.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/05_kriging/08_measurement_errors.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_05_kriging_08_measurement_errors.py>`
        to download the full example code.

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

.. _sphx_glr_examples_05_kriging_08_measurement_errors.py:


Incorporating measurement errors
--------------------------------

To incorporate the nugget effect and/or given measurement errors,
one can set `exact` to `False` and provide either individual measurement errors
for each point or set the nugget as a constant measurement error everywhere.

In the following we will show the influence of the nugget and
measurement errors.

.. GENERATED FROM PYTHON SOURCE LINES 12-26

.. code-block:: Python


    import numpy as np

    import gstools as gs

    # condtions
    cond_pos = [0.3, 1.1, 1.9, 3.3, 4.7]
    cond_val = [0.47, 0.74, 0.56, 1.47, 1.74]
    cond_err = [0.01, 0.0, 0.1, 0.05, 0]
    # resulting grid
    gridx = np.linspace(0.0, 15.0, 151)
    # spatial random field class
    model = gs.Gaussian(dim=1, var=0.9, len_scale=1, nugget=0.1)








.. GENERATED FROM PYTHON SOURCE LINES 27-29

Here we will use Simple kriging (`unbiased=False`) to interpolate the given
conditions.

.. GENERATED FROM PYTHON SOURCE LINES 29-41

.. code-block:: Python


    krig = gs.Krige(
        model=model,
        cond_pos=cond_pos,
        cond_val=cond_val,
        mean=1,
        unbiased=False,
        exact=False,
        cond_err=cond_err,
    )
    krig(gridx)








.. GENERATED FROM PYTHON SOURCE LINES 42-45

Let's plot the data. You can see, that the estimated values differ more from
the input, when the given measurement errors get bigger.
In addition we plot the standard deviation.

.. GENERATED FROM PYTHON SOURCE LINES 45-57

.. code-block:: Python


    ax = krig.plot()
    ax.scatter(cond_pos, cond_val, color="k", zorder=10, label="Conditions")
    ax.fill_between(
        gridx,
        # plus/minus standard deviation (70 percent confidence interval)
        krig.field - np.sqrt(krig.krige_var),
        krig.field + np.sqrt(krig.krige_var),
        alpha=0.3,
        label="Standard deviation",
    )
    ax.legend()



.. image-sg:: /examples/05_kriging/images/sphx_glr_08_measurement_errors_001.png
   :alt: Field 1D: (151,)
   :srcset: /examples/05_kriging/images/sphx_glr_08_measurement_errors_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.051 seconds)


.. _sphx_glr_download_examples_05_kriging_08_measurement_errors.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 08_measurement_errors.ipynb <08_measurement_errors.ipynb>`

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

      :download:`Download Python source code: 08_measurement_errors.py <08_measurement_errors.py>`

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

      :download:`Download zipped: 08_measurement_errors.zip <08_measurement_errors.zip>`


.. only:: html

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

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