paper_note/lynx/two_phase_algo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 2100x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(\n",
    "    figsize=(7, 14 / 6), ncols=1, nrows=1, constrained_layout=True, dpi=300\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": 13,
   "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": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "legend_labels = [\"Lynx without Local Search\", \"Lynx\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(13.333333333333332, 0.5, 'MFU (%)')"
      ]
     },
     "execution_count": 16,
     "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": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f0582807530>"
      ]
     },
     "execution_count": 17,
     "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,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2100x700 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
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    "fig"
   ]
  }
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