.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples\LinearModels\PolynomialFeatures.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_LinearModels_PolynomialFeatures.py:


Polynomial Surface Regression with Total Least Squares
======================================================

This script demonstrates polynomial regression on a 2D dataset using total least squares (TLS).
It generates a grid of input points, applies polynomial feature expansion, and fits a linear regression model.
Predictions are visualized in 3D, comparing model output (blue) against actual values (red).

.. GENERATED FROM PYTHON SOURCE LINES 9-33



.. image-sg:: /auto_examples/LinearModels/images/sphx_glr_PolynomialFeatures_001.png
   :alt: PolynomialFeatures
   :srcset: /auto_examples/LinearModels/images/sphx_glr_PolynomialFeatures_001.png
   :class: sphx-glr-single-img





.. code-block:: Python

    import torch
    import matplotlib.pyplot as plt

    from DLL.MachineLearning.SupervisedLearning.LinearModels import LinearRegression
    from DLL.Data.Preprocessing import PolynomialFeatures, data_split


    model = LinearRegression()

    n = 30
    X, Y = torch.meshgrid(torch.linspace(-1, 1, n, dtype=torch.float32), torch.linspace(-1, 1, n, dtype=torch.float32), indexing="xy")
    x = torch.stack((X.flatten(), Y.flatten()), dim=1)
    y = X.flatten() ** 2 + Y.flatten() ** 2 + 0.1 * torch.randn(size=Y.flatten().size()) - 5
    x_train, y_train, x_val, y_val, x_test, y_test = data_split(x, y, train_split=0.6, validation_split=0.2)
    features = PolynomialFeatures(degree=2, include_bias=True)  # Both polynomial features and linear regression must not include a bias
    x_train = features.transform(x_train)

    model.fit(x_train, y_train, method="tls", include_bias=False)  # Both polynomial features and linear regression must not include a bias
    z = model.predict(features.transform(x_test))
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    surf = ax.scatter(x_test[:, 0], x_test[:, 1], z, color="blue")
    surf = ax.scatter(x_test[:, 0], x_test[:, 1], y_test, color="red")
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.088 seconds)


.. _sphx_glr_download_auto_examples_LinearModels_PolynomialFeatures.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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