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

.. only:: html

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

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

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

.. _sphx_glr_examples_mlearning_regression_model_plot_pce_regression.py:


PCE regression
==============

We want to approximate a discipline with two inputs and two outputs:

- :math:`y_1=1+2x_1+3x_2`
- :math:`y_2=-1-2x_1-3x_2`

over the unit hypercube :math:`[0,1]\times[0,1]`.

.. GENERATED FROM PYTHON SOURCE LINES 32-47

.. code-block:: Python


    from __future__ import annotations

    from numpy import array

    from gemseo import configure_logger
    from gemseo import create_design_space
    from gemseo import create_discipline
    from gemseo import create_parameter_space
    from gemseo import create_scenario
    from gemseo.mlearning import create_regression_model

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 48-52

Create the discipline to learn
------------------------------
We can implement this analytic discipline by means of the
:class:`.AnalyticDiscipline` class.

.. GENERATED FROM PYTHON SOURCE LINES 52-57

.. code-block:: Python

    expressions = {"y_1": "1+2*x_1+3*x_2", "y_2": "-1-2*x_1-3*x_2"}
    discipline = create_discipline(
        "AnalyticDiscipline", name="func", expressions=expressions
    )








.. GENERATED FROM PYTHON SOURCE LINES 58-61

Create the input sampling space
-------------------------------
We create the input sampling space by adding the variables one by one.

.. GENERATED FROM PYTHON SOURCE LINES 61-65

.. code-block:: Python

    design_space = create_design_space()
    design_space.add_variable("x_1", lower_bound=0.0, upper_bound=1.0)
    design_space.add_variable("x_2", lower_bound=0.0, upper_bound=1.0)








.. GENERATED FROM PYTHON SOURCE LINES 66-71

Create the learning set
-----------------------
We can build a learning set by means of a
:class:`.DOEScenario` with a full factorial design of
experiments. The number of samples can be equal to 9 for example.

.. GENERATED FROM PYTHON SOURCE LINES 71-80

.. code-block:: Python

    scenario = create_scenario(
        [discipline],
        "y_1",
        design_space,
        scenario_type="DOE",
        formulation_name="DisciplinaryOpt",
    )
    scenario.execute(algo_name="PYDOE_FULLFACT", n_samples=9)





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

 .. code-block:: none

        INFO - 08:37:49:  
        INFO - 08:37:49: *** Start DOEScenario execution ***
        INFO - 08:37:49: DOEScenario
        INFO - 08:37:49:    Disciplines: func
        INFO - 08:37:49:    MDO formulation: DisciplinaryOpt
        INFO - 08:37:49: Optimization problem:
        INFO - 08:37:49:    minimize y_1(x_1, x_2)
        INFO - 08:37:49:    with respect to x_1, x_2
        INFO - 08:37:49:    over the design space:
        INFO - 08:37:49:       +------+-------------+-------+-------------+-------+
        INFO - 08:37:49:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 08:37:49:       +------+-------------+-------+-------------+-------+
        INFO - 08:37:49:       | x_1  |      0      |  None |      1      | float |
        INFO - 08:37:49:       | x_2  |      0      |  None |      1      | float |
        INFO - 08:37:49:       +------+-------------+-------+-------------+-------+
        INFO - 08:37:49: Solving optimization problem with algorithm PYDOE_FULLFACT:
        INFO - 08:37:49:     11%|█         | 1/9 [00:00<00:00, 397.00 it/sec, obj=1]
        INFO - 08:37:49:     22%|██▏       | 2/9 [00:00<00:00, 659.43 it/sec, obj=2]
        INFO - 08:37:49:     33%|███▎      | 3/9 [00:00<00:00, 865.10 it/sec, obj=3]
        INFO - 08:37:49:     44%|████▍     | 4/9 [00:00<00:00, 1028.08 it/sec, obj=2.5]
        INFO - 08:37:49:     56%|█████▌    | 5/9 [00:00<00:00, 1154.37 it/sec, obj=3.5]
        INFO - 08:37:49:     67%|██████▋   | 6/9 [00:00<00:00, 1263.28 it/sec, obj=4.5]
        INFO - 08:37:49:     78%|███████▊  | 7/9 [00:00<00:00, 1349.15 it/sec, obj=4]
        INFO - 08:37:49:     89%|████████▉ | 8/9 [00:00<00:00, 1416.76 it/sec, obj=5]
        INFO - 08:37:49:    100%|██████████| 9/9 [00:00<00:00, 1482.55 it/sec, obj=6]
        INFO - 08:37:49: Optimization result:
        INFO - 08:37:49:    Optimizer info:
        INFO - 08:37:49:       Status: None
        INFO - 08:37:49:       Message: None
        INFO - 08:37:49:       Number of calls to the objective function by the optimizer: 9
        INFO - 08:37:49:    Solution:
        INFO - 08:37:49:       Objective: 1.0
        INFO - 08:37:49:       Design space:
        INFO - 08:37:49:          +------+-------------+-------+-------------+-------+
        INFO - 08:37:49:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 08:37:49:          +------+-------------+-------+-------------+-------+
        INFO - 08:37:49:          | x_1  |      0      |   0   |      1      | float |
        INFO - 08:37:49:          | x_2  |      0      |   0   |      1      | float |
        INFO - 08:37:49:          +------+-------------+-------+-------------+-------+
        INFO - 08:37:49: *** End DOEScenario execution (time: 0:00:00.010095) ***




.. GENERATED FROM PYTHON SOURCE LINES 81-85

Create the regression model
---------------------------
Then, we build the linear regression model from the database and
displays this model.

.. GENERATED FROM PYTHON SOURCE LINES 85-95

.. code-block:: Python

    prob_space = create_parameter_space()
    prob_space.add_random_variable("x_1", "OTUniformDistribution")
    prob_space.add_random_variable("x_2", "OTUniformDistribution")
    dataset = scenario.to_dataset(opt_naming=False)
    model = create_regression_model(
        "PCERegressor", dataset, probability_space=prob_space, transformer={}
    )
    model.learn()
    model






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='background-color: #fafae2; padding: 10px;'>PCERegressor(cleaning_options=None, degree=2, discipline=None, hyperbolic_parameter=1.0, input_names=(), n_quadrature_points=0, output_names=(), parameters={}, probability_space=Uncertain space:
    +------+-------------------------------+
    | Name |          Distribution         |
    +------+-------------------------------+
    | x_1  | Uniform(lower=0.0, upper=1.0) |
    | x_2  | Uniform(lower=0.0, upper=1.0) |
    +------+-------------------------------+, transformer={}, use_cleaning=False, use_lars=False, use_quadrature=False)<br/><ul><li>based on the OpenTURNS library</li><li>built from 9 learning samples</li></ul></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 96-99

Predict output
--------------
Once it is built, we can use it for prediction.

.. GENERATED FROM PYTHON SOURCE LINES 99-102

.. code-block:: Python

    input_value = {"x_1": array([1.0]), "x_2": array([2.0])}
    output_value = model.predict(input_value)
    output_value




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

 .. code-block:: none


    {'y_1': array([9.])}




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

   **Total running time of the script:** (0 minutes 0.047 seconds)


.. _sphx_glr_download_examples_mlearning_regression_model_plot_pce_regression.py:

.. only:: html

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

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

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

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

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

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

      :download:`Download zipped: plot_pce_regression.zip <plot_pce_regression.zip>`


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