Class 14 PCA.ipynb

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   "source": [
    "# En estadística hay un problema llamado la maldición de la dimensión \n",
    "\n",
    "# Por cada variable que se agrega al conjunto de dato, se necesita exponencialmente más muestras para tener la misma relevancia estadística\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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    }
   ],
   "source": [
    "np.random.seed(42) #Definimos la semilla como un número fijo\n",
    "\n",
    "x = 3*np.random.rand(200)\n",
    "y = 20*x + 2*np.random.randn(200)\n",
    "\n",
    "x = x.reshape(200, 1)\n",
    "y = y.reshape(200, 1)\n",
    "\n",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 2)\n"
     ]
    }
   ],
   "source": [
    "xy = np.hstack([x, y])# .hstack nos permite unir los dos vectores en uno solo\n",
    "print(xy.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xy[:,0], xy[:,1], '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "xy_centrado = xy - np.mean(xy, axis = 0) # .mean es promedio, resta sobre cada eje"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(xy_centrado[:,0], xy_centrado[:,1], '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.9987754  -0.04947417]\n",
      " [ 0.04947417 -0.9987754 ]]\n"
     ]
    }
   ],
   "source": [
    "# Para calcular las componentes principales, buscamos un d que nos da un máximo como Traza(d.T * x.T * Xd) y d.T * d = 1\n",
    "\n",
    "autovalores, autovectores = np.linalg.eig(xy_centrado.T.dot(xy_centrado))\n",
    "print(autovectores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# El vector asociado con el autovalor más grande nos dice la dirección de máxima varianza\n",
    "\n",
    "%run \".\\\\funciones_auxiliares\\graficarvectores.ipynb\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rd/T3cSAxmbv6NVanvxikPSnIi9RRsXx9JaP7bM18tmRSV7dKJRTkReoo7KKphYzuVUEjC6UgL1IHwZF6MF8P8JmHf8C52RSOcutSfwryIgtQKt0SHKl3BRbUhvMLZjvp0jbl1qXeFORFKlSuC2ReA7G5FPuPTXBwZJKd/X25x2MG79hwKR+77k0axUtdKciLVCAxPp2Xbsl2gUy55/Lr2Tx89jXZtEx24Y9sfl4BXhaDgrxIRMERfDbdEovN7wJ5+7UbuOfD6Q6SB46fIplyurti7OxPp23UZ0YWk4K8SATZEXxhuuWGzStDu0Bmq2F2hAR1BXdZTAryImVkR/DZ9EvM0mmXbLqlVBdIlT5KoynIt5BUCpJJ6O5u9JF0luxEajZFUzhhmg3kifFp/vL+JzFQAzFpGgryTe6VV+CRR+DIERgZgW9+U0F+MSXGpzl99jW6YpbLrYdNmGY7Rc4kHYADiUn2f6T2LYdFKlX3IG9m1wP/CMSBu939U/XeZ6ubmIAvfxm+9CX42tfg3Ln045/5DFx4YWOPrZP84vWr8urd37t1dW4ZvsI6+eGxKWYzAR7Sk7AHRyY1ySoNV9cgb2ZxYA/w28Ak8LiZHXb379Vzv60mlYLHHkuP1o8cgSeeCH/dsWNw223p2xZoTZi9HfZYtc934jbXjX2NH0/s5ILBydxEazKZ4sqLL8wF+MK2BIPrl9Mdt9xIvituHDh+irmU120hEZEozN3Lv2qhGzd7G3Cnu787c/8TAO7+38Nev2zZMh8YGKjb8TSbVKqHiYmbOX3695mdvaTRhyPAr/AE3+A3+Vf+M//tqmMs2/5f8FgMS6W4/Kl7ueDnpzm76mrOrv4NsBh4igtfPMmSV35MbPY1Zl53GenmwM7PL//VzGuSXHzq/3Lx6WONPj1pU1//+tcT7r4l7Ll6p2uuBE4F7k8CVwdfYGa7gF0AS5YsqfPhNJdYbIa1a/+NFSu+ydTU25iaejsvv/wWiq3l0tMzRfrSmvPDTvewbuM273b464KvbZVt1m+dmzWM8wA3cBEv81H+N5/7cRevf+pefn7pJtK/97QLXj6V/vMrZoDx2iVX8dolG7BUMvdF8IvXr+KVFZvxmGOpVPo9Ig1Q7yAf9n9s3p8O7r4X2AuwZcsWP3r0aJ0Pqbm98ML5fPyDD6YnXrMOHVrO9dc37tiaVeLZaYZ/NMXgG5bza2vOp0TcYWQinTu/+g3L6V/TS/AP1+xtd/h/J8Y5fuffcSZxEStfeZXj8R5+b+Vl7NyzJ5eamVs9kEu7fPL+J9l3bCLwH7MR64rxgb/Yze3XbkgfV17e/vcX5Xchncms2OCo/kF+ElgduN8HnK7zPlvaZZfBhz6U/veLX8DRo3D4cDro33knvPvd+fnjTpcYn+b9/xretjcxPs0HPle+pW9i7Kd88N4nmHnLDfT88nu457arGfrjGwG4skg/+B39fell+bIXRzG/2Zhq5KUZ1DvIPw5cZWZvAJ4DbgbeV+d9to0LLoDrr0//27MnPSH7yivw+tc3+siaR6lFtKMu2DE8fpYZi6dfl4Lh8bO57Yf1g4f8Jf+0kIc0s7oGeXefM7M/Bb5KuoTyc+5+op77bFdm8Na3Nvoomk+xIFzsuWKVMYWvO5DZxsDaXoa2beKB0TPcsHllXhDXSF1aQd3r5N39K8BX6r0f6UylFtEOe27Poyfnje6zDcXCtpEYn2b3kRPMzKV4/NkX2XjFMgV2aSm64lVaXnBEXZiKKRxtl0q/hAXvUukgkVagIC9tI8raqaVG/mFKpYNEWoGCvLSNqKPuSnLplX4piDQbBXlpWYWpmXqNujXBKq1MQV6aWrEFs4ulZjTqFsmnIC9Nq1SOvVhqRqNukXz1awQiUqWwQJ6VTc3Ebf6VpiJynkby0rQG1y+nK2bMJp14zOa1DAhLzRRL74h0KgV5qYuaBVtLt+0Na9hTmJoJpne64jFuHOjLLfIh0qkU5KXmotSrF77+vpHJeWujDo9NMZdMr62aTJa/ECmY3pmZS7H/2AQHRya1YId0NOXkpeZK5dILZddG3XdsgnuOTXDLZ4dJjE8Dlefds6/Pjvmd8vsXaXcayUvNRalXz6Zznjv72ry1UYOVMpWURGZff3BkkgPHT+UW3takrHQyBXmpuXLBuTB3Ho/BXCr9XLU92bOv39HfpwlYERTkpU5KBedgOieZTHHz1jW5RQ131GiiVPXyImkK8rLoCtM5tQrsIjKfgrzUXLnySbUfEFk8CvJSU1HLJ0v1gBeR2lGQl5qqdJGNwi+FoW2btF6qSA0pyEtNVdrut/ACpqFDo6TcI11EJSLlKchLze3s78MzP8ulZIJfCmZGMuV5FzEpyItUR0FeaqYw9bKzvy/08eAIPTgJ27u0h91HTmipPZEaUpCXmrlvZJJzs+leM+dmUxwcmWRgbW/RPH1wdH/7tRsA2HjFMk3CitRQVUHezG4C7gTeDGx19+OB5z4B3AYkgT9z969Wsy85rxmrURLj03wxMUm2QYEDB46fYkd/X2ievtjoXhcxidRWtSP5UWAH8C/BB83sLcDNwCZgFfCwmb3J3ZNV7q/jVdrhcbFkO0YGJVPO8NgUt1+7YV5d/J5HT1ZUhSMiC1NVkHf3pwBsfq/v7cAX3P0c8CMzOwlsBb5dzf6k8hLFakX5qyExPs1zZ1+jKx5jLpk+thj5fWgKR+j1WnRbRPLVKyd/JTAcuD+ZeWweM9sF7AJYs2ZNnQ6nfSxmcIzyV0Nes7GYccvWNWxadVHZWndd9SqyOMoGeTN7GLgi5KlPuvuhYm8LecxDHsPd9wJ7AbZs2RL6GjlvMYNjlL8a8pqNpZxVF1/I+66O9mWt/LtI/ZUN8u5+3QK2OwmsDtzvA04vYDsSYrGCY/Cvhng8xnNnXyMxPl1V2qUZJ41F2lm90jWHgX1m9mnSE69XAY/VaV9SQ4VBOLgIxxceO7+cHpB7XdS/LJp10liknVVbQvkHwP8EVgBfNrPvuPu73f2Emd0LfA+YA25XZU3zKxaEh8emmEt5Lm1zcGSS+0Ym816XrXMvtt3hsSlOn31NFTUii6za6pr7gfuLPHcXcFc125fFVSwHX5iScQhdwzVsNF84MdsVj5FMqqJGZLHoitcOFZYbL5ZfL5zsffrHP8vNrMdjRu/SnqJpmMKJ2fduXc2VF1+onLzIIlGQ70ClrjYtll/PPp8Yn+bOL50gu/Z2Cjhx+qWiaZjB9cvpip+fvN2pVaBEFpWCfAcqVRpZrnJneGyK2bnzV7Ymk+mukSUrbNzzf4rIolGQ70ALuaAqm97pXdpDd1eMmUyg744bm1ddBIQvxJ2dtHXOtznQSF5k8SjId4iw0shSZY+J8WkOjqQbjm1edRG7j5zIpXfu/N1NnDj9UuhzOzLthbPUvkCksRTkO0A2B39uNkU8Zuzevpn3Xb2mZC+aWz47nButxw1STm4xj+lXZ7jrD34ZoGyjMbUvEGksBfkWUO1VosNjU7k+73MpZ+jQKBuvWFZ0W4V595Snq2jcfd5oPMpIXe0LRBpHQb7J1eIq0cH1y4nHjLlUeuIz5aVz44Prl8/Lu9/5e5uLNh3b0d8Xmo8XkcZTkG9y1bQWDv4FsHv75rxFskvlxgfW9rL/I4O5nHyxssfCL6DCfLyINJ6CfJNb6MRlYQAe2raJP/z11fNG3PuOTfDA6Blu2Lwyr3tklBTLYve2F5HKKcg3uagTl4V5+2AAnplN5Y3iN626iOGxKX722iz//I0xAL75zE8BIrcJBlXOiLQCBfkGizKpWm5UHZa3DwZgMyPl6QZj52ZT/NV/PBna3P+B0TMVBXlVzog0PwX5BqpV692wtElwXdXepT3c+aV0LbtDriVB4couN2xeWfG+VTkj0twU5BsoSk47yki/VGOx7HtGT7/E/mMTuRG8AUu6Y3zwbes4cebleTl5EWkPCvINVC6nXewipkJR0iY7+/s4ODKZaxR240CfmoWJdAAF+QYqFZwT49N85uEf8IvZdK16uYuYwtImlbYyEJH2oyDfYMWCczZXH1TuIqZi2yhsJywinSPW6ANoR4nxafY8epLE+PSC3n9wZJJzs+lcvQExy/5ML9ARZR9h+X4R6TwayddYtRUzifFpDhw/lZsg7e6K8cdvX8dnvzlGMuXceXgUIK/zY9g+epf2EDODkH4zCz0vpXpEWo+CfI1VexVotv86pEfvNw708fK5uVzZ40zS+ffHJ0ruY9+xCYYOjZJMOfGYMbRtU1WBuValniKy+JSuqbFsxUzciDSCLky7BN+/pDu9XF5hPfvlv3RB0X0kxqcZOjSaW6gj5c70qzNVnZNSPyKtSyP5GqukiqXYCDns/QcSk7lSyz955xv5k3e+MXQfw2NTJFPnr2eNmVWdqlH7ApHWpSBfB1GrWIqldgrfn+0KWRjUw/YxuH45S7pjzMymiGVq66tNraj8UqR1VRXkzezvgd8FZoAfAh9y97OZ5z4B3AYkgT9z969Weaxtp5IRctQvjnoFZJVfirSmakfyDwGfcPc5M/tb4BPAx83sLcDNwCZgFfCwmb3J3ZNV7m9R1bqipHB7CsgiUm9VBXl3fzBwdxi4MXN7O/AFdz8H/MjMTgJbgW9Xs7/FVOuKkuD2umLGTVtW5/q6V7pdlTOKSFS1rK75Y+CBzO0rgVOB5yYzj81jZrvM7LiZHf/JT35Sw8OpTq0rSvL6uyedfccmeP/dwxVfMJX9sviHB59e0PtFpLOUDfJm9rCZjYb82x54zSeBOeCe7EMhmwprYY6773X3Le6+ZcWKFQs5h7qopBSysAwy7GrU7PayvxhnYV8eKmcUkUqUTde4+3WlnjezW4FtwLvcPRvIJ4HVgZf1AacXepCNUMmKTIXL7GWvRo3Z+c6R2e3dNzLJFxOTJJMLK0dUOaOIVKLa6prrgY8D73T3VwNPHQb2mdmnSU+8XgU8Vs2+GqHSdU7Pzab43LfGcp0jU57fOTK4rcK1VqPm2VXOKCKVqLa65n8BS4CHzAxg2N0/6u4nzOxe4Huk0zi3t1plTVSD65fTFTNmkukrTE/+5JW851Op850jC0f9O/r7gMoneVU9IyJRVTXx6u4b3H21u7818++jgefucvc3uvtGd3+g1HZaSWG+fWBtLzdtWR06CQHQ030+pVIsn648u4jUi654rUCxEfeO/j7uG5nMBeoY0NWVv/pSYnya02dfoytmJFP5nSGVZxeReumYIF+L2vJsn/dgZUzhRU29S3uYfnUmbz95NfLxGO/dujpv6T3l2UWkXjoiyC/0wqbgFwOQ1+edwAIeUDpPHkzHJJMprrz4wnmvVZ5dROqhI4L8Qnq8h02SzgW6OyZTzu4jJ4quuRqkdIyINEpbBvnC1MxCgmzhF4MBPV2xXLoG5n9hFEsJKR0jIo3SdkG+kh7txd6fza0Hvxh29PflJljDLmYqlxJSOkZEGqHtgnzUHu1hwq5eLZxEHVjby87+vnlfGNUu+yciUg9tF+SryX8XBupsgM/WrQcDfWEAV95dRJpR2wX5avLfhYG6d2lP5Koc5d1FpBm1XZCHaPnvsEnSwkBdaQpGeXcRaTZtGeSh9MVPUevmlYIRkVbXlkG+XBAvNkIPe59SMCLSytoyyJcK4veNTPLTn50L7SET9r7br90QGty1BJ+ItIK2DPJhaZZ9xyb4q/94kmTmSqbuuPHerWvyeshETc/Uev1XEZF6acsgXziBCjB0aDQX4AHmkj6vh0zUChnVxItIq2jLIA/5lS57Hj1JMpW/xGyxkXqUChlNyIpIq2jbIB80uH45S7pjzMymMIN3vfly/uSdb8zl6SvNrasmXkRaRUcE+bCgnBif5i/vf5IvJiaZS6b7vAcX+YiyTQV3EWl2HRHkIT8oZydOgx0lZ+ZS7D82wcGRSU2kikjbqGqN12ZSuPZqKdmJUy94PLjik4hIO2iLkXylJY3BidN4zLhm42UcffqFeXXzIiKtri2C/EJ6zITl6DWRKiLtpqogb2Z/A2wHUsALwAfd/XTmuU8AtwFJ4M/c/atVHmtRCylpLJw41USqiLSjanPyf+/uv+LubwWOAEMAZvYW4GZgE3A98E9mFq9yX0UNrO1laOktArsAAAT4SURBVNsm3r7hUoa2bVKwFhHJqGok7+4vB+6+DnJzmduBL7j7OeBHZnYS2Ap8u5r9FZMYn2b3kRPMzKV4/NkX8xbXVhpGRDpZ1Tl5M7sL+CPgJeDazMNXAsOBl01mHgt7/y5gF8CaNWsWdAyVdJVUoBeRTlI2XWNmD5vZaMi/7QDu/kl3Xw3cA/xp9m0hmyqsWCTz/r3uvsXdt6xYsWJBJ5HNyceNsl0lRUQ6SdmRvLtfF3Fb+4AvA39NeuS+OvBcH3C64qOLqFibAfWYEZFOV211zVXu/kzm7u8B38/cPgzsM7NPA6uAq4DHqtlXOWHVMeoxIyKdrtqc/KfMbCPpEspx4KMA7n7CzO4FvgfMAbe7e7LKfS2ISiNFpJNVW12zs8RzdwF3VbN9ERGpTtv0rhERkfkU5EVE2piCvIhIG1OQFxFpYwryIiJtzNxDL0RtCDP7CelSzFIuBX66CIezWNrpfNrpXEDn08za6Vyg+vNZ6+6hLQOaKshHYWbH3X1Lo4+jVtrpfNrpXEDn08za6VygvuejdI2ISBtTkBcRaWOtGOT3NvoAaqydzqedzgV0Ps2snc4F6ng+LZeTFxGR6FpxJC8iIhEpyIuItLGmD/JmdpOZnTCzlJkVLTEys2fN7Ekz+46ZHV/MY4yqgnO53syeNrOTZnbHYh5jJczsEjN7yMyeyfwM7enc7J9Nud+3pf2PzPPfNbP+RhxnFBHO5RozeynzWXzHzIYacZxRmNnnzOwFMxst8nzLfC4Q6Xzq89m4e1P/A94MbASOAltKvO5Z4NJGH2+15wLEgR8C64Ee4AngLY0+9iLH+nfAHZnbdwB/22qfTZTfN/Ae4AHSy1oOAscafdxVnMs1wJFGH2vE8/lNoB8YLfJ8S3wuFZxPXT6bph/Ju/tT7v50o4+jFiKey1bgpLuPufsM8AVge/2PbkG2A5/P3P488PsNPJaFivL73g78m6cNAxeb2crFPtAIWum/nbLc/RvAiyVe0iqfCxDpfOqi6YN8BRx40MwSZrar0QdThSuBU4H7k5nHmtHl7n4GIPPzsiKva+bPJsrvu1U+k6jH+TYze8LMHjCzTYtzaHXRKp9LJWr+2VS7/F9NmNnDwBUhT33S3Q9F3Mw73P20mV0GPGRm3898cy6qGpyLhTzWsDrXUudTwWaa4rMpIsrvu6k+kxKiHOcI6T4nPzez9wD/QXoN5lbUKp9LVHX5bJoiyLv7dTXYxunMzxfM7H7Sf7oueiCpwblMAqsD9/uA01Vuc8FKnY+ZPW9mK939TObP5BeKbKMpPpsiovy+m+ozKaHscbr7y4HbXzGzfzKzS929FZt9tcrnEkm9Ppu2SNeY2evMbFn2NvA7QOgMdgt4HLjKzN5gZj3AzcDhBh9TMYeBWzO3bwXm/aXSAp9NlN/3YeCPMtUcg8BL2TRVkyl7LmZ2hZlZ5vZW0jFgatGPtDZa5XOJpG6fTaNnnCPMSP8B6W/sc8DzwFczj68CvpK5vZ50JcETwAnSqZGGH/tCziVz/z3AD0hXSjTluWSOcznwCPBM5uclrfjZhP2+gY8CH83cNmBP5vknKVHl1eh/Ec7lTzOfwxPAMPD2Rh9ziXPZD5wBZjP/39zWqp9LxPOpy2ejtgYiIm2sLdI1IiISTkFeRKSNKciLiLQxBXkRkTamIC8i0sYU5EVE2piCvIhIG/v/BJ9WfjcXzJoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "graficarvectores(autovectores.T, ['blue', 'red'])\n",
    "\n",
    "plt.plot(xy_centrado[:, 0], xy_centrado[:, 1], '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Amplificando el vector rojo\n",
    "\n",
    "graficarvectores(autovectores.T, ['blue', 'red'])\n",
    "\n",
    "plt.plot(xy_centrado[:, 0], xy_centrado[:, 1]/20, '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.85050946e+00 6.28759594e+04]\n"
     ]
    }
   ],
   "source": [
    "print(autovalores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "xy_nuevo = autovectores.T.dot(xy_centrado.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Gráfico ideal para ver la dispersión y varianza de nuestros datos.\n",
    "\n",
    "plt.plot(xy_nuevo[0, :], xy_nuevo[1, :], '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}