{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams[\"font.family\"] = \"Times New Roman\"\n",
    "plt.rcParams[\"font.size\"] = 16\n",
    "\n",
    "g_label_fontsize = 16\n",
    "\n",
    "colors = [\n",
    "    \"#5D7599\",\n",
    "    \"#233142\",\n",
    "    \"#F95959\",\n",
    "]\n",
    "\n",
    "edgecolors = [\n",
    "    \"#FFFFFF\",\n",
    "    \"#FFFFFF\",\n",
    "    \"#FFFFFF\",\n",
    "]\n",
    "\n",
    "hatches = [\"\\\\\\\\\", \"\", \"\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "data": {
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FxcUxfPjwSCQS0bVr17jtttu2ynMBAIDKcmnPMXny5KT1gQMHRtOmTWP+/Pnx3//937HzzjvH6aefHpMmTYp33nknli9fHhs3bowvvvgiZs+eHVdccUX06tUrTj/99CoB2QAAQN3l0r7j35o0aRKPPvpo7LfffknPb9q0Kc4666z4n//5nygvL49ly5bFkUceGe+//34UFhbGxIkT4/777/cLeAAAgIioft8UEdG5c+eU+6b774htiaAIarR48eKk9fpupqv7wWiMDwZzYQ0AAJCrvK9XNm3atErHp556avTq1Ss9wwAAQI7I1X3HOeecE0uWLIn8/Py49957Y/vtt98qzwUAACrLlT1HeXl5PP7440nPHXrooXHhhRfGvvvuG3feeWds2LAhWrZsGV27do3WrVtX2/O+++6LHj16xOzZsxtlZgAA2Fbkyr7jm9q0aRPPPfdc7L///tVec+2118bgwYPju9/9bsybNy8OPPDAePPNN+P888/fKjMCAADZobp9U0T99k7p3jdtiaAIarR27dqk9cb6A4XqnlcfubAGAADIVd7X/5/169fHY489VnHcpEmT+N3vfpfGiQAAIDfk4r7j7rvvjgcffDAiIkaPHh3f/e53G/2ZAABAcrmy55gzZ06sWbMm6blf/vKXMXHixGjXrl2MHTs25s6dG+vXr4/PPvss1q5dG++9915ceOGFsd1221W5d/Xq1TFgwICYMWNGo8wNAADbglzZdyTToUOHeOGFF6Jfv37VXvPUU0/FwoUL4/DDD49Zs2ZFjx49ttp8AABAdtjSPqZ58+Yp982EfVN1BEVQo6+//jppvT4/FBERBQUFSeulpaX16ptMLqwBAABylff1/+fuu++u9IcFo0aNit133z2NEwEAQG7ItX1HUVFRXHDBBRER0bdv3xg/fnyjPg8AANiyXNlzvPDCC1s8P3bs2Pj0009j3Lhxse+++1Y6t88++8RNN90UM2fOjPbt21e5d/369XHSSSfFF1980aAzAwDAtiJX9h3Vadu2bbzwwgvxwx/+cIvXzZgxI84777zYtGnTVpoMAADIFtXtm5o1axZ5eXkp982UfVMygiKoUXU/GPVNnty8eXPS+saNG+vVN5lcWAMAAOQq7+v/snHjxrj22msrjrt37x5jx45N40QAAJA7cmnfUV5eHsOGDYu1a9dGy5Yt47777osmTZo02vMAAICa5cqe4+23305aP+igg+L999+PcePGRcuWLbfYo1+/fvHUU09F06ZNq5xbuXJlDBs2rCFGBQCAbU6u7Du2pHnz5vHwww/HWWedtcXrbr/99jjyyCNjxYoVW2kyAAAgG2wL+6ZvEhRBjRKJRNJ6fZMny8vLk9YLCwvr1TeZXFgDAADkKu/r/3LHHXdEUVFRRPwrcfLOO+/M2FkBACDb5NK+4/e//338/e9/j4iIm266Kfbcc89GexYAAFA7ubLn+OCDD5LWBw8eHF27dq11n4MPPjguu+yypOemT58e06dPT2k+AADYluXKvqMmM2bMiCeffDKaNGkS/fr1q/a6V155JQ455JD46KOPtuJ0AABAJttW9k3/SVAENWrVqlWj9C0pKUlar28ySzK5sAYAAMhV3tcjVq9eHWPHjq04Hj9+fHznO99J40QAAJBbcmXf8cYbb8T48eMjIuLEE0+s8TdqAQAAW0eu7DkWLFiQtN6tW7c697rkkkuiXbt2Sc9dffXVde4HAADbulzZd2zJddddF8ccc0wUFxfHI488Eq+88kr86le/qvb6Tz75JA455JCYNWvWVpwSAADIVNvCvumbBEVQo9atWyetV/d/7NoqLS1NWq9vMksyubAGAADIVd7XIy666KJYs2ZNRER873vfi1//+tdpnggAAHJLLuw7vv766zjttNNi06ZN8a1vfSv++Mc/NvgzAACA1OTCnmPTpk2xbt26pOe+9a1v1blfy5Yt47zzzkt67vnnn6/4XAQAAKidXNh3VGfz5s3xi1/8IkaNGhXl5eUxadKkGDx4cOTn58dVV10Vf/rTn6Jp06ZJ712zZk0cd9xx8dprr221eQEAgMyUy/um6giKoEaN9YOxfv36pPW2bdvWq28yubAGAADIVdv6+/rjjz8e99xzT0RE7LrrrnHvvfdGXl5emqcCAIDckgv7josvvjg++uijyMvLiz/96U/V/mZeAABg68uFPUd1IREREZ07d06p51lnnZW0nkgkYubMmSn1BACAbVUu7DuS2bx5c5xyyilx2223RUTEiBEj4rTTTqt0zU9+8pN49tlnq51p7dq1cdxxx8W7777b2OMCAAAZLFf3TVsiKIIa7bDDDknr9f3BWLt2bdL6LrvsUq++yeTCGgAAIFdty+/rixcvjjPPPDMiItq1axdPP/10tG/fPs1TAQBA7sn2fceTTz4Zt99+e0REXHLJJTFgwIAG7Q8AANRPtu85IiK+/vrras+l+tnFLrvsEvvuu2/Sc//4xz9S6gkAANuqXNh3fFMikYjhw4fHww8/HBERu+22W1x11VVJrz388MPj5Zdfji5duiQ9v27duhg0aFAUFxc32rwAAEBmy8V9U00ERVCj7t27J61Xl4BSW19++WXSeteuXevVN5lcWAMAAOSqbfV9fdOmTXHKKafE6tWro2nTpjF16tRq/1sAAAD1k+37jv/8LbzXXXdd5OXlpfTPT3/606T9q7seAAConWzfc0REbLfddtWea9OmTcp9jzvuuKT1ZcuWpdwTAAC2Rbmw7/imK6+8Mu67776K4//93/+NwsLCaq/v2bNnvPzyy9GtW7ek5z/77LMYNWpUQ48JAABkier2TZs3b65XWEQmfzdFUAQ16tGjR9L6ypUro6ysLOW+K1euTFqvbtNeH7mwBgAAyFXb6vv6BRdcEK+88krk5+fH3XffHf3790/3SAAAkLOyfd+xYsWKBu0HAAA0rGzfc0REtGzZstpzTZs2Tblvr169ktZXr16dck8AANgW5cK+4z/94x//iDFjxlQcf+tb34qhQ4fWeN9uu+0WL774YrVfyLrrrrvizTffbLA5AQCA7PHtb3+72vDrpUuXptw3k7+bIiiCGrVr1y46d+5cpV5eXh5ffPFFyn2XL1+etN6nT5+Ue1YnF9YAAAC5alt8X7/lllvi9ttvj4iIiRMnxsknn5zmiQAAILdti/sOAABg68mFPUerVq2qDYsoLS1NuW91X2bbuHFjyj0BAGBblAv7jv90wQUXRHl5ecXxiSeeGE2aNKnVvd26dYtnn302OnTokPT8dddd1yAzAgAA2WefffZJWl+yZEnKPTP574gJiqBWevfunbS+ePHilPqVlJTEqlWrqtR33HHH2H333VPqWZNcWAMAAOSqbel9/YknnogRI0ZERMT48ePj3HPPTes8AACwrdiW9h0AAMDWlwt7jt122y1pfc2aNSn37NSpU9J6+/btU+4JAADbqlzYd0REvPTSS/H6669Xqg0YMKBOPbp37x6PPPJI0nCJqVOnxoYNG+o1IwAAkJ0aet8UEfH5559XqeXn58dBBx2Ucs+GIiiCWvn+97+ftP7pp5+m1K+oqChpvV+/fin1q41cWAMAAOSqbeV9fdasWXHKKafE5s2bY8SIETFmzJi0zgMAANuSbWXfAQAApEcu7Dl69uyZtJ7qGiIiWrdunbRe3W/+BQAAqpcL+46IiPvuu69Krbr9yJb0///Zu/PoKut7X/yfEDQBFHFikrkqCAoowqEOIFLpEYWiQqx34UG013LUVttq9dRq9aqtw8VZemyVUhwrFNA6ccSi0iJFAUEqKKARkTLIzBHCkP37o+vkZ+7egeydhOTB12st1uL73vv5PJ+Niy6eBt7p0yduueWWtLykpCRmzpyZy2oAAEDCVfdz07Zt22LNmjVpeZcuXSr8Gsi+pCiCShk8eHDGfO7cuTnNW7JkScZ80KBBOc2rjP3hMwAAwP7q6/Dn9YULF8bAgQPjyy+/jBEjRsR9991Xa7sAAMDXUZKfO1KpVLX8+N3vfpfVfAAAoPKS/MzxP0499dSM+cKFC3Oe2ahRo4x5Lv8IDAAAvu72h+eOiIgZM2akZc2bN89p1nXXXRdt27ZNy5cuXZrTPAAAINnOOuusKCwsTMtzfW5aunRpxr9HVVf+LbmiCCqlffv20aVLl7R8zpw5Oc1bsGBBWla/fv04//zzc5pXGfvDZwAAgP3V/v7n9WXLlsW3v/3t2LBhQ5x33nnx+OOPR15eXq3sAgAAX1f7+3MHAABQu/aHZ46zzjorY/63v/0t55lbt27NmJ9++uk5zwQAgK+r/eG5IyJixYoVaVmmf8hVGQceeGBccsklafn69etzmgcAACRbw4YNo3///ml5dT43RURceOGFOc2rbooiqLSLL744LZs3b15O31EqU/PKWWedFYcffnhOu1XW/vAZAABgf7W//nn9008/jTPPPDNWrlwZAwYMiGeeeSby8/P3+R4AAMD++9wBAADUDUl/5jj22GOje/fuafm0adNynrlx48a0rGXLltGpU6ecZwIAwNdZ0p87IiLjrpmeHSqrT58+aVmTJk1yngcAACRbpuem4uLinArlMj03HXfccdG1a9ecdqtuiiKotFGjRkXjxo3LZZs2bYpZs2ZlPeuvf/1rWnbNNdfkulql7Q+fAQAA9lf745/XP/vsszjzzDNj+fLlcfrpp8fkyZOjoKCgSjPvuuuuKv2FTAAA+DrbH587AACAumN/eOb43ve+l5Z99tlnFX7HrL1ZvHhxpe4BAABUzv7w3NG8efO0bNWqVTnPO+qoo9KyFi1a5DwPAABItqFDh0aHDh3S8qlTp2Y96y9/+UtaVpf+jpiiCCrtkEMOiVGjRqXlkydPzmrOnDlzYvXq1eWyk046KQYMGFCl/Spjf/gMAACwv9rf/rz+6aefRt++fePjjz+OXr16xUsvvRQNGzas0sxHH300brjhBt+hGAAAcrS/PXcAAAB1y/7wzDFy5Mg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lEfvss0+W0wAAwJdDS33nqKioiCOPPLJeScTEiROVRAAAwHaW7+8d//Vf/1VbEhERcdppp6VUEhER0aFDhzjjjDPqzG688cY6v8gFAACkr02bNvHBBx/EQw89FKNHj44DDzwwzjjjjJgyZUq2ozXK3XffXackIiLiZz/72TZLIiIi/u3f/i1OOumkOrNzzjknVq5c2aQZM6UogpSUlZXFhAkT6sz23nvvGDp0aKN3nH322XWOFy5cGJMmTWqSfI3REu4BAABaqnz+eX3t2rW1/8CjX79+8fLLL8dZZ521zT983XXXXePBBx+MCy+8sMHv/O53v4vy8vImzQsAAF9W+fzekarZs2fHVVddFRH/918RGzNmTHYDAQDAl0BLfedYv359fOtb34p//OMfdeYXXnhhXHzxxVlKBQAAX075/t5RUVERTz31VJ1ZKtm/6IgjjqhzvGrVqnj++efTjQYAAPyLDh061JuNHDmyUSV12bRu3bp6/65U586d4/TTT2/0jn99b1qzZk388pe/bIp4TUZRBCm5+uqro7Kyss7sxBNPTGnHqFGjorCwsN7eNWvWZJyvMVrCPQAAQEuVzz+v33///VFZWRndu3ePp556Kvr06dPocwsKCmLy5Mlx/PHHJ/28uro6Zs6c2URJAQDgyy2f3ztSsX79+hg9enRs2bIlSkpK4s4774xWrfzRIAAANLeW+M5RWVkZxx9/fL2SiBEjRmS9wAIAAL6M8v2944UXXojPP/+8zqxz585p7erVq1e92cKFC9PaBQAANE779u2ja9eu2Y6xVVOnTq33H+scPnx4FBUVNXrHUUcdVe8+b7/99nj77bebJGNT8G+D0WjLly+P6dOn15uPGDEipT0lJSUxcODAOrP169fHLbfckkm8RmkJ9wAAAC1Vvv+8fu+990ZExB133BG77bZbyucXFBTEtGnTkjZuRkQ8/fTTGeUDAADy/70jFRdeeGG8//77ERHxP//zP9GzZ88sJwIAgJavpb5z/PCHP6z3X+T92te+Fvfcc49COgAA2M5awnvH0qVL682WL1+e1q5k/67VJ598ktYuAACg8Tp16pTtCA3atGlT0qLrVN+bWrVqFUcccUSd2ZYtW2Ly5MkZpGta/pSGRvv9738fVVVVdWZt27aN/fffP+VdRx55ZL3Z1KlTo6amJu18jdES7gEAAFqqfP55fcuWLfHSSy/Ft7/97TjmmGPS3tOlS5f40Y9+lPSzZH9ACgAApCaf3ztS8ac//an2XxIdPXp0nHrqqdkNBAAAXxIt8Z3jd7/7XdJfQvuf//mfaN++/XbNAgAAtIz3joqKinqzl19+Oa1d69evrzfr1q1bWrsAAIDGa9u2bbYjNOi+++6LVatW1ZsfeuihKe9K9t505513xtq1a9PK1tQURdBo//yv437RPvvsE4WFhSnvGjx4cL3Z0qVL44UXXkgrW2O1hHsAAICWKp9/Xn/nnXfis88+i0suuSTjXaNGjUo6T/YPKgAAgNTk83tHYy1fvjzOOeeciIjo06dP3HTTTVnNAwAAXyYt7Z3j3XffjTFjxtSbf/e7341hw4ZttxwAAMD/ryW8d5SUlNSb3XvvvfUKMBpj4cKF9Wbf+MY30okFAACkoE2bNtmO0KB77rmn3qxr167Ro0ePlHcle2/atGlTzJw5M51oTU5RBI3y+uuvxzvvvFNvvu+++6a1b88990w6f+CBB9La1xgt4R4AAKClyvef14uKimLKlClx2GGHZbzrgAMOiOLi4nrzXG7cBACAfJDv7x2NkUgk4swzz4xPPvkkCgsL4w9/+EN07Ngxa3kAAODLpKW9cyQSiTjnnHPq/aJWhw4dYtKkSdslAwAAUFdLee/Ya6+96s0qKiri2muvTXnXc889V+f4kEMOib7/X3t3HmRVeeYP/GlAGmkxLKIskS0mJBDQRFFcAJEBFAdGDY5agsg4mWDEYGIYcWMx6iSliWWRpHRCEImUFUaEoEYRBIEoiGIUGVEg0sgmshmglEW6f39Y0z879zZ9+3Y33ff051PlH+c59zznfdVLnS+3+7lf/3rWawMAADJTr17tHFGwc+fOeOmll1Lq2eamzp07p91rbfld8tr5X4Fa54UXXkhbb9++fVb9TjvttGjYsGFKfeHChVn1y0QS9gAAAEmV68/rp512WowePbpKetWrVy/tpMpWrVpVSX8AAKircj13ZOLhhx+O+fPnR0TEXXfdFeeee26NrQUAAOqapGWOadOmxZIlS1LqN954Y7Rs2fKYrAEAACgtKbnjnHPOiYKCgpT6fffdF6tXr864z4EDB2LmzJmlauPHj6/0+gAAgPLVr1+/ppeQ1oIFC+Lzzz9PqWebm44//vjo0KFDSn3JkiVx5MiRrHpWJYMiyMirr76atv7Vr341q37169ePdu3apdTXrFkTO3fuzKpneZKwBwAASCrP66U1b948pdatW7caWAkAACRH0nPH6tWr4/bbb4+IL74t6+677z7mawAAgLosSZnj8OHDMXHixJR6gwYN4pZbbqnWewMAAGVLSu5o3LhxDB06NKV+8ODBGDRoUGzZsiWjPg899FCpdV5zzTVx8cUXV9k6AQCA3FPVuSkiolOnTim1vXv3xttvv511z6piUAQZWbZsWdp6Zd4Yp5xySkqtuLg43nrrrax7Hk0S9gAAAEnleb20gwcPptT69OlTAysBAIDkSHLuOHjwYFx77bVx4MCBaNKkSTzxxBO1dmo/AAAkVZIyx9SpU+PDDz9MqQ8ZMiTatGlTrfcGAADKlqTccfvtt6f9LGPTpk1x0UUXxfr16496/Ztvvhn33HNPyfF3v/vdmDJlSpWvEwAAyC3VMSgiXW6K+CKX1DSDIijXli1bypwGWZk3xsknn5y2/u6772bdsyxJ2AMAACSV5/VUmzdvLnXcuHHj6NevXw2tBgAAcl/Sc8cdd9wRq1atioiIX//612mn2AMAANUnaZnjwQcfTFu//vrrq/W+AABA2ZKWOzp37hx33HFH2nNr166Nnj17xuLFi9Oe37JlS1x22WVx4MCBiIg477zzYsGCBdG4ceNqWy8AAFD7FRUVxTvvvJP2XC7mpkwYFEG5NmzYUOa5yrwxWrZsmba+bt26rHuWJQl7AACApPK8XtrOnTtj+/btpWrXXHONDzIBAKASkpw7XnrppXjooYciIuLqq6+O66677pjdGwAA+EKSMseSJUvSfnNvs2bNYuDAgSXHu3fvjhkzZsQNN9wQp59+erRq1Sry8/OjTZs2cc4558Tdd98dq1evrrZ1AgBAXZOk3PF/xo8fX+aX5+zatSv69+8fU6dOLVXfuXNn9O/fPzZt2hQRX3w2Mn/+/GjWrFm1rxcAAKjdtm7dGocOHUp7LldzU3kMiqBchYWFaesFBQVxwgknZN03Pz8/bf2jjz7KumdZkrAHAABIKs/rpS1ZsqTUcV5eXowZM6aGVgMAAMmQ1NyxZ8+eGDFiRBQXF0e7du3ikUceOSb3BQAASktS5njsscfS1i+99NJo2LBhvPvuu/H9738/vvrVr8awYcNi6tSpsWrVqti+fXscOnQotm3bFitWrIh77703unXrFsOGDUsZkA0AAFRcknLH/2nQoEE8/fTTccYZZ6Q9f/jw4bjhhhviP//zP6OoqCg++uij6Nu3b6xZsyby8/Nj8uTJ8eSTT/oCHgAAICLKzk0REa1atcq6b03/jNjRGBRBuTZv3py2XtkwXdYbozo+GEzCHgAAIKk8r5c2Z86cUsfXXHNNdOvWrWYWAwAACZHU3DFq1KjYsmVL1KtXL5544on4yle+ckzuCwAAlJaUzFFUVBRz585Ne+68886LH/3oR9G9e/eYMmVKfPbZZ1FQUBDt2rWLJk2alNlzxowZ0bVr11ixYkW1rBkAAOqKpOSOf3TiiSfG/Pnz4zvf+U6Zr3nggQdiyJAh0atXr1i9enWcddZZsXLlyhg9evQxWSMAAJAbyspNEZXLTjWdm47GoAjKtXfv3rT16voLhbLuVxlJ2AMAACSV5/X/b//+/fGnP/2p5LhBgwZxzz331OCKAAAgGZKYO6ZPnx4zZ86MiIhx48ZFr169qv2eAABAeknJHH/9619j9+7dac/99Kc/jcmTJ0fz5s1jwoQJ8fbbb8f+/ftj48aNsXfv3vjf//3f+NGPfhTHHXdcyrW7du2Kfv36xeLFi6tl3QAAUBckJXekc9JJJ8XChQujZ8+eZb7mueeei/Xr10efPn1i+fLl0bVr12O2PgAAIDccLcccf/zxWfetDbmpLAZFUK5PP/00bb0yb4qIiPr166etHzx4sFJ900nCHgAAIKk8r/9/06dPL/WXBWPHjo2vfe1rNbgiAABIhqTljsLCwrj55psjIqJHjx4xadKkar0fAABwdEnJHAsXLjzq+QkTJsSGDRti4sSJ0b1791LnunTpEg8//HAsWbIkWrRokXLt/v3748orr4xt27ZV6ZoBAKCuSEruKEvTpk1j4cKFcfnllx/1dYsXL46bbropDh8+fIxWBgAA5IqyclOjRo0iLy8v6761JTelY1AE5SrrjVHZyZNHjhxJWz906FCl+qaThD0AAEBSeV7/wqFDh+KBBx4oOe7cuXNMmDChBlcEAADJkaTcUVRUFMOHD4+9e/dGQUFBzJgxIxo0aFBt9wMAAMqXlMzx1ltvpa2fffbZsWbNmpg4cWIUFBQctUfPnj3jueeei4YNG6ac27FjRwwfPrwqlgoAAHVOUnLH0Rx//PHx1FNPxQ033HDU1z366KPRt2/f+Pjjj4/RygAAgFxQF3LTPzIognIVFxenrVd28mRRUVHaen5+fqX6ppOEPQAAQFJ5Xv/Cf//3f0dhYWFEfDFxcsqUKbV2rQAAkGuSlDv+67/+K/7yl79ERMTDDz8cX//616vtXgAAQGaSkjnee++9tPUhQ4ZEu3btMu5zzjnnxJ133pn23EsvvRQvvfRSVusDAIC6LCm5ozyLFy+OZ599Nho0aBA9e/Ys83WvvPJKnHvuubF27dpjuDoAAKA2qyu56csMiqBcJ5xwQrX0PXDgQNp6ZSezpJOEPQAAQFJ5Xo/YtWtXTJgwoeR40qRJccEFF9TgigAAIFmSkjveeOONmDRpUkREXHHFFeV+oxYAAHBsJCVzrFu3Lm29Q4cOFe516623RvPmzdOe+8UvflHhfgAAUNclJXcczYMPPhj9+/ePPXv2xKxZs+KVV16J2267rczXf/DBB3HuuefG8uXLj+EqAQCA2qou5KZ/ZFAE5WrSpEnaeln/Y2fq4MGDaeuVncySThL2AAAASeV5PeLHP/5x7N69OyIiLr744rjjjjtqeEUAAJAsScgdn376aVx77bVx+PDhaNu2bfzud7+r8nsAAADZSULmOHz4cOzbty/tubZt21a4X0FBQdx0001pzy1YsKDkcxEAACAzScgdZTly5EjceOONMXbs2CgqKoqpU6fGkCFDol69evHzn/88Hn/88WjYsGHaa3fv3h0DBw6MZcuWHbP1AgAAtVOSc1NZDIqgXNX1xti/f3/aetOmTSvVN50k7AEAAJKqrj+vz507N/7whz9ERETHjh3jiSeeiLy8vBpeFQAAJEsScsdPfvKTWLt2beTl5cXjjz9e5jfzAgAAx14SMkdZQyIiIlq1apVVzxtuuCFtvbi4OJYsWZJVTwAAqKuSkDvSOXLkSFx99dXxyCOPRETEmDFj4tprry31muuuuy5efPHFMte0d+/eGDhwYLzzzjvVvVwAAKAWS2puOhqDIihXs2bN0tYr+8bYu3dv2nr79u0r1TedJOwBAACSqi4/r2/evDn+7d/+LSIimjdvHs8//3y0aNGihlcFAADJk+u549lnn41HH300IiJuvfXW6NevX5X2BwAAKifXM0dExKefflrmuWw/u2jfvn1079497bnXXnstq54AAFBXJSF3/KPi4uIYMWJEPPXUUxER0alTp/j5z3+e9rV9+vSJpUuXRps2bdKe37dvXwwePDj27NlTbesFAABqtyTmpvIYFEG5OnfunLZe1gSUTH3yySdp6+3atatU33SSsAcAAEiquvq8fvjw4bj66qtj165d0bBhw5g9e3aZ/y4AAIDKyfXc8eVv4X3wwQcjLy8vq39GjhyZtn9ZrwcAADKT65kjIuK4444r89yJJ56Ydd+BAwemrX/00UdZ9wQAgLooCbnjH91///0xY8aMkuP77rsv8vPzy3z9t7/97Vi6dGl06NAh7fmNGzfG2LFjq3qZAABAjigrNx05cqRSwyJq8++mGBRBubp27Zq2vmPHjvj888+z7rtjx4609bJCe2UkYQ8AAJBUdfV5/eabb45XXnkl6tWrF9OnT4/evXvX9JIAACCxcj13fPzxx1XaDwAAqFq5njkiIgoKCso817Bhw6z7duvWLW19165dWfcEAIC6KAm548tee+21GD9+fMlx27ZtY+jQoeVe16lTp1i0aFGZv5D1+9//PlauXFll6wQAAHLHqaeeWubw661bt2bdtzb/bopBEZSrefPm0apVq5R6UVFRbNu2Leu+27dvT1s/88wzs+5ZliTsAQAAkqouPq//5je/iUcffTQiIiZPnhxXXXVVDa8IAACSrS7mDgAA4NhJQuY44YQTyhwWcfDgwaz7lvXLbIcOHcq6JwAA1EVJyB1fdvPNN0dRUVHJ8RVXXBENGjTI6NoOHTrEiy++GCeddFLa8w8++GCVrBEAAMg9Xbp0SVvfsmVL1j1r88+IGRRBRk4//fS09c2bN2fV78CBA7Fz586UesuWLeNrX/taVj3Lk4Q9AABAUtWl5/VnnnkmxowZExERkyZNih/+8Ic1uh4AAKgr6lLuAAAAjr0kZI5OnTqlre/evTvrnqecckraeosWLbLuCQAAdVUSckdExMsvvxyvv/56qVq/fv0q1KNz584xa9astMMlZs+eHZ999lml1ggAAOSmqs5NERGbNm1KqdWrVy/OPvvsrHtWFYMiyMgll1yStr5hw4as+hUWFqat9+zZM6t+mUjCHgAAIKnqyvP68uXL4+qrr44jR47EmDFjYvz48TW6HgAAqEvqSu4AAABqRhIyx7e//e209Wz3EBHRpEmTtPWyvvkXAAAoWxJyR0TEjBkzUmpl5ZGj6d27d0ycODGlfvDgwXj11VezWRoAAJDjqjo3ffbZZ/Hxxx+n1Lt27VrmZyDHkkERZGTIkCFp62+++WZW/datW5e2Pnjw4Kz6ZSIJewAAgKSqC8/rq1evjkGDBsWnn34aI0aMiIceeqjG1gIAAHVRLueO4uLiKvnnscceq1B/AAAgc7mcOf7P+eefn7a+evXqrHsWFBSkrWfzS2AAAFDXJSF3REQsXbo0pdaqVauseo0dOzbat2+fUl+/fn1W/QAAgNzWv3//aNSoUUo929y0fv36tD9HVVt+l9ygCDLSsWPH6Nq1a0p95cqVWfVbtWpVSq1BgwZxxRVXZNUvE0nYAwAAJFXSn9f/9re/xcCBA2PPnj1x+eWXx+9///vIy8urkbUAAEBdlfTcAQAA1KwkZI7+/funrb/22mtZ99y/f3/aeq9evbLuCQAAdVUSckdExObNm1Nq6X6RKxMNGzaM66+/PqW+e/furPoBAAC5rXHjxtGvX7+UelXmpoiIq666Kqt+Vc2gCDI2fPjwlNpf//rXrL5RKt3klf79+0eLFi2yWlumkrAHAABIqqQ+r2/cuDEuuuii2Lp1awwYMCCefPLJqF+//jFfBwAAkNzcAQAA1A65njm+8Y1vxBlnnJFSX7BgQdY9P/nkk5RamzZt4pvf/GbWPQEAoC7L9dwREWnXmi47ZKp3794ptaZNm2bdDwAAyG3pclNhYWFWA+XS5aZvfetb0b1796zWVtUMiiBjo0aNihNPPLFU7e9//3ssX768wr1eeeWVlNott9yS7dIyloQ9AABAUiXxeX3Tpk1x0UUXxYcffhi9evWK2bNnR35+fqV6/uIXv6jUD2QCAEBdlsTcAQAA1B5JyBz//u//nlLbtGlTmd+YVZ733nsvo3sAAACZSULuaNWqVUrto48+yrpf27ZtU2qtW7fOuh8AAJDbhg4dGp06dUqpz5s3r8K9/vKXv6TUatPPiBkUQca+8pWvxKhRo1Lqs2fPrlCflStXxvbt20vVvvvd78aAAQMqtb5MJGEPAACQVEl7Xt+4cWP06dMnPvjggzj77LPjueeei8aNG1eq56OPPhrjxo3zDcUAAJClpOUOAACgdklC5hg5cmScdNJJKfXp06dn1e/1118vddygQYP4wQ9+kFUvAAAgGbnj7LPPTqktW7Ys634HDhwodVyvXr0477zzsu4HAADktvr168dPf/rTlHpFc9OOHTvijTfeKFVr3bp1jBgxolLrq0oGRVAht9xySxQUFJSqVfSN8fTTT6fUfvazn1VqXRWRhD0AAEBSJeV5vbCwMC688MLYsGFDnHXWWTFv3rxo0qRJ1v2KioriV7/6Vfzwhz+Mrl27xne+850qXC0AANQtSckdAABA7ZTrmaNx48YxYcKElPq0adNi3759Fe43a9asUsc33nhjtGnTJuv1AQAAuZ87/uVf/iWl9swzz2Td7/333y91fP7558fJJ5+cdT8AAKB8n3/+eUqtqKioBlaS3siRI6Nt27alas8//3zKoLmjmTNnTsqe7rrrrsjPz6+SNVYFgyKokNatW8f48eNL1davXx+LFy/O6PoDBw7ElClTStW+973vxaBBgzJew5w5c+KMM86I/Pz8aN++fdx///0V+sOjNuwBAABIrzY8r1c2c6xduzZ69eoVhYWF0bNnz5g/f340bdo0o2uLi4vj888/j/3798eWLVtixYoV8ctf/jJOP/30uPXWW6OoqCiGDRuW8VoAAIBUScgdAABA7ZWEzHHjjTfGmWeeWaq2a9eu+NWvfpVxj4iIV199Nd56662S4zZt2sS9995boR4AAECqXM8dQ4cOjU6dOpWqPfvss7Fu3bqM7/9lM2fOLHU8duzYrPoAAACZO3z4cErt0KFDVdZ/6dKlccEFF0SjRo2idevWceutt1ZoyEOjRo1SPtfYv39//PGPf8y4x69//etSxz169IhRo0ZlfP2xkFdcXFxc04sgtxw+fDjOP//8eP3110tq//RP/xTz588v99r77rsv7rrrrpLjU045Jd58882Mp8T/z//8T/zrv/5rSn306NExefLkjHpE1OweAACAo8vlzLFq1aro379/fPzxxxndr6Ly8vJi48aNceqpp1ZLfwAAqCtyOXdUxrRp02LkyJEpdR8XAgBA1UpC5li7dm2cddZZsW/fvpJafn5+rFy5Mrp27Vru9YcOHYoePXrEqlWrIuKLzzjmzJkTQ4YMyXgNAABA2XI9dzz99NPxve99r1Std+/esXDhwqhfv35GPSIili9fHuedd17JZx0DBgyIefPmZXw9AACQnS5dusSaNWtK1S655JL485//XOner776alx44YUpwygGDx4cc+fOrVCvK664ImbPnl1y/M1vfjPeeeedaNCgwVGvmzFjRqkv+SwoKIhly5ZFt27dKnT/6mZQBFkpLCyMM888M3bv3l1SmzZtWowYMaLMa5YsWRIDBgyIgwcPRsQX01gWLVoUPXv2zPi+6f7giIioV69ebN26NU455ZRavwcAAKB8uZg5li9fHoMGDYo9e/ZkfL+KuvDCC2PRokXV1h8AAOqSXMwdlWVQBAAAHDtJyBxz5syJoUOHxpEjR0pqnTt3jqVLl0bLli3LvK6oqChGjhwZ06dPL6ndfffdcc8992R8bwAAoHy5njtuuumm+O1vf1uq9v3vfz8eeeSRqFevXrnXb9iwIS644ILYunVrRER07Ngxli1bVq2ftQAAAF9o2rRp/P3vfy9V6969e7z99tuV7j1o0KB4/vnn055bsWJF9OjRI+Nen3zySZx55pnxwQcflNQmTpwYEyZMKPOaNWvWxAUXXFCStfLy8mLWrFlx+eWXZ3zfY6X85ARpdOjQIZ577rk44YQTSmo/+MEPSk1V+bI//vGPcemll5b8ZUKTJk1i9uzZFR6wsH79+rT1oqKiUm/STNTUHgAAgPLlWuaYN29e9OvXr1qHREREDB8+vFr7AwBAXZJruQMAAMgtScgcl112WUyZMiXy8vJKau+//37069cv1q1bl/aanTt3xtChQ0sNiRgzZowhEQAAUA1yPXc8/PDDKT8P9bvf/S7++Z//OTZs2FDmdcXFxfHUU09Fjx49SoZEtG7dOl544QVDIgAA4Bh44YUXUoZERESsXr06Vq1aVen+ZWWO8s6l07Rp05g3b160atWqpDZp0qT4zW9+k/b1ixYtir59+5YMiTjuuONi6tSptXJIREREXrGvCKISVqxYEZdddlls27atpHbZZZfF0KFDo02bNlFYWBjTp0+Pl19+ueR8586dY+bMmdG9e/cK369r167x7rvvptQr8y1bx3oPAABA5nIhc8yePTuuuuqqOHz4cIXvVxGNGjWK7du3x4knnlit9wEAgLomF3JHVZk2bVqMHDkype7jQgAAqD5JyBxz5syJ6667Lvbt21dSa9iwYVxzzTUxYMCAaN26dezatSuWLl0af/jDH0oGazds2DB++ctfxujRoyt8TwAAIHO5nDuKi4vj9ttvjwceeCCKiopK6vn5+XHJJZfExRdfHKeeemrk5+fHrl274s0334y5c+fGmjVrSl7bt2/fePLJJw2JAACAarR///7YsmVLvPjii3HnnXeW+szgy04++eS4//77o3fv3tG2bdto3Lhxhe916aWXxp///Oe051asWBE9evSocM9169bFkCFD4r333iup9e3bN4YNGxYdO3aMbdu2xcyZM+NPf/pTyfk2bdrEE088EX379q3w/Y4VgyKotO3bt8ePf/zjePLJJ4/6uhNPPDF+8pOfxLhx4yI/Pz+rez311FNx5ZVXptRHjx4dkydPzqpnxLHdAwAAUDG1PXNcf/318fjjj2d1v4q48sorY+bMmdV+HwAAqItqe+6oKgZFAABAzUhC5nj//fdj7Nix8cwzz5T72ry8vBg8eHA88MAD8Y1vfCPrewIAAJnL9dzx9ttvx2233Rbz5s3L+Jpvfetbcdttt8WwYcOifv36Wd0XAAA4uunTp8eIESMq1ePll1+OPn36ZPz6ZcuWRZ8+fVK+zHPw4MExd+7crNexb9++uPPOO+O3v/1tHDlypMzXNWrUKP7jP/4jfvazn9X6L/o0KIIqs2bNmnjsscdi0aJF8be//S32798fJ510Upxxxhlx6aWXxvDhw6vkDTFnzpyYOHFivPvuu9GqVasYNWpUjBs3LurVq5czewAAACouCZkDAACo3eQOAACgOiUhc7z11lsxa9asWLBgQXz44Yexc+fOqF+/frRs2TK6dOkSffr0iaFDh8Zpp51W6XsBAAAVl+u5Y/369fH888/Hiy++GIWFhbFjx47YvXt3FBQURIsWLeLUU0+N3r17x0UXXRS9e/eOvLy8Su8FAAAo2yeffBKbN2+uVI+OHTtGQUFBha5ZunRpjBs3Lt54441o1qxZDBs2LO69995o1KhRpdYSEfHhhx/G1KlTY8GCBfHee+/F3r17o1mzZtGlS5e45JJL4vrrr4+TTz650vc5FgyKAAAAAAAAAAAAAAAAAAAAAMgRvpYIAAAAAAAAAAAAAAAAAAAAIEcYFAEAAAAAAAAAAAAAAAAAAACQIwyKAAAAAAAAAAAAAAAAAAAAAMgRBkUAAAAAAAAAAAAAAAAAAAAA5AiDIgAAAAAAAAAAAAAAAAAAAAByhEERAAAAAAAAAAAAAAAAAAAAADnCoAgAAAAAAAAAAAAAAAAAAACAHGFQBAAAAAAAAAAAAAAAAAAAAECOMCgCAAAAAAAAAAAAAAAAAAAAIEcYFAEAAAAAAAAAAAAAAAAAAACQIwyKAAAAAAAAAAAAAAAAAAAAAMgRBkUAAAAAAAAAAAAAAAAAAAAA5AiDIgAAAAAAAAAAAAAAAAAAAAByhEERAAAAAAAAAAAAAAAAAAAAADnCoAgAAAAAAAAAAAAAAAAAAACAHGFQBAAAAAAAAAAAAAAAAAAAAECOMCgCAAAAAAAAAAAAAAAAAAAAIEcYFAEAAAAAAAAAAAAAAAAAAACQIwyKAAAAAAAAAAAAAAAAAAAAAMgRBkUAAAAAAAAAAAAAAAAAAAAA5AiDIgAAAAAAAAAAAAAAAAAAAAByhEERAAAAAAAAAAAAAAAAAAAAADnCoAgAAAAAAAAAAAAAAAAAAACAHGFQBAAAAAAAAAAAAAAAAAAAAECOMCgCAAAAAAAAAAAAAAAAAAAAIEcYFAEAAAAAAAAAAAAAAAAAAACQIwyKAAAAAAAAAAAAAAAAAAAAAMgRBkUAAAAAAAAAAAAAAAAAAAAA5AiDIgAAAAAAAAAAAAAAAAAAAAByhEERAAAAAAAAAAAAAAAAAAAAADnCoAgAAAAAAAAAAAAAAAAAAACAHGFQBAAAAAAAAAAAAAAAAAAAAECOMCgCAAAAAAAAAAAAAAAAAAAAIEcYFAEAAAAAAAAAAAAAAAAAAACQIwyKAAAAAAAAAAAAAAAAAAAAAMgRBkUAAAAAAAAAAAAAAAAAAAAA5AiDIgAAAAAAAAAAAAAAAAAAAAByhEERAAAAAAAAAAAAAAAAAAAAADnCoAgAAAAAAAAAAAAAAAAAAACAHGFQBAAAAAAAAAAAAAAAAAAAAECOMCgCAAAAAAAAAAAAAAAAAAAAIEf8PxSE6D392n/IAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 4200x1400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(\n",
    "    figsize=(14, 14 / 3), ncols=1, nrows=2, constrained_layout=True, dpi=300\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels_name_a = [\n",
    "    \"ModelA\\n8DP\",\n",
    "    \"ModelA\\n8TP\",\n",
    "    \"ModelB\\n8TP\",\n",
    "]\n",
    "labels_name_c = [\n",
    "    \"ModelA\\n2DP$\\\\times$4TP\",\n",
    "    \"ModelA\\n2DP$\\\\times$8TP\",\n",
    "    \"ModelA\\n4DP$\\\\times$2TP\",\n",
    "    \"ModelB\\n4DP$\\\\times$2TP\",\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MFU\n",
    "data_a = {\n",
    "    labels_name_a[0]: [41.0, 34.2, 44.4],  # modela 8DP\n",
    "    labels_name_a[1]: [26.2, 36.8, 43.6],  # modela 8TP\n",
    "    labels_name_a[2]: [30.1, 39.6, 49.4],  # modelb 8tp\n",
    "}\n",
    "data_c = {\n",
    "    labels_name_c[0]: [37.1, 30.4, 44.6],  # modela 2DP 4TP\n",
    "    labels_name_c[1]: [39.6, 41.9, 0],  # modela 2DP 8TP\n",
    "    labels_name_c[2]: [40.4, 30.5, 44.7],  # modela 4DP 2TP\n",
    "    labels_name_c[3]: [-1, 31.7, 38.0],  # modeb 4DP 2TP\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [],
   "source": [
    "legend_labels = [\"Megatron-LM\", \"XLA\", \"DLRover-Lynx\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [],
   "source": [
    "bar_width = 0.2\n",
    "group_spaing = 0.15\n",
    "\n",
    "group_positions = {}\n",
    "current_pos = 0\n",
    "\n",
    "x_label_cnt = len(data_a.keys())\n",
    "x_label_group_cnt = 3\n",
    "\n",
    "for idx in range(x_label_cnt):\n",
    "    group_positions[idx] = []\n",
    "    for _ in range(x_label_group_cnt):\n",
    "        group_positions[idx].append(current_pos)\n",
    "        current_pos += bar_width\n",
    "    current_pos += group_spaing\n",
    "\n",
    "group_centers = {}\n",
    "for idx, positions in group_positions.items():\n",
    "    group_centers[idx] = sum(positions) / len(positions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '(a) Single parallel')"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "label_set = set()\n",
    "for idx, (x_label, y_data) in enumerate(data_a.items()):\n",
    "    positions = group_positions[idx]\n",
    "    tmp = sorted(y_data)[-2]\n",
    "    ax[0].text(\n",
    "        positions[2],\n",
    "        y_data[2] + 2,\n",
    "        f\"$\\\\times${str(round(y_data[2]/tmp, 2))}\",\n",
    "        ha=\"center\",\n",
    "        color=colors[2],\n",
    "    )\n",
    "    for i, (pos, value, color, edgecolor, hatch, label) in enumerate(\n",
    "        zip(\n",
    "            positions,\n",
    "            y_data,\n",
    "            colors,\n",
    "            edgecolors,\n",
    "            hatches,\n",
    "            legend_labels,\n",
    "        )\n",
    "    ):\n",
    "        if label in label_set:\n",
    "            local_label = None\n",
    "        else:\n",
    "            local_label = label\n",
    "            label_set.add(local_label)\n",
    "        ax[0].bar(\n",
    "            pos,\n",
    "            value,\n",
    "            width=bar_width,\n",
    "            color=color,\n",
    "            label=local_label,\n",
    "            hatch=hatch,\n",
    "            edgecolor=edgecolor,\n",
    "        )\n",
    "\n",
    "ax[0].set_xticks(list(group_centers.values()))\n",
    "ax[0].set_xticklabels(list(data_a.keys()))\n",
    "\n",
    "ax[0].set_ylim(0, 100)\n",
    "ax[0].set_yticks([0, 50, 100])\n",
    "ax[0].set_yticklabels([\"0\", \"50\", \"100\"], rotation=90, ha=\"center\", va=\"center\")\n",
    "\n",
    "ax[0].tick_params(axis=\"x\", bottom=False, labelsize=g_label_fontsize, pad=1)\n",
    "ax[0].tick_params(axis=\"y\", left=True, labelsize=g_label_fontsize, pad=5)\n",
    "\n",
    "ax[0].set_ylabel(\"MFU (%)\", fontsize=g_label_fontsize)\n",
    "ax[0].set_title(\"(a) Single parallel\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {},
   "outputs": [],
   "source": [
    "bar_width = 0.2\n",
    "group_spaing = 0.15\n",
    "\n",
    "group_positions = {}\n",
    "current_pos = 0\n",
    "\n",
    "x_label_cnt = len(data_c.keys())\n",
    "x_label_group_cnt = 3\n",
    "\n",
    "for idx in range(x_label_cnt):\n",
    "    group_positions[idx] = []\n",
    "    for _ in range(x_label_group_cnt):\n",
    "        group_positions[idx].append(current_pos)\n",
    "        current_pos += bar_width\n",
    "    current_pos += group_spaing\n",
    "\n",
    "group_centers = {}\n",
    "for idx, positions in group_positions.items():\n",
    "    group_centers[idx] = sum(positions) / len(positions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '(c) Hybrid parallel')"
      ]
     },
     "execution_count": 265,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for idx, (x_label, y_data) in enumerate(data_c.items()):\n",
    "    positions = group_positions[idx]\n",
    "    tmp = sorted(y_data)[-2]\n",
    "    ax[1].text(\n",
    "        positions[2],\n",
    "        y_data[2]+2,\n",
    "        f\"$\\\\times${str(round(y_data[2]/tmp, 2))}\",\n",
    "        ha=\"center\",\n",
    "        color=colors[2],\n",
    "    )\n",
    "    for i, (pos, value, color, edgecolor, hatch) in enumerate(\n",
    "        zip(\n",
    "            positions,\n",
    "            y_data,\n",
    "            colors,\n",
    "            edgecolors,\n",
    "            hatches,\n",
    "        )\n",
    "    ):\n",
    "        if value == -1:\n",
    "            ax[1].text(\n",
    "                pos,\n",
    "                1,\n",
    "                \"OOM$\\\\times$\",\n",
    "                rotation=90,\n",
    "                ha=\"center\",\n",
    "                va=\"bottom\",\n",
    "                color=\"red\",\n",
    "            )\n",
    "        ax[1].bar(\n",
    "            pos,\n",
    "            value,\n",
    "            width=bar_width,\n",
    "            color=color,\n",
    "            label=local_label,\n",
    "            hatch=hatch,\n",
    "            edgecolor=edgecolor,\n",
    "        )\n",
    "\n",
    "ax[1].set_xticks(list(group_centers.values()))\n",
    "ax[1].set_xticklabels(list(data_c.keys()))\n",
    "\n",
    "ax[1].set_ylim(0, 100)\n",
    "ax[1].set_yticks([0, 50, 100])\n",
    "ax[1].set_yticklabels([\"0\", \"50\", \"100\"], rotation=90, ha=\"center\", va=\"center\")\n",
    "\n",
    "ax[1].tick_params(axis=\"x\", bottom=False, labelsize=g_label_fontsize, pad=1)\n",
    "ax[1].tick_params(axis=\"y\", left=True, labelsize=g_label_fontsize, pad=5)\n",
    "\n",
    "ax[1].set_ylabel(\"MFU (%)\", fontsize=g_label_fontsize)\n",
    "ax[1].set_title(\"(c) Hybrid parallel\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fa82abb0470>"
      ]
     },
     "execution_count": 266,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig.legend(\n",
    "    ncol=3,\n",
    "    loc=\"upper center\",\n",
    "    frameon=False,\n",
    "    shadow=False,\n",
    "    bbox_to_anchor=(0.5, 1.1),\n",
    "    fontsize=g_label_fontsize,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 4200x1400 with 2 Axes>"
      ]
     },
     "execution_count": 267,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig.savefig(\"end_to_end_mfu.pdf\", bbox_inches=\"tight\", dpi=1000)\n",
    "fig"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.12.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}