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

.. only:: html

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

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

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

.. _sphx_glr_examples_vectorrotation.py:


Fixed-point vector rotation
===========================

This illustrates the effect of performing a vector rotation
using different number of fractional bits and different quantization schemes.

.. GENERATED FROM PYTHON SOURCE LINES 8-64



.. image-sg:: /examples/images/sphx_glr_vectorrotation_001.png
   :alt: vectorrotation
   :srcset: /examples/images/sphx_glr_vectorrotation_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    8 fractional bits. Gain: 1.0000076293654276. Angle: 0.0039062301319669718.
    12 fractional bits. Gain: 1.0000042915252152. Angle: 0.0029296791181399936.
    16 fractional bits. Gain: 1.000004517952019. Angle: 0.003005972391421174.






|

.. code-block:: Python


    import apytypes as apy
    import math
    import matplotlib.pyplot as plt
    import numpy as np

    angle = 0.003


    def print_rotation_properties(angle, frac_bits):
        cosa = math.cos(angle)
        sina = math.sin(angle)
        rotation_matrix = apy.fx([[cosa, -sina], [sina, cosa]], 2, frac_bits)
        rm = rotation_matrix.to_numpy()
        print(
            f"{frac_bits} fractional bits. Gain: {np.hypot(*rm[0, :])}. Angle: {np.arctan2(*rm[1, :])}."
        )


    def rotate(angle, frac_bits, iterations, quantization):
        results = apy.zeros((iterations + 1, 2), int_bits=2, frac_bits=frac_bits)
        cosa = math.cos(angle)
        sina = math.sin(angle)
        rotation_matrix = apy.fx([[cosa, -sina], [sina, cosa]], 2, frac_bits)
        current_value = apy.fx([1, 0], 2, frac_bits)

        results[0, :] = current_value.T
        for i in range(iterations):
            tmp_res = rotation_matrix @ current_value
            current_value = tmp_res.cast(2, frac_bits, quantization)
            results[i + 1, :] = current_value.T

        return results


    fig, ax = plt.subplots()

    for frac_bits in (8, 12, 16):
        print_rotation_properties(angle, frac_bits)
        for quantization in (
            "RND",
            "JAM",
            "TRN",
        ):
            results = rotate(
                angle, frac_bits, 3000, eval(f"apy.QuantizationMode.{quantization}")
            )
            ax.plot(
                results[:, 0],
                results[:, 1],
                label=f"{frac_bits} frac. bits, {quantization}",
            )

    ax.set_aspect("equal")
    fig.legend(ncols=3, loc="upper center")
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.113 seconds)


.. _sphx_glr_download_examples_vectorrotation.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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