tutorials/tutorial7/tutorial-7-dmdc.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyDMD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tutorial 7: Dynamic mode decomposition with control"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial we will show how to extend the dynamic mode decomposition to incorporate the effect of control (this technique has been introduced in the paper [Dynamic mode decomposition with control](https://arxiv.org/abs/1409.6358))."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First of all we import the `DMDc` class from the pydmd package, we set matplotlib for the notebook and we import numpy and scipy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy\n",
    "\n",
    "from pydmd import DMDc\n",
    "from pydmd.plotter import plot_eigs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we create our dataset: since we want to add the control, the evolution of the complex system can be formally summarized as:\n",
    "$$\n",
    "\\mathbf{x}_{k+1} = \\mathbf{A}\\mathbf{x}_k + \\mathbf{B}\\mathbf{u}_k,\n",
    "$$where the operators $\\mathbf{A}$ and $\\mathbf{B}$ are the ones we will approximate using DMD. So, for a demostrative purpose, we create the original snapshots by using two random operators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_system(n, m):\n",
    "    A = scipy.linalg.helmert(n, True)\n",
    "    B = np.random.rand(n, n) - 0.5\n",
    "    x0 = np.array([0.25] * n)\n",
    "    u = np.random.rand(n, m - 1) - 0.5\n",
    "    snapshots = [x0]\n",
    "    for i in range(m - 1):\n",
    "        snapshots.append(A.dot(snapshots[i]) + B.dot(u[:, i]))\n",
    "    snapshots = np.array(snapshots).T\n",
    "    return {\"snapshots\": snapshots, \"u\": u, \"B\": B, \"A\": A}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We got 10 snapshots of the evolving system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(25, 10)\n"
     ]
    }
   ],
   "source": [
    "s = create_system(25, 10)\n",
    "print(s[\"snapshots\"].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can compute as usually the DMD algorithm on the data: the `fit` method in this version take as arguments the snapshots and the control input (the $\\mathbf{B}$ operator can be also passed). In this case, we do not perform any truncation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pydmd.dmdc.DMDc at 0x1236d4bb0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dmdc = DMDc(svd_rank=-1)\n",
    "dmdc.fit(s[\"snapshots\"], s[\"u\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us visualize the original system and the reconstructed one: also because without truncation, the plots are the same!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1600x600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16, 6))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.title(\"Original system\")\n",
    "plt.pcolor(s[\"snapshots\"].real)\n",
    "plt.colorbar()\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.title(\"Reconstructed system\")\n",
    "plt.pcolor(dmdc.reconstructed_data().real)\n",
    "plt.colorbar()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, we built the approximation for $\\mathbf{A}$ and for $\\mathbf{B}$; we can now test the system with a different control input: differently by the other versions, we can pass as argument of the `reconstructed_data` method the control input we want to test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_u = np.exp(s[\"u\"])\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.pcolor(dmdc.reconstructed_data(new_u).real)\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can also use a different timestep for the reconstruction, obviously passing the proper control input (the number of inputs we pass has to be the number of reconstructed snapshots we try to compute, except for the first snapshots). We continue halving the timestep and create a new random input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Vc5gVAADANatWrWryePny5crKytK2bdt01VVXeZJJMQcAAALBeHCfOfPFeJWVlU2eD4fDCofDbf5+RUWFJCkzM9PV5foyDrMCAIBAcP0Q6xeTJOXl5SkjIyM2FRcXt708jqM5c+boiiuu0IUXXujZ66YzBwAA0IaDBw8qEonEHrenK1dUVKSdO3dq8+bNXi4axRwAAAgGL29NEolEmhRzbZk9e7Zef/11bdq0SQMHDnR1mb6KYg4AAMAlxhjdfffdeu2117RhwwYVFBR4nkkxBwAAAuHL57i5OWZHFBUV6YUXXtDKlSuVnp6u0tJSSVJGRobS0tJcXbbTuAACAADAJUuXLlVFRYXGjh2rAQMGxKaXX37Zs0w6cwAAIBAcD25N0tHxjDGu5rcHnTkAAAAfozMHAAACoTucM9cVKOYAAEAgxGsxx2FWAAAAH4vrzlxaaoOVnMbkqJWchAQ7J1326VljJceWQ6V9rGWZhkQrOcMuPmAlp1dyvZWcHfu9veHmaQca+lrJGTiszErO0Yp0KzmfHe9lJadnRq2VHElKTbOzbdeGkq3kOA3e926caNd3sOjMAQAAwHfiujMHAACCg84cAAAAfIfOHAAACASjjt/ktz1jdnd05gAAAHyMzhwAAAiEeD1njmIOAAAEQrwWcxxmBQAA8DE6cwAAIBDozAEAAMB36MwBAIBAoDMHAAAA36EzBwAAAsGYkIzLnTS3x/MCnTkAAAAfozMHAAACwVHI9a/zcns8L1DMAQCAQOACCAAAAPgOnTkAABAI8XoBRFwXc7Zap6GQsZJjSzix0UpOTUOKlZzQsbCVHElKrrazzeVdVG4l55L0/VZytr0/xEpOyrFEKzn5wz63ktMYtfN6So/1tZJzMsnOPkGSUlLt7OcSEx0rOU4DB+KCLK6LOQAAEBycMwcAAADfoTMHAAACIV7PmaMzBwAA4GN05gAAQCAYD86Z80NnjmIOAAAEgpFkXL6BhB/uR8FhVgAAAB+jMwcAAALBUUihOPxuVjpzAAAAPkZnDgAABAK3JgEAAIDv0JkDAACB4JiQQnydFwAAAPyEzhwAAAgEYzy4z5wPbjRHZw4AAMDH6MwBAIBAiNerWSnmAABAIFDMxaHqijQ7QY6dGCXaObC/93gPKzmhZDsr7pwLy6zkSNLJhmQrOZtWjbSSsz51hJWciwpLrORUNaRYyfnT6vOt5NRnNVrJGXxuqZWcssp0KzmSVPO5nb8PoQQ7++2U9HrPM6LGzvaGM8V1MQcAAIKDW5MAAADAd+jMAQCAQODWJAAAAPAdOnMAACAQTnXm3L6a1dXhPEFnDgAAwMfozAEAgEDgPnMAAAA+Zr6Y3B6zu+MwKwAAgI/RmQMAAIEQr4dZ6cwBAAD4GMUcAAAIBuPR1AlLlizR4MGDlZqaqsLCQr3zzjudflltoZgDAABw0csvv6y5c+dqwYIF2r59u0aOHKkJEybo6NGjnuR1uJjbtGmTJk+erNzcXIVCIa1YsaLJz2fMmKFQKNRkmjhxolvLCwAA0Lwvzplzc1InzplbvHixZs2apZkzZ+r888/Xk08+qR49euiZZ57x4EV3opirrq7WyJEjtWTJkhbnmThxoo4cORKbXnzxxbNaSAAAAD+or6/Xtm3bNG7cuNhzCQkJGjdunLZs2eJJZoevZp00aZImTZrU6jzhcFg5OTmdXigAAICOOvV1Xu6PKUmVlZVNng+HwwqHw2fMf/z4cUWjUWVnZzd5Pjs7W7t27XJ34b7gyTlzGzZsUFZWloYNG6a77rpLn376aYvz1tXVqbKysskEAADQUW4fYv3yrU7y8vKUkZERm4qLi7v41f6d6/eZmzhxom644QYVFBRo3759+vd//3dNmjRJW7ZsUWJi4hnzFxcXa+HChW4vBgAAgGsOHjyoSCQSe9xcV06S+vXrp8TERJWVlTV5vqyszLOjlq4Xc7fcckvs3xdddJFGjBihoUOHasOGDbr22mvPmH/+/PmaO3du7HFlZaXy8vLcXqxmhSrt3DM58aSlGw46dnJ6HrISoxND7XyJysNX/Y+VHEl68bNvWsnZ8+BuKzlJ5w61kvOft9p5j3Y39LKSU3z3jVZyDkztZyXnH8e+bSXnV3u/bSVHkho+TbeS09jLsZKT1q/e84xotMHzjDZ18oKFNseUFIlEmhRzLUlJSdGoUaO0du1aTZ06VZLkOI7Wrl2r2bNnu7tsX/C8mhkyZIj69eunvXv3NlvMtXTMGQAAwI/mzp2r6dOna/To0brsssv02GOPqbq6WjNnzvQkz/Ni7pNPPtGnn36qAQMGeB0FAADimJcXQHTEzTffrGPHjunBBx9UaWmpLr74Yq1ateqMiyLc0uFirqqqSnv37o09Likp0bvvvqvMzExlZmZq4cKFmjZtmnJycrRv3z7dd999+trXvqYJEya4uuAAAADd1ezZsz07rPpVHS7m/vznP+vqq6+OPT59vtv06dO1dOlSvffee3r22WdVXl6u3NxcjR8/Xj/96U85lAoAALx1Fl+/1eqY3VyHi7mxY8fKtNJzfPPNN89qgQAAANB+di7nBAAA8NiX7wvn5pjdHcUcAAAIDh8cFnWbJ98AAQAAADvozAEAgECI18OsdOYAAAB8jM4cAAAIhji9NQmdOQAAAB+jMwcAAAIi9MXk9pjdG505AAAAH6MzBwAAgiFOz5mjmAMAAMEQp8Uch1kBAAB8LK47cznnHbOSU1OfbCUnKdGxktPvm9VWcnrVh63kTF/5r1ZyJMlJi1rJ+f7O9VZy9p88ZCXnyhd+aCXHCdv5L/i3l++0knO4NNFKzv/93f+xkpN0jp19jyRFLvjMSs6J6lQrOeVH0z3PcE7a+VvXKhM6Nbk9ZjdHZw4AAMDH4rozBwAAgsOYU5PbY3Z3dOYAAAB8jM4cAAAIBq5mBQAAgN/QmQMAAMEQp1ezUswBAIBACJlTk9tjdnccZgUAAPAxOnMAACAYuAACAAAAfkNnDgAABEOcXgBBZw4AAMDH6MwBAIBg4Jw5AAAA+A2dOQAAEAxx2pmjmAMAAMEQp8Uch1kBAAB8jM4cAAAIhji9NUlcF3NHDvexE1RtaTWnOFZiyiv6WsmJ9m+wknPb1Zut5EjSX08MsJLz2x9dYyWnto+d5v5P/v1lKzmHG3pbyXm1eIKVnJqLrMToumu3Wcl5+2i+lRxJOvq3TDtBSXaO4aX1O+l5RjSl1vMMNC+uizkAABAcIXNqcnvM7o5z5gAAAHyMzhwAAAgGrmYFAACA31DMAQAA+BiHWQEAQCCE5MEFEO4O5wk6cwAAAD5GZw4AAARDnN40mM4cAACAj9GZAwAAwcCtSQAAAOA3dOYAAEAw0JkDAACA39CZAwAAgRAyHtxnzgedOYo5AAAQDBxmBQAAgN/QmQMAAMEQp525+C7mahOtxIQcKzEy9XYarbbOHwgl2llxVdGwlRxJ+rAs20pOzsmolZya8+x8hpJDjVZy1h8bZiUnocHOh6ixl52cpAQ721tlTaqVHElKsLQ/jabYWXeJNvaniT6oegIqvos5AAAQGPF6AQTnzAEAAPgYxRwAAAgGE/Jm8sjHH3+sO+64QwUFBUpLS9PQoUO1YMEC1dfXd2gcDrMCAAB0gV27dslxHD311FP62te+pp07d2rWrFmqrq7WokWL2j0OxRwAAAgGn13NOnHiRE2cODH2eMiQIdq9e7eWLl1KMQcAAOCmysrKJo/D4bDCYffvhlBRUaHMzMwO/Q7nzAEAgEA4fTWr25Mk5eXlKSMjIzYVFxe7vvx79+7VE088oe9///sd+j2KOQAAEAzGo0nSwYMHVVFREZvmz5/f4mLMmzdPoVCo1WnXrl1NfufQoUOaOHGibrzxRs2aNatDL5vDrAAAAG2IRCKKRCLtmvfee+/VjBkzWp1nyJAhsX8fPnxYV199tS6//HL9+te/7vCyUcwBAIBg8OCmwZ25AKJ///7q379/u+Y9dOiQrr76ao0aNUrLli1TQkLHD5pSzAEAAHSBQ4cOaezYscrPz9eiRYt07Nix2M9ycnLaPQ7FHAAACAaf3Zpk9erV2rt3r/bu3auBAwc2jTXtD+YCCAAAgC4wY8YMGWOanTqCzhwAAAgGn3Xm3EJnDgAAwMfozAEAgEAIeXA1q+tXx3qAzhwAAICPxXVnLimz1kpOKGQlRklJUSs5jY2JVnKSLf136Hf7zreSI0mhBDuv6fCseis5kp2cH+2YaiWn/mSylRxNbLQSE8mstpLz+/3DreTU11r8k5Vt5+9DOMXOfjsa9b53E41a+mOHM8R1MQcAAAKECyAAAADgN3TmAABAIHABBAAAAHyHzhwAAAgOH3TS3EZnDgAAwMfozAEAgGCI06tZKeYAAEAgcAEEAAAAfIfOHAAACIY4PcxKZw4AAMDH6MwBAIBA4Jw5AAAA+E6Hi7lNmzZp8uTJys3NVSgU0ooVK5r83BijBx98UAMGDFBaWprGjRunPXv2uLW8AAAAzTMeTd1ch4u56upqjRw5UkuWLGn254888ogef/xxPfnkk3r77bfVs2dPTZgwQbW1tWe9sAAAAGiqw+fMTZo0SZMmTWr2Z8YYPfbYY/rxj3+sKVOmSJKee+45ZWdna8WKFbrlllvObmkBAABawtWsZ6+kpESlpaUaN25c7LmMjAwVFhZqy5Ytzf5OXV2dKisrm0wAAAAddfoCCLen7s7VYq60tFSSlJ2d3eT57Ozs2M++qri4WBkZGbEpLy/PzUUCAAAItC6/Ncn8+fM1d+7c2OPKykprBV2PtHo7OSkNVnISExwrOTk9T1jJKa1Ot5JTtiPHSo5NC/7Py1ZyBicft5Iz89V/tZLT62jISs53b3/LSk5ZnZ3P0Po/XWAlR0n2WiRp/Wvs5ITt/H2oOhn2PMMxdj4/reIw69nLyTn1R7GsrKzJ82VlZbGffVU4HFYkEmkyAQAAoH1cLeYKCgqUk5OjtWvXxp6rrKzU22+/rTFjxrgZBQAA0FSc3pqkw4dZq6qqtHfv3tjjkpISvfvuu8rMzNSgQYM0Z84c/exnP9O5556rgoICPfDAA8rNzdXUqVPdXG4AAACoE8Xcn//8Z1199dWxx6fPd5s+fbqWL1+u++67T9XV1fre976n8vJyXXnllVq1apVSU1PdW2oAAICviNev8+pwMTd27FgZ0/IrC4VC+slPfqKf/OQnZ7VgAAAAaFuXX80KAADgiji9mpViDgAABEK8HmZ19WpWAAAA2EVnDgAABEOcHmalMwcAAOBjdOYAAEAw0JkDAACA39CZAwAAgRD6YnJ7zO6OzhwAAICP0ZkDAADBEKfnzFHMAQCAQOCmwQAAAPCduO7MhSyV2ycbgrWay5NSreRU1aVYybHZQo/2cKzkHG+MWMn54ORAKzkJdXZOQa7tZyVGjrHzej74dICVnMSTdvoC0ax6KzmSlJwUtZJTU2tnP1df7X2Oc9LO/q1VcXqYlc4cAACAjwWrZQQAAOKbDzppbqMzBwAA4GN05gAAQCBwNSsAAAB8h84cAAAIhji9mpViDgAABAKHWQEAAOA7dOYAAEAwxOlhVjpzAAAAPkZnDgAABALnzAEAAKBL1NXV6eKLL1YoFNK7777bod+lmAMAAMFgPJosuO+++5Sbm9up36WYAwAA6EK/+93v9Pvf/16LFi3q1O9zzhwAAAgGD69mraysbPJ0OBxWOBw+6+HLyso0a9YsrVixQj169OjUGHTmAABAIJy+AMLtSZLy8vKUkZERm4qLi896eY0xmjFjhu68806NHj260+PQmQMAAGjDwYMHFYlEYo9b68rNmzdPP//5z1sd78MPP9Tvf/97nThxQvPnzz+rZaOYAwAAweDhYdZIJNKkmGvNvffeqxkzZrQ6z5AhQ7Ru3Tpt2bLljMJw9OjRuu222/Tss8+2Ky+ui7mGxkQrOWnhBis5jVE7R81LK9u3MZ+tkzUpVnKcnHorOZKU0tNO1rrjw6zkHKvpZSWnobdjJcck27ls7a2jQ6zk1Eft7OOi/ezs40y9vTODqmvO/lyo9uiRZmefEEqv9Twjmuh9hl/0799f/fv3b3O+xx9/XD/72c9ijw8fPqwJEybo5ZdfVmFhYbvz4rqYAwAAwREyRiHj7n/K3B7vywYNGtTkca9ep/6DPHToUA0cOLDd43ABBAAAgI/RmQMAAMHg4TlzNgwePFimE51AOnMAAAA+RmcOAAAEwpfvC+fmmN0dnTkAAAAfozMHAACCwefnzHUWxRwAAAgEDrMCAADAd+jMAQCAYIjTw6x05gAAAHyMzhwAAAgEzpkDAACA79CZAwAAwcA5cwAAAPAbOnMAACAw/HCOm9so5gAAQDAYc2pye8xuLq6LucbGRCs5lQ12VrPjhKzkRGuDtdlk9j9hLSsSrrWS895HeVZyksrtbAvhgiorOTkZlVZyPj6QZSXHVosiHKmzkmMs7eMkKWrp78PJ2mQrOQmJ3m8LUYczt7pKsP4qAwCAuMWtSQAAAOA7dOYAAEAwcGsSAAAA+A2dOQAAEAgh59Tk9pjdHZ05AAAAH6MzBwAAgiFOz5mjmAMAAIHArUkAAADgO3TmAABAMMTp13nRmQMAAPAxOnMAACAQOGcOAAAAvkNnDgAABEOc3pqEzhwAAICP0ZkDAACBEK/nzFHMAQCAYODWJAAAAPCb+O7MhSzlWCrqU1IareREEx0rOY5j5w36/POeVnIkqTI51UpOz741VnKifez8f7C+1s6u6uOq/lZyEsJ2PqvhtAYrOY2NiVZyog3B6z+ELL0kY2N/ammf3Zp4PcwavE8GAABAHInvzhwAAAgObk0CAAAAv6EzBwAAAoFz5gAAAOA7dOYAAEAwOObU5PaY3RzFHAAACAYugAAAAIDf0JkDAACBEJIHF0C4O5wn6MwBAAD4GJ05AAAQDMacmtwes5ujMwcAAOBjdOYAAEAgcNNglzz00EMKhUJNpuHDh7sdAwAAAHnUmbvgggu0Zs2av4ck0QAEAAAei9P7zHlSZSUlJSknJ8eLoQEAAJoVMkYhly9YcHs8L3hyAcSePXuUm5urIUOG6LbbbtOBAwdanLeurk6VlZVNJgAAALSP6525wsJCLV++XMOGDdORI0e0cOFCfetb39LOnTuVnp5+xvzFxcVauHCh24vRLkmJUSs5JsHOLQfDKY1WcnqF66zkfF7dw0pOdXnYSo4kRXvayRmV/7GVnPL6NCs57+/Ns5KjJMdKzKDsz6zkHP48w0pOQ62dU2nSetnZ90hSyNJZ73W1KVZyHAubttPQDW6Q4XwxuT1mN+f6mp80aZJuvPFGjRgxQhMmTNBvf/tblZeX65VXXml2/vnz56uioiI2HTx40O1FAgAACCzPy+jevXvrvPPO0969e5v9eTgcViQSaTIBAAB01Olz5tyevPbGG2+osLBQaWlp6tOnj6ZOndqh3/e8mKuqqtK+ffs0YMAAr6MAAAB85X/+5390++23a+bMmfrLX/6it956S//wD//QoTFcP9Hhhz/8oSZPnqz8/HwdPnxYCxYsUGJiom699Va3owAAAP7OZ7cmaWxs1D333KNHH31Ud9xxR+z5888/v0PjuN6Z++STT3Trrbdq2LBhuummm9S3b19t3bpV/fv3dzsKAADAt7Zv365Dhw4pISFB3/jGNzRgwABNmjRJO3fu7NA4rnfmXnrpJbeHBAAAaJsxpya3x5TOuHVaOBxWOHx2d0P429/+JunUt2ctXrxYgwcP1i9+8QuNHTtWH330kTIzM9s1Tje4jhgAAODsnf5uVrcnScrLy1NGRkZsKi4ubnE55s2bd8ZXm3512rVrl5wv7hnzox/9SNOmTdOoUaO0bNkyhUIhvfrqq+1+3XzPFgAAQBsOHjzY5I4brXXl7r33Xs2YMaPV8YYMGaIjR45IanqOXDgc1pAhQ1r9woWvopgDAADB4OFh1o7cPq1///7tulZg1KhRCofD2r17t6688kpJUkNDgz7++GPl5+e3exEp5gAAALpAJBLRnXfeqQULFigvL0/5+fl69NFHJUk33nhju8ehmAMAAIEQck5Nbo/ppUcffVRJSUm6/fbbdfLkSRUWFmrdunXq06dPu8egmAMAAOgiycnJWrRokRYtWtTpMSjmAABAMHh4zlx3xq1JAAAAfIzOHAAACAaffZ2XWyjmAABAIISMUcjlw6Juj+cFDrMCAAD4GJ05AAAQDHF6AURcF3O1+9t3J+ezlVBvJUb1lvqsjWUhKznVBVErOY+Of9FKjiQ9d/hyKznHrrOzMdRdMtBKzrpnfmkl58WKUVZy/nDTSCs55vZeVnIWTmv/d0iejZ9/MN5KjiQ1fJhhJSfa285+rvegCs8zosl1nmegeXFdzAEAgAAxkty+yW/3b8xxzhwAAICf0ZkDAACBwNWsAAAA8B06cwAAIBiMPLia1d3hvEBnDgAAwMfozAEAgGDgPnMAAAA+5khy+1aobt/qxAMcZgUAAPAxOnMAACAQuDUJAAAAfIfOHAAACIY4vQCCzhwAAICP0ZkDAADBQGcOAAAAfkNnDgAABEOcduYo5gAAQDDE6U2D47qYczIa7OS4vWG1ICnNzuup6p9sJSchKWol5xd7x1vJkaTPqnrYCZrby0pM/Tn1VnIWHv6OlZwtBwZbyUmaauf9CZ1bZSXn959dYCWn9mSKlRxJcjLs7H9C6Xb22wkh77tLxkIGmhfXxRwAAAgObhoMAAAA36EzBwAAgiFOL4CgMwcAAOBjdOYAAEAwOEZy+0IMh84cAAAAPERnDgAABEOcnjNHMQcAAALCg2JO3b+Y4zArAACAj9GZAwAAwRCnh1npzAEAAPgYnTkAABAMjpHr57hxaxIAAAB4ic4cAAAIBuOcmtwes5ujMwcAAOBjdOYAAEAwxOnVrBRzAAAgGLgAAgAAAH4T1525nn1OdvUiuCohZOd/DzUmZCXHOHZyPq3saSVHkvpGqq3kOJfY2baPHotYydn47nArOYmRBis5SZdWWMlJS4payfnj3iFWckzUzj5BksI5NXZykhut5FTXpnieEa3tBhcKxOlhVjpzAAAAPhbXnTkAABAgRh505twdzgt05gAAAHyMzhwAAAgGzpkDAACA39CZAwAAweA4kly+qtbpBlfptoFiDgAABAOHWQEAAOA3dOYAAEAw0JkDAACA31DMAQCAYHCMN5OHPvroI02ZMkX9+vVTJBLRlVdeqfXr13doDIo5AACALvLd735XjY2NWrdunbZt26aRI0fqu9/9rkpLS9s9BsUcAAAIBGMcTyavHD9+XHv27NG8efM0YsQInXvuuXr44YdVU1OjnTt3tnscijkAAIA2VFZWNpnq6urOesy+fftq2LBheu6551RdXa3GxkY99dRTysrK0qhRo9o9DsUcAAAIBuPB+XJfXM2al5enjIyM2FRcXHzWixsKhbRmzRrt2LFD6enpSk1N1eLFi7Vq1Sr16dOn3eNQzAEAgGA4fWsStydJBw8eVEVFRWyaP39+i4sxb948hUKhVqddu3bJGKOioiJlZWXpD3/4g9555x1NnTpVkydP1pEjR9r9srnPHAAAQBsikYgikUi75r333ns1Y8aMVucZMmSI1q1bp9dff12ff/55bOxf/epXWr16tZ599lnNmzevXXlxXcyd37/MSk5KYqOVnPK6NCs5eed8biWnpKqvlZyP3suzkiNJRxvtNMM/HPtfVnL+34lzrOT88ukbrORUDw5Zyfnt5Ces5PzT7n+0klO7PdNKTnR4tZUcSRqR0/6uyNk4UpNuJeeTcu/fI+dkN/gOU8eRQi4vRycugOjfv7/69+/f5nw1NTWSpISEpn8bEhIS5HTgO2E5zAoAANAFxowZoz59+mj69On6y1/+oo8++kj/9m//ppKSEl133XXtHodiDgAABIOH58x5oV+/flq1apWqqqp0zTXXaPTo0dq8ebNWrlypkSNHtnucuD7MCgAA0JVGjx6tN99886zGoJgDAACBYBxHxuVz5ry8abBbOMwKAADgY3TmAABAMBgjyeVz3Dw8Z84tFHMAACAYHCOF4q+Y4zArAACAj9GZAwAAwWCMJLdvGkxnDgAAAB6iMwcAAALBOEbG5XPmDJ05AAAAeInOHAAACAbjyP1z5uL4psFLlizR4MGDlZqaqsLCQr3zzjteRQEAAMQtT4q5l19+WXPnztWCBQu0fft2jRw5UhMmTNDRo0e9iAMAADh1zpwHU3fnSTG3ePFizZo1SzNnztT555+vJ598Uj169NAzzzzjRRwAAMCpQ6JeTN2c6+fM1dfXa9u2bZo/f37suYSEBI0bN05btmw5Y/66ujrV1dXFHldUVEiSnJN1Z8zrtobqes8zJCmU2Gglp6Eu0UpOvbGz3hqrvd8GJMk5WWslR5JCNXZeU+UJOzufk1V2tu1onZ33yDkZtZJzwtL7Y+szFK219P7U2Pus2vr70Ghpn2BjP3f673ZXXv3ZqAbXv82rUQ3uDugB14u548ePKxqNKjs7u8nz2dnZ2rVr1xnzFxcXa+HChWc8X/K9xW4v2hn2eZ4AdI0sa0n7LeVstZRjx4h7bSU9YSsocEq6egF87MSJE8rIyLCamZKSopycHG0u/a0n4+fk5CglJcWTsd3Q5Vezzp8/X3Pnzo09Li8vV35+vg4cOGB9Y+hOKisrlZeXp4MHDyoSiXT14nQJ1gHrQGIdnMZ6YB1I3XsdGGN04sQJ5ebmWs9OTU1VSUmJ6uu96aimpKQoNTXVk7Hd4Hox169fPyUmJqqsrKzJ82VlZcrJyTlj/nA4rHA4fMbzGRkZ3W5D7QqRSCTu1wPrgHUgsQ5OYz2wDqTuuw66sgmTmprarQsuL7l+AURKSopGjRqltWvXxp5zHEdr167VmDFj3I4DAACIa54cZp07d66mT5+u0aNH67LLLtNjjz2m6upqzZw504s4AACAuOVJMXfzzTfr2LFjevDBB1VaWqqLL75Yq1atOuOiiOaEw2EtWLCg2UOv8YT1wDqQWAcS6+A01gPrQGIdoHkh44dvkAUAAECzPPs6LwAAAHiPYg4AAMDHKOYAAAB8jGIOAADAx7qkmFuyZIkGDx6s1NRUFRYW6p133ml1/ldffVXDhw9XamqqLrroIv32t958XYctxcXFuvTSS5Wenq6srCxNnTpVu3fvbvV3li9frlAo1GTy880RH3rooTNez/Dhw1v9naBtB4MHDz5jHYRCIRUVFTU7f1C2gU2bNmny5MnKzc1VKBTSihUrmvzcGKMHH3xQAwYMUFpamsaNG6c9e/a0OW5H9ytdqbV10NDQoPvvv18XXXSRevbsqdzcXP3TP/2TDh8+3OqYnflMdaW2toMZM2ac8XomTpzY5rhB2Q4kNbt/CIVCevTRR1sc02/bAdxhvZh7+eWXNXfuXC1YsEDbt2/XyJEjNWHCBB09erTZ+f/4xz/q1ltv1R133KEdO3Zo6tSpmjp1qnbu3Gl5yd2zceNGFRUVaevWrVq9erUaGho0fvx4VVdXt/p7kUhER44ciU3799v6XkxvXHDBBU1ez+bNm1ucN4jbwZ/+9Kcmr3/16tWSpBtvvLHF3wnCNlBdXa2RI0dqyZIlzf78kUce0eOPP64nn3xSb7/9tnr27KkJEyaotpUvc+/ofqWrtbYOampqtH37dj3wwAPavn27fvOb32j37t26/vrr2xy3I5+prtbWdiBJEydObPJ6XnzxxVbHDNJ2IKnJaz9y5IieeeYZhUIhTZs2rdVx/bQdwCXGsssuu8wUFRXFHkejUZObm2uKi4ubnf+mm24y1113XZPnCgsLzfe//31Pl9Omo0ePGklm48aNLc6zbNkyk5GRYW+hPLZgwQIzcuTIds8fD9vBPffcY4YOHWocx2n250HbBowxRpJ57bXXYo8dxzE5OTnm0UcfjT1XXl5uwuGwefHFF1scp6P7le7kq+ugOe+8846RZPbv39/iPB39THUnza2D6dOnmylTpnRonKBvB1OmTDHXXHNNq/P4eTtA51ntzNXX12vbtm0aN25c7LmEhASNGzdOW7ZsafZ3tmzZ0mR+SZowYUKL8/tRRUWFJCkzM7PV+aqqqpSfn6+8vDxNmTJFH3zwgY3F88yePXuUm5urIUOG6LbbbtOBAwdanDfo20F9fb2ef/55/fM//7NCoVCL8wVtG/iqkpISlZaWNnmvMzIyVFhY2OJ73Zn9it9UVFQoFAqpd+/erc7Xkc+UH2zYsEFZWVkaNmyY7rrrLn366actzhv07aCsrExvvPGG7rjjjjbnDdp2gLZZLeaOHz+uaDR6xjdBZGdnq7S0tNnfKS0t7dD8fuM4jubMmaMrrrhCF154YYvzDRs2TM8884xWrlyp559/Xo7j6PLLL9cnn3xicWndU1hYqOXLl2vVqlVaunSpSkpK9K1vfUsnTpxodv6gbwcrVqxQeXm5ZsyY0eI8QdsGmnP6/ezIe92Z/Yqf1NbW6v7779ett97a6herd/Qz1d1NnDhRzz33nNauXauf//zn2rhxoyZNmqRoNNrs/EHfDp599lmlp6frhhtuaHW+oG0HaB9Pvs4L7VdUVKSdO3e2eU7DmDFjNGbMmNjjyy+/XF//+tf11FNP6ac//anXi+m6SZMmxf49YsQIFRYWKj8/X6+88kq7/ucZNE8//bQmTZqk3NzcFucJ2jaAtjU0NOimm26SMUZLly5tdd6gfaZuueWW2L8vuugijRgxQkOHDtWGDRt07bXXduGSdY1nnnlGt912W5sXPQVtO0D7WO3M9evXT4mJiSorK2vyfFlZmXJycpr9nZycnA7N7yezZ8/W66+/rvXr12vgwIEd+t3k5GR94xvf0N69ez1aOrt69+6t8847r8XXE+TtYP/+/VqzZo3+5V/+pUO/F7RtQFLs/ezIe92Z/YofnC7k9u/fr9WrV7falWtOW58pvxkyZIj69evX4usJ6nYgSX/4wx+0e/fuDu8jpOBtB2ie1WIuJSVFo0aN0tq1a2PPOY6jtWvXNuk4fNmYMWOazC9Jq1evbnF+PzDGaPbs2Xrttde0bt06FRQUdHiMaDSq999/XwMGDPBgCe2rqqrSvn37Wnw9QdwOTlu2bJmysrJ03XXXdej3grYNSFJBQYFycnKavNeVlZV6++23W3yvO7Nf6e5OF3J79uzRmjVr1Ldv3w6P0dZnym8++eQTffrppy2+niBuB6c9/fTTGjVqlEaOHNnh3w3adoAW2L7i4qWXXjLhcNgsX77c/PWvfzXf+973TO/evU1paakxxpjbb7/dzJs3Lzb/W2+9ZZKSksyiRYvMhx9+aBYsWGCSk5PN+++/b3vRXXPXXXeZjIwMs2HDBnPkyJHYVFNTE5vnq+th4cKF5s033zT79u0z27ZtM7fccotJTU01H3zwQVe8hLN27733mg0bNpiSkhLz1ltvmXHjxpl+/fqZo0ePGmPiYzsw5tTVdoMGDTL333//GT8L6jZw4sQJs2PHDrNjxw4jySxevNjs2LEjdqXmww8/bHr37m1Wrlxp3nvvPTNlyhRTUFBgTp48GRvjmmuuMU888UTscVv7le6mtXVQX19vrr/+ejNw4EDz7rvvNtlH1NXVxcb46jpo6zPV3bS2Dk6cOGF++MMfmi1btpiSkhKzZs0ac8kll5hzzz3X1NbWxsYI8nZwWkVFhenRo4dZunRps2P4fTuAO6wXc8YY88QTT5hBgwaZlJQUc9lll5mtW7fGfvbtb3/bTJ8+vcn8r7zyijnvvPNMSkqKueCCC8wbb7xheYndJanZadmyZbF5vroe5syZE1tn2dnZ5jvf+Y7Zvn27/YV3yc0332wGDBhgUlJSzDnnnGNuvvlms3fv3tjP42E7MMaYN99800gyu3fvPuNnQd0G1q9f3+z2f/q1Oo5jHnjgAZOdnW3C4bC59tprz1g/+fn5ZsGCBU2ea22/0t20tg5KSkpa3EesX78+NsZX10Fbn6nuprV1UFNTY8aPH2/69+9vkpOTTX5+vpk1a9YZRVmQt4PTnnrqKZOWlmbKy8ubHcPv2wHcETLGGE9bfwAAAPAM380KAADgYxRzAAAAPkYxBwAA4GMUcwAAAD5GMQcAAOBjFHMAAAA+RjEHAADgYxRzAAAAPkYxBwAA4GMUcwAAAD5GMQcAAOBjFHMAAAA+9v8BU9Iozt7nyPgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dmdc.dmd_time[\"dt\"] = 0.5\n",
    "new_u = np.random.rand(s[\"u\"].shape[0], dmdc.dynamics.shape[1] - 1)\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.pcolor(dmdc.reconstructed_data(new_u).real)\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Recovering unstable dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this subsection of the `DMDc` tutorial we are going to investigate the stabilizing effect of control in an unstable linear system. For simplicity we consider a 3D system with a known `B` operator. This tutorial is inspired by `Example 1` in the paper [Dynamic mode decomposition with control](https://arxiv.org/abs/1409.6358)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_instants = 5\n",
    "\n",
    "A = np.array([[2.1, 0, 0], [0, 0.5, 0], [0, 0, 6.9]])\n",
    "B = np.array([1.3, 0, 3])[:, None] * 2\n",
    "\n",
    "snapshots = np.zeros((3, time_instants))\n",
    "snapshots[:, 0] = np.array([5, 6, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We construct our snapshots matrix using the usual formula: $\\mathbf{x}_{k+1} = \\mathbf{A}\\mathbf{x}_k + \\mathbf{B}\\mathbf{u}_k$, where `A`,`B` are specified above, and $\\mathbf{u}_k = -\\mathbf{x}_k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5.     -2.5     1.25   -0.625   0.3125]\n",
      " [ 6.      3.      1.5     0.75    0.375 ]\n",
      " [ 3.      2.7     2.43    2.187   1.9683]]\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, time_instants):\n",
    "    previous_snapshot = snapshots[:, i - 1][:, None]\n",
    "    snapshots[:, i] = (\n",
    "        A.dot(previous_snapshot) - B * previous_snapshot\n",
    "    ).flatten()\n",
    "print(snapshots)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We construct the control input matrix used in the formula, in order to feed it to the `DMDc` constructor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-5.     2.5   -1.25   0.625]\n",
      " [-6.    -3.    -1.5   -0.75 ]\n",
      " [-3.    -2.7   -2.43  -2.187]]\n"
     ]
    }
   ],
   "source": [
    "I = -snapshots[:, :-1]\n",
    "print(I)\n",
    "\n",
    "dmdc = DMDc(svd_rank=-1).fit(snapshots, I, np.diag(B.flatten()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now pause `DMDc` for one moment, and analyze the system resulting from the set of snapshots, as if we did not know that it is a control system. Therefore we use the standard DMD algorithm, and then plot the eigenvalues to assess the stability of its dynamics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/francescoandreuzzi/code/units/PyDMD/pydmd/plotter.py:185: UserWarning: Legend does not support handles for list instances.\n",
      "A proxy artist may be used instead.\n",
      "See: https://matplotlib.org/stable/tutorials/intermediate/legend_guide.html#controlling-the-legend-entries\n",
      "  plt.legend(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pydmd import DMD\n",
    "\n",
    "dmd = DMD(svd_rank=-1)\n",
    "dmd.fit(snapshots)\n",
    "plot_eigs(\n",
    "    dmd,\n",
    "    show_axes=True,\n",
    "    show_unit_circle=True,\n",
    "    figsize=(5, 5),\n",
    "    filename=\"eigs_ex1.pdf\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see the eigenvalues are all inside the unit sphere, therefore the corresponding dynamics are all stable. \n",
    "\n",
    "By contrast, if we use DMD with control we see that there are some unstable dynamics in the \"real\" `A` operator, which we lose when we use the original algorithm, but are recovered if we employ the modified one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/francescoandreuzzi/code/units/PyDMD/pydmd/plotter.py:185: UserWarning: Legend does not support handles for list instances.\n",
      "A proxy artist may be used instead.\n",
      "See: https://matplotlib.org/stable/tutorials/intermediate/legend_guide.html#controlling-the-legend-entries\n",
      "  plt.legend(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalue 6.900000000000041: distance from unit circle 5.900000000000041\n",
      "Eigenvalue 0.49999999999999917: distance from unit circle 0.5000000000000009\n",
      "Eigenvalue 2.0999999999999948: distance from unit circle 1.0999999999999948\n"
     ]
    }
   ],
   "source": [
    "plot_eigs(dmdc, show_axes=True, show_unit_circle=True, figsize=(5, 5))\n",
    "\n",
    "for eig in dmdc.eigs:\n",
    "    print(\n",
    "        \"Eigenvalue {}: distance from unit circle {}\".format(\n",
    "            eig, np.abs(1 - np.linalg.norm(eig))\n",
    "        )\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We seek a confirmation about this fact by computing the eigenvalues of the operator `A` which we used when we constructed the system, and we compare them with the eigenvalues of `dmd.atilde` which holds the approximation of `A` built by DMD with control."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues of A: [2.1 0.5 6.9] ; eigenvalues of A_tilde:  [6.9 0.5 2.1]\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    \"Eigenvalues of A:\",\n",
    "    np.linalg.eigvals(A),\n",
    "    \"; eigenvalues of A_tilde: \",\n",
    "    np.linalg.eigvals(dmdc.operator.as_numpy_array),\n",
    ")"
   ]
  }
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