.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/02_kriging3D.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_kriging3D.py>`
        to download the full example code.

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

.. _sphx_glr_examples_02_kriging3D.py:


Three-Dimensional Kriging Example
=================================

.. GENERATED FROM PYTHON SOURCE LINES 6-27

.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt

    from pykrige.ok3d import OrdinaryKriging3D
    from pykrige.uk3d import UniversalKriging3D

    data = np.array(
        [
            [0.1, 0.1, 0.3, 0.9],
            [0.2, 0.1, 0.4, 0.8],
            [0.1, 0.3, 0.1, 0.9],
            [0.5, 0.4, 0.4, 0.5],
            [0.3, 0.3, 0.2, 0.7],
        ]
    )

    gridx = np.arange(0.0, 0.6, 0.05)
    gridy = np.arange(0.0, 0.6, 0.01)
    gridz = np.arange(0.0, 0.6, 0.1)








.. GENERATED FROM PYTHON SOURCE LINES 28-30

Create the 3D ordinary kriging object and solves for the three-dimension kriged
volume and variance. Refer to OrdinaryKriging3D.__doc__ for more information.

.. GENERATED FROM PYTHON SOURCE LINES 30-36

.. code-block:: Python


    ok3d = OrdinaryKriging3D(
        data[:, 0], data[:, 1], data[:, 2], data[:, 3], variogram_model="linear"
    )
    k3d1, ss3d = ok3d.execute("grid", gridx, gridy, gridz)








.. GENERATED FROM PYTHON SOURCE LINES 37-39

Create the 3D universal kriging object and solves for the three-dimension kriged
volume and variance. Refer to UniversalKriging3D.__doc__ for more information.

.. GENERATED FROM PYTHON SOURCE LINES 39-50

.. code-block:: Python


    uk3d = UniversalKriging3D(
        data[:, 0],
        data[:, 1],
        data[:, 2],
        data[:, 3],
        variogram_model="linear",
        drift_terms=["regional_linear"],
    )
    k3d2, ss3d = uk3d.execute("grid", gridx, gridy, gridz)








.. GENERATED FROM PYTHON SOURCE LINES 51-55

To use the generic 'specified' drift term, the user must provide the drift values
at each data point and at every grid point. The following example is equivalent to
using a linear drift in all three spatial dimensions. Refer to
UniversalKriging3D.__doc__ for more information.

.. GENERATED FROM PYTHON SOURCE LINES 55-70

.. code-block:: Python


    zg, yg, xg = np.meshgrid(gridz, gridy, gridx, indexing="ij")
    uk3d = UniversalKriging3D(
        data[:, 0],
        data[:, 1],
        data[:, 2],
        data[:, 3],
        variogram_model="linear",
        drift_terms=["specified"],
        specified_drift=[data[:, 0], data[:, 1], data[:, 2]],
    )
    k3d3, ss3d = uk3d.execute(
        "grid", gridx, gridy, gridz, specified_drift_arrays=[xg, yg, zg]
    )








.. GENERATED FROM PYTHON SOURCE LINES 71-75

To use the generic 'functional' drift term, the user must provide a callable
function that takes only the spatial dimensions as arguments. The following example
is equivalent to using a linear drift only in the x-direction. Refer to
UniversalKriging3D.__doc__ for more information.

.. GENERATED FROM PYTHON SOURCE LINES 75-88

.. code-block:: Python


    func = lambda x, y, z: x
    uk3d = UniversalKriging3D(
        data[:, 0],
        data[:, 1],
        data[:, 2],
        data[:, 3],
        variogram_model="linear",
        drift_terms=["functional"],
        functional_drift=[func],
    )
    k3d4, ss3d = uk3d.execute("grid", gridx, gridy, gridz)








.. GENERATED FROM PYTHON SOURCE LINES 89-93

Note that the use of the 'specified' and 'functional' generic drift capabilities is
essentially identical in the two-dimensional universal kriging class (except for a
difference in the number of spatial coordinates for the passed drift functions).
See UniversalKriging.__doc__ for more information.

.. GENERATED FROM PYTHON SOURCE LINES 93-105

.. code-block:: Python


    fig, (ax1, ax2, ax3, ax4) = plt.subplots(4)
    ax1.imshow(k3d1[:, :, 0], origin="lower")
    ax1.set_title("ordinary kriging")
    ax2.imshow(k3d2[:, :, 0], origin="lower")
    ax2.set_title("regional lin. drift")
    ax3.imshow(k3d3[:, :, 0], origin="lower")
    ax3.set_title("specified drift")
    ax4.imshow(k3d4[:, :, 0], origin="lower")
    ax4.set_title("functional drift")
    plt.tight_layout()
    plt.show()



.. image-sg:: /examples/images/sphx_glr_02_kriging3D_001.png
   :alt: ordinary kriging, regional lin. drift, specified drift, functional drift
   :srcset: /examples/images/sphx_glr_02_kriging3D_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.169 seconds)


.. _sphx_glr_download_examples_02_kriging3D.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 02_kriging3D.ipynb <02_kriging3D.ipynb>`

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

      :download:`Download Python source code: 02_kriging3D.py <02_kriging3D.py>`

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

      :download:`Download zipped: 02_kriging3D.zip <02_kriging3D.zip>`


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

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