Imputation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "355a3d74",
   "metadata": {},
   "source": [
    "# \"Imputation\"\n",
    "\n",
    "Goal is as follows:\n",
    "\n",
    "Moving to irregular grid\n",
    "For each initial condition (and from REAL SOLUTION)\n",
    " - arbitrary # of time points (big enough)\n",
    " - arbitrary spacing between them\n",
    " - sample section @ those time points\n",
    "     - https://stackoverflow.com/questions/6482889/get-random-sample-from-list-while-maintaining-ordering-of-items\n",
    " - fit a polynomial (cubic spline)\n",
    " - sample from the fit on a regular grid\n",
    " - Run SINDy on regular grid fit\n",
    " - test the solution MSE (SINDy - real)\n",
    " - MSE (polynomial values - real) as an extra\n",
    " \n",
    " ### 7/13\n",
    "    Have sampled 75% of tvals at random spacing while preserving order in ONE trajectory using stackoverflow code. Need to apply to multiple trajectories. Same # of time points and spacing for all trajectories or no? \n",
    "\n",
    "    Maybe just wrap the code into a for loop of n_of_ic and conglomerate? But then need to resolve difference in length. That's what the polynomial is for? Build poly from sampled points and then use it to \"put back\" points onto our structure?\n",
    "    \n",
    "    NEXT STEP, look into fitting poly w/ cubic spline\n",
    "\n",
    " ### 7/14\n",
    "    Had worries that I'd have trouble getting points outside of our sample time range (i.e. sampled points start at `t=2` and we want to guess t=0 but spline only accounts for max(t)>t>2. Calling the constructed cubicspline method on something slightly outside seems to work though.\n",
    "    End of the day, I also implemented it for multiple trajectories and had it in a 'stack' structure similar to the true data set so that `model.fit()` could operate on it.\n",
    "    \n",
    " ### 7/15\n",
    "     Made SINDy model from cubicspline imputed set. Came out with higher error than the cubicspline... Also found that Radau method of integration takes much longer than LSODA and BDF methods. SINDy error increases more when timestep # is decreased. With `n_of_t=5000`, error is low but still larger than cubic spline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "17576b59",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import pysindy as ps\n",
    "#import colorednoise as cn\n",
    "import random\n",
    "from scipy.interpolate import CubicSpline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "2e97e531",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "list indices must be integers or slices, not tuple",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Input \u001b[1;32mIn [23]\u001b[0m, in \u001b[0;36m<cell line: 13>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     11\u001b[0m rng \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mdefault_rng()\n\u001b[0;32m     12\u001b[0m rng\u001b[38;5;241m.\u001b[39mintegers(low\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mint\u001b[39m(\u001b[38;5;241m0.25\u001b[39m \u001b[38;5;241m*\u001b[39m n_of_t), high\u001b[38;5;241m=\u001b[39mn_of_t)\n\u001b[1;32m---> 13\u001b[0m \u001b[43mnetswitch_train_multi\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m:\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\n",
      "\u001b[1;31mTypeError\u001b[0m: list indices must be integers or slices, not tuple"
     ]
    }
   ],
   "source": [
    "# test cell\n",
    "len(netswitch_train_multi[0][:, 0])\n",
    "sample_size\n",
    "range(len(first_traj[:, 0]))\n",
    "mylist = [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ,9  , 10 ]\n",
    "indices = random.sample(range(len(mylist)), 3)\n",
    "[mylist[i] for i in sorted(indices)]\n",
    "\n",
    "[first_traj[i, :] for i in sorted(random.sample(range(len(first_traj[:, 0])), 3000)) ]\n",
    "(np.random.randint(int(0.5 * n_of_t), n_of_t + 1))\n",
    "rng = np.random.default_rng()\n",
    "rng.integers(low=int(0.25 * n_of_t), high=n_of_t)\n",
    "# error in line below because netswitch_train_multi is a list so I have to access it like [i][:, 0]\n",
    "#etswitch_train_multi[1, :, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e9219973",
   "metadata": {},
   "outputs": [],
   "source": [
    "# contains functions + basic parameters\n",
    "a_u, a_v = 2, 1\n",
    "beta, gamma = 2, 2\n",
    "dudt = lambda u, v: -u + (a_u / (1+v**beta))\n",
    "dvdt = lambda u, v: -v + (a_v / (1+u**gamma))\n",
    "sigma = 0.01\n",
    "sigma_list = np.linspace(0.001, 0.8, 10)\n",
    "netswitch = lambda t, x: np.array([dudt(x[0], x[1]), dvdt(x[0], x[1])])\n",
    "# 0-5 minus some value between 0-1, no negatives for IC?\n",
    "n_of_ic = 1000\n",
    "u_ic = np.random.random(size=n_of_ic) * 5 - np.random.random(size=n_of_ic)\n",
    "v_ic = np.random.random(size=n_of_ic) * 5 - np.random.random(size=n_of_ic)\n",
    "\n",
    "def plot_data_and_derivative(x, dt, deriv):\n",
    "    feature_name = [\"u\", \"v\"]\n",
    "    plt.figure(figsize=(20, 5))\n",
    "    for i in range(2):\n",
    "        plt.subplot(1, 2, i + 1)\n",
    "        plt.plot(x[:, i], label=feature_name[i])\n",
    "        plt.grid(True)\n",
    "        plt.xlabel(\"t\", fontsize=24)\n",
    "        plt.xticks(fontsize=18)\n",
    "        plt.yticks(fontsize=18)\n",
    "        plt.legend(fontsize=24)\n",
    "    x_dot = deriv(x, t=dt)\n",
    "    plt.figure(figsize=(20, 5))\n",
    "    for i in range(2):\n",
    "        plt.subplot(1, 2, i + 1)\n",
    "        plt.plot(x_dot[:, i], label=r\"$\\dot{\" + feature_name[i] + \"}$\")\n",
    "        plt.grid(True)\n",
    "        plt.xlabel(\"t\", fontsize=24)\n",
    "        plt.xticks(fontsize=18)\n",
    "        plt.yticks(fontsize=18)\n",
    "        plt.legend(fontsize=24)\n",
    "library_functions = [\n",
    "    lambda x: x,\n",
    "    lambda x: 1 / (1 + x**1),\n",
    "    lambda x: 1 / (1 + x**2),\n",
    "    lambda x: 1 / (1 + x**3),\n",
    "    lambda x: 1 / (1 + x**4),\n",
    "    lambda x: 1 / (1 + x**5)\n",
    "]\n",
    "library_function_names = [\n",
    "    lambda x: x,\n",
    "    lambda x: '1/(1 + ' + x + '^1)',\n",
    "    lambda x: '1/(1 + ' + x + '^2)',\n",
    "    lambda x: '1/(1 + ' + x + '^3)',\n",
    "    lambda x: '1/(1 + ' + x + '^4)',\n",
    "    lambda x: '1/(1 + ' + x + '^5)'\n",
    "]\n",
    "netswitch_library = ps.CustomLibrary(\n",
    "    library_functions=library_functions, function_names=library_function_names\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4cff477c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'rtol': 1e-12, 'method': 'LSODA', 'atol': 1e-12}\n",
      "0.0037493429521123778\n",
      "0.0016683899516911627\n"
     ]
    }
   ],
   "source": [
    "# creation of TRUE set\n",
    "T = 20\n",
    "dt = 0.01\n",
    "trange = np.array([0, T])\n",
    "#tvals = np.arange(0, T + dt, dt)\n",
    "n_of_t = 5000\n",
    "tvals = np.linspace(0, T, n_of_t)\n",
    "n_of_ic = 500\n",
    "feature_count = 2\n",
    "netswitch_x0s = (np.random.rand(n_of_ic, feature_count) * 5)\n",
    "sparse_regression_optimizer = ps.STLSQ(threshold=0.3)\n",
    "MSE_list = []\n",
    "netswitch_train_multi = []\n",
    "integrator_keywords = {}\n",
    "#integrator_keywords['full_output'] = True\n",
    "integrator_keywords['rtol'] = 1e-12\n",
    "integrator_keywords['method'] = 'LSODA'\n",
    "integrator_keywords['atol'] = 1e-12\n",
    "\n",
    "print(integrator_keywords)\n",
    "\n",
    "# actual creation\n",
    "for i in range(n_of_ic):     \n",
    "    netswitch_train_temp = solve_ivp(\n",
    "        netswitch, trange, netswitch_x0s[i], t_eval=tvals\n",
    "    ).y.T\n",
    "    netswitch_train_multi.append(netswitch_train_temp)\n",
    "print(min(netswitch_x0s[:,0]))\n",
    "print(min(netswitch_x0s[:,1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "8ec972a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5000,)\n",
      "(3, 2)\n",
      "[0.60000117 1.84123864 1.87817951]\n",
      "<scipy.interpolate._cubic.CubicSpline object at 0x000001E2F624A590>\n",
      "\n",
      "3\n",
      "3\n",
      "5000\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
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\n",
      "text/plain": [
       "<Figure size 1152x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "## one trajectory\n",
    "rng = np.random.default_rng()\n",
    "first_traj = netswitch_train_multi[0]\n",
    "\n",
    "\n",
    "sample_size = 3#rng.integers(low=int(0.25 * n_of_t), high=int(0.75 * n_of_t))\n",
    "\n",
    "indices = sorted(\n",
    "    random.sample(range(len(first_traj[:, 0])), int(sample_size)))\n",
    "sorted_sample = np.asarray([\n",
    "    first_traj[j, :] for j in indices\n",
    "])\n",
    "\n",
    "# fit to corresponding time values and not the indices\n",
    "cs_u = CubicSpline(tvals[indices[0:2]], sorted_sample[0:2, 0])\n",
    "cs_v = CubicSpline(tvals[indices], sorted_sample[:, 1])\n",
    "\n",
    " # for testing one trajectory\n",
    "\n",
    "fig, axs = plt.subplots()\n",
    "plt.figure(figsize=(16, 12))\n",
    "plt.plot(tvals, cs_u(tvals), \"v\", label=\"fitted u\")\n",
    "plt.plot(tvals, first_traj[:,0], 'k', label=\"true u\")\n",
    "plt.plot(tvals, cs_v(tvals), \"c+\", label=\"fitted v\")\n",
    "plt.plot(tvals, first_traj[:, 1], 'g', label=\"true v\")\n",
    "plt.plot(tvals[indices], sorted_sample[:, 0],\"mx\",label=\"sampled u\", markersize=15)\n",
    "plt.plot(tvals[indices], sorted_sample[:, 1], \"x\",label=\"sampled v\", markersize=15)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "print(tvals.shape)\n",
    "print(sorted_sample.shape)\n",
    "print(sorted_sample[0:3, 0])\n",
    "print(CubicSpline(tvals[indices[0:2]], sorted_sample[0:2, 0]))\n",
    "\n",
    "print()\n",
    "\n",
    "print(len(indices))\n",
    "print(len(sorted_sample[:,0]))\n",
    "print(len(tvals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "fbe3afbc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.33816411e+00 4.91530858e+00]\n",
      " [1.87185789e+00 1.11940009e+00]\n",
      " [2.01595499e+00 1.26571589e+00]\n",
      " [1.63979692e+00 2.81059623e+00]\n",
      " [6.89644648e-01 4.26969425e+00]\n",
      " [2.62116703e+00 4.95518327e+00]\n",
      " [8.56949213e-01 4.18861468e-01]\n",
      " [3.08374043e+00 3.42439751e+00]\n",
      " [3.52762846e+00 3.14782994e+00]\n",
      " [2.86091937e-01 4.70969330e+00]\n",
      " [1.09699942e+00 4.04372201e-01]\n",
      " [1.87848524e+00 8.82544727e-02]\n",
      " [7.20920296e-01 6.24549839e-01]\n",
      " [5.41418137e-02 3.95359756e+00]\n",
      " [4.23439399e-01 3.88751618e+00]\n",
      " [3.96181873e+00 1.58993866e+00]\n",
      " [3.33008165e+00 4.76364203e+00]\n",
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      " [1.01338936e+00 3.65142270e+00]\n",
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      " [3.39411441e+00 2.69153711e+00]\n",
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      " [6.16916370e-01 2.87789010e-01]\n",
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      " [1.91393186e+00 1.46535373e+00]\n",
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      " [4.19684490e+00 2.51711204e+00]\n",
      " [1.74148635e+00 5.21479820e-02]\n",
      " [3.47852377e-01 3.00926908e+00]\n",
      " [1.10834259e-02 3.33501069e+00]\n",
      " [1.16306542e+00 2.36971446e+00]\n",
      " [3.34798125e+00 2.48597053e+00]\n",
      " [3.50462852e+00 1.26386523e+00]\n",
      " [3.57512739e+00 1.28953198e+00]\n",
      " [4.94027717e+00 1.96371260e+00]\n",
      " [3.60447431e+00 4.54972833e+00]\n",
      " [3.22511544e-01 3.88363799e+00]\n",
      " [4.03582302e+00 5.73421362e-01]\n",
      " [1.51520984e+00 5.18570910e-01]\n",
      " [3.96503486e+00 1.06988832e-01]\n",
      " [4.99179798e+00 7.05228117e-02]\n",
      " [9.09939627e-01 3.96810930e+00]\n",
      " [2.71430485e+00 8.49521382e-01]\n",
      " [2.47858063e+00 4.84217820e+00]\n",
      " [5.95401276e-02 3.76873253e+00]\n",
      " [1.82330076e+00 2.64041492e+00]\n",
      " [3.81629698e+00 1.02175383e+00]\n",
      " [4.27537164e+00 1.70526567e+00]\n",
      " [4.91932963e+00 2.34909032e+00]\n",
      " [4.14458522e+00 3.92564987e+00]\n",
      " [3.42332431e+00 2.14498544e+00]\n",
      " [4.93071519e-01 1.65437325e+00]\n",
      " [1.20840704e+00 2.06442866e+00]\n",
      " [3.04310514e+00 4.26550581e+00]\n",
      " [2.97826673e-01 4.25093638e+00]\n",
      " [4.04444035e+00 4.56451053e-01]\n",
      " [1.25868581e+00 1.85337733e+00]\n",
      " [3.06665119e+00 3.85238349e+00]\n",
      " [3.22086944e+00 1.89188696e+00]\n",
      " [3.21729113e+00 6.73459746e-02]\n",
      " [2.70293934e+00 3.83799709e+00]\n",
      " [2.26630998e+00 4.72925239e+00]\n",
      " [4.11014538e+00 4.18752314e+00]\n",
      " [4.44168225e+00 2.38683501e+00]\n",
      " [4.07425824e+00 3.12675691e+00]\n",
      " [7.21547837e-01 3.27690201e+00]\n",
      " [4.68870030e+00 3.44645208e+00]\n",
      " [1.50442629e+00 2.25280883e+00]\n",
      " [2.84101129e+00 1.52418333e+00]\n",
      " [3.97585178e+00 3.20500564e+00]\n",
      " [2.17842593e+00 1.58637162e-01]\n",
      " [5.45785145e-01 6.39184903e-01]\n",
      " [9.73568794e-02 5.14376769e-01]\n",
      " [6.81452945e-01 4.27866672e+00]\n",
      " [4.30399560e-01 2.57378052e+00]\n",
      " [1.70512351e+00 3.74885737e+00]\n",
      " [2.61853840e+00 7.23383148e-01]\n",
      " [2.89661482e-01 4.93095341e-01]\n",
      " [5.80277296e-01 1.23011945e+00]\n",
      " [3.13490793e+00 1.35633020e+00]\n",
      " [3.53098541e+00 3.55403006e+00]\n",
      " [2.75231090e+00 4.35328307e+00]\n",
      " [1.15462743e+00 1.03361984e+00]\n",
      " [1.24096376e+00 1.98927779e-01]\n",
      " [4.50319656e+00 2.44519239e+00]\n",
      " [3.68139676e+00 2.11644290e+00]\n",
      " [2.92989966e+00 4.54804057e+00]\n",
      " [4.03285777e-01 2.13974878e+00]\n",
      " [2.75245772e-01 1.37644875e-01]\n",
      " [4.02720257e-01 4.39548443e+00]\n",
      " [9.54075064e-01 3.10279626e+00]\n",
      " [3.07804205e+00 2.92919108e-01]\n",
      " [3.49326638e+00 1.72516463e+00]\n",
      " [2.91756171e+00 4.56395191e+00]\n",
      " [1.56223463e+00 3.41154332e+00]\n",
      " [8.67605982e-01 4.75078652e-01]\n",
      " [3.90081919e-01 1.04968170e+00]\n",
      " [3.96748459e+00 1.57012300e+00]\n",
      " [4.98699682e+00 2.38720118e+00]]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(u)' = -0.400 u + 0.801 1/(1 + v^2)\n",
      "(v)' = -0.400 v + 0.400 1/(1 + u^2)\n",
      "65.49723679625914\n",
      "5.7911688715619324e-12\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x22809777b20>]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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p9lzT0FZypW3vdRckMtA4FfgEdn5LtQlmdCqIFrXU/lfOKr7pk2pdS9UL7FwGAys0roLuBd/1IXX2FbSKYX3ZrVu1aedoYj+vzIG9qXeTlHE2s9AEnSpEUEudndaximEtdX6O62bKEth5DAZW9T2IZBUmqKUOzo1Q8a+XSXaHSMWc1pd5OHNyfKSgUEEtdfDB44OTeGCbpB8H3MrOOpyZPoe0FS6opQ4+iBVvWUvJ919PCaVbJOtwpksDWeoqqM3sS5IulPS8u78zzhMmEdQdzW+lZS0pucUyM/X1mHZduyrxnxuFcEZVdBvU50l6WdJXsgxqqfNrxvFhq0krsKV0W9mEM6qo664PMxuUdFfWQS11Pv+VD9/r0uoSmZJEaBPOqLpCB7XU+XxYPoxvlPSg43Ttdo1kGs6MYSBwmQS1ma2WtFqSTjnllF976qmnOqu2iU4vaURYN5ZmYEvNp/llGs6MWaBACt+intLph5ypVc0lvXCmkaNfkb7whXkpP0uN9ZuWvbYsk+cCklSaoJa6aJHRuop00+bdum7DE8n9QG98+6hx6ea/Sza0CWeUQbezPr4maVjSQknPSfprd78l6jFpX4W8m6/PdIW01lW3SKvf+zO23/a5zkK7SucmRzUUcsFLK532WUvVuGBuUiJDe+bxtxbbWzy+VWgTziizUga1JG0+arN8rPP6aV3Ht+jKuzXpen32zcxQnqnL0H7zz03XfXEu4YzKKG1QS50viplC/2ZrM7uaLvurV47cIenQbvCYUJaxA2kpdVBLyVxOifMIv66dX36Jhnarx9blsZQdSFvpg3pKEnN0q9odksSx6zq0O1TEU7MCM1UmqKXkFlSUPbC77d9vpWloJxTOURYtnKeNa4fTfyIgQZUKaqn7fuvpyrJYJq8LukrS5R97JfVFNVHm9PdoxzUrc6wAaK1yQT0l6eXKRWplJ/nLqhPNjtXy6zdpz75XGm7LEoOTCE1lg1pKL7BCC+08rhV4hA5PepT2OUfiGj5tQLddvjTvMlBhlQ7qKakGWcZnZss9lOuS7hZK8/zZnaDVjSwR1NNkGXLdtLpDCeOZsvwmEUprezrCG2khqGdIYt51VYS0MjDE4JYIbySDoG6CwG4stP73ZkINbknqMWnPpwlwxEdQxxBqV0MWihLMrYQc3FNYnINmCOo25D2tLQtlCeZW3vrxezQ+mecM7vhM0o/pQqk0grpDeS4SSQqndD1SEVrdM7HSshoI6oR0cw7sLFSlpZyk0KYEtou+8PIgqFOUdVcJLeT0nXHVBh0a6+Cy9wEiyIuDoAa6lPg1JQPCAGcYCGogJUXs8+4UgZ4ughrIWJUCvBkWArWHoAYCceq6u0Mej85dlU9JS1ADBUArPBlFnc5IUAMFR4iHIc3uHIIaKDmCPEztBHtUUPclVhGA3MQJBMI8W7N6k7tAKEENVETc1h2B3r1Zvaadn1qV2M8jqAEcoZ2v62VaxZmkJENaoo8aQA7K3mrvpEXNYCKA0gk97NsNawYTAZROWlPlFl15t5I4jfmrE8k1gglqAJgmxLMN9uRdAAAgGkENAIEjqAEgcAQ1AASOoAaAwKUyj9rMRiU91eHDF0ral2A5SaGu9lBXe6irPWWs61fdfaDRhlSCuhtmNtJs0neeqKs91NUe6mpP1eqi6wMAAkdQA0DgQgzqm/MuoAnqag91tYe62lOpuoLrowYAHCnEFjUAYBqCGgACl1tQm9n5ZrbTzHaZ2boG22eZ2e317VvMbDCDmk42s/vN7Idm9riZfbjBPsNm9qKZPVz/sz7tuurPu9fMHq0/5xtO9m01n68fr+1mtiSDmk6bdhweNrMDZvaRGftkcrzM7Etm9ryZPTbtvvlmdp+ZPVn/+/gmj720vs+TZnZpBnV9zsyeqL9Od5jZcU0eG/map1DXJ83smWmvVcOTKbf67KZQ1+3TatprZg83eWyax6thNmT2HnP3zP9I6pW0W9IiSUdJekTS22fs8+eSbqrfvljS7RnUdaKkJfXbx0j6UYO6hiXdlcMx2ytpYcT2VZI2SDJJZ0vaksNr+jPVJu1nfrwknSdpiaTHpt33WUnr6rfXSfpMg8fNl7Sn/vfx9dvHp1zXCkl99dufaVRXnNc8hbo+KWltjNc58rObdF0ztv+tpPU5HK+G2ZDVeyyvFvVSSbvcfY+7vybp65IumrHPRZK+XL/9n5Leb2bJXda3AXd/1t231W+/JGmHpLek+ZwJukjSV7zm+5KOM7MTM3z+90va7e6drkjtirt/V9L+GXdPfw99WdLvNnjo70i6z933u/vPJd0n6fw063L3e919vP7P70s6Kann66aumOJ8dlOpq/75/0NJX0vq+eKKyIZM3mN5BfVbJP102r+f1hsD8Zf71N/UL0pakEl1kupdLe+VtKXB5l83s0fMbIOZvSOjklzSvWb2kJmtbrA9zjFN08Vq/gHK43hJ0gnu/mz99s8kndBgn7yP2wdV+ybUSKvXPA0fqnfJfKnJ1/g8j9dvSHrO3Z9ssj2T4zUjGzJ5jzGY2ICZHS3pG5I+4u4HZmzeptrX+3dL+kdJ/5VRWee6+xJJKyVdYWbnZfS8LZnZUZI+IOk/GmzO63gdwWvfQYOai2pmn5A0LumrTXbJ+jX/J0mLJb1H0rOqdTOE5I8U3ZpO/XhFZUOa77G8gvoZSSdP+/dJ9fsa7mNmfZKOlfRC2oWZWb9qL8RX3f2bM7e7+wF3f7l++x5J/Wa2MO263P2Z+t/PS7pDta+g08U5pmlZKWmbuz83c0Nex6vuuanun/rfzzfYJ5fjZmaXSbpQ0h/XP+BvEOM1T5S7P+fuE+4+KemfmzxfXserT9LvS7q92T5pH68m2ZDJeyyvoP6BpLeZ2an11tjFku6csc+dkqZGR/9A0sZmb+ik1PvAbpG0w91vaLLPm6f6ys1sqWrHMNVfIGY2z8yOmbqt2mDUYzN2u1PSJVZztqQXp30lS1vTlk4ex2ua6e+hSyV9q8E+35a0wsyOr3/VX1G/LzVmdr6kj0r6gLsfbLJPnNc86bqmj2n8XpPni/PZTcNvSXrC3Z9utDHt4xWRDdm8x9IYIY05irpKtZHT3ZI+Ub/vatXevJI0W7Wv0rskbZW0KIOazlXtq8t2SQ/X/6yStEbSmvo+H5L0uGqj3d+X9L4M6lpUf75H6s89dbym12WSbqwfz0clDWX0Os5TLXiPnXZf5sdLtV8Uz0oaU60P8M9UG9P4H0lPSvqOpPn1fYckfXHaYz9Yf5/tknR5BnXtUq3Pcuo9NjW76Vck3RP1mqdc17/U3zvbVQugE2fWVf/3Gz67adZVv/+2qffUtH2zPF7NsiGT9xhLyAEgcAwmAkDgCGoACBxBDQCBI6gBIHAENQAEjqAGgMAR1AAQuP8HE+QM2wz2/SQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.default_rng()\n",
    "first_traj = netswitch_train_multi[0]\n",
    "netswitch_fitted_multi = []\n",
    "# Takes a random sample of values from the strue solution to emulate missingess\n",
    "# and then uses fits it as cubic spline\n",
    "print(netswitch_x0s)\n",
    "for i in range(n_of_ic):\n",
    "    sample_size = rng.integers(low=int(0.25 * n_of_t), high=int(0.75 * n_of_t))\n",
    "\n",
    "    indices = sorted(\n",
    "        random.sample(range(len(netswitch_train_multi[i][:, 0])), int(sample_size)))\n",
    "    sorted_sample = np.asarray([\n",
    "        netswitch_train_multi[i][j, :] for j in indices\n",
    "    ])\n",
    "\n",
    "    # fit to corresponding time values and not the indices\n",
    "    cs_u = CubicSpline(tvals[indices], sorted_sample[:, 0])\n",
    "    cs_v = CubicSpline(tvals[indices], sorted_sample[:, 1])\n",
    "    fitted_sheet = np.array([cs_u(tvals), cs_v(tvals)]).T\n",
    "    netswitch_fitted_multi.append(fitted_sheet)\n",
    "\n",
    "model = ps.SINDy(feature_names=['u', 'v'], optimizer=sparse_regression_optimizer, feature_library=netswitch_library)\n",
    "model.fit(netswitch_fitted_multi, t=dt, multiple_trajectories=True)\n",
    "model.print()\n",
    "\n",
    "# create simulations list to hold simulated data for corresponding IC\n",
    "simulations = []\n",
    "for k in range(n_of_ic):\n",
    "    # problem area with warnings\n",
    "    netswitch_sim = model.simulate(netswitch_x0s[k], t=tvals, integrator=\"odeint\", integrator_kws=integrator_keywords)\n",
    "    simulations.append(netswitch_sim)\n",
    "MSE_SINDy_real = np.square(np.subtract(netswitch_train_multi, simulations)).sum() / (len(tvals) * feature_count * n_of_ic)\n",
    "MSE_poly_real = np.square(np.subtract(netswitch_train_multi, netswitch_fitted_multi)).sum() / (len(tvals) * feature_count * n_of_ic)\n",
    "print(MSE_SINDy_real)\n",
    "print(MSE_poly_real)\n",
    "plt.plot(tvals, simulations[0][:, 0],\"mx\",label=\"sampled u\")\n",
    "plt.plot(tvals, simulations[0][:, 1], \"x\",label=\"sampled v\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "8368a2ca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.004000800160032006\n",
      "5000\n",
      "[0.00000000e+00 4.00080016e-03 8.00160032e-03 ... 1.99919984e+01\n",
      " 1.99959992e+01 2.00000000e+01]\n"
     ]
    }
   ],
   "source": [
    "print(tvals[1]-tvals[0])\n",
    "print(len(tvals))\n",
    "print(tvals)"
   ]
  }
 ],
 "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}