{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "200\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "a = np.array([1, 11, 23, 13, 200, 10, 11])\n",
    "\n",
    "# find max of a\n",
    "\n",
    "# alogorithm mymax = a[0], \n",
    "# loop through array and if a[i] > a[0], then mymax = a[i]\n",
    "\n",
    "mymax = a[0]\n",
    "N = len(a)\n",
    "for i in range(N):\n",
    "#     print(i)\n",
    "    if a[i] > mymax:\n",
    "        mymax = a[i]\n",
    "print(mymax)\n",
    "\n",
    "np.max(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAFXCAYAAABOYlxEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJzt3Xl0VPX9//HXLCRhkkmYaNyogFQiBGotUIFvIYGKYosogcjWgm0QUVFB+aGIFG1RcUUQVKg1WLEgSAWttm4UZZVWi0gxrCqCC2skgYQks/z+QIM094YkM3Nnez7O6ZF8PpOZ9/kwp2/undd8PrZAIBAQAACIK/ZIFwAAAEKPBg8AQByiwQMAEIdo8AAAxCEaPAAAcYgGDwBAHHJGuoBQ2r+/LKTP5/G4VFJSHtLnTESsY/BYw+CxhsFjDYMXjjXMynIbjnMFXwen0xHpEuIC6xg81jB4rGHwWMPgWbmGNHgAAOIQDR4AgDhEgwcAIA7R4AEAiEM0eAAA4hANHgCAOESDBwAgDtHgAQCIQ5Y2+I0bN2r48OGSpF27dmno0KEaNmyY7r77bvn9/pMee+zYMd18880aNmyYRo0apUOHDllWZ/LSJfLkdZOcTnnyuil56RLLXhsAgFCwrME//fTTmjx5siorKyVJ06ZN07hx47RgwQIFAgEtX778pMcvXLhQ2dnZWrBggfr3768nn3zSkjqTly5R+uhCOYs3Sz6fnMWblT66kCYPAIgpljX4Fi1aaNasWTU/b968WRdffLEkKTc3V2vXrj3p8R988IF69OhRM79u3TpL6nTNeNR4fOZ0S14fAIBQsOywmT59+mjPnj01PwcCAdlsNklSamqqyspOPijmyJEjcrvdpvNGPB5X8Pv8bttiOOzctsV0Q3+cGmsXPNYweKxh8FjD4Fm1hhE7Tc5uP3Hz4OjRo0pPTz9pPi0tTUePHjWdNxKKE3o82W2P357/H77TTtehvYclO7nEhsrKcof8pL9EwxoGjzUMHmsYvHCsYdSdJpeTk6P169dLklauXKnOnTufNN+xY0e9++67NfOdOnWypK7yceMNxx17v1b6rwfJduCAJXUAABCMiDX4O+64Q7NmzdLgwYNVXV2tPn36SJIKCwtVVVWloUOHavv27Ro6dKgWLVqkm266yZK6KvMLVDq3SN6cDpLTKW9OB5U+NENVPX+u5LfflOfSXOno0Zqk/elne0jaAwCiji0QCAQiXUSohOO2R81z+v1q+sTjsvm88rVspfTRhbUeXzq3SJX5BSGtIR5wWy94rGHwWMPgsYbBs/IWfcQ+g485drsqbh4nSce/I2/ANXM6DR4AEBVIjDWCwyRpbzYOAIDVaPCN4MtuazzeJtviSgAAMEaDbwSzpL2trEyO7dssrgYAgNpo8I3w/aR9wOmUt22OqrrnybFntxwG36EHAMBqhOwaqTK/oFagzvnhf+S9qKMkKXnBc3I9NVuOHdvly26r8nHjCeABACxDgw+hmub+0otKH3fie/vfHVhTKtHkAQCW4BZ9GLhmcmANACCyaPBh4Ni21WScr9EBAKxBgw8Ds6/RyWaTjh2zthgAQEKiwYeB2dfojg0cJKWkWFwNACAR0eDDoNbX6HI6qHRukY48/tS3D6hURn5fef6vE4fVAADCghR9mBh9je47qXdPUtKaVTU/k7IHAIQaV/ARkLRureE4KXsAQKjQ4CPA9LCarcUWVwIAiFc0+AgwS9n7m59rcSUAgHhFg48As5T90bumSJJs+/bJtn+/lSUBAOIMDT4CzFL2lfkFkt+v9DGj5On1f3Ld/3t58rqRtAcANBgp+gipK2Vf1fMSpa56V6kzTmx5S9IeANAQXMFHG7tdFWNuka9lK8NpkvYAgPqgwUcpx+e7jMfZzx4AUA80+ChllrQ33eceAIDvocFHKbOkffnoG5UxZICc/3nf4ooAALGEBh+lzJL2gTS3mqxYrmZXXCb36EJ58rqSsgcA1EKKPoqZJe0Pv/iy0kcOV8r3GjopewDA93EFH4Oqc3vKf+ZZhnOk7AEAEg0+Zjl27jAeJ2UPABANPmaZpuzPay3Hx5strgYAEG1o8DHKLGUvn1+ePj2V8sxcKRCwtigAQNSgwccos5T90XvuVSA1Ve47J6jZpbnydP8pKXsASECk6GOYWcq+5J11yri6v5p8tLFmjJQ9ACQWruDjkP+ssyW7zXCOlD0AJAYafJxybNtqMk7KHgASAQ0+TpnuWW+3K+UvzxHAA4A4R4OPU2Yp+4DDIfetNyn92mtk+6bE4qoAAFahwccps5R9yep/q7pLNyX/bZkyu/xEmT+9kJQ9AMQhUvRxzCxl/83S1+QeXaiUvy2TSg5JImUPAPGGK/hE5HTKuWO74RQpewCIDzT4BGWWpnds+ZgAHgDEARp8gjJL2dv8frlH/1a2w99YXBEAIJRo8AnKLGXvbX2+Upa9JE+vn6nJe2uVvHSJPHndCOIBQIwhZJegKvMLVKrjn7k7tm2RL7utysfepsp+/eV67GG5Hn1QGVf9Qrbv3a4niAcAscMWCMTPB67795eF9Pmystwhf85Y4fzXejXL/6Vs1dW15rw5HVTyztp6P1cir2OosIbBYw2DxxoGLxxrmJXlNhznFj0MeS/uIvn9hnNsdwsA0Y8GD1NmQTzfD9tYXAkAoKFo8DBlFsSz79urJmtXW1wNAKAhaPAwVXu72/Y61q+/bKWHlZHfV677/6DkJYtI2QNAFCJFjzoZbXdb8f6/lH7DtUqd8chJ46TsASB6cAWPBvN2vlgl/1wtfzOP4Tzb3QJA5NHg0SgBd7psZaWGc6TsASDyaPBoNLOUvb/5DyyuBADwv2jwaDSzlL1j12dKnTJJqqy0uCIAwHci2uCrqqo0fvx4DRo0SIWFhfrss89Omn/mmWc0YMAADRw4UG+99VZkioSp2in7DjoyaYq8Pzxfrjmz5bn850p5eo504YWk7AHAYhHdqvb555/X1q1bNXXqVH3yySe677779Mwzz0iSSktLdeWVV+rNN99URUWF+vfvrxUrVtT5fGxVGyWOHlXa3Xcp6R+vyrF/X63p0rlFpOwbiPdi8FjD4LGGwUuYrWp37Nih3NxcSVLr1q21c+fOmrmmTZvqnHPOUUVFhSoqKmSz2SJVJhoqNVVHHpmhQGam4TQpewAIv4h+D75du3ZasWKFevfurY0bN2rv3r3y+XxyOBySpLPPPlt9+/aVz+fT6NGjT/l8Ho9LTqcjpDWa/csI9bBju+Gwc9sW1rURWLPgsYbBYw2DZ9UaRrTBDxw4UDt37tSIESPUsWNHtW/fvqa5r1y5Uvv27dPy5cslSSNHjlTHjh114YUXmj5fSUl5SOvjdlRwPNlt5SzeXGvc73br4GdfS6mpEagqNvFeDB5rGDzWMHgJc4t+06ZN6tSpk+bPn6/evXvr3HPPrZnLyMhQSkqKkpKSlJycLLfbrdJS4+9dIzqZ7mVfUiLPJd3l3PCBxRUBQOKIaINv2bKlFi5cqMGDB2vmzJmaOHGi5s2bp+XLl6tz58760Y9+pEGDBmnw4MFq1aqVfvazn0WyXDTQdyl7XXhhTcq+dPYfVX79TXJ+slOuh6dJkpKXLmE/ewAIsYim6EONFH10MlrHJivfkS/7AjVZt0bpowtr/Q5J+5PxXgweaxg81jB4CXOLHomrOren/GedLdeMRw3nSdoDQHBo8Igos33r2c8eAIJDg0dEsZ89AIQHDR4RVdd+9kmv/93iagAgftDgEVGG+9lPnKzKvleqqufPJZGyB4DGiOhGN4B0vMn/b2K+4tv/Ji9dclLK3lm8WemjC1X67e8BAIxxBY+o5nrsEeNxUvYAUCcaPKKaY/tW43FS9gBQJxo8oppZyj6QmipVVVlcDQDEDho8oppZyt7X+nypSROLqwGA2EGDR1QzStmXPvm0Di95WbLZJEmpkyfKk9uVlD0AfA8pekQ9o5T9d1L/8Du5/vhkzc+k7AHgOK7gEdOS3nrTcJyUPYBER4NHTHPs2GY8TsoeQIKjwSOmme5ln3maxZUAQHShwSOmmaXsj95z7/E/eL1KXvAcW90CSDiE7BDTKvMLVKrjn7k7tm2RL7utysfeVhOwc4/+rVL+9nLN4wnhAUgUNHjEvLpS9knvrTMcd82cToMHENe4RY+4Zjt00HCcEB6AeEeDR1wzC+H5WrW2uBIAsBYNHnHNLIRXPmGixZUAgLVo8Ihrhlvdzi06/vl7ICD3LTcoeeHzSn7pRZL2AOIKITvEPbMQnv3zXUp67W9KeeEvJ42TtAcQD7iCR8Lyt2ylknfWyu9yGc6z3S2AWEaDR0Lzn9tCtspKwzmS9gBiGQ0eCc80aW8yDgCxgAaPhGeatL/xZjV9arZUVWVxRQAQPBo8Ep5Z0t6xZ7fS7p6kZpf/XE1nzyRlDyCmkKIHZJy0tx0pk33PbjV9/s9q8t+PasZJ2QOIBVzBAyYCaW4dmT5LvnNbGM6TsgcQzWjwwCnYv/zCcJyUPYBoRoMHTsE0Zd/6fNn277e4GgCoHxo8cApmKXs5HMrM66Kkf7xmbUEAUA80eOAUDFP2c57RsaG/kq2sTBnXDFVG/1/K0+NiUvYAogYpeqAezPazr+rVW+m/ulpJa1fXjJGyBxANuIIHguC7oK2Ummo4R8oeQCTR4IEgObZtNRknZQ8gcmjwQJBM96y32+V65AGputraggBANHggaGYp+0BqqlIful/NrrhUju3blLx0CdvdArAMITsgSJX5BSrV8c/cHdu2yJfdVuVjb1PVz3srbdLtSnnxBXl6dpPte1fyBPEAhBsNHggBs5R92RN/VOXlfZV+3W8Mf881czoNHkBYcIseCLOqfleZzhHEAxAuNHjAAnVtdwsA4UCDByxgFsSzf7lHSX972eJqACQCGjxggdrb3bbXsUFDZfN6lTFyuNw3jlLyX54jZQ8gZGyBQCAQ6SJCZf/+spA+X1aWO+TPmYhYR3OO7dvkvuk6NdnwH8P50rlFqswvYA1DgDUMHmsYvHCsYVaW23CcK3gggnxtsvXNa2/Ln3WG4Tzb3QJoLBo8EGlOp2yHDhpOkbIH0Fg0eCAKmKXsAxnNpGPHLK4GQDyod4P/6KOPNG/ePFVVVamwsFBdu3bVypUrw1kbkDBMU/YHD8hzaa70wQcWVwQg1tW7wd97771q06aN3njjDaWkpGjp0qWaOXNmOGsDEkbtlH0HlT7+lCpGXifn1i1S165yFw6XJ68rKXsA9VLvrWr9fr+6d++u8ePH67LLLtPZZ58tn88XztqAhGK03W3lkF+p8vK+anZ9oVJePfF9efayB3Aq9b6Cb9q0qYqKivTee++pV69eeu6555SamhrUi1dVVWn8+PEaNGiQCgsL9dlnn500/+6772rQoEEaNGiQ7rnnHsXRN/qAeqvO6yWdeabhHCl7AGbq3eAfeeQRlZeXa/bs2crIyNDevXv16KOPBvXiixcvlsvl0uLFizV58mRNnTq1Zu7IkSN6+OGHNWfOHC1evFjNmzdXSUlJUK8HxKytWw2HHVtJ2QMwVu8Gf+aZZ6pFixZ65513VFFRoTZt2uiss84K6sV37Nih3NxcSVLr1q21c+fOmrkNGzYoOztbDz74oIYNG6bTTz9dmZmZQb0eELNycozH/T6lPDNX8vutrQdA1Kv3Z/CPPPKIvv76a23evFmjRo3SX//6V23ZskUTJ05s9Iu3a9dOK1asUO/evbVx40bt3btXPp9PDodDJSUlWr9+vZYtWyaXy6Vf/epXuuiii3TeeeeZPp/H45LT6Wh0PUbMdghCw7COQZo0SRo6tNawzeWS+84Jcr/1D6l/f+npp6WPPz7+D4JJk6QhQyJQbPTifRg81jB4Vq1hvRv86tWrtXTpUuXn5ystLU3z5s3TlVdeGVSDHzhwoHbu3KkRI0aoY8eOat++vRyO4w26WbNm+tGPfqSsrCxJUufOnVVcXFxngy8pKW90LUbYljE0WMfgZQ0ZotLSCrlmTpdj2xb5stuqfOxtqv6/7kobf4uS33xd+uc/T/zCpk3S0KEqLa0ghPct3ofBYw2DF5Vb1drtxx9qs9kkHQ/IfTfWWJs2bVKnTp00f/589e7dW+eee27NXIcOHbRt2zYdOnRIXq9XGzdu1Pnnc7QmEldlfoFK3lmrA18eUsk7a1WZXyD/mWepdP4i+c5pbvg7hPCAxFXvK/jLL79c48aN0+HDh/Xss8/qlVde0RVXXBHUi7ds2VIzZ85UUVGR3G637rvvPs2bN08tWrTQJZdcovHjx+vaa6+tef3s7OygXg+ISzab7Hu/Npxiq1sgcTXoNLlVq1Zp7dq18vv96tq1q3r16hXO2hqM0+SiE+sYvFOtoSevm5zFm2uN+93pOvTeBgW+/agrkfE+DB5rGDwrb9HX+wpeknr06KEePXqEpCAAoVM+brzSRxfWGreXlSozr4vKHnxMVf2uikBlACLllA1++PDhNZ+7G3nuuedCWhCAhqvML1CpdHII75ZbZd+/T6n3/V4ZI4fr8LMLZKs8JteMR088Ztx4QnhAnDplg7/55putqANAkIy2upWkqksuU9O5T8pWflTpN46qGWe7WyC+nbLBX3zxxZKkQCCghQsX6r333pPX61WXLl00fPjwsBcIIDi+89voyMOPyZPXzXDeNXM6DR6IQ/X+DP6hhx7Srl27NHDgQAUCAb300kvas2eP7rrrrnDWByBEzBL1JO2B+FTvBr9mzRotW7as5rvvPXv2VL9+/cJWGIDQ8mW3NUzaB9xu2Y6UKZDGDmVAPKn3TjU+n09er/ekn7/bdQ5A9CsfN95w3F5SIk9eN9kOf6PkpUvkyevGmfNAHKj3FXy/fv00YsQI9e3bV5L02muv1fwZQPQzTNqPuUWOndtlP3BQSf98+6Sv2hHCA2Jbgza6WblypdatWydJ6tq1q/Ly8sJWWGOw0U10Yh2DF/Y1DATk6fl/hrfwvTkdVPLO2vC9tkV4HwaPNQxeVO5Ff+jQIe3atUupqalKTU3Vpk2bNHv27JAVCCCCbDZCeECcqXeDHzVqlD7++ONw1gIggnzZbY3Hf9DC4koAhEKDtqqdNm1auOoAEGFm2906PvtErgfuVfnEyRGoCkBj1fsKvnfv3nrxxRe1e/duffnllzX/AxAfKvMLVDq3SN6cDgo4nfLmdNCRCXfKd15r+b89rIaUPRA76n0FX15ervvvv18ej6dmzGazafny5WEpDID1jLa7rRgzVkpJUfLSJaTsgRhS7wa/YsUKrVu3TikpKeGsB0C0cbmO/2fGo8bTbHULRKV636Jv3ry5Dh8+HM5aAEQxUvZAbKn3FXx1dbX69u2rNm3aqEmTJjXjHBcLJAazrW7lcMj50YfyXniR9UUBMFXvBn/99deHsw4AUc4sZa+qKtmOHrW+IAB1qneD/+7YWACJyXCr27G3qfrHP5G/9Q8lSfbdnyt5ySKlLHvpxGPGjeczeiACGvQ9eACJzShlXyMQUMavB8lZfGJDLJL2QOTUO2QHAHWy2WQ7Wm445Zo53eJiAATV4Pfv36+jfPYG4Fv2L3YbjpO0B6wXVIMfNWqUZs2apVdffTVU9QCIYab72X/7GT0A6wT1GfyyZctCVQeAOGCWtC8ff4ckybFzu5wffCDXEzMJ4QFhRsgOQMiYJe0r8wtkO1KmZldcJvvBgzWPJ4QHhE+jGrzX69WWLVv00UcfadOmTZwyB6CGWdI+YLNLfr/h77DdLRB6DW7w11xzjVwul1q3bq3i4mLddddd4agLQLxJTZWttNRwihAeEHoNDtl16dJF5513nm644Qade+65+uEPCc8AqB/TEF72BRZXAsS/Bjf4G2+8UQMGDNCdd96p3buNvxIDAEbKx403Hh97fNx24ICV5QBx7ZQNft26dXrjjTdOGjv//PP1+OOPKy8vT2PHjg1bcQDiS2V+gUrnFsmb00EBp1PenA4qnVukyvwCOT7ZodM6/0jpw66WJ7eLTj/bI09eNyUvXRLpsoGYdMrP4GfPnq177rmn1vjq1av105/+VL179w5HXQDilFkIz1ZWJn9qqpLfPnFBQcoeaLxTXsEfOnRIbdq0qTWelZWlRx99VM2bNw9LYQASi/fHP1HgtNMM59jqFmi4UzZ4p9P4Ir9t27bas2dPyAsCkLgc27cZj5OyBxrslA3+Bz/4gdatW2c4l5KSEvKCACQu85T9t+OVlRZWA8S2Uzb4m2++WXfeeafeeuutk8Y3b96spk2bhq0wAInHPGV/m5Le/Icyf9ZZrvt/L09eN0J4wCmcMmSXk5OjRx55RHfccYceeOABtW/fXpK0fv16zZgxI+wFAkgcdW112/Sp2bLv/lypMx6teTwhPMCcLRAIBOrzQK/Xq1WrVqm4uFipqanKy8tTq1atwlxew+zfXxbS58vKcof8ORMR6xg81vA4T5eL5Pz0k1rj3pwOKnlnbZ2/yxoGjzUMXjjWMCvLbThe761qnU6nevXqpV69eoWsKABoCMfnu4zHCeEBtQR1HjwAWKnOEF79bkYCCYMGDyBm1BXCc814RO7rR8p28KCSly4hiIeEx3nwAGKGaQjvqgHKyO+rpHVrlPTW67KXnfiM87sgntKbSpf0jVzxgMVo8ABiitlWt4dfelVN5z6p1N9PNv7FadNo8Ego3KIHEB8cDlXceLNkN/m/tY8/trYeIMJo8ADiilkQTzk51hYCRBgNHkBcMQviKTNTKfOfJW2PhEGDBxBXjM6cL5v2sPSf/8g9/hZlFFyllKefImWPuFfvnexiATvZRSfWMXisYfCyKg+rcuQoJb/5uuF86dwitrs9Bd6HwbNyJzuu4AEkhh/8QKXzF8l3TnPDac6cR7yhwQNIHDab7Hu/Npxiu1vEGxo8gIRilrIPpKbK8d9NFlcDhA8NHkBCMUvZ2w8flueyPLkeuFfJi18ghIeYx052ABKK2Xa3/owMucePVer0h056PGfOI1ZFtMFXVVXpzjvv1O7du5WWlqYpU6bUOmPe7/fruuuu0yWXXKKhQ4dGplAAccVsu9uSVeuV2amD7CUlteZcM6fT4BFTInqLfvHixXK5XFq8eLEmT56sqVOn1nrMjBkzdPjw4QhUByDRBNLcspWWGs4RwkOsiWiD37Fjh3JzcyVJrVu31s6dO0+af/3112Wz2WoeAwDhZhrCS0+XrZSLDcSOiN6ib9eunVasWKHevXtr48aN2rt3r3w+nxwOh7Zt26ZXX31Vjz/+uJ544ol6PZ/H45LT6QhpjWYbCKBhWMfgsYbBq9caTpksGXwcaD90SKfndZXmzJGuuCIM1cUG3ofBs2oNI9rgBw4cqJ07d2rEiBHq2LGj2rdvL4fjeINetmyZ9u7dq2uuuUZffPGFmjRpoubNm9d5NV9SUh7S+ti1KTRYx+CxhsGr9xpe0lfJc4tODuGNuUWOXZ/J9djDsvXrp6qfdpH98Ddy7NxxfH7c+IT4fJ73YfCs3Mkuog1+06ZN6tSpkyZNmqRNmzbp888/r5m7/fbba/48a9YsnX766dyqB2AJsxBe5RVXKf2aoUr69/qaMVL2iFYR/Qy+ZcuWWrhwoQYPHqyZM2dq4sSJmjdvnpYvXx7JsgDAkK9tOyklxXCOrW4RbThspg7cjgoN1jF4rGHwQrWGp5/tkc3nqzUesNt14MtDkj1+9w/jfRg8DpsBgChllrK3+f3KGNhP9k92Gs4DVqPBA0ADmG11W/3jnyhpzSpl9uymprNnKnnJIra7RUSxVS0ANIDZVreV/Qcq6W/L5J74/5T2h9+d9DsE8RAJfAZfBz5vCg3WMXisYfCsWkPboYPK7HKR7AY7cHpzOqjknbVhryFceB8Gj8/gASBGBTJPk+3IEcM5truFlWjwABBiptvdutNlO8IVMKxBgweAEDM9c77kkDw9uijp7TeUvHQJITyEFSE7AAgxwyDejbfI8ckOuR6froxhV5/0eEJ4CAcaPACEgel2t1fmy3N5L9mOHas1x5nzCCVu0QOAhXw57aXqasM5QngIJRo8AFjMLITnPz1L8vstrgbxigYPABYzC+E5vv5Kza64TI6tXMkjeDR4ALBYZX6BSucWyZvTQQGnU96cDip96DEdu2qAmrz/L3ku6S73db8lZY+gsJNdHdi1KTRYx+CxhsGLlTVMev3vct98veyHv6k1Vzq3KKIhvFhZw2jGTnYAkKCqLv+l/GedZTjHmfNoCBo8AEQZx47txuNbiy2uBLGMBg8AUcb0zHmfT+4brpXtwAGLK0IsosEDQJQxS9l7W7VSyl8XK7N7ZyX97WW2u0WdaPAAEGUMU/Zzi1SyboOOTJ0m27FjarJ+ndJHF8pZvFk2n69mu1uaPL5Dir4OJEZDg3UMHmsYvHhaQ9u+fWp29VVyFm+uNRfOM+fjaQ0jhRQ9AMBU4IwzTLe1ZbtbfIcGDwAxyPTM+WbNpIoKi6tBNKLBA0AMMj1z/sABeXp2k/M/7xPCS3AcFwsAMcjwzPnrx8j58WY1/fMzarJurdJ+P7nm8Zw5n3ho8AAQo4zOnK+UVH7zrWpWcKXh73DmfOLgFj0AxJlAVhYhPNDgASAe1XnmvM9ncTWIBBo8AMShOs+c79tb9l2fWVsQLEeDB4A4ZLgb3sMzdGxAgexffqmAx0PKPs4RsgOAOGUYwrumULaDB5W0/C2ljy6sGSdlH3+4ggeABBM47TS5ZjxqOMeZ8/GDBg8ACcg0Zb+lWIqfI0oSGg0eABKQ6Znzfp8yhgyQrfSwxRUh1GjwAJCATM+cb5cjVVQokOauFcLTCy9YXCWCQYMHgARkeub8O+tU+vwiJb/8Uq3z5jV0KEn7GEKKHgASlFHKXpIC6Rl1hvBI2ccGruABALWYhvC2FltcCRqLBg8AqMU0hOfzyT36t5Lfb3FFaCgaPACgFtMQXusfKpB5mmQ/3j7YDS968Rk8AKAWo/Pmnb+7SyW9fiFVVUmSkl96UenXj6z5HXbDiy40eACAof8N4WVluaX9ZVJKiiQp9f4/GP4eQbzowC16AECj2L/YYzjOmfPRgQYPAGgUsyBeID3D4kpghAYPAGgUsyBeZd9+NX8mhBc5fAYSkTscAAALRElEQVQPAGgUoyBe+U1jVTngaklS8sLnlT72xprHE8KzFg0eANBoZrvhSVLqtKmG44TwrMEtegBAWNj37zMcJ4RnDRo8ACAszEJ4/szTLK4kMdHgAQBhYRbCqygcVfNnQnjhw2fwAICwMAzh3XJrTQiv6VOzlHb3XTWPJ4QXWjR4AEDY1BXCcz3+mPE4IbyQiGiDr6qq0p133qndu3crLS1NU6ZMUatWrWrmn332Wb322muSpLy8PN10000RqhQAEGq2b0oMxwnhhUZEP4NfvHixXC6XFi9erMmTJ2vq1BNfqdi9e7deeeUVvfDCC1q0aJFWr16tLVv4SweAeGEawjvjTIsriU8RbfA7duxQbm6uJKl169bauXNnzdxZZ52lP/3pT3I4HLLb7fJ6vUpOTo5UqQCAEDML4R29dcKJHwIBi6qJPxFt8O3atdOKFSsUCAT04Ycfau/evfL5fJKkJk2aKDMzU4FAQA8++KBycnJ03nnnRbJcAEAIVeYXqHRukbw5HRRwOuXN6aDSuUWqvKZQkpT091eVMThfKXOfJGnfCLZAIHL/PPJ6vXrooYdUXFysjh07as2aNVqy5MRfXGVlpSZNmqTU1FTdfffdcjgcp3g+n5zOuh8DAIgRI0dKRUXGcwsXSkOGWFtPjIlog9+wYYP27dunPn36aNOmTSoqKtJjjx1PVQYCAV177bXq0qWLrrvuuno93/79ZSGtLyvLHfLnTESsY/BYw+CxhsGzfA0DAWV2bC+HwbG03pwOKnlnrXW1hEg41jAry204HtEUfcuWLTVz5kwVFRXJ7Xbrvvvu07x589SiRQv5/X7961//UlVVlVatWiVJuu222/STn/wkkiUDAKxis8n+9VeGUyTtTy2iDT4zM1PPPvvsSWO//e1va/68adMmiysCAEQTX3ZbOYs3G47L65UcDslmi0Bl0Y+tagEAUcssaV8+9ja5pj+kjAFXqOlTswjhGWAnOwBA1DLc7nbsbarsP1Dp116jpDWrlLRmVc3j2e72BBo8ACCqmW13W/qnPyuzUwc59uyuNcd2t9yiBwDEKptN9q++NJwihEeDBwDEMLPtbn3ZbWUrPSz5/RZXFD1o8ACAmFVXCM9902g169tbTR9/LCFDeHwGDwCIWaYhvF/2U9Lrr6nJB++ryQfv1zw+kUJ4NHgAQEwzC+GVzZ2nJh+8L8fnu2rNJUIIj1v0AIC4ZTfY5lZKjBAeDR4AELfqCuHZP/tUqq62uCLr0OABAHHLNIR34y3KGDpQnku6q+lD0+IyhMdn8ACAuGUWwqu6tI+a/Os9NX2uSGlbimseH08hvIgeFxtqHBcbnVjH4LGGwWMNgxePa+i5+MdyfvZprfFwHUdr5XGx3KIHACQsx+7PjcfjIIRHgwcAJKy6QnhN1q2Rjh61uKLQocEDABKWWQivYsRvlDG0QJk9LlbS639X8tIlMRfEI2QHAEhYpjvh9fml7F9/LdcTM5UxYshJvxMrQTxCdnWIx0BJJLCOwWMNg8caBi8R19CxbauaXZYne3l5rbnGBPEI2QEAEAV82RfIVllpOBftQTwaPAAAdTAL4vmzzpBt/36Lq6k/GjwAAHUwC+I5vvpSmT/rpJQ/Fyn5pRejLoRHyA4AgDoYBvFuGit7ySG5pt0r94RxJz0+WkJ4NHgAAE7B7Ejayivz5flZZ9lLS2vNRfpIWm7RAwDQSP4zz5LNZDOcSIfwaPAAAATBLIQXcKfLsWO7xdWcQIMHACAIZiE8e8kheXp2k+uBqUpetECevG6S02lZCI/P4AEACIJhCO+WWxVITlHaXbcrdfrDJz3eqhAeDR4AgCCZhfAO5fXSaT+9UPaDB2rNhTuExy16AADCJS1Ntm9KDKfCHcKjwQMAEEZ1HUkbTjR4AADCyCyEVz72trC+Lg0eAIAwqswvUOncInlzOkhOp7w5HVQ6tyjsm+AQsgMAIMy+C+FlZblVYtGRu1zBAwAQh2jwAADEIRo8AABxiAYPAEAcosEDABCHaPAAAMQhGjwAAHGIBg8AQByiwQMAEIdsgUAgEOkiAABAaHEFDwBAHKLBAwAQh2jwAADEIRo8AABxiAYPAEAcosEDABCHaPAG/H6/pkyZosGDB2v48OHatWtXpEuKOdXV1ZowYYKGDRumgoICLV++PNIlxayDBw8qLy9PO3fujHQpMWvu3LkaPHiwBgwYoBdffDHS5cSc6upqjR8/XkOGDNGwYcN4LzbQxo0bNXz4cEnSrl27NHToUA0bNkx33323/H5/2F6XBm/g7bffVlVVlRYtWqTx48frgQceiHRJMeeVV15Rs2bNtGDBAj399NOaOnVqpEuKSdXV1ZoyZYpSUlIiXUrMWr9+vTZs2KCFCxdq/vz5+vrrryNdUsx599135fV69cILL2jMmDGaMWNGpEuKGU8//bQmT56syspKSdK0adM0btw4LViwQIFAIKwXPzR4Ax988IF69OghSbrooov03//+N8IVxZ7LL79cY8eOrfnZ4XBEsJrY9eCDD2rIkCE644wzIl1KzFq9erWys7M1ZswYXX/99erZs2ekS4o55513nnw+n/x+v44cOSKn0xnpkmJGixYtNGvWrJqfN2/erIsvvliSlJubq7Vr14bttflbMnDkyBGlpaXV/OxwOOT1enlTN0Bqaqqk42t5yy23aNy4cRGuKPa89NJLyszMVI8ePfTHP/4x0uXErJKSEn355ZeaM2eO9uzZoxtuuEGvv/66bDZbpEuLGS6XS1988YV+8YtfqKSkRHPmzIl0STGjT58+2rNnT83PgUCg5r2XmpqqsrKysL02V/AG0tLSdPTo0Zqf/X4/zb0RvvrqK40YMUJXXXWV+vXrF+lyYs5f//pXrV27VsOHD1dxcbHuuOMO7d+/P9JlxZxmzZqpe/fuSkpKUuvWrZWcnKxDhw5FuqyY8uyzz6p79+5644039PLLL2vixIk1t5zRMHb7ibZ79OhRpaenh++1wvbMMaxjx45auXKlJOnDDz9UdnZ2hCuKPQcOHFBhYaEmTJiggoKCSJcTk/7yl7/o+eef1/z589WuXTs9+OCDysrKinRZMadTp05atWqVAoGA9u7dq4qKCjVr1izSZcWU9PR0ud1uSVJGRoa8Xq98Pl+Eq4pNOTk5Wr9+vSRp5cqV6ty5c9hei8tSA5deeqnWrFmjIUOGKBAI6P777490STFnzpw5Ki0t1ZNPPqknn3xS0vGwCWExWK1Xr17697//rYKCAgUCAU2ZMoVMSAP95je/0aRJkzRs2DBVV1fr1ltvlcvlinRZMemOO+7Q7373O02fPl2tW7dWnz59wvZanCYHAEAc4hY9AABxiAYPAEAcosEDABCHaPAAAMQhGjwAAHGIBg8AQByiwQOol7KyMo0ZMybSZQCoJxo8gHo5fPiwiouLI10GgHqiwQOol3vvvVf79u2r8yq+urpaEyZMUP/+/dW/f38tXrzYwgoBfB8NHkC9TJ48WWeccYaeeOIJ08ds2LBBhw8f1rJlyzR37ly9//77FlYI4PvYix5AyLRp00affvqpRo4cqdzcXN1+++2RLglIWFzBAwgZj8ej1157Tb/+9a/16aefKj8/X6WlpZEuC0hINHgA9eJ0OuX1eut8zPLlyzVhwgT17NlTkydPlsvl0ldffWVRhQC+jwYPoF5OO+00nXPOORo+fLgkadSoUdq0adNJj8nNzVVKSor69u2rq6++WldeeaUuuOCCSJQLJDyOiwXQKPPmzVP37t3Vpk2bSJcCwABX8AAaJTMzU+eff36kywBggit4AADiEFfwAADEIRo8AABxiAYPAEAcosEDABCHaPAAAMSh/w+gPChYEuun9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1079d6080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import numpy as np #for arrays\n",
    "import matplotlib.pyplot as plt #for plotting\n",
    "from scipy.integrate import odeint\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn')\n",
    "\n",
    "# ODE\n",
    "# Batch reactor\n",
    "# -ra = k CA^2\n",
    "\n",
    "# dCA/dt = -(-ra) = -k CA^2\n",
    "\n",
    "# step 0 - modules\n",
    "\n",
    "# step 1 : define a function that needs to be solved\n",
    "# dy/dt = f(y,t)\n",
    "\n",
    "def f(y,t):\n",
    "    return -k*y**2\n",
    "\n",
    "# step 2: define arrays\n",
    "# \n",
    "\n",
    "time_init = 0\n",
    "time_final = 10 \n",
    "N_points = 50\n",
    "time_array = np.linspace(time_init,time_final, N_points)\n",
    "\n",
    "k = 0.001\n",
    "C_A0 = 10.\n",
    "\n",
    "\n",
    "#step 3: solving the stuff\n",
    "# odeint(function, initial value, time array)\n",
    "C_A_calc = odeint(f, C_A0, time_array)\n",
    "\n",
    "#step 4: plotting\n",
    "# plt.plot(x, y, 'go-')\n",
    "plt.plot(time_array, C_A_calc, 'ro--')\n",
    "plt.xlabel('t, s')\n",
    "plt.ylabel('$C_{A}$, moles')\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# REGRESSION \n",
    "import numpy as np\n",
    "\n",
    "time_array = np.array([   0.,  125.,  250.,  375.,  500.,  625.,  750.,  875., 1000.,\n",
    "       1125., 1250., 1375., 1500., 1625., 1750., 1875., 2000., 2125.,\n",
    "       2250., 2375., 2500., 2625., 2750., 2875.])\n",
    "\n",
    "C_A_array = np.array([10.28148623,  8.92676003,  7.47370739,  7.20498621,  6.01448975,\n",
    "        4.85174028,  4.68868558,  4.01410753,  3.94055544,  3.04186757,\n",
    "        2.40544184,  2.62290428,  2.18704979,  1.31502537,  1.03730156,\n",
    "        2.28837979,  0.45062549,  1.43886825,  1.26808295,  1.24125421,\n",
    "        0.28353151,  0.90117414,  0.74132173,  0.73710597])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1516211208>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a9d2208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#step 1 : plot the data:\n",
    "\n",
    "plt.plot(time_array, C_A_array, 'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10fa954a8>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fa95358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# step 2: define the function (that we think will fit the data)\n",
    "# and define parameters\n",
    "\n",
    "def f(x, k, C_A0):\n",
    "    return C_A0*np.exp(-k*x)\n",
    "\n",
    "k_test_1 = 0.01\n",
    "C_A0 = 10.\n",
    "\n",
    "#step 3: plotting stuff\n",
    "\n",
    "plt.plot(time_array, C_A_array, 'o')\n",
    "\n",
    "plt.plot(time_array, f(time_array, k_test_1, C_A0), 'r-')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10fa9c9e8>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1516a28c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# step 2: define the function (that we think will fit the data)\n",
    "# and define parameters\n",
    "\n",
    "def f(x, k, C_A0):\n",
    "    return C_A0*np.exp(-k*x)\n",
    "\n",
    "k_test_1 = 0.001\n",
    "C_A0 = 10.\n",
    "\n",
    "#step 3: plotting stuff\n",
    "\n",
    "plt.plot(time_array, C_A_array, 'o')\n",
    "\n",
    "plt.plot(time_array, f(time_array, k_test_1, C_A0), 'r-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.05224035e-03 1.01564581e+01]\n",
      "k = 0.0010522403492450425\n",
      "C_A0 = 10.156458126293051\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "\n",
    "\n",
    "time_array = np.array([   0.,  125.,  250.,  375.,  500.,  625.,  750.,  875., 1000.,\n",
    "       1125., 1250., 1375., 1500., 1625., 1750., 1875., 2000., 2125.,\n",
    "       2250., 2375., 2500., 2625., 2750., 2875.])\n",
    "\n",
    "C_A_array = np.array([10.28148623,  8.92676003,  7.47370739,  7.20498621,  6.01448975,\n",
    "        4.85174028,  4.68868558,  4.01410753,  3.94055544,  3.04186757,\n",
    "        2.40544184,  2.62290428,  2.18704979,  1.31502537,  1.03730156,\n",
    "        2.28837979,  0.45062549,  1.43886825,  1.26808295,  1.24125421,\n",
    "        0.28353151,  0.90117414,  0.74132173,  0.73710597])\n",
    "\n",
    "#LEts start fitting the data\n",
    "\n",
    "# Step 1: function\n",
    "\n",
    "\n",
    "def f(x, k, C_A0):\n",
    "    return C_A0*np.exp(-k*x)\n",
    "\n",
    "#Step 2: init parameters:\n",
    "\n",
    "k_guess = 0.005\n",
    "C_A0_guess = 11.\n",
    "\n",
    "#step 3: fitting the data:\n",
    "# curve_fit(function, time_array, C_A_array initial parameters)\n",
    "popt, pcov = curve_fit(f, time_array,C_A_array, p0=(k_guess, C_A0_guess))\n",
    "\n",
    "print(popt)\n",
    "\n",
    "print(\"k = {0}\".format(popt[0]))\n",
    "# print(popt[0])\n",
    "print(\"C_A0 = {0}\".format(popt[1]))\n",
    "# print(popt[1])\n",
    "\n",
    "C_A_final = f(time_array, popt[0], popt[1])"
   ]
  },
  {
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}