LDDS Review process at JOSS https://github.com/openjournals/joss-reviews/issues/3482

simple_pendulum.ipynb

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   "cell_type": "code",
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   "id": "afd3fd23",
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   "source": [
    "from ldds.base import compute_lagrangian_descriptor\n",
    "from ldds.tools import draw_all_lds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2843727f",
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   "source": [
    "def pendulum(t, u):\n",
    "    x, y = u.T\n",
    "    v = np.column_stack([y, -np.sin(x)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0c7ec93b",
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   "source": [
    "# Mesh parameters to calculate LDs\n",
    "\n",
    "# 2D Domain\n",
    "x_min,x_max = [-4, 4]\n",
    "y_min,y_max = [-4, 4]\n",
    "\n",
    "# Grid size\n",
    "Nx, Ny = [50, 50]\n",
    "\n",
    "grid_parameters = [(x_min, x_max, Nx), (y_min, y_max, Ny)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "376e4bf1",
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   "source": [
    "vector_field = lambda t,u: pendulum(t, u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e1fb9633",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Integration parameters (Calculate LDs at time t = t0 by integrating in the interval [t0-tau,t0+tau])\n",
    "t0 = 0\n",
    "tau = 1\n",
    "\n",
    "# LDs definition (we will use the p-value seminorm)\n",
    "p_value = 0.5\n",
    "\n",
    "LD_forward = compute_lagrangian_descriptor(grid_parameters, vector_field, tau, p_value)\n",
    "LD_backward = compute_lagrangian_descriptor(grid_parameters, vector_field, -tau, p_value)\n",
    "\n",
    "figs = draw_all_lds(LD_forward, LD_backward, grid_parameters, tau, p_value)"
   ]
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   "cell_type": "code",
   "execution_count": null,
   "id": "84c58748",
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