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

.. only:: html

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

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

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

.. _sphx_glr_gallery_plot_single_curvelet.py:


1. Visualize a Single Curvelet
==============================
This example shows a single curvelet coefficient in
spatial and frequency domains.

.. GENERATED FROM PYTHON SOURCE LINES 9-16

.. code-block:: default

    import matplotlib.pyplot as plt
    import numpy as np
    from matplotlib.ticker import MultipleLocator

    from curvelops import FDCT2D
    from curvelops.plot import create_colorbar








.. GENERATED FROM PYTHON SOURCE LINES 17-19

Setup
=====

.. GENERATED FROM PYTHON SOURCE LINES 19-24

.. code-block:: default

    m = 512
    n = 512
    x = np.zeros((m, n))
    DCT = FDCT2D(x.shape)








.. GENERATED FROM PYTHON SOURCE LINES 25-27

Curvelet Domain
===============

.. GENERATED FROM PYTHON SOURCE LINES 29-35

.. code-block:: default

    y = DCT * x

    # Convert to a curvelet struct indexed by
    # [scale, wedge (angle), x, y]
    y_reshape = DCT.struct(y)








.. GENERATED FROM PYTHON SOURCE LINES 36-38

Select single curvelet
======================

.. GENERATED FROM PYTHON SOURCE LINES 38-47

.. code-block:: default

    s = 4
    w = 0
    a, b = y_reshape[s][w].shape
    normalization = np.sqrt(y_reshape[s][w].size)
    y_reshape[s][w][a // 2, b // 2] = 1 * normalization
    y_reshape[s][w + len(y_reshape[s]) // 2][a // 2, b // 2] = -1j * normalization

    y = DCT.vect(y_reshape)








.. GENERATED FROM PYTHON SOURCE LINES 48-50

Perform adjoint transform and reshape
=====================================

.. GENERATED FROM PYTHON SOURCE LINES 50-52

.. code-block:: default

    x = DCT.H @ y








.. GENERATED FROM PYTHON SOURCE LINES 53-55

F-K domain
==========

.. GENERATED FROM PYTHON SOURCE LINES 55-57

.. code-block:: default

    x_fk = np.fft.fftshift(np.fft.fft2(np.fft.ifftshift(x), norm="ortho"))








.. GENERATED FROM PYTHON SOURCE LINES 58-60

Visualize
=========

.. GENERATED FROM PYTHON SOURCE LINES 60-92

.. code-block:: default

    vmin, vmax = 0.8 * np.array([-1, 1]) * np.abs(np.max(x))
    fig, ax = plt.subplots(2, 2, figsize=(8, 8), sharex="row", sharey="row")

    im = ax[0, 0].imshow(x.real.T, cmap="gray", vmin=vmin, vmax=vmax)
    create_colorbar(im, ax[0, 0])

    im = ax[0, 1].imshow(x.imag.T, cmap="gray", vmin=vmin, vmax=vmax)
    create_colorbar(im, ax[0, 1])

    im = ax[1, 0].imshow(np.abs(x_fk).T, cmap="turbo", vmin=0)
    create_colorbar(im, ax[1, 0])

    mask = np.abs(x_fk) > 0.01 * np.abs(x_fk).max()
    im = ax[1, 1].imshow(
        (mask * np.angle(x_fk, deg=True)).T,
        cmap="twilight_shifted",
        vmin=-180,
        vmax=180,
    )
    cax, cb = create_colorbar(im, ax[1, 1])
    cax.get_yaxis().set_major_locator(MultipleLocator(45))


    ax[0, 0].set(
        xlim=(m // 2 - 50, m // 2 + 50),
        ylim=(n // 2 - 50, n // 2 + 50),
        title="Space domain (Real) magnified",
    )
    ax[0, 1].set(title="Space domain (Imag) magnified")
    ax[1, 0].set(title="Frequency domain (Abs)")
    ax[1, 1].set(title="Frequency domain (Phase)")
    fig.tight_layout()



.. image-sg:: /gallery/images/sphx_glr_plot_single_curvelet_001.png
   :alt: Space domain (Real) magnified, Space domain (Imag) magnified, Frequency domain (Abs), Frequency domain (Phase)
   :srcset: /gallery/images/sphx_glr_plot_single_curvelet_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  1.330 seconds)


.. _sphx_glr_download_gallery_plot_single_curvelet.py:

.. only:: html

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




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

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

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

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


.. only:: html

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

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