.. 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

        Click :ref:`here <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 34-50

.. code-block:: default

    from __future__ import division, unicode_literals

    from numpy import array

    from gemseo.api import (
        configure_logger,
        create_design_space,
        create_discipline,
        create_parameter_space,
        create_scenario,
    )
    from gemseo.mlearning.api import create_regression_model, import_regression_model

    configure_logger()






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

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 51-55

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

.. GENERATED FROM PYTHON SOURCE LINES 55-60

.. code-block:: default

    expressions_dict = {"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_dict=expressions_dict
    )








.. GENERATED FROM PYTHON SOURCE LINES 61-64

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

.. GENERATED FROM PYTHON SOURCE LINES 64-68

.. 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 69-74

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

.. GENERATED FROM PYTHON SOURCE LINES 74-80

.. code-block:: default

    discipline.set_cache_policy(discipline.MEMORY_FULL_CACHE)
    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

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 .. code-block:: none

        INFO - 21:50:36:  
        INFO - 21:50:36: *** Start DOE Scenario execution ***
        INFO - 21:50:36: DOEScenario
        INFO - 21:50:36:    Disciplines: func
        INFO - 21:50:36:    MDOFormulation: DisciplinaryOpt
        INFO - 21:50:36:    Algorithm: fullfact
        INFO - 21:50:36: Optimization problem:
        INFO - 21:50:36:    Minimize: y_1(x_1, x_2)
        INFO - 21:50:36:    With respect to: x_1, x_2
        INFO - 21:50:36: Full factorial design required. Number of samples along each direction for a design vector of size 2 with 9 samples: 3
        INFO - 21:50:36: Final number of samples for DOE = 9 vs 9 requested
        INFO - 21:50:36: DOE sampling:   0%|          | 0/9 [00:00<?, ?it]
        INFO - 21:50:36: DOE sampling: 100%|██████████| 9/9 [00:00<00:00, 580.56 it/sec, obj=6]
        INFO - 21:50:36: Optimization result:
        INFO - 21:50:36: Objective value = 1.0
        INFO - 21:50:36: The result is feasible.
        INFO - 21:50:36: Status: None
        INFO - 21:50:36: Optimizer message: None
        INFO - 21:50:36: Number of calls to the objective function by the optimizer: 9
        INFO - 21:50:36: Design space:
        INFO - 21:50:36: +------+-------------+-------+-------------+-------+
        INFO - 21:50:36: | name | lower_bound | value | upper_bound | type  |
        INFO - 21:50:36: +------+-------------+-------+-------------+-------+
        INFO - 21:50:36: | x_1  |      0      |   0   |      1      | float |
        INFO - 21:50:36: | x_2  |      0      |   0   |      1      | float |
        INFO - 21:50:36: +------+-------------+-------+-------------+-------+
        INFO - 21:50:36: *** DOE Scenario run terminated ***

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



.. GENERATED FROM PYTHON SOURCE LINES 81-85

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

.. GENERATED FROM PYTHON SOURCE LINES 85-95

.. code-block:: default

    prob_space = create_parameter_space()
    prob_space.add_random_variable("x_1", "OTUniformDistribution")
    prob_space.add_random_variable("x_2", "OTUniformDistribution")
    dataset = discipline.cache.export_to_dataset()
    model = create_regression_model(
        "PCERegression", data=dataset, probability_space=prob_space, transformer=None
    )
    model.learn()
    print(model)





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 .. code-block:: none

    PCERegression(degree=2, n_quad=None, probability_space=<gemseo.algos.parameter_space.ParameterSpace object at 0x7f61942f17c0>, sparse_param=None, stieltjes=True, strategy='LS')
       based on the openturns library
       built from 9 learning samples




.. GENERATED FROM PYTHON SOURCE LINES 96-99

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

.. GENERATED FROM PYTHON SOURCE LINES 99-103

.. code-block:: default

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





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

 Out:

 .. code-block:: none

    {'y_1': array([9.]), 'y_2': array([-9.])}




.. GENERATED FROM PYTHON SOURCE LINES 104-107

Save the regression model
-------------------------
Lastly, we save the model.

.. GENERATED FROM PYTHON SOURCE LINES 107-109

.. code-block:: default

    directory = model.save()








.. GENERATED FROM PYTHON SOURCE LINES 110-113

Load the regression model
-------------------------
In an other study, we could load this model.

.. GENERATED FROM PYTHON SOURCE LINES 113-116

.. code-block:: default

    loaded_model = import_regression_model(directory)
    print(loaded_model)





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

 Out:

 .. code-block:: none

    PCERegression(degree=2, n_quad=None, probability_space=<gemseo.algos.parameter_space.ParameterSpace object at 0x7f61942c99d0>, sparse_param=None, stieltjes=True, strategy='LS')
       based on the openturns library
       built from 0 learning samples




.. GENERATED FROM PYTHON SOURCE LINES 117-120

Use the loaded regression model
-------------------------------
And use it!

.. GENERATED FROM PYTHON SOURCE LINES 120-121

.. code-block:: default

    print(loaded_model.predict(input_value))




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

 Out:

 .. code-block:: none

    {'y_1': array([9.]), 'y_2': array([-9.])}





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

   **Total running time of the script:** ( 0 minutes  0.241 seconds)


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