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

.. only:: html

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

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

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

.. _sphx_glr_tutorials_spherical_rotation.py:


Rotate a signal
===============

This tutorial demonstrates how to use ``S2FFT`` to rotate a signal on the sphere.

.. image:: https://colab.research.google.com/assets/colab-badge.svg
    :align: center
    :alt: Open in Google Colab
    :target: https://colab.research.google.com/github/astro-informatics/s2fft/tree/gh-pages/_colab_notebooks/spherical_rotation.ipynb

If you are working on this notebook in Google Colab, you will need to have Google Colab install ``s2fft``.
You can do this by adding a cell to the top of the notebook with the following content:

.. code-block:: bash

    !pip install s2fft &> /dev/null

and then running that cell.

.. GENERATED FROM PYTHON SOURCE LINES 23-32

A signal can be rotated in pixel space, however this can introduce artifacts.
The best way to perform a rotation is through spherical harmonic space using the Wigner d-matrices, that is:

* forward spherical harmonic transform,
* rotation on the flm coefficients,
* inverse spherical harmonic transform.

Specifically, we will adopt the sampling scheme of `McEwen & Wiaux (2012) <https://arxiv.org/abs/1110.6298>`_.
For our purposes here we'll just generate a random bandlimited signal.

.. GENERATED FROM PYTHON SOURCE LINES 32-46

.. code-block:: Python


    import jax
    import numpy as np

    import s2fft

    jax.config.update("jax_enable_x64", True)

    L = 128
    sampling = "mw"
    rng = np.random.default_rng(12346161)
    flm = s2fft.utils.signal_generator.generate_flm(rng, L)
    f = s2fft.inverse(flm, L)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    JAX is not using 64-bit precision. This will dramatically affect numerical precision at even moderate L.




.. GENERATED FROM PYTHON SOURCE LINES 47-51

Execute the rotation steps
--------------------------

First, we will run the ``JAX`` function to compute the spherical harmonic transform of our signal

.. GENERATED FROM PYTHON SOURCE LINES 51-54

.. code-block:: Python


    flm = s2fft.forward_jax(f, L, reality=True)








.. GENERATED FROM PYTHON SOURCE LINES 55-56

Now apply the rotation (here :math:`\pi/2` in each of ``alpha``, ``beta``, ``gamma``) on the harmonic coefficients ``flm``.

.. GENERATED FROM PYTHON SOURCE LINES 56-59

.. code-block:: Python


    flm_rotated = s2fft.rotate_flms(flm, L, (np.pi / 2, np.pi / 2, np.pi / 2))








.. GENERATED FROM PYTHON SOURCE LINES 60-61

Finally, we will run the ``JAX`` function to compute the inverse spherical harmonic transform to get back to pixel space.

.. GENERATED FROM PYTHON SOURCE LINES 61-63

.. code-block:: Python


    f_rotated = s2fft.inverse_jax(flm_rotated, L, reality=True)








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

   **Total running time of the script:** (0 minutes 33.816 seconds)


.. _sphx_glr_download_tutorials_spherical_rotation.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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