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

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

.. _sphx_glr_auto_examples_elliptic_lcs_plot_qge_elliptic_lcs.py:


Quasi-geostrophic Elliptic LCS
==============================

Compute the LAVD-based elliptic lcs for the QGE.

.. GENERATED FROM PYTHON SOURCE LINES 8-28

.. 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 matplotlib.animation import FuncAnimation
    from numbacs.flows import (
        get_interp_arrays_2D,
        get_flow_2D,
        get_callable_2D,
        get_interp_arrays_scalar,
        get_callable_scalar,
    )
    from numbacs.integration import flowmap_n_grid_2D, flowmap_n
    from numbacs.diagnostics import lavd_grid_2D
    from numbacs.extraction import rotcohvrt
    from numbacs.utils import curl_func_tspan, gen_filled_circ, interp_curve, pts_in_poly_mask







.. GENERATED FROM PYTHON SOURCE LINES 29-33

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 33-61

.. 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 = 0.5
    T = 0.3
    params = np.array([copysign(1, T)])  # important this is an array of type float
    n = 601

    # 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")

    # get callable for flow
    vel_spline = get_callable_2D(grid_vel, C_eval_u, C_eval_v, extrap_mode="linear")








.. GENERATED FROM PYTHON SOURCE LINES 62-65

Integrate
---------
Integrate grid of particles and return positions at n times between [t0,t0+T] (inclusive).

.. GENERATED FROM PYTHON SOURCE LINES 65-67

.. code-block:: Python

    flowmap, tspan = flowmap_n_grid_2D(funcptr, t0, T, x, y, params, n=n)








.. GENERATED FROM PYTHON SOURCE LINES 68-71

Vorticity
---------
Copmute vorticity on the grid and over the times for which the flowmap was returned.

.. GENERATED FROM PYTHON SOURCE LINES 71-77

.. code-block:: Python


    # compute vorticity and create interpolant for it
    vort = curl_func_tspan(vel_spline, tspan, x, y, h=1e-3)
    grid_domain, C_vort = get_interp_arrays_scalar(tspan, x, y, vort)
    vort_spline = get_callable_scalar(grid_domain, C_vort)








.. GENERATED FROM PYTHON SOURCE LINES 78-81

LAVD
----
Compute LAVD from vorticity and particle positions.

.. GENERATED FROM PYTHON SOURCE LINES 81-90

.. code-block:: Python


    # need to pass raveled arrays into lavd_grid_2D
    X, Y = np.meshgrid(x, y, indexing="ij")
    xrav = X.ravel()
    yrav = Y.ravel()

    # compute lavd
    lavd = lavd_grid_2D(flowmap, tspan, T, vort_spline, xrav, yrav)








.. GENERATED FROM PYTHON SOURCE LINES 91-94

LAVD-based elliptic LCS
-----------------------
Compute elliptic LCS from LAVD.

.. GENERATED FROM PYTHON SOURCE LINES 94-100

.. code-block:: Python


    # set parameters and compute lavd-based elliptic lcs
    r = 0.2
    convexity_deficiency = 1e-3
    min_len = 0.1
    elcs = rotcohvrt(lavd, x, y, r, convexity_deficiency=convexity_deficiency, min_len=min_len)







.. GENERATED FROM PYTHON SOURCE LINES 101-104

Plot
----
Plot the elliptic LCS over the LAVD field.

.. GENERATED FROM PYTHON SOURCE LINES 104-114

.. code-block:: Python


    # sphinx_gallery_thumbnail_number = 1
    fig, ax = plt.subplots(dpi=200)
    ax.contourf(x, y, lavd.T, levels=80)
    ax.set_aspect("equal")
    for rcv, c in elcs:
        ax.plot(rcv[:, 0], rcv[:, 1], lw=1.5)
        ax.scatter(c[0], c[1], 1.5)
    plt.show()




.. image-sg:: /auto_examples/elliptic_lcs/images/sphx_glr_plot_qge_elliptic_lcs_001.png
   :alt: plot qge elliptic lcs
   :srcset: /auto_examples/elliptic_lcs/images/sphx_glr_plot_qge_elliptic_lcs_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 115-119

Advect elliptic LCS
-------------------
Advect an elliptic LCS and nearby filled circle of points to demonstrate
coherence.

.. GENERATED FROM PYTHON SOURCE LINES 119-136

.. code-block:: Python


    # pick an elliptic lcs and create more refined curve by interpolating
    c0 = elcs[0][1]
    rcv0 = elcs[0][0]
    rcvi = interp_curve(rcv0, 2500, per=1)

    # create a filled circle which has a center a distance delta away from
    # vortex center
    delta = 1e-2
    circ_delta = gen_filled_circ(0.1, 10000, c=c0 + delta, xlims=(0, 1), ylims=(0, 2))

    # advect both the elliptic lcs and the nearby filled circle
    frames = 301
    adv_rcv, teval = flowmap_n(funcptr, t0, T, rcvi, params, n=frames)
    adv_circ, _ = flowmap_n(funcptr, t0, T, circ_delta, params, n=frames)









.. GENERATED FROM PYTHON SOURCE LINES 137-140

Animate
-------
Create animation of advected elliptic LCS and nearby filled circle.

.. GENERATED FROM PYTHON SOURCE LINES 140-183

.. code-block:: Python


    # find which points from the filled circle are inside elliptic lcs
    # for plotting purposes
    mask = pts_in_poly_mask(rcv0, circ_delta)

    # create plot
    fig, ax = plt.subplots(dpi=100)
    scatter0 = ax.scatter(adv_rcv[:, 0, 0], adv_rcv[:, 0, 1], 1)
    scatter_in = ax.scatter(adv_circ[mask, 0, 0], adv_circ[mask, 0, 1], 0.5, "purple", zorder=0)
    scatter_out = ax.scatter(adv_circ[~mask, 0, 0], adv_circ[~mask, 0, 1], 0.5, "orange", zorder=0)
    ax.set_xlim([x[0], x[-1]])
    ax.set_ylim([y[0], 1.25])  # only focus on part of domain where particles go
    ax.set_aspect("equal")
    ax.set_title(f"t = {round(teval[0], 2):.2f}")


    # function for animation
    def update(frame):
        # for each frame, update the data stored on each artist
        x0 = adv_rcv[:, frame, 0]
        y0 = adv_rcv[:, frame, 1]
        x_in = adv_circ[mask, frame, 0]
        y_in = adv_circ[mask, frame, 1]
        x_out = adv_circ[~mask, frame, 0]
        y_out = adv_circ[~mask, frame, 1]
        data0 = np.column_stack((x0, y0))
        data_in = np.column_stack((x_in, y_in))
        data_out = np.column_stack((x_out, y_out))

        # update each scatter plot
        scatter0.set_offsets(data0)
        scatter_in.set_offsets(data_in)
        scatter_out.set_offsets(data_out)

        # update title
        ax.set_title(f"t = {round(teval[frame], 2):.2f}")

        return (scatter0, scatter_in, scatter_out)


    # create animation
    ani = FuncAnimation(fig=fig, func=update, frames=frames, interval=30)
    plt.show()



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         /* set a timeout to make sure all the above elements are created before
            the object is initialized. */
         setTimeout(function() {
             anim6e0f70fa94e5443d949e34b76304948f = new Animation(frames, img_id, slider_id, 29.0,
                                      loop_select_id);
         }, 0);
       })()
     </script>







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

   **Total running time of the script:** (1 minutes 39.224 seconds)


.. _sphx_glr_download_auto_examples_elliptic_lcs_plot_qge_elliptic_lcs.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_elliptic_lcs.ipynb <plot_qge_elliptic_lcs.ipynb>`

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

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

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

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


.. only:: html

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

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