Positional_Encoding.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from math import sin, cos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   classes  x_min  x_max  y_min  y_max\n",
      "0        3    765    841    441    534\n",
      "1       15    742    933    478    672\n",
      "2        9   1214   1467    288    356\n",
      "3       11   1168   1404    778    907\n",
      "4        7    617    692    774   1042\n",
      "5        2    775    956    274    511\n",
      "6        0    485    737    259    508\n",
      "7        8   1279   1532    509    634\n",
      "8       19    994   1105    401    569\n",
      "9       16   1030   1285    760    967\n"
     ]
    }
   ],
   "source": [
    "# plant the seed for random variable\n",
    "np.random.seed(20)\n",
    "\n",
    "# assume that image is HD\n",
    "h, w = (1080, 1920)\n",
    "\n",
    "# assume the size of bbox\n",
    "min_offset = 50\n",
    "max_offset = 300\n",
    "\n",
    "# generate classes\n",
    "classes = np.random.randint(0, 20, size=(10,))\n",
    "\n",
    "# generate positions \n",
    "x_min = np.random.randint(0, w-max_offset, size=(10,))\n",
    "x_max = np.random.randint(min_offset, max_offset, size=(10,)) + x_min\n",
    "y_min = np.random.randint(0, h-max_offset, size=(10,))\n",
    "y_max = np.random.randint(min_offset, max_offset, size=(10,)) + y_min\n",
    "\n",
    "fake_input = pd.DataFrame({\n",
    "    'classes': classes, \n",
    "    'x_min': x_min, \n",
    "    'x_max': x_max, \n",
    "    'y_min': y_min, \n",
    "    'y_max': y_max\n",
    "})\n",
    "\n",
    "print(fake_input)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Formular 1: <font size=\"5\"> $f_m = 1024^{\\frac{2m}{d_model}}$</font>\n",
    "\n",
    "\n",
    "\n",
    "Formular 2:  <font size=\"5\"> $e(t) = [sin(\\frac{t}{f_1}), cos(\\frac{t}{f_1}), ... , sin(\\frac{t}{f_{\\frac{d_model}{2}}}), cos(\\frac{t}{f_{\\frac{d_model}{2}}})] $ </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# f value for one note with Hari's formula\n",
    "def fValueOneNode(m, d):\n",
    "    '''\n",
    "    Input:\n",
    "    + m: the input value for formula 1\n",
    "    + d: dimension of embedded vector\n",
    "    Output:\n",
    "    + f value of 1 node\n",
    "    '''\n",
    "    return 1024*(2*m/d)\n",
    "\n",
    "# one pair value\n",
    "def EValue(t, f):\n",
    "    '''\n",
    "    Input:\n",
    "    + t and f are the variable for formula 2\n",
    "    Output:\n",
    "    + e value for 1 node t\n",
    "    '''\n",
    "    meat = (float)(t/f)\n",
    "    return [sin(meat), cos(meat)]\n",
    "\n",
    "# generate embedded vector function\n",
    "def embedingVector(max_index, dim):\n",
    "    '''\n",
    "    Input:\n",
    "    + max_index: number of buttons in image\n",
    "    + dim: dimension of embedded vector\n",
    "    Output:\n",
    "    + a vector with len dim//2, each node is e(t)\n",
    "    '''\n",
    "    f_value =  list(map(fValueOneNode, \n",
    "                        range(1, dim//2+1), \n",
    "                        [dim]*max_index))\n",
    "    buck_of_vectors = []\n",
    "    for t in range(1, max_index+1):\n",
    "        buck_of_vectors.append(list(map(EValue, \n",
    "                                        [t]*(dim//2), \n",
    "                                        f_value)))\n",
    "    result = np.array(buck_of_vectors)\n",
    "    return result.reshape(result.shape[0],-1)\n",
    "\n",
    "\n",
    "def main(df, dimension):\n",
    "    '''\n",
    "    Input: \n",
    "    + df: dataframe contain classes and positions of buttons\n",
    "    + dimension: dimension of embedded vector\n",
    "    Output:\n",
    "    + A numpy array with shape (4, max_index, dim), with 4 in order is x_min, x_max, y_min, y_max\n",
    "    each one contain max_index embedded vectors\n",
    "    '''\n",
    "    max_index = len(df.classes)\n",
    "    vector = embedingVector(max_index, dimension)\n",
    "    x_min = vector[np.argsort(np.array(df.x_min))]\n",
    "    x_max = vector[np.argsort(~np.array(df.x_max))]\n",
    "    y_min = vector[np.argsort(np.array(df.y_min))]\n",
    "    y_max = vector[np.argsort(~np.array(df.y_max))]\n",
    "    result = np.array([x_min, x_max, y_min, y_max])\n",
    "    return result\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "\n",
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       "         5.20830979e-03, 9.99986437e-01, 3.90624007e-03, 9.99992371e-01,\n",
       "         3.12499491e-03, 9.99995117e-01, 2.60416372e-03, 9.99996609e-01,\n",
       "         2.23214100e-03, 9.99997509e-01, 1.95312376e-03, 9.99998093e-01],\n",
       "        [6.24593178e-02, 9.98047511e-01, 3.12449140e-02, 9.99511758e-01,\n",
       "         2.08318263e-02, 9.99782994e-01, 1.56243642e-02, 9.99877932e-01,\n",
       "         1.24996745e-02, 9.99921876e-01, 1.04164783e-02, 9.99945747e-01,\n",
       "         8.92845280e-03, 9.99960141e-01, 7.81242053e-03, 9.99969483e-01],\n",
       "        [7.02545786e-02, 9.97529094e-01, 3.51490085e-02, 9.99382083e-01,\n",
       "         2.34353543e-02, 9.99725354e-01, 1.75772198e-02, 9.99845509e-01,\n",
       "         1.40620365e-02, 9.99901125e-01, 1.17184818e-02, 9.99931336e-01,\n",
       "         1.00444739e-02, 9.99949553e-01, 8.78894934e-03, 9.99961376e-01],\n",
       "        [7.81242053e-03, 9.99969483e-01, 3.90624007e-03, 9.99992371e-01,\n",
       "         2.60416372e-03, 9.99996609e-01, 1.95312376e-03, 9.99998093e-01,\n",
       "         1.56249936e-03, 9.99998779e-01, 1.30208297e-03, 9.99999152e-01,\n",
       "         1.11607120e-03, 9.99999377e-01, 9.76562345e-04, 9.99999523e-01],\n",
       "        [4.68578357e-02, 9.98901568e-01, 2.34353543e-02, 9.99725354e-01,\n",
       "         1.56243642e-02, 9.99877932e-01, 1.17184818e-02, 9.99931336e-01,\n",
       "         9.37486267e-03, 9.99956055e-01, 7.81242053e-03, 9.99969483e-01,\n",
       "         6.69637852e-03, 9.99977579e-01, 5.85934147e-03, 9.99982834e-01],\n",
       "        [5.46602449e-02, 9.98505011e-01, 2.73403427e-02, 9.99626183e-01,\n",
       "         1.82281571e-02, 9.99833853e-01, 1.36714491e-02, 9.99906541e-01,\n",
       "         1.09372819e-02, 9.99940186e-01, 9.11445713e-03, 9.99958462e-01,\n",
       "         7.81242053e-03, 9.99969483e-01, 6.83588426e-03, 9.99976635e-01],\n",
       "        [2.34353543e-02, 9.99725354e-01, 1.17184818e-02, 9.99931336e-01,\n",
       "         7.81242053e-03, 9.99969483e-01, 5.85934147e-03, 9.99982834e-01,\n",
       "         4.68748283e-03, 9.99989014e-01, 3.90624007e-03, 9.99992371e-01,\n",
       "         3.34820803e-03, 9.99994395e-01, 2.92968331e-03, 9.99995708e-01]]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "embedded_vectors = main(fake_input, 16)\n",
    "embedded_vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6     485\n",
       "4     617\n",
       "1     742\n",
       "0     765\n",
       "5     775\n",
       "8     994\n",
       "9    1030\n",
       "3    1168\n",
       "2    1214\n",
       "7    1279\n",
       "Name: x_min, dtype: int32"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fake_input[\"x_min\"].sort_values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([14, 12, 10,  8,  6,  4,  2,  0,  1,  3,  5,  7,  9, 11, 13, 15],\n",
       "      dtype=int64)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argsort(embedded_vectors[0][:][:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.46602449e-02, 9.98505011e-01, 2.73403427e-02, 9.99626183e-01,\n",
       "        1.82281571e-02, 9.99833853e-01, 1.36714491e-02, 9.99906541e-01,\n",
       "        1.09372819e-02, 9.99940186e-01, 9.11445713e-03, 9.99958462e-01,\n",
       "        7.81242053e-03, 9.99969483e-01, 6.83588426e-03, 9.99976635e-01],\n",
       "       [3.90525667e-02, 9.99237158e-01, 1.95300083e-02, 9.99809271e-01,\n",
       "        1.30204654e-02, 9.99915230e-01, 9.76546978e-03, 9.99952317e-01,\n",
       "        7.81242053e-03, 9.99969483e-01, 6.51037068e-03, 9.99978807e-01,\n",
       "        5.58032818e-03, 9.99984430e-01, 4.88279310e-03, 9.99988079e-01],\n",
       "       [1.56243642e-02, 9.99877932e-01, 7.81242053e-03, 9.99969483e-01,\n",
       "        5.20830979e-03, 9.99986437e-01, 3.90624007e-03, 9.99992371e-01,\n",
       "        3.12499491e-03, 9.99995117e-01, 2.60416372e-03, 9.99996609e-01,\n",
       "        2.23214100e-03, 9.99997509e-01, 1.95312376e-03, 9.99998093e-01],\n",
       "       [7.81242053e-03, 9.99969483e-01, 3.90624007e-03, 9.99992371e-01,\n",
       "        2.60416372e-03, 9.99996609e-01, 1.95312376e-03, 9.99998093e-01,\n",
       "        1.56249936e-03, 9.99998779e-01, 1.30208297e-03, 9.99999152e-01,\n",
       "        1.11607120e-03, 9.99999377e-01, 9.76562345e-04, 9.99999523e-01],\n",
       "       [4.68578357e-02, 9.98901568e-01, 2.34353543e-02, 9.99725354e-01,\n",
       "        1.56243642e-02, 9.99877932e-01, 1.17184818e-02, 9.99931336e-01,\n",
       "        9.37486267e-03, 9.99956055e-01, 7.81242053e-03, 9.99969483e-01,\n",
       "        6.69637852e-03, 9.99977579e-01, 5.85934147e-03, 9.99982834e-01],\n",
       "       [7.02545786e-02, 9.97529094e-01, 3.51490085e-02, 9.99382083e-01,\n",
       "        2.34353543e-02, 9.99725354e-01, 1.75772198e-02, 9.99845509e-01,\n",
       "        1.40620365e-02, 9.99901125e-01, 1.17184818e-02, 9.99931336e-01,\n",
       "        1.00444739e-02, 9.99949553e-01, 8.78894934e-03, 9.99961376e-01],\n",
       "       [7.80455514e-02, 9.96949794e-01, 3.90525667e-02, 9.99237158e-01,\n",
       "        2.60387233e-02, 9.99660935e-01, 1.95300083e-02, 9.99809271e-01,\n",
       "        1.56243642e-02, 9.99877932e-01, 1.30204654e-02, 9.99915230e-01,\n",
       "        1.11604826e-02, 9.99937720e-01, 9.76546978e-03, 9.99952317e-01],\n",
       "       [3.12449140e-02, 9.99511758e-01, 1.56243642e-02, 9.99877932e-01,\n",
       "        1.04164783e-02, 9.99945747e-01, 7.81242053e-03, 9.99969483e-01,\n",
       "        6.24995931e-03, 9.99980469e-01, 5.20830979e-03, 9.99986437e-01,\n",
       "        4.46427089e-03, 9.99990035e-01, 3.90624007e-03, 9.99992371e-01],\n",
       "       [2.34353543e-02, 9.99725354e-01, 1.17184818e-02, 9.99931336e-01,\n",
       "        7.81242053e-03, 9.99969483e-01, 5.85934147e-03, 9.99982834e-01,\n",
       "        4.68748283e-03, 9.99989014e-01, 3.90624007e-03, 9.99992371e-01,\n",
       "        3.34820803e-03, 9.99994395e-01, 2.92968331e-03, 9.99995708e-01],\n",
       "       [6.24593178e-02, 9.98047511e-01, 3.12449140e-02, 9.99511758e-01,\n",
       "        2.08318263e-02, 9.99782994e-01, 1.56243642e-02, 9.99877932e-01,\n",
       "        1.24996745e-02, 9.99921876e-01, 1.04164783e-02, 9.99945747e-01,\n",
       "        8.92845280e-03, 9.99960141e-01, 7.81242053e-03, 9.99969483e-01]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "embedded_vectors[0][:][:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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