paper_note/lynx/two_phase_algo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import random\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",
    "    \"#233142\",\n",
    "    \"#F95959\",\n",
    "]\n",
    "\n",
    "edgecolors = [\n",
    "    \"#FFFFFF\",\n",
    "    \"#FFFFFF\",\n",
    "]\n",
    "\n",
    "hatches = [\"\", \"\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2100x1050 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(\n",
    "    figsize=(7, 7 / 2), ncols=1, nrows=1, constrained_layout=True, dpi=300\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels_name_a = [\n",
    "    \"ModelA\\n8DP\",\n",
    "    \"ModelA\\n8TP\",\n",
    "    \"ModelA\\n2DP$\\\\times$4TP\",\n",
    "    \"ModelA\\n2DP$\\\\times$8TP\",\n",
    "    \"ModelA\\n4DP$\\\\times$2TP\",\n",
    "    \"ModelB\\n8TP\",\n",
    "    \"ModelB\\n4DP$\\\\times$2TP\",\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MFU\n",
    "data_a = {\n",
    "    labels_name_a[0]: [43.0, 44.4],  # modela 8DP\n",
    "    labels_name_a[1]: [42.2, 43.6],  # modela 8TP\n",
    "    labels_name_a[2]: [43.1, 44.6],  # modela 2DP 4TP\n",
    "    labels_name_a[3]: [41.0, 42.6],  # modela 2DP 8TP\n",
    "    labels_name_a[4]: [44.7, 44.7],  # modela 4DP 2TP\n",
    "    labels_name_a[5]: [48.1, 49.4],  # modelb 8TP\n",
    "    labels_name_a[6]: [38.0, 38.0],  # modelb 4DP 2TP\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "legend_labels = [\"DLRover-Lynx without Local Search\", \"DLRover-Lynx\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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 = 2\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": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(13.333333333333346, 0.5, 'MFU (%)')"
      ]
     },
     "execution_count": 25,
     "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",
    "\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",
    "\n",
    "        ax.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.set_xticks(list(group_centers.values()))\n",
    "ax.set_xticklabels(list(data_a.keys()))\n",
    "\n",
    "ax.set_ylim(0, 100)\n",
    "ax.set_yticks([0, 50, 100])\n",
    "ax.set_yticklabels([\"0\", \"50\", \"100\"], rotation=90, ha=\"center\", va=\"center\")\n",
    "\n",
    "ax.tick_params(axis=\"x\", bottom=False, labelsize=g_label_fontsize - 4, pad=1)\n",
    "ax.tick_params(axis=\"y\", left=True, labelsize=g_label_fontsize, pad=5)\n",
    "ax.set_ylabel(\"MFU (%)\", fontsize=g_label_fontsize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f70583d8710>"
      ]
     },
     "execution_count": 26,
     "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, 0.9),\n",
    "    fontsize=g_label_fontsize - 2,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2100x1050 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig.savefig(\"two_phase_algo.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
}