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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext watermark \n",
      "%watermark -d -v -a 'Sebastian Raschka' -p numpy,pandas"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The watermark extension is already loaded. To reload it, use:\n",
        "  %reload_ext watermark\n",
        "Sebastian Raschka 24/12/2014 \n",
        "\n",
        "CPython 3.4.2\n",
        "IPython 2.3.1\n",
        "\n",
        "numpy 1.9.1\n",
        "pandas 0.15.2\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "4 Simple Tricks To Speed up the Sum Calculation in Pandas"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I wanted to improve the performance of some passages in my code a little bit and found that some simple tweaks can speed up the  `pandas` section significantly. I thought that it might be one useful thing to share -- and no Cython or just-in-time compilation is required! "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In my case, I had a large dataframe where I wanted to calculate the sum of specific columns for different combinations of rows (approx. 100,000,000 of them, that's why I was looking for ways to speed it up). Anyway, below is a simple toy DataFrame to explore the `.sum()` method a little bit."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "import numpy as np\n",
      "\n",
      "df = pd.DataFrame()\n",
      "\n",
      "for col in ('a', 'b', 'c', 'd'):\n",
      "    df[col] = pd.Series(range(1000), index=range(1000))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df.tail()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\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",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>995</th>\n",
        "      <td> 995</td>\n",
        "      <td> 995</td>\n",
        "      <td> 995</td>\n",
        "      <td> 995</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>996</th>\n",
        "      <td> 996</td>\n",
        "      <td> 996</td>\n",
        "      <td> 996</td>\n",
        "      <td> 996</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>997</th>\n",
        "      <td> 997</td>\n",
        "      <td> 997</td>\n",
        "      <td> 997</td>\n",
        "      <td> 997</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>998</th>\n",
        "      <td> 998</td>\n",
        "      <td> 998</td>\n",
        "      <td> 998</td>\n",
        "      <td> 998</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>999</th>\n",
        "      <td> 999</td>\n",
        "      <td> 999</td>\n",
        "      <td> 999</td>\n",
        "      <td> 999</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "       a    b    c    d\n",
        "995  995  995  995  995\n",
        "996  996  996  996  996\n",
        "997  997  997  997  997\n",
        "998  998  998  998  998\n",
        "999  999  999  999  999"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's assume we are interested in calculating the sum of column `a`, `c`, and `d`, which would look like this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df.loc[:, ['a', 'c', 'd']].sum(axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "a    499500\n",
        "c    499500\n",
        "d    499500\n",
        "dtype: int64"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, the `.loc` method is probably the most \"costliest\" one for this kind of operation. Since we are only intersted in the resulting numbers (i.e., the column sums), there is no need to make a copy of the array. Anyway, let's use the method above as a reference for comparison:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 1\n",
      "%timeit -n 1000 -r 5 df.loc[:, ['a', 'c', 'd']].sum(axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 5: 1.37 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Although this is a rather small DataFrame (1000 x 4), let's see by how much we can speed it up using a different slicing method:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 2\n",
      "%timeit -n 1000 -r 5 df[['a', 'c', 'd']].sum(axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 5: 986 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, let us use the Numpy representation of  the `NDFrame` via the `.values` attribue:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 3\n",
      "%timeit -n 1000 -r 5 df[['a', 'c', 'd']].values.sum(axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 5: 687 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "While the speed improvements in #2 and #3 were not really a surprise, the next \"trick\" surprised me a little bit. Here, we are calculating the sum of each column separately rather than slicing the array."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "[df[col].values.sum(axis=0) for col in ('a', 'c', 'd')]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "[499500, 499500, 499500]"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 4\n",
      "%timeit -n 1000 -r 5 [df[col].values.sum(axis=0) for col in ('a', 'c', 'd')]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 5: 64.4 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this case, this is an almost 10x improvement!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One more thing: Let's try the Einstein summation convention [`einsum`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.einsum.html)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import einsum\n",
      "[einsum('i->', df[col].values) for col in ('a', 'c', 'd')]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "[499500, 499500, 499500]"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 5\n",
      "%timeit -n 1000 -r 5 [einsum('i->', df[col].values) for col in ('a', 'c', 'd')]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 5: 55.7 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Conclusion:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using some simple tricks, the column sum calculation improved from 1370 to 57.7 \u00b5s per loop (approx. 25x faster!)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "What about larger DataFrames?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So, what does this trend look like for larger DataFrames?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import timeit\n",
      "import random\n",
      "from numpy import einsum\n",
      "import pandas as pd\n",
      "\n",
      "def run_loc_sum(df):\n",
      "    return df.loc[:, ['a', 'c', 'd']].sum(axis=0)\n",
      "\n",
      "def run_einsum(df):\n",
      "    return [einsum('i->', df[col].values) for col in ('a', 'c', 'd')]\n",
      "\n",
      "orders = [10**i for i in range(4, 8)]\n",
      "loc_res = []\n",
      "einsum_res = []\n",
      "\n",
      "for n in orders:\n",
      "\n",
      "    df = pd.DataFrame()\n",
      "    for col in ('a', 'b', 'c', 'd'):\n",
      "        df[col] = pd.Series(range(n), index=range(n))\n",
      "    \n",
      "    print('n=%s (%s of %s)' %(n, orders.index(n)+1, len(orders)))\n",
      "\n",
      "    loc_res.append(min(timeit.Timer('run_loc_sum(df)' , \n",
      "            'from __main__ import run_loc_sum, df').repeat(repeat=5, number=1)))\n",
      "\n",
      "    einsum_res.append(min(timeit.Timer('run_einsum(df)' , \n",
      "            'from __main__ import run_einsum, df').repeat(repeat=5, number=1)))\n",
      "\n",
      "print('finished')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "n=10000 (1 of 4)\n",
        "n=100000 (2 of 4)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "n=1000000 (3 of 4)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "n=10000000 (4 of 4)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "finished"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "\n",
      "def plot_1():\n",
      "    \n",
      "    fig = plt.figure(figsize=(12,6))\n",
      "    \n",
      "    plt.plot(orders, loc_res, \n",
      "             label=\"df.loc[:, ['a', 'c', 'd']].sum(axis=0)\", \n",
      "             lw=2, alpha=0.6)\n",
      "    plt.plot(orders,einsum_res, \n",
      "             label=\"[einsum('i->', df[col].values) for col in ('a', 'c', 'd')]\", \n",
      "             lw=2, alpha=0.6)\n",
      "\n",
      "    plt.title('Pandas Column Sums', fontsize=20)\n",
      "    plt.xlim([min(orders), max(orders)])\n",
      "    plt.grid()\n",
      "\n",
      "    #plt.xscale('log')\n",
      "    plt.ticklabel_format(style='plain', axis='x')\n",
      "    plt.legend(loc='upper left', fontsize=14)\n",
      "    plt.xlabel('Number of rows', fontsize=16)\n",
      "    plt.ylabel('time in seconds', fontsize=16)\n",
      "    \n",
      "    plt.tight_layout()\n",
      "    plt.show()\n",
      "    \n",
      "plot_1()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1As+yncWegisREZEySHNgxJ/U3sSXs2dh9WoXVP30kysLCoKoKDefqlkzKKaJ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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109989550>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It looks like that the benefit of calculating the sums separately for each column becomes even larger the more rows the DataFrame has."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another question to ask: How does this scale if we have a growing number of columns?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import timeit\n",
      "import random\n",
      "from numpy import einsum\n",
      "import pandas as pd\n",
      "\n",
      "def run_loc_sum(df, n):\n",
      "    return df.loc[:, 0:n-1].sum(axis=0)\n",
      "\n",
      "def run_einsum(df, n):\n",
      "    return [einsum('i->', df[col].values) for col in range(0,n-1)]\n",
      "\n",
      "orders = [10**i for i in range(2, 5)]\n",
      "loc_res = []\n",
      "einsum_res = []\n",
      "\n",
      "for n in orders:\n",
      "\n",
      "    df = pd.DataFrame()\n",
      "    for col in range(n):\n",
      "        df[col] = pd.Series(range(1000), index=range(1000))\n",
      "    \n",
      "    print('n=%s (%s of %s)' %(n, orders.index(n)+1, len(orders)))\n",
      "\n",
      "    loc_res.append(min(timeit.Timer('run_loc_sum(df, n)' , \n",
      "            'from __main__ import run_loc_sum, df, n').repeat(repeat=5, number=1)))\n",
      "\n",
      "    einsum_res.append(min(timeit.Timer('run_einsum(df, n)' , \n",
      "            'from __main__ import run_einsum, df, n').repeat(repeat=5, number=1)))\n",
      "\n",
      "print('finished')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "n=100 (1 of 3)\n",
        "n=1000 (2 of 3)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "n=10000 (3 of 3)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "finished"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "\n",
      "def plot_2():\n",
      "    \n",
      "    fig = plt.figure(figsize=(12,6))\n",
      "    \n",
      "    plt.plot(orders, loc_res, \n",
      "             label=\"df.loc[:, 0:n-1].sum(axis=0)\", \n",
      "             lw=2, alpha=0.6)\n",
      "    plt.plot(orders,einsum_res, \n",
      "             label=\"[einsum('i->', df[col].values) for col in range(0,n-1)]\", \n",
      "             lw=2, alpha=0.6)\n",
      "\n",
      "    plt.title('Pandas Column Sums', fontsize=20)\n",
      "    plt.xlim([min(orders), max(orders)])\n",
      "    plt.grid()\n",
      "\n",
      "    #plt.xscale('log')\n",
      "    plt.ticklabel_format(style='plain', axis='x')\n",
      "    plt.legend(loc='upper left', fontsize=14)\n",
      "    plt.xlabel('Number of columns', fontsize=16)\n",
      "    plt.ylabel('time in seconds', fontsize=16)\n",
      "    \n",
      "    plt.tight_layout()\n",
      "    plt.show()\n",
      "    \n",
      "plot_2()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KFXMP/O3WDWrXDm37giEs1A2Q8+vatSthYWGEhYXx448/+n3e5MmTiYqKCmDL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H1+I1BUHDwJDKdxxoG30vgj7n6gyZjPEc83bScKYCwDnilp1858221bOAJcTwSLB4CXiP+P/z2T\nJiLSbcx9KZbci4iIiIiI9BZlrkRERERERCqg4EpERERERKQCCq5EREREREQqoOBKRERERESkAgqu\nREREREREKqDgSkREREREpAIKrkRERERERCqg4EpERERERKQCCq5EREREREQq8A/8v0nMEi/XJgAA\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109334240>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<br>"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}