.. 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 Click :ref:`here ` 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 34-51 .. code-block:: default from __future__ import absolute_import, division, print_function, unicode_literals from future import standard_library from numpy import array from gemseo.api import ( configure_logger, create_design_space, create_discipline, create_scenario, ) from gemseo.mlearning.api import create_regression_model configure_logger() standard_library.install_aliases() .. GENERATED FROM PYTHON SOURCE LINES 52-56 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 56-64 .. code-block:: default expressions_dict = { "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_dict=expressions_dict ) .. GENERATED FROM PYTHON SOURCE LINES 65-68 Create the input sampling space ------------------------------- We create the input sampling space by adding the variables one by one. .. GENERATED FROM PYTHON SOURCE LINES 68-72 .. 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 73-78 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 78-84 .. 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 Out: .. code-block:: none {'eval_jac': False, 'algo': 'fullfact', 'n_samples': 9} .. GENERATED FROM PYTHON SOURCE LINES 85-89 Create the regression model --------------------------- Then, we build the linear regression model from the discipline cache and displays this model. .. GENERATED FROM PYTHON SOURCE LINES 89-96 .. code-block:: default dataset = discipline.cache.export_to_dataset() model = create_regression_model( "PolynomialRegression", data=dataset, degree=2, transformer=None ) model.learn() print(model) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none PolynomialRegression(fit_intercept=True, penalty_level=0.0, l2_penalty_ratio=1.0, degree=2) | based on the scikit-learn library | built from 9 learning samples .. GENERATED FROM PYTHON SOURCE LINES 97-100 Predict output -------------- Once it is built, we can use it for prediction. .. GENERATED FROM PYTHON SOURCE LINES 100-104 .. 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([10.]), 'y_2': array([-13.])} .. GENERATED FROM PYTHON SOURCE LINES 105-108 Predict Jacobian ---------------- We can also use it to predict the jacobian of the discipline. .. GENERATED FROM PYTHON SOURCE LINES 108-111 .. code-block:: default jacobian_value = model.predict_jacobian(input_value) print(jacobian_value) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none {'y_1': {'x_1': array([[4.]]), 'x_2': array([[3.]])}, 'y_2': {'x_1': array([[1.33226763e-15]]), 'x_2': array([[-11.]])}} .. GENERATED FROM PYTHON SOURCE LINES 112-117 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 117-120 .. code-block:: default print(model.intercept) print(model.get_intercept()) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none [ 1. -1.] {'y_1': [1.0], 'y_2': [-0.9999999999999987]} .. GENERATED FROM PYTHON SOURCE LINES 121-126 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 126-127 .. code-block:: default print(model.coefficients) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none [[ 2.00000000e+00 3.00000000e+00 1.00000000e+00 -2.22044605e-16 -8.88178420e-16] [-2.00000000e+00 -3.21964677e-15 -2.77555756e-16 1.00000000e+00 -3.00000000e+00]] .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.124 seconds) .. _sphx_glr_download_examples_mlearning_regression_model_plot_polynomial_regression.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_polynomial_regression.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_polynomial_regression.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_