.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples\SVM\SupportVectorRegression.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_SVM_SupportVectorRegression.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_SVM_SupportVectorRegression.py:


Support Vector Regression for 3D Surface Fitting
====================================================

This script demonstrates the use of Support Vector Regression (SVR) to model and predict a synthetic 3D surface. The objective is to train the model to approximate the surface defined by the equation:

    Z = 2 * X^2 - 5 * Y^2 + noise

The script performs the following steps:

1. Generates a synthetic 3D dataset with two input features (X, Y) and one output (Z).
2. Splits the dataset into training and test sets.
3. Trains an SVR model with a linear kernel (product of two linear kernels) and compares its predictions against a Scikit-learn SVR model with a radial basis function (RBF) kernel.
4. Visualizes the true values and the predictions from both models in a 3D scatter plot.

The comparison allows an evaluation of the model's performance in approximating the underlying surface.

.. GENERATED FROM PYTHON SOURCE LINES 18-54



.. image-sg:: /auto_examples/SVM/images/sphx_glr_SupportVectorRegression_001.png
   :alt: SupportVectorRegression
   :srcset: /auto_examples/SVM/images/sphx_glr_SupportVectorRegression_001.png
   :class: sphx-glr-single-img





.. code-block:: Python

    import torch
    import matplotlib.pyplot as plt
    from sklearn import svm

    from DLL.MachineLearning.SupervisedLearning.SupportVectorMachines import SVR
    from DLL.Data.Preprocessing import data_split
    from DLL.MachineLearning.SupervisedLearning.Kernels import Linear


    torch.manual_seed(10)

    x = torch.linspace(-2, 2, 20)
    y = torch.linspace(-2, 2, 20)
    XX, YY = torch.meshgrid(x, y, indexing="xy")
    X = XX.flatten()
    Y = YY.flatten()
    X_input = torch.stack((X, Y), dim=1)
    Z = 2 * X ** 2 - 5 * Y ** 2 + torch.normal(0, 1, size=X.size())
    x_train, y_train, x_test, y_test, _, _ = data_split(X_input, Z, train_split=0.8, validation_split=0.2)

    model = SVR(kernel=Linear() ** 2)
    # model = SVR()
    model.fit(x_train, y_train)
    y_pred = model.predict(x_test)

    correct = svm.SVR(kernel="rbf", C=1)
    correct.fit(x_train, y_train)
    y_pred_true = correct.predict(x_test)

    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    ax.scatter(x_test[:, 0].numpy(), x_test[:, 1].numpy(), y_test.numpy(), label="True")
    ax.scatter(x_test[:, 0].numpy(), x_test[:, 1].numpy(), y_pred.numpy(), label="Prediction")
    ax.scatter(x_test[:, 0].numpy(), x_test[:, 1].numpy(), y_pred_true, label="sklearn")
    ax.legend()
    plt.show()


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

   **Total running time of the script:** (0 minutes 4.356 seconds)


.. _sphx_glr_download_auto_examples_SVM_SupportVectorRegression.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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