto_examples/c_fields/images/sphx_glr_plot_elem_wise_diff_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 70-73

Compute and plot the partial derivatives
----------------------------------------
Use the `element_wise_partial_derivative` method from DenseField.

.. GENERATED FROM PYTHON SOURCE LINES 73-99

.. code-block:: Python

    gradF = field.element_wise_partial_derivatives()

    # Create the subplots
    fig, axes = plt.subplots(1, 3, figsize=(12, 4), sharex=True, sharey=True)

    # Plot original field
    a = axes[0].pcolormesh(X, Y, field[...], shading="auto", cmap="seismic")
    axes[0].set_title(r"$f(x, y)$")
    plt.colorbar(a, ax=axes[0], location="top", orientation="horizontal")

    # Partial w.r.t x
    b = axes[1].pcolormesh(X, Y, gradF[..., 0], shading="auto", cmap="seismic")
    axes[1].set_title(r"$\partial f / \partial x$")
    plt.colorbar(b, ax=axes[1], location="top", orientation="horizontal")

    # Partial w.r.t y
    c = axes[2].pcolormesh(X, Y, gradF[..., 1], shading="auto", cmap="seismic")
    axes[2].set_title(r"$\partial f / \partial y$")
    plt.colorbar(c, ax=axes[2], location="top", orientation="horizontal")

    for ax in axes:
        ax.set_xlabel("x")
        ax.set_ylabel("y")

    plt.tight_layout()
    plt.show()



.. image-sg:: /auto_examples/c_fields/images/sphx_glr_plot_elem_wise_diff_002.png
   :alt: $f(x, y)$, $\partial f / \partial x$, $\partial f / \partial y$
   :srcset: /auto_examples/c_fields/images/sphx_glr_plot_elem_wise_diff_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.490 seconds)


.. _sphx_glr_download_auto_examples_c_fields_plot_elem_wise_diff.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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