key_delay.csv

optimal_keyboard.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random\n",
    "import copy\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "data_path = 'alphabet_pairs.csv'\n",
    "df = pd.read_csv(data_path)\n",
    "\n",
    "# Create a list of unique keys\n",
    "keys = sorted(set(df['first_key_down'].unique().tolist() + df['next_key_down'].unique().tolist()))\n",
    "\n",
    "# Create a mapping for keys to indices\n",
    "key_to_index = {key: index for index, key in enumerate(keys)}\n",
    "\n",
    "# Initialize a matrix with zeros\n",
    "matrix = np.zeros((len(keys), len(keys)))\n",
    "\n",
    "# Fill the matrix with costs\n",
    "for index, row in df.iterrows():\n",
    "    i = key_to_index[row['first_key_down']]\n",
    "    j = key_to_index[row['next_key_down']]\n",
    "    if row['freq'] != 0:  # To avoid division by zero\n",
    "        matrix[i, j] = row['mean'] / row['freq']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_keyboard(layout):\n",
    "    # The layout should be a list of 26 characters (A-Z)\n",
    "    assert len(layout) == 26, \"The layout should be a list of 26 characters (A-Z)\"\n",
    "    \n",
    "    # Get the three rows\n",
    "    first_row = layout[:10]\n",
    "    second_row = layout[10:19]\n",
    "    third_row = layout[19:]\n",
    "    \n",
    "    # Add the necessary spaces to align the keys\n",
    "    first_row_str = \"  \" + \"   \".join(first_row)\n",
    "    second_row_str = \"   \".join(second_row)\n",
    "    third_row_str = \"    \" + \"   \".join(third_row)\n",
    "    \n",
    "    # Print the keyboard\n",
    "    print(first_row_str)\n",
    "    print(second_row_str)\n",
    "    print(third_row_str)\n",
    "\n",
    "def calculate_total_cost(layout, cost_matrix, key_to_index):\n",
    "    total_cost = 0\n",
    "    for i in range(len(layout) - 1):\n",
    "        total_cost += cost_matrix[key_to_index[layout[i]], key_to_index[layout[i+1]]]\n",
    "    return total_cost\n",
    "\n",
    "def simulated_annealing(keys, cost_matrix, key_to_index, num_iterations=10000, start_temperature=10, end_temperature=0.01):\n",
    "    # Create a random initial layout\n",
    "    current_layout = random.sample(keys, len(keys))\n",
    "    current_cost = calculate_total_cost(current_layout, cost_matrix, key_to_index)\n",
    "    \n",
    "    # Store the best solution found\n",
    "    best_layout = copy.deepcopy(current_layout)\n",
    "    best_cost = current_cost\n",
    "    \n",
    "    # Store the cost over time\n",
    "    costs_over_time = [current_cost]\n",
    "    \n",
    "    for iteration in range(num_iterations):\n",
    "        # Calculate the current temperature (decreases over time)\n",
    "        temperature = start_temperature * ((end_temperature / start_temperature) ** (iteration / num_iterations))\n",
    "        \n",
    "        # Choose two keys randomly and swap them\n",
    "        new_layout = copy.deepcopy(current_layout)\n",
    "        i, j = random.sample(range(len(new_layout)), 2)\n",
    "        new_layout[i], new_layout[j] = new_layout[j], new_layout[i]\n",
    "        \n",
    "        # Calculate the new cost\n",
    "        new_cost = calculate_total_cost(new_layout, cost_matrix, key_to_index)\n",
    "        \n",
    "        # If the new layout is better, accept it\n",
    "        if new_cost < current_cost or random.random() < np.exp((current_cost - new_cost) / temperature):\n",
    "            current_layout = new_layout\n",
    "            current_cost = new_cost\n",
    "            \n",
    "            # Update the best solution found\n",
    "            if new_cost < best_cost:\n",
    "                best_layout = copy.deepcopy(new_layout)\n",
    "                best_cost = new_cost\n",
    "                \n",
    "        costs_over_time.append(current_cost)\n",
    "                \n",
    "    return best_layout, costs_over_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Z   A   J   N   K   C   X   E   V   O\n",
      "D   L   P   S   Y   B   M   R   F\n",
      "    I   W   T   H   G   U   Q\n",
      "{'QWERTY': 8.140831212028026, 'Dvorak': 17.207374702349316, 'Colemak': 9.215131291772037, 'Optimized': 0.02956733896325039}\n"
     ]
    }
   ],
   "source": [
    "# Perform simulated annealing to find the optimal layout and store the cost over time\n",
    "optimal_layout, costs_over_time = simulated_annealing(keys, matrix, key_to_index,\n",
    "    num_iterations=5000000, start_temperature=1000, end_temperature=0.0001)\n",
    "\n",
    "# Plot the cost over time\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(costs_over_time)\n",
    "plt.title('Cost over time')\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Cost')\n",
    "plt.show()\n",
    "\n",
    "# Test the function with the optimized layout\n",
    "print_keyboard(optimal_layout)\n",
    "\n",
    "# Define popular keyboard layouts\n",
    "qwerty = ['Q', 'W', 'E', 'R', 'T', 'Y', 'U', 'I', 'O', 'P', 'A', 'S', 'D', 'F', 'G', 'H', 'J', 'K', 'L', 'Z', 'X', 'C', 'V', 'B', 'N', 'M']\n",
    "dvorak = ['P', 'Y', 'F', 'G', 'C', 'R', 'L', 'A', 'O', 'E', 'U', 'I', 'D', 'H', 'T', 'N', 'S', 'Q', 'J', 'K', 'X', 'B', 'M', 'W', 'V', 'Z']\n",
    "colemak = ['Q', 'W', 'F', 'P', 'G', 'J', 'L', 'U', 'Y', 'A', 'R', 'S', 'T', 'D', 'H', 'N', 'E', 'I', 'O', 'Z', 'X', 'C', 'V', 'B', 'K', 'M']\n",
    "\n",
    "# Calculate the total cost for each layout\n",
    "qwerty_cost = calculate_total_cost(qwerty, matrix, key_to_index)\n",
    "dvorak_cost = calculate_total_cost(dvorak, matrix, key_to_index)\n",
    "colemak_cost = calculate_total_cost(colemak, matrix, key_to_index)\n",
    "optimized_cost = calculate_total_cost(optimal_layout, matrix, key_to_index)\n",
    "\n",
    "# Store the costs in a dictionary for easier access\n",
    "costs = {\n",
    "    'QWERTY': qwerty_cost,\n",
    "    'Dvorak': dvorak_cost,\n",
    "    'Colemak': colemak_cost,\n",
    "    'Optimized': optimized_cost\n",
    "}\n",
    "\n",
    "print(costs)"
   ]
  }
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