.. 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 32-44

.. code-block:: default

    from __future__ import annotations

    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
    from numpy import array

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 45-49

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

.. GENERATED FROM PYTHON SOURCE LINES 49-57

.. code-block:: default

    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 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:: default

    design_space = create_design_space()
    design_space.add_variable("x_1", l_b=0.0, u_b=1.0)
    design_space.add_variable("x_2", l_b=0.0, u_b=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 71-76

.. code-block:: default

    scenario = create_scenario(
        [discipline], "DisciplinaryOpt", "y_1", design_space, scenario_type="DOE"
    )
    scenario.execute({"algo": "fullfact", "n_samples": 9})





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

 .. code-block:: none

        INFO - 13:53:55:  
        INFO - 13:53:55: *** Start DOEScenario execution ***
        INFO - 13:53:55: DOEScenario
        INFO - 13:53:55:    Disciplines: func
        INFO - 13:53:55:    MDO formulation: DisciplinaryOpt
        INFO - 13:53:55: Optimization problem:
        INFO - 13:53:55:    minimize y_1(x_1, x_2)
        INFO - 13:53:55:    with respect to x_1, x_2
        INFO - 13:53:55:    over the design space:
        INFO - 13:53:55:    +------+-------------+-------+-------------+-------+
        INFO - 13:53:55:    | name | lower_bound | value | upper_bound | type  |
        INFO - 13:53:55:    +------+-------------+-------+-------------+-------+
        INFO - 13:53:55:    | x_1  |      0      |  None |      1      | float |
        INFO - 13:53:55:    | x_2  |      0      |  None |      1      | float |
        INFO - 13:53:55:    +------+-------------+-------+-------------+-------+
        INFO - 13:53:55: Solving optimization problem with algorithm fullfact:
        INFO - 13:53:55: ...   0%|          | 0/9 [00:00<?, ?it]
        INFO - 13:53:55: ...  11%|█         | 1/9 [00:00<00:00, 272.96 it/sec, obj=1]
        INFO - 13:53:55: ...  22%|██▏       | 2/9 [00:00<00:00, 429.81 it/sec, obj=2.25]
        INFO - 13:53:55: ...  33%|███▎      | 3/9 [00:00<00:00, 541.13 it/sec, obj=4]
        INFO - 13:53:55: ...  44%|████▍     | 4/9 [00:00<00:00, 634.54 it/sec, obj=2.5]
        INFO - 13:53:55: ...  56%|█████▌    | 5/9 [00:00<00:00, 710.25 it/sec, obj=3.75]
        INFO - 13:53:55: ...  67%|██████▋   | 6/9 [00:00<00:00, 769.71 it/sec, obj=5.5]
        INFO - 13:53:55: ...  78%|███████▊  | 7/9 [00:00<00:00, 821.01 it/sec, obj=4]
        INFO - 13:53:55: ...  89%|████████▉ | 8/9 [00:00<00:00, 860.77 it/sec, obj=5.25]
        INFO - 13:53:55: ... 100%|██████████| 9/9 [00:00<00:00, 897.75 it/sec, obj=7]
        INFO - 13:53:55: Optimization result:
        INFO - 13:53:55:    Optimizer info:
        INFO - 13:53:55:       Status: None
        INFO - 13:53:55:       Message: None
        INFO - 13:53:55:       Number of calls to the objective function by the optimizer: 9
        INFO - 13:53:55:    Solution:
        INFO - 13:53:55:       Objective: 1.0
        INFO - 13:53:55:       Design space:
        INFO - 13:53:55:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:55:       | name | lower_bound | value | upper_bound | type  |
        INFO - 13:53:55:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:55:       | x_1  |      0      |   0   |      1      | float |
        INFO - 13:53:55:       | x_2  |      0      |   0   |      1      | float |
        INFO - 13:53:55:       +------+-------------+-------+-------------+-------+
        INFO - 13:53:55: *** End DOEScenario execution (time: 0:00:00.022026) ***

    {'eval_jac': False, 'n_samples': 9, 'algo': 'fullfact'}



.. GENERATED FROM PYTHON SOURCE LINES 77-81

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

.. GENERATED FROM PYTHON SOURCE LINES 81-88

.. code-block:: default

    dataset = scenario.to_dataset(opt_naming=False)
    model = create_regression_model(
        "PolynomialRegressor", data=dataset, degree=2, transformer=None
    )
    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, l2_penalty_ratio=1.0, penalty_level=0.0)<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 89-92

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

.. GENERATED FROM PYTHON SOURCE LINES 92-96

.. code-block:: default

    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 97-100

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

.. GENERATED FROM PYTHON SOURCE LINES 100-103

.. code-block:: default

    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 104-109

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 109-111

.. code-block:: default

    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 112-117

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 117-118

.. code-block:: default

    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 0.076 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-python

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

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

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


.. only:: html

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

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