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

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

.. _sphx_glr_auto_examples_ftle_plot_qge_ftle_ridges.py:


Quasi-geostrophic FTLE ridges
=============================

Compute the FTLE field and ridges for the QGE.

.. GENERATED FROM PYTHON SOURCE LINES 8-21

.. code-block:: Python


    # Author: ajarvis
    # Data: We thank Changhong Mou and Traian Iliescu for providing us with this dataset
    #       and allowing it to be used here.

    import numpy as np
    from math import copysign
    import matplotlib.pyplot as plt
    from numbacs.flows import get_interp_arrays_2D, get_flow_2D
    from numbacs.integration import flowmap_grid_2D
    from numbacs.diagnostics import ftle_from_eig, C_eig_2D
    from numbacs.extraction import ftle_ordered_ridges
    from scipy.ndimage import gaussian_filter







.. GENERATED FROM PYTHON SOURCE LINES 22-26

Get flow data
--------------
Load velocity data, set up domain, set the integration span and direction, create
interpolant of velocity data and retrieve necessary arrays.

.. GENERATED FROM PYTHON SOURCE LINES 26-50

.. code-block:: Python


    # load in qge velocity data
    u = np.load("../data/qge/qge_u.npy")
    v = np.load("../data/qge/qge_v.npy")

    # set up domain
    nt, nx, ny = u.shape
    x = np.linspace(0, 1, nx)
    y = np.linspace(0, 2, ny)
    t = np.linspace(0, 1, nt)
    dx = x[1] - x[0]
    dy = y[1] - y[0]

    # set integration span and integration direction
    t0 = 0.0
    T = 0.1
    params = np.array([copysign(1, T)])  # important this is an array of type float

    # get interpolant arrays of velocity field
    grid_vel, C_eval_u, C_eval_v = get_interp_arrays_2D(t, x, y, u, v)

    # get flow to be integrated
    funcptr = get_flow_2D(grid_vel, C_eval_u, C_eval_v, extrap_mode="linear")








.. GENERATED FROM PYTHON SOURCE LINES 51-54

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

.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 57-60

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

.. GENERATED FROM PYTHON SOURCE LINES 60-72

.. 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)

    # smooth ftle field, usually a good idea for numerical velocity field
    sigma = 1.2
    ftle_c = gaussian_filter(ftle, sigma, mode="nearest")







.. GENERATED FROM PYTHON SOURCE LINES 73-76

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

.. GENERATED FROM PYTHON SOURCE LINES 76-95

.. code-block:: Python


    # set parameters for ridge function
    # function is fast after first call so experiment with these parameters
    percentile = 50
    sdd_thresh = 5e3

    # identify ridge points, link points in each ridge in an ordered manner,
    # connect close enough ridges
    dist_tol = 5e-2
    ridge_curves = ftle_ordered_ridges(
        ftle_c,
        eigvec_max,
        x,
        y,
        dist_tol,
        percentile=percentile,
        sdd_thresh=sdd_thresh,
        min_ridge_pts=25,
    )







.. GENERATED FROM PYTHON SOURCE LINES 96-99

Plot
----
Plot the results.

.. GENERATED FROM PYTHON SOURCE LINES 99-105

.. code-block:: Python

    fig, ax = plt.subplots(dpi=200)
    ax.contourf(x, y, ftle_c.T, levels=80)
    for rc in ridge_curves:
        ax.plot(rc[:, 0], rc[:, 1], "r", lw=1.0)
    ax.set_aspect("equal")
    plt.show()



.. image-sg:: /auto_examples/ftle/images/sphx_glr_plot_qge_ftle_ridges_001.png
   :alt: plot qge ftle ridges
   :srcset: /auto_examples/ftle/images/sphx_glr_plot_qge_ftle_ridges_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 4.412 seconds)


.. _sphx_glr_download_auto_examples_ftle_plot_qge_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_qge_ftle_ridges.ipynb <plot_qge_ftle_ridges.ipynb>`

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

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

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

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


.. only:: html

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

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