.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/eigenmodes_1d/example_0.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_1d_example_0.py>`
        to download the full example code.

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

.. _sphx_glr_gallery_eigenmodes_1d_example_0.py:


Example: 1D eigenmodes 0
========================

In this example, we calculate and visualize the eigenmodes of a 1D 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 12-19

.. list-table:: 1D Finite-difference parameters
   :widths: 25
   :header-rows: 0

   * - boundaries: {left: none, right: none}
   * - derivative: 2
   * - accuracy: 6

.. GENERATED FROM PYTHON SOURCE LINES 21-24

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

.. GENERATED FROM PYTHON SOURCE LINES 24-30

.. code-block:: Python


    from scipy.sparse import linalg
    import matplotlib.pyplot as plt
    from PyFinitDiff.finite_difference_1D import FiniteDifference, get_circular_mesh_triplet, Boundaries
    from PyFinitDiff import BoundaryValue








.. GENERATED FROM PYTHON SOURCE LINES 31-34

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 34-45

.. code-block:: Python


    n_x = 100

    sparse_instance = FiniteDifference(
        n_x=n_x,
        dx=1,
        derivative=2,
        accuracy=2,
        boundaries=Boundaries(left=BoundaryValue.NONE, right=BoundaryValue.NONE)
    )








.. GENERATED FROM PYTHON SOURCE LINES 46-49

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 49-58

.. code-block:: Python


    mesh_triplet = get_circular_mesh_triplet(
        n_x=n_x,
        radius=60,
        value_out=1,
        value_in=1.4444,
        x_offset=0
    )








.. GENERATED FROM PYTHON SOURCE LINES 59-62

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

.. GENERATED FROM PYTHON SOURCE LINES 62-65

.. code-block:: Python


    dynamic_triplet = sparse_instance.triplet + mesh_triplet








.. GENERATED FROM PYTHON SOURCE LINES 66-69

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 69-77

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 78-81

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 81-94

.. code-block:: Python


    fig, axes = plt.subplots(2, 2, figsize=(10, 8), constrained_layout=True)
    axes = axes.flatten()

    for i, ax in enumerate(axes):
        vector = eigen_vectors[:, i].real
        ax.plot(vector)
        ax.set_title(f'eigenvalue: {eigen_values[i]:.3f}')
        ax.set_xlabel('Index')
        ax.set_ylabel('Amplitude')
        ax.grid(True)

    plt.show()



.. image-sg:: /gallery/eigenmodes_1d/images/sphx_glr_example_0_001.png
   :alt: eigenvalue: 1.442+0.000j, eigenvalue: 1.435+0.000j, eigenvalue: 1.422+0.000j, eigenvalue: 1.405+0.000j
   :srcset: /gallery/eigenmodes_1d/images/sphx_glr_example_0_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.646 seconds)


.. _sphx_glr_download_gallery_eigenmodes_1d_example_0.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: example_0.ipynb <example_0.ipynb>`

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

      :download:`Download Python source code: example_0.py <example_0.py>`

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

      :download:`Download zipped: example_0.zip <example_0.zip>`


.. only:: html

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

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