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

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

.. _sphx_glr_gallery_extras_plot_WM_field.py:


Generating Whittle-Matérn field
=================================

In this example, we generate a Whittle-Matérn field using a finite difference Laplacian operator.
We will explore different correlation lengths and observe their effect on the resulting fields.

.. 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 13-20

.. code-block:: Python


    import numpy as np
    from scipy import linalg
    import matplotlib.pyplot as plt
    from PyFinitDiff.finite_difference_2D import FiniteDifference, Boundaries
    from PyFinitDiff import BoundaryValue








.. GENERATED FROM PYTHON SOURCE LINES 21-24

Setting up the finite difference Laplacian
------------------------------------------
We define a grid and create a finite difference instance that provides us with a Laplacian operator.

.. GENERATED FROM PYTHON SOURCE LINES 24-39

.. code-block:: Python


    n_x = n_y = 20

    sparse_instance = FiniteDifference(
        n_x=n_x,
        n_y=n_y,
        dx=1000 / n_x,
        dy=1000 / n_y,
        derivative=2,
        accuracy=2,
        boundaries=Boundaries(top=BoundaryValue.SYMMETRIC)
    )

    laplacian = sparse_instance.triplet.to_dense()








.. GENERATED FROM PYTHON SOURCE LINES 40-43

Defining the function to generate the Whittle-Matérn field
-----------------------------------------------------------
The following function generates a field by solving a linear system involving the Laplacian and random noise.

.. GENERATED FROM PYTHON SOURCE LINES 43-56

.. code-block:: Python



    def get_field(D: float, lc: float, Nc: float, shape: list):
        n_x, n_y = shape
        eta = np.random.rand(n_x * n_y)

        left_hand_side = (-laplacian + lc**2) ** (3 / 2)
        right_hand_side = eta

        field = linalg.solve(left_hand_side, right_hand_side)

        return Nc * field








.. GENERATED FROM PYTHON SOURCE LINES 57-60

Visualizing the fields for different correlation lengths
---------------------------------------------------------
We generate and visualize fields with varying correlation lengths to see their impact on the structure of the field.

.. GENERATED FROM PYTHON SOURCE LINES 60-73

.. code-block:: Python



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

    for ax, correlation_length in zip(axes, [1, 2, 4]):
        field = get_field(D=3, lc=correlation_length, Nc=1, shape=[n_x, n_y]).reshape([n_x, n_y])
        mesh = ax.pcolormesh(field, shading='auto', cmap='viridis')
        ax.set_title(f'Correlation length: {correlation_length}')
        ax.set_aspect('equal')
        plt.colorbar(mesh, ax=ax)

    plt.show()



.. image-sg:: /gallery/extras/images/sphx_glr_plot_WM_field_001.png
   :alt: Correlation length: 1, Correlation length: 2, Correlation length: 4
   :srcset: /gallery/extras/images/sphx_glr_plot_WM_field_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.766 seconds)


.. _sphx_glr_download_gallery_extras_plot_WM_field.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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