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

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

.. _sphx_glr_auto_examples_ftle_plot_bickley_ftle_ridges.py:


Bickley jet FTLE ridges
=======================

Compute the FTLE field and ridges for the bickley jet.

.. GENERATED FROM PYTHON SOURCE LINES 8-18

.. code-block:: Python


    # Author: ajarvis

    import numpy as np
    from math import copysign
    import matplotlib.pyplot as plt
    from numbacs.flows import get_predefined_flow
    from numbacs.integration import flowmap_grid_2D
    from numbacs.diagnostics import ftle_from_eig, C_eig_2D
    from numbacs.extraction import ftle_ordered_ridges







.. GENERATED FROM PYTHON SOURCE LINES 19-22

Get flow
--------------
Set the integration span and direction, retrieve the flow, and set up domain.

.. GENERATED FROM PYTHON SOURCE LINES 22-39

.. code-block:: Python


    # set initial time, integration time, and integration direction
    t0 = 0.0
    T = 6.0
    int_direction = copysign(1, T)

    # retrieve function pointer, parameters, and domain for bickley jet flow.
    funcptr, params, domain = get_predefined_flow("bickley_jet", int_direction=int_direction)

    # set up domain
    dx = 0.05
    dy = 0.05
    x = np.arange(domain[0][0], domain[0][1] + dx, dx)
    y = np.arange(domain[1][0], domain[1][1] + dy, dy)
    dx = x[1] - x[0]
    dy = y[1] - y[0]








.. GENERATED FROM PYTHON SOURCE LINES 40-43

Integrate
---------
Integrate grid of particles and return final positions.

.. GENERATED FROM PYTHON SOURCE LINES 43-45

.. code-block:: Python

    flowmap = flowmap_grid_2D(funcptr, t0, T, x, y, params)








.. GENERATED FROM PYTHON SOURCE LINES 46-49

CG eigenvalues, eigenvectors, and FTLE
----------------------------------------------
Compute eigenvalues/vectors of CG tensor from final particle positions and compute FTLE.

.. GENERATED FROM PYTHON SOURCE LINES 49-58

.. code-block:: Python


    # compute eigenvalues/vectors of Cauchy Green tensor
    eigvals, eigvecs = C_eig_2D(flowmap, dx, dy)
    eigval_max = eigvals[:, :, 1]
    eigvec_max = eigvecs[:, :, :, 1]

    # compute FTLE from max eigenvalue
    ftle = ftle_from_eig(eigval_max, T)








.. GENERATED FROM PYTHON SOURCE LINES 59-62

Ridge extraction
----------------
Compute ordered FTLE ridges.

.. GENERATED FROM PYTHON SOURCE LINES 62-73

.. code-block:: Python


    # set parameters for ridge function
    percentile = 90
    sdd_thresh = 10.0

    # identify ridge points, link points in each ridge in an ordered manner,
    # connect close enough ridges
    dist_tol = 1e-1
    ridge_curves = ftle_ordered_ridges(
        ftle, eigvec_max, x, y, dist_tol, percentile=percentile, sdd_thresh=sdd_thresh, min_ridge_pts=25
    )







.. GENERATED FROM PYTHON SOURCE LINES 74-77

Plot
----
Plot the results.

.. GENERATED FROM PYTHON SOURCE LINES 77-83

.. code-block:: Python

    fig, ax = plt.subplots(dpi=200)
    ax.contourf(x, y, ftle.T, levels=80)
    for rc in ridge_curves:
        ax.plot(rc[:, 0], rc[:, 1], lw=1.5)
    ax.set_aspect("equal")
    plt.show()



.. image-sg:: /auto_examples/ftle/images/sphx_glr_plot_bickley_ftle_ridges_001.png
   :alt: plot bickley ftle ridges
   :srcset: /auto_examples/ftle/images/sphx_glr_plot_bickley_ftle_ridges_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 15.322 seconds)


.. _sphx_glr_download_auto_examples_ftle_plot_bickley_ftle_ridges.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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