.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/01_random_field/07_higher_dimensions.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_01_random_field_07_higher_dimensions.py>`
        to download the full example code.

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

.. _sphx_glr_examples_01_random_field_07_higher_dimensions.py:


Higher Dimensions
-----------------

GSTools provides experimental support for higher dimensions.

Anisotropy is the same as in lower dimensions:

- in `n` dimensions we need `(n-1)` anisotropy ratios

Rotation on the other hand is a bit more complex.
With increasing dimensions more and more rotation angles are added in order
to properply describe the rotated axes of anisotropy.

By design the first rotation angles coincide with the lower ones:

- 2D (rotation in x-y plane) -> 3D: first angle describes xy-plane rotation
- 3D (Tait-Bryan angles) -> 4D: first 3 angles coincide with Tait-Bryan angles

By increasing the dimension from `n` to `(n+1)`, `n` angles are added:

- 2D (1 angle) -> 3D: 3 angles (2 added)
- 3D (3 angles) -> 4D: 6 angles (3 added)

the following list of rotation-planes are described by the list of
angles in the model:

1. x-y plane
2. x-z plane
3. y-z plane
4. x-v plane
5. y-v plane
6. z-v plane
7. ...

The rotation direction in these planes have alternating signs
in order to match Tait-Bryan in 3D.

Let's have a look at a 4D example, where we naively add a 4th dimension.

.. GENERATED FROM PYTHON SOURCE LINES 41-53

.. code-block:: Python


    import matplotlib.pyplot as plt

    import gstools as gs

    dim = 4
    size = 20
    pos = [range(size)] * dim
    model = gs.Exponential(dim=dim, len_scale=5)
    srf = gs.SRF(model, seed=20170519)
    field = srf.structured(pos)








.. GENERATED FROM PYTHON SOURCE LINES 54-56

In order to "prove" correctness, we can calculate an empirical variogram
of the generated field and fit our model to it.

.. GENERATED FROM PYTHON SOURCE LINES 56-63

.. code-block:: Python


    bin_center, vario = gs.vario_estimate(
        pos, field, sampling_size=2000, mesh_type="structured"
    )
    model.fit_variogram(bin_center, vario)
    print(model)





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

 .. code-block:: none

    Exponential(dim=4, var=0.977, len_scale=4.91)




.. GENERATED FROM PYTHON SOURCE LINES 64-68

As you can see, the estimated variance and length scale match our input
quite well.

Let's have a look at the fit and a x-y cross-section of the 4D field:

.. GENERATED FROM PYTHON SOURCE LINES 68-77

.. code-block:: Python


    f, a = plt.subplots(1, 2, gridspec_kw={"width_ratios": [2, 1]}, figsize=[9, 3])
    model.plot(x_max=max(bin_center), ax=a[0])
    a[0].scatter(bin_center, vario)
    a[1].imshow(field[:, :, 0, 0].T, origin="lower")
    a[0].set_title("isotropic empirical variogram with fitted model")
    a[1].set_title("x-y cross-section")
    f.show()




.. image-sg:: /examples/01_random_field/images/sphx_glr_07_higher_dimensions_001.png
   :alt: isotropic empirical variogram with fitted model, x-y cross-section
   :srcset: /examples/01_random_field/images/sphx_glr_07_higher_dimensions_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 78-81

GSTools also provides plotting routines for higher dimensions.
Fields are shown by 2D cross-sections, where other dimensions can be
controlled via sliders.

.. GENERATED FROM PYTHON SOURCE LINES 81-83

.. code-block:: Python


    srf.plot()



.. image-sg:: /examples/01_random_field/images/sphx_glr_07_higher_dimensions_002.png
   :alt: Field 4D structured (20, 20, 20, 20),   Plane
   :srcset: /examples/01_random_field/images/sphx_glr_07_higher_dimensions_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 5.924 seconds)


.. _sphx_glr_download_examples_01_random_field_07_higher_dimensions.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 07_higher_dimensions.ipynb <07_higher_dimensions.ipynb>`

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

      :download:`Download Python source code: 07_higher_dimensions.py <07_higher_dimensions.py>`

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

      :download:`Download zipped: 07_higher_dimensions.zip <07_higher_dimensions.zip>`


.. only:: html

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

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