.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/02_cov_model/06_fitting_para_ranges.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_cov_model_06_fitting_para_ranges.py>`
        to download the full example code.

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

.. _sphx_glr_examples_02_cov_model_06_fitting_para_ranges.py:


Fitting variogram data
======================

The model class comes with a routine to fit the model-parameters to given
variogram data. In the following we will use the self defined stable model
from a previous example.

.. GENERATED FROM PYTHON SOURCE LINES 9-33

.. code-block:: Python


    import numpy as np

    import gstools as gs


    class Stab(gs.CovModel):
        def default_opt_arg(self):
            return {"alpha": 1.5}

        def cor(self, h):
            return np.exp(-(h**self.alpha))


    # Exemplary variogram data (e.g. estimated from field observations)
    bins = [1.0, 3.0, 5.0, 7.0, 9.0, 11.0]
    est_vario = [0.2, 0.5, 0.6, 0.8, 0.8, 0.9]
    # fitting model
    model = Stab(dim=2)
    # we have to provide boundaries for the parameters
    model.set_arg_bounds(alpha=[0, 3])
    results, pcov = model.fit_variogram(bins, est_vario, nugget=False)
    print("Results:", results)





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

 .. code-block:: none

    Results: {'var': np.float64(1.024573980819835), 'len_scale': np.float64(5.081592149596026), 'nugget': 0.0, 'alpha': np.float64(0.9067040924530624)}




.. GENERATED FROM PYTHON SOURCE LINES 34-40

.. code-block:: Python


    ax = model.plot()
    ax.scatter(bins, est_vario, color="k", label="sample variogram")
    ax.legend()





.. image-sg:: /examples/02_cov_model/images/sphx_glr_06_fitting_para_ranges_001.png
   :alt: 06 fitting para ranges
   :srcset: /examples/02_cov_model/images/sphx_glr_06_fitting_para_ranges_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 41-77

As you can see, we have to provide boundaries for the parameters.
As a default, the following bounds are set:

- additional parameters: ``[-np.inf, np.inf]``
- variance: ``[0.0, np.inf]``
- len_scale: ``[0.0, np.inf]``
- nugget: ``[0.0, np.inf]``

Also, you can deselect parameters from fitting, so their predefined values
will be kept. In our case, we fixed a ``nugget`` of ``0.0``, which was set
by default. You can deselect any standard or
optional argument of the covariance model.
The second return value ``pcov`` is the estimated covariance of ``popt`` from
the used scipy routine :any:`scipy.optimize.curve_fit`.

You can use the following methods to manipulate the used bounds:

.. currentmodule:: gstools.covmodel

.. autosummary::
   CovModel.default_opt_arg_bounds
   CovModel.default_arg_bounds
   CovModel.set_arg_bounds
   CovModel.check_arg_bounds

You can override the :any:`CovModel.default_opt_arg_bounds`
to provide standard bounds for your additional parameters.

To access the bounds you can use:

.. autosummary::
   CovModel.var_bounds
   CovModel.len_scale_bounds
   CovModel.nugget_bounds
   CovModel.opt_arg_bounds
   CovModel.arg_bounds


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

   **Total running time of the script:** (0 minutes 0.083 seconds)


.. _sphx_glr_download_examples_02_cov_model_06_fitting_para_ranges.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 06_fitting_para_ranges.ipynb <06_fitting_para_ranges.ipynb>`

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

      :download:`Download Python source code: 06_fitting_para_ranges.py <06_fitting_para_ranges.py>`

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

      :download:`Download zipped: 06_fitting_para_ranges.zip <06_fitting_para_ranges.zip>`


.. only:: html

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

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