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

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

.. _sphx_glr_auto_examples_hyp_lcs_plot_dg_hyp_lcs.py:


Double gyre Hyperbolic LCS
==========================

Compute hyperbolic LCS using the variational theory for the double gyre.

.. GENERATED FROM PYTHON SOURCE LINES 8-18

.. code-block:: Python


    # Author: ajarvis

    import numpy as np
    from math import copysign
    from numbacs.flows import get_predefined_flow
    from numbacs.integration import flowmap_aux_grid_2D
    from numbacs.diagnostics import C_eig_aux_2D, ftle_from_eig
    from numbacs.extraction import hyperbolic_lcs
    import matplotlib.pyplot as plt







.. 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 22-38

.. code-block:: Python


    # set initial time, integration time, and integration direction
    t0 = 0.0
    T = -10.0
    int_direction = copysign(1, T)

    # retrieve function pointer and parameters for double gyre flow.
    funcptr, params, domain = get_predefined_flow("double_gyre", int_direction=int_direction)

    # set up domain
    nx, ny = 401, 201
    x = np.linspace(domain[0][0], domain[0][1], nx)
    y = np.linspace(domain[1][0], domain[1][1], ny)
    dx = x[1] - x[0]
    dy = y[1] - y[0]








.. GENERATED FROM PYTHON SOURCE LINES 39-42

Integrate
---------
Integrate grid of particles and auxillary grid with spacing h, return final positions

.. GENERATED FROM PYTHON SOURCE LINES 42-48

.. code-block:: Python


    # computes final position of particle trajectories over grid + auxillary grid
    # with spacing h
    h = 1e-5
    flowmap = flowmap_aux_grid_2D(funcptr, t0, T, x, y, params, h=h)








.. GENERATED FROM PYTHON SOURCE LINES 49-52

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

.. GENERATED FROM PYTHON SOURCE LINES 52-60

.. code-block:: Python


    # compute eigenvalues/vectors of Cauchy Green tensor
    eigvals, eigvecs = C_eig_aux_2D(flowmap, dx, dy, h=h)
    eigval_max = eigvals[:, :, 1]
    eigvec_max = eigvecs[:, :, :, 1]

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







.. GENERATED FROM PYTHON SOURCE LINES 61-64

Hyperbolic LCS
--------------
Compute hyperbolic LCS using the variational theory.

.. GENERATED FROM PYTHON SOURCE LINES 64-100

.. code-block:: Python


    # set parameters for hyperbolic lcs extraction,
    # see function description for more details
    step_size = 1e-3
    steps = 3000
    lf = 0.1
    lmin = 1.5
    r = 0.1
    nmax = -1
    dtol = 1e-1
    nlines = 10
    percentile = 40
    ep_dist_tol = 1e-2
    lambda_avg_min = 600
    arclen_flag = True

    # extract hyperbolic lcs
    lcs = hyperbolic_lcs(
        eigval_max,
        eigvecs,
        x,
        y,
        step_size,
        steps,
        lf,
        lmin,
        r,
        nmax,
        dist_tol=dtol,
        nlines=nlines,
        ep_dist_tol=ep_dist_tol,
        percentile=percentile,
        lambda_avg_min=lambda_avg_min,
        arclen_flag=arclen_flag,
    )








.. GENERATED FROM PYTHON SOURCE LINES 101-104

Plot
----
Plot the results.

.. GENERATED FROM PYTHON SOURCE LINES 104-110

.. code-block:: Python

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



.. image-sg:: /auto_examples/hyp_lcs/images/sphx_glr_plot_dg_hyp_lcs_001.png
   :alt: plot dg hyp lcs
   :srcset: /auto_examples/hyp_lcs/images/sphx_glr_plot_dg_hyp_lcs_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 29.687 seconds)


.. _sphx_glr_download_auto_examples_hyp_lcs_plot_dg_hyp_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_dg_hyp_lcs.ipynb <plot_dg_hyp_lcs.ipynb>`

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

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

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