.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/01_quick-start/01_03_extension_modes.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_01_quick-start_01_03_extension_modes.py>`
        to download the full example code. or to run this example in your browser via JupyterLite or Binder

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

.. _sphx_glr_auto_examples_01_quick-start_01_03_extension_modes.py:


Extension modes
===============

Plotting different extension modes of signals.

.. GENERATED FROM PYTHON SOURCE LINES 13-18

Imports and Utilities
---------------------

Visualize how the extension modes allow one to control the values that a signal is assumed to take outside of its original domain.
Generate a signal that is mostly linear but includes a "bump."

.. GENERATED FROM PYTHON SOURCE LINES 18-53

.. code-block:: Python


    import numpy as np
    import matplotlib.pyplot as plt
    from splineops.interpolate.tensorspline import TensorSpline

    x_values = np.linspace(0, 6, 101)

    def create_signal_with_bump(x_values, bump_location=3, bump_width=0.5, bump_height=5):
        linear_part = x_values
        bump = np.where(
            (x_values > (bump_location - bump_width / 2))
            & (x_values < (bump_location + bump_width / 2)),
            bump_height,
            0,
        )
        return linear_part + bump

    def plot_extension_modes_for_bump_function(mode_name, x_values, title):
        plt.figure(figsize=(12, 6))
        data = create_signal_with_bump(x_values)
        tensor_spline = TensorSpline(
            data=data, coordinates=(x_values,), bases="linear", modes=mode_name
        )
        eval_x_values = np.linspace(-10, 10, 2000)
        extended_data = tensor_spline.eval(coordinates=(eval_x_values,))
        plt.plot(eval_x_values, extended_data, label="Extended Signal")
        plt.axvline(x=x_values[0], color="red", linestyle="--", label="Original Start")
        plt.axvline(x=x_values[-1], color="blue", linestyle="--", label="Original End")
        plt.title(title)
        plt.xlabel("x")
        plt.ylabel("Interpolated Value")
        plt.grid(True)
        plt.legend()
        plt.show()








.. GENERATED FROM PYTHON SOURCE LINES 54-56

Finite-Support Coefficients
---------------------------

.. GENERATED FROM PYTHON SOURCE LINES 56-63

.. code-block:: Python


    plot_extension_modes_for_bump_function(
        mode_name="zero",
        x_values=x_values,
        title="Extension Mode: Finite Support Coefficients",
    )




.. image-sg:: /auto_examples/01_quick-start/images/sphx_glr_01_03_extension_modes_001.png
   :alt: Extension Mode: Finite Support Coefficients
   :srcset: /auto_examples/01_quick-start/images/sphx_glr_01_03_extension_modes_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 64-66

Narrow Mirroring
----------------

.. GENERATED FROM PYTHON SOURCE LINES 66-73

.. code-block:: Python


    plot_extension_modes_for_bump_function(
        mode_name="mirror",
        x_values=x_values,
        title="Extension Mode: Narrow Mirroring",
    )




.. image-sg:: /auto_examples/01_quick-start/images/sphx_glr_01_03_extension_modes_002.png
   :alt: Extension Mode: Narrow Mirroring
   :srcset: /auto_examples/01_quick-start/images/sphx_glr_01_03_extension_modes_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 74-76

Periodic Padding
----------------

.. GENERATED FROM PYTHON SOURCE LINES 76-81

.. code-block:: Python


    plot_extension_modes_for_bump_function(
        mode_name="periodic",
        x_values=x_values,
        title="Extension Mode: Periodic Padding",
    )


.. image-sg:: /auto_examples/01_quick-start/images/sphx_glr_01_03_extension_modes_003.png
   :alt: Extension Mode: Periodic Padding
   :srcset: /auto_examples/01_quick-start/images/sphx_glr_01_03_extension_modes_003.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.261 seconds)


.. _sphx_glr_download_auto_examples_01_quick-start_01_03_extension_modes.py:

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        :alt: Launch binder
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        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: 01_03_extension_modes.ipynb <01_03_extension_modes.ipynb>`

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      :download:`Download Python source code: 01_03_extension_modes.py <01_03_extension_modes.py>`

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      :download:`Download zipped: 01_03_extension_modes.zip <01_03_extension_modes.zip>`


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