{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "   div#notebook-container    { width: 100%; }\n",
       "   div#menubar-container     { width: 100%; }\n",
       "   div#maintoolbar-container { width: 100%; }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from eda_imports import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def q2k(q, delta=100):\n",
    "    \"\"\"scale function\"\"\"\n",
    "    return delta / (2 * np.pi) * np.arcsin(2 * q - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def k2q(k, delta=100):\n",
    "    return (np.sin(2 * np.pi * k / delta) + 1) / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x119b4cf40>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 255,
       "width": 375
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ks = np.arange(-25, 25 + 1, 1)\n",
    "plt.plot(_ks, k2q(_ks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "qs = np.arange(0, 1.01, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 270,
       "width": 478
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for delta in [1, 5, 10, 20, 30, 100]:\n",
    "    plt.plot(qs, q2k(qs, delta=delta), label=f\"δ={delta}\")\n",
    "    plt.grid()\n",
    "    plt.xlabel(\"quantile\")\n",
    "    plt.ylabel(\"k (cluster size)\")\n",
    "    plt.legend(loc='upper left', bbox_to_anchor=(1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = np.log(np.random.uniform(size=10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11e1d74c0>"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 549,
       "width": 851
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12, 9))\n",
    "\n",
    "# plot data\n",
    "ax.scatter(\n",
    "    np.arange(len(samples)) / len(samples), np.sort(samples), marker=\"+\", color=\"gray\"\n",
    ")\n",
    "\n",
    "# # plot true quantiless\n",
    "# ref_qs = np.arange(0, 1.01, 0.01)\n",
    "# ref_q_vals = np.quantile(samples, ref_qs)\n",
    "# ax.scatter(ref_qs, ref_q_vals, label=\"true quantiles\", color=\"green\", edgecolor=\"none\", marker=\"o\", s=100)\n",
    "# ax.set(xlabel=\"quantile\", ylabel=\"quantile vals\")\n",
    "\n",
    "# plot uniform quantiles\n",
    "uniform_q_bins = np.linspace(0, 1, 50)\n",
    "uniform_qs = (uniform_q_bins[:-1] + uniform_q_bins[1:]) / 2\n",
    "uniform_bin2q_map = dict(zip(np.arange(len(uniform_q_bins)), uniform_qs))\n",
    "uniform_q_val_bins = np.quantile(samples, uniform_q_bins)\n",
    "adf = (\n",
    "    pd.DataFrame(\n",
    "        list(zip(np.digitize(samples, uniform_q_val_bins[1:-1]), samples)),\n",
    "        columns=[\"bin\", \"val\"],\n",
    "    )\n",
    "    .groupby(\"bin\")\n",
    "    .mean()\n",
    "    .sort_values(\"bin\")\n",
    "    .reset_index()\n",
    "    .assign(quantile=lambda df: df[\"bin\"].replace(uniform_bin2q_map))\n",
    ")\n",
    "adf.plot.scatter(\n",
    "    x=\"quantile\",\n",
    "    y=\"val\",\n",
    "    marker=\"o\",\n",
    "    color=\"blue\",\n",
    "    edgecolor=\"none\",\n",
    "    label=\"uniform_bin\",\n",
    "#     s=60,\n",
    "    ax=ax,\n",
    ")\n",
    "\n",
    "adf_with_head = pd.concat([pd.DataFrame([[0, np.min(samples)]], columns=['quantile', 'val']), adf[[\"quantile\", \"val\"]]])\n",
    "for (x1, y1), (x2, y2) in zip(\n",
    "    adf_with_head.values[1:], adf_with_head.values[:-1]\n",
    "):\n",
    "    ax.plot([x1, x2], [y1, y2], color=\"blue\")\n",
    "\n",
    "\n",
    "# plot t-digest quantiles\n",
    "delta = 100\n",
    "ks = np.arange(-delta / 4, delta / 4 + 1, 1)\n",
    "t_q_bins = k2q(ks)\n",
    "t_qs = (t_q_bins[:-1] + t_q_bins[1:]) / 2\n",
    "t_bin2q_map = dict(zip(np.arange(len(t_qs)), t_qs))\n",
    "t_q_val_bins = np.quantile(samples, t_q_bins)\n",
    "\n",
    "# t_q_val_bins[1:-1]: to make sure the returned indices are between 0-49\n",
    "bdf = (\n",
    "    pd.DataFrame(\n",
    "        list(zip(np.digitize(samples, t_q_val_bins[1:-1]), samples)),\n",
    "        columns=[\"bin\", \"val\"],\n",
    "    )\n",
    "    .groupby(\"bin\")\n",
    "    .mean()\n",
    "    .sort_values(\"bin\")\n",
    "    .reset_index()\n",
    "    .assign(quantile=lambda df: df[\"bin\"].replace(t_bin2q_map))\n",
    ")\n",
    "bdf.plot.scatter(\n",
    "    x=\"quantile\",\n",
    "    y=\"val\",\n",
    "    marker=\"o\",\n",
    "    color=\"red\",\n",
    "    edgecolor=\"none\",\n",
    "    label=\"t_digest_bins\",\n",
    "#     s=30,\n",
    "    ax=ax,\n",
    ")\n",
    "\n",
    "bdf_with_head = pd.concat([pd.DataFrame([[0, np.min(samples)]], columns=['quantile', 'val']), bdf[[\"quantile\", \"val\"]]])\n",
    "for (x1, y1), (x2, y2) in zip(\n",
    "    bdf_with_head.values[1:], bdf_with_head.values[:-1]\n",
    "):\n",
    "    ax.plot([x1, x2], [y1, y2], color=\"red\")\n",
    "\n",
    "ax.set_xlim(-0.001, 0.02)\n",
    "ax.grid()\n",
    "ax.legend(loc=\"upper left\", bbox_to_anchor=(1, 1))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.2"
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 },
 "nbformat": 4,
 "nbformat_minor": 4
}