{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.patches as mp\n",
    "import math as math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:42: DeprecationWarning: object of type <class 'float'> cannot be safely interpreted as an integer.\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.6        0.3        0.2       ]\n",
      " [1.52245427 0.37251846 0.20502727]\n",
      " [1.42718741 0.45957456 0.21323804]\n",
      " [1.31292104 0.56178748 0.22529148]\n",
      " [1.17987925 0.67815274 0.24196801]\n",
      " [1.03080802 0.80503654 0.26415544]\n",
      " [0.87199516 0.93519375 0.29281109]\n",
      " [0.71364075 1.05746318 0.32889607]\n",
      " [0.56856657 1.15814754 0.3732859 ]\n",
      " [0.44873484 1.22459574 0.42666942]\n",
      " [0.36103755 1.24951462 0.48944784]\n",
      " [0.30552661 1.2328447  0.56162869]\n",
      " [0.27741703 1.17989576 0.64268721]\n",
      " [0.27058169 1.09804951 0.7313688 ]\n",
      " [0.27984889 0.99470219 0.82544891]\n",
      " [0.30158397 0.87688137 0.92153466]\n",
      " [0.33333154 0.75160709 1.01506138]\n",
      " [0.37324368 0.626091   1.10066531]\n",
      " [0.41965266 0.50732721 1.17302012]\n",
      " [0.47090364 0.4011356  1.22796076]\n",
      " [0.52540865 0.31116814 1.26342321]\n",
      " [0.58178415 0.23849737 1.27971848]\n",
      " [0.63893897 0.18201226 1.27904877]\n",
      " [0.69607034 0.13930911 1.26462055]\n",
      " [0.7526047  0.10758078 1.23981452]\n",
      " [0.80813178 0.08420747 1.20766075]\n",
      " [0.86235514 0.06702124 1.17062362]\n",
      " [0.91506042 0.05435081 1.13058877]\n",
      " [0.96609536 0.04496067 1.08894398]\n",
      " [1.01535606 0.03795893 1.04668501]\n",
      " [1.06277661 0.03270947 1.00451391]\n",
      " [1.10832063 0.02876076 0.96291861]\n",
      " [1.15197429 0.02579249 0.92223322]\n",
      " [1.19374051 0.02357727 0.88268222]\n",
      " [1.2336342  0.02195362 0.84441219]\n",
      " [1.27167831 0.02080729 0.80751439]\n",
      " [1.30790063 0.02005841 0.77204096]\n",
      " [1.34233101 0.01965263 0.73801637]\n",
      " [1.37499908 0.01955517 0.70544575]\n",
      " [1.40593218 0.01974685 0.67432097]\n",
      " [1.43515344 0.02022158 0.64462498]\n",
      " [1.46267989 0.02098488 0.61633523]\n",
      " [1.48852054 0.02205331 0.58942615]\n",
      " [1.5126743  0.02345455 0.56387115]\n",
      " [1.53512764 0.02522809 0.53964427]\n",
      " [1.55585192 0.02742655 0.51672154]\n",
      " [1.57480024 0.03011752 0.49508224]\n",
      " [1.59190378 0.03338611 0.47471011]\n",
      " [1.60706738 0.03733807 0.45559456]\n",
      " [1.62016432 0.04210372 0.43773196]\n",
      " [1.63103022 0.04784265 0.42112713]\n",
      " [1.6394559  0.05474917 0.40579493]\n",
      " [1.64517915 0.06305855 0.3917623 ]\n",
      " [1.64787557 0.07305389 0.37907055]\n",
      " [1.64714875 0.08507311 0.36777814]\n",
      " [1.64252022 0.09951568 0.3579641 ]\n",
      " [1.63342055 0.11684743 0.34973203]\n",
      " [1.61918288 0.13760217 0.34321494]\n",
      " [1.5990424  0.16237662 0.33858098]\n",
      " [1.57214547 0.19181461 0.33603993]\n",
      " [1.53757503 0.22657436 0.3358506 ]\n",
      " [1.49440028 0.26727114 0.33832858]\n",
      " [1.44176104 0.31438534 0.34385362]\n",
      " [1.37899771 0.36812686 0.35287543]\n",
      " [1.3058351  0.42824928 0.36591562]\n",
      " [1.22261856 0.4938188  0.38356264]\n",
      " [1.1305809  0.56296346 0.40645564]\n",
      " [1.03208226 0.63266554 0.4352522 ]\n",
      " [0.93072111 0.69870375 0.47057514]\n",
      " [0.83118328 0.75588214 0.51293459]\n",
      " [0.738727   0.79864871 0.5626243 ]\n",
      " [0.65834297 0.82206222 0.61959481]\n",
      " [0.59384307 0.82284517 0.68331176]\n",
      " [0.54725803 0.80012673 0.75261523]\n",
      " [0.51878895 0.75560225 0.8256088 ]\n",
      " [0.5072304  0.69314421 0.89962539]\n",
      " [0.51055671 0.61810894 0.97133435]\n",
      " [0.52640363 0.53654877 1.0370476 ]\n",
      " [0.55236455 0.45441075 1.0932247 ]\n",
      " [0.58615573 0.37677666 1.13706761]\n",
      " [0.62572135 0.30727753 1.16700113]\n",
      " [0.66930451 0.24784896 1.18284653]\n",
      " [0.71547703 0.19888398 1.18563899]\n",
      " [0.76312423 0.15966579 1.17720998]\n",
      " [0.81139893 0.12887494 1.15972613]\n",
      " [0.85966557 0.10500623 1.1353282 ]\n",
      " [0.90744956 0.08663213 1.10591831]\n",
      " [0.95439733 0.07252799 1.07307467]\n",
      " [1.00024675 0.06170497 1.03804827]\n",
      " [1.04480533 0.05339413 1.00180054]\n",
      " [1.0879339  0.04701142 0.96505468]\n",
      " [1.12953417 0.04211957 0.92834626]\n",
      " [1.16953888 0.0383942  0.89206693]\n",
      " [1.20790397 0.03559633 0.8564997 ]\n",
      " [1.24460235 0.03355124 0.82184641]\n",
      " [1.27961867 0.03213266 0.78824867]\n",
      " [1.31294514 0.0312513  0.75580356]\n",
      " [1.34457788 0.03084659 0.72457553]\n",
      " [1.37451379 0.03088093 0.69460528]\n",
      " [1.40274773 0.03133581 0.66591647]\n",
      " [1.42926983 0.03220927 0.6385209 ]\n",
      " [1.45406293 0.03351457 0.6124225 ]\n",
      " [1.47709981 0.03527972 0.58762047]\n",
      " [1.49834042 0.03754771 0.56411187]\n",
      " [1.51772868 0.04037753 0.54189379]\n",
      " [1.53518901 0.0438457  0.52096529]\n",
      " [1.55062238 0.04804848 0.50132914]\n",
      " [1.56390183 0.0531046  0.48299357]\n",
      " [1.57486748 0.05915849 0.46597403]\n",
      " [1.58332084 0.06638407 0.45029509]\n",
      " [1.58901882 0.07498866 0.43599252]\n",
      " [1.5916673  0.08521707 0.42311563]\n",
      " [1.59091491 0.09735509 0.41173   ]\n",
      " [1.58634754 0.1117319  0.40192056]\n",
      " [1.57748481 0.12871998 0.39379521]\n",
      " [1.56377999 0.14873111 0.3874889 ]\n",
      " [1.54462597 0.17220575 0.38316829]\n",
      " [1.51937052 0.19959277 0.38103671]\n",
      " [1.48734532 0.23131523 0.38133944]\n",
      " [1.44791404 0.26771734 0.38436861]\n",
      " [1.40054526 0.30898773 0.39046701]\n",
      " [1.34491505 0.3550554  0.40002955]\n",
      " [1.2810401  0.40545949 0.41350041]\n",
      " [1.20943504 0.45920157 0.43136339]\n",
      " [1.13127311 0.51460474 0.45412216]\n",
      " [1.04851062 0.56922252 0.48226686]\n",
      " [0.96391688 0.6198593  0.51622382]\n",
      " [0.88094425 0.66276969 0.55628606]\n",
      " [0.80339978 0.69407543 0.60252479]\n",
      " [0.73494984 0.71036413 0.65468604]\n",
      " [0.67858171 0.70933611 0.71208219]\n",
      " [0.6361997  0.69030403 0.77349628]\n",
      " [0.60848734 0.65438546 0.8371272 ]\n",
      " [0.59503942 0.60434704 0.90061354]\n",
      " [0.59465343 0.54417114 0.96117543]\n",
      " [0.60564744 0.47845863 1.01589393]\n",
      " [0.62612578 0.41177522 1.062099  ]\n",
      " [0.65417661 0.34805041 1.09777298]\n",
      " [0.68801154 0.29014837 1.1218401 ]\n",
      " [0.72605487 0.2397029  1.13424223]\n",
      " [0.766985   0.19722199 1.13579301]\n",
      " [0.8097347  0.16237451 1.12789079]\n",
      " [0.85346418 0.13433068 1.11220514]\n",
      " [0.89752281 0.11205472 1.09042247]\n",
      " [0.94141078 0.0945052  1.06408402]\n",
      " [0.98474609 0.08074514 1.03450877]\n",
      " [1.02723818 0.06998578 1.00277604]\n",
      " [1.06866732 0.06159069 0.96974198]\n",
      " [1.10886869 0.05506034 0.93607097]\n",
      " [1.14771972 0.05000987 0.90227041]\n",
      " [1.18513021 0.04614671 0.86872308]\n",
      " [1.22103423 0.043251   0.83571477]\n",
      " [1.25538366 0.04115957 0.80345678]\n",
      " [1.28814276 0.03975356 0.77210369]\n",
      " [1.31928369 0.03894902 0.7417673 ]\n",
      " [1.34878261 0.03869003 0.71252736]\n",
      " [1.37661627 0.03894381 0.68443992]\n",
      " [1.40275885 0.03969741 0.65754374]\n",
      " [1.42717898 0.04095559 0.63186543]\n",
      " [1.4498368  0.04273977 0.60742343]\n",
      " [1.47068094 0.04508772 0.58423133]\n",
      " [1.4896453  0.04805409 0.56230061]\n",
      " [1.50664564 0.0517114  0.54164296]\n",
      " [1.52157579 0.05615171 0.5222725 ]\n",
      " [1.53430359 0.06148868 0.50420773]\n",
      " [1.54466642 0.06786002 0.48747356]\n",
      " [1.55246642 0.07543023 0.47210336]\n",
      " [1.55746558 0.08439328 0.45814114]\n",
      " [1.55938101 0.09497503 0.44564396]\n",
      " [1.55788068 0.10743477 0.43468455]\n",
      " [1.5525806  0.12206508 0.42535431]\n",
      " [1.54304455 0.13918882 0.41776663]\n",
      " [1.52878763 0.15915185 0.41206052]\n",
      " [1.50928637 0.18230906 0.40840457]\n",
      " [1.48399793 0.20900111 0.40700096]\n",
      " [1.45239194 0.23951873 0.40808933]\n",
      " [1.41399912 0.27405109 0.41194979]\n",
      " [1.36847983 0.31261575 0.41890442]\n",
      " [1.3157147  0.3549696  0.4293157 ]\n",
      " [1.25591491 0.40050468 0.4435804 ]\n",
      " [1.18974279 0.44814082 0.46211639]\n",
      " [1.11842273 0.49623746 0.48533981]\n",
      " [1.04380953 0.54256053 0.51362994]\n",
      " [0.96837251 0.58434814 0.54727935]\n",
      " [0.89505608 0.61851526 0.58642866]\n",
      " [0.82700397 0.64200859 0.63098744]\n",
      " [0.7671828  0.65227024 0.68054696]\n",
      " [0.71799583 0.6477083  0.73429587]\n",
      " [0.68099953 0.62804343 0.79095705]\n",
      " [0.65680082 0.59442793 0.84877125]\n",
      " [0.64513646 0.54930658 0.90555695]\n",
      " [0.64507017 0.49606003 0.9588698 ]\n",
      " [0.65522683 0.43851167 1.0062615 ]\n",
      " [0.67400841 0.38039378 1.04559782]\n",
      " [0.69976909 0.32487559 1.07535531]\n",
      " [0.73094485 0.27424911 1.09480604]\n",
      " [0.76613723 0.22982757 1.10403519]\n",
      " [0.80415398 0.19204316 1.10380286]\n",
      " [0.84401427 0.16067045 1.09531528]\n",
      " [0.88493097 0.13508346 1.07998556]]\n"
     ]
    }
   ],
   "source": [
    "#Franks et al (1986) NPZ model\n",
    "\n",
    "#List assumptions here:\n",
    "#1.\n",
    "#2...\n",
    "\n",
    "checksum = []\n",
    "times = []\n",
    "\n",
    "#solve using odeint\n",
    "def npz(initial, t):\n",
    "    nN = initial[0]   #Nutrients biomass           \n",
    "    nP = initial[1]   #phytoplankton biomass\n",
    "    nZ = initial[2]   #Zooplankton biomass\n",
    "\n",
    "    v = 2.     #rate of nutrient update\n",
    "    mZ = .2    #rate of Zooplankton mortality\n",
    "    mP = .1    #rate of Phytoplankton mortality\n",
    "    γ = .7    #Zooplankton efficiency\n",
    "\n",
    "    k  = 1.    #1/2 saturation constant for Nutrient update\n",
    "    Λ = 1.     #Ivlev grazing constant\n",
    "    Rm = 1.5   #maximum zooplankton grazing rate\n",
    "\n",
    "    zG = Rm*(1-math.exp(-Λ*nP))\n",
    "    \n",
    "    f = [\n",
    "       ((-v*nN*nP)/(k+nN) + mP*nP + mZ*nZ + (1-γ)*nZ*zG),\n",
    "       ((v*nP*nN)/(k+nN) - mP*nP - nZ*zG),\n",
    "       (γ*nZ*zG - mZ*nZ)\n",
    "    ]\n",
    "    \n",
    "    checksum.append(nN + nP + nZ)\n",
    "    times.append(t)\n",
    "    \n",
    "    return f\n",
    "    \n",
    "t = .25\n",
    "tmax = 50.\n",
    "steps = tmax/t\n",
    "\n",
    "time = np.linspace(0, tmax, steps)\n",
    "initial = [1.6, 0.3, 0.2]\n",
    "pop = odeint(npz, initial, time)\n",
    "    \n",
    "plt.subplots(figsize=(15, 10))\n",
    "plt.plot(time, pop)\n",
    "\n",
    "blue_patch = mp.Patch(color='blue', label='nutrients')\n",
    "green_patch = mp.Patch(color='green', label='phytoplankton')\n",
    "red_patch = mp.Patch(color='red', label='zooplankton')\n",
    "\n",
    "plt.legend(handles=[blue_patch, green_patch, red_patch])\n",
    "plt.show()\n",
    "\n",
    "print(pop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABJsAAAG5CAYAAAApqzWHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAIABJREFUeJzt3X24ZnVdL/73BwYdFRR5UHkMUDyJglIDanZS0wSRA2rgwcykRKqTqZXH8ClL85z62VEz7YHM1KNJppGkpEOKoR4VBwMFRwNJYxyCkWcEFOTz++Neg5txz549zNr73jO8Xte1r73Wd33Xd33ue1/rmnve93etVd0dAAAAABjDdtMuAAAAAIBth7AJAAAAgNEImwAAAAAYjbAJAAAAgNEImwAAAAAYjbAJAAAAgNEImwCArUJV/W5VvWcBxu2qesjY424rqurGqjpg2nUAAFsPYRMAsGRU1c9V1aoh4Li8qv6pqn5y2nXdXVTVJ6vqpJlt3b1jd186rZoAgK2PsAkAWBKq6jeTvDnJ/0rywCT7JvnTJMdOs65tVVVtP+0aAIBtk7AJAJi6qrpfktcm+bXu/vvu/k5339rd/9jd/3NG13tU1bur6oaquqiqVswYY8+q+mBVrauqf6+qF83Ytn1VvaKqvj7se15V7TNLHT9ZVZdV1RNr4k1VdWVVXVdVX6qqRwz97jQDqKpOrKpPz1jvqvofVXXxcLzXVdWDq+qzVXV9Vb2/qu6xkfdiu6p6VVV9czj2u4f3J1X10ap64Qb9L6iqZw7LP1pVZ1XV1VX1tap61ox+76yqP6uqM6vqO0meuME4r0/yX5O8dZhZ9tYZr+UhM8b402HG2Y1V9ZmqelBVvbmqrqmqr1bVofP5mwAA2y5hEwCwFDw2yfIkp2+i3zFJTkuyc5IzkqwPRLZL8o9JLkiyV5InJXlJVR0x7PebSZ6d5Kgk903yS0lumjnw0Pd9SX62u89O8pQkP5XkocPx/nuSqzbjNR2Z5MeTPCbJy5KcmuQ5SfZJ8oihntmcOPw8MckBSXZc/zqT/M3M/arqoCQ/kuQjVXWfJGcNfR4w9PvTqnr4jLF/Lsnrk+yU5NMz2tPdr0zyqSQvHC6du1OoNcOzkrwqyW5Jvpvks0m+OKx/IMkbh9o29TcBALZR22zYVFXvGL4NvHCk8T5aVddW1Yc3aH/v8M3hhcMxd5jnePtU1dlVtXr4ZvbFG+n3o8O3oN+tqpeO8VoAYAnaNcm3u/u2TfT7dHef2d3fT/J/kzxyaD8sye7d/dru/t5wj6G/THLCsP2kJK/q7q/1xAXdPTM4Oj6TMOio7j53aLs1k1DmR5NUd6/u7ss34zX9YXdf390XJbkwycruvrS7r0vyT0kO3ch+z0nyxqHvjUlenuSEqlqWSRj3qKr6kRl9/767v5vk6CTf6O6/7u7buvuLST6Y5LgZY3+ouz/T3bd39y2b8VpmOr27zxv2Pz3JLd397uFv8rczXtem/iYAwDZqmw2bkrwzk28Ux/KGJM+dpf29mXwIPTjJvTL5MHsnw5TzJ2zQfFuS3+ruh2XyjeevDd9ObujqJC9K8kd3vXQAWPKuSrLbEKjM5T9nLN+UZPmwz48k2XP4Yujaqro2ySsyufdTMplN9PU5xn1Jkvd395fXN3T3JzKZUfS2JFdU1alVdd/NeE1XzFi+eZb1HTey355Jvjlj/ZtJliV5YHffkOQj+UFgc0Imn0WSyXvw6A3eg+ckedCMsS7bjPo3Zr6va1N/EwBgG7XNhk3dfU4mQc0dhnslfHS4T8OnqupHN2O8jye5YZb2M4dvSDvJuUn2nud4lw/fOGb44Lg6kynmG/a7sru/kMm3qwCwrfpskluSPP0u7n9Zkn/v7p1n/OzU3UfN2P7gOfY/PsnTq+olMxu7+y3d/eNJHp7J5XTr7x/1nST3ntF1ZqCzpdZmEtSst28mX1KtD3Xel+TZVfXYTL7oOntovyzJv2zwHuzY3b868yVt4tib2r45NvU3AQC2Udts2LQRpyb59eFD40szecLNKIbL556b5KN3Yd/9Mply/vmx6gGArclwadnvJHlbVT29qu5dVTtU1VOr6v+bxxDnJrm+qn67qu5VkxuCP6KqDhu2vz3J66rqwMl9v+uQqtp1xv5rM7mn0Iuq6n8kSVUdVlWPHv6N/04mYdj3h/7nJ3nmUOdDkjx/i9+EH3hfkt+oqv2rasdMns73tzMuMTwzkzDqtUP77UP7h5M8tKqeO7x3Owyv4WGbcewrMrlP1Bg29TcBALZRd5uwafiw9hNJ/q6qzk/yF0n2GLY9c7jn0oY/H9uMQ/xpknO6+1PDmEdU1fnDsY5J8vZh/U6B0lDXB5O8pLuv3/JXCgBbp+5+YyY38n5VknWZzIx5YZJ/mMe+30/y35I8Ksm/J/l2JgHT/YYub0zy/iQrk1yf5K8ymRU0c4z/yCRw+u2aPGnuvpncY+iaTC5luyo/uKz9TUm+l0k486784FK2Mbwjk/tRnTO8lluS/PqMOr+b5O+TPDmTm4Gvb78hk5uan5BJePafSf4wyT0349h/nOS44clyb9mSFzGPvwkAsI2qydVf26ZhxtCHu/sRwz0Wvtbde2zBeE9I8tLuPnqD9tdkMjPpmTO+XZy5/Z1J3tndn9ygfYdMvoX82PABe65j/26SG7vbvZsAAACAJetuM7NpmDX071V1fJIMU+gfuYndNmn45vOIJM+eLWiaY7/K5FvV1ZsKmgAAAAC2Ftts2FRV78vkZqP/parWVNXzM3kiy/Or6oIkFyU5djPG+1SSv0vypGG8I4ZNf57JU1U+O1wm9zvzHPJxmdzj6afXX25XVUcNx/qVqvqVYflBVbUmw2UFw7E350k4AAAAAItmm76MDgAAAIDFtc3ObAIAAABg8S2bdgELYbfdduv99ttv2mUAAAAAbDPOO++8b3f37pvqt02GTfvtt19WrVo17TIAAAAAthlV9c359HMZHQAAAACjETYBAAAAMBphEwAAAACjETYBAAAAMJqphU1VtU9VnV1Vq6vqoqp68Sx9qqreUlWXVNWXqurHplErAAAAAPMzzafR3Zbkt7r7i1W1U5Lzquqs7v7KjD5PTXLg8PPoJH82/AYAAABgCZrazKbuvry7vzgs35BkdZK9Nuh2bJJ398TnkuxcVXsscqkAAAAAzNOSuGdTVe2X5NAkn99g015JLpuxviY/HEitH+PkqlpVVavWrVu3EGUCAAAAsAlTD5uqasckH0zyku6+fsPNs+zSs43T3ad294ruXrH77ruPXSYAAAAA8zDVsKmqdsgkaHpvd//9LF3WJNlnxvreSdYuRm0AAAAAbL5pPo2ukvxVktXd/caNdDsjyS8MT6V7TJLruvvyRSsSAAAAgM0yzafRPS7Jc5N8uarOH9pekWTfJOnuP09yZpKjklyS5KYkvziFOgEAAACYp6mFTd396cx+T6aZfTrJry1ORQAAAABsqanfIBwAAACAbYewCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGI2wCQAAAIDRCJsAAAAAGM1Uw6aqekdVXVlVF25k+xOq6rqqOn/4+Z3FrhEAAACA+Vs25eO/M8lbk7x7jj6f6u6jF6ccAAAAALbEVGc2dfc5Sa6eZg0AAAAAjGdruGfTY6vqgqr6p6p6+MY6VdXJVbWqqlatW7duMesDAAAAYLDUw6YvJvmR7n5kkj9J8g8b69jdp3b3iu5esfvuuy9agQAAAAD8wJIOm7r7+u6+cVg+M8kOVbXblMsCAAAAYCOWdNhUVQ+qqhqWD8+k3qumWxUAAAAAGzPVp9FV1fuSPCHJblW1JslrkuyQJN3950mOS/KrVXVbkpuTnNDdPaVyAQAAANiEqYZN3f3sTWx/a5K3LlI5AAAAAGyhJX0ZHQAAAABbF2ETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKOZathUVe+oqiur6sKNbK+qektVXVJVX6qqH1vsGgEAAACYv2nPbHpnkiPn2P7UJAcOPycn+bNFqAkAAACAu2iqYVN3n5Pk6jm6HJvk3T3xuSQ7V9Uei1MdAAAAAJtr2jObNmWvJJfNWF8ztP2Qqjq5qlZV1ap169YtSnEAAAAA3NlSD5tqlraerWN3n9rdK7p7xe67777AZQEAAAAwm6UeNq1Jss+M9b2TrJ1SLQAAAABswlIPm85I8gvDU+kek+S67r582kUBAAAAMLtl0zx4Vb0vyROS7FZVa5K8JskOSdLdf57kzCRHJbkkyU1JfnE6lQIAAAAwH1MNm7r72ZvY3kl+bZHKAQAAAGALLfXL6AAAAADYigibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABiNsAkAAACA0QibAAAAABjNVMOmqjqyqr5WVZdU1SmzbD+xqtZV1fnDz0nTqBMAAACA+Vk2rQNX1fZJ3pbkZ5KsSfKFqjqju7+yQde/7e4XLnqBAAAAAGy2ac5sOjzJJd19aXd/L8lpSY6dYj0AAAAAbKFphk17JblsxvqaoW1DP1tVX6qqD1TVPhsbrKpOrqpVVbVq3bp1Y9cKAAAAwDxMM2yqWdp6g/V/TLJfdx+S5J+TvGtjg3X3qd29ortX7L777iOWCQAAAMB8TTNsWpNk5kylvZOsndmhu6/q7u8Oq3+Z5McXqTYAAAAA7oJphk1fSHJgVe1fVfdIckKSM2Z2qKo9Zqwek2T1ItYHAAAAwGaa2tPouvu2qnphko8l2T7JO7r7oqp6bZJV3X1GkhdV1TFJbktydZITp1UvAAAAAJtW3RveJmnrt2LFil61atW0ywAAAADYZlTVed29YlP9pnkZHQAAAADbGGETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKMRNgEAAAAwGmETAAAAAKPZaNhUVfeeY9v+C1MOAAAAAFuzuWY2XVdVv1dVs/X54EIVBAAAAMDWa66w6dIkD07ymVlmMtXClQQAAADA1mqusOk73f3zSd6W5Jyq+oUZ23phywIAAABga7TJG4R393uS/NckL6iq06rqfgtfFgAAAABbo7nCpjsulevubyR5fJLVSf41yR4LWxYAAAAAW6O5wqaPzFzp7tu7+/eS/FySCxa0KgAAAAC2Sss2tqG7X7WR9s8lOXLBKgIAAABgq7XJezYBAAAAwHwJmwAAAAAYjbAJAAAAgNHMO2yqqpcvZCEAAAAAbP02Z2bT8QtWBQAAAADbBJfRAQAAADCaZXNtrKp/T9JJKskeVXXpsNzdfcAi1AcAAADAVmTOsKm791+/XFX/2t2HLnxJAAAAAJt26623Zs2aNbnlllumXco2Zfny5dl7772zww473KX95wybAAAAAJaqNWvWZKeddsp+++2Xqpp2OduE7s5VV12VNWvWZP/999/0DrPYnHs2feYuHQEAAABgAdxyyy3ZddddBU0jqqrsuuuuWzRbbN5hU3e/8C4fBQAAAGABCJrGt6XvqafRAQAAAIzoxBNPzAc+8IElM85im2rYVFVHVtXXquqSqjpllu33rKq/HbZ/vqr2W/wqAQAAAJivqYVNVbV9krcleWqSg5I8u6oO2qDb85Nc090PSfKmJH+4uFUCAAAAzO3d7353DjnkkDzykY/Mc5/73CTJOeeck5/4iZ/IAQcccKfZSW94wxty2GGH5ZBDDslrXvOaOceY6dWvfnVOPPHE3H777TnllFNy0EEH5ZBDDslLX/rSJD88C2rHHXdMknzyk5/M4x//+DzrWc/KQx/60Jxyyil573vfm8MPPzwHH3xwvv71r4/+fmz0aXRV9YAkr0jykCRfTvK/u/v6EY99eJJLuvvS4XinJTk2yVdm9Dk2ye8Oyx9I8taqqu7uEetYktZee3O+edVN8+o730sp59NtvtdljnnMzRlvPiOOX9s835N5jzefscb9O8zX/N+78eqbxjEn482z3yY63t7JTsuXpVK5vTudydMbupPu3NF2+9AGAACM59bv355bbv1+kuR/nbk6qy8fM7ZIHrbHffOKox42Z5+vXHRRfv/3X59P/Ms52W233XL11Vfnt//nS7PmW2tz5lln55tfvzg/+8yn57jjjsvKlStz8cUX59xzz01355hjjsk555yTXXfdNa9//evzmc985o4xZnrZy16W6667Ln/913+da665Jqeffnq++tWvpqpy7bXXbvJ1XHDBBVm9enV22WWXHHDAATnppJNy7rnn5o//+I/zJ3/yJ3nzm9+8Re/ThjYaNiV5d5LzkvxJkqOTvCXJiSMee68kl81YX5Pk0Rvr0923VdV1SXZN8u0R61iSPvKly/P6M1dPuwwAAABYsv7ymD2SK25Iklxz0/dy8/e+P+r419z0vfzbMP7GvP8fP5rHH3F0rv7+PXP1FTck2SHX33xrHvOEp+Q/rrk5u+/74FxxxRVJkpUrV2blypU59NBDkyQ33nhjLr744lxwwQU57rjjsttuuyVJdtlllzvGf93rXpdHP/rROfXUU5Mk973vfbN8+fKcdNJJedrTnpajjz56k6/jsMMOyx577JEkefCDH5ynPOUpSZKDDz44Z5999ua9KfMwV9j0oO5+5bD8sar64sjHnm2+wIbf+8+nz6Rj1clJTk6Sfffdd8sqWwKedsgeecRe99tkv5797Zit4xhdJv3mfcj5dZz/ePMZa57HnN8h591xzNc65vsxGW/c92T+s3M23XH81zrf8cb7e6299ubsuHxZtqvJ3KuqyWy4SiZt9YPfiSdlAADAmHbJ1dl3l3snSV537COmUsP977Ust937HnfUkST3ueey7LnLfbPvLvfOjvdcdsf/y7o7L3/5y/PLv/zLdxrjLW95y0b/r3DYYYflvPPOy9VXX51ddtkly5Yty7nnnpuPf/zjOe200/LWt741n/jEJ7Js2bLcfvvtdxzne9/73h1j3POe97xjebvttrtjfbvttsttt902zhsxw1xhU1XV/fODwGf7mevdffVG95yfNUn2mbG+d5K1G+mzpqqWJblfklmP292nJjk1SVasWLHVX6yy5873yp4732vaZQAAAMCStXr1ddn53veYag1HP/WIPOMZz8jLX/bS7Lrrrrn66qtzj2Xb5T73XPZDtR1xxBF59atfnec85znZcccd861vfSs77LBDnvSkJ+UZz3hGfuM3fuOOMdbPbjryyCNzxBFH5GlPe1pWrlyZqspNN92Uo446Ko95zGPykIc8JEmy33775bzzzsuznvWsfOhDH8qtt9666O/FenOFTffL5DK6mdHa+tlNneSALTz2F5IcWFX7J/lWkhOS/NwGfc5I8rwkn01yXJJP3B3u1wQAAABsHR7+8Ifnla98ZR7/+Mdn++23v+MSudk85SlPyerVq/PYxz42yeQm3u95z3tmHeOd73znHfsdf/zxueGGG3LMMcfkb/7mb3LsscfmlltuSXfnTW96U5LkBS94QY499tgcfvjhedKTnpT73Oc+C/q651LTzG6q6qgkb06yfZJ3dPfrq+q1SVZ19xlVtTzJ/01yaCYzmk5Yf0PxuaxYsaJXrVq1kKUDAAAAU7Z69eo87GFz38Cbu2a297aqzuvuFZvad66ZTQuuu89McuYGbb8zY/mWJMcvdl0AAAAA3DXbTbsAAAAAALYdwiYAAAAARiNsAgAAALZaniM2vi19T+cdNlXVZ7foSAAAAAAjWr58ea666iqB04i6O1dddVWWL19+l8fYnBuE3/WjAAAAAIxs7733zpo1a7Ju3bppl7JNWb58efbee++7vP+cYVNV/dT6xST3mbGe7j7nLh8VAAAAYAvtsMMO2X///addBhvY1MymX5yxvGuSEzMJnjqJsAkAAACAO5kzbOruO8Kmqvpid//SwpcEAAAAwNZqc55GVwtWBQAAAADbhM0Jm357waoAAAAAYJsw77Cpu1cuZCEAAAAAbP02Z2YTAAAAAMxJ2AQAAADAaIRNAAAAAIxm2cY2VNXvzLFfd/frFqAeAAAAALZiGw2bknxnlrZ7Jzkpya5JhE0AAAAA3MlGw6bu/j/rl6tqpyQvTvJLSU5L8n82th8AAAAAd19zzWxKVe2S5DeTPCfJu5L8WHdfsxiFAQAAALD1meueTW9I8swkpyY5uLtvXLSqAAAAANgqzfU0ut9KsmeSVyVZW1XXDz83VNX1i1MeAAAAAFuTue7ZNFcQBQAAAAA/RKAEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMZiphU1XtUlVnVdXFw+/7b6Tf96vq/OHnjMWuEwAAAIDNM62ZTack+Xh3H5jk48P6bG7u7kcNP8csXnkAAAAA3BXTCpuOTfKuYfldSZ4+pToAAAAAGNG0wqYHdvflSTL8fsBG+i2vqlVV9bmqmjOQqqqTh76r1q1bN3a9AAAAAMzDsoUauKr+OcmDZtn0ys0YZt/uXltVByT5RFV9ubu/PlvH7j41yalJsmLFit7sggEAAADYYgsWNnX3kze2raquqKo9uvvyqtojyZUbGWPt8PvSqvpkkkOTzBo2AQAAADB907qM7owkzxuWn5fkQxt2qKr7V9U9h+XdkjwuyVcWrUIAAAAANtu0wqY/SPIzVXVxkp8Z1lNVK6rq7UOfhyVZVVUXJDk7yR90t7AJAAAAYAlbsMvo5tLdVyV50iztq5KcNCz/vyQHL3JpAAAAAGyBac1sAgAAAGAbJGwCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDTCJgAAAABGI2wCAAAAYDRTCZuq6viquqiqbq+qFXP0O7KqvlZVl1TVKYtZIwAAAACbb1ozmy5M8swk52ysQ1Vtn+RtSZ6a5KAkz66qgxanPAAAAADuimXTOGh3r06Sqpqr2+FJLunuS4e+pyU5NslXFrxAAAAAAO6SpXzPpr2SXDZjfc3QNquqOrmqVlXVqnXr1i14cQAAAAD8sAWb2VRV/5zkQbNsemV3f2g+Q8zS1hvr3N2nJjk1SVasWLHRfgAAAAAsnAULm7r7yVs4xJok+8xY3zvJ2i0cEwAAAIAFtJQvo/tCkgOrav+qukeSE5KcMeWaAAAAAJjDVMKmqnpGVa1J8tgkH6mqjw3te1bVmUnS3bcleWGSjyVZneT93X3RNOoFAAAAYH6m9TS605OcPkv72iRHzVg/M8mZi1gaAAAAAFtgKV9GBwAAAMBWRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGiETQAAAACMRtgEAAAAwGimEjZV1fFVdVFV3V5VK+bo942q+nJVnV9VqxazRgAAAAA237IpHffCJM9M8hfz6PvE7v72AtcDAAAAwAimEjZ19+okqappHB4AAACABbLU79nUSVZW1XlVdfJcHavq5KpaVVWr1q1bt0jlAQAAADDTgs1sqqoTavCwAAAKsUlEQVR/TvKgWTa9srs/NM9hHtfda6vqAUnOqqqvdvc5s3Xs7lOTnJokK1as6LtUNAAAAABbZMHCpu5+8ghjrB1+X1lVpyc5PMmsYRMAAAAA07dkL6OrqvtU1U7rl5M8JZMbiwMAAACwRE0lbKqqZ1TVmiSPTfKRqvrY0L5nVZ05dHtgkk9X1QVJzk3yke7+6DTqBQAAAGB+pvU0utOTnD5L+9okRw3LlyZ55CKXBgAAAMAWWLKX0QEAAACw9RE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADAaYRMAAAAAoxE2AQAAADCaqYRNVfWGqvpqVX2pqk6vqp030u/IqvpaVV1SVacsdp0AAAAAbJ5pzWw6K8kjuvuQJP+W5OUbdqiq7ZO8LclTkxyU5NlVddCiVgkAAADAZplK2NTdK7v7tmH1c0n2nqXb4Uku6e5Lu/t7SU5Lcuxi1QgAAADA5lsK92z6pST/NEv7Xkkum7G+ZmgDAAAAYIlatlADV9U/J3nQLJte2d0fGvq8MsltSd472xCztPUcxzs5yclJsu+++252vQAAAABsuQULm7r7yXNtr6rnJTk6yZO6e7YQaU2SfWas751k7RzHOzXJqUmyYsWKjYZSAAAAACycaT2N7sgkv53kmO6+aSPdvpDkwKrav6rukeSEJGcsVo0AAAAAbL5p3bPprUl2SnJWVZ1fVX+eJFW1Z1WdmSTDDcRfmORjSVYneX93XzSlegEAAACYhwW7jG4u3f2QjbSvTXLUjPUzk5y5WHUBAAAAsGWWwtPoAAAAANhGCJsAAAAAGI2wCQAAAIDRCJsAAAAAGE1197RrGF1VrUvyzWnXMYLdknx72kXAVsC5AvPjXIH5ca7A/DhXYH62pXPlR7p790112ibDpm1FVa3q7hXTrgOWOucKzI9zBebHuQLz41yB+bk7nisuowMAAABgNMImAAAAAEYjbFraTp12AbCVcK7A/DhXYH6cKzA/zhWYn7vdueKeTQAAAACMxswmAAAAAEYjbAIAAABgNMKmJaqqjqyqr1XVJVV1yrTrgaWiqt5RVVdW1YUz2napqrOq6uLh9/2nWSMsBVW1T1WdXVWrq+qiqnrx0O58gUFVLa+qc6vqguE8+b2hff+q+vxwnvxtVd1j2rXCUlBV21fVv1bVh4d15wpsoKq+UVVfrqrzq2rV0Ha3+/wlbFqCqmr7JG9L8tQkByV5dlUdNN2qYMl4Z5IjN2g7JcnHu/vAJB8f1uHu7rYkv9XdD0vymCS/Nvxb4nyBH/hukp/u7kcmeVSSI6vqMUn+MMmbhvPkmiTPn2KNsJS8OMnqGevOFZjdE7v7Ud29Yli/233+EjYtTYcnuaS7L+3u7yU5LcmxU64JloTuPifJ1Rs0H5vkXcPyu5I8fVGLgiWouy/v7i8Oyzdk8p+DveJ8gTv0xI3D6g7DTyf56SQfGNqdJ5CkqvZO8rQkbx/WK84VmK+73ecvYdPStFeSy2asrxnagNk9sLsvTyb/wU7ygCnXA0tKVe2X5NAkn4/zBe5kuCzo/CRXJjkrydeTXNvdtw1dfA6DiTcneVmS24f1XeNcgdl0kpVVdV5VnTy03e0+fy2bdgHMqmZp60WvAoCtXlXtmOSDSV7S3ddPvogG1uvu7yd5VFXtnOT0JA+brdviVgVLS1UdneTK7j6vqp6wvnmWrs4VSB7X3Wur6gFJzqqqr067oGkws2lpWpNknxnreydZO6VaYGtwRVXtkSTD7yunXA8sCVW1QyZB03u7+++HZucLzKK7r03yyUzucbZzVa3/UtbnMEgel+SYqvpGJrf4+OlMZjo5V2AD3b12+H1lJl9iHJ674ecvYdPS9IUkBw5Pd7hHkhOSnDHlmmApOyPJ84bl5yX50BRrgSVhuJfGXyVZ3d1vnLHJ+QKDqtp9mNGUqrpXkidncn+zs5McN3RznnC3190v7+69u3u/TP5v8onufk6cK3AnVXWfqtpp/XKSpyS5MHfDz1/VbabjUlRVR2XybcH2Sd7R3a+fckmwJFTV+5I8IcluSa5I8pok/5Dk/Un2TfIfSY7v7g1vIg53K1X1k0k+leTL+cH9NV6RyX2bnC+QpKoOyeRGrdtn8iXs+7v7tVV1QCazN3ZJ8q9Jfr67vzu9SmHpGC6je2l3H+1cgTsbzonTh9VlSf6mu19fVbvmbvb5S9gEAAAAwGhcRgcAAADAaIRNAAAAAIxG2AQAAADAaIRNAAAAAIxG2AQAAADAaIRNAABJqmrXqjp/+PnPqvrWjPX/t0DHPLSq3r6Rbd+oqt1GPNZpVXXgWOMBAGxMdfe0awAAWFKq6neT3Njdf7TAx/m7JL/f3RfMsu0bSVZ097dHOtbjk/x8d79gjPEAADbGzCYAgE2oqhuH30+oqn+pqvdX1b9V1R9U1XOq6tyq+nJVPXjot3tVfbCqvjD8PG6WMXdKcsj6oGmYWbWyqv61qv4iSc3o+w9VdV5VXVRVJw9tz6+qN83o84KqemNV3aeqPlJVF1TVhVX134cun0ry5KpatlDvEwBAImwCANhcj0zy4iQHJ3lukod29+FJ3p7k14c+f5zkTd19WJKfHbZtaEWSC2esvybJp7v70CRnJNl3xrZf6u4fH/Z5UVXtmuS0JMdU1Q5Dn19M8tdJjkyytrsf2d2PSPLRJOnu25NcMtQPALBgfLMFALB5vtDdlydJVX09ycqh/ctJnjgsPznJQVV3TE66b1Xt1N03zBhnjyTrZqz/VJJnJkl3f6Sqrpmx7UVV9YxheZ8kB3b356rqE0mOrqrVSXbo7i9X1XeT/FFV/WGSD3f3p2aMc2WSPZOcd5dfPQDAJgibAAA2z3dnLN8+Y/32/OCz1XZJHtvdN88xzs1Jlm/Q9kM306yqJ2QSXj22u2+qqk/O2O/tSV6R5KuZzGpKd/9bVf14kqOS/O+qWtndrx36Lx+OCwCwYFxGBwAwvpVJXrh+paoeNUuf1UkeMmP9nCTPGfo/Ncn9h/b7JblmCJp+NMlj1u/Q3Z/PZKbTzyV537Dvnklu6u73JPmjJD824xgPTXLRFr0yAIBNMLMJAGB8L0rytqr6Uiaft85J8iszO3T3V6vqfjMur/u9JO+rqi8m+Zck/zF0/WiSXxnG+lqSz21wrPcneVR3r7/s7uAkb6iq25PcmuRXk6SqHpjk5vWXAAIALJTq/qHZ2gAALIKq+o0kN3T3bDcQn+8YH87kZuQfn8exru/uv7qrxwIAmA+X0QEATM+f5c73gJq3qtq5qv4tk9lKcwZNg2uTvOuuHAsAYHOY2QQAAADAaMxsAgAAAGA0wiYAAAAARiNsAgAAAGA0wiYAAAAARiNsAgAAAGA0/z8KokFqvXqFugAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplots(figsize=(20, 7))\n",
    "plt.plot(times, checksum, label='checksum')\n",
    "plt.ylabel('N + P + Z')\n",
    "plt.xlabel('Time (days)')\n",
    "plt.title('Checksum over time')\n",
    "plt.legend(loc='center right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:38: DeprecationWarning: object of type <class 'float'> cannot be safely interpreted as an integer.\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "'float' object is not subscriptable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-f94ded3b6978>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     38\u001b[0m \u001b[0mtime\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtmax\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msteps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0minitial\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1.6\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0.15\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 40\u001b[0;31m \u001b[0mpop\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0modeint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnpz\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minitial\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtfirst\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     41\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     42\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m15\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/anaconda3/lib/python3.6/site-packages/scipy/integrate/odepack.py\u001b[0m in \u001b[0;36modeint\u001b[0;34m(func, y0, t, args, Dfun, col_deriv, full_output, ml, mu, rtol, atol, tcrit, h0, hmax, hmin, ixpr, mxstep, mxhnil, mxordn, mxords, printmessg, tfirst)\u001b[0m\n\u001b[1;32m    231\u001b[0m                              \u001b[0mfull_output\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrtol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0matol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtcrit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mh0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhmax\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhmin\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    232\u001b[0m                              \u001b[0mixpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmxstep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmxhnil\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmxordn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmxords\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 233\u001b[0;31m                              int(bool(tfirst)))\n\u001b[0m\u001b[1;32m    234\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0moutput\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    235\u001b[0m         \u001b[0mwarning_msg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_msgs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0moutput\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;34m\" Run with full_output = 1 to get quantitative information.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-6-f94ded3b6978>\u001b[0m in \u001b[0;36mnpz\u001b[0;34m(initial, t)\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;31m#solve using odeint\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mnpz\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minitial\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mnN\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minitial\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m   \u001b[0;31m#Nutrients biomass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m     \u001b[0mnP\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minitial\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m   \u001b[0;31m#phytoplankton biomass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m     \u001b[0mnZ\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minitial\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m   \u001b[0;31m#Zooplankton biomass\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: 'float' object is not subscriptable"
     ]
    }
   ],
   "source": [
    "checksum = []\n",
    "times = []\n",
    "\n",
    "#solve using odeint\n",
    "def npz(initial, t):\n",
    "    nN = initial[0]   #Nutrients biomass           \n",
    "    nP = initial[1]   #phytoplankton biomass\n",
    "    nZ = initial[2]   #Zooplankton biomass\n",
    "\n",
    "    v = 1.     #rate of nutrient update\n",
    "    mZ = .5    #rate of Zooplankton mortality\n",
    "    mP = .1    #rate of Phytoplankton mortality\n",
    "    γ = .3     #Zooplankton growth efficiency\n",
    "\n",
    "    k  = 1.    #1/2 saturation constant for Nutrient update\n",
    "    Λ = 1.     #Ivlev grazing constant\n",
    "    Rm = 1.5   #maximum zooplankton grazing rate\n",
    "    T = .02    #turbulent mixing rate\n",
    "    Ni = 1.6   #initial nutrient concentration\n",
    "\n",
    "    zG = Rm*(1-math.exp(-Λ*nP))\n",
    "    \n",
    "    f = [\n",
    "       ((-v*nN*nP)/(k+nN) + mP*nP + mZ*nZ + (1-γ)*nZ*zG - T*nN + T*Ni),\n",
    "       ((v*nP*nN)/(k+nN) - mP*nP - nZ*zG) - T*nP,\n",
    "       (γ*nZ*zG - mZ*nZ)\n",
    "    ]\n",
    "    \n",
    "    checksum.append(nN + nP + nZ)\n",
    "    times.append(t)\n",
    "    \n",
    "    return f\n",
    "    \n",
    "t = .25\n",
    "tmax = 50.\n",
    "steps = tmax/t\n",
    "\n",
    "time = np.linspace(0, tmax, steps)\n",
    "initial = [1.6, 0.4, 0.15]\n",
    "pop = odeint(npz, initial, time, tfirst=True)\n",
    "    \n",
    "plt.subplots(figsize=(15, 10))\n",
    "plt.plot(time, pop)\n",
    "\n",
    "blue_patch = mp.Patch(color='blue', label='nutrients')\n",
    "green_patch = mp.Patch(color='green', label='phytoplankton')\n",
    "red_patch = mp.Patch(color='red', label='zooplankton')\n",
    "\n",
    "plt.legend(handles=[blue_patch, green_patch, red_patch])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}