{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_list_unimodal = [4, 7, 4, 0, 3, 4, 7]  # sorted [0, 3, 4, 4, 4, 7, 7]\n",
    "x_list_bimodal  = [5, 0, 5, 0, 3, 5, 0]  # sorted [0, 0, 0, 3, 5, 5, 5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Function to explicitly compute the mode from its definition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def modes_of_list(values):\n",
    "    \"\"\"\n",
    "    Compute the mode(s) of a list of values.\n",
    "    @param values the list of values.\n",
    "    @return the list of mode(s)\n",
    "    \"\"\"\n",
    "    \n",
    "    count = len(values)\n",
    "    modes = [];\n",
    "    \n",
    "    if count == 0:  # if no values then no modes\n",
    "        return []\n",
    "    \n",
    "    sorted_values = sorted(values)     # sort to group the values\n",
    "    longest_length = 0                 # longest length of consecutive values so far\n",
    "    current_length = 1                 # current length of consecutive values\n",
    "    previous_value = sorted_values[0]  # previous value in the sorted list\n",
    "    \n",
    "    for i in range(1, count + 1):      # start at 1, go up to and include the count\n",
    "        if (i == count) or (sorted_values[i] != previous_value):\n",
    "            # End of the values or the value has changed from the previous one.\n",
    "            if current_length == longest_length:\n",
    "                modes.append(previous_value)     # ties the longest_length, so append to modes\n",
    "            elif current_length > longest_length:\n",
    "                longest_length = current_length  # found a longer length\n",
    "                modes = [previous_value]         # so start a new modes list\n",
    "                \n",
    "            if i < count:\n",
    "                previous_value = sorted_values[i]  # start new consecutive values\n",
    "                current_length = 1\n",
    "        else:\n",
    "            # The value hasn't changed, so increment the current length.\n",
    "            current_length += 1\n",
    "    \n",
    "    return modes "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "modes_of_list(x_list_unimodal) = [4]\n"
     ]
    }
   ],
   "source": [
    "modes_unimodal = modes_of_list(x_list_unimodal)\n",
    "\n",
    "print(f'modes_of_list(x_list_unimodal) = {modes_unimodal}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "modes_of_list(my_modes_bimodal) = [0, 5]\n"
     ]
    }
   ],
   "source": [
    "modes_bimodal = modes_of_list(x_list_bimodal)\n",
    "\n",
    "print(f'modes_of_list(my_modes_bimodal) = {modes_bimodal}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## statistics.mode function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistics.mode(x_list_unimodal)  = 4\n"
     ]
    }
   ],
   "source": [
    "import statistics\n",
    "mode_list_unimodal = statistics.mode(x_list_unimodal)\n",
    "\n",
    "print(f'statistics.mode(x_list_unimodal)  = {mode_list_unimodal}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "StatisticsError",
     "evalue": "no unique mode; found 2 equally common values",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStatisticsError\u001b[0m                           Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-6134c7a591f9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmode_list_bimodal\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstatistics\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_list_bimodal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf'statistics.mode(x_list_bimodal)  = {mode_list_bimodal}'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/statistics.py\u001b[0m in \u001b[0;36mmode\u001b[0;34m(data)\u001b[0m\n\u001b[1;32m    504\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mtable\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    505\u001b[0m         raise StatisticsError(\n\u001b[0;32m--> 506\u001b[0;31m                 \u001b[0;34m'no unique mode; found %d equally common values'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtable\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    507\u001b[0m                 )\n\u001b[1;32m    508\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mStatisticsError\u001b[0m: no unique mode; found 2 equally common values"
     ]
    }
   ],
   "source": [
    "mode_list_bimodal = statistics.mode(x_list_bimodal)\n",
    "print(f'statistics.mode(x_list_bimodal)  = {mode_list_bimodal}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## String values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistics.mode(colors) = red\n"
     ]
    }
   ],
   "source": [
    "colors = ['red', 'white', 'red', 'blue', 'white', 'red']\n",
    "colors_mode = statistics.mode(colors)\n",
    "\n",
    "print(f'statistics.mode(colors) = {colors_mode}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create NumPy arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "x_array_unimodal = np.array(x_list_unimodal)\n",
    "x_array_bimodal  = np.array(x_list_bimodal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scipy.stats.mode function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stats.mode(x_list_unimodal) = ModeResult(mode=array([4]), count=array([3]))\n",
      "stats.mode(x_list_bimodal)  = ModeResult(mode=array([0]), count=array([3]))\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "stats_mode_list_unimodal = stats.mode(x_list_unimodal)    # operate on a unimodal list\n",
    "stats_mode_list_bimodal  = stats.mode(x_list_bimodal)     # operate on a bimodal list\n",
    "\n",
    "print(f'stats.mode(x_list_unimodal) = {stats_mode_list_unimodal}')\n",
    "print(f'stats.mode(x_list_bimodal)  = {stats_mode_list_bimodal}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2-d arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stats.mode(matrix) = ModeResult(mode=array([[0, 3, 2, 2, 1, 1]]), count=array([[1, 3, 2, 3, 2, 4]]))\n"
     ]
    }
   ],
   "source": [
    "matrix = np.array([[1, 3, 4, 2, 2, 1],\n",
    "                   [5, 2, 2, 1, 4, 1],\n",
    "                   [3, 3, 2, 2, 1, 1],\n",
    "                   [0, 3, 4, 2, 1, 1]])\n",
    "\n",
    "matrix_modes_columns = stats.mode(matrix)\n",
    "print(f'stats.mode(matrix) = {matrix_modes_columns}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stats.mode(matrix, axis=None) = ModeResult(mode=array([1]), count=array([8]))\n"
     ]
    }
   ],
   "source": [
    "matrix_modes_all = stats.mode(matrix, axis=None)\n",
    "print(f'stats.mode(matrix, axis=None) = {matrix_modes_all}')"
   ]
  }
 ],
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