5 - Rolling_Sum.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b1b0a153",
   "metadata": {},
   "source": [
    "## Rolling sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f83b5c75",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import string\n",
    "\n",
    "from numba import jit\n",
    "\n",
    "import warnings\n",
    "from numba.core.errors import NumbaTypeSafetyWarning\n",
    "warnings.simplefilter(\"ignore\", category=NumbaTypeSafetyWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19b8a70f",
   "metadata": {},
   "source": [
    "In this notebook I'm comparing several approaches to compute the rolling sum in a pandas dataframe.\n",
    "\n",
    "I'm collecting the computational time and at the end we can see all the times collected inside a table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d24934d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "WINDOW = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c650c0d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "time_result = {}    # table for the time comparisons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8e3f581b",
   "metadata": {},
   "outputs": [],
   "source": [
    "rows = 30000\n",
    "cols = 14\n",
    "col_names = list(string.ascii_uppercase[:cols])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2b71e90c",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=12345)\n",
    "df = pd.DataFrame(np.random.randint(0, 11, size=(rows, cols)), columns=col_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fdaf5fc7",
   "metadata": {},
   "outputs": [
    {
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       "    A  B   C  D  E  F   G  H   I  J  K  L  M  N\n",
       "0   2  5   1  4  9  5   2  1   6  1  9  7  6  0\n",
       "1   2  9  10  1  2  6   7  7   7  8  7  1  7  4\n",
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   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b67dab42",
   "metadata": {},
   "source": [
    "#### Approach that uses numpy roll"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "33ef12bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rolling_sum(df: pd.DataFrame, window: int) -> pd.DataFrame:\n",
    "    \"\"\" Rolling sum using np.roll approach \"\"\"\n",
    "    dt = df.values.astype(np.float64)\n",
    "    dt_arr = [dt]\n",
    "    for i in range(1, window):\n",
    "        dt_i = np.roll(dt, shift=i, axis=0)\n",
    "        dt_arr.append(dt_i)\n",
    "    df_sum = np.sum(dt_arr, axis=0)\n",
    "    df_sum[:window-1,:] = np.nan\n",
    "    return pd.DataFrame(df_sum, columns=df.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ea532e6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_roll = rolling_sum(df, window=WINDOW)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f7781b07",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "      A     B     C     D     E     F     G     H     I     J     K     L  \\\n",
       "0   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
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    "df_roll.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed3a61eb",
   "metadata": {},
   "source": [
    "#### Direct approach:   O(n * window)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5857049a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rolling_classic(df: pd.DataFrame, window: int) -> pd.DataFrame:\n",
    "    \"\"\" Rolling sum using manual rolling \"\"\"\n",
    "    \n",
    "    arr = df.values.astype(np.float64)\n",
    "    rows, cols = arr.shape\n",
    "    result = np.full((rows, cols), np.nan, dtype=np.float64)\n",
    "\n",
    "    for i in range(window - 1, rows):\n",
    "        sum_row = np.zeros(cols, dtype=np.float64)\n",
    "        for j in range(window):\n",
    "            sum_row += arr[i - j]  # Accumulate the sum of the window\n",
    "        result[i] = sum_row\n",
    "\n",
    "    return pd.DataFrame(result, columns=df.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "06626661",
   "metadata": {},
   "outputs": [],
   "source": [
    "roll_class = rolling_classic(df, WINDOW)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ea9879c2",
   "metadata": {},
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       "      A     B     C     D     E     F     G     H     I     J     K     L  \\\n",
       "0   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
       "1   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
       "2   4.0  17.0  16.0  12.0  14.0  12.0  14.0  10.0  18.0  12.0  24.0  13.0   \n",
       "3   5.0  12.0  21.0  16.0   5.0  12.0  22.0  15.0  20.0  20.0  17.0   8.0   \n",
       "4  13.0  10.0  16.0  22.0   4.0   6.0  25.0  17.0  23.0  15.0  10.0  10.0   \n",
       "\n",
       "      M     N  \n",
       "0   NaN   NaN  \n",
       "1   NaN   NaN  \n",
       "2  15.0   9.0  \n",
       "3  11.0  18.0  \n",
       "4   4.0  20.0  "
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     "execution_count": 12,
     "metadata": {},
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   ],
   "source": [
    "roll_class.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "feaddbff",
   "metadata": {},
   "source": [
    "#### Pandas rolling function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "49f13a01",
   "metadata": {},
   "outputs": [],
   "source": [
    "roll = df.rolling(window=WINDOW).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "bdcc5384",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "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>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "      <th>G</th>\n",
       "      <th>H</th>\n",
       "      <th>I</th>\n",
       "      <th>J</th>\n",
       "      <th>K</th>\n",
       "      <th>L</th>\n",
       "      <th>M</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>20.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      A     B     C     D     E     F     G     H     I     J     K     L  \\\n",
       "0   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
       "1   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
       "2   4.0  17.0  16.0  12.0  14.0  12.0  14.0  10.0  18.0  12.0  24.0  13.0   \n",
       "3   5.0  12.0  21.0  16.0   5.0  12.0  22.0  15.0  20.0  20.0  17.0   8.0   \n",
       "4  13.0  10.0  16.0  22.0   4.0   6.0  25.0  17.0  23.0  15.0  10.0  10.0   \n",
       "\n",
       "      M     N  \n",
       "0   NaN   NaN  \n",
       "1   NaN   NaN  \n",
       "2  15.0   9.0  \n",
       "3  11.0  18.0  \n",
       "4   4.0  20.0  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roll.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a788cd7e",
   "metadata": {},
   "source": [
    "### Let's time the functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "8682087c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3 ms ± 21 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "r_np_roll = %timeit -o rolling_sum(df, window=WINDOW)\n",
    "\n",
    "time_result[\"numpy.roll\"] = r_np_roll.average * 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "57d02ad5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "35.9 ms ± 138 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "r_class = %timeit -o rolling_classic(df, window=WINDOW)\n",
    "\n",
    "time_result[\"O(n * window)\"] = r_class.average * 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2bb0ae61",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.99 ms ± 47.8 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "r_cyth = %timeit -o df.rolling(window=WINDOW).sum(engine=\"cython\")\n",
    "\n",
    "time_result[\"pandas cython\"] = r_cyth.average * 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2aaa6393",
   "metadata": {},
   "source": [
    "----------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f56b0e71",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.71 ms ± 108 μs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "r_p_num = %timeit -o df.rolling(window=WINDOW).sum(engine=\"numba\", \\\n",
    "            engine_kwargs={\"parallel\": False, \"nogil\": False, \"nopython\": True})\n",
    "\n",
    "time_result[\"pandas numba\"] = r_p_num.average * 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "11663f13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.11 ms ± 97.6 μs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "OMP: Info #276: omp_set_nested routine deprecated, please use omp_set_max_active_levels instead.\n"
     ]
    }
   ],
   "source": [
    "r_p_par = %timeit -o df.rolling(window=WINDOW).sum(engine=\"numba\", \\\n",
    "        engine_kwargs={\"parallel\": True, \"nogil\": True, \"nopython\": True})\n",
    "\n",
    "time_result[\"pandas parallel\"] = r_p_par.average * 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d7a2c6e",
   "metadata": {},
   "source": [
    "### The for loops in rolling_classic are slow. Let's use numba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "26d79df8",
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(nopython=True)\n",
    "def rolling_sum_numba(arr: np.ndarray, window: int) -> np.ndarray:\n",
    "    \"\"\" Rolling sum using manual rolling approach compatible with Numba JIT compilation \"\"\"\n",
    "    \n",
    "    rows, cols = arr.shape\n",
    "    result = np.full((rows, cols), np.nan, dtype=np.float64)\n",
    "\n",
    "    for i in range(window - 1, rows):\n",
    "        sum_row = np.zeros(cols, dtype=np.float64)\n",
    "        for j in range(window):\n",
    "            sum_row += arr[i - j]  # Accumulate the sum of the window\n",
    "        result[i] = sum_row\n",
    "\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "31f7c2a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rolling_classic_numba(df: pd.DataFrame, window: int) -> pd.DataFrame:\n",
    "    arr = df.values.astype(np.float64)\n",
    "    result_array = rolling_sum_numba(arr, window)\n",
    "    result_df = pd.DataFrame(result_array, columns=df.columns)\n",
    "    return result_df\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c23c2a2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "roll_numb = rolling_classic_numba(df, window=WINDOW)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7c56d220",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "      <th>G</th>\n",
       "      <th>H</th>\n",
       "      <th>I</th>\n",
       "      <th>J</th>\n",
       "      <th>K</th>\n",
       "      <th>L</th>\n",
       "      <th>M</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>20.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      A     B     C     D     E     F     G     H     I     J     K     L  \\\n",
       "0   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
       "1   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
       "2   4.0  17.0  16.0  12.0  14.0  12.0  14.0  10.0  18.0  12.0  24.0  13.0   \n",
       "3   5.0  12.0  21.0  16.0   5.0  12.0  22.0  15.0  20.0  20.0  17.0   8.0   \n",
       "4  13.0  10.0  16.0  22.0   4.0   6.0  25.0  17.0  23.0  15.0  10.0  10.0   \n",
       "\n",
       "      M     N  \n",
       "0   NaN   NaN  \n",
       "1   NaN   NaN  \n",
       "2  15.0   9.0  \n",
       "3  11.0  18.0  \n",
       "4   4.0  20.0  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roll_numb.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "467f29fd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.52 ms ± 26.8 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "r_c_n = %timeit -o rolling_classic_numba(df, window=WINDOW)\n",
    "\n",
    "time_result[\"O(n * window) numba\"] = r_c_n.average * 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbf9640e",
   "metadata": {},
   "source": [
    "### Rolling approach that is O(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ebb3c761",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rolling_fast(arr: np.ndarray, window: int) -> np.ndarray:\n",
    "    \"\"\" Rolling sum using the approach that add the first and remove the last \"\"\"\n",
    "    rows, cols = arr.shape\n",
    "    result = np.full((rows, cols), np.nan, dtype=np.float64)  # initialize\n",
    "    running_sum = np.zeros(cols, dtype=np.float64)\n",
    "    for i in range(rows):\n",
    "        running_sum += arr[i]                 # add the first \n",
    "        if i >= window:\n",
    "            running_sum -= arr[i - window]    # remove the last\n",
    "        if i >= window - 1:\n",
    "            result[i] = running_sum           # store value\n",
    "    return result\n",
    "\n",
    "def rolling_sum_fast(df: pd.DataFrame, window: int) -> pd.DataFrame:\n",
    "    arr = df.values.astype(np.float64)\n",
    "    result_array = rolling_fast(arr, window)\n",
    "    result_df = pd.DataFrame(result_array, columns=df.columns)\n",
    "    return result_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "6aa427c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "      <th>G</th>\n",
       "      <th>H</th>\n",
       "      <th>I</th>\n",
       "      <th>J</th>\n",
       "      <th>K</th>\n",
       "      <th>L</th>\n",
       "      <th>M</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>20.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      A     B     C     D     E     F     G     H     I     J     K     L  \\\n",
       "0   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
       "1   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
       "2   4.0  17.0  16.0  12.0  14.0  12.0  14.0  10.0  18.0  12.0  24.0  13.0   \n",
       "3   5.0  12.0  21.0  16.0   5.0  12.0  22.0  15.0  20.0  20.0  17.0   8.0   \n",
       "4  13.0  10.0  16.0  22.0   4.0   6.0  25.0  17.0  23.0  15.0  10.0  10.0   \n",
       "\n",
       "      M     N  \n",
       "0   NaN   NaN  \n",
       "1   NaN   NaN  \n",
       "2  15.0   9.0  \n",
       "3  11.0  18.0  \n",
       "4   4.0  20.0  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roll_fast = rolling_sum_fast(df, WINDOW)\n",
    "roll_fast.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e306d129",
   "metadata": {},
   "outputs": [],
   "source": [
    "rolling_fast_numba = jit(rolling_fast, nopython=True)\n",
    "\n",
    "def rolling_sum_fast_numba(df: pd.DataFrame, window: int) -> pd.DataFrame:\n",
    "    arr = df.values.astype(np.float64)\n",
    "    result_array = rolling_fast_numba(arr, window)\n",
    "    result_df = pd.DataFrame(result_array, columns=df.columns)\n",
    "    return result_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "df7662dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "      <th>G</th>\n",
       "      <th>H</th>\n",
       "      <th>I</th>\n",
       "      <th>J</th>\n",
       "      <th>K</th>\n",
       "      <th>L</th>\n",
       "      <th>M</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>25.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>20.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      A     B     C     D     E     F     G     H     I     J     K     L  \\\n",
       "0   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
       "1   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   NaN   \n",
       "2   4.0  17.0  16.0  12.0  14.0  12.0  14.0  10.0  18.0  12.0  24.0  13.0   \n",
       "3   5.0  12.0  21.0  16.0   5.0  12.0  22.0  15.0  20.0  20.0  17.0   8.0   \n",
       "4  13.0  10.0  16.0  22.0   4.0   6.0  25.0  17.0  23.0  15.0  10.0  10.0   \n",
       "\n",
       "      M     N  \n",
       "0   NaN   NaN  \n",
       "1   NaN   NaN  \n",
       "2  15.0   9.0  \n",
       "3  11.0  18.0  \n",
       "4   4.0  20.0  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roll_fast = rolling_sum_fast_numba(df, WINDOW)\n",
    "roll_fast.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b7f338ee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "808 μs ± 32.9 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "r_f_n = %timeit -o rolling_sum_fast_numba(df, window=WINDOW)\n",
    "\n",
    "time_result[\"O(n) numba\"] = r_f_n.average * 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "03d20eec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21.6 ms ± 236 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "r_f = %timeit -o rolling_sum_fast(df, window=WINDOW)\n",
    "\n",
    "time_result[\"O(n)\"] = r_f.average * 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c1b472b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_time = pd.DataFrame.from_dict(time_result, orient=\"index\", columns=[\"ms\"]).sort_values(\n",
    "    by=\"ms\", ascending=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "7f57ba4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>ms</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>O(n) numba</th>\n",
       "      <td>0.807695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pandas parallel</th>\n",
       "      <td>1.111458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>numpy.roll</th>\n",
       "      <td>1.298949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>O(n * window) numba</th>\n",
       "      <td>1.520822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pandas numba</th>\n",
       "      <td>2.706935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pandas cython</th>\n",
       "      <td>3.991259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>O(n)</th>\n",
       "      <td>21.625995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>O(n * window)</th>\n",
       "      <td>35.852639</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            ms\n",
       "O(n) numba            0.807695\n",
       "pandas parallel       1.111458\n",
       "numpy.roll            1.298949\n",
       "O(n * window) numba   1.520822\n",
       "pandas numba          2.706935\n",
       "pandas cython         3.991259\n",
       "O(n)                 21.625995\n",
       "O(n * window)        35.852639"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_time"
   ]
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