.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/ex03_custom_extension.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_ex03_custom_extension.py>`
        to download the full example code.

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

.. _sphx_glr_examples_ex03_custom_extension.py:


Custom Extensions
-----------------
Custom functions (extensions) are easy to implement in `tensortrax`. Beside the function
expression, three additional (dual) variation expressions have to be defined. 

.. GENERATED FROM PYTHON SOURCE LINES 7-25

.. code-block:: Python

    import numpy as np

    from tensortrax import Tensor, Δ, Δδ, f, δ


    def sin(A):
        return Tensor(
            x=np.sin(f(A)),
            δx=np.cos(f(A)) * δ(A),
            Δx=np.cos(f(A)) * Δ(A),
            Δδx=-np.sin(f(A)) * δ(A) * Δ(A) + np.cos(f(A)) * Δδ(A),
            ntrax=A.ntrax,
        )


    x = np.eye(3)
    y = sin(Tensor(x))








.. GENERATED FROM PYTHON SOURCE LINES 26-34

.. note::
   Contrary to NumPy's ``w, v = np.linalg.eigh(C)``, which returns eigenvalues and
   -vectors, the differentiable ``w, M = tm.linalg.eigh(C)`` function returns
   eigenvalues and eigenbases of symmetric real-valued tensors.

.. tip::
   Feel free to `contribute <https://github.com/adtzlr/tensortrax/fork>`_ missing
   math-functions to `src/tensortrax/math/_math_tensor.py <https://github.com/adtzlr/tensortrax/blob/main/src/tensortrax/math/_math_tensor.py>`_ 📃 ✏️.


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

   **Total running time of the script:** (0 minutes 0.001 seconds)


.. _sphx_glr_download_examples_ex03_custom_extension.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: ex03_custom_extension.ipynb <ex03_custom_extension.ipynb>`

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

      :download:`Download Python source code: ex03_custom_extension.py <ex03_custom_extension.py>`

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

      :download:`Download zipped: ex03_custom_extension.zip <ex03_custom_extension.zip>`


.. only:: html

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

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