parameter_studies.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from src.simulator import Simulator\n",
    "from src.parameters import ModelParameters, MPCParameters\n",
    "from src.controller import MPC\n",
    "from src.plotter import Plotter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import threading\n",
    "import tikzplotlib\n",
    "from tqdm import tqdm\n",
    "%config InlineBackend.figure_formats = ['svg']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "m1 = 0.5\n",
    "m2 = 0.5\n",
    "L1 = 0.5\n",
    "L2 = 0.5\n",
    "l2 = 0.5*L2\n",
    "l1 = 0.5*L1\n",
    "I1 = m1*l1**2\n",
    "I2 = m2*l2**2\n",
    "f1 = 0.1\n",
    "f2 = 0.1\n",
    "\n",
    "model_params_sim = ModelParameters\n",
    "\n",
    "model_params_sim.m1 = m1\n",
    "model_params_sim.m2 = m2\n",
    "model_params_sim.L1 = L1\n",
    "model_params_sim.L2 = L2\n",
    "model_params_sim.l1 = l2\n",
    "model_params_sim.l2 = l1\n",
    "model_params_sim.I1 = I1\n",
    "model_params_sim.I2 = I2\n",
    "model_params_sim.f1 = f1\n",
    "model_params_sim.f2 = f2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim = Simulator(dt=0.05)\n",
    "sim.set_model_params(model_parameters=model_params_sim)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parameter Studies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate(sim, steps=300, x0=[0, 0, 0.25, 0], N=2.5, dt=0.05, u_lim=4, max_iter=100):\n",
    "  mpc_params = MPCParameters\n",
    "\n",
    "  mpc_params.N = int(np.round(N/dt))   # horizon in time domain\n",
    "  mpc_params.dt = dt\n",
    "  mpc_params.u_lim = u_lim\n",
    "  mpc_params.max_iter = max_iter\n",
    "\n",
    "  # Same model for simulator and controller\n",
    "  model_params_mpc = model_params_sim\n",
    "\n",
    "  mpc = MPC()\n",
    "  mpc.set_controller_params(controller_parameters=mpc_params)\n",
    "  mpc.set_model_params(model_parameters=model_params_mpc)\n",
    "\n",
    "  x_sim = np.ndarray((steps, 4))\n",
    "  x_sim[0] = x0\n",
    "\n",
    "  u_sim = np.ndarray(steps-1)\n",
    "  J_sim = np.ndarray(steps-1)\n",
    "  E_kin_sim = np.ndarray(steps-1)\n",
    "  E_pot_sim = np.ndarray(steps-1)\n",
    "\n",
    "\n",
    "  for i in tqdm(range(steps-1)):\n",
    "\n",
    "    model, feas, xOpt, uOpt, JOpt = mpc.solve_cftoc(x_sim[i])\n",
    "    u = uOpt[0,0]\n",
    "    u_sim[i] = u\n",
    "    E_kin_sim[i], E_pot_sim[i] = sim.calculate_energies(x_sim[i])\n",
    "\n",
    "    J_sim[i] = E_kin_sim[i]-E_pot_sim[i]\n",
    "    x_sim[i+1] = sim.simulate_step(x=x_sim[i], u=u)\n",
    "\n",
    "  return x_sim, u_sim, J_sim"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Horizon Length Analysis\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "u_lim = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating for N=0.10s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 199/199 [00:06<00:00, 29.25it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating for N=0.20s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 199/199 [00:07<00:00, 25.07it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating for N=1.00s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 199/199 [00:28<00:00,  6.98it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating for N=1.20s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 199/199 [00:28<00:00,  7.08it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating for N=1.80s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 199/199 [00:36<00:00,  5.52it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating for N=2.10s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 199/199 [00:44<00:00,  4.42it/s]\n"
     ]
    }
   ],
   "source": [
    "# N_values = np.arange(0.1, 0.5, 0.1).tolist()\n",
    "N_values = [0.1, 0.2, 1.0, 1.2, 1.8, 2.1]\n",
    "\n",
    "x_sim_results = []\n",
    "u_sim_results = []\n",
    "J_sim_results = []\n",
    "\n",
    "for i, N in enumerate(N_values):\n",
    "  print('Calculating for N={:.2f}s'.format(N))\n",
    "  x_sim, u_sim, J_sim = simulate(sim=sim,steps=200, N=N, u_lim=4)\n",
    "  \n",
    "  x_sim_results.append(x_sim)\n",
    "  u_sim_results.append(u_sim)\n",
    "  J_sim_results.append(J_sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"422.843437pt\" height=\"310.86825pt\" viewBox=\"0 0 422.843437 310.86825\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2022-12-16T19:06:10.406930</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.6.2, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n  <g id=\"patch_1\">\n   <path d=\"M 0 310.86825 \nL 422.843437 310.86825 \nL 422.843437 0 \nL 0 0 \nz\n\" style=\"fill: #ffffff\"/>\n  </g>\n  <g id=\"axes_1\">\n   <g id=\"patch_2\">\n    <path d=\"M 58.523438 273.312 \nL 415.643438 273.312 \nL 415.643438 7.2 \nL 58.523438 7.2 \nz\n\" style=\"fill: #ffffff\"/>\n   </g>\n   <g id=\"matplotlib.axis_1\">\n    <g id=\"xtick_1\">\n     <g id=\"line2d_1\">\n      <defs>\n       <path id=\"m6f8a5940bc\" d=\"M 0 0 \nL 0 3.5 \n\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </defs>\n      <g>\n       <use xlink:href=\"#m6f8a5940bc\" x=\"74.756165\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_1\">\n      <!-- 0 -->\n      <g transform=\"translate(71.574915 287.910437) scale(0.1 -0.1)\">\n       <defs>\n        <path id=\"DejaVuSans-30\" d=\"M 2034 4250 \nQ 1547 4250 1301 3770 \nQ 1056 3291 1056 2328 \nQ 1056 1369 1301 889 \nQ 1547 409 2034 409 \nQ 2525 409 2770 889 \nQ 3016 1369 3016 2328 \nQ 3016 3291 2770 3770 \nQ 2525 4250 2034 4250 \nz\nM 2034 4750 \nQ 2819 4750 3233 4129 \nQ 3647 3509 3647 2328 \nQ 3647 1150 3233 529 \nQ 2819 -91 2034 -91 \nQ 1250 -91 836 529 \nQ 422 1150 422 2328 \nQ 422 3509 836 4129 \nQ 1250 4750 2034 4750 \nz\n\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-30\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_2\">\n     <g id=\"line2d_2\">\n      <g>\n       <use xlink:href=\"#m6f8a5940bc\" x=\"140.01336\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_2\">\n      <!-- 2 -->\n      <g transform=\"translate(136.83211 287.910437) scale(0.1 -0.1)\">\n       <defs>\n        <path id=\"DejaVuSans-32\" d=\"M 1228 531 \nL 3431 531 \nL 3431 0 \nL 469 0 \nL 469 531 \nQ 828 903 1448 1529 \nQ 2069 2156 2228 2338 \nQ 2531 2678 2651 2914 \nQ 2772 3150 2772 3378 \nQ 2772 3750 2511 3984 \nQ 2250 4219 1831 4219 \nQ 1534 4219 1204 4116 \nQ 875 4013 500 3803 \nL 500 4441 \nQ 881 4594 1212 4672 \nQ 1544 4750 1819 4750 \nQ 2544 4750 2975 4387 \nQ 3406 4025 3406 3419 \nQ 3406 3131 3298 2873 \nQ 3191 2616 2906 2266 \nQ 2828 2175 2409 1742 \nQ 1991 1309 1228 531 \nz\n\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-32\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_3\">\n     <g id=\"line2d_3\">\n      <g>\n       <use xlink:href=\"#m6f8a5940bc\" x=\"205.270555\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_3\">\n      <!-- 4 -->\n      <g transform=\"translate(202.089305 287.910437) scale(0.1 -0.1)\">\n       <defs>\n        <path id=\"DejaVuSans-34\" d=\"M 2419 4116 \nL 825 1625 \nL 2419 1625 \nL 2419 4116 \nz\nM 2253 4666 \nL 3047 4666 \nL 3047 1625 \nL 3713 1625 \nL 3713 1100 \nL 3047 1100 \nL 3047 0 \nL 2419 0 \nL 2419 1100 \nL 313 1100 \nL 313 1709 \nL 2253 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-34\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_4\">\n     <g id=\"line2d_4\">\n      <g>\n       <use xlink:href=\"#m6f8a5940bc\" x=\"270.52775\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_4\">\n      <!-- 6 -->\n      <g transform=\"translate(267.3465 287.910437) scale(0.1 -0.1)\">\n       <defs>\n        <path id=\"DejaVuSans-36\" d=\"M 2113 2584 \nQ 1688 2584 1439 2293 \nQ 1191 2003 1191 1497 \nQ 1191 994 1439 701 \nQ 1688 409 2113 409 \nQ 2538 409 2786 701 \nQ 3034 994 3034 1497 \nQ 3034 2003 2786 2293 \nQ 2538 2584 2113 2584 \nz\nM 3366 4563 \nL 3366 3988 \nQ 3128 4100 2886 4159 \nQ 2644 4219 2406 4219 \nQ 1781 4219 1451 3797 \nQ 1122 3375 1075 2522 \nQ 1259 2794 1537 2939 \nQ 1816 3084 2150 3084 \nQ 2853 3084 3261 2657 \nQ 3669 2231 3669 1497 \nQ 3669 778 3244 343 \nQ 2819 -91 2113 -91 \nQ 1303 -91 875 529 \nQ 447 1150 447 2328 \nQ 447 3434 972 4092 \nQ 1497 4750 2381 4750 \nQ 2619 4750 2861 4703 \nQ 3103 4656 3366 4563 \nz\n\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-36\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_5\">\n     <g id=\"line2d_5\">\n      <g>\n       <use xlink:href=\"#m6f8a5940bc\" x=\"335.784945\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_5\">\n      <!-- 8 -->\n      <g transform=\"translate(332.603695 287.910437) scale(0.1 -0.1)\">\n       <defs>\n        <path id=\"DejaVuSans-38\" d=\"M 2034 2216 \nQ 1584 2216 1326 1975 \nQ 1069 1734 1069 1313 \nQ 1069 891 1326 650 \nQ 1584 409 2034 409 \nQ 2484 409 2743 651 \nQ 3003 894 3003 1313 \nQ 3003 1734 2745 1975 \nQ 2488 2216 2034 2216 \nz\nM 1403 2484 \nQ 997 2584 770 2862 \nQ 544 3141 544 3541 \nQ 544 4100 942 4425 \nQ 1341 4750 2034 4750 \nQ 2731 4750 3128 4425 \nQ 3525 4100 3525 3541 \nQ 3525 3141 3298 2862 \nQ 3072 2584 2669 2484 \nQ 3125 2378 3379 2068 \nQ 3634 1759 3634 1313 \nQ 3634 634 3220 271 \nQ 2806 -91 2034 -91 \nQ 1263 -91 848 271 \nQ 434 634 434 1313 \nQ 434 1759 690 2068 \nQ 947 2378 1403 2484 \nz\nM 1172 3481 \nQ 1172 3119 1398 2916 \nQ 1625 2713 2034 2713 \nQ 2441 2713 2670 2916 \nQ 2900 3119 2900 3481 \nQ 2900 3844 2670 4047 \nQ 2441 4250 2034 4250 \nQ 1625 4250 1398 4047 \nQ 1172 3844 1172 3481 \nz\n\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-38\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"xtick_6\">\n     <g id=\"line2d_6\">\n      <g>\n       <use xlink:href=\"#m6f8a5940bc\" x=\"401.04214\" y=\"273.312\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_6\">\n      <!-- 10 -->\n      <g transform=\"translate(394.67964 287.910437) scale(0.1 -0.1)\">\n       <defs>\n        <path id=\"DejaVuSans-31\" d=\"M 794 531 \nL 1825 531 \nL 1825 4091 \nL 703 3866 \nL 703 4441 \nL 1819 4666 \nL 2450 4666 \nL 2450 531 \nL 3481 531 \nL 3481 0 \nL 794 0 \nL 794 531 \nz\n\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-31\"/>\n       <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"text_7\">\n     <!-- Time [s] -->\n     <g transform=\"translate(216.754531 301.588562) scale(0.1 -0.1)\">\n      <defs>\n       <path id=\"DejaVuSans-54\" d=\"M -19 4666 \nL 3928 4666 \nL 3928 4134 \nL 2272 4134 \nL 2272 0 \nL 1638 0 \nL 1638 4134 \nL -19 4134 \nL -19 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-69\" d=\"M 603 3500 \nL 1178 3500 \nL 1178 0 \nL 603 0 \nL 603 3500 \nz\nM 603 4863 \nL 1178 4863 \nL 1178 4134 \nL 603 4134 \nL 603 4863 \nz\n\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-6d\" d=\"M 3328 2828 \nQ 3544 3216 3844 3400 \nQ 4144 3584 4550 3584 \nQ 5097 3584 5394 3201 \nQ 5691 2819 5691 2113 \nL 5691 0 \nL 5113 0 \nL 5113 2094 \nQ 5113 2597 4934 2840 \nQ 4756 3084 4391 3084 \nQ 3944 3084 3684 2787 \nQ 3425 2491 3425 1978 \nL 3425 0 \nL 2847 0 \nL 2847 2094 \nQ 2847 2600 2669 2842 \nQ 2491 3084 2119 3084 \nQ 1678 3084 1418 2786 \nQ 1159 2488 1159 1978 \nL 1159 0 \nL 581 0 \nL 581 3500 \nL 1159 3500 \nL 1159 2956 \nQ 1356 3278 1631 3431 \nQ 1906 3584 2284 3584 \nQ 2666 3584 2933 3390 \nQ 3200 3197 3328 2828 \nz\n\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-65\" d=\"M 3597 1894 \nL 3597 1613 \nL 953 1613 \nQ 991 1019 1311 708 \nQ 1631 397 2203 397 \nQ 2534 397 2845 478 \nQ 3156 559 3463 722 \nL 3463 178 \nQ 3153 47 2828 -22 \nQ 2503 -91 2169 -91 \nQ 1331 -91 842 396 \nQ 353 884 353 1716 \nQ 353 2575 817 3079 \nQ 1281 3584 2069 3584 \nQ 2775 3584 3186 3129 \nQ 3597 2675 3597 1894 \nz\nM 3022 2063 \nQ 3016 2534 2758 2815 \nQ 2500 3097 2075 3097 \nQ 1594 3097 1305 2825 \nQ 1016 2553 972 2059 \nL 3022 2063 \nz\n\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-20\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-5b\" d=\"M 550 4863 \nL 1875 4863 \nL 1875 4416 \nL 1125 4416 \nL 1125 -397 \nL 1875 -397 \nL 1875 -844 \nL 550 -844 \nL 550 4863 \nz\n\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-73\" d=\"M 2834 3397 \nL 2834 2853 \nQ 2591 2978 2328 3040 \nQ 2066 3103 1784 3103 \nQ 1356 3103 1142 2972 \nQ 928 2841 928 2578 \nQ 928 2378 1081 2264 \nQ 1234 2150 1697 2047 \nL 1894 2003 \nQ 2506 1872 2764 1633 \nQ 3022 1394 3022 966 \nQ 3022 478 2636 193 \nQ 2250 -91 1575 -91 \nQ 1294 -91 989 -36 \nQ 684 19 347 128 \nL 347 722 \nQ 666 556 975 473 \nQ 1284 391 1588 391 \nQ 1994 391 2212 530 \nQ 2431 669 2431 922 \nQ 2431 1156 2273 1281 \nQ 2116 1406 1581 1522 \nL 1381 1569 \nQ 847 1681 609 1914 \nQ 372 2147 372 2553 \nQ 372 3047 722 3315 \nQ 1072 3584 1716 3584 \nQ 2034 3584 2315 3537 \nQ 2597 3491 2834 3397 \nz\n\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-5d\" d=\"M 1947 4863 \nL 1947 -844 \nL 622 -844 \nL 622 -397 \nL 1369 -397 \nL 1369 4416 \nL 622 4416 \nL 622 4863 \nL 1947 4863 \nz\n\" transform=\"scale(0.015625)\"/>\n      </defs>\n      <use xlink:href=\"#DejaVuSans-54\"/>\n      <use xlink:href=\"#DejaVuSans-69\" x=\"57.958984\"/>\n      <use xlink:href=\"#DejaVuSans-6d\" x=\"85.742188\"/>\n      <use xlink:href=\"#DejaVuSans-65\" x=\"183.154297\"/>\n      <use xlink:href=\"#DejaVuSans-20\" x=\"244.677734\"/>\n      <use xlink:href=\"#DejaVuSans-5b\" x=\"276.464844\"/>\n      <use xlink:href=\"#DejaVuSans-73\" x=\"315.478516\"/>\n      <use xlink:href=\"#DejaVuSans-5d\" x=\"367.578125\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"matplotlib.axis_2\">\n    <g id=\"ytick_1\">\n     <g id=\"line2d_7\">\n      <defs>\n       <path id=\"maa858e138a\" d=\"M 0 0 \nL -3.5 0 \n\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </defs>\n      <g>\n       <use xlink:href=\"#maa858e138a\" x=\"58.523438\" y=\"272.761066\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_8\">\n      <!-- −10.0 -->\n      <g transform=\"translate(20.878125 276.560285) scale(0.1 -0.1)\">\n       <defs>\n        <path id=\"DejaVuSans-2212\" d=\"M 678 2272 \nL 4684 2272 \nL 4684 1741 \nL 678 1741 \nL 678 2272 \nz\n\" transform=\"scale(0.015625)\"/>\n        <path id=\"DejaVuSans-2e\" d=\"M 684 794 \nL 1344 794 \nL 1344 0 \nL 684 0 \nL 684 794 \nz\n\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-2212\"/>\n       <use xlink:href=\"#DejaVuSans-31\" x=\"83.789062\"/>\n       <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n       <use xlink:href=\"#DejaVuSans-2e\" x=\"211.035156\"/>\n       <use xlink:href=\"#DejaVuSans-30\" x=\"242.822266\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_2\">\n     <g id=\"line2d_8\">\n      <g>\n       <use xlink:href=\"#maa858e138a\" x=\"58.523438\" y=\"237.554074\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_9\">\n      <!-- −7.5 -->\n      <g transform=\"translate(27.240625 241.353292) scale(0.1 -0.1)\">\n       <defs>\n        <path id=\"DejaVuSans-37\" d=\"M 525 4666 \nL 3525 4666 \nL 3525 4397 \nL 1831 0 \nL 1172 0 \nL 2766 4134 \nL 525 4134 \nL 525 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n        <path id=\"DejaVuSans-35\" d=\"M 691 4666 \nL 3169 4666 \nL 3169 4134 \nL 1269 4134 \nL 1269 2991 \nQ 1406 3038 1543 3061 \nQ 1681 3084 1819 3084 \nQ 2600 3084 3056 2656 \nQ 3513 2228 3513 1497 \nQ 3513 744 3044 326 \nQ 2575 -91 1722 -91 \nQ 1428 -91 1123 -41 \nQ 819 9 494 109 \nL 494 744 \nQ 775 591 1075 516 \nQ 1375 441 1709 441 \nQ 2250 441 2565 725 \nQ 2881 1009 2881 1497 \nQ 2881 1984 2565 2268 \nQ 2250 2553 1709 2553 \nQ 1456 2553 1204 2497 \nQ 953 2441 691 2322 \nL 691 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n       </defs>\n       <use xlink:href=\"#DejaVuSans-2212\"/>\n       <use xlink:href=\"#DejaVuSans-37\" x=\"83.789062\"/>\n       <use xlink:href=\"#DejaVuSans-2e\" x=\"147.412109\"/>\n       <use xlink:href=\"#DejaVuSans-35\" x=\"179.199219\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_3\">\n     <g id=\"line2d_9\">\n      <g>\n       <use xlink:href=\"#maa858e138a\" x=\"58.523438\" y=\"202.347081\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_10\">\n      <!-- −5.0 -->\n      <g transform=\"translate(27.240625 206.1463) scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-2212\"/>\n       <use xlink:href=\"#DejaVuSans-35\" x=\"83.789062\"/>\n       <use xlink:href=\"#DejaVuSans-2e\" x=\"147.412109\"/>\n       <use xlink:href=\"#DejaVuSans-30\" x=\"179.199219\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_4\">\n     <g id=\"line2d_10\">\n      <g>\n       <use xlink:href=\"#maa858e138a\" x=\"58.523438\" y=\"167.140089\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_11\">\n      <!-- −2.5 -->\n      <g transform=\"translate(27.240625 170.939307) scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-2212\"/>\n       <use xlink:href=\"#DejaVuSans-32\" x=\"83.789062\"/>\n       <use xlink:href=\"#DejaVuSans-2e\" x=\"147.412109\"/>\n       <use xlink:href=\"#DejaVuSans-35\" x=\"179.199219\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_5\">\n     <g id=\"line2d_11\">\n      <g>\n       <use xlink:href=\"#maa858e138a\" x=\"58.523438\" y=\"131.933096\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_12\">\n      <!-- 0.0 -->\n      <g transform=\"translate(35.620313 135.732315) scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-30\"/>\n       <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n       <use xlink:href=\"#DejaVuSans-30\" x=\"95.410156\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_6\">\n     <g id=\"line2d_12\">\n      <g>\n       <use xlink:href=\"#maa858e138a\" x=\"58.523438\" y=\"96.726104\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_13\">\n      <!-- 2.5 -->\n      <g transform=\"translate(35.620313 100.525323) scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-32\"/>\n       <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n       <use xlink:href=\"#DejaVuSans-35\" x=\"95.410156\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_7\">\n     <g id=\"line2d_13\">\n      <g>\n       <use xlink:href=\"#maa858e138a\" x=\"58.523438\" y=\"61.519111\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_14\">\n      <!-- 5.0 -->\n      <g transform=\"translate(35.620313 65.31833) scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-35\"/>\n       <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n       <use xlink:href=\"#DejaVuSans-30\" x=\"95.410156\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"ytick_8\">\n     <g id=\"line2d_14\">\n      <g>\n       <use xlink:href=\"#maa858e138a\" x=\"58.523438\" y=\"26.312119\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n      </g>\n     </g>\n     <g id=\"text_15\">\n      <!-- 7.5 -->\n      <g transform=\"translate(35.620313 30.111338) scale(0.1 -0.1)\">\n       <use xlink:href=\"#DejaVuSans-37\"/>\n       <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n       <use xlink:href=\"#DejaVuSans-35\" x=\"95.410156\"/>\n      </g>\n     </g>\n    </g>\n    <g id=\"text_16\">\n     <!-- Cost -->\n     <g transform=\"translate(14.798438 151.371625) rotate(-90) scale(0.1 -0.1)\">\n      <defs>\n       <path id=\"DejaVuSans-43\" d=\"M 4122 4306 \nL 4122 3641 \nQ 3803 3938 3442 4084 \nQ 3081 4231 2675 4231 \nQ 1875 4231 1450 3742 \nQ 1025 3253 1025 2328 \nQ 1025 1406 1450 917 \nQ 1875 428 2675 428 \nQ 3081 428 3442 575 \nQ 3803 722 4122 1019 \nL 4122 359 \nQ 3791 134 3420 21 \nQ 3050 -91 2638 -91 \nQ 1578 -91 968 557 \nQ 359 1206 359 2328 \nQ 359 3453 968 4101 \nQ 1578 4750 2638 4750 \nQ 3056 4750 3426 4639 \nQ 3797 4528 4122 4306 \nz\n\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-6f\" d=\"M 1959 3097 \nQ 1497 3097 1228 2736 \nQ 959 2375 959 1747 \nQ 959 1119 1226 758 \nQ 1494 397 1959 397 \nQ 2419 397 2687 759 \nQ 2956 1122 2956 1747 \nQ 2956 2369 2687 2733 \nQ 2419 3097 1959 3097 \nz\nM 1959 3584 \nQ 2709 3584 3137 3096 \nQ 3566 2609 3566 1747 \nQ 3566 888 3137 398 \nQ 2709 -91 1959 -91 \nQ 1206 -91 779 398 \nQ 353 888 353 1747 \nQ 353 2609 779 3096 \nQ 1206 3584 1959 3584 \nz\n\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-74\" d=\"M 1172 4494 \nL 1172 3500 \nL 2356 3500 \nL 2356 3053 \nL 1172 3053 \nL 1172 1153 \nQ 1172 725 1289 603 \nQ 1406 481 1766 481 \nL 2356 481 \nL 2356 0 \nL 1766 0 \nQ 1100 0 847 248 \nQ 594 497 594 1153 \nL 594 3053 \nL 172 3053 \nL 172 3500 \nL 594 3500 \nL 594 4494 \nL 1172 4494 \nz\n\" transform=\"scale(0.015625)\"/>\n      </defs>\n      <use xlink:href=\"#DejaVuSans-43\"/>\n      <use xlink:href=\"#DejaVuSans-6f\" x=\"69.824219\"/>\n      <use xlink:href=\"#DejaVuSans-73\" x=\"131.005859\"/>\n      <use xlink:href=\"#DejaVuSans-74\" x=\"183.105469\"/>\n     </g>\n    </g>\n   </g>\n   <g id=\"line2d_15\">\n    <path d=\"M 74.756165 131.795569 \nL 81.314842 131.967427 \nL 84.594181 131.7542 \nL 89.51319 131.169613 \nL 91.152859 131.122097 \nL 92.792528 131.300816 \nL 94.432198 131.811282 \nL 96.071867 132.745913 \nL 97.711537 134.165717 \nL 99.351206 136.08704 \nL 100.990876 138.478154 \nL 102.630545 141.265185 \nL 105.909884 147.593123 \nL 109.189223 154.124677 \nL 112.468561 160.071744 \nL 114.108231 162.690869 \nL 115.7479 165.059801 \nL 117.38757 167.199511 \nL 120.666909 170.958071 \nL 125.585917 176.042985 \nL 130.504925 180.800606 \nL 143.62228 193.013981 \nL 146.901619 196.431733 \nL 150.180958 200.146951 \nL 151.820628 202.136078 \nL 156.739636 208.520174 \nL 160.018975 212.443521 \nL 163.298314 216.030249 \nL 166.577652 219.295047 \nL 169.856991 222.275706 \nL 173.13633 224.996757 \nL 176.415669 227.449561 \nL 179.695008 229.595874 \nL 182.974347 231.387744 \nL 186.253685 232.790942 \nL 189.533024 233.803822 \nL 192.812363 234.470352 \nL 196.091702 234.883584 \nL 202.65038 235.384637 \nL 207.569388 235.587987 \nL 212.488396 235.557285 \nL 219.047074 235.472717 \nL 233.804099 235.513923 \nL 253.480132 235.522747 \nL 399.41071 235.546782 \nL 399.41071 235.546782 \n\" clip-path=\"url(#pe530d5151b)\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square\"/>\n   </g>\n   <g id=\"line2d_16\">\n    <path d=\"M 74.756165 131.795569 \nL 76.395834 131.393698 \nL 78.035504 131.654212 \nL 79.675173 131.80058 \nL 81.314842 131.050421 \nL 82.954512 131.308809 \nL 84.594181 131.255847 \nL 86.233851 131.80751 \nL 87.87352 131.898244 \nL 89.51319 130.858634 \nL 91.152859 130.9679 \nL 92.792528 131.51622 \nL 94.432198 131.378826 \nL 96.071867 131.838821 \nL 97.711537 131.872358 \nL 99.351206 131.194303 \nL 102.630545 132.004747 \nL 104.270214 131.293396 \nL 107.549553 131.585255 \nL 109.189223 131.341917 \nL 110.828892 131.920287 \nL 112.468561 132.011288 \nL 114.108231 130.907532 \nL 115.7479 130.960266 \nL 117.38757 131.365654 \nL 119.027239 131.331686 \nL 120.666909 131.901781 \nL 122.306578 131.897005 \nL 123.946247 130.927052 \nL 125.585917 131.190324 \nL 127.225586 131.683491 \nL 128.865256 131.393496 \nL 130.504925 131.74165 \nL 132.144595 131.804881 \nL 133.784264 131.234039 \nL 135.423933 131.703887 \nL 137.063603 132.000318 \nL 138.703272 131.191217 \nL 140.342942 131.295125 \nL 141.982611 131.523906 \nL 143.62228 131.315351 \nL 145.26195 131.880529 \nL 146.901619 131.953971 \nL 148.541289 130.91031 \nL 150.180958 131.031626 \nL 151.820628 131.455218 \nL 153.460297 131.335634 \nL 155.099966 131.842382 \nL 156.739636 131.870374 \nL 158.379305 131.024862 \nL 161.658644 131.779248 \nL 163.298314 131.342377 \nL 164.937983 131.625594 \nL 166.577652 131.737398 \nL 168.217322 131.256299 \nL 169.856991 131.74137 \nL 171.496661 131.973987 \nL 173.13633 131.111044 \nL 174.775999 131.227202 \nL 176.415669 131.504478 \nL 178.055338 131.302082 \nL 179.695008 131.842558 \nL 181.334677 131.912484 \nL 182.974347 130.943485 \nL 184.614016 131.129024 \nL 186.253685 131.549684 \nL 187.893355 131.331758 \nL 189.533024 131.77598 \nL 191.172694 131.837227 \nL 192.812363 131.099392 \nL 196.091702 131.836375 \nL 197.731371 131.281801 \nL 201.01071 131.679699 \nL 202.65038 131.263384 \nL 204.290049 131.753743 \nL 205.929718 131.94196 \nL 207.569388 131.06254 \nL 209.209057 131.205525 \nL 210.848727 131.517429 \nL 212.488396 131.295592 \nL 214.128066 131.803699 \nL 215.767735 131.880439 \nL 217.407404 130.991492 \nL 219.047074 131.232449 \nL 220.686743 131.634633 \nL 222.326413 131.316204 \nL 223.966082 131.704303 \nL 225.605752 131.79905 \nL 227.245421 131.151574 \nL 230.52476 131.864211 \nL 232.164429 131.22291 \nL 235.443768 131.639086 \nL 237.083438 131.263997 \nL 238.723107 131.750749 \nL 240.362776 131.910878 \nL 242.002446 131.042225 \nL 243.642115 131.219477 \nL 245.281785 131.5517 \nL 246.921454 131.291013 \nL 248.561123 131.762329 \nL 250.200793 131.852326 \nL 251.840462 131.041959 \nL 255.119801 131.702784 \nL 256.759471 131.290616 \nL 258.39914 131.632664 \nL 260.038809 131.760276 \nL 261.678479 131.185664 \nL 263.318148 131.600918 \nL 264.957818 131.872395 \nL 266.597487 131.173635 \nL 269.876826 131.617828 \nL 271.516495 131.262509 \nL 273.156165 131.738213 \nL 274.795834 131.883102 \nL 276.435504 131.043249 \nL 278.075173 131.256888 \nL 279.714842 131.596359 \nL 281.354512 131.284358 \nL 282.994181 131.71783 \nL 284.633851 131.825136 \nL 286.27352 131.087652 \nL 289.552859 131.752438 \nL 291.192528 131.259114 \nL 292.832198 131.566722 \nL 294.471867 131.725573 \nL 296.111537 131.206667 \nL 297.751206 131.63305 \nL 299.390876 131.868769 \nL 301.030545 131.138001 \nL 304.309884 131.614295 \nL 305.949553 131.260443 \nL 307.589223 131.71934 \nL 309.228892 131.858588 \nL 310.868561 131.058044 \nL 314.1479 131.642713 \nL 315.78757 131.27362 \nL 317.427239 131.671303 \nL 319.066909 131.798198 \nL 320.706578 131.125239 \nL 323.985917 131.785176 \nL 325.625586 131.226496 \nL 328.904925 131.698591 \nL 330.544595 131.219125 \nL 332.184264 131.649239 \nL 333.823933 131.858867 \nL 335.463603 131.116451 \nL 338.742942 131.624437 \nL 340.382611 131.257476 \nL 342.02228 131.695766 \nL 343.66195 131.836318 \nL 345.301619 131.07987 \nL 348.580958 131.684963 \nL 350.220628 131.258718 \nL 351.860297 131.625054 \nL 353.499966 131.772423 \nL 355.139636 131.154162 \nL 358.418975 131.804277 \nL 360.058644 131.196828 \nL 363.337983 131.681104 \nL 364.977652 131.226142 \nL 366.617322 131.653975 \nL 368.256991 131.846072 \nL 369.896661 131.107467 \nL 373.175999 131.643529 \nL 374.815669 131.252827 \nL 376.455338 131.668782 \nL 378.095008 131.815514 \nL 379.734677 131.103795 \nL 383.014016 131.719967 \nL 384.653685 131.240825 \nL 386.293355 131.581748 \nL 387.933024 131.749397 \nL 389.572694 131.175297 \nL 391.212363 131.558967 \nL 392.852033 131.813171 \nL 394.491702 131.172843 \nL 397.771041 131.673265 \nL 399.41071 131.22955 \nL 399.41071 131.22955 \n\" clip-path=\"url(#pe530d5151b)\" style=\"fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square\"/>\n   </g>\n   <g id=\"line2d_17\">\n    <path d=\"M 74.756165 131.795569 \nL 76.395834 130.321264 \nL 78.035504 129.854388 \nL 79.675173 128.218601 \nL 81.314842 127.015121 \nL 82.954512 126.501003 \nL 84.594181 127.183151 \nL 86.233851 129.503216 \nL 87.87352 133.68874 \nL 89.51319 139.689935 \nL 91.152859 153.555535 \nL 92.792528 160.029928 \nL 94.432198 161.366598 \nL 96.071867 156.612298 \nL 97.711537 147.778275 \nL 99.351206 134.055582 \nL 100.990876 117.203052 \nL 102.630545 98.729966 \nL 104.270214 82.271448 \nL 105.909884 71.045188 \nL 107.549553 67.51281 \nL 109.189223 72.408709 \nL 110.828892 84.930456 \nL 112.468561 103.040149 \nL 114.108231 124.094496 \nL 115.7479 161.208525 \nL 117.38757 181.458959 \nL 119.027239 200.026755 \nL 120.666909 210.7121 \nL 122.306578 216.398017 \nL 123.946247 216.590909 \nL 125.585917 211.218412 \nL 127.225586 200.623563 \nL 128.865256 184.572298 \nL 130.504925 162.371852 \nL 135.423933 83.751771 \nL 137.063603 57.685664 \nL 138.703272 39.355685 \nL 140.342942 29.237673 \nL 141.982611 32.614954 \nL 143.62228 45.169162 \nL 145.26195 69.005816 \nL 146.901619 94.686036 \nL 148.541289 133.48752 \nL 151.820628 186.208856 \nL 155.099966 223.926027 \nL 156.739636 233.19511 \nL 158.379305 244.152981 \nL 160.018975 248.270867 \nL 161.658644 251.963924 \nL 163.298314 253.727159 \nL 164.937983 254.324351 \nL 166.577652 253.237984 \nL 168.217322 250.687527 \nL 169.856991 246.241811 \nL 171.496661 239.701869 \nL 173.13633 230.504715 \nL 174.775999 218.076763 \nL 176.415669 201.635062 \nL 178.055338 180.422508 \nL 179.695008 153.846946 \nL 181.334677 132.736792 \nL 184.614016 64.950103 \nL 187.893355 25.583093 \nL 189.533024 25.078607 \nL 191.172694 19.296 \nL 192.812363 49.460499 \nL 194.452033 68.323212 \nL 196.091702 106.266606 \nL 197.731371 134.207352 \nL 199.371041 165.407366 \nL 201.01071 188.355276 \nL 202.65038 205.650538 \nL 204.290049 219.887026 \nL 205.929718 228.003021 \nL 207.569388 232.201429 \nL 209.209057 233.082671 \nL 210.848727 230.191642 \nL 212.488396 224.162495 \nL 214.128066 214.107393 \nL 215.767735 200.078262 \nL 217.407404 181.806288 \nL 219.047074 159.108314 \nL 222.326413 107.270157 \nL 225.605752 52.698421 \nL 227.245421 33.766611 \nL 228.88509 23.273013 \nL 230.52476 42.585766 \nL 232.164429 54.50303 \nL 233.804099 90.555972 \nL 235.443768 110.762296 \nL 237.083438 146.281895 \nL 240.362776 182.258378 \nL 242.002446 199.869943 \nL 245.281785 226.516759 \nL 248.561123 245.227201 \nL 250.200793 251.889016 \nL 251.840462 256.248159 \nL 253.480132 259.867759 \nL 255.119801 259.9026 \nL 256.759471 261.216 \nL 258.39914 260.014558 \nL 260.038809 259.234738 \nL 261.678479 257.107069 \nL 263.318148 254.022517 \nL 264.957818 249.995882 \nL 266.597487 244.525217 \nL 269.876826 234.333857 \nL 271.516495 230.422165 \nL 273.156165 227.477709 \nL 274.795834 225.796192 \nL 276.435504 225.290279 \nL 278.075173 225.498776 \nL 279.714842 225.872727 \nL 281.354512 226.126398 \nL 282.994181 226.115267 \nL 284.633851 233.931838 \nL 286.27352 232.880822 \nL 287.91319 230.359153 \nL 289.552859 230.519294 \nL 291.192528 230.484685 \nL 292.832198 233.548888 \nL 294.471867 222.814889 \nL 296.111537 224.087089 \nL 297.751206 215.859966 \nL 299.390876 203.980292 \nL 301.030545 188.599935 \nL 302.670214 168.664404 \nL 304.309884 145.578421 \nL 305.949553 120.810429 \nL 307.589223 108.398166 \nL 309.228892 110.87436 \nL 310.868561 134.540401 \nL 312.508231 144.816843 \nL 314.1479 158.046877 \nL 317.427239 187.229285 \nL 319.066909 200.236156 \nL 320.706578 210.564499 \nL 322.346247 218.049378 \nL 323.985917 223.432505 \nL 325.625586 227.671034 \nL 327.265256 230.998109 \nL 328.904925 232.405455 \nL 330.544595 228.348714 \nL 332.184264 218.807438 \nL 333.823933 204.977026 \nL 335.463603 186.925691 \nL 337.103272 164.62228 \nL 338.742942 151.837346 \nL 340.382611 140.616324 \nL 342.02228 130.236545 \nL 343.66195 122.123476 \nL 345.301619 117.151692 \nL 346.941289 115.577044 \nL 348.580958 117.076792 \nL 350.220628 120.85037 \nL 353.499966 130.799421 \nL 355.139636 134.892858 \nL 356.779305 137.338463 \nL 358.418975 137.777606 \nL 360.058644 136.333028 \nL 361.698314 133.334427 \nL 363.337983 129.725662 \nL 364.977652 126.542957 \nL 366.617322 124.908715 \nL 368.256991 125.640444 \nL 369.896661 129.020513 \nL 371.53633 134.847727 \nL 373.175999 149.913583 \nL 374.815669 158.663408 \nL 376.455338 161.424333 \nL 378.095008 161.465322 \nL 391.212363 166.088993 \nL 396.131371 168.09748 \nL 399.41071 169.702213 \nL 399.41071 169.702213 \n\" clip-path=\"url(#pe530d5151b)\" style=\"fill: none; stroke: #2ca02c; stroke-width: 1.5; stroke-linecap: square\"/>\n   </g>\n   <g id=\"line2d_18\">\n    <path d=\"M 74.756165 131.795569 \nL 76.395834 131.393698 \nL 78.035504 131.451361 \nL 81.314842 131.146402 \nL 82.954512 130.841055 \nL 84.594181 131.162753 \nL 86.233851 131.729351 \nL 87.87352 131.320299 \nL 89.51319 131.40282 \nL 91.152859 131.257934 \nL 92.792528 130.920924 \nL 94.432198 131.214482 \nL 96.071867 131.653931 \nL 97.711537 131.110306 \nL 99.351206 131.340507 \nL 100.990876 131.316397 \nL 102.630545 131.167051 \nL 104.270214 131.250365 \nL 105.909884 131.597761 \nL 107.549553 130.909699 \nL 109.189223 131.328507 \nL 110.828892 131.441285 \nL 114.108231 131.237918 \nL 115.7479 131.478416 \nL 117.38757 130.91541 \nL 120.666909 131.582647 \nL 122.306578 131.109279 \nL 123.946247 131.212641 \nL 125.585917 131.506348 \nL 127.225586 131.190946 \nL 130.504925 131.278475 \nL 132.144595 131.628727 \nL 133.784264 130.755361 \nL 137.063603 131.474247 \nL 138.703272 131.25541 \nL 140.342942 131.233368 \nL 141.982611 131.495851 \nL 143.62228 131.229409 \nL 145.26195 131.359056 \nL 146.901619 131.277801 \nL 148.541289 131.52689 \nL 150.180958 130.615357 \nL 151.820628 131.160478 \nL 153.460297 131.477317 \nL 156.739636 131.230602 \nL 158.379305 131.485409 \nL 160.018975 131.230937 \nL 161.658644 131.328596 \nL 163.298314 131.255751 \nL 164.937983 131.549955 \nL 166.577652 131.223845 \nL 168.217322 131.430611 \nL 169.856991 131.27823 \nL 171.496661 131.500436 \nL 173.13633 131.253869 \nL 174.775999 131.539149 \nL 176.415669 131.257907 \nL 178.055338 131.392754 \nL 179.695008 131.266383 \nL 181.334677 131.572834 \nL 182.974347 131.221571 \nL 184.614016 131.320627 \nL 186.253685 131.270885 \nL 187.893355 131.589608 \nL 189.533024 131.204873 \nL 191.172694 131.321763 \nL 192.812363 131.277525 \nL 194.452033 131.565589 \nL 196.091702 131.21923 \nL 197.731371 131.432429 \nL 199.371041 131.276624 \nL 201.01071 131.494673 \nL 202.65038 131.244748 \nL 204.290049 131.521517 \nL 205.929718 131.252101 \nL 207.569388 131.40519 \nL 209.209057 131.257595 \nL 210.848727 131.53876 \nL 212.488396 131.228416 \nL 214.128066 131.363677 \nL 215.767735 131.265597 \nL 217.407404 131.547292 \nL 219.047074 131.222352 \nL 220.686743 131.377982 \nL 222.326413 131.270227 \nL 223.966082 131.521684 \nL 225.605752 131.234097 \nL 227.245421 131.430517 \nL 228.88509 131.266555 \nL 230.52476 131.471697 \nL 232.164429 131.24988 \nL 233.804099 131.529775 \nL 235.443768 131.245729 \nL 237.083438 131.402348 \nL 238.723107 131.258962 \nL 240.362776 131.534323 \nL 242.002446 131.229128 \nL 243.642115 131.374435 \nL 245.281785 131.265428 \nL 246.921454 131.536287 \nL 248.561123 131.226637 \nL 250.200793 131.393101 \nL 251.840462 131.267984 \nL 253.480132 131.509261 \nL 255.119801 131.237549 \nL 256.759471 131.440963 \nL 258.39914 131.26268 \nL 260.038809 131.463112 \nL 261.678479 131.250772 \nL 263.318148 131.491052 \nL 264.957818 131.248795 \nL 266.597487 131.415432 \nL 268.237157 131.259407 \nL 269.876826 131.523185 \nL 271.516495 131.234271 \nL 273.156165 131.387985 \nL 274.795834 131.263975 \nL 276.435504 131.530104 \nL 278.075173 131.229005 \nL 279.714842 131.393719 \nL 281.354512 131.265863 \nL 282.994181 131.512982 \nL 284.633851 131.23503 \nL 286.27352 131.427455 \nL 287.91319 131.262886 \nL 289.552859 131.477867 \nL 291.192528 131.245993 \nL 292.832198 131.470507 \nL 294.471867 131.253281 \nL 296.111537 131.436925 \nL 297.751206 131.255081 \nL 299.390876 131.504044 \nL 301.030545 131.24101 \nL 302.670214 131.407095 \nL 304.309884 131.260461 \nL 305.949553 131.517967 \nL 307.589223 131.233677 \nL 309.228892 131.401788 \nL 310.868561 131.262944 \nL 312.508231 131.510689 \nL 314.1479 131.235296 \nL 315.78757 131.422003 \nL 317.427239 131.261802 \nL 319.066909 131.48604 \nL 320.706578 131.243079 \nL 322.346247 131.460145 \nL 323.985917 131.255152 \nL 325.625586 131.451633 \nL 327.265256 131.251485 \nL 328.904925 131.488242 \nL 330.544595 131.245556 \nL 332.184264 131.423459 \nL 333.823933 131.257261 \nL 335.463603 131.5051 \nL 337.103272 131.23822 \nL 338.742942 131.413052 \nL 340.382611 131.260174 \nL 342.02228 131.504182 \nL 343.66195 131.237356 \nL 345.301619 131.423778 \nL 346.941289 131.260008 \nL 348.580958 131.487589 \nL 350.220628 131.242271 \nL 351.860297 131.448804 \nL 353.499966 131.255916 \nL 355.139636 131.461726 \nL 356.779305 131.249107 \nL 358.418975 131.475831 \nL 360.058644 131.248715 \nL 361.698314 131.436629 \nL 363.337983 131.254672 \nL 364.977652 131.49418 \nL 366.617322 131.241921 \nL 368.256991 131.422763 \nL 369.896661 131.257935 \nL 371.53633 131.53859 \nL 373.175999 131.234451 \nL 374.815669 131.414559 \nL 376.455338 131.260162 \nL 378.095008 131.497259 \nL 379.734677 131.240343 \nL 381.374347 131.441122 \nL 383.014016 131.25889 \nL 384.653685 131.467058 \nL 386.293355 131.249026 \nL 387.933024 131.47825 \nL 389.572694 131.250276 \nL 391.212363 131.431074 \nL 392.852033 131.256424 \nL 394.491702 131.506294 \nL 396.131371 131.23958 \nL 397.771041 131.406734 \nL 399.41071 131.260824 \nL 399.41071 131.260824 \n\" clip-path=\"url(#pe530d5151b)\" style=\"fill: none; stroke: #d62728; stroke-width: 1.5; stroke-linecap: square\"/>\n   </g>\n   <g id=\"line2d_19\">\n    <path d=\"M 74.756165 131.795569 \nL 76.395834 131.393698 \nL 78.035504 131.431181 \nL 81.314842 131.202381 \nL 82.954512 131.31976 \nL 84.594181 131.208221 \nL 86.233851 131.310214 \nL 87.87352 131.203615 \nL 89.51319 131.318047 \nL 91.152859 131.185468 \nL 92.792528 131.328559 \nL 94.432198 131.157849 \nL 96.071867 131.334363 \nL 97.711537 131.128873 \nL 99.351206 131.334136 \nL 100.990876 131.107831 \nL 102.630545 131.329825 \nL 104.270214 131.101823 \nL 105.909884 131.322768 \nL 107.549553 131.113478 \nL 109.189223 131.312834 \nL 110.828892 131.140321 \nL 112.468561 131.298462 \nL 114.108231 131.176065 \nL 115.7479 131.2778 \nL 119.027239 131.250408 \nL 153.460297 131.202425 \nL 155.099966 131.270089 \nL 156.739636 131.181314 \nL 158.379305 131.279087 \nL 160.018975 131.167289 \nL 161.658644 131.282589 \nL 163.298314 131.162979 \nL 164.937983 131.281349 \nL 166.577652 131.168842 \nL 168.217322 131.275694 \nL 169.856991 131.183091 \nL 171.496661 131.265635 \nL 173.13633 131.202403 \nL 176.415669 131.223002 \nL 186.253685 131.266193 \nL 187.893355 131.184408 \nL 189.533024 131.271301 \nL 191.172694 131.178142 \nL 192.812363 131.272046 \nL 194.452033 131.179528 \nL 196.091702 131.268772 \nL 197.731371 131.1879 \nL 199.371041 131.261715 \nL 202.65038 131.251176 \nL 209.209057 131.223141 \nL 214.128066 131.255459 \nL 215.767735 131.197462 \nL 217.407404 131.261453 \nL 219.047074 131.190553 \nL 220.686743 131.263672 \nL 222.326413 131.189276 \nL 223.966082 131.262327 \nL 225.605752 131.193592 \nL 227.245421 131.257678 \nL 230.52476 131.250062 \nL 235.443768 131.226306 \nL 304.309884 131.244519 \nL 309.228892 131.209699 \nL 314.1479 131.24395 \nL 320.706578 131.235168 \nL 337.103272 131.213879 \nL 342.02228 131.241671 \nL 350.220628 131.22433 \nL 376.455338 131.235302 \nL 392.852033 131.220239 \nL 399.41071 131.219858 \nL 399.41071 131.219858 \n\" clip-path=\"url(#pe530d5151b)\" style=\"fill: none; stroke: #9467bd; stroke-width: 1.5; stroke-linecap: square\"/>\n   </g>\n   <g id=\"line2d_20\">\n    <path d=\"M 74.756165 131.795569 \nL 76.395834 130.321264 \nL 78.035504 129.903521 \nL 79.675173 128.256685 \nL 81.314842 127.051713 \nL 82.954512 126.528285 \nL 84.594181 127.189726 \nL 86.233851 129.478976 \nL 87.87352 133.627913 \nL 89.51319 139.592342 \nL 91.152859 147.080696 \nL 94.432198 164.796508 \nL 97.711537 183.067726 \nL 99.351206 191.51934 \nL 100.990876 199.229617 \nL 102.630545 206.088877 \nL 104.270214 212.046296 \nL 105.909884 217.086334 \nL 107.549553 221.203252 \nL 110.828892 227.770898 \nL 112.468561 235.49186 \nL 114.108231 235.644528 \nL 115.7479 238.229679 \nL 117.38757 232.146569 \nL 119.027239 224.682116 \nL 122.306578 214.546819 \nL 123.946247 213.873498 \nL 125.585917 212.653515 \nL 127.225586 211.673092 \nL 128.865256 211.249569 \nL 130.504925 211.427616 \nL 132.144595 212.144873 \nL 133.784264 213.309602 \nL 135.423933 214.830828 \nL 137.063603 216.626041 \nL 140.342942 220.716486 \nL 141.982611 222.808631 \nL 143.62228 224.714675 \nL 145.26195 226.14216 \nL 146.901619 228.21074 \nL 148.541289 235.500164 \nL 150.180958 234.46049 \nL 151.820628 237.931335 \nL 153.460297 231.737416 \nL 155.099966 223.066597 \nL 158.379305 227.092539 \nL 160.018975 226.797601 \nL 163.298314 230.099127 \nL 164.937983 232.410878 \nL 166.577652 237.362678 \nL 168.217322 235.324851 \nL 169.856991 239.722045 \nL 171.496661 237.906461 \nL 174.775999 223.564156 \nL 176.415669 224.698745 \nL 178.055338 226.57018 \nL 179.695008 226.227322 \nL 181.334677 228.355578 \nL 184.614016 231.508277 \nL 186.253685 237.665035 \nL 187.893355 236.994093 \nL 189.533024 235.175614 \nL 191.172694 231.741209 \nL 192.812363 237.611837 \nL 194.452033 233.19795 \nL 196.091702 223.055618 \nL 197.731371 233.070301 \nL 199.371041 231.810523 \nL 201.01071 233.168948 \nL 202.65038 233.919143 \nL 204.290049 232.972503 \nL 205.929718 237.588282 \nL 207.569388 231.931857 \nL 209.209057 222.648806 \nL 210.848727 233.306929 \nL 212.488396 231.589551 \nL 214.128066 233.931552 \nL 215.767735 234.799093 \nL 217.407404 235.29799 \nL 219.047074 237.034082 \nL 220.686743 232.430469 \nL 222.326413 225.025713 \nL 223.966082 233.802215 \nL 225.605752 231.401963 \nL 227.245421 234.601924 \nL 228.88509 232.92634 \nL 230.52476 236.914486 \nL 232.164429 232.284601 \nL 233.804099 234.984251 \nL 235.443768 230.528751 \nL 237.083438 232.125962 \nL 238.723107 234.576573 \nL 240.362776 231.791683 \nL 242.002446 231.389533 \nL 243.642115 232.505215 \nL 245.281785 232.135301 \nL 246.921454 234.637559 \nL 248.561123 232.711234 \nL 250.200793 229.0246 \nL 251.840462 231.835568 \nL 253.480132 231.167759 \nL 255.119801 233.802274 \nL 256.759471 234.68686 \nL 258.39914 234.984773 \nL 260.038809 233.397921 \nL 261.678479 236.035169 \nL 263.318148 236.067792 \nL 264.957818 235.833282 \nL 266.597487 232.18503 \nL 268.237157 230.87454 \nL 269.876826 233.220221 \nL 271.516495 232.526154 \nL 273.156165 231.610515 \nL 274.795834 235.591111 \nL 276.435504 232.868665 \nL 278.075173 235.907883 \nL 279.714842 233.532756 \nL 281.354512 231.403773 \nL 282.994181 232.156412 \nL 284.633851 233.456576 \nL 286.27352 231.421849 \nL 287.91319 233.260198 \nL 289.552859 234.382296 \nL 291.192528 234.352929 \nL 292.832198 235.500038 \nL 294.471867 232.660118 \nL 296.111537 230.886202 \nL 297.751206 232.196703 \nL 299.390876 231.049408 \nL 301.030545 234.068755 \nL 302.670214 236.026662 \nL 304.309884 236.471682 \nL 305.949553 233.824518 \nL 307.589223 235.79372 \nL 309.228892 231.380402 \nL 312.508231 233.410475 \nL 314.1479 233.61529 \nL 315.78757 235.393366 \nL 317.427239 232.413553 \nL 319.066909 231.566074 \nL 320.706578 232.92025 \nL 322.346247 231.350362 \nL 323.985917 235.722802 \nL 325.625586 236.441116 \nL 327.265256 236.189257 \nL 328.904925 234.663081 \nL 330.544595 234.027076 \nL 332.184264 231.677591 \nL 333.823933 232.873949 \nL 335.463603 232.633288 \nL 337.103272 231.99891 \nL 338.742942 230.307331 \nL 340.382611 234.819244 \nL 342.02228 232.925441 \nL 343.66195 229.567544 \nL 345.301619 232.334174 \nL 346.941289 231.376286 \nL 348.580958 234.33587 \nL 350.220628 236.327973 \nL 351.860297 234.446595 \nL 353.499966 236.050886 \nL 355.139636 232.451707 \nL 356.779305 230.182946 \nL 358.418975 232.759502 \nL 360.058644 231.176762 \nL 361.698314 235.259966 \nL 363.337983 234.229072 \nL 364.977652 234.914643 \nL 366.617322 232.706517 \nL 368.256991 235.47754 \nL 369.896661 234.02835 \nL 371.53633 230.425848 \nL 373.175999 233.048827 \nL 374.815669 232.563124 \nL 376.455338 232.609849 \nL 378.095008 231.437724 \nL 379.734677 234.026562 \nL 381.374347 236.25492 \nL 383.014016 234.442235 \nL 384.653685 235.351729 \nL 387.933024 231.176838 \nL 389.572694 230.381313 \nL 391.212363 230.874741 \nL 392.852033 229.723986 \nL 394.491702 232.877872 \nL 396.131371 234.585427 \nL 397.771041 235.12494 \nL 399.41071 235.300094 \nL 399.41071 235.300094 \n\" clip-path=\"url(#pe530d5151b)\" style=\"fill: none; stroke: #8c564b; stroke-width: 1.5; stroke-linecap: square\"/>\n   </g>\n   <g id=\"patch_3\">\n    <path d=\"M 58.523438 273.312 \nL 58.523438 7.2 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n   </g>\n   <g id=\"patch_4\">\n    <path d=\"M 415.643438 273.312 \nL 415.643438 7.2 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n   </g>\n   <g id=\"patch_5\">\n    <path d=\"M 58.523438 273.312 \nL 415.643438 273.312 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n   </g>\n   <g id=\"patch_6\">\n    <path d=\"M 58.523438 7.2 \nL 415.643438 7.2 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n   </g>\n   <g id=\"legend_1\">\n    <g id=\"patch_7\">\n     <path d=\"M 339.67 103.26875 \nL 408.643438 103.26875 \nQ 410.643438 103.26875 410.643438 101.26875 \nL 410.643438 14.2 \nQ 410.643438 12.2 408.643438 12.2 \nL 339.67 12.2 \nQ 337.67 12.2 337.67 14.2 \nL 337.67 101.26875 \nQ 337.67 103.26875 339.67 103.26875 \nz\n\" style=\"fill: #ffffff; opacity: 0.8; stroke: #cccccc; stroke-linejoin: miter\"/>\n    </g>\n    <g id=\"line2d_21\">\n     <path d=\"M 341.67 20.298437 \nL 351.67 20.298437 \nL 361.67 20.298437 \n\" style=\"fill: none; stroke: #1f77b4; stroke-width: 1.5; stroke-linecap: square\"/>\n    </g>\n    <g id=\"text_17\">\n     <!-- N=0.1s -->\n     <g transform=\"translate(369.67 23.798437) scale(0.1 -0.1)\">\n      <defs>\n       <path id=\"DejaVuSans-4e\" d=\"M 628 4666 \nL 1478 4666 \nL 3547 763 \nL 3547 4666 \nL 4159 4666 \nL 4159 0 \nL 3309 0 \nL 1241 3903 \nL 1241 0 \nL 628 0 \nL 628 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-3d\" d=\"M 678 2906 \nL 4684 2906 \nL 4684 2381 \nL 678 2381 \nL 678 2906 \nz\nM 678 1631 \nL 4684 1631 \nL 4684 1100 \nL 678 1100 \nL 678 1631 \nz\n\" transform=\"scale(0.015625)\"/>\n      </defs>\n      <use xlink:href=\"#DejaVuSans-4e\"/>\n      <use xlink:href=\"#DejaVuSans-3d\" x=\"74.804688\"/>\n      <use xlink:href=\"#DejaVuSans-30\" x=\"158.59375\"/>\n      <use xlink:href=\"#DejaVuSans-2e\" x=\"222.216797\"/>\n      <use xlink:href=\"#DejaVuSans-31\" x=\"254.003906\"/>\n      <use xlink:href=\"#DejaVuSans-73\" x=\"317.626953\"/>\n     </g>\n    </g>\n    <g id=\"line2d_22\">\n     <path d=\"M 341.67 34.976562 \nL 351.67 34.976562 \nL 361.67 34.976562 \n\" style=\"fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square\"/>\n    </g>\n    <g id=\"text_18\">\n     <!-- N=0.2s -->\n     <g transform=\"translate(369.67 38.476562) scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-4e\"/>\n      <use xlink:href=\"#DejaVuSans-3d\" x=\"74.804688\"/>\n      <use xlink:href=\"#DejaVuSans-30\" x=\"158.59375\"/>\n      <use xlink:href=\"#DejaVuSans-2e\" x=\"222.216797\"/>\n      <use xlink:href=\"#DejaVuSans-32\" x=\"254.003906\"/>\n      <use xlink:href=\"#DejaVuSans-73\" x=\"317.626953\"/>\n     </g>\n    </g>\n    <g id=\"line2d_23\">\n     <path d=\"M 341.67 49.654687 \nL 351.67 49.654687 \nL 361.67 49.654687 \n\" style=\"fill: none; stroke: #2ca02c; stroke-width: 1.5; stroke-linecap: square\"/>\n    </g>\n    <g id=\"text_19\">\n     <!-- N=1.0s -->\n     <g transform=\"translate(369.67 53.154687) scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-4e\"/>\n      <use xlink:href=\"#DejaVuSans-3d\" x=\"74.804688\"/>\n      <use xlink:href=\"#DejaVuSans-31\" x=\"158.59375\"/>\n      <use xlink:href=\"#DejaVuSans-2e\" x=\"222.216797\"/>\n      <use xlink:href=\"#DejaVuSans-30\" x=\"254.003906\"/>\n      <use xlink:href=\"#DejaVuSans-73\" x=\"317.626953\"/>\n     </g>\n    </g>\n    <g id=\"line2d_24\">\n     <path d=\"M 341.67 64.332812 \nL 351.67 64.332812 \nL 361.67 64.332812 \n\" style=\"fill: none; stroke: #d62728; stroke-width: 1.5; stroke-linecap: square\"/>\n    </g>\n    <g id=\"text_20\">\n     <!-- N=1.2s -->\n     <g transform=\"translate(369.67 67.832812) scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-4e\"/>\n      <use xlink:href=\"#DejaVuSans-3d\" x=\"74.804688\"/>\n      <use xlink:href=\"#DejaVuSans-31\" x=\"158.59375\"/>\n      <use xlink:href=\"#DejaVuSans-2e\" x=\"222.216797\"/>\n      <use xlink:href=\"#DejaVuSans-32\" x=\"254.003906\"/>\n      <use xlink:href=\"#DejaVuSans-73\" x=\"317.626953\"/>\n     </g>\n    </g>\n    <g id=\"line2d_25\">\n     <path d=\"M 341.67 79.010937 \nL 351.67 79.010937 \nL 361.67 79.010937 \n\" style=\"fill: none; stroke: #9467bd; stroke-width: 1.5; stroke-linecap: square\"/>\n    </g>\n    <g id=\"text_21\">\n     <!-- N=1.8s -->\n     <g transform=\"translate(369.67 82.510937) scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-4e\"/>\n      <use xlink:href=\"#DejaVuSans-3d\" x=\"74.804688\"/>\n      <use xlink:href=\"#DejaVuSans-31\" x=\"158.59375\"/>\n      <use xlink:href=\"#DejaVuSans-2e\" x=\"222.216797\"/>\n      <use xlink:href=\"#DejaVuSans-38\" x=\"254.003906\"/>\n      <use xlink:href=\"#DejaVuSans-73\" x=\"317.626953\"/>\n     </g>\n    </g>\n    <g id=\"line2d_26\">\n     <path d=\"M 341.67 93.689062 \nL 351.67 93.689062 \nL 361.67 93.689062 \n\" style=\"fill: none; stroke: #8c564b; stroke-width: 1.5; stroke-linecap: square\"/>\n    </g>\n    <g id=\"text_22\">\n     <!-- N=2.1s -->\n     <g transform=\"translate(369.67 97.189062) scale(0.1 -0.1)\">\n      <use xlink:href=\"#DejaVuSans-4e\"/>\n      <use xlink:href=\"#DejaVuSans-3d\" x=\"74.804688\"/>\n      <use xlink:href=\"#DejaVuSans-32\" x=\"158.59375\"/>\n      <use xlink:href=\"#DejaVuSans-2e\" x=\"222.216797\"/>\n      <use xlink:href=\"#DejaVuSans-31\" x=\"254.003906\"/>\n      <use xlink:href=\"#DejaVuSans-73\" x=\"317.626953\"/>\n     </g>\n    </g>\n   </g>\n  </g>\n </g>\n <defs>\n  <clipPath id=\"pe530d5151b\">\n   <rect x=\"58.523438\" y=\"7.2\" width=\"357.12\" height=\"266.112\"/>\n  </clipPath>\n </defs>\n</svg>\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "steps = 199\n",
    "dt = 0.05\n",
    "time = np.linspace(0,steps*dt, num=steps)\n",
    "\n",
    "# plt.style.use(\"ggplot\")\n",
    "\n",
    "for i, J in enumerate(J_sim_results):\n",
    "  plt.plot(time, J, label='N={:.1f}s'.format(N_values[i]))\n",
    "plt.legend()\n",
    "plt.xlabel(\"Time [s]\")\n",
    "plt.ylabel(\"Cost\")\n",
    "\n",
    "plt.show()\n",
    "# tikzplotlib.save(\"results/plots/cost_for_different_horizon_lengths.tex\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "u_lim = 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# N_values = [0.1, 0.2, 1.0, 1.8, 2.1]\n",
    "\n",
    "# x_sim_results = []\n",
    "# u_sim_results = []\n",
    "# J_sim_results = []\n",
    "\n",
    "# for i, N in enumerate(N_values):\n",
    "#   print('Calculating for N={:.2f}s'.format(N))\n",
    "#   x_sim, u_sim, J_sim = simulate(sim=sim,steps=200, N=N, u_lim=8)\n",
    "  \n",
    "#   x_sim_results.append(x_sim)\n",
    "#   u_sim_results.append(u_sim)\n",
    "#   J_sim_results.append(J_sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for i, J in enumerate(J_sim_results):\n",
    "#   plt.plot(J, label='N={:.2f}s'.format(N_values[i]))\n",
    "# plt.legend()\n",
    "# plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Animate and save"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "MovieWriter imagemagick unavailable; using Pillow instead.\n",
      "MovieWriter imagemagick unavailable; using Pillow instead.\n"
     ]
    }
   ],
   "source": [
    "plotter = Plotter\n",
    "\n",
    "for i, x_sim in enumerate(x_sim_results):\n",
    "  anim = plotter.animate_pendulum(x_sim[:,0], x_sim[:,1], model_params_sim.L1, model_params_sim.L2, dt=0.05)\n",
    "  f = r\"results/animations/animation-N-{}.gif\".format(int(N_values[i]*10))\n",
    "  anim.save(f, writer='imagemagick', fps=20)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Mismatch Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# mismatch_values = [0.0001, 0.001, 0.01, 0.1]\n",
    "\n",
    "# x_sim_mismatched_results = []\n",
    "# u_sim_mismatched_results = []\n",
    "# J_sim_mismatched_results = []\n",
    "\n",
    "# for i, mismatch in enumerate(mismatch_values):\n",
    "#   print('Calculating for mismatch={:f}'.format(mismatch))\n",
    "\n",
    "#   m1 = 0.5 + mismatch\n",
    "#   m2 = 0.5 - mismatch\n",
    "#   L1 = 0.5 + mismatch\n",
    "#   L2 = 0.5 - mismatch\n",
    "#   l2 = 0.5*L2\n",
    "#   l1 = 0.5*L1\n",
    "#   I1 = m1*l1**2\n",
    "#   I2 = m2*l2**2\n",
    "#   f1 = 0.1\n",
    "#   f2 = 0.1\n",
    "  \n",
    "#   model_params_mismatched = ModelParameters\n",
    "\n",
    "#   model_params_mismatched.m1 = m1\n",
    "#   model_params_mismatched.m2 = m2\n",
    "#   model_params_mismatched.L1 = L1\n",
    "#   model_params_mismatched.L2 = L2\n",
    "#   model_params_mismatched.l1 = l2\n",
    "#   model_params_mismatched.l2 = l1\n",
    "#   model_params_mismatched.I1 = I1\n",
    "#   model_params_mismatched.I2 = I2\n",
    "#   model_params_mismatched.f1 = f1\n",
    "#   model_params_mismatched.f2 = f2\n",
    "\n",
    "#   sim_mismatch = Simulator(dt=0.05)\n",
    "#   sim_mismatch.set_model_params(model_parameters=model_params_mismatched)\n",
    "\n",
    "#   x_sim, u_sim, J_sim = simulate(sim=sim_mismatch, N=1.0)\n",
    "\n",
    "#   x_sim_results.append(x_sim)\n",
    "#   u_sim_results.append(u_sim)\n",
    "#   J_sim_results.append(J_sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for i, J in enumerate(J_sim_results[-4:]):\n",
    "#   plt.plot(J, label='mismatch={:.2f}s'.format(mismatch_values[i]))\n",
    "# plt.legend()\n",
    "# plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'model_params_mismatched' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [13], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m x_sim\u001b[39m=\u001b[39mx_sim_results[\u001b[39m-\u001b[39m\u001b[39m1\u001b[39m]\n\u001b[0;32m----> 2\u001b[0m \u001b[39mprint\u001b[39m(model_params_mismatched\u001b[39m.\u001b[39mL1)\n\u001b[1;32m      3\u001b[0m plotter \u001b[39m=\u001b[39m Plotter\n\u001b[1;32m      4\u001b[0m anim \u001b[39m=\u001b[39m plotter\u001b[39m.\u001b[39manimate_pendulum(x_sim[:,\u001b[39m0\u001b[39m], x_sim[:,\u001b[39m1\u001b[39m], \u001b[39m0.6\u001b[39m, \u001b[39m0.4\u001b[39m, dt\u001b[39m=\u001b[39m\u001b[39m0.05\u001b[39m)\n",
      "\u001b[0;31mNameError\u001b[0m: name 'model_params_mismatched' is not defined"
     ]
    }
   ],
   "source": [
    "x_sim=x_sim_results[-1]\n",
    "print(model_params_mismatched.L1)\n",
    "plotter = Plotter\n",
    "anim = plotter.animate_pendulum(x_sim[:,0], x_sim[:,1], 0.6, 0.4, dt=0.05)\n",
    "anim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "MovieWriter imagemagick unavailable; using Pillow instead.\n"
     ]
    }
   ],
   "source": [
    "# f = r\"results/animations/animation.gif\" \n",
    "\n",
    "# anim.save(f, writer='imagemagick', fps=20)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.9.15"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "e5f612b63848b98226aeead1cb489ad5e5d11deefbf43212d00d6d4334fa6b93"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}