Key Distance.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b26f050f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d580e9cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import lru_cache"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "66dc5222",
   "metadata": {},
   "outputs": [],
   "source": [
    "keyboard = {0: ['q', 'w', 'e', 'r', 't', 'y', 'u', 'i', 'o', 'p'], \n",
    "            1: ['a', 's', 'd', 'f', 'g', 'h', 'j', 'k', 'l'],\n",
    "            2: ['z', 'x', 'c', 'v', 'b', 'n', 'm']}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1d5f9999",
   "metadata": {},
   "outputs": [],
   "source": [
    "xoffset = [0, 0.25, 0.75]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d37a6580",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Computes real (x, y) coordinates given the keyboard position (xi, yi)\n",
    "def coordinates(xi, yi):\n",
    "    return (xi + xoffset[yi], yi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b4588c13",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Distance to travel to space bar, assuming it only depends on y axis.\n",
    "def space(yi):\n",
    "    return 3-yi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "55e49c79",
   "metadata": {},
   "outputs": [],
   "source": [
    "key_metrics = {\n",
    "    letter: (coordinates(xi, yi), space(yi))\n",
    "    for (yi, row) in keyboard.items()\n",
    "    for (xi, letter) in enumerate(row)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a032dd4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Returns Euclidean distance between two vectors:\n",
    "def dist(u, v):\n",
    "    def vec_sub(u, v):\n",
    "        return (u[0] - v[0], u[1] - v[1])\n",
    "    def hypot(v):\n",
    "        return sqrt(sum(x ** 2 for x in v))\n",
    "    return hypot(vec_sub(u, v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fe1258cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# LRU cache ensures that the distance is not recomputed for the\n",
    "# same pair of letters\n",
    "@lru_cache(maxsize=None)\n",
    "def travel(letter1, letter2):\n",
    "    def position(letter):\n",
    "        return key_metrics[letter][0]\n",
    "    return dist(position(letter1), position(letter2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c524af37",
   "metadata": {},
   "outputs": [],
   "source": [
    "def distance(word):\n",
    "    if len(word) == 0:\n",
    "        return 0\n",
    "\n",
    "    prevLetter = None    \n",
    "    dist = 0\n",
    "    \n",
    "    for letter in word:\n",
    "        if prevLetter is not None:\n",
    "            dist += travel(prevLetter, letter)\n",
    "        prevLetter = letter\n",
    "        \n",
    "        \n",
    "    dist += (key_metrics[word[0]][1] + key_metrics[word[-1]][1])/2\n",
    "    return dist * 19.05 # Scale to mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e99c60dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "703.3426198050789"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance(\"papal\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b26b20f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38.1"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance(\"a\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "599d4317",
   "metadata": {},
   "outputs": [],
   "source": [
    "word = \"papal\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f844e68b",
   "metadata": {},
   "source": [
    "Using word frequency as listed in\n",
    "https://www.kaggle.com/rtatman/english-word-frequency\n",
    "download, and unzip to get file unigram_freq.csv\n",
    "```sh\n",
    "unzip ~/Downloads/archive.zip\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "57e06ccb",
   "metadata": {},
   "outputs": [],
   "source": [
    "filename = \"unigram_freq.csv\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "38582d39",
   "metadata": {},
   "outputs": [],
   "source": [
    "word_norm = {}\n",
    "global total_count\n",
    "total_count = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7cdedb60",
   "metadata": {},
   "outputs": [],
   "source": [
    "def register(word, count):\n",
    "    global total_count\n",
    "    d = distance(word)    \n",
    "    word_norm[word] = (d, d *count)\n",
    "    total_count = total_count + count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e42d9185",
   "metadata": {},
   "outputs": [],
   "source": [
    "firstLine = True\n",
    "with open(filename, 'r', encoding='UTF-8') as file:\n",
    "    while line := file.readline().rstrip():\n",
    "        if not firstLine:\n",
    "            (word, count) = line.split(\",\")\n",
    "            count = int(count)\n",
    "            register(word, count)\n",
    "        else:\n",
    "            firstLine = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "46748687",
   "metadata": {},
   "outputs": [],
   "source": [
    "word_items = list(map(lambda wp: (wp[0], (wp[1][0], wp[1][1]/total_count)), word_norm.items()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b0d94e14",
   "metadata": {},
   "outputs": [],
   "source": [
    "word_items.sort(reverse=True, key = lambda p: p[1][1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4b73cf3a",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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       " ('talk', (293.0088819909384, 0.048750184683996285)),\n",
       " ('whole', (336.28027994915, 0.048717481200936906)),\n",
       " ('transport', (608.4639904759806, 0.048668183933218714)),\n",
       " ('hot', (179.56863332480222, 0.04863425116227747)),\n",
       " ('francisco', (628.6753469985542, 0.04861638393693184)),\n",
       " ('regulations', (646.5800102165312, 0.048594690587878436)),\n",
       " ('scientific', (673.7327118360528, 0.04858952555447041)),\n",
       " ('otherwise', (535.0660644511979, 0.048588371808768516)),\n",
       " ('star', (233.0461486405428, 0.048540307443342194)),\n",
       " ...]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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    "word_items"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9ec2ac7c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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