{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f389f465-1007-443d-873b-d27bfa74cbc7",
   "metadata": {},
   "source": [
    "# Vector space tutorial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "358fb709-9c81-45a3-a871-2549de121580",
   "metadata": {},
   "outputs": [],
   "source": [
    "#First, let's import the relavant modules:\n",
    "import romtools\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from romtools import vector_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b1ffa4be-246c-44a9-b486-f517b9f7acb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now, we will load in snapshots from a FOM. Here, we use pre-computed snapshots of the 1D Euler equations obtained using pressio-demo-apps\n",
    "snapshots = np.load('snapshots.npz')['snapshots']\n",
    "\n",
    "## The snapshots are in tensor form:\n",
    "n_vars, nx, nt = snapshots.shape\n",
    "\n",
    "#Let's look at the first density snapshot:\n",
    "\n",
    "plt.plot(snapshots[0,:,0])\n",
    "plt.xlabel(r'$x$')\n",
    "plt.ylabel(r'$\\rho$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "217759fb-6ec9-4488-897b-e5b4db9f4b2c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8dddecd2-01f7-4b7c-955e-456a1974fefb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}