{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# sPyRMSD: A symmetry-corrected Python tool for RMSD calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import os\n",
    "import warnings\n",
    "\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Utility Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function is an helper function to create a `pd.DataFrame` for every each system, containing the RMSD for each rank."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def systemdata(RMSD: np.ndarray, system: str, name: str):\n",
    "    dfs = pd.DataFrame()\n",
    "    \n",
    "    n = len(RMSD)\n",
    "    \n",
    "    dfs[name] = RMSD\n",
    "    dfs[\"system\"] = [system] * n\n",
    "    dfs[\"rank\"] = range(1,n+1)\n",
    "    \n",
    "    return dfs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_to_df(col_name, systems, fname, path=\"docking\"):\n",
    "    df = pd.DataFrame(columns=[\"system\", \"rank\", col_name])\n",
    "    \n",
    "    for system in systems:\n",
    "    \n",
    "        infname = os.path.join(path, system, fname)\n",
    "\n",
    "        with warnings.catch_warnings(): # Avoid UserWarning for empty file\n",
    "            warnings.simplefilter(\"ignore\")\n",
    "\n",
    "            try:\n",
    "                RMSD = np.loadtxt(infname)\n",
    "            except:\n",
    "                print(system)\n",
    "                raise\n",
    "    \n",
    "        if RMSD.shape == tuple(): # Check if file is empty\n",
    "            continue\n",
    "            \n",
    "        dfs = systemdata(RMSD, system, col_name)\n",
    "    \n",
    "        df = df.append(dfs, sort=False, ignore_index=True)\n",
    "        \n",
    "    return df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Systems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All ligand crystal structures and docking poses are stored in `pdbbind/PDBID` folders, where `PDBID` it the [PDB](https://www.rcsb.org/) identifier for a particular protein-ligand complex. Let's list all the systems:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "outputPrepend"
    ]
   },
   "outputs": [],
   "source": [
    "allsystems = [s for s in os.listdir(\"docking\") if not s.startswith('.')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "outputPrepend"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "['2v25', '2xxx', '4jpx', '4io2', '1laf', '4io5', '3zi8', '4oeu', '2p2a', '4jpy', '4xmr', '2a5s', '1lan', '4io4', '1lag', '3s9e', '4io3', '6h2t', '4zv2', '3ip6', '4kqp', '6h1u', '2cht', '3dln', '3lir', '3ff3', '4bkt', '4g4p', '4ts1', '6gg4', '4crf', '1lst', '5vja', '5mby', '3rv4', '5tcj', '5vih', '1usk', '4ymx', '6hke', '3q1x', '3mi3', '3lp4', '4igt', '4us3', '3f3e', '2pyy', '5dex', '3f6g', '1qaw', '3tk2', '3fuz', '3f3d', '2a4m', '5ey0', '3b3w', '5ave', '2pvu', '4io6', '3f48', '2xxr', '1o86', '4n07', '3u93', '4io7', '5fhm', '3b7i', '4uc5', '1hsl', '1phw', '4zv1', '3ip5', '5u8c', '3a9i', '2xii', '2ypo', '1ii5', '2rio', '4x48', '4ykj', '4o3c', '4yb5', '1usi', '2y7i', '5vij', '3lmk', '3fas', '4ykk', '1xff', '2q2a', '1ssq', '6mj7', '5l8a', '1xt8', '1t7d', '3b3s', '5gs9', '1wdn']\n"
    }
   ],
   "source": [
    "systems = []\n",
    "missing = [] # Systems with missing data\n",
    "for system in allsystems:\n",
    "    allfiles = True\n",
    "    for f in [\"obrms.dat\", \"obrms-min.dat\", \"spyrmsd.dat\", \"spyrmsd-min.dat\"]:\n",
    "        fname = os.path.join(\"docking\", system, f)\n",
    "        if os.path.getsize(fname) == 0:\n",
    "            missing.append(system)\n",
    "            allfiles = False\n",
    "            break\n",
    "    \n",
    "    if allfiles:\n",
    "        systems.append(system)\n",
    "\n",
    "print(missing)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OpenBabel Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to test `pyRMSD`, we compare our results with [OpenBabel](http://openbabel.org) `obrms` tool. RMSD calculations performed with `obrms` on a series of docking calculations are stored in `obrms.dat` (for standard RMSD calculations) and in `obrms-min.dat` (for minimised RMSD calculations)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "      system rank     obrms\n0       4rdn    1  3.385690\n1       4rdn    2  0.600406\n2       4rdn    3  6.571630\n3       4rdn    4  7.721690\n4       4rdn    5  6.976840\n...      ...  ...       ...\n40434   5umx    6  5.077780\n40435   5umx    7  8.807000\n40436   5umx    8  6.399600\n40437   5umx    9  8.682270\n40438   5umx   10  5.332780\n\n[40439 rows x 3 columns]",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>system</th>\n      <th>rank</th>\n      <th>obrms</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>4rdn</td>\n      <td>1</td>\n      <td>3.385690</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>4rdn</td>\n      <td>2</td>\n      <td>0.600406</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>4rdn</td>\n      <td>3</td>\n      <td>6.571630</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>4rdn</td>\n      <td>4</td>\n      <td>7.721690</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4rdn</td>\n      <td>5</td>\n      <td>6.976840</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>40434</th>\n      <td>5umx</td>\n      <td>6</td>\n      <td>5.077780</td>\n    </tr>\n    <tr>\n      <th>40435</th>\n      <td>5umx</td>\n      <td>7</td>\n      <td>8.807000</td>\n    </tr>\n    <tr>\n      <th>40436</th>\n      <td>5umx</td>\n      <td>8</td>\n      <td>6.399600</td>\n    </tr>\n    <tr>\n      <th>40437</th>\n      <td>5umx</td>\n      <td>9</td>\n      <td>8.682270</td>\n    </tr>\n    <tr>\n      <th>40438</th>\n      <td>5umx</td>\n      <td>10</td>\n      <td>5.332780</td>\n    </tr>\n  </tbody>\n</table>\n<p>40439 rows × 3 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "df_obrms = load_to_df(\"obrms\", systems, \"obrms.dat\")\n",
    "df_obrms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "      system rank    obrmsm\n0       4rdn    1  0.864598\n1       4rdn    2  0.421085\n2       4rdn    3  0.525745\n3       4rdn    4  1.385680\n4       4rdn    5  0.615616\n...      ...  ...       ...\n40434   5umx    6  2.018260\n40435   5umx    7  0.491282\n40436   5umx    8  1.385560\n40437   5umx    9  1.395160\n40438   5umx   10  1.441860\n\n[40439 rows x 3 columns]",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>system</th>\n      <th>rank</th>\n      <th>obrmsm</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>4rdn</td>\n      <td>1</td>\n      <td>0.864598</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>4rdn</td>\n      <td>2</td>\n      <td>0.421085</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>4rdn</td>\n      <td>3</td>\n      <td>0.525745</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>4rdn</td>\n      <td>4</td>\n      <td>1.385680</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4rdn</td>\n      <td>5</td>\n      <td>0.615616</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>40434</th>\n      <td>5umx</td>\n      <td>6</td>\n      <td>2.018260</td>\n    </tr>\n    <tr>\n      <th>40435</th>\n      <td>5umx</td>\n      <td>7</td>\n      <td>0.491282</td>\n    </tr>\n    <tr>\n      <th>40436</th>\n      <td>5umx</td>\n      <td>8</td>\n      <td>1.385560</td>\n    </tr>\n    <tr>\n      <th>40437</th>\n      <td>5umx</td>\n      <td>9</td>\n      <td>1.395160</td>\n    </tr>\n    <tr>\n      <th>40438</th>\n      <td>5umx</td>\n      <td>10</td>\n      <td>1.441860</td>\n    </tr>\n  </tbody>\n</table>\n<p>40439 rows × 3 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "df_obrmsm = load_to_df(\"obrmsm\", systems, \"obrms-min.dat\")\n",
    "df_obrmsm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can marge `df_obrms` and `df_obrmsm` in a single dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "      system rank     obrms    obrmsm\n0       4rdn    1  3.385690  0.864598\n1       4rdn    2  0.600406  0.421085\n2       4rdn    3  6.571630  0.525745\n3       4rdn    4  7.721690  1.385680\n4       4rdn    5  6.976840  0.615616\n...      ...  ...       ...       ...\n40434   5umx    6  5.077780  2.018260\n40435   5umx    7  8.807000  0.491282\n40436   5umx    8  6.399600  1.385560\n40437   5umx    9  8.682270  1.395160\n40438   5umx   10  5.332780  1.441860\n\n[40439 rows x 4 columns]",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>system</th>\n      <th>rank</th>\n      <th>obrms</th>\n      <th>obrmsm</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>4rdn</td>\n      <td>1</td>\n      <td>3.385690</td>\n      <td>0.864598</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>4rdn</td>\n      <td>2</td>\n      <td>0.600406</td>\n      <td>0.421085</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>4rdn</td>\n      <td>3</td>\n      <td>6.571630</td>\n      <td>0.525745</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>4rdn</td>\n      <td>4</td>\n      <td>7.721690</td>\n      <td>1.385680</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4rdn</td>\n      <td>5</td>\n      <td>6.976840</td>\n      <td>0.615616</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>40434</th>\n      <td>5umx</td>\n      <td>6</td>\n      <td>5.077780</td>\n      <td>2.018260</td>\n    </tr>\n    <tr>\n      <th>40435</th>\n      <td>5umx</td>\n      <td>7</td>\n      <td>8.807000</td>\n      <td>0.491282</td>\n    </tr>\n    <tr>\n      <th>40436</th>\n      <td>5umx</td>\n      <td>8</td>\n      <td>6.399600</td>\n      <td>1.385560</td>\n    </tr>\n    <tr>\n      <th>40437</th>\n      <td>5umx</td>\n      <td>9</td>\n      <td>8.682270</td>\n      <td>1.395160</td>\n    </tr>\n    <tr>\n      <th>40438</th>\n      <td>5umx</td>\n      <td>10</td>\n      <td>5.332780</td>\n      <td>1.441860</td>\n    </tr>\n  </tbody>\n</table>\n<p>40439 rows × 4 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "df = pd.merge(df_obrms, df_obrmsm, left_on=[\"system\", \"rank\"], right_on=[\"system\", \"rank\"], how=\"outer\")\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sPyRMSD Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
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   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "      system rank     rmsd\n0       4rdn    1  3.38569\n1       4rdn    2  0.60041\n2       4rdn    3  6.57163\n3       4rdn    4  7.72169\n4       4rdn    5  6.97684\n...      ...  ...      ...\n40434   5umx    6  5.07778\n40435   5umx    7  8.80700\n40436   5umx    8  6.39960\n40437   5umx    9  8.68227\n40438   5umx   10  5.33278\n\n[40439 rows x 3 columns]",
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     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "source": [
    "df_rmsd = load_to_df(\"rmsd\", systems, \"spyrmsd.dat\")\n",
    "df_rmsd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
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   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "      system rank    rmsdm\n0       4rdn    1  0.86460\n1       4rdn    2  0.42108\n2       4rdn    3  0.52575\n3       4rdn    4  1.38568\n4       4rdn    5  0.61562\n...      ...  ...      ...\n40434   5umx    6  2.01826\n40435   5umx    7  0.49128\n40436   5umx    8  1.38556\n40437   5umx    9  1.39516\n40438   5umx   10  1.44186\n\n[40439 rows x 3 columns]",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>system</th>\n      <th>rank</th>\n      <th>rmsdm</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>4rdn</td>\n      <td>1</td>\n      <td>0.86460</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>4rdn</td>\n      <td>2</td>\n      <td>0.42108</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>4rdn</td>\n      <td>3</td>\n      <td>0.52575</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>4rdn</td>\n      <td>4</td>\n      <td>1.38568</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4rdn</td>\n      <td>5</td>\n      <td>0.61562</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>40434</th>\n      <td>5umx</td>\n      <td>6</td>\n      <td>2.01826</td>\n    </tr>\n    <tr>\n      <th>40435</th>\n      <td>5umx</td>\n      <td>7</td>\n      <td>0.49128</td>\n    </tr>\n    <tr>\n      <th>40436</th>\n      <td>5umx</td>\n      <td>8</td>\n      <td>1.38556</td>\n    </tr>\n    <tr>\n      <th>40437</th>\n      <td>5umx</td>\n      <td>9</td>\n      <td>1.39516</td>\n    </tr>\n    <tr>\n      <th>40438</th>\n      <td>5umx</td>\n      <td>10</td>\n      <td>1.44186</td>\n    </tr>\n  </tbody>\n</table>\n<p>40439 rows × 3 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "df_rmsdm = load_to_df(\"rmsdm\", systems, \"spyrmsd-min.dat\")\n",
    "df_rmsdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.merge(df, df_rmsd, left_on=[\"system\", \"rank\"], right_on=[\"system\", \"rank\"])\n",
    "df = pd.merge(df, df_rmsdm, left_on=[\"system\", \"rank\"], right_on=[\"system\", \"rank\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "  system rank     obrms    obrmsm     rmsd    rmsdm\n0   4rdn    1  3.385690  0.864598  3.38569  0.86460\n1   4rdn    2  0.600406  0.421085  0.60041  0.42108\n2   4rdn    3  6.571630  0.525745  6.57163  0.52575\n3   4rdn    4  7.721690  1.385680  7.72169  1.38568\n4   4rdn    5  6.976840  0.615616  6.97684  0.61562",
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     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "              obrms        obrmsm          rmsd         rmsdm\ncount  40439.000000  40439.000000  40439.000000  40439.000000\nmean       4.770393      1.478122      4.770393      1.478123\nstd        2.707172      1.060373      2.707172      1.060373\nmin        0.070833      0.000000      0.070830      0.000000\n25%        2.716360      0.660768      2.716360      0.660765\n50%        4.422400      1.306030      4.422400      1.306030\n75%        6.525090      2.077525      6.525090      2.077525\nmax       21.327900      7.729380     21.327900      7.729380",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>obrms</th>\n      <th>obrmsm</th>\n      <th>rmsd</th>\n      <th>rmsdm</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>count</th>\n      <td>40439.000000</td>\n      <td>40439.000000</td>\n      <td>40439.000000</td>\n      <td>40439.000000</td>\n    </tr>\n    <tr>\n      <th>mean</th>\n      <td>4.770393</td>\n      <td>1.478122</td>\n      <td>4.770393</td>\n      <td>1.478123</td>\n    </tr>\n    <tr>\n      <th>std</th>\n      <td>2.707172</td>\n      <td>1.060373</td>\n      <td>2.707172</td>\n      <td>1.060373</td>\n    </tr>\n    <tr>\n      <th>min</th>\n      <td>0.070833</td>\n      <td>0.000000</td>\n      <td>0.070830</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>25%</th>\n      <td>2.716360</td>\n      <td>0.660768</td>\n      <td>2.716360</td>\n      <td>0.660765</td>\n    </tr>\n    <tr>\n      <th>50%</th>\n      <td>4.422400</td>\n      <td>1.306030</td>\n      <td>4.422400</td>\n      <td>1.306030</td>\n    </tr>\n    <tr>\n      <th>75%</th>\n      <td>6.525090</td>\n      <td>2.077525</td>\n      <td>6.525090</td>\n      <td>2.077525</td>\n    </tr>\n    <tr>\n      <th>max</th>\n      <td>21.327900</td>\n      <td>7.729380</td>\n      <td>21.327900</td>\n      <td>7.729380</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## spyRMSD vs OpenBabel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from scipy.stats import pearsonr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon = 1e-4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard RMSD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df[\"rmsd\"].to_numpy()\n",
    "y = df[\"obrms\"].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "m = min(min(x), min(y))\n",
    "M = max(max(x), max(y))\n",
    "\n",
    "d = np.linspace(m, M, 1000)\n",
    "\n",
    "plt.figure(figsize=(6.72, 6.72))\n",
    "plt.plot(d, d)\n",
    "plt.plot(x, y, \"o\", alpha=0.1)\n",
    "plt.xlabel(\"spyrmsd (Å)\")\n",
    "plt.ylabel(\"obrms (Å)\")\n",
    "plt.title(\"Symmetry-Corrected RMSD\")\n",
    "plt.savefig(\"spyrmsd-obrms.pdf\")\n",
    "plt.savefig(\"spyrmsd-obrms.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "3.8042069289522724e-11"
     },
     "metadata": {},
     "execution_count": 20
    }
   ],
   "source": [
    "mean_squared_error(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(0.9999999999974054, 0.0)"
     },
     "metadata": {},
     "execution_count": 21
    }
   ],
   "source": [
    "pearsonr(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "5.000000000165983e-05"
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "source": [
    "error = abs(x - y)\n",
    "max(error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0/40439\n"
    }
   ],
   "source": [
    "print(f\"{len(error[error > epsilon])}/{len(error)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Minimised RMSD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "xm = df[\"rmsdm\"].to_numpy()\n",
    "ym = df[\"obrmsm\"].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 483.84x483.84 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "m = min(min(xm), min(ym))\n",
    "M = max(max(xm), max(ym))\n",
    "\n",
    "d = np.linspace(m, M, 1000)\n",
    "\n",
    "plt.figure(figsize=(6.72, 6.72))\n",
    "plt.plot(d, d)\n",
    "plt.plot(xm, ym, \"o\", alpha=0.1)\n",
    "plt.xlabel(\"spyrmsd (Å)\")\n",
    "plt.ylabel(\"obrms (Å)\")\n",
    "plt.title(\"Minimised Symmetry-Corrected RMSD\")\n",
    "plt.savefig(\"spyrmsd-obrms-min.pdf\")\n",
    "plt.savefig(\"spyrmsd-obrms-min.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "3.283622226884007e-12"
     },
     "metadata": {},
     "execution_count": 26
    }
   ],
   "source": [
    "mean_squared_error(xm, ym)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(0.9999999999985398, 0.0)"
     },
     "metadata": {},
     "execution_count": 27
    }
   ],
   "source": [
    "pearsonr(xm, ym)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "5.000000000032756e-06"
     },
     "metadata": {},
     "execution_count": 28
    }
   ],
   "source": [
    "error = abs(xm - ym)\n",
    "max(error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "0/40439\n"
    }
   ],
   "source": [
    "print(f\"{len(error[error > epsilon])}/{len(error)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hungarian RMSD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from spyrmsd import rmsd, io"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_systems = 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Randomly select systems\n",
    "idxs = np.random.randint(0, len(systems), n_systems)\n",
    "idxs = np.random.randint(0, len(systems), n_systems)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hrmsd_vs_symmrmsd(system, df):\n",
    "    fref = os.path.join(\"docking\", system, f\"{system}_ligand.sdf\")\n",
    "    fmol = os.path.join(\"docking\", system, f\"{system}_dock.sdf\")\n",
    "\n",
    "    ref = io.loadmol(fref)\n",
    "    mols = io.loadallmols(fmol)\n",
    "\n",
    "    ref.strip()\n",
    "\n",
    "    for m in mols:\n",
    "        m.strip()\n",
    "\n",
    "    for i, m in enumerate(mols):\n",
    "\n",
    "        rh  = rmsd.hrmsd(ref.coordinates, m.coordinates, ref.atomicnums, m.atomicnums)\n",
    "        rs = rmsd.symmrmsd(ref.coordinates, m.coordinates, \n",
    "            ref.atomicnums, m.atomicnums, \n",
    "            ref.adjacency_matrix, m.adjacency_matrix,)\n",
    "\n",
    "        rank = i + 1\n",
    "        \n",
    "        df = df.append({\"system\": system, \n",
    "                        \"r\": rank, \n",
    "                        \"hrmsd\": rh,\n",
    "                        \"srmsd\": rs,\n",
    "                        }, \n",
    "                        sort=False, ignore_index=True)\n",
    "\n",
    "    return df\n",
    "\n",
    "# Results\n",
    "df_hungarian = pd.DataFrame(columns=[\"system\", \"r\", \"hrmsd\", \"srmsd\"])\n",
    "\n",
    "for idx in idxs:\n",
    "    system = systems[idx]\n",
    "\n",
    "    df_hungarian = hrmsd_vs_symmrmsd(system, df_hungarian)\n",
    "\n",
    "# Add simple system 1DJR\n",
    "df_hungarian = hrmsd_vs_symmrmsd(\"1drj\", df_hungarian)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "             hrmsd        srmsd\ncount  4545.000000  4545.000000\nmean      3.305647     4.727237\nstd       1.607200     2.683198\nmin       0.070833     0.070833\n25%       2.157206     2.757365\n50%       3.214788     4.398454\n75%       4.331581     6.399601\nmax       9.780200    15.267620",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>hrmsd</th>\n      <th>srmsd</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>count</th>\n      <td>4545.000000</td>\n      <td>4545.000000</td>\n    </tr>\n    <tr>\n      <th>mean</th>\n      <td>3.305647</td>\n      <td>4.727237</td>\n    </tr>\n    <tr>\n      <th>std</th>\n      <td>1.607200</td>\n      <td>2.683198</td>\n    </tr>\n    <tr>\n      <th>min</th>\n      <td>0.070833</td>\n      <td>0.070833</td>\n    </tr>\n    <tr>\n      <th>25%</th>\n      <td>2.157206</td>\n      <td>2.757365</td>\n    </tr>\n    <tr>\n      <th>50%</th>\n      <td>3.214788</td>\n      <td>4.398454</td>\n    </tr>\n    <tr>\n      <th>75%</th>\n      <td>4.331581</td>\n      <td>6.399601</td>\n    </tr>\n    <tr>\n      <th>max</th>\n      <td>9.780200</td>\n      <td>15.267620</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 34
    }
   ],
   "source": [
    "df_hungarian.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "xh = df_hungarian[\"srmsd\"].to_numpy()\n",
    "yh = df_hungarian[\"hrmsd\"].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "system  r     hrmsd     srmsd\n4542   1drj  2  0.996866  2.456633\n"
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "m = min(min(xh), min(yh))\n",
    "M = max(max(xh), max(yh))\n",
    "\n",
    "d = np.linspace(m, M, 1000)\n",
    "\n",
    "df_p = df_hungarian.loc[(df_hungarian.system == \"1drj\") & (df_hungarian.r == 2)]\n",
    "print(df_p)\n",
    "\n",
    "p = df_p[[\"srmsd\", \"hrmsd\"]].to_numpy()\n",
    "\n",
    "plt.figure(figsize=(6.72, 6.72))\n",
    "plt.plot(d, d)\n",
    "plt.plot(xh, yh, \".\", alpha=0.1)\n",
    "plt.plot(p[0,0], p[0,1], \"X\", ms=10)\n",
    "plt.xlabel(\"graph isomorphism (Å)\")\n",
    "plt.ylabel(\"hungarian method (Å)\")\n",
    "plt.savefig(\"iso-hung.pdf\")\n",
    "plt.savefig(\"iso-hung.png\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.6.10 64-bit ('spyrmsd-conda': conda)",
   "language": "python",
   "name": "python361064bitspyrmsdcondacondad043ff532f194564b58ddfe200e0b505"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}