{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2500x500 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_lists = {\n",
    "    \"sst2\": \"test_400\",\n",
    "    \"agnews\": \"test_400\",\n",
    "    \"dbpedia\": \"test_700\",\n",
    "    \"20newsgroups\": \"test_800\",\n",
    "    \"banking77\": \"test_1000\",\n",
    "}\n",
    "\n",
    "dataset2name = {\n",
    "    \"sst2\": \"SST-2\",\n",
    "    \"agnews\": \"AG News\",\n",
    "    \"dbpedia\": \"DBpedia\",\n",
    "    \"20newsgroups\": \"20 Newsgroups\",\n",
    "    \"banking77\": \"Banking77\",\n",
    "}\n",
    "\n",
    "def plot_priors(datasets):\n",
    "\n",
    "    # fig, ax = plt.subplots(1, len(datasets), figsize=(5*len(datasets), 5))\n",
    "    fig = plt.figure(figsize=(5*len(datasets), 5))\n",
    "    cum_width = 0\n",
    "\n",
    "    factor = 1.\n",
    "    for i, dataset in enumerate(datasets):\n",
    "        test_list = np.loadtxt(f\"../lists/{dataset}/{test_lists[dataset]}.txt\", dtype=int)\n",
    "        df = pd.read_csv(f\"../data/{dataset}/all.csv\", header=0, index_col=0)\n",
    "        labels = df.loc[:,\"label\"].values\n",
    "        priors = np.bincount(labels[test_list]) / len(test_list)\n",
    "        n_classes = priors.size\n",
    "        \n",
    "        width = n_classes / 50\n",
    "        ax = fig.add_axes([cum_width, 0, width * factor, 1])\n",
    "        cum_width += width * factor + 0.05\n",
    "        factor = 0.8 * factor\n",
    "        ax.bar(range(len(priors)), np.sort(priors)[::-1])\n",
    "        ax.set_title(dataset2name[dataset], fontsize=28)\n",
    "        ax.set_xlim(-1, n_classes)\n",
    "        ax.set_xticks([])\n",
    "        ax.set_yticks(ax.get_yticks())\n",
    "        ax.set_yticklabels(ax.get_yticklabels(), fontsize=15)\n",
    "\n",
    "    \n",
    "    # fig.suptitle(\"Prior Probabilities for each dataset sorted by number\", fontsize=16, y=1.12)\n",
    "\n",
    "    # plt.tight_layout()\n",
    "\n",
    "\n",
    "plot_priors([\"sst2\", \"agnews\", \"dbpedia\", \"20newsgroups\", \"banking77\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "llmcal",
   "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": "3.11.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}