.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_03_direction_disk.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_plot_03_direction_disk.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_03_direction_disk.py:


Multiscale Direction Disks
==========================
This example shows how to use the UDCT curvelets transform to visualize
multiscale preferrential directions in an image. Inspired by
`Kymatio's Scattering disks <https://www.kymat.io/gallery_2d/plot_scattering_disk.html>`__.

.. GENERATED FROM PYTHON SOURCE LINES 8-20

.. code-block:: Python


    # sphinx_gallery_thumbnail_number = 2

    from __future__ import annotations

    import matplotlib.pyplot as plt
    import numpy as np

    from curvelets.numpy import UDCT
    from curvelets.plot import create_inset_axes_grid, overlay_arrows, overlay_disk
    from curvelets.utils import apply_along_wedges, normal_vector_field








.. GENERATED FROM PYTHON SOURCE LINES 21-23

Input Data
##########

.. GENERATED FROM PYTHON SOURCE LINES 23-30

.. code-block:: Python

    inputfile = "../testdata/sigmoid.npz"
    data = np.load(inputfile)
    data = data["sigmoid"][:120, :64]
    nx, nz = data.shape
    dx, dz = 0.005, 0.004
    x, z = np.arange(nx) * dx, np.arange(nz) * dz








.. GENERATED FROM PYTHON SOURCE LINES 31-44

.. code-block:: Python

    aspect = dz / dx
    figsize_aspect = aspect * nz / nx
    opts_space = {
        "extent": (x[0], x[-1], z[-1], z[0]),
        "cmap": "gray",
        "interpolation": "lanczos",
        "aspect": aspect,
    }
    vmax = 0.5 * np.max(np.abs(data))
    fig, ax = plt.subplots(figsize=(8, figsize_aspect * 8))
    ax.imshow(data.T, vmin=-vmax, vmax=vmax, **opts_space)
    ax.set(xlabel="Position [km]", ylabel="Depth [km]", title="Data")




.. image-sg:: /auto_examples/images/sphx_glr_plot_03_direction_disk_001.png
   :alt: Data
   :srcset: /auto_examples/images/sphx_glr_plot_03_direction_disk_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    [Text(0.5, 34.64692810457516, 'Position [km]'), Text(53.972222222222214, 0.5, 'Depth [km]'), Text(0.5, 1.0, 'Data')]



.. GENERATED FROM PYTHON SOURCE LINES 45-47

UDCT
####

.. GENERATED FROM PYTHON SOURCE LINES 47-50

.. code-block:: Python

    Cop = UDCT(data.shape, num_scales=3, wedges_per_direction=3)
    d_c = Cop.forward(data)








.. GENERATED FROM PYTHON SOURCE LINES 51-55

Normal Directions via FFT2D
###########################
Compute average normal vector. This vector indicates the direction normal to the structures
of the image

.. GENERATED FROM PYTHON SOURCE LINES 55-58

.. code-block:: Python

    kvecs = normal_vector_field(data, 1, 1)
    kvecs *= 0.4 * min(x[-1] - x[0], z[-1] - z[0])








.. GENERATED FROM PYTHON SOURCE LINES 59-64

Scattering Disk via UDCT
########################
Now we compute the average energy of each curvelet "wedge". We will plot this on a
multiscale disk to show the distribution of energies along different directions of the various
scales in the data.

.. GENERATED FROM PYTHON SOURCE LINES 64-66

.. code-block:: Python

    energy_c = apply_along_wedges(d_c, lambda w, *_: np.sqrt((np.abs(w) ** 2).mean()))








.. GENERATED FROM PYTHON SOURCE LINES 67-73

.. code-block:: Python

    fig, ax = plt.subplots(figsize=(12, figsize_aspect * 8))
    ax.imshow(data.T, vmin=-vmax, vmax=vmax, **opts_space)
    overlay_arrows(kvecs, ax, arrowprops={"edgecolor": "w", "facecolor": "k"})
    ax_o = create_inset_axes_grid(ax, width=0.4, kwargs_inset_axes={"projection": "polar"})
    overlay_disk(energy_c, ax=ax_o, vmin=0, cmap="turbo", linecolor="w", linewidth=5)
    ax.set(xlabel="Position [km]", ylabel="Depth [km]", title="Data")



.. image-sg:: /auto_examples/images/sphx_glr_plot_03_direction_disk_002.png
   :alt: Data
   :srcset: /auto_examples/images/sphx_glr_plot_03_direction_disk_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    [Text(0.5, 8.26888888888889, 'Position [km]'), Text(181.12037037037038, 0.5, 'Depth [km]'), Text(0.5, 1.0, 'Data')]




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

   **Total running time of the script:** (0 minutes 0.330 seconds)


.. _sphx_glr_download_auto_examples_plot_03_direction_disk.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_03_direction_disk.ipynb <plot_03_direction_disk.ipynb>`

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

      :download:`Download Python source code: plot_03_direction_disk.py <plot_03_direction_disk.py>`

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

      :download:`Download zipped: plot_03_direction_disk.zip <plot_03_direction_disk.zip>`


.. only:: html

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

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