Code - Python/Learning Sequence/7.1 Euler's Method for a First Order ODE.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Euler's Method for a First Order Ordinary Differential Equation\n",
    "\n",
    "One of the simplest models for how a quantity changes with time is a first order ODE like this one for a temperature sensor.\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{dT_m}{dt}=\\dot{T}_m = \\frac{(T-T_m)}{\\tau}\n",
    "\\end{equation}\n",
    "\n",
    "where $\\tau$ is a time constant representing how quickly things change. Euler's method breaks down the derivative into a simple approximation\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\Delta T_m}{\\Delta t} = \\frac{(T-T_m)}{\\tau}\n",
    "\\end{equation}\n",
    "\n",
    "and rearranges to predict how much $T_m$ will change from it's current state over a short time $\\Delta t$\n",
    "\n",
    "\\begin{equation}\n",
    "\\Delta T_m= \\frac{(T-T_m)}{\\tau} {\\Delta t} \n",
    "\\end{equation}\n",
    "\n",
    "If we know the old temperature $T_m(old)$ and the ambient temperature $T$, then we can predict the new temperature $T_m(new)$\n",
    "\n",
    "\\begin{equation}\n",
    "T_m(new) = T_m(old) + \\Delta T_m = T_m(old) + \\frac{(T-T_m)}{\\tau} {\\Delta t} \n",
    "\\end{equation}\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "# gets all of numpy but you will still need to refer to e.g. numpy.random.randn() as random.randn()\n",
    "from numpy import *               # all of the array capable elements for numerical data          \n",
    "from scipy.stats import norm      # comprehensive functions for Gaussian normal distributions\n",
    "import csv                        # library for reading and writing comma separated value files\n",
    "from matplotlib.pyplot import *   # all of pyplot to graph the results of our calculations\n",
    "\n",
    "# put figures inline in the notebook, so you don't have to call show()\n",
    "%matplotlib inline\n",
    "\n",
    "# This lets you make the default figure size larger (or smaller)\n",
    "from IPython.core.pylabtools import figsize\n",
    "figsize(14, 7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Set up the intial conditions**, a time base $t$, and define how the ambient temperature will change with time. Make sure everything is defined at time $t=0$, including the time constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100\n",
    "stepStart = int(n/20)+1\n",
    "t = linspace(0,100,n)\n",
    "T = zeros(n)\n",
    "T[:] = 25\n",
    "T[:stepStart] = 10\n",
    "Tm = zeros(n)\n",
    "Tm[0] = 10\n",
    "tau = 10\n",
    "deltat = t[1]-t[0]\n",
    "ii = 0     # the step we just took"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Go one time step into the future** using the values at the old time, then **do it again**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n"
     ]
    }
   ],
   "source": [
    "dTdt = (T[0]-Tm[0])/tau\n",
    "Tm[1] = Tm[0] + dTdt * deltat\n",
    "print(Tm[1])\n",
    "ii = 1     # the step we just took"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n"
     ]
    }
   ],
   "source": [
    "dTdt = (T[1]-Tm[1])/tau\n",
    "Tm[2] = Tm[1] + dTdt * deltat\n",
    "print(Tm[2])\n",
    "ii = 2     # the step we just took"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run this plot any time to check on the progress of the solution after each step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plotT():\n",
    "    plot(t,T,label=\"Ambient Temperature\")\n",
    "    plot(t,Tm,label = 'Measured Temperature')\n",
    "    grid()\n",
    "    legend()\n",
    "    xlabel(\"Time [s]\")\n",
    "    ylabel('Temperature [C]')\n",
    "plotT()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This next cell takes us one step further, every time it is run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0AAAAGtCAYAAAA/JhQ3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAIABJREFUeJzt3Xt8VPWd//H3J4RMlMQrmlrQjRdkBYkJBkREDZZFcf15WwX81Vuxpd3aij+tra1la3VtWVfbWu3WUu3K+lDQFVHXy66gpl4oyMUIKF1qFS0VxaJWEpkwl+/vj5mMIcwtw5zMyZnX8/HIYzJnZs75hPl2PO9+v+cz5pwTAAAAAJSDilIXAAAAAAB9hQAEAAAAoGwQgAAAAACUDQIQAAAAgLJBAAIAAABQNghAAAAAAMoGAQgAAABA2SAAAQAAACgbBCAAAAAAZaOy1AXkY/Dgwa6+vr7UZUiSOjo6NGjQoFKXgX6GcYNCMXZQCMYNCsG4QSH8NG5WrVr1F+fcAbme1y8CUH19vVauXFnqMiRJra2tamlpKXUZ6GcYNygUYweFYNygEIwbFMJP48bM3s7neSyBAwAAAFA2CEAAAAAAygYBCAAAAEDZIAABAAAAKBsEIAAAAABlgwAEAAAAoGwQgAAAAACUDQIQAAAAgLJBAAIAAABQNghAAAAAAMoGAQgAAABA2SAAAQAAACgbngUgMzvYzJ4zs/Vm9pqZzUpuv97M/mxmbcmf072qAQAAAAC6q/Rw31FJVzvnVptZraRVZrY4+dhPnXO3eHhsAAAAANiFZwHIObdZ0ubk79vMbL2kIV4dD7v604ef6tMdsVKXAUmbtsX1v+9tK3UZ6IcYOygE4waFYNygEO07XKlL6DUvZ4BSzKxeUpOk5ZJOkPQNM7tY0kolZok+6os6yslr7/5Vf//zF0tdBrp76flSV4D+irGDQjBuUAjGDXrpSyOrdEapi+glzwOQmdVIWijpSufcJ2b2S0k3SnLJ21slzUjzupmSZkpSXV2dWltbvS41L+3t7b6pJZs1H0QlSecNG6i6QfS6KLVwOKzq6upSl4F+iLGDQjBuUAjGDQpxQGW4X5wbd+dpADKzgUqEn/uccw9LknPu/W6P/1rS4+le65ybK2muJDU3N7uWlhYvS81ba2ur/FJLNuF1m6VVq/WlKcdp5Of3LnU5Za+/jBv4D2MHhWDcoBCMGxSiP44bL7vAmaS7Ja13zv2k2/aDuj3tHEnrvKqhnIUjcUlS9cABJa4EAAAA8A8vZ4BOkHSRpLVm1pbc9j1JF5hZoxJL4DZK+qqHNZStcCTR/IAABAAAAHzGyy5wL0qyNA896dUx8ZlUAKrk+h8AAACgC2fHARWOsgQOAAAA6IkAFFCdXAMEAAAA7IIAFFDhaEwDB5gGVKRbhQgAAACUJwJQQIUjMYUqmf0BAAAAuiMABVQ4Elf1QN5eAAAAoDvOkAOqkxkgAAAAYBcEoIAKR2PMAAEAAAA9cIYcUJ2ROB3gAAAAgB4IQAGVmAEiAAEAAADdEYACKhyJK1TJ2wsAAAB0xxlyQIUjzAABAAAAPRGAAioRgHh7AQAAgO44Qw6ocCSuatpgAwAAADshAAVUZzSmEEvgAAAAgJ0QgAIq0QabtxcAAADojjPkgKINNgAAALArAlAAxeJOkZijDTYAAADQA2fIARSOxCSJGSAAAACgBwJQAKUCEDNAAAAAwE44Qw6gcDQuiRkgAAAAoCcCUACxBA4AAABIjwAUQJ2Rrhkg3l4AAACgO86QAygcTcwAhSqZAQIAAAC6IwAFUNcSuBAzQAAAAMBOOEMOoM+WwDEDBAAAAHRHAAqgz9pgE4AAAACA7ghAAdR1DRBNEAAAAICdcYYcQCyBAwAAANIjAAUQ3wMEAAAApEcACqBwNDEDFKrk7QUAAAC64ww5gJgBAgAAANIjAAVQOBLXwAGmARVW6lIAAAAAXyEABVA4EqMFNgAAAJAGASiAOqMxhVj+BgAAAOyCABRAnZE43wEEAAAApMFZcgCFozEaIAAAAABpEIACKByJ0wIbAAAASIOz5AAKR5gBAgAAANIhAAVQIgDx1gIAAAA9cZYcQOFInDbYAAAAQBoEoADqpAkCAAAAkBYBKIDCkbhCLIEDAAAAdsFZcgB1RmMKsQQOAAAA2AUBKIDCfBEqAAAAkBZnyQFEG2wAAAAgPQJQwERjcUXjji5wAAAAQBoEoIAJR+OSxBI4AAAAIA3OkgOmMxKTJJbAAQAAAGkQgAKGGSAAAAAgM86SAyacnAGiDTYAAACwKwJQwIRTS+B4awEAAICeOEsOmHAksQQuxDVAAAAAwC4IQAGTaoLAEjgAAABgFwSggOmkCQIAAACQEWfJAROmDTYAAACQEQEoYMLRri5wvLUAAABAT5wlB0xXEwRmgAAAAIBdEYAChiVwAAAAQGYEoID5bAaItxYAAADoibPkgAnTBhsAAADIyLMAZGYHm9lzZrbezF4zs1nJ7fuZ2WIz+0Pydl+vaihHndG4qgZUqKLCSl0KAAAA4DtezgBFJV3tnDtK0jhJl5vZCEnXSnrGOTdM0jPJ+yiScCSmEMvfAAAAgLQ8O1N2zm12zq1O/r5N0npJQySdJWle8mnzJJ3tVQ3lqDMaU4jlbwAAAEBafTJVYGb1kpokLZdU55zbLCVCkqQD+6KGchGOxGmAAAAAAGRgzjlvD2BWI+m3km5yzj1sZh875/bp9vhHzrldrgMys5mSZkpSXV3dsQsWLPC0zny1t7erpqam1GVkdMcrYb3bHtePTtyz1KWgG7+PG/gXYweFYNygEIwbFMJP42bixImrnHPNuZ5X6WURZjZQ0kJJ9znnHk5uft/MDnLObTazgyRtSfda59xcSXMlqbm52bW0tHhZat5aW1vll1rSmffWy9qvslMtLSeWuhR04/dxA/9i7KAQjBsUgnGDQvTHceNlFziTdLek9c65n3R76DFJlyR/v0TSo17VUI7CkTgtsAEAAIAMvJwBOkHSRZLWmllbctv3JM2R9KCZXSbpHUnne1hD2emMxrRnlacTewAAAEC/5dmZsnPuRUmZvozmC14dt9yFI3HtuydNEAAAAIB0OFMOmHA0puqBLIEDAAAA0iEABUxnJM4XoQIAAAAZcKYcMOEIM0AAAABAJgSggAlHYnSBAwAAADIgAAVMZzSuapbAAQAAAGlxphwg0Vhc0bhjCRwAAACQAQEoQMLRuCQpVMnbCgAAAKTDmXKAhCMxSWIGCAAAAMiAABQgnwUg3lYAAAAgHc6UAyQcSSyBYwYIAAAASI8AFCBdM0Ah2mADAAAAaRGAAqQz2jUDxNsKAAAApMOZcoB00gQBAAAAyIoAFCDhaNcSON5WAAAAIB3OlAOEJggAAABAdgSgAOF7gAAAAIDsCEAB8tkMEG8rAAAAkA5nygHSmbwGqJo22AAAAEBaBKAA4RogAAAAIDsCUIB89kWovK0AAABAOpwpB0g4GlPVgApVVFipSwEAAAB8iQAUIJ2RuEI0QAAAAAAy4mw5QMKRGNf/AAAAAFkQgAIkEYB4SwEAAIBMOFsOkM5onBbYAAAAQBYEoABhCRwAAACQHQEoQMKROC2wAQAAgCw4Ww6QcJQZIAAAACAbAlCAhCNxmiAAAAAAWXC2HCCdkZhCzAABAAAAGRGAAoQucAAAAEB2BKAA4XuAAAAAgOw4Ww6QcCSmEDNAAAAAQEYEoAAJR2mCAAAAAGTD2XJARGJxxeKONtgAAABAFgSggAhHYpLEDBAAAACQBWfLARGOxCWJGSAAAAAgCwJQQHRGkzNANEEAAAAAMiIABUTXDFCIJXAAAABARpwtB0TXNUC0wQYAAAAyIwAFRGoJHDNAAAAAQEacLQcETRAAAACA3AhAAfFZG2wCEAAAAJAJASggPpsB4i0FAAAAMuFsOSBogw0AAADkRgAKCNpgAwAAALlxthwQqWuAmAECAAAAMiIABUQ4ShMEAAAAIBcCUECklsBV8pYCAAAAmXC2HBCdkZiqKitUUWGlLgUAAADwLQJQQHRG46pm9gcAAADIijPmgAhHYlz/AwAAAORAAAqIcCRGC2wAAAAgB86YAyIcidMCGwAAAMiBABQQ4ShL4AAAAIBcCEABkbgGiLcTAAAAyIYz5oAIR+LMAAEAAAA5EIACojMaV4hrgAAAAICsCEAB0ckSOAAAACCnykwPmNmHOV5rkjY750YUtyQUIhyJMQMEAAAA5JBtyuBtSQfk+OnM9GIz+42ZbTGzdd22XW9mfzaztuTP6cX4IyCFo3FmgAAAAIAcsp0xT3POxbL8RCVNy/L6eySdlmb7T51zjcmfJ3eneHwm0QWOGSAAAAAgm2wBKGpmx/fcaGYnmNmhkuSc25Dpxc655yXlWkaHInDO0QYbAAAAyEO2M+bbJG1Psz0i6We7ccxvmNma5BK5fXdjP0iKxp3iTqrmGiAAAAAgK3POpX/AbJ1z7ugMj61xzjXk3LlZvaTHu/ZjZnWS/iLJSbpR0kHOuRkZXjtT0kxJqqurO3bBggU5/5i+0N7erpqamlKXsZPtUad/XPKppg2v0pRDB5a6HKThx3GD/oGxg0IwblAIxg0K4adxM3HixFXOueZcz8vYBU5SKMtje/a+JMk5937X72b2a0mPZ3nuXElzJam5udm1tLQUcsiia21tlV9q6fLBtk5pyRKN/Nthajm+vtTlIA0/jhv0D4wdFIJxg0IwblCI/jhusi2BW21mX+q50cwulfRKIQczs4O63T1H0rpMz0X+wpGYJJbAAQAAALlkmwG6UtIjZvZFSauS25ol1Uo6K9eOzWy+pBZJg81sk6QfSGoxs0YllsBtlPTVgitHSmc0EYBCNEEAAAAAssoYgJxzmyUdZ2Z/J6nrWqB/cc49nc+OnXMXpNl8d+9LRC7hSFySaIMNAAAA5JBtBkiS5JxbLGlxH9SCAqWWwBGAAAAAgKwyrpkys5dzvTif58B7ndHkDFAlS+AAAACAbLLNAI0ys9VZHjdJ+xe5HhSAGSAAAAAgP9kCUNrvAOohWqxCULiua4BoggAAAABkl60Jwh/7shAUjjbYAAAAQH6YMgiAcJQlcAAAAEA+CEAB8FkbbN5OAAAAIJu8zpjNbKiZTUz+HjKzQd6Whd7oZAYIAAAAyEvOAGRmMyQ9Jumu5Ka/kfSol0Whd1JNEGiDDQAAAGSVzxnzFZLGSfpEkpxzGyQd6GVR6J3OSExVlRUys1KXAgAAAPhaPgEo7Jzb0XXHzAYo8R1A8IlwJMaXoAIAAAB5yOes+SUz+7ak6uR1QA9IetzbstAb4Uic638AAACAPOQTgL4taZuk30uaJekZSdd5WRR6JxyNEYAAAACAPGT8IlQptdztN865SyT9sm9KQm+FIzFaYAMAAN+IRCLatGmTwuFwqUuBx/bee2+tX7++T49ZXV2toUOHauDAgQW9PmsAcs7FzOwgMxvonIsUdAR4rjPKEjgAAOAfmzZtUm1trerr62nSFHDbtm1TbW1tnx3POaetW7dq06ZNOvTQQwvaR9YAlPSmpBfM7FFJHd0O/vOCjoiiSzRBIAABAAB/CIfDhB94wsy0//7764MPPih4H/kEoA8kLZa0Z/IHPhOOxFVbnc9bCQAA0DcIP/DK7o6tnBeOOOdmp/vZraOiqMKRmELMAAEAAOxk0aJFMjP9/ve/7/VrL730Uj300EO7bF+5cqWuuOKKgmv60Y9+lHb7cccdp8bGRh1yyCE64IAD1NjYqMbGRm3cuLHgY3nt4Ycf1oYNG0pdRq/lDEBmttjMnu750xfFIT+Ja4BoggAAANDd/PnzNWHCBC1YsKBo+2xubtbPf174lSCZAtDy5cvV1tamG264QdOmTVNbW5va2tpUX19f8LGKIRqNZnyskACUbX99JZ+z5u9Lmp38uUmJdtivelkUeifRBY4ZIAAAgC7t7e166aWXdPfdd+8UgFpbW3XyySdr6tSpOvLII3Xttdfqvvvu09ixYzVq1Cj98Y9/TD13yZIlOvHEE3XkkUfq8ccfT73+jDPOkCR1dHRoxowZGjNmjJqamvToo49Kku655x6de+65Ou200zRs2DB9+9vfliRde+212r59uxobG/XFL34x77/lqaee0vHHH6/Ro0dr2rRp6uhIXJY/dOhQXXfddRo3bpzGjBmj1atXa/LkyTr88MP161//OvU3TJw4UWeffbZGjBihyy+/XM65nPu98cYbdcIJJ2jRokW68847NWbMGB1zzDE6//zztX37dr3wwgt68skn9d3vfjc1UzVhwgS1tbVJkt577z0dccQRkqS77rpL06dP1xlnnKEpU6ZIkubMmaOxY8eqoaFBN9xwQ2/e2t2WzxK45d1+fuucu0LS2D6oDXmiDTYAAMDOHnnkEZ122mk68sgjtd9++2n16tWpx1599VXddtttWrt2re69915t2LBBL7/8sr785S/r9ttvTz1v48aN+u1vf6snnnhCX/va13Zp633TTTfplFNO0YoVK/Tcc8/pmmuuSYWItrY2PfDAA1q7dq0eeOAB/elPf9KcOXO0xx57qK2tTffdd19ef8eWLVs0Z84cPfPMM1q9erUaGhp02223pR6vr6/XsmXLNG7cOF122WVatGiRli5dqtmzP7tiZfny5frZz36mtWvXav369Xr00Udz7nfQoEF66aWXdP755+v888/XihUr9Oqrr+rwww/XPffcoxNPPFGnn366fvzjH+c1U/W73/1O9957rxYvXqwnn3xS77zzTmrWa+nSpVq6dGle/x7FkPPKeTPbq9vdCknHSjrIs4rQa53ROF3gAACAL/3wv17T6+9+UtR9jvj8XvrB/xmZ9Tnz58/XlVdeKUmaPn265s+fr9GjR0uSxowZo4MOSpzOHn744Zo8ebIkadSoUXruuedS+5g6daoqKio0bNgwHXbYYbtcS/T000/rscce0y233CIp0f3unXfekSR94Qtf0N57752od8QIvf322zr44IN7/bcuXbpUr7/+usaPHy9J2rFjhyZMmJB6/Mwzz0zVHo1GNWjQIA0aNEgVFRVqb2+XJI0bNy4VUKZPn64XX3xRkrLud9q0aanf16xZo3/6p3/Sxx9/rG3btqVmwHpj8uTJ2nfffSUl/t2eeuopNTU1SUrM1m3YsCFVi9fyaR32miQnySRFJb0l6SteFoX8OecSTRCYAQIAAJAkbd26Vc8++6zWrVsnM1MsFpOZ6eabb5YkhUKh1HMrKipS9ysqKna6RqVnt7Ge951zWrhwoYYPH77T9uXLl+90jAEDBhR87YtzTqeddpruvffetI93r73n39V1zHR/R679Dho0KPX7xRdfrKeeekpHH3207rrrLi1btiztayorKxWPxyVpl9my7vtzzun73/++LrvssrT78Vo+Aeiwnl+Camb0XPaJSMwp7sQMEAAA8KVcMzVeeOihh3TxxRfrV7/6VWrbySefnJr5yNd//ud/6pJLLtFbb72lN998U8OHD9/p5P/UU0/V7bffrttvv11mpldeeSU1q5HJwIEDFYlENHDgwLxqGD9+vGbNmqU333xThx12mDo6OvTuu+9q2LBhef8dy5Yt0zvvvKMhQ4bowQcf1De/+U2NGzcu7/12dHToc5/7nCKRiO6//34ddthhkqTa2lpt27Yt9bz6+nqtWrVKo0ePTttBr8upp56qf/7nf9b06dM1aNAgbdq0SdXV1Ro8eHDef9PuyGfaYHmabS8XuxAUJhyNSRJNEAAAAJLmz5+vc845Z6dt//AP/6D777+/V/sZPny4Tj75ZE2ZMkV33nmnqqurd3p89uzZikQiamho0NFHH73TdTeZzJw5Uw0NDXk3Qairq9Pdd9+tadOm6ZhjjtH48eN73Xlt/PjxuvrqqzVq1CgdeeSROvPMM3u13xtuuEFjx47V3/3d32nEiBGp7RdccIFuvfXWVBOEa665RrfddpvGjx+vjz76KGM9p59+us477zyNGzdOo0aN0tSpU1PL9fqCdXWB2OUBswOVuNZngaSpSiyBk6S9JN3lnPvbPqlQUnNzs1u5cmVfHS6r1tZWtbS0lLqMlC3bwhp70zO68ayRuuj4+lKXgwz8Nm7QfzB2UAjGDQpRzHGzfv16HXXUUUXZF3bPkiVLdMcdd+iRRx7xZP/btm1TbW2tJ/vOJt0YM7NVzrnmXK/NtpTt7yXNkDRU0r91275NiZbY8IHOSGKdZYgZIAAAACCnjAHIOffvkv7dzKY65x7sw5rQC50sgQMAAEAGkyZN0qRJk0pdhq/kbGbgnHvQzE6VNFJSdbft6b/GFn0qnJwBqq6kCxwAAACQSz7fA/RvkvaRdJKkf5f0D5LS975DnwtHEjNALIEDAAAAcstn2mCCc+7/StrqnJst6TglrguCDzADBAAAAOQvn7Pmrm8xCpvZ55L36z2rCL3SNQPENUAAAABAbvkEoCfNbB9Jt0hqk7RRUuZvNkKf4nuAAAAAdmVmuuiii1L3o9GoDjjgAJ1xxhklrCq3lpYW9fz6l3POOUeNjY064ogjtPfee6uxsVGNjY1aunRpiarM7dlnn93pS2P9JOs1QGZWIekp59zHkv7TzB6XtIdz7sM+qQ45pZbADWQJHAAAQJdBgwZp3bp12r59u/bYYw8tXrxYQ4YMKUkt0WhUlZU5L73PaNGiRZIS39V0yy236PHHHy9WabslGo1mfOzZZ5/V4MGDNW7cuF7tb3f+nfKV9azZOReXdFu3+9sJP/5CG2wAAID0pkyZoieeeEKSNH/+fF1wwQWpxzo6OjRjxgyNGTNGTU1NevTRRyVJGzdu1IknnqjRo0dr9OjRqVmWzZs366STTlJjY6OOPvpovfDCC5Kkmpqa1D4feughXXrppZKkSy+9VFdddZUmTpyo73znOxmPt337dk2fPl0NDQ2aNm2atm/f3qu/ccWKFTr55JN17LHHasqUKXr//fclSRMmTNBVV12lE088USNGjNDKlSt1zjnnaNiwYbr++uslSW+88YZGjhypiy66SKNGjdLUqVNTx8+23+uuu04nnXSS7rjjDj3xxBM67rjj1NTUpMmTJ2vLli364x//qLvuukv/+q//mpqpuvDCC3f6Mtauf7clS5Zo0qRJmj59upqamiRJ8+bN09ixY9XY2Kivf/3risfjvfo3ySWfaYPFZnZWUY+KoumaAQrRBAEAAGAn06dP14IFCxQOh7VmzRodd9xxqcduuukmnXLKKVqxYoWee+45XXPNNero6NCBBx6oxYsXa/Xq1XrggQd0xRVXSJLuv/9+nXrqqWpra9Orr76qxsbGnMffsGGDlixZoltvvTXj8X75y19qzz331Jo1a3Tddddp1apVef99nZ2dmjVrlhYuXKhVq1bpwgsv1OzZs1OP77HHHnrhhRd02WWX6eyzz9add96ptWvXau7cufr4448lSa+//rouv/xyrV27VtXV1frVr36Vc7+ffPKJnn/+eV155ZUaP368li1bpldeeUXnnnuubr31Vh1++OH68pe/rGuuuUZtbW0aP3581r9j2bJluvnmm7V27VqtW7dOixYt0tKlS9XW1qZoNKoFCxbk/W+Sj3zmmL4haW8z65S0XZJJcs65/YpaCQpCEwQAAOBrT10rvbe2uPv83ChpypycT2toaNDGjRs1f/58nX766Ts99vTTT+uxxx7TLbfcIkkKh8N655139PnPf17f+MY31NbWpgEDBmjDhg2SpDFjxmjGjBmKRCI6++yz8wpA559/vgYMGJD1eM8//3wqZDU0NKihoSHvf4b169frtddeS33RaSwW09ChnzVrPvPMMyVJo0aN0qhRo1RXVydJqq+v16ZNm1RdXa1DDz00tUztwgsv1Ny5c9XS0pJ1v9OnT0/9vmnTJl122WV677331NnZqSOPPDLv+rscf/zxOuSQQyQlZoRWrFih5uZmSYkZsoMPPrjX+8wmnwA0uKhHRFF1dn0PEDNAAAAAuzjzzDP1rW99S62trdq6dWtqu3NOCxcu1PDhw3d6/vXXX6+6ujq9+uqrisfjqq6uliSddNJJev755/XEE0/ooosu0jXXXKOLL75YZpZ6bTgc3mlfgwYNynk8STvtozecc2poaEgtx+spFApJkioqKlK/d93vun6n57HNLOd+u/9dV199tWbPnq3TTz9dS5Ys0Zw56YNpZWVlailbLBbb6fqhnv9OM2bM0I033pjx795dOQOQcy5mZtMlHeac+5GZDZVUJyn/+Tl4JhyNK1RZUfD/cAAAADyVx0yNl2bMmKG9995bo0aNUmtra2r7qaeeqttvv1233367zEyvvPKKmpqa9Ne//lVDhw5VRUWF5s2bp1gs8X82v/322xoyZIi+8pWvqKOjQ6tXr9bFF1+suro6rV+/XsOHD9eiRYtUW1ubto5MxzvppJN03333aeLEiVq3bp3WrFmT9982YsQI/fnPf9bLL7+ssWPHaseOHfrDH/6gkSNH5r2Pt956SytWrNCYMWM0f/58TZgwoVf7/eSTTzRkyBA55zRv3rzU9traWm3bti11v76+XqtWrdK5556rRYsWpf5de5o0aZLOO+88zZo1S4MHD9bWrVvV0dGRmiEqhpzTBmZ2h6SJkrr6CH4q6c6iVYDdEo7EWP4GAACQwdChQzVr1qxdts+ePVuRSEQNDQ06+uijU9e4fP3rX9e8efM0btw4bdiwITU70draqsbGRjU1NWnhwoWpfc6ZM0dnnHGGTjnlFB100EEZ68h0vH/8x39Ue3u7GhoadPPNN2vs2LF5/22hUEgPPfSQrrrqKh1zzDFqamrS8uXL8369JI0cOVK//vWv1dDQoI6ODs2cObNX+/3ud7+rc845RyeffHJqiZ0knXXWWXrwwQfV1NSkpUuX6qtf/aoWL16ssWPHqq2tbacZqe5GjRqlH/zgB5o0aZIaGho0efLkVAOGYjHnXPYnmK12zo02s1ecc03Jba86544paiVZNDc3u5790EultbVVLS0tpS4j5TsPrVHrhi1a/r1JpS4FWfht3KD/YOygEIwbFKKY42b9+vU66qijirIveOeNN97Qeeedp7a2toL3sW3btoxos6maAAAU6ElEQVSzXl5KN8bMbJVzrjnXa/O5cCSS/D4gl9zx/pKK24sOBQtHmQECAAAA8pVPAPqFpIWSDjCzH0p6UdK/eFoV8haOxGiAAAAAgF474ogjdmv2p7/KpwnCf5jZKklda6zOd86t87Ys5CsciTMDBAAAAOQpnzbYkjRAUkSJZXBMN/hIOBJTdSUBCAAA+Itzji618ESuHga55NMF7jpJ8yV9XtJQSfeb2Xd366gomnA0rtBAMikAAPCP6upqbd26dbdPVIGenHPaunVr6vuZCpHPDNCFko51zn0qSWZ2kxLfAfTjgo+KoumMxFRdm76NIAAAQCkMHTpUmzZt0gcffFDqUuCxcDi8W2GkENXV1Ro6dGjBr88nAL3d43mVkt4s+Igoqs4o1wABAAB/GThwoA499NBSl4E+0NraqqamplKX0Sv5BKBPJb1mZv+jxDVAkyW9aGY/kSTn3FUe1occEtcAsQQOAAAAyEc+AeiJ5E+XZR7VggKEIzGuAQIAAADylE8b7Lv7ohAUJhyJ0wUOAAAAyFM+XeBOM7MVZrbFzD40s4/M7MO+KA7ZOecUjsa4BggAAADIUz5L4O6QNFXSWklxb8tBb+yIxeWcVM0SOAAAACAv+QSgTZLanHOEH5/pjCbeEmaAAAAAgPzkE4C+Lem/zKxVUmfXRufcz70qCvkJR2KSpBABCAAAAMhLPgHoh5IikvYRS+B8pTOSeDtCtMEGAAAA8pJPADrQOXes55Wg17pmgFgCBwAAAOQnn6mDZ8zsFM8rQa+FkzNAfBEqAAAAkJ98zpy/ImmJmbXTBttfwlFmgAAAAIDeyGcJ3GDPq0BBWAIHAAAA9E7OGSDnXEzS+ZK+k/z9IEmNXheG3LqaIPA9QAAAAEB+cp45m9kdkiZKuii56VNJd+bxut+Y2RYzW9dt235mttjM/pC83bfQwsESOAAAAKC38pk6GO+c+6qksCQ55z6UVJXH6+6RdFqPbddKesY5N0zSM8n7KFCYNtgAAABAr+RzDVDEzCokOUkys/2Vx/cBOeeeN7P6HpvPktSS/H2epFZJ38mv1NJ7c91y2e9+qpfbflX0fa/d62T9vvb43tXzlw5JzAABAAAA+coYgMys0jkXlfQLSQslHWBmP5Q0VYkvRy1EnXNusyQ55zab2YFZjj9T0kxJqqurU2tra4GHLJ6/vt2mseG1Umdx97ufPlHFx2/pFzqk1689Yp8KrV35O62vsOIWhaJqb2/3xRhG/8PYQSEYNygE4waF6I/jxpxz6R8wW+2cG538faSkSZJM0hLn3Lq0L9p1H/WSHnfOHZ28/7Fzbp9uj3/knMt5HVBzc7NbuXJlPof0XGtrq1paWoq70/umSts2S197obj7hW94Mm5QFhg7KATjBoVg3KAQfho3ZrbKOdec63nZlsClphScc69Jeq0Idb1vZgclZ38OkrSlCPvs/0K10tY/lLoKAAAAIPCyBaADzOyqTA86535SwPEek3SJpDnJ20cL2EfwhGqkzvZSVwEAAAAEXrYANEBSjbrNBPWGmc1XouHBYDPbJOkHSgSfB83sMknvKPH9QqiqkXYQgAAAAACvZQtAm51zNxS6Y+fcBRke+kKh+wysUK0U+VSKRaUB+TTmAwAAAFCIbF8gQ1uxvhKqTdwyCwQAAAB4KlsAYqamr1TVJG4JQAAAAICnMgYg59yHfVlIWQslAxCNEAAAAABPZZsBQl8J7ZW47dxW2joAAACAgCMA+UFqCRwBCAAAAPASAcgPWAIHAAAA9AkCkB90zQCxBA4AAADwFAHID7quAaILHAAAAOApApAfhJgBAgAAAPoCAcgPKkNSxUBmgAAAAACPEYD8IlTDDBAAAADgMQKQX4Rq6QIHAAAAeIwA5BdVtSyBAwAAADxGAPILlsABAAAAniMA+UUVAQgAAADwGgHIL0IsgQMAAAC8RgDyi1ANTRAAAAAAjxGA/KKqliVwAAAAgMcIQH7RtQTOuVJXAgAAAAQWAcgvQjWSnLSjo9SVAAAAAIFFAPKLqprELY0QAAAAAM8QgPwiVJu45TogAAAAwDMEIL8gAAEAAACeIwD5BUvgAAAAAM8RgPwilAxAfBcQAAAA4BkCkF9UsQQOAAAA8BoByC+6rgHaQQACAAAAvEIA8guWwAEAAACeIwD5xcA9JaugCQIAAADgIQKQX5glrgPiGiAAAADAMwQgPwnVsAQOAAAA8BAByE+qamiCAAAAAHiIAOQnoRqWwAEAAAAeIgD5SaiWJXAAAACAhwhAflJVQxc4AAAAwEMEID9hBggAAADwFAHIT6pqpM5PSl0FAAAAEFgEID8J1SaWwDlX6koAAACAQCIA+UmoRopHpWhnqSsBAAAAAokA5CdVtYlbGiEAAAAAniAA+UkoGYC4DggAAADwBAHIT0I1iVs6wQEAAACeIAD5SVUyALEEDgAAAPAEAchPUkvgtpW2DgAAACCgCEB+QgACAAAAPEUA8hOWwAEAAACeIgD5CU0QAAAAAE8RgPykawaIJXAAAACAJwhAflIxQBo4iCVwAAAAgEcIQH4TqmEGCAAAAPAIAchvqmqYAQIAAAA8QgDym1AtM0AAAACARwhAfhOqpQscAAAA4BECkN9U1Ug7mAECAAAAvEAA8huaIAAAAACeIQD5DUvgAAAAAM8QgPyGLnAAAACAZwhAfhOqlaJhKRYpdSUAAABA4BCA/KaqJnHLdUAAAABA0RGA/CZUm7hlGRwAAABQdJWlOKiZbZS0TVJMUtQ511yKOnwp1DUDRAACAAAAiq0kAShponPuLyU8vj9VMQMEAAAAeIUlcH7TtQSu85PS1gEAAAAEkDnn+v6gZm9J+kiSk/Qr59zcNM+ZKWmmJNXV1R27YMGCvi0yg/b2dtXU1Hi2/0HtGzVm5Sy9NuLb+uDAEzw7DvqW1+MGwcXYQSEYNygE4waF8NO4mThx4qp8Lq0p1RK4E5xz75rZgZIWm9nvnXPPd39CMhTNlaTm5mbX0tJSgjJ31draKk9r+ehtaaU0ctjfSE0eHgd9yvNxg8Bi7KAQjBsUgnGDQvTHcVOSJXDOuXeTt1skLZI0thR1+FJqCRxtsAEAAIBi6/MAZGaDzKy263dJkyWt6+s6fKuKLnAAAACAV0qxBK5O0iIz6zr+/c65/y5BHf5UWSUNCEk7mAECAAAAiq3PA5Bz7k1Jx/T1cfuVUA0zQAAAAIAHaIPtR1U1XAMEAAAAeIAA5EehvfgiVAAAAMADBCA/CjEDBAAAAHiBAORHVTXMAAEAAAAeIAD5UaiWGSAAAADAAwQgP6ILHAAAAOAJApAfVdWyBA4AAADwAAHIj0LJa4Di8VJXAgAAAAQKAciPQrWJW2aBAAAAgKIiAPlRVU3ilgAEAAAAFBUByI+6ZoBohAAAAAAUFQHIj7pmgGiFDQAAABQVAciPUtcAEYAAAACAYiIA+VGoawaIJXAAAABAMRGA/IgmCAAAAIAnCEB+FNorccs1QAAAAEBREYD8KEQTBAAAAMALBCA/qqyWbABL4AAAAIAiIwD5kVliFogZIAAAAKCoCEB+FdqLLnAAAABAkRGA/Kqqhu8BAgAAAIqMAORXoRpmgAAAAIAiIwD5VRXXAAEAAADFRgDyq1AtXeAAAACAIiMA+VWoliVwAAAAQJERgPyKJggAAABA0RGA/CpUm7gGyLlSVwIAAAAEBgHIr0I1kotLke2lrgQAAAAIDAKQX1XVJG5phAAAAAAUDQHIr0K1iVtaYQMAAABFQwDyKwIQAAAAUHQEIL9iCRwAAABQdAQgvwolAxDfBQQAAAAUDQHIr6pYAgcAAAAUGwHIr7quAeLLUAEAAICiIQD5FUvgAAAAgKIjAPnVwEGJW5ogAAAAAEVDAPKriopEJziuAQIAAACKhgDkZ6FaAhAAAABQRAQgP6uqYQkcAAAAUEQEID8LsQQOAAAAKCYCkJ+FaukCBwAAABQRAcjPqmpZAgcAAAAUEQHIz1gCBwAAABQVAcjPaIMNAAAAFBUByM9CLIEDAAAAiokA5GehGim2Q4ruKHUlAAAAQCAQgPysqjZxyywQAAAAUBQEID8L1SRuOz8pbR0AAABAQBCA/CyUnAHiu4AAAACAoiAA+VlVcgaIJXAAAABAURCA/Cw1A0QrbAAAAKAYCEB+RgACAAAAiooA5GcsgQMAAACKigDkZ6kucAQgAAAAoBgIQH5WxRI4AAAAoJgIQH42oFKq3EPaQQACAAAAioEA5HehGpbAAQAAAEVCAPK7qhqaIAAAAABFQgDyu1AN1wABAAAARVKSAGRmp5nZ/5rZG2Z2bSlq6DdCe7EEDgAAACiSPg9AZjZA0i8kTZE0QtIFZjair+voN6pqaIIAAAAAFEllCY45VtIbzrk3JcnMFkg6S9LrJajF/0I10vt/kTa+WOpKsBv2/nidtLEU/3NDf8fYQSEYNygE4waFqOr8sNQl9FopRvkQSX/qdn+TpONKUEf/UFMnffJn6Z6/L3Ul2A1NktRW6irQHzF2UAjGDQrBuEEh9j/ycknnlrqMXilFALI029wuTzKbKWmmJNXV1am1tdXjsvLT3t7ep7UMqDxJtcd8Xmn+idCPbN++XXvssUepy0A/xNhBIRg3KATjBoX4wO2rzT45T89XKQLQJkkHd7s/VNK7PZ/knJsraa4kNTc3u5aWlj4pLpfW1lb5pRb0H62trTqecYMCMHZQCMYNCsG4QSH647lxKbrArZA0zMwONbMqSdMlPVaCOgAAAACUmT6fAXLORc3sG5L+R9IASb9xzr3W13UAAAAAKD8lafXhnHtS0pOlODYAAACA8lWSL0IFAAAAgFIgAAEAAAAoGwQgAAAAAGWDAAQAAACgbBCAAAAAAJQNAhAAAACAskEAAgAAAFA2CEAAAAAAygYBCAAAAEDZIAABAAAAKBsEIAAAAABlgwAEAAAAoGyYc67UNeRkZh9IervUdSQNlvSXUheBfodxg0IxdlAIxg0KwbhBIfw0bv7GOXdArif1iwDkJ2a20jnXXOo60L8wblAoxg4KwbhBIRg3KER/HDcsgQMAAABQNghAAAAAAMoGAaj35pa6APRLjBsUirGDQjBuUAjGDQrR78YN1wABAAAAKBvMAAEAAAAoGwSgXjCz08zsf83sDTO7ttT1wJ/M7GAze87M1pvZa2Y2K7l9PzNbbGZ/SN7uW+pa4T9mNsDMXjGzx5P3DzWz5clx84CZVZW6RviLme1jZg+Z2e+TnzvH83mDXMzs/yX/G7XOzOabWTWfN+jJzH5jZlvMbF23bWk/Xyzh58nz5DVmNrp0lWdHAMqTmQ2Q9AtJUySNkHSBmY0obVXwqaikq51zR0kaJ+ny5Fi5VtIzzrlhkp5J3gd6miVpfbf7/yLpp8lx85Gky0pSFfzsNkn/7Zz7W0nHKDF++LxBRmY2RNIVkpqdc0dLGiBpuvi8wa7ukXRaj22ZPl+mSBqW/Jkp6Zd9VGOvEYDyN1bSG865N51zOyQtkHRWiWuCDznnNjvnVid/36bEycgQJcbLvOTT5kk6uzQVwq/MbKikv5d0V/K+STpF0kPJpzBusBMz20vSSZLuliTn3A7n3Mfi8wa5VUraw8wqJe0pabP4vEEPzrnnJX3YY3Omz5ezJP2HS1gmaR8zO6hvKu0dAlD+hkj6U7f7m5LbgIzMrF5Sk6Tlkuqcc5ulREiSdGDpKoNP/UzStyXFk/f3l/Sxcy6avM/nDno6TNIHkv49uXTyLjMbJD5vkIVz7s+SbpH0jhLB56+SVonPG+Qn0+dLvzlXJgDlz9Jso4UeMjKzGkkLJV3pnPuk1PXA38zsDElbnHOrum9O81Q+d9BdpaTRkn7pnGuS1CGWuyGH5DUbZ0k6VNLnJQ1SYvlST3zeoDf6zX+zCED52yTp4G73h0p6t0S1wOfMbKAS4ec+59zDyc3vd00FJ2+3lKo++NIJks40s41KLLE9RYkZoX2SS1QkPnewq02SNjnnlifvP6REIOLzBtlMkvSWc+4D51xE0sOSxovPG+Qn0+dLvzlXJgDlb4WkYckOKVVKXCz4WIlrgg8lr9u4W9J659xPuj30mKRLkr9fIunRvq4N/uWc+65zbqhzrl6Jz5dnnXNflPScpPOST2PcYCfOufck/cnMhic3fUHS6+LzBtm9I2mcme2Z/G9W17jh8wb5yPT58piki5Pd4MZJ+mvXUjm/4YtQe8HMTlfi/5EdIOk3zrmbSlwSfMjMJkh6QdJafXYtx/eUuA7oQUmHKPEfn/Odcz0vLARkZi2SvuWcO8PMDlNiRmg/Sa9IutA511nK+uAvZtaoROOMKklvSvqSEv8HJ583yMjMfihpmhKdS1+R9GUlrtfg8wYpZjZfUoukwZLel/QDSY8ozedLMkzfoUTXuE8lfck5t7IUdedCAAIAAABQNlgCBwAAAKBsEIAAAAAAlA0CEAAAAICyQQACAAAAUDYIQAAAAADKBgEIAAAAQNkgAAEAPGdm+5tZW/LnPTP7c7f7Sz043qVm9oGZ3ZXlOXskj7/DzAYXuwYAgD9VlroAAEDwOee2SmqUJDO7XlK7c+4Wjw/7gHPuG1lq2i6p0cw2elwHAMBHmAECAJSUmbUnb1vM7Ldm9qCZbTCzOWb2RTN72czWmtnhyecdYGYLzWxF8ueEPI4xMrmfNjNbY2bDvP67AAD+xAwQAMBPjpF0lKQPJb0p6S7n3FgzmyXpm5KulHSbpJ865140s0Mk/U/yNdl8TdJtzrn7zKxK0gDP/gIAgK8RgAAAfrLCObdZkszsj5KeTm5fK2li8vdJkkaYWddr9jKzWufctiz7/Z2k68xsqKSHnXN/KH7pAID+gCVwAAA/6ez2e7zb/bg++z/tKiQd75xrTP4MyRF+5Jy7X9KZkrZL+h8zO6XIdQMA+gkCEACgv3laUqq5gZk15nqBmR0m6U3n3M8lPSapwbvyAAB+RgACAPQ3V0hqTjYzeF2J63tymSZpnZm1SfpbSf/hZYEAAP8y51ypawAAoKjM7FJJzdnaYHd77sbkc//idV0AgNJjBggAEETbJU3J54tQJQ1U4hojAEAZYAYIAAAAQNlgBggAAABA2SAAAQAAACgbBCAAAAAAZYMABAAAAKBsEIAAAAAAlI3/D/tWKBFQ9ezJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dTdt = (T[ii]-Tm[ii])/tau\n",
    "Tm[ii+1] = Tm[ii] + dTdt * deltat\n",
    "ii += 1     # the step we just took\n",
    "plotT()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take multiple steps at a time and plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nSteps = int(n/20)+1\n",
    "for i in range(ii,ii+nSteps):\n",
    "    Tm[i+1] = Tm[i] + dTdt * deltat\n",
    "    dTdt = (T[i]-Tm[i])/tau\n",
    "ii += nSteps\n",
    "plotT()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now take all the rest of the steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(ii,n-1):\n",
    "    dTdt = (T[i]-Tm[i])/tau\n",
    "    Tm[i+1] = Tm[i] + dTdt * deltat\n",
    "ii = n-1\n",
    "plotT()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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
}