{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Algebra and Embeddings\n",
    "\n",
    "(C) 2023-2024 by [Damir Cavar](http://damir.cavar.me/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Prerequisites:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install -U numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install -U pip setuptools wheel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following installation of spaCy is ideal for my environment, i.e., using a GPU and CUDA 12.x. See the [spaCy homepage](https://spacy.io/usage) for detailed installation instructions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install -U 'spacy[cuda12x,transformers,lookups,ja]'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Installing language module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!python -m spacy download en_core_web_trf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using spaCy Word Embeddings\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import spacy\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "nlp = spacy.load(\"en_core_web_lg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.0969249 ,  3.5422752 ,  0.23759246, -0.555475  ,  5.2427    ,\n",
       "       -2.4753752 ,  2.3339748 ,  2.8237414 ,  0.33422732, -0.3434676 ,\n",
       "       12.083975  ,  0.33232486, -3.362825  , -1.320285  ,  0.388     ,\n",
       "        4.3468122 ,  3.9268746 ,  6.310725  ,  1.81281   ,  3.459995  ,\n",
       "       -0.60847497,  0.6960525 , -3.12215   ,  1.7629642 , -3.78505   ,\n",
       "       -3.615975  , -2.401775  , -3.773425  , -4.586575  , -0.17040491,\n",
       "       -2.2923126 ,  0.20159996, -2.092505  , -0.081205  , -3.5820775 ,\n",
       "        1.7506775 , -0.04733169, -1.336425  ,  6.71595   , -1.0187502 ,\n",
       "       -3.2500327 ,  1.653998  , -1.67977   ,  0.19409996, -1.7241253 ,\n",
       "        3.2048974 ,  5.43085   , -2.63674   , -3.197685  , -0.8757375 ,\n",
       "       -1.1576226 , -1.9054224 ,  4.32505   , -3.5928502 , -0.06439996,\n",
       "       -0.49245   ,  3.9352    ,  0.5091    , -1.5124725 , -1.2777625 ,\n",
       "        3.9715326 ,  1.292665  , -1.6772001 , -0.33407497, -3.6834948 ,\n",
       "        4.0337377 , -2.8430524 , -8.60705   ,  3.8568497 ,  3.188225  ,\n",
       "       -1.6995806 ,  5.7394476 , -5.68779   ,  0.86530495, -2.75266   ,\n",
       "        3.5973    , -2.9996974 ,  4.636125  , -4.753975  , -0.2553249 ,\n",
       "       -5.2018423 , -4.1078873 ,  1.892025  , -2.5739925 ,  3.290225  ,\n",
       "        0.91276246,  2.585525  ,  0.35443497,  7.3732    , -2.6650624 ,\n",
       "       -0.56189257, -5.0054746 ,  4.42545   , -6.362225  ,  1.3437551 ,\n",
       "       -5.9611998 , -0.04044253,  1.149175  , -2.2931252 , -5.1349    ,\n",
       "        0.47136992,  0.9424001 ,  6.57765   ,  5.74815   ,  1.3653026 ,\n",
       "        6.008925  ,  2.159755  , -0.08589995, -3.4470825 ,  4.2521124 ,\n",
       "        0.10369492,  4.1392746 , -1.749475  ,  7.122425  ,  0.04479751,\n",
       "       -2.5704076 , -5.2203474 ,  0.983475  ,  0.13849998, -0.45529997,\n",
       "       -1.576725  , -2.256875  ,  1.4163951 ,  7.4344    , -1.99145   ,\n",
       "       -8.1637745 , -1.7708502 , -1.64675   ,  2.368075  , -4.5596    ,\n",
       "       -4.775775  , -0.41967502,  5.3922496 , -8.33895   ,  0.11092576,\n",
       "        0.98969454,  4.9369574 , -2.4393501 ,  6.700625  , -3.98615   ,\n",
       "       -1.87852   ,  0.36134487,  4.5063353 ,  2.10782   ,  3.9655325 ,\n",
       "        1.5841775 , -3.2904477 ,  1.2405727 , -0.65805   ,  7.336225  ,\n",
       "        1.882325  ,  7.14828   ,  0.38635895,  3.0701375 ,  0.289495  ,\n",
       "        1.954175  ,  4.4154773 ,  4.4448624 ,  0.21266496, -0.7630849 ,\n",
       "       -1.7062174 , -1.5508088 ,  3.17329   ,  0.08830002, -4.14565   ,\n",
       "       -3.20905   , -5.540575  ,  7.433675  ,  1.93855   , -0.79538745,\n",
       "        2.7830474 , -1.2273326 ,  2.6722    ,  3.1045501 ,  1.9526999 ,\n",
       "       -3.207857  ,  0.6988225 , -0.47439998, -4.4026175 , -2.2394    ,\n",
       "        0.28175497,  2.4338498 ,  2.2315974 , -4.188975  , -1.8792049 ,\n",
       "       -1.2445525 , -4.4771748 , -3.99115   , -0.74327505,  3.2435255 ,\n",
       "       -3.2351851 , -2.325425  , -1.6298001 , -0.8707749 ,  4.8065248 ,\n",
       "        2.1342926 , -3.81695   , -0.85352504,  4.0910277 , -1.7153752 ,\n",
       "        0.04182005, -1.887125  , -5.3869495 , -5.5109253 ,  2.2279    ,\n",
       "        2.9002626 , -7.1083503 ,  0.454875  , -2.0965447 , -2.765925  ,\n",
       "        4.333975  ,  2.377125  ,  0.51845   ,  5.481675  ,  3.5761576 ,\n",
       "       -0.91882753,  0.7577725 , -2.49445   , -1.6242576 ,  1.6717949 ,\n",
       "       -2.1889749 , -2.0408049 ,  2.3667    , -1.1684225 , -0.07747507,\n",
       "       -2.3084002 ,  3.493225  ,  0.72685254,  3.7181323 , -3.602925  ,\n",
       "        0.64301497, -8.118751  ,  1.93061   ,  3.2603297 , -5.6989703 ,\n",
       "        0.41267496,  2.078825  ,  0.18630004,  2.070035  ,  1.38596   ,\n",
       "        1.1946499 ,  0.78668505,  2.7850251 ,  5.969575  , -1.6403899 ,\n",
       "       -2.9643674 , -4.727984  ,  1.2468748 ,  1.7687201 ,  4.2653275 ,\n",
       "        2.348125  , -1.56483   , -4.87081   , -6.1311    , -1.8386024 ,\n",
       "       -0.61717516,  4.7199774 ,  5.5335    ,  1.6379997 , -1.7111676 ,\n",
       "       -0.9985751 ,  4.558325  ,  3.0915775 ,  7.3542247 , -2.38635   ,\n",
       "        1.1966676 , -2.45665   ,  1.8378799 , -6.0176997 , -2.69588   ,\n",
       "        4.44735   , -3.6373749 , -0.8115974 , -5.8442    ,  0.4275999 ,\n",
       "        1.28295   ,  3.026945  ,  3.9658577 , -1.0834899 ,  0.150175  ,\n",
       "       -0.14967   , -5.245175  , -3.9003997 ,  2.0858262 , 10.94865   ,\n",
       "       -0.87130004,  5.7962255 , -1.77914   , -2.003475  ,  4.728225  ,\n",
       "        2.3407001 ,  1.0157275 ,  5.048585  ,  0.57595   , -0.27465004,\n",
       "        4.7957    ,  2.306925  , -0.85118246, -3.8584175 ,  2.6602824 ],\n",
       "      dtype=float32)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "doc = nlp(\"This is a text\")\n",
    "doc.vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "doc_v = [ v.vector for v in doc ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.5, 2.5])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([ 1.0, 2.0 ])\n",
    "b = np.array([ 2.0, 3.0 ])\n",
    "(a + b) / 2.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.5, 2. ])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = [ a, b ]\n",
    "sum(c) / len(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean([a, b], dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.5, 2.5])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean([a, b], dtype=float, axis=0)"
   ]
  }
 ],
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