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.. only:: html

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

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.. _sphx_glr_examples_mlearning_quality_measure_plot_from_surrogate.py:


Error from surrogate discipline
===============================

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.. code-block:: Python


    from numpy import array
    from numpy import newaxis
    from numpy import sin

    from gemseo.datasets.io_dataset import IODataset
    from gemseo.disciplines.surrogate import SurrogateDiscipline








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The quality of a :class:`.SurrogateDiscipline` can easily be quantified
from its methods :meth:`~.SurrogateDiscipline.get_error_measure`.

To illustrate this point,
let us consider the function :math:`f(x)=(6x-2)^2\sin(12x-4)` :cite:`forrester2008`:

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.. code-block:: Python



    def f(x):
        return (6 * x - 2) ** 2 * sin(12 * x - 4)









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and try to approximate it with an :class:`.RBFRegressor`.

For this,
we can take these 7 learning input points

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.. code-block:: Python

    x_train = array([0.1, 0.3, 0.5, 0.6, 0.8, 0.9, 0.95])








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and evaluate the model ``f`` over this design of experiments (DOE):

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.. code-block:: Python

    y_train = f(x_train)








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Then,
we create an :class:`.IODataset` from these 7 learning samples:

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.. code-block:: Python

    dataset_train = IODataset()
    dataset_train.add_input_group(x_train[:, newaxis], ["x"])
    dataset_train.add_output_group(y_train[:, newaxis], ["y"])








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and build a :class:`.SurrogateDiscipline` from it:

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.. code-block:: Python

    surrogate_discipline = SurrogateDiscipline("RBFRegressor", dataset_train)








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Lastly,
we can get its :class:`.R2Measure`

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.. code-block:: Python

    r2 = surrogate_discipline.get_error_measure("R2Measure")








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and evaluate it:

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.. code-block:: Python

    r2.compute_learning_measure()





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    array([1.])



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In presence of additional data,
the generalization quality can also be approximated:

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.. code-block:: Python

    x_test = array([0.2, 0.4, 0.7])
    y_test = f(x_test)
    dataset_test = IODataset()
    dataset_test.add_input_group(x_test[:, newaxis], ["x"])
    dataset_test.add_output_group(y_test[:, newaxis], ["y"])
    result = r2.compute_test_measure(dataset_test)
    r2.compute_test_measure(dataset_test)





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 .. code-block:: none


    array([0.98752693])



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We can conclude that
the regression model on which the :class:`.SurrogateDiscipline` is based
is a very good approximation of the original function :math:`f`.


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

   **Total running time of the script:** (0 minutes 0.027 seconds)


.. _sphx_glr_download_examples_mlearning_quality_measure_plot_from_surrogate.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_from_surrogate.ipynb <plot_from_surrogate.ipynb>`

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

      :download:`Download Python source code: plot_from_surrogate.py <plot_from_surrogate.py>`


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