.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/eigenmodes_2d/example_2.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_gallery_eigenmodes_2d_example_2.py>`
        to download the full example code.

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

.. _sphx_glr_gallery_eigenmodes_2d_example_2.py:


Example: eigenmodes 2
======================

In this example, we calculate and visualize the eigenmodes of a finite difference operator combined
with a circular mesh potential. The boundary conditions, mesh properties, and eigenmode calculations
are all set up for demonstration purposes.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

+-------------+------------+--------------+------------+------------+
| Boundaries  |    left    |     right    |    top     |   bottom   |
+=============+============+==============+============+============+
|      -      |  anti-sym  |     zero     |   zero     |   zero     |
+-------------+------------+--------------+------------+------------+

.. GENERATED FROM PYTHON SOURCE LINES 18-21

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

.. GENERATED FROM PYTHON SOURCE LINES 21-27

.. code-block:: Python


    from scipy.sparse import linalg
    from PyFinitDiff.finite_difference_2D import FiniteDifference, get_circular_mesh_triplet, Boundaries
    import matplotlib.pyplot as plt
    from PyFinitDiff import BoundaryValue








.. GENERATED FROM PYTHON SOURCE LINES 28-31

Setting up the finite difference instance and boundaries
---------------------------------------------------------
We define the grid size and set up the finite difference instance with specified boundary conditions.

.. GENERATED FROM PYTHON SOURCE LINES 31-46

.. code-block:: Python


    n_y = n_x = 80

    sparse_instance = FiniteDifference(
        n_x=n_x,
        n_y=n_y,
        dx=1,
        dy=1,
        derivative=2,
        accuracy=4,
        boundaries=Boundaries(left=BoundaryValue.ANTI_SYMMETRIC)
    )

    triplet = sparse_instance.triplet








.. GENERATED FROM PYTHON SOURCE LINES 47-50

Creating the circular mesh potential
-------------------------------------
We create a circular mesh triplet, specifying the inner and outer values, and offset parameters.

.. GENERATED FROM PYTHON SOURCE LINES 50-61

.. code-block:: Python


    mesh_triplet = get_circular_mesh_triplet(
        n_x=n_x,
        n_y=n_y,
        value_out=1.0,
        value_in=1.4444,
        x_offset=-100,
        y_offset=0,
        radius=70
    )








.. GENERATED FROM PYTHON SOURCE LINES 62-65

Combining the finite difference and mesh triplets
--------------------------------------------------
We add the circular mesh triplet to the finite difference Laplacian to form the dynamic triplet.

.. GENERATED FROM PYTHON SOURCE LINES 65-68

.. code-block:: Python


    dynamic_triplet = sparse_instance.triplet + mesh_triplet








.. GENERATED FROM PYTHON SOURCE LINES 69-72

Calculating the eigenmodes
---------------------------
We compute the first four eigenmodes of the combined operator using the scipy sparse linear algebra package.

.. GENERATED FROM PYTHON SOURCE LINES 72-82

.. code-block:: Python


    eigen_values, eigen_vectors = linalg.eigs(
        dynamic_triplet.to_scipy_sparse(),
        k=4,
        which='LM',
        sigma=1.4444
    )

    shape = [sparse_instance.n_x, sparse_instance.n_y]








.. GENERATED FROM PYTHON SOURCE LINES 83-86

Visualizing the eigenmodes with matplotlib
-------------------------------------------
We visualize the first four eigenmodes by reshaping the eigenvectors and plotting them using matplotlib.

.. GENERATED FROM PYTHON SOURCE LINES 86-97

.. code-block:: Python


    fig, axes = plt.subplots(1, 4, figsize=(16, 4), constrained_layout=True)

    for i, ax in enumerate(axes):
        vector = eigen_vectors[:, i].real.reshape(shape)
        mesh = ax.pcolormesh(vector, shading='auto', cmap='viridis')
        ax.set_title(f'eigenvalue: {eigen_values[i]:.3f}')
        ax.set_aspect('equal')
        plt.colorbar(mesh, ax=ax)

    plt.show()



.. image-sg:: /gallery/eigenmodes_2d/images/sphx_glr_example_2_001.png
   :alt: eigenvalue: 1.427+0.000j, eigenvalue: 1.413+0.000j, eigenvalue: 1.397+0.000j, eigenvalue: 1.387+0.000j
   :srcset: /gallery/eigenmodes_2d/images/sphx_glr_example_2_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 2.061 seconds)


.. _sphx_glr_download_gallery_eigenmodes_2d_example_2.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: example_2.ipynb <example_2.ipynb>`

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

      :download:`Download Python source code: example_2.py <example_2.py>`

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

      :download:`Download zipped: example_2.zip <example_2.zip>`


.. only:: html

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

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