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.. "examples/05_kriging/00_simple_kriging.py"
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.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_05_kriging_00_simple_kriging.py>`
        to download the full example code.

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

.. _sphx_glr_examples_05_kriging_00_simple_kriging.py:


Simple Kriging
--------------

Simple kriging assumes a known mean of the data.
For simplicity we assume a mean of 0,
which can be achieved by subtracting the mean from the observed values and
subsequently adding it to the resulting data.

The resulting equation system for :math:`W` is given by:

.. math::

   W = \begin{pmatrix}c(x_1,x_1) & \cdots & c(x_1,x_n) \\
   \vdots & \ddots & \vdots  \\
   c(x_n,x_1) & \cdots & c(x_n,x_n)
   \end{pmatrix}^{-1}
   \begin{pmatrix}c(x_1,x_0) \\ \vdots \\ c(x_n,x_0) \end{pmatrix}

Thereby :math:`c(x_i,x_j)` is the covariance of the given observations.


Example
^^^^^^^

Here we use simple kriging in 1D (for plotting reasons) with 5 given observations/conditions.
The mean of the field has to be given beforehand.

.. GENERATED FROM PYTHON SOURCE LINES 30-43

.. code-block:: Python


    import numpy as np

    from gstools import Gaussian, krige

    # condtions
    cond_pos = [0.3, 1.9, 1.1, 3.3, 4.7]
    cond_val = [0.47, 0.56, 0.74, 1.47, 1.74]
    # resulting grid
    gridx = np.linspace(0.0, 15.0, 151)
    # spatial random field class
    model = Gaussian(dim=1, var=0.5, len_scale=2)








.. GENERATED FROM PYTHON SOURCE LINES 44-47

.. code-block:: Python

    krig = krige.Simple(model, mean=1, cond_pos=cond_pos, cond_val=cond_val)
    krig(gridx)








.. GENERATED FROM PYTHON SOURCE LINES 48-51

.. code-block:: Python

    ax = krig.plot()
    ax.scatter(cond_pos, cond_val, color="k", zorder=10, label="Conditions")
    ax.legend()



.. image-sg:: /examples/05_kriging/images/sphx_glr_00_simple_kriging_001.png
   :alt: Field 1D: (151,)
   :srcset: /examples/05_kriging/images/sphx_glr_00_simple_kriging_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.072 seconds)


.. _sphx_glr_download_examples_05_kriging_00_simple_kriging.py:

.. only:: html

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

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

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

      :download:`Download Python source code: 00_simple_kriging.py <00_simple_kriging.py>`

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

      :download:`Download zipped: 00_simple_kriging.zip <00_simple_kriging.zip>`


.. only:: html

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

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