using sympy for numeric calculations with arbitrary precision

hausarbeit_stein.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "%matplotlib inline\n",
    "import locale\n",
    "locale.setlocale(locale.LC_ALL, 'C')\n",
    "import os, timeit, collections\n",
    "\n",
    "import IPython.display\n",
    "\n",
    "import numpy as np, scipy, scipy.stats as stats, scipy.special, scipy.linalg, pandas as pd, \\\n",
    "    matplotlib.pyplot as plt, matplotlib.dates, matplotlib.ticker, xarray as xr, seaborn as sns\n",
    "import sklearn.preprocessing\n",
    "\n",
    "pd.set_option('display.max_columns', 500)\n",
    "pd.set_option('display.width', 1000)\n",
    "pd.set_option('display.float_format', lambda x: '%.4f' % x)\n",
    "np.set_printoptions(edgeitems=10)\n",
    "np.set_printoptions(suppress=True)\n",
    "np.set_printoptions(precision=8)\n",
    "np.core.arrayprint._line_width = 180\n",
    "\n",
    "sns.set()\n",
    "\n",
    "SEED = 42\n",
    "np.random.seed(SEED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import sympy, sympy.plotting\n",
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$x$$"
      ],
      "text/plain": [
       "x"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sx = sympy.symbols('x')\n",
    "sx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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ZiV0a6ucoa9B5y9igwbbWBDJZ0fYvlUdJPxr/6+mzj9JcdqmVCzSUyfgadN7r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\nCIJg7/n/MsreEclLBVIAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$- 9.957371 \\cdot 10^{-7} x^{16} + 5.6100257831 \\cdot 10^{-5} x^{15} - 0.0014371151322 x^{14} + 0.022152182049259 x^{13} - 0.229167949577895 x^{12} + 1.68030725097713 x^{11} - 8.98984498449258 x^{10} + 35.5984674750492 x^{9} - 104.741981193492 x^{8} + 227.945596249527 x^{7} - 362.299494189794 x^{6} + 411.665048543851 x^{5} - 323.90017508493 x^{4} + 168.639704423053 x^{3} - 54.9047289051861 x^{2} + 11.5154981935778 x$$"
      ],
      "text/plain": [
       "               16                    15                    14                 \n",
       "- 9.957371e-7⋅x   + 5.6100257831e-5⋅x   - 0.0014371151322⋅x   + 0.022152182049\n",
       "\n",
       "     13                      12                     11                     10 \n",
       "259⋅x   - 0.229167949577895⋅x   + 1.68030725097713⋅x   - 8.98984498449258⋅x   \n",
       "\n",
       "                    9                     8                     7             \n",
       "+ 35.5984674750492⋅x  - 104.741981193492⋅x  + 227.945596249527⋅x  - 362.299494\n",
       "\n",
       "        6                     5                    4                     3    \n",
       "189794⋅x  + 411.665048543851⋅x  - 323.90017508493⋅x  + 168.639704423053⋅x  - 5\n",
       "\n",
       "                 2                     \n",
       "4.9047289051861⋅x  + 11.5154981935778⋅x"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sfx = \\\n",
    "      -0.0000009957371   * sx**16 + \\\n",
    "       0.000056100257831 * sx**15 + \\\n",
    "      -0.0014371151322   * sx**14 + \\\n",
    "       0.022152182049259 * sx**13 + \\\n",
    "      -0.229167949577895 * sx**12 + \\\n",
    "       1.680307250977133 * sx**11 + \\\n",
    "      -8.98984498449258  * sx**10 + \\\n",
    "      35.59846747504916  * sx** 9 + \\\n",
    "    -104.74198119349185  * sx**8  + \\\n",
    "     227.94559624952703  * sx**7  + \\\n",
    "    -362.2994941897943   * sx**6  + \\\n",
    "     411.6650485438511   * sx**5  + \\\n",
    "    -323.9001750849299   * sx**4  + \\\n",
    "     168.63970442305256  * sx**3  + \\\n",
    "     -54.90472890518606  * sx**2  + \\\n",
    "      11.515498193577798 * sx\n",
    "sfx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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b+f4F7fe/I2y3hMdyVJlu6tjuJo8hGfHNv9M56iz7392voK1cee54Ynv92SPf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\nQRAEQRAEQRAEQRAEQRAEQbCd/w/Jpzq6/s4UXQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left(- 9.957371 \\cdot 10^{-7} x^{16} + 5.6100257831 \\cdot 10^{-5} x^{15} - 0.0014371151322 x^{14} + 0.022152182049259 x^{13} - 0.229167949577895 x^{12} + 1.68030725097713 x^{11} - 8.98984498449258 x^{10} + 35.5984674750492 x^{9} - 104.741981193492 x^{8} + 227.945596249527 x^{7} - 362.299494189794 x^{6} + 411.665048543851 x^{5} - 323.90017508493 x^{4} + 168.639704423053 x^{3} - 54.9047289051861 x^{2} + 11.5154981935778 x\\right)^{2}$$"
      ],
      "text/plain": [
       "                                                                              \n",
       "⎛               16                    15                    14                \n",
       "⎝- 9.957371e-7⋅x   + 5.6100257831e-5⋅x   - 0.0014371151322⋅x   + 0.02215218204\n",
       "\n",
       "                                                                              \n",
       "      13                      12                     11                     10\n",
       "9259⋅x   - 0.229167949577895⋅x   + 1.68030725097713⋅x   - 8.98984498449258⋅x  \n",
       "\n",
       "                                                                              \n",
       "                     9                     8                     7            \n",
       " + 35.5984674750492⋅x  - 104.741981193492⋅x  + 227.945596249527⋅x  - 362.29949\n",
       "\n",
       "                                                                              \n",
       "         6                     5                    4                     3   \n",
       "4189794⋅x  + 411.665048543851⋅x  - 323.90017508493⋅x  + 168.639704423053⋅x  - \n",
       "\n",
       "                                         2\n",
       "                  2                     ⎞ \n",
       "54.9047289051861⋅x  + 11.5154981935778⋅x⎠ "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sfx2 = sfx**2\n",
    "sfx2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xqTwH+HIdc2WsNrJ2//fRRhwzXr/B72e9umWd9xx2bS5OzWU7PXqS2zd6+pJD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\n",
      "text/latex": [
       "$$\\int \\left(- 9.957371 \\cdot 10^{-7} x^{16} + 5.6100257831 \\cdot 10^{-5} x^{15} - 0.0014371151322 x^{14} + 0.022152182049259 x^{13} - 0.229167949577895 x^{12} + 1.68030725097713 x^{11} - 8.98984498449258 x^{10} + 35.5984674750492 x^{9} - 104.741981193492 x^{8} + 227.945596249527 x^{7} - 362.299494189794 x^{6} + 411.665048543851 x^{5} - 323.90017508493 x^{4} + 168.639704423053 x^{3} - 54.9047289051861 x^{2} + 11.5154981935778 x\\right)^{2}\\, dx$$"
      ],
      "text/plain": [
       "⌠                                                                             \n",
       "⎮                                                                             \n",
       "⎮ ⎛               16                    15                    14              \n",
       "⎮ ⎝- 9.957371e-7⋅x   + 5.6100257831e-5⋅x   - 0.0014371151322⋅x   + 0.022152182\n",
       "⌡                                                                             \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "        13                      12                     11                     \n",
       "049259⋅x   - 0.229167949577895⋅x   + 1.68030725097713⋅x   - 8.98984498449258⋅x\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "10                     9                     8                     7          \n",
       "   + 35.5984674750492⋅x  - 104.741981193492⋅x  + 227.945596249527⋅x  - 362.299\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "           6                     5                    4                     3 \n",
       "494189794⋅x  + 411.665048543851⋅x  - 323.90017508493⋅x  + 168.639704423053⋅x  \n",
       "                                                                              \n",
       "\n",
       "                                               \n",
       "                                           2   \n",
       "                    2                     ⎞    \n",
       "- 54.9047289051861⋅x  + 11.5154981935778⋅x⎠  dx\n",
       "                                               "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isfx2 = sympy.Integral(sfx2, sx)\n",
    "isfx2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIwAAAASCAYAAACJrDYNAAAABHNCSVQICAgIfAhkiAAABP9JREFU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\njn5CmucqnW/uAQxgAAMYwADWF/4FAwLN5reaE20AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$- 1429.9375 \\pi$$"
      ],
      "text/plain": [
       "-1429.9375⋅π"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isfx2 = sympy.integrate(sfx2, (sx,0,6.56))\n",
    "isfx2*sympy.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANcAAAASCAYAAADIWEuyAAAABHNCSVQICAgIfAhkiAAABchJREFU\naIHt2mmsJFUVB/Af8AiyOgriJLKvQ4CgGEBCAm8AJ7IIBBg+waCCIUgQIwITVPLgA2ExZFgSlriw\nJYRIGEgI+2Rk5wNEomyCME8hYhTMLMCwjY8P51ZeTb2u7qrq6p4Y+59Uqvvc+z9V5567nHtuMcII\nI/xP4hRMpev0Fjnr4Qd4FqvwIf6IH2ODQt0tk57F+CtWYwWexGlYv+J79avrKDyMtxPvTfweB5bU\nPxHX4gmsFO1xe4/3a8LJo0rbT+bqFK9/dtG9DX6Lf+DjpGcRvlRSfxg+bmJLZc5YiYI2sK1w9PvY\nrGXOLaIj/At34gMcjqtxMOYLY6Xf1+MdLMXf8VUcj1/jiEL9bmiq63Kcj/dwD97FLjgWJ2CBmYPg\nF9hHtMXbmFPh/ZpwMtTx1woxMIp4v6T+zngaW+NevIr9cQ6+g4NE2+QxLB/XtaUppzWsh0fxBq5U\nbeWqyjkulb2JrXLyDcXMNYXv5eSH4rtmzl6zhROmRAevgia6ZmONmNW2LpTNzdlSxFzsKtplXLVV\nqAmHev6aTFcdPJR0nl2QX5XkNxTkw/LxpPq2NOG0inPwXzHDTKg2uKpybk1lZ3Uo2yuVPV/xPS9M\n9a+tWL+JrgOS/N4S3koR9nTDuPohXh1OHX9Nqte5dkr6lpnZ+TcXs/0H2DQnH5aPJw1wcA0iLNwD\nl4nl+3Exq7TJmZ3unWb7TLYvZmF5j+d+mu6fVXjHXijT9To+EWHQViIkzHCw6GD3tPD8pmjir41w\nMrYTA+NPibumQ91M38NiAOexCk9hHr6FJUk+TB/XsaUWp+3BNYbbxFJ84YA4WefcsUPZTrnfc8Rm\nuNtzF6TfD1Z4bjd00/UfXCBCoJfFQHpP7EOOwSM4o8/nN0UTfxGd/7aCbBm+j8cK8t3T/bUSXa+L\nwbWb6cE1TB/XsaUWp06mrAouwjdEPLx6QJz70v2n+HJOPoaLc//LslAZLhMhxv1iT9APeulaJDbX\nY/ghFooN9lu4WWza1wWa+Ot3OEx0sE2xN27EDnhAJFTy+GK6ryjRl8ln5WTD8nFdW5py0D3N2OnK\nx/P7i6X3ioLOCeUxfBPO+qKxstTnTaLzvig6yGupbF6ZkSKdO4VXrO28Jqii63xh51Vi5t1EhDXZ\nRr9ofxHj2t9zNWn7bvhV4i0uyG/qoe/SVL4wJ1vXPi6zpS/OEpEmrXpljhnDX0TYs1FB54TOjduE\nk+eeixdEY68Uy/438Uzifr2Ee1Yqf8l0bN8UVXSNpzp3dyjbRKTM11g73CnT0dbg6qfty7BL4hVT\n6ln28dwS3nWp/MwO77iufFxmS9ucSpil+mq3qA9OL2wsHPGhSNsW8ZOk789mpsXroqqubEYrpqEz\n3K33ccC4dgfXINp+i1T/o4L89CS/sYSXrd6HVXzOMHxcZkstTlsJjY/xm5KyfUVc/6SYLZ/pg9ML\np+AL4gDy00LZBSIGfwHftnbWri7q6MpWhq+UlGfyT/p4n7oYRNtnX5oUM3xL032eCPfyGcPNxQHy\nat0TE3kMw8dltrTN6RsT6ocZvThbdJDtJzJzq8wMsX6Z9D2nevy9s8hGFWfHurpOMr13+Fqh7AjR\n2VaLT3jKMG6w51x5TChv+z11tnl7kfWb0jnrWPcQmcH7uIkttTiD/PxpkHhEdMgXRUPviSPFjHy8\ntWePU3GJ2Nc8ITa6RUyKrF0eS0Sj7Wj60LCJrrvE1w+Hi831YjHQ9sDR4uuIhWbG6seli+l9w4E5\n3e/iZy1w6mB+etelIvW8SkxCR4nV5H4RBhfxI/H50zUi/HtFHK7PFcmJn3fgDNrHTWxpav/AMKH9\nles8cUK/XDT2MjH77dBFV7frDx14k6ksr7Oprg3FXuBZsTH/TKTf71Oe8er1rMmWOGU6OrX9IbhD\nJLOWi7Ds32IgLBATRRm2FWnsd0QI/DdxcF22ygzax01s6cf+EUYYYYQRRhhhhBH+P/E5EXbUBVGX\n7a0AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$-4492.28114509255$$"
      ],
      "text/plain": [
       "-4492.28114509255"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.N(isfx2*sympy.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XtpRDoZDhxqlZmJxnEbskItHJZDJMzkvGuGFJ2LKvFvtPtmD1xhPYU9qE/7ghj6NVNGjY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\noL9+xAS5PxBATbMD6SYd1Cq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KzgOpBKF319FVq1aipOQUfvKTB/HOOxsk9/MS9kH+1e1c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\niIgkjEFOREQkYQxyIiIiCfv/Qbve7DEpumYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f20e0e714e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f20e0e71518>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# https://stackoverflow.com/questions/30131366/plotting-sympy-results-in-python\n",
    "# https://stackoverflow.com/questions/40747474/sympy-and-plotting\n",
    "sympy.plotting.plot(sfx, (sx, 0, 6.56))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0800</td>\n",
       "      <td>0.6300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2700</td>\n",
       "      <td>1.1800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.6100</td>\n",
       "      <td>1.6400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0000</td>\n",
       "      <td>2.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.4300</td>\n",
       "      <td>2.2700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.9500</td>\n",
       "      <td>2.4300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2.5700</td>\n",
       "      <td>2.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.3100</td>\n",
       "      <td>2.4900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.9000</td>\n",
       "      <td>2.4000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>4.4600</td>\n",
       "      <td>2.2400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5.1600</td>\n",
       "      <td>1.8800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>5.6900</td>\n",
       "      <td>1.5100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>6.0100</td>\n",
       "      <td>1.2300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>6.2800</td>\n",
       "      <td>0.8700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6.4300</td>\n",
       "      <td>0.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>6.5600</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        x      y\n",
       "0  0.0000 0.0000\n",
       "1  0.0800 0.6300\n",
       "2  0.2700 1.1800\n",
       "3  0.6100 1.6400\n",
       "4  1.0000 2.0000\n",
       "5  1.4300 2.2700\n",
       "6  1.9500 2.4300\n",
       "7  2.5700 2.5000\n",
       "8  3.3100 2.4900\n",
       "9  3.9000 2.4000\n",
       "10 4.4600 2.2400\n",
       "11 5.1600 1.8800\n",
       "12 5.6900 1.5100\n",
       "13 6.0100 1.2300\n",
       "14 6.2800 0.8700\n",
       "15 6.4300 0.5000\n",
       "16 6.5600 0.0000"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame([\n",
    "    [0.0 , 0.0],\n",
    "    [0.08, 0.63],\n",
    "    [0.27, 1.18],\n",
    "    [0.61, 1.64],\n",
    "    [1.0, 2.0],\n",
    "    [1.43, 2.27],\n",
    "    [1.95, 2.43],\n",
    "    [2.57, 2.5],\n",
    "    [3.31, 2.49],\n",
    "    [3.9, 2.4],\n",
    "    [4.46, 2.24],\n",
    "    [5.16, 1.88],\n",
    "    [5.69, 1.51],\n",
    "    [6.01, 1.23],\n",
    "    [6.28, 0.87],\n",
    "    [6.43, 0.5],\n",
    "    [6.56, 0.0]\n",
    "             ],\n",
    "    columns=['x', 'y'],\n",
    "    dtype=np.float64)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FVvzgtjkwxupFl0U0SpRei5uvyseP71mArGQDGtoc+Okf9+Kj/ach8MBjorDCcEHCVTf1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\nniJcAAAATxEuAACApwgXAADAU/8HZf08axtRutsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f20e07cd588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# https://stackoverflow.com/questions/15833190/sympy-generate-figure-with-multiple-subplots\n",
    "# https://stackoverflow.com/questions/19932072/plotting-2-or-more-functions-in-the-same-graph\n",
    "# https://tonysyu.github.io/plotting-streamlines-with-matplotlib-and-sympy.html\n",
    "fig=plt.figure(figsize=(8, 8), dpi= 80, facecolor='w', edgecolor='k')\n",
    "ax = plt.subplot(111)\n",
    "#hp = sympy.plotting.plot(sfx, (sx, 0, 6.56))\n",
    "#hp._backend.fig\n",
    "#ax = hp._backend.ax\n",
    "ax.scatter(df.x, df.y, marker=\"x\", c='r', linewidth=0.5)\n",
    "\n",
    "x = np.linspace(0,6.56,100)\n",
    "lsfx = sympy.lambdify(sx, sfx)\n",
    "ax.plot(x,lsfx(x));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# https://groups.google.com/forum/#!topic/sympy/twjvFft6i3w\n",
    "\n",
    "def fit_poly(x, y, sym, degree=1, precision=50): \n",
    "\n",
    "    \"\"\" \n",
    "    Fit polynomial of degree k through n points (x[i],y[i]), i=0..n \n",
    "    Returns tuple (fit function, residual) \n",
    "    Implementation: Least squares of vertical offset. \n",
    "\n",
    "    Example: Fit line \n",
    "    --------------------- \n",
    "    x = Symbol('x') \n",
    "    p,r = fit_poly([0,8], [1,5], x, 1) \n",
    "    p \n",
    "    >>> x/2 + 1 \n",
    "    r \n",
    "    >>> 0 \n",
    "\n",
    "    Example: Fit parabula \n",
    "    --------------------- \n",
    "    data_x = [0,1,2,5] \n",
    "    data_y = [1,1,3,5] \n",
    "    x = Symbol('x') \n",
    "    p,r = fit_poly(data_x, data_y, x, 2) \n",
    "    p \n",
    "    >>> -3/181*x**2 + 171/181*x + 133/181 \n",
    "    r \n",
    "    >>> 0.840941329964219 \n",
    "    \"\"\" \n",
    "\n",
    "    def fit_matrix(x,y, degree, precision=50): \n",
    "        \"\"\"calculate matrix for fit\"\"\" \n",
    "        n = len(x) \n",
    "        k = degree+1 \n",
    "        array=[ [0 for i in range(k)] for j in range(n)] \n",
    "        for j in range(n): \n",
    "            for i in range(k): \n",
    "                array[j][i] = sympy.N(x[j]**i, precision)\n",
    "        return sympy.Matrix(array) \n",
    "\n",
    "    def fit_coeffs(m, v, precision=50): \n",
    "        \"\"\"calculate polynomial coefficients\"\"\" \n",
    "        mt = m.transpose() \n",
    "        return list( sympy.N((mt*m).inv()*mt*sympy.Matrix(v), precision) )\n",
    "\n",
    "    def expr_from_coeff(coeff, sym): \n",
    "        e = coeff[0] \n",
    "        for i in range(1,len(coeff)): \n",
    "            e += coeff[i]*sym**i \n",
    "        return e \n",
    "    \n",
    "    def residual(x, y, e, precision=50): \n",
    "        \"\"\"calculate residual\"\"\" \n",
    "        f = sympy.lambdify( e.atoms(sympy.Symbol).pop(), e ) \n",
    "        r = sympy.Float(0.0) \n",
    "        for i in range(len(x)): \n",
    "            r += sympy.N(( y[i] - f(x[i]) )**2, precision)\n",
    "        return sympy.sqrt(r) \n",
    "\n",
    "    # check and normalize arguments \n",
    "    assert( isinstance(x, (tuple,list)) ) \n",
    "    assert( isinstance(y, (tuple,list)) ) \n",
    "    assert( isinstance(sym, sympy.Symbol) ) \n",
    "    assert( len(x) == len(y) ) \n",
    "    degree = int(degree) \n",
    "    assert( int(0) <= degree ) \n",
    "    assert( len(x) > degree ) \n",
    "    for i in range(len(x)): \n",
    "        x[i] = sympy.S(x[i]) \n",
    "        y[i] = sympy.S(y[i]) \n",
    "        if not x[i].is_Number: \n",
    "            x[i] = x[i].n() \n",
    "        if not y[i].is_Number: \n",
    "            y[i] = y[i].n() \n",
    "\n",
    "    # fit polynomial and calculate residual \n",
    "    m = fit_matrix(x, y, degree, precision=precision) \n",
    "    coeff = fit_coeffs(m, y, precision=precision) \n",
    "    e = expr_from_coeff(coeff, sym) \n",
    "    res = sympy.Float(0.0)\n",
    "    res = residual(x, y, e) \n",
    "    return e, res "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  -0.0000006 ,    0.00003489,   -0.00092342,    0.01467431,   -0.15618824,    1.17612253,   -6.45214038,   26.16443086,  -78.76539892,  175.32025855, -285.15817213,\n",
       "        332.20001837, -269.0342106 ,  145.15387945,  -49.49285683,   11.0304721 ,    0.00000007])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.polyfit.html\n",
    "z = np.polyfit(df.x, df.y, 16)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAAAWCAYAAACbiSE3AAAABHNCSVQICAgIfAhkiAAAAtVJREFU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\n",
      "text/latex": [
       "$$1.23 x^{2}$$"
      ],
      "text/plain": [
       "      2\n",
       "1.23⋅x "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.S(\"{:6.2f}\".format(1.23))*sx**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1IVJQ+Va9z6X13IZkGL/Xu+5g5j5dKnTGXrOOUeX2tSWtCF1KmltXdqy7pUZm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\ngiAIFvL/AUx/4yHrWApjAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$- 5.977603041 \\cdot 10^{-7} x^{16} + 3.4886433396 \\cdot 10^{-5} x^{15} - 0.0009234190807935 x^{14} + 0.0146743096097556 x^{13} - 0.1561882363442246 x^{12} + 1.1761225348877742 x^{11} - 6.4521403801144865 x^{10} + 26.1644308640816483 x^{9} - 78.7653989219277406 x^{8} + 175.3202585528163979 x^{7} - 285.1581721322946805 x^{6} + 332.2000183667062743 x^{5} - 269.0342105979859753 x^{4} + 145.1538794468587241 x^{3} - 49.4928568310922543 x^{2} + 11.0304720954715556 x + 6.51266 \\cdot 10^{-8}$$"
      ],
      "text/plain": [
       "                  16                    15                       14           \n",
       "- 5.977603041e-7⋅x   + 3.4886433396e-5⋅x   - 0.0009234190807935⋅x   + 0.014674\n",
       "\n",
       "            13                       12                       11              \n",
       "3096097556⋅x   - 0.1561882363442246⋅x   + 1.1761225348877742⋅x   - 6.452140380\n",
       "\n",
       "         10                        9                        8                 \n",
       "1144865⋅x   + 26.1644308640816483⋅x  - 78.7653989219277406⋅x  + 175.3202585528\n",
       "\n",
       "        7                         6                         5                 \n",
       "163979⋅x  - 285.1581721322946805⋅x  + 332.2000183667062743⋅x  - 269.0342105979\n",
       "\n",
       "        4                         3                        2                  \n",
       "859753⋅x  + 145.1538794468587241⋅x  - 49.4928568310922543⋅x  + 11.030472095471\n",
       "\n",
       "                   \n",
       "5556⋅x + 6.51266e-8"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly = sum(sympy.S(\"{:6.16f}\".format(v))*sx**i for i, v in enumerate(z[::-1]))\n",
    "poly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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N/MfZ578z/PvxC++/++S/780f/YjqO+mF8RnAq+k3db0DuAfwRfS/CPtVpHE9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\n94d0/3mlnGs8akj3/J3n7g3cdeHzWwH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hhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQ\nLXMX4EPAd9QuiBBCCCGEEGfK19P/1uWD9h68Lf0vkj6/dImEEEIIIYQQQgghhBBCCCGEEEIIIYQQ\nQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEKIAB4BvB+4a+2CCCGEEEII\ncYbcDvgt4LmpCR4MPBm4Q6kSCSGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQ\nQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQojmuQ9wCfz5usUQQgghhBBCCCGEEEIIIYQQ\nQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEII\nIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGE\nEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBC\nCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghkvif/j4pXgSZmpMAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( - 0.0000005982735566201228742997001 x^{16} + 0.00003491346829349571413825431 x^{15} - 0.0009240646097657030103980947 x^{14} + 0.01468355061921252096969295 x^{13} - 0.1562766219249199469773407 x^{12} + 1.176718317932891610931154 x^{11} - 6.455049636273961658198142 x^{10} + 26.17484620466959440067655 x^{9} - 78.79275353428412479144704 x^{8} + 175.372462376449877824583 x^{7} - 285.229094322039432131444 x^{6} + 332.2662920337061821095658 x^{5} - 269.0745444802285934360224 x^{4} + 145.1685144948298031850918 x^{3} - 49.49556862923103330681112 x^{2} + 11.03065716026647773812819 x - 0.000001045200214303397193827355, \\quad 0.00047243780004930073962519454729989522090082400219346\\right )$$"
      ],
      "text/plain": [
       "⎛                                     16                                    15\n",
       "⎝- 0.0000005982735566201228742997001⋅x   + 0.00003491346829349571413825431⋅x  \n",
       "\n",
       "                                   14                                 13      \n",
       " - 0.0009240646097657030103980947⋅x   + 0.01468355061921252096969295⋅x   - 0.1\n",
       "\n",
       "                          12                               11                 \n",
       "562766219249199469773407⋅x   + 1.176718317932891610931154⋅x   - 6.455049636273\n",
       "\n",
       "              10                               9                              \n",
       "961658198142⋅x   + 26.17484620466959440067655⋅x  - 78.79275353428412479144704⋅\n",
       "\n",
       " 8                              7                              6              \n",
       "x  + 175.372462376449877824583⋅x  - 285.229094322039432131444⋅x  + 332.2662920\n",
       "\n",
       "                 5                               4                            \n",
       "337061821095658⋅x  - 269.0745444802285934360224⋅x  + 145.168514494829803185091\n",
       "\n",
       "   3                               2                                          \n",
       "8⋅x  - 49.49556862923103330681112⋅x  + 11.03065716026647773812819⋅x - 0.000001\n",
       "\n",
       "                                                                              \n",
       "045200214303397193827355, 0.00047243780004930073962519454729989522090082400219\n",
       "\n",
       "   ⎞\n",
       "346⎠"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision=25\n",
    "sympy_poly = fit_poly(list(df.x), list(df.y), sx, degree=16, precision=precision)\n",
    "sympy_poly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hDKL6OQC/A8DzAbwfgI/COFBzrM/46QDe9d7nH8brEiK2+CgAfxOjAHohgP8E4K0AfASA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\nPHvPZxyMfOkb8m3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bf58hPzPjOlh5N9a+9eAnj459bPXe3siYE9a4MOqZsfLrWfv73mhd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\n3uNZrwx7kSVHsnWJpw3PHKv1lZToH28bjHns2Q9b5wtrTzjBsElLkH7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EEEIIIYQQQggh\nhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQ\nQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEII\nIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGE\nEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBC\nCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQggh\nhBBCCCGEEKfm/wcmrPjr/kuq8QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$3.579312485508913707129975 \\cdot 10^{-13} x^{32} - 4.177560969978714575637378 \\cdot 10^{-11} x^{31} + 2.324637109543556670980537 \\cdot 10^{-9} x^{30} - 8.209416101392848911856765 \\cdot 10^{-8} x^{29} + 0.000002066195101812272669039744 x^{28} - 0.00003945741562143526859108578 x^{27} + 0.0005943164564712406721038504 x^{26} - 0.007246174662081511313230943 x^{25} + 0.07283094294632572127668693 x^{24} - 0.6114394196407105553774247 x^{23} + 4.329098263133642112823728 x^{22} - 26.03092337694862554698354 x^{21} + 133.5962826901753265442902 x^{20} - 587.1762328361735566097275 x^{19} + 2214.487278733143559888899 x^{18} - 7172.145517029649373188716 x^{17} + 19941.75160426200694142443 x^{16} - 47537.50128680952516826097 x^{15} + 96928.7281256830300843735 x^{14} - 168483.0512615785957582439 x^{13} + 248563.0801151039484812954 x^{12} - 309530.4965995355471959303 x^{11} + 323191.0215722202247801563 x^{10} - 280719.9614281581723472056 x^{9} + 200974.4181562203074589449 x^{8} - 117306.251012002556290459 x^{7} + 55040.12446895268427094258 x^{6} - 20306.53513996688515843696 x^{5} + 5652.420104119746955824644 x^{4} - 1091.937600463301220235185 x^{3} + 121.6755008528959914217581 x^{2} - 0.00002305849045563565051482858 x + 1.092443487979867419922753 \\cdot 10^{-12}$$"
      ],
      "text/plain": [
       "                                32                                   31       \n",
       "3.579312485508913707129975e-13⋅x   - 4.177560969978714575637378e-11⋅x   + 2.32\n",
       "\n",
       "                           30                                  29             \n",
       "4637109543556670980537e-9⋅x   - 8.209416101392848911856765e-8⋅x   + 0.00000206\n",
       "\n",
       "                        28                                    27              \n",
       "6195101812272669039744⋅x   - 0.00003945741562143526859108578⋅x   + 0.000594316\n",
       "\n",
       "                     26                                  25                   \n",
       "4564712406721038504⋅x   - 0.007246174662081511313230943⋅x   + 0.07283094294632\n",
       "\n",
       "              24                                23                            \n",
       "572127668693⋅x   - 0.6114394196407105553774247⋅x   + 4.32909826313364211282372\n",
       "\n",
       "   22                               21                               20       \n",
       "8⋅x   - 26.03092337694862554698354⋅x   + 133.5962826901753265442902⋅x   - 587.\n",
       "\n",
       "                        19                               18                   \n",
       "1762328361735566097275⋅x   + 2214.487278733143559888899⋅x   - 7172.14551702964\n",
       "\n",
       "            17                               16                               \n",
       "9373188716⋅x   + 19941.75160426200694142443⋅x   - 47537.50128680952516826097⋅x\n",
       "\n",
       "15                              14                               13           \n",
       "   + 96928.7281256830300843735⋅x   - 168483.0512615785957582439⋅x   + 248563.0\n",
       "\n",
       "                    12                               11                       \n",
       "801151039484812954⋅x   - 309530.4965995355471959303⋅x   + 323191.0215722202247\n",
       "\n",
       "        10                               9                               8    \n",
       "801563⋅x   - 280719.9614281581723472056⋅x  + 200974.4181562203074589449⋅x  - 1\n",
       "\n",
       "                          7                               6                   \n",
       "17306.251012002556290459⋅x  + 55040.12446895268427094258⋅x  - 20306.5351399668\n",
       "\n",
       "            5                               4                               3 \n",
       "8515843696⋅x  + 5652.420104119746955824644⋅x  - 1091.937600463301220235185⋅x  \n",
       "\n",
       "                              2                                               \n",
       "+ 121.6755008528959914217581⋅x  - 0.00002305849045563565051482858⋅x + 1.092443\n",
       "\n",
       "                      \n",
       "487979867419922753e-12"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly2 = sympy.expand(sympy_poly[0]**2)\n",
    "poly2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUUAAAASCAYAAADMiMymAAAABHNCSVQICAgIfAhkiAAACMRJREFU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\nUaNGjRo1atSoUaNGjRrJ+BjJ5dUXYb7qowAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$86.90423804898152524701077$$"
      ],
      "text/plain": [
       "86.90423804898152524701077"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly = sympy_poly[0]\n",
    "# ipoly_volume = sympy.N(sympy.Integral(sympy.N(poly**2, precision), (sx, 0, 6.56)), precision)\n",
    "ipoly_volume = sympy.N(sympy.Integral(sympy.N(poly2, precision), (sx, 0, 6.56)), precision)\n",
    "sympy.N(ipoly_volume*sympy.pi, precision)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hx/3r5uKfn/8S//1OJWYlRCEj0Sy6LAphkizwCLaOjv5peV5J8s0HdXaqaw7s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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f20d6aab550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(8, 8), dpi= 80, facecolor='w', edgecolor='k')\n",
    "ax = plt.subplot(111)\n",
    "#hp = sympy.plotting.plot(sfx, (sx, 0, 6.56))\n",
    "#hp._backend.fig\n",
    "#ax = hp._backend.ax\n",
    "ax.scatter(df.x, df.y, marker=\"x\", c='r', linewidth=0.5)\n",
    "\n",
    "x = np.linspace(0,6.56,100)\n",
    "lsfx = sympy.lambdify(sx, poly)\n",
    "ax.plot(x,lsfx(x));"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

Here is the link for nbviewer:
https://nbviewer.jupyter.org/gist/cs224/bd417ab58d3aa0babc9ba5a9c6dea978