metakermit/pandas-integration.ipynb

## pandas-integration.ipynb
{
 "metadata": {
  "name": "pandas-integration"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A numerical integration recipe as discussed [here](https://github.com/pydata/pandas/issues/3759)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import integrate\n",
      "import pandas as pd\n",
      "import numpy as np\n",
      "\n",
      "def integrate_method(self, how='trapz', unit='s'):\n",
      "    '''Numerically integrate the time series.\n",
      "\n",
      "    @param how: the method to use (trapz by default)\n",
      "    @return \n",
      "\n",
      "    Available methods:\n",
      "     * trapz - trapezoidal\n",
      "     * cumtrapz - cumulative trapezoidal\n",
      "     * simps - Simpson's rule\n",
      "     * romb - Romberger's rule\n",
      "\n",
      "    See http://docs.scipy.org/doc/scipy/reference/integrate.html for the method details.\n",
      "    or the source code\n",
      "    https://github.com/scipy/scipy/blob/master/scipy/integrate/quadrature.py\n",
      "    '''\n",
      "    available_rules = set(['trapz', 'cumtrapz', 'simps', 'romb'])\n",
      "    if how in available_rules:\n",
      "        rule = integrate.__getattribute__(how)\n",
      "    else:\n",
      "        print('Unsupported integration rule: %s' % (how))\n",
      "        print('Expecting one of these sample-based integration rules: %s' % (str(list(available_rules))))\n",
      "        raise AttributeError\n",
      "    \n",
      "    result = rule(self.values, self.index.astype(np.int64) / 10**9)\n",
      "    #result = rule(self.values)\n",
      "    return result\n",
      "\n",
      "pd.TimeSeries.integrate = integrate_method"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 103
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Example of usage\n",
      "===\n",
      "Sample data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.abs(np.random.randn(10000))\n",
      "ts = pd.Series(x, pd.date_range(start='2013-05-03', periods=len(x), freq='s'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 96
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Default args"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ts.integrate()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 97,
       "text": [
        "8023.3962287465547"
       ]
      }
     ],
     "prompt_number": 97
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Different methods:\n",
      "\n",
      "- Cumulative trapezoidal rule - TODO: maybe convert output to pandas timespans in this case"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ts.integrate('cumtrapz')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 65,
       "text": [
        "array([  1.50979200e+00,   2.36680665e+00,   2.91839588e+00, ...,\n",
        "         7.94300517e+03,   7.94440820e+03,   7.94510764e+03])"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " - Simpson's rule"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ts.integrate('simps')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 64,
       "text": [
        "7945.0431120912626"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " - Romberger's rule - number of samples must be one plus a non-negative power of 2."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ts[:1+2**3].integrate('romb')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 72,
       "text": [
        "array([  8.43726871e+09,   8.43726872e+09,   8.43726873e+09,\n",
        "         8.43726873e+09,   8.43726874e+09,   8.43726875e+09,\n",
        "         8.43726875e+09,   8.43726876e+09,   8.43726876e+09])"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Testing for correctness on predictable series\n",
      "---"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A straight line covering an area of 12 * 2 = 24"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "twos = pd.Series(2, pd.date_range(start='2012-01-23', periods=13, freq='1s'))\n",
      "twos.plot()\n",
      "print(twos.integrate('simps'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "24.0\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x36d3210>"
       ]
      }
     ],
     "prompt_number": 104
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We should get the same result even if we sampled the data e.g. every 3 seconds"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "twos_sparse = pd.Series(2, pd.date_range(start='2012-01-23 00:00', end='2012-01-23 00:12', freq='3s'))\n",
      "twos_sparse.plot()\n",
      "print(twos_sparse.integrate('simps'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1440.0\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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lcrm0Y8eO0JzNZtPChQuVk5OjqqqqkX6pT6Xx/h9yPPc3nnuT6A//w4Th4sWLJj09vd+5\nH/7wh2bDhg3GGGMuXLhg4uPjzY0bN4wxxrS0tBhjjLl8+bJxuVzm+PHjfY6XxIsXL168PsbLSv9/\nPedjeuONN/Tyyy9LkhISEhQfH6/z588rJydHM2bMkCRNmzZNhYWF8vl8mjdvXq/jzX1+GQkAPglG\nfJkoJSVFR48elSS1tbXp/PnzevTRR3X79m3dvHlTknTr1i0dOXJkwCeSAABja8h3BqtWrdKxY8fU\n3t6uuLg4bdmyRV1dXZKksrIyfe9739PatWvlcrn03//+Vz/+8Y81depU/ec//9FTTz0lSeru7tbq\n1au1ePHiyHYDAPh4rLzmdPjwYZOcnGwSExPN1q1bjTHGXL161SxcuNAkJSWZRYsWmWvXroV97HCO\nHw2R6O9b3/qWSUlJMZmZmaawsNBcv359VHoJt8aR9veRn/70p8Zms5mrV69GtIfBRKq/yspKk5KS\nYmbNmmW+/e1vR7yPgUSiv1OnTpk5c+YYt9ttcnJyjM/nG5Vewqkv3N7Wrl1rHn744T73PcfL2jJQ\nf8NdWywLg+7ubpOQkGAuXrxoOjs7jcvlMg0NDeall14y27ZtM8YYs3XrVrN58+awjzXGhHX8aIhU\nf0eOHDE9PT3GGGM2b9487vozxpimpiazZMkS43Q6xywMItXfX//6V7Nw4ULT2dlpjLn7sMRYiFR/\n8+fPNx6PxxhjTG1trcnLyxu9poaoL9y14fjx4+add97ps1iOh7XFmIH7G+7aYlkYvPHGG2bJkiWh\ncUVFhSkvLzfJycmmtbXVGGPMe++9Z5KTk8M6tqKiwhhjwjp+NESqv3vt37/frF69OgLVDy2S/RUV\nFZnTp0+PaRhEqr+nn37a/OUvf4lw9UOLVH/FxcVm3759xhhjfv/734/J/8+R9PaR/p6IHA9ry0cG\ne+LTmPDWFss+mygYDCouLi40djgcCgaDamtrU0xMjCQpJiZGbW1tkqSWlhZ95StfGfRYSQMeP9oi\n1d+9du3apaVLl0ayjQFFqr+DBw/K4XAoMzNztFrpV6T6a2xs1PHjx/XYY48pLy9Pb7311mi11Euk\n+tu6das2bdqkRx55RC+99JIqKipGq6WQkfQ2mPGwtoQrnLXFsjCw2WxDbrPZbKFtM2fO1J/+9Kd+\n9zPGDHi+/raPBiv768+PfvQjPfDAA3r22WctqHb4ItHfBx98oPLycm3ZsiW0zYzRo8SR+vfr7u7W\ntWvXVFdXp5/85Cd65plnLKw6fJHqr7S0VJWVlWpqatL27du1bt06C6sOz0h6G87X+DSuLeEId22x\nLAxiY2MVCARC40AgoNjYWMXExKi1tVWS9N577+nhhx8e8tjm5mbFxsZKUljHjwYr+wsEAnI4HKFx\ndXW1amtr9bvf/S6CHQwuEv39+9//lt/vl8vlUnx8vJqbm5Wdna3Lly9HvqEwarTi38/hcISempsz\nZ44mTJigq1evRrKVfkWqP5/Pp8LCQklSUVGRfD5fJNvo10h6G8x4WFuGMqy1ZVgXtwbR1dVlHn30\nUXPx4kVz586dXjdBPro7XlFR0e9NjIGONcaEdfxoiFR/hw8fNmlpaebKlSuj2k+4NY60v3uN5T2D\nSPX3y1/+0rzyyivGGGPOnz9v4uLiRq+pMGocaX9ZWVnG6/UaY4w5evSoycnJGb2mhqhvOGtDf9fU\nx8Pa8pH++hvu2mLpo6W1tbXmC1/4gklISDDl5eXGmLuPRy1YsKDP41HBYNAsXbp00GMHO34sRKK/\nxMRE88gjjxi3223cbrdZv3796DZ1j0j0d6/4+PgxfbQ0Ev11dnaaNWvWmPT0dDN79mzzt7/9bVR7\nulck+nvzzTfN3LlzjcvlMo899ph55513RrepQeoLt7fi4mIzY8YM88ADDxiHw2F27do16PFjIRL9\nDXdtGfIjrAEA4x+/6QwAQBgAAAgDAIAsCoNAIKD8/HzNmjVL6enpqqyslCR9//vfl8vlktvt1oIF\nC3o9PnUvv9/PJ5oCwBiy5AZya2urWltb5Xa71dHRoezsbB04cEAOh0OTJ0+WJL322ms6ffq0fv3r\nX/c53u/3a/ny5f3+jmUAQORZ8s5g+vTpcrvdkiS73a7U1FS1tLSEgkCSOjo69PnPf37Ic/n9fj3x\nxBPKzs5Wdna2/vGPf0i6+yvs8vLy9PTTTys1NVVr1qyxonQAgML4fQbD5ff7VV9fr9zcXEnSyy+/\nrN/+9rf67Gc/q7q6uiGPj4mJ0Z///Gc9+OCDamxs1LPPPqs333xTkvTPf/5TDQ0NmjFjhh5//HGd\nPHlSjz/+uNUtAMB9x9IbyB0dHSoqKtKOHTtkt9sl3f1cjKamJpWUlOib3/zmkOfo7OzU1772NWVm\nZuqZZ57RuXPnQnNz587VzJkzZbPZ5Ha75ff7rSwfAO5bloVBV1eXVq5cqTVr1mjFihV95u/9Dn/t\n2rXKysrSsmXL+uy3fft2zZgxQ//617/01ltv6c6dO6G5Bx98MPT3iRMnqru726ryAeC+ZsllImOM\nSktLlZaWpo0bN4a2NzY2KikpSdLdjzLOysqSJO3evXvAc924cSP0IVk1NTXq6emxokQAwCAsCYOT\nJ09qz549yszMDC345eXl2rlzp86fP6+JEycqISFBv/jFL/o9vru7O/Rd/ze+8Q2tXLlSNTU1evLJ\nJ0OXm6T+P9YVADByn4jPJjp48KD27t2rP/zhD2NdCgDclyx/mmi4XnnlFR06dEi/+c1vxroUALhv\nfSLeGQAAxhafTQQAIAwAAIQBAECEAQBAhAEAQIQBAEDS/wGc493QdxTrogAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x36c5410>"
       ]
      }
     ],
     "prompt_number": 105
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A diagonal, closing a triangle 12 * 12 / 2 = 72"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lin = pd.Series(np.arange(13), pd.date_range(start='2012-01-23', periods=13, freq='1s'))\n",
      "lin.plot()\n",
      "print(lin.integrate())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "72.0\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAELCAYAAADDZxFQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nuAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3a3cc50>"
       ]
      }
     ],
     "prompt_number": 89
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Benchmarking\n",
      "---------------\n",
      "Overcomes the bottleneck illustrated [here](http://nbviewer.ipython.org/5512857)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit ts.integrate()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 237 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Tests\n",
      "======="
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Non-existing method"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ts.integrate('homers')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "AttributeError",
       "evalue": "",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-73-9795db05ffcd>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mts\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mintegrate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'homers'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;32m<ipython-input-63-e2ac6ebfcf13>\u001b[0m in \u001b[0;36mintegrate_method\u001b[1;34m(self, how, unit)\u001b[0m\n\u001b[0;32m     24\u001b[0m         \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Unsupported integration rule: %s'\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mhow\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     25\u001b[0m         \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Expecting one of these sample-based integration rules: %s'\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mavailable_rules\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 26\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     27\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     28\u001b[0m     \u001b[1;31m#result = integrate.trapz(ts.values, ts.index.astype(np.int64) / 10**9)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mAttributeError\u001b[0m: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Unsupported integration rule: homers\n",
        "Expecting one of these sample-based integration rules: ['romb', 'simps', 'trapz', 'cumtrapz']\n"
       ]
      }
     ],
     "prompt_number": 73
    }
   ],
   "metadata": {}
  }
 ]
}