.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/mlearning/regression_model/plot_polynomial_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_polynomial_regression.py>`
        to download the full example code.

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

.. _sphx_glr_examples_mlearning_regression_model_plot_polynomial_regression.py:


Polynomial 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 32-46

.. 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_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 47-51

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

.. GENERATED FROM PYTHON SOURCE LINES 51-59

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 60-63

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

.. GENERATED FROM PYTHON SOURCE LINES 63-67

.. 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 68-73

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 73-82

.. 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 - 08:37:50:  
        INFO - 08:37:50: *** Start DOEScenario execution ***
        INFO - 08:37:50: DOEScenario
        INFO - 08:37:50:    Disciplines: func
        INFO - 08:37:50:    MDO formulation: DisciplinaryOpt
        INFO - 08:37:50: Optimization problem:
        INFO - 08:37:50:    minimize y_1(x_1, x_2)
        INFO - 08:37:50:    with respect to x_1, x_2
        INFO - 08:37:50:    over the design space:
        INFO - 08:37:50:       +------+-------------+-------+-------------+-------+
        INFO - 08:37:50:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 08:37:50:       +------+-------------+-------+-------------+-------+
        INFO - 08:37:50:       | x_1  |      0      |  None |      1      | float |
        INFO - 08:37:50:       | x_2  |      0      |  None |      1      | float |
        INFO - 08:37:50:       +------+-------------+-------+-------------+-------+
        INFO - 08:37:50: Solving optimization problem with algorithm PYDOE_FULLFACT:
        INFO - 08:37:50:     11%|█         | 1/9 [00:00<00:00, 359.01 it/sec, obj=1]
        INFO - 08:37:50:     22%|██▏       | 2/9 [00:00<00:00, 609.46 it/sec, obj=2.25]
        INFO - 08:37:50:     33%|███▎      | 3/9 [00:00<00:00, 807.58 it/sec, obj=4]
        INFO - 08:37:50:     44%|████▍     | 4/9 [00:00<00:00, 967.27 it/sec, obj=2.5]
        INFO - 08:37:50:     56%|█████▌    | 5/9 [00:00<00:00, 1090.00 it/sec, obj=3.75]
        INFO - 08:37:50:     67%|██████▋   | 6/9 [00:00<00:00, 1192.13 it/sec, obj=5.5]
        INFO - 08:37:50:     78%|███████▊  | 7/9 [00:00<00:00, 1283.78 it/sec, obj=4]
        INFO - 08:37:50:     89%|████████▉ | 8/9 [00:00<00:00, 1359.63 it/sec, obj=5.25]
        INFO - 08:37:50:    100%|██████████| 9/9 [00:00<00:00, 1421.32 it/sec, obj=7]
        INFO - 08:37:50: Optimization result:
        INFO - 08:37:50:    Optimizer info:
        INFO - 08:37:50:       Status: None
        INFO - 08:37:50:       Message: None
        INFO - 08:37:50:       Number of calls to the objective function by the optimizer: 9
        INFO - 08:37:50:    Solution:
        INFO - 08:37:50:       Objective: 1.0
        INFO - 08:37:50:       Design space:
        INFO - 08:37:50:          +------+-------------+-------+-------------+-------+
        INFO - 08:37:50:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 08:37:50:          +------+-------------+-------+-------------+-------+
        INFO - 08:37:50:          | x_1  |      0      |   0   |      1      | float |
        INFO - 08:37:50:          | x_2  |      0      |   0   |      1      | float |
        INFO - 08:37:50:          +------+-------------+-------+-------------+-------+
        INFO - 08:37:50: *** End DOEScenario execution (time: 0:00:00.010329) ***




.. GENERATED FROM PYTHON SOURCE LINES 83-87

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

.. GENERATED FROM PYTHON SOURCE LINES 87-94

.. code-block:: Python

    dataset = scenario.to_dataset(opt_naming=False)
    model = create_regression_model(
        "PolynomialRegressor", dataset, degree=2, transformer={}
    )
    model.learn()
    model






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='background-color: #fafae2; padding: 10px;'>PolynomialRegressor(degree=2, fit_intercept=True, input_names=(), l2_penalty_ratio=1.0, output_names=(), parameters={}, penalty_level=0.0, random_state=0, transformer={})<br/><ul><li>based on the scikit-learn library</li><li>built from 9 learning samples</li></ul></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 95-98

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

.. GENERATED FROM PYTHON SOURCE LINES 98-102

.. 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([10.])}



.. GENERATED FROM PYTHON SOURCE LINES 103-106

Predict Jacobian
----------------
We can also use it to predict the jacobian of the discipline.

.. GENERATED FROM PYTHON SOURCE LINES 106-109

.. code-block:: Python

    jacobian_value = model.predict_jacobian(input_value)
    jacobian_value





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

 .. code-block:: none


    {'y_1': {'x_1': array([[4.]]), 'x_2': array([[3.]])}}



.. GENERATED FROM PYTHON SOURCE LINES 110-115

Get intercept
-------------
In addition, it is possible to access the intercept of the model,
either directly or by means of a method returning either a dictionary
(default option) or an array.

.. GENERATED FROM PYTHON SOURCE LINES 115-117

.. code-block:: Python

    model.intercept, model.get_intercept()





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

 .. code-block:: none


    (array([1.]), {'y_1': [1.0]})



.. GENERATED FROM PYTHON SOURCE LINES 118-123

Get coefficients
----------------
In addition, it is possible to access the coefficients of the model,
either directly or by means of a method returning either a dictionary
(default option) or an array.

.. GENERATED FROM PYTHON SOURCE LINES 123-124

.. code-block:: Python

    model.coefficients




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

 .. code-block:: none


    array([[ 2.00000000e+00,  3.00000000e+00,  1.00000000e+00,
            -6.22449391e-16, -5.07973866e-16]])




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

   **Total running time of the script:** (0 minutes 0.053 seconds)


.. _sphx_glr_download_examples_mlearning_regression_model_plot_polynomial_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_polynomial_regression.ipynb <plot_polynomial_regression.ipynb>`

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

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

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

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


.. only:: html

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

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