.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/02_cov_model/02_aniso_rotation.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_02_cov_model_02_aniso_rotation.py>`
        to download the full example code.

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

.. _sphx_glr_examples_02_cov_model_02_aniso_rotation.py:


Anisotropy and Rotation
=======================

The internally used (semi-) variogram
represents the isotropic case for the model.
Nevertheless, you can provide anisotropy ratios by:

.. GENERATED FROM PYTHON SOURCE LINES 9-17

.. code-block:: Python


    import gstools as gs

    model = gs.Gaussian(dim=3, var=2.0, len_scale=10, anis=0.5)
    print(model.anis)
    print(model.len_scale_vec)






.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [1.  0.5]
    [10. 10.  5.]




.. GENERATED FROM PYTHON SOURCE LINES 18-25

As you can see, we defined just one anisotropy-ratio
and the second transversal direction was filled up with ``1.``.
You can get the length-scales in each direction by
the attribute :any:`CovModel.len_scale_vec`. For full control you can set
a list of anistropy ratios: ``anis=[0.5, 0.4]``.

Alternatively you can provide a list of length-scales:

.. GENERATED FROM PYTHON SOURCE LINES 25-34

.. code-block:: Python


    model = gs.Gaussian(dim=3, var=2.0, len_scale=[10, 5, 4])
    model.plot("vario_spatial")
    print("Anisotropy representations:")
    print("Anis. ratios:", model.anis)
    print("Main length scale", model.len_scale)
    print("All length scales", model.len_scale_vec)





.. image-sg:: /examples/02_cov_model/images/sphx_glr_02_aniso_rotation_001.png
   :alt: Field 3D structured (50, 50, 50),   Plane
   :srcset: /examples/02_cov_model/images/sphx_glr_02_aniso_rotation_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Anisotropy representations:
    Anis. ratios: [0.5 0.4]
    Main length scale 10.0
    All length scales [10.  5.  4.]




.. GENERATED FROM PYTHON SOURCE LINES 35-41

Rotation Angles
---------------

The main directions of the field don't have to coincide with the spatial
directions :math:`x`, :math:`y` and :math:`z`. Therefore you can provide
rotation angles for the model:

.. GENERATED FROM PYTHON SOURCE LINES 41-46

.. code-block:: Python


    model = gs.Gaussian(dim=3, var=2.0, len_scale=[10, 2], angles=2.5)
    model.plot("vario_spatial")
    print("Rotation angles", model.angles)




.. image-sg:: /examples/02_cov_model/images/sphx_glr_02_aniso_rotation_002.png
   :alt: Field 3D structured (50, 50, 50),   Plane
   :srcset: /examples/02_cov_model/images/sphx_glr_02_aniso_rotation_002.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Rotation angles [2.5 0.  0. ]




.. GENERATED FROM PYTHON SOURCE LINES 47-57

Again, the angles were filled up with ``0.`` to match the dimension and you
could also provide a list of angles. The number of angles depends on the
given dimension:

- in 1D: no rotation performable
- in 2D: given as rotation around z-axis
- in 3D: given by yaw, pitch, and roll (known as
  `Tait–Bryan <https://en.wikipedia.org/wiki/Euler_angles#Tait-Bryan_angles>`_
  angles)
- in nD: See the random field example about higher dimensions


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

   **Total running time of the script:** (0 minutes 0.356 seconds)


.. _sphx_glr_download_examples_02_cov_model_02_aniso_rotation.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 02_aniso_rotation.ipynb <02_aniso_rotation.ipynb>`

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

      :download:`Download Python source code: 02_aniso_rotation.py <02_aniso_rotation.py>`

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

      :download:`Download zipped: 02_aniso_rotation.zip <02_aniso_rotation.zip>`


.. only:: html

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

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