{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1381,
   "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",
    "    \"#455D7A\",\n",
    "    \"#233142\",\n",
    "    \"#F95959\",\n",
    "]\n",
    "\n",
    "edgecolors = [\n",
    "    \"#FFFFFF\",\n",
    "    \"#FFFFFF\",\n",
    "    \"#FFFFFF\",\n",
    "]\n",
    "\n",
    "hatches = [\"\", \"\", \"\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1382,
   "metadata": {},
   "outputs": [
    {
     "data": {
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RRxER8fvf/z5t6jwAAFAzsm0fufnmm9PWzzzzzG16XwAAoPKybR/p0qVL/PKXv0x77tNPP41evXrFlClT0p5fvHhxDBkyJAoKCiIionfv3jFp0qRo1KjRNpsXAABItuLi4vj444/TnkviTlURgiJqsfnz55d7rio/kDvttFPa+ty5czPuWZ5seAYAAKiLvJcva+XKlbFs2bIytVNPPdUHjwAAsI1k804yefLkuO222yIi4pRTTokzzjhju90bAADYumzaR6ZOnZr2G3pbtGgRRx11VOnx6tWr49FHH41zzjkn9ttvv2jTpk3k5eVFu3bt4uCDD46rrroqZs6cuc3mBAAA/iWb9pF/Gz16dLlfxrNq1aoYMGBAjB07tkx95cqVMWDAgFi4cGFE/OvzlFdeeSVatGixzecFAACSa8mSJbFx48a055K6U22NoIhabMGCBWnrjRs3jiZNmmTcNy8vL2196dKlGfcsTzY8AwAA1EXey5c1derUMsc5OTkxYsSIGpoGAACyX7buJGvWrInhw4dHSUlJdOjQIe6+++7tcl8AAKDismkfeeCBB9LWjzvuuGjQoEHMmjUr/t//+3+x6667xrBhw2Ls2LHx0UcfxbJly2Ljxo3x5Zdfxttvvx3XXXdd7LvvvjFs2LCUYG0AAKD6ZNM+8m/169ePZ555Jvbff/+05zdt2hTnnHNO/Nd//VcUFxfH0qVLo1+/fjF79uzIy8uLO++8Mx577DFf6AMAAGxVeTtVRESbNm0y7lvTv3O2JYIiarFFixalrVd1wS3vB3JbfIiXDc8AAAB1kffyZU2YMKHM8amnnhr77rtvzQwDAAB1QLbuJBdccEEsXrw46tWrF3/605/iO9/5zna5LwAAUHHZso8UFxfHs88+m/Zc796945JLLolu3brFfffdFxs2bIjGjRtHhw4domnTpuX2fPTRR6Nr167x9ttvb5OZAQCgrsuWfeT/atasWbzyyitxwAEHlPuam266KQYPHhzf//73Y+bMmdG9e/d477334uKLL94uMwIAAMlX3k4VUbW9qqZ3qi0RFFGLrV27Nm19Wy355d2vKrLhGQAAoC7yXv5/rV+/Pv7yl7+UHtevXz9+/etf1+BEAACQ/bJxJ3n44Ydj3LhxERFxxRVXxPe///1tfk8AAKDysmUfef/992P16tVpz1122WVx5513RsuWLePqq6+ODz/8MNavXx+ff/55rF27Nv7xj3/EJZdcEjvssEPKtatWrYr+/fvHlClTtsncAABQl2XLPpLOjjvuGK+++mr06tWr3Ne88MILMW/evOjbt2+89dZb0bVr1+02HwAAkHxb2nEaNmyYcd/asFOVR1BELfbtt9+mrVflhzEiIjc3N229sLCwSn3TyYZnAACAush7+f/18MMPl1ngR40aFd/97ndrcCIAAMh+2baTLFiwIH76059GRESPHj3immuu2ab3AwAAMpct+8irr766xfNXX311zJ8/P8aMGRPdunUrc27vvfeO22+/PaZOnRqtWrVKuXb9+vVx0kknxZdfflmtMwMAQF2XLftIeZo3bx6vvvpqnHDCCVt83ZQpU+Kiiy6KTZs2bafJAACAbFDeTpWfnx85OTkZ960tO1U6giJqsfJ+IKuaBllUVJS2vnHjxir1TScbngEAAOoi7+X/ZePGjXHTTTeVHnfp0iWuvvrqGpwIAADqhmzaSYqLi+P000+PtWvXRuPGjePRRx+N+vXrb7P7AQAAVZMt+8gHH3yQtt6zZ8+YPXt2jBkzJho3brzFHr169YoXXnghGjRokHJuxYoVcfrpp1fHqAAAwP8vW/aRLWnYsGE89dRTcc4552zxdffcc0/069cvli9fvp0mAwAAkq4u7FT/l6CIWqykpCRtvappkMXFxWnreXl5VeqbTjY8AwAA1EXey//LH//4x1iwYEFE/CsF8r777qu1swIAQDbJpp3kv//7v+Nvf/tbRETcfvvtsccee2yzewEAAFWXLfvIJ598krY+ePDg6NChQ4X7HHzwwfGrX/0q7bnJkyfH5MmTM5oPAABIlS37yNZMmTIlnn/++ahfv3706tWr3Ne98cYbccghh8Snn366HacDAACSqq7sVP9JUEQt1qRJk23St6CgIG29qoko6WTDMwAAQF3kvXzEqlWr4uqrry49vuaaa+Kwww6rwYkAAKDuyJad5N13341rrrkmIiJOPPHErX47FgAAUPOyZR+ZO3du2nqnTp0q3evSSy+Nli1bpj33m9/8ptL9AACA9LJlH9mSm2++OQYMGBBr1qyJp59+Ot544424/PLLy339Z599Focccki89dZb23FKAAAgierCTvV/CYqoxZo2bZq2Xt4PVEUVFhamrVc1ESWdbHgGAACoi7yXj/jZz34Wq1evjoiIo48+On75y1/W8EQAAFB3ZMNO8u2338Zpp50WmzZtil122SXuvffear8HAABQ/bJhH9m0aVOsW7cu7blddtml0v0aN24cF110UdpzkyZNKv08BQAAqJps2EfKU1RUFBdeeGGMGjUqiouLY+zYsTF48OCoV69e3HjjjfHQQw9FgwYN0l67evXqOOqoo2L69OnbbV4AACB5snmnKo+giFpsW/1Arl+/Pm29efPmVeqbTjY8AwAA1EV1/b38s88+G4888khEROy2227xpz/9KXJycmp4KgAAqDuyYSf5+c9/Hp9++mnk5OTEQw89VO637wIAALVLNuwj5YVERES0adMmo57nnHNO2npJSUlMnTo1o54AAEBZ2bCPpFNUVBSnnHJK3H333RERMWLEiDjttNPKvOaMM86Il19+udyZ1q5dG0cddVR8/PHH23pcAAAgobJ1p9oSQRG1WIsWLdLWq/oDuXbt2rT1jh07VqlvOtnwDAAAUBfV5ffyixYtirPPPjsiIlq2bBkvvvhitGrVqoanAgCAuiXpO8nzzz8f99xzT0REXHrppdG/f/9q7Q8AAGw7Sd9HIiK+/fbbcs9l+plHx44do1u3bmnP/f3vf8+oJwAAUFY27CP/V0lJSQwfPjyeeuqpiIjo3Llz3HjjjWlf27dv35g2bVq0a9cu7fl169bFoEGDYs2aNdtsXgAAILmycafaGkERtViXLl3S1stLHqmor776Km29Q4cOVeqbTjY8AwAA1EV19b38pk2b4pRTTolVq1ZFgwYNYvz48eX+dwEAAGw7Sd9J/vObdm+++ebIycnJ6D9nnXVW2v7lvR4AAKi6pO8jERE77LBDueeaNWuWcd+jjjoqbX3p0qUZ9wQAAP5XNuwj/9cNN9wQjz76aOnx9ddfH3l5eeW+fp999olp06ZFp06d0p7//PPPY9SoUdU9JgAAkAXK26mKioqqFBZRm/8ORlBELda1a9e09RUrVsTmzZsz7rtixYq09fIW6arIhmcAAIC6qK6+l//pT38ab7zxRtSrVy8efvjh6NOnT02PBAAAdVLSd5Lly5dXaz8AAGD7Sfo+EhHRuHHjcs81aNAg47777rtv2vqqVasy7gkAAPyvbNhH/tPf//73GD16dOnxLrvsEkOHDt3qdZ07d47XXnut3D+6uv/+++O9996rtjkBAIDs0L59+3IDs5csWZJx39r8dzCCImqxli1bRps2bVLqxcXF8eWXX2bcd9myZWnrBx10UMY9y5MNzwAAAHVRXXwv/4c//CHuueeeiIi4884740c/+lENTwQAAHVXXdxJAACA2iEb9pEmTZqUGxZRWFiYcd/y/mht48aNGfcEAAD+VzbsI//ppz/9aRQXF5cen3jiiVG/fv0KXdupU6d4+eWXY8cdd0x7/uabb66WGQEAgOyy9957p60vXrw44561+XfOBEXUcvvtt1/a+qJFizLqV1BQECtXrkyp77TTTvHd7343o55bkw3PAAAAdVFdei//3HPPxYgRIyIi4pprromf/OQnNToPAABQt3YSAACgdsmGfaRz585p66tXr864584775y23qpVq4x7AgAAZWXDPhIR8frrr8c777xTpta/f/9K9ejSpUs8/fTTacMlxo8fHxs2bKjSjAAAQPap7p0qImLhwoUptXr16kXPnj0z7lldBEXUcsccc0za+vz58zPqt2DBgrT1Xr16ZdSvIrLhGQAAoC6qK+/l33rrrTjllFOiqKgoRowYEaNHj67ReQAAgH+pKzsJAABQ+2TDPrLPPvukrWf6DBERTZs2TVsv7xt+AQCAysuGfSQi4tFHH02plbenbEmfPn1izJgxKfXCwsJ48803MxkNAADIYtW9U23YsCGWL1+eUu/atWu5n5tsT4IiarnBgwenrc+YMSOjfnPnzk1bHzRoUEb9KiIbngEAAOqiuvBefubMmXHsscfGt99+G8OHD4/bbrutxmYBAADKSvJOUlJSUi3/eeCBByrVHwAAqB5J3kf+7dBDD01bnzlzZsY9GzdunLaeyR97AQAA6WXDPhIRMW3atJRamzZtMuo1atSo6NixY0p93rx5GfUDAACy14ABAyI/Pz+lnulONW/evLS/l1Vb/qZdUEQtt9tuu0XXrl1T6u+9915G/T766KOUWv369ePEE0/MqF9FZMMzAABAXZTt7+X/+c9/xlFHHRVr1qyJE044Ie6///7IycmpkVkAAIBU2b6TAAAAtVc27CMDBgxIW//73/+ecc/169enrX//+9/PuCcAAFBWNuwjERGLFi1KqaX7Y62KaNCgQZx55pkp9dWrV2fUDwAAyF6NGjWK/v37p9Src6eKiPjRj36UUb/qJigiAU4//fSU2vvvv5/RN0OlSzwZMGBAtGrVKqPZKiobngEAAOqibH0v//nnn8cRRxwRS5YsiYEDB8Zjjz0Wubm5230OAABgy7J1JwEAAGq/pO8je+65Z+y///4p9UmTJmXc86uvvkqptWvXLr73ve9l3BMAAEiV9H0kItLOmm6nqKg+ffqk1Jo3b55xPwAAIHul26kWLFiQUdhcup1qr732im7dumU0W3UTFJEAF1x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",
      "text/plain": [
       "<Figure size 4200x1680 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(\n",
    "    figsize=(14, 14 / 2.5), ncols=1, nrows=2, constrained_layout=True, dpi=300\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1383,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MFU\n",
    "data_a = {\n",
    "    \"ModelA\\n#8GPUs\": [53, 53, 65],  # 22.64\n",
    "    \"ModelA\\n#16GPUs\": [53, 53, 65],  # 22.64\n",
    "    \"ModelB\\n#8GPUs\": [35, 35, 48],  # 37\n",
    "    \"ModelB\\n#16GPUs\": [35, 35, 48],  # 37\n",
    "    \"ModelC\\n#8GPUs\": [53, 53, 65],  # 22.64\n",
    "    \"ModelC\\n#16GPUs\": [53, 53, 65],  # 22.64\n",
    "    \"ModelD\\n#8GPUs\": [53, 53, 65],  # 22.64\n",
    "    \"ModelD\\n#16GPUs\": [53, 53, 65],  # 22.64\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1384,
   "metadata": {},
   "outputs": [],
   "source": [
    "# overlapping rate\n",
    "data_b = {\n",
    "    \"ModelA\\n#8GPUs\":  [54, 62, 12],\n",
    "    \"ModelA\\n#16GPUs\": [54, 62, 12],\n",
    "    \"ModelB\\n#8GPUs\":  [52, 62, 12],\n",
    "    \"ModelB\\n#16GPUs\": [52, 62, 12],\n",
    "    \"ModelC\\n#8GPUs\":  [52, 62, 12],\n",
    "    \"ModelC\\n#16GPUs\": [52, 62, 12],\n",
    "    \"ModelD\\n#8GPUs\":  [53, 62, 12],\n",
    "    \"ModelD\\n#16GPUs\": [52, 62, 12],\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1385,
   "metadata": {},
   "outputs": [],
   "source": [
    "# communication baseline\n",
    "data_c = {\n",
    "    \"ModelA\\n#8GPUs\": 70,\n",
    "    \"ModelA\\n#16GPUs\": 70,\n",
    "    \"ModelB\\n#8GPUs\": 70,\n",
    "    \"ModelB\\n#16GPUs\": 70,\n",
    "    \"ModelC\\n#8GPUs\": 70,\n",
    "    \"ModelC\\n#16GPUs\": 70,\n",
    "    \"ModelD\\n#8GPUs\": 70,\n",
    "    \"ModelD\\n#16GPUs\": 70,\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1386,
   "metadata": {},
   "outputs": [],
   "source": [
    "legend_labels = [\"FSDP\", \"XLA\", \"DLRover-Lynx\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1387,
   "metadata": {},
   "outputs": [],
   "source": [
    "bar_width = 0.2\n",
    "group_spaing = 0.15\n",
    "\n",
    "group_positions = {}\n",
    "current_pos = 0\n",
    "\n",
    "for x_label, y_data in data_a.items():\n",
    "    group_positions[x_label] = []\n",
    "    for i in range(len(y_data)):\n",
    "        group_positions[x_label].append(current_pos)\n",
    "        current_pos += bar_width\n",
    "    current_pos += group_spaing\n",
    "\n",
    "group_centers = {}\n",
    "for x_label, positions in group_positions.items():\n",
    "    group_centers[x_label] = sum(positions) / len(positions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1388,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '(a)')"
      ]
     },
     "execution_count": 1388,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "label_set = set()\n",
    "for x_label, y_data in data_a.items():\n",
    "    positions = group_positions[x_label]\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=11, 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)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1389,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '(b)')"
      ]
     },
     "execution_count": 1389,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "label_set = set()\n",
    "total_label = \"Communication Ratio\"\n",
    "\n",
    "for x_label, y_data in data_b.items():\n",
    "    positions = group_positions[x_label]\n",
    "    for i, (pos, value, diff_value, color, edgecolor, label, hatch) in enumerate(\n",
    "        zip(\n",
    "            positions,\n",
    "            y_data,\n",
    "            list(data_c.values()),\n",
    "            colors,\n",
    "            edgecolors,\n",
    "            legend_labels,\n",
    "            hatches,\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",
    "\n",
    "        ax[1].bar(\n",
    "            pos,\n",
    "            value,\n",
    "            width=bar_width,\n",
    "            color=color,\n",
    "            edgecolor=edgecolor,\n",
    "            hatch=hatch,\n",
    "            label=local_label,\n",
    "        )\n",
    "\n",
    "        ax[1].bar(\n",
    "            pos,\n",
    "            diff_value - value,\n",
    "            bottom=value,\n",
    "            color=\"#E3E3E3\",\n",
    "            edgecolor=edgecolor,\n",
    "            width=bar_width,\n",
    "        )\n",
    "\n",
    "ax[1].set_xticks(list(group_centers.values()))\n",
    "ax[1].set_xticklabels(list(data_a.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=11, pad=1)\n",
    "ax[1].tick_params(axis=\"y\", left=True, labelsize=g_label_fontsize, pad=5)\n",
    "\n",
    "ax[1].set_ylabel(\"Overlapping Ratio (%)\", fontsize=g_label_fontsize)\n",
    "ax[1].set_title(\"(b)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1390,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f5c680ea030>"
      ]
     },
     "execution_count": 1390,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax[0].legend(\n",
    "    ncol=3,\n",
    "    loc=\"upper center\",\n",
    "    frameon=False,\n",
    "    shadow=False,\n",
    "    fontsize=g_label_fontsize,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1391,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.52, 78, 'Proportion of Communication in the Total Latency.')"
      ]
     },
     "execution_count": 1391,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax[1].arrow(\n",
    "    0.5,\n",
    "    80,\n",
    "    -0.1,\n",
    "    -10,\n",
    "    width=0.01,\n",
    "    head_width=0.1,\n",
    "    head_length=0.1,\n",
    "    color=\"red\",\n",
    ")\n",
    "\n",
    "ax[1].text(\n",
    "    0.52,\n",
    "    78,\n",
    "    \"Proportion of Communication in the Total Latency.\",\n",
    "    color=\"red\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 4200x1680 with 2 Axes>"
      ]
     },
     "execution_count": 1392,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig.savefig(\"end_to_end.pdf\", bbox_inches=\"tight\", dpi=1000)\n",
    "fig"
   ]
  }
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