{
 "cells": [
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['dimensions: 1, cases when observation is the nearest: 0.0%',\n",
       " 'dimensions: 2, cases when observation is the nearest: 0.0%',\n",
       " 'dimensions: 3, cases when observation is the nearest: 0.0%',\n",
       " 'dimensions: 10, cases when observation is the nearest: 14.000000000000002%',\n",
       " 'dimensions: 20, cases when observation is the nearest: 65.0%',\n",
       " 'dimensions: 30, cases when observation is the nearest: 100.0%',\n",
       " 'dimensions: 40, cases when observation is the nearest: 100.0%',\n",
       " 'dimensions: 50, cases when observation is the nearest: 100.0%',\n",
       " 'dimensions: 60, cases when observation is the nearest: 100.0%',\n",
       " 'dimensions: 70, cases when observation is the nearest: 100.0%',\n",
       " 'dimensions: 80, cases when observation is the nearest: 100.0%',\n",
       " 'dimensions: 90, cases when observation is the nearest: 100.0%']"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random\n",
    "from numpy.linalg import norm\n",
    "\n",
    "dimensions=[1,2,3]+[10*i for i in range(1,10)]\n",
    "nb_vectors=10000\n",
    "trials=100\n",
    "k=1 # by setting k=1 we want to check how often the closest vector to the avarage of 2 random vectors is one of these 2 vectors\n",
    "\n",
    "result=[]\n",
    "for dimension in dimensions:\n",
    "    vectors=np.random.normal(0,1,size=(nb_vectors, dimension))\n",
    "    successes=0\n",
    "    for i in range(trials):\n",
    "        i1,i2=random.sample(range(nb_vectors),2)\n",
    "        target=(vectors[i1]+vectors[i2])/2\n",
    "\n",
    "        distances=pd.DataFrame(enumerate(np.dot(target, vectors.transpose())/norm(target)/norm(vectors.transpose(), axis=0)))\n",
    "        distances=distances.sort_values(by=[1], ascending=False)\n",
    "        if (i1 in (list(distances[0][:k]))) | (i2 in (list(distances[0][:k]))):\n",
    "            successes+=1\n",
    "    result.append(successes/trials)\n",
    "    \n",
    "[f'dimensions: {i}, cases when observation is the nearest: {100*round(j,3)}%' for i,j in zip(dimensions, result)]"
   ]
  }
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