.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/10_normalizer/01_auto_fit.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_10_normalizer_01_auto_fit.py>`
        to download the full example code.

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

.. _sphx_glr_examples_10_normalizer_01_auto_fit.py:


Automatic fitting
-----------------

In order to demonstrate how to automatically fit normalizer and variograms,
we generate synthetic log-normal data, that should be interpolated with
ordinary kriging.

Normalizers are fitted by minimizing the likelihood function and variograms
are fitted by estimating the empirical variogram with automatic binning and
fitting the theoretical model to it. Thereby the sill is constrained to match
the field variance.

Artificial data
^^^^^^^^^^^^^^^

Here we generate log-normal data following a Gaussian covariance model.
We will generate the "original" field on a 60x60 mesh, from which we will take
samples in order to pretend a situation of data-scarcity.

.. GENERATED FROM PYTHON SOURCE LINES 21-35

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import gstools as gs

    # structured field with edge length of 50
    x = y = range(51)
    pos = gs.generate_grid([x, y])
    model = gs.Gaussian(dim=2, var=1, len_scale=10)
    srf = gs.SRF(model, seed=20170519, normalizer=gs.normalizer.LogNormal())
    # generate the original field
    srf(pos)








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Here, we sample 60 points and set the conditioning points and values.

.. GENERATED FROM PYTHON SOURCE LINES 37-45

.. code-block:: Python


    ids = np.arange(srf.field.size)
    samples = np.random.RandomState(20210201).choice(ids, size=60, replace=False)

    # sample conditioning points from generated field
    cond_pos = pos[:, samples]
    cond_val = srf.field[samples]








.. GENERATED FROM PYTHON SOURCE LINES 46-61

Fitting and Interpolation
^^^^^^^^^^^^^^^^^^^^^^^^^

Now we want to interpolate the "measured" samples
and we want to normalize the given data with the BoxCox transformation.

Here we set up the kriging routine and use a :any:`Stable` model, that should
be fitted automatically to the given data
and we pass the :any:`BoxCox` normalizer in order to gain normality.

The normalizer will be fitted automatically to the data,
by setting ``fit_normalizer=True``.

The covariance/variogram model will be fitted by an automatic workflow
by setting ``fit_variogram=True``.

.. GENERATED FROM PYTHON SOURCE LINES 61-71

.. code-block:: Python


    krige = gs.krige.Ordinary(
        model=gs.Stable(dim=2),
        cond_pos=cond_pos,
        cond_val=cond_val,
        normalizer=gs.normalizer.BoxCox(),
        fit_normalizer=True,
        fit_variogram=True,
    )








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First, let's have a look at the fitting results:

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.. code-block:: Python


    print(krige.model)
    print(krige.normalizer)





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

 .. code-block:: none

    Stable(dim=2, var=0.576, len_scale=8.85, nugget=0.00682, alpha=2.0)
    BoxCox(lmbda=-0.0754)




.. GENERATED FROM PYTHON SOURCE LINES 78-87

As we see, it went quite well. Variance is a bit underestimated, but
length scale and nugget are good. The shape parameter of the stable model
is correctly estimated to be close to `2`,
so we result in a Gaussian like model.

The BoxCox parameter `lmbda` was estimated to be almost 0, which means,
the log-normal distribution was correctly fitted.

Now let's run the kriging interpolation.

.. GENERATED FROM PYTHON SOURCE LINES 87-90

.. code-block:: Python


    krige(pos)








.. GENERATED FROM PYTHON SOURCE LINES 91-97

Plotting
^^^^^^^^

Finally let's compare the original, sampled and interpolated fields.
As we'll see, there is a lot of information in the covariance structure
of the measurement samples and the field is reconstructed quite accurately.

.. GENERATED FROM PYTHON SOURCE LINES 97-108

.. code-block:: Python


    fig, ax = plt.subplots(1, 3, figsize=[8, 3])
    ax[0].imshow(srf.field.reshape(len(x), len(y)).T, origin="lower")
    ax[1].scatter(*cond_pos, c=cond_val)
    ax[2].imshow(krige.field.reshape(len(x), len(y)).T, origin="lower")
    # titles
    ax[0].set_title("original field")
    ax[1].set_title("sampled field")
    ax[2].set_title("interpolated field")
    # set aspect ratio to equal in all plots
    [ax[i].set_aspect("equal") for i in range(3)]



.. image-sg:: /examples/10_normalizer/images/sphx_glr_01_auto_fit_001.png
   :alt: original field, sampled field, interpolated field
   :srcset: /examples/10_normalizer/images/sphx_glr_01_auto_fit_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.239 seconds)


.. _sphx_glr_download_examples_10_normalizer_01_auto_fit.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 01_auto_fit.ipynb <01_auto_fit.ipynb>`

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

      :download:`Download Python source code: 01_auto_fit.py <01_auto_fit.py>`

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

      :download:`Download zipped: 01_auto_fit.zip <01_auto_fit.zip>`


.. only:: html

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

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