{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "# How do I quantify the uniformity of sampling time?\n",
    "\n",
    "https://stats.stackexchange.com/questions/how-do-i-quantify-the-uniformity-of-sampling-time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "from __future__ import division\n",
    "import scipy as sp\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')\n",
    "sns.set_context('paper', font_scale=2)\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def calculate_shannon_entropy(p):\n",
    "    ''' \n",
    "    Parameters\n",
    "    ----------\n",
    "    p: list\n",
    "        list of probability values such that sum(p) = 1\n",
    "    Returns\n",
    "    -------\n",
    "    entropy: float\n",
    "        Shannon Entropy        \n",
    "    '''\n",
    "    assert np.allclose(sum(p), 1)\n",
    "    entropy = -np.nansum(np.array(p) * np.log2(np.array(p)).T)\n",
    "    return entropy\n",
    "\n",
    "def calculate_uniformity_index(x, a, b):\n",
    "    '''\n",
    "    Parameters\n",
    "    ----------\n",
    "    '''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "## Entropy is maximal for a uniform distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/saket/anaconda2/lib/python2.7/site-packages/ipykernel/__main__.py:13: RuntimeWarning: divide by zero encountered in log2\n",
      "/home/saket/anaconda2/lib/python2.7/site-packages/ipykernel/__main__.py:13: RuntimeWarning: invalid value encountered in multiply\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7efd7ec563d0>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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ggUHbwsPD4e7ujspKOhXPUihVGry95yxqb3bhL6viEeTnynYkQgY4O/Hxl1USCB3tsH5H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\n0RuVByGEEL1ReRBCCNEblQchhBC9/X9VXPUMaaOXIgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efd82671cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(0, 1.1, 0.1), [calculate_shannon_entropy([x, 1-x]) for x in np.arange(0, 1.1, 0.1)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "## Entropy increase monotonically with sample size for a uniform distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7efd7eb52250>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PYB9+iL3owz70Gew+DBgKQggAgIuLi0njP5ScnHxDRb2QnIySkpIbfr4jYR/6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\nEUOBiIiMGApERGTEUCAiIqP/D4VDx7stqKO4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efd82671a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "entropies = []\n",
    "\n",
    "for n in range(1, 100):\n",
    "    p_vec = [1/n] * n \n",
    "    entropies.append(calculate_shannon_entropy(p_vec))\n",
    "\n",
    "plt.plot(entropies)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.3820635625174496"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Rj9i7dy+nT592tT9x4gQbNmzgj3/8I2FhYTzzzDPk5eW57fPw4cNs3ryZTz/9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\n4v8DOP3qhXZxdqMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efd7e478f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Uniform index\n",
    "hist_bins = 20\n",
    "\n",
    "s = np.random.uniform(1,10,1000)\n",
    "count, bins, ignored = plt.hist(s, 10, normed=True)\n",
    "\n",
    "count, boundaries = np.histogram(s, bins=1000)\n",
    "normalized_count = count/np.sum(count)\n",
    "\n",
    "U = np.sqrt(1+(10-1)**2)/np.sum(np.sqrt(1+normalized_count**2))\n",
    "(U-0.707)/(1-0.707)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "## Uniformity index \n",
    "https://arxiv.org/pdf/1508.01146.pdf defines uniformity index as :\n",
    "        $$\n",
    "        \\mathcal{U}(f_X) = \\frac{\\sqrt{1+(b-a)^2}}{\\sqrt{1+[f_X(t)]^2}dt}\n",
    "        $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "count, boundaries = np.histogram(s, bins=1000, density=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(np.diff(boundaries)*count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.0467435677217765"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#denom = np.trapz(np.sqrt(1+count**2), np.diff(boundaries))\n",
    "denom = sum(np.diff(boundaries)*np.sqrt(1+count**2))\n",
    "denom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.003260113892593"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U = np.sqrt(1+(10-1)**2)/denom\n",
    "(U-0.707)/(1-0.707)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "s[np.where( (s>7) & (s<9) )] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "#count = np.histogram(s)\n",
    "#normalized_count = count[0]/np.sum(count[0])\n",
    "count, boundaries = np.histogram(s, bins=1000, density=True)\n",
    "\n",
    "U = np.sqrt(1+(10-1)**2)/np.sum(np.sqrt(1+normalized_count**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.59534182460272966"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "denom = sum(np.diff(boundaries)*np.sqrt(1+count**2))\n",
    "\n",
    "U = np.sqrt(1+(10-1)**2)/denom\n",
    "(U-0.707)/(1-0.707)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "len(count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XXtDZs2eVmZmpNWvWKCcnx9b0AAAXWN3racWKFTp69KhaWlr00ksvDauQaG1t1be//W3l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\nH0/mYWGTva8QAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efd7e356650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s[np.where( (s>1) )] = 0\n",
    "count, bins, ignored = plt.hist(s, 10, normed=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.12073095937549529"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count, boundaries = np.histogram(s, bins=10, density=True)\n",
    "denom = sum(np.diff(boundaries)*np.sqrt(1+count**2))\n",
    "\n",
    "U = np.sqrt(1+(2-1)**2)/denom\n",
    "(U-0.707)/(1-0.707)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9990004999998734"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "denom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efd7e5ae390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count, bins, ignored = plt.hist(s, 10, normed=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
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   "codemirror_mode": {
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
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   "hotkeys": {
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   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
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   "moveMenuLeft": true,
   "nav_menu": {
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   "toc_position": {
    "height": "119px",
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    "right": "2356px",
    "top": "130px",
    "width": "200px"
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   "toc_section_display": "none",
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 },
 "nbformat": 4,
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}