DRC_CO_oxidation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import autograd.numpy as np\n",
    "from autograd.scipy.integrate import odeint\n",
    "from autograd import elementwise_grad, grad, jacobian\n",
    "from autograd.builtins import tuple\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oxidation of $CO$ to form $O_2$ using $Pt(111)$ catalyst at 300 K. <br>\n",
    "The pressure for $CO$ is 10 bar and the pressure for $O_2$ is 1 bar. The partial pressure of $CO_2$ is considered to be 0. \n",
    "\n",
    "Overall reaction: <br>\n",
    "$CO + O_2 \\rightarrow CO_2$\n",
    "\n",
    "The reaction proceeds in the following way:  <br>\n",
    "R1:$O_2 + 2* \\rightarrow 2O*$ <br>\n",
    "R2:$CO + * \\rightarrow CO*$ <br>\n",
    "R3:$O* + CO* \\rightarrow CO_2 + 2*$<br>\n",
    "\n",
    "Energies (all in eV) obtained from CATAPP: <br>\n",
    "$G_{TS_1} = 0$ <br>\n",
    "$G_{TS_2} = -0.62$ <br>\n",
    "$G_{TS_3} = -0.72$ <br>\n",
    "$G_{O*} = -1.5/2 = -0.72$ <br>\n",
    "$G_{CO*} = -1.2$ <br>\n",
    "$G_{CO_2} = -0.96$ <br>\n",
    "\n",
    "The mole balances used are: <br> \n",
    "$\\frac{\\theta_{O*}}{dt} = k_1P_{O_2}{\\theta_{*}}^2 - k_{-1}{\\theta_{O*}}^2 - k_{3}\\theta_{O*}\\theta_{CO*} + k_{-3}P_{CO_2}{\\theta_{*}}^2$\n",
    "\n",
    "$\\frac{\\theta_{CO*}}{dt} = k_2P_{CO*}\\theta_{*} - k_{-2}\\theta_{CO*} - k_{3}\\theta_{O*}\\theta_{CO*} + k_{-3}P_{CO_2}{\\theta_{*}}^2$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Iteration 0\n",
      "x0 = 0.24\n",
      "f(0.24) = -0.09337600000000013\n",
      "df(0.24)/dx = 4.612799999999999\n",
      "\n",
      "Iteration 1\n",
      "x1 = 0.2602428026361429\n",
      "f(0.2602428026361429) = 0.001532643252529553\n",
      "df(0.2602428026361429)/dx = 4.764635764788601\n",
      "\n",
      "Iteration 2\n",
      "x2 = 0.2599211320346132\n",
      "f(0.2599211320346132) = 3.911661545785705e-07\n",
      "df(0.2599211320346132)/dx = 4.762203776842144\n",
      "\n",
      "Iteration 3\n",
      "x3 = 0.2599210498948786\n",
      "f(0.2599210498948786) = 2.5757174171303632e-14\n",
      "df(0.2599210498948786)/dx = 4.76220315590464\n",
      "\n",
      "Iteration 4\n",
      "x4 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 5\n",
      "x5 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 6\n",
      "x6 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 7\n",
      "x7 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 8\n",
      "x8 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 9\n",
      "x9 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 10\n",
      "x10 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 11\n",
      "x11 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 12\n",
      "x12 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 13\n",
      "x13 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 14\n",
      "x14 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 15\n",
      "x15 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 16\n",
      "x16 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 17\n",
      "x17 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 18\n",
      "x18 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 19\n",
      "x19 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 20\n",
      "x20 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 21\n",
      "x21 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 22\n",
      "x22 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 23\n",
      "x23 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 24\n",
      "x24 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 25\n",
      "x25 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 26\n",
      "x26 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 27\n",
      "x27 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 28\n",
      "x28 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 29\n",
      "x29 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 30\n",
      "x30 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 31\n",
      "x31 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 32\n",
      "x32 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 33\n",
      "x33 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 34\n",
      "x34 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 35\n",
      "x35 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 36\n",
      "x36 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 37\n",
      "x37 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 38\n",
      "x38 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 39\n",
      "x39 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 40\n",
      "x40 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 41\n",
      "x41 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 42\n",
      "x42 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 43\n",
      "x43 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 44\n",
      "x44 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 45\n",
      "x45 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 46\n",
      "x46 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 47\n",
      "x47 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 48\n",
      "x48 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 49\n",
      "x49 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 50\n",
      "x50 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 51\n",
      "x51 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 52\n",
      "x52 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 53\n",
      "x53 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 54\n",
      "x54 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 55\n",
      "x55 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 56\n",
      "x56 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 57\n",
      "x57 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 58\n",
      "x58 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 59\n",
      "x59 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 60\n",
      "x60 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 61\n",
      "x61 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 62\n",
      "x62 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 63\n",
      "x63 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 64\n",
      "x64 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 65\n",
      "x65 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 66\n",
      "x66 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 67\n",
      "x67 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 68\n",
      "x68 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 69\n",
      "x69 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 70\n",
      "x70 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 71\n",
      "x71 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 72\n",
      "x72 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 73\n",
      "x73 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 74\n",
      "x74 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 75\n",
      "x75 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 76\n",
      "x76 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 77\n",
      "x77 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 78\n",
      "x78 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 79\n",
      "x79 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 80\n",
      "x80 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 81\n",
      "x81 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 82\n",
      "x82 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 83\n",
      "x83 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "x86 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "x87 = 0.2599210498948732\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x212 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "x268 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "x361 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x362 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x363 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x364 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x365 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x366 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x367 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x368 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x369 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x370 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x371 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x372 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x373 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x374 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x375 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x376 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x377 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x378 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x379 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x380 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x381 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x382 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x383 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x384 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x385 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x386 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x387 = 0.2599210498948732\n",
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      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x388 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 389\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x389 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x390 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x391 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x392 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x393 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "x394 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "x395 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "x396 = 0.2599210498948732\n",
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      "x397 = 0.2599210498948732\n",
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      "x398 = 0.2599210498948732\n",
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      "x399 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x400 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "x402 = 0.2599210498948732\n",
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      "x403 = 0.2599210498948732\n",
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      "\n",
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      "x404 = 0.2599210498948732\n",
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      "\n",
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      "x405 = 0.2599210498948732\n",
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      "x406 = 0.2599210498948732\n",
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      "x408 = 0.2599210498948732\n",
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      "\n",
      "Iteration 453\n",
      "x453 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 454\n",
      "x454 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 455\n",
      "x455 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 456\n",
      "x456 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 457\n",
      "x457 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 458\n",
      "x458 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 459\n",
      "x459 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 460\n",
      "x460 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 461\n",
      "x461 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 462\n",
      "x462 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 463\n",
      "x463 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 464\n",
      "x464 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 465\n",
      "x465 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 466\n",
      "x466 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 467\n",
      "x467 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 468\n",
      "x468 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 469\n",
      "x469 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 470\n",
      "x470 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 471\n",
      "x471 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 472\n",
      "x472 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 473\n",
      "x473 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 474\n",
      "x474 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 475\n",
      "x475 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x476 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 477\n",
      "x477 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x478 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x479 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x480 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x481 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x482 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x483 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x484 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x485 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 486\n",
      "x486 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x487 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x488 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x489 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x490 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x491 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x492 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x493 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x494 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x495 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x497 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "x499 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x500 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x503 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x509 = 0.2599210498948732\n",
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      "\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x520 = 0.2599210498948732\n",
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      "\n",
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      "x521 = 0.2599210498948732\n",
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      "\n",
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      "\n",
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      "x523 = 0.2599210498948732\n",
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      "\n",
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      "x524 = 0.2599210498948732\n",
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      "\n",
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      "x525 = 0.2599210498948732\n",
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      "\n",
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      "x526 = 0.2599210498948732\n",
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      "\n",
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      "x527 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x528 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x529 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x530 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x531 = 0.2599210498948732\n",
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      "\n",
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      "x532 = 0.2599210498948732\n",
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      "\n",
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      "x533 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x534 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x535 = 0.2599210498948732\n",
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      "\n",
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      "x536 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x537 = 0.2599210498948732\n",
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      "\n",
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      "x538 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x539 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x540 = 0.2599210498948732\n",
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      "\n",
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      "x542 = 0.2599210498948732\n",
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      "\n",
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      "x544 = 0.2599210498948732\n",
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      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x546 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 547\n",
      "x547 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x548 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 549\n",
      "x549 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 550\n",
      "x550 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 551\n",
      "x551 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 552\n",
      "x552 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x553 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x554 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x555 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "Iteration 556\n",
      "x556 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "x557 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 558\n",
      "x558 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
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      "Iteration 559\n",
      "x559 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 560\n",
      "x560 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 561\n",
      "x561 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 562\n",
      "x562 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 563\n",
      "x563 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 564\n",
      "x564 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x565 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 566\n",
      "x566 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x567 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x568 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x569 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x570 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 571\n",
      "x571 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 572\n",
      "x572 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 573\n",
      "x573 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 574\n",
      "x574 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x575 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 576\n",
      "x576 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x577 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 578\n",
      "x578 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x579 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x580 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x581 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x582 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x583 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x584 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x585 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x586 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x587 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "x588 = 0.2599210498948732\n",
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      "\n",
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      "x589 = 0.2599210498948732\n",
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      "x590 = 0.2599210498948732\n",
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      "\n",
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      "x591 = 0.2599210498948732\n",
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      "x592 = 0.2599210498948732\n",
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      "\n",
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      "x593 = 0.2599210498948732\n",
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      "x597 = 0.2599210498948732\n",
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      "x598 = 0.2599210498948732\n",
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      "x607 = 0.2599210498948732\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "\n",
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      "\n",
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      "Iteration 637\n",
      "x637 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 638\n",
      "x638 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 639\n",
      "x639 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 640\n",
      "x640 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 641\n",
      "x641 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 642\n",
      "x642 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 643\n",
      "x643 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 644\n",
      "x644 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 645\n",
      "x645 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 646\n",
      "x646 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 647\n",
      "x647 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 648\n",
      "x648 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 649\n",
      "x649 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 650\n",
      "x650 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 651\n",
      "x651 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 652\n",
      "x652 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 653\n",
      "x653 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 654\n",
      "x654 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x655 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 656\n",
      "x656 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 657\n",
      "x657 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 658\n",
      "x658 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 659\n",
      "x659 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 660\n",
      "x660 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 661\n",
      "x661 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 662\n",
      "x662 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 663\n",
      "x663 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x664 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 665\n",
      "x665 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x666 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x667 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x668 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x669 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x670 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x671 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x672 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x673 = 0.2599210498948732\n",
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      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x674 = 0.2599210498948732\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x676 = 0.2599210498948732\n",
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      "\n",
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      "x678 = 0.2599210498948732\n",
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      "\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
      "Iteration 729\n",
      "x729 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 730\n",
      "x730 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 731\n",
      "x731 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 732\n",
      "x732 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 733\n",
      "x733 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 734\n",
      "x734 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 735\n",
      "x735 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 736\n",
      "x736 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 737\n",
      "x737 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 738\n",
      "x738 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 739\n",
      "x739 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 740\n",
      "x740 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 741\n",
      "x741 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 742\n",
      "x742 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 743\n",
      "x743 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 744\n",
      "x744 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 745\n",
      "x745 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 746\n",
      "x746 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 747\n",
      "x747 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 748\n",
      "x748 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 749\n",
      "x749 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 750\n",
      "x750 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 751\n",
      "x751 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 752\n",
      "x752 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Iteration 753\n",
      "x753 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 754\n",
      "x754 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 755\n",
      "x755 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 756\n",
      "x756 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 757\n",
      "x757 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 758\n",
      "x758 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 759\n",
      "x759 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 760\n",
      "x760 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 761\n",
      "x761 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 762\n",
      "x762 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 763\n",
      "x763 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 764\n",
      "x764 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 765\n",
      "x765 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 766\n",
      "x766 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 767\n",
      "x767 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 768\n",
      "x768 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 769\n",
      "x769 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 770\n",
      "x770 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 771\n",
      "x771 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 772\n",
      "x772 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 773\n",
      "x773 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 774\n",
      "x774 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 775\n",
      "x775 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 776\n",
      "x776 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x777 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 778\n",
      "x778 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 779\n",
      "x779 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 780\n",
      "x780 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 781\n",
      "x781 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x782 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x783 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x784 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x785 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x786 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
      "Iteration 787\n",
      "x787 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x788 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x789 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x790 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x791 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x792 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x793 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x794 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x796 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x797 = 0.2599210498948732\n",
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      "\n",
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      "x798 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x799 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x800 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
      "Iteration 801\n",
      "x801 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
      "Iteration 803\n",
      "x803 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x804 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x805 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x806 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 807\n",
      "x807 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x808 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
      "Iteration 820\n",
      "x820 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 821\n",
      "x821 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 822\n",
      "x822 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 823\n",
      "x823 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 824\n",
      "x824 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 825\n",
      "x825 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 826\n",
      "x826 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 827\n",
      "x827 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 828\n",
      "x828 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 829\n",
      "x829 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 830\n",
      "x830 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 831\n",
      "x831 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 832\n",
      "x832 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 833\n",
      "x833 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 834\n",
      "x834 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 835\n",
      "x835 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 836\n",
      "x836 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 837\n",
      "x837 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 838\n",
      "x838 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 839\n",
      "x839 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 840\n",
      "x840 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 841\n",
      "x841 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 842\n",
      "x842 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 843\n",
      "x843 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 844\n",
      "x844 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 845\n",
      "x845 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 846\n",
      "x846 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 847\n",
      "x847 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 848\n",
      "x848 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 849\n",
      "x849 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 850\n",
      "x850 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 851\n",
      "x851 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 852\n",
      "x852 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 853\n",
      "x853 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 854\n",
      "x854 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 855\n",
      "x855 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 856\n",
      "x856 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 857\n",
      "x857 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 858\n",
      "x858 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 859\n",
      "x859 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 860\n",
      "x860 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x861 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 862\n",
      "x862 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x863 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x864 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x865 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x866 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x867 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x868 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x869 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x870 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x872 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x873 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x874 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x875 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x877 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x878 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x879 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x880 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x881 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x882 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x883 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x884 = 0.2599210498948732\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "\n",
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      "x887 = 0.2599210498948732\n",
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      "\n",
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      "x888 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
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      "x889 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x890 = 0.2599210498948732\n",
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      "\n",
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      "x891 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x892 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x893 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "x894 = 0.2599210498948732\n",
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      "\n",
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      "\n",
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      "x896 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "\n",
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      "x898 = 0.2599210498948732\n",
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      "\n",
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      "\n",
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      "x900 = 0.2599210498948732\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "f(0.2599210498948732) = 0.0\n",
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      "\n",
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      "\n",
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      "\n",
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      "x908 = 0.2599210498948732\n",
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      "\n",
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      "\n",
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      "\n",
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      "x911 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 912\n",
      "x912 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 913\n",
      "x913 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 914\n",
      "x914 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 915\n",
      "x915 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 916\n",
      "x916 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 917\n",
      "x917 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 918\n",
      "x918 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 919\n",
      "x919 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 920\n",
      "x920 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 921\n",
      "x921 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 922\n",
      "x922 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 923\n",
      "x923 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 924\n",
      "x924 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 925\n",
      "x925 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 926\n",
      "x926 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 927\n",
      "x927 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 928\n",
      "x928 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 929\n",
      "x929 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 930\n",
      "x930 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 931\n",
      "x931 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 932\n",
      "x932 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 933\n",
      "x933 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 934\n",
      "x934 = 0.2599210498948732\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 935\n",
      "x935 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 936\n",
      "x936 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 937\n",
      "x937 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 938\n",
      "x938 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 939\n",
      "x939 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 940\n",
      "x940 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 941\n",
      "x941 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 942\n",
      "x942 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 943\n",
      "x943 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 944\n",
      "x944 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 945\n",
      "x945 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 946\n",
      "x946 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 947\n",
      "x947 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 948\n",
      "x948 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 949\n",
      "x949 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 950\n",
      "x950 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 951\n",
      "x951 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 952\n",
      "x952 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 953\n",
      "x953 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 954\n",
      "x954 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 955\n",
      "x955 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 956\n",
      "x956 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 957\n",
      "x957 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 958\n",
      "x958 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 959\n",
      "x959 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 960\n",
      "x960 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 961\n",
      "x961 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 962\n",
      "x962 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 963\n",
      "x963 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 964\n",
      "x964 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 965\n",
      "x965 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 966\n",
      "x966 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 967\n",
      "x967 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 968\n",
      "x968 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 969\n",
      "x969 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 970\n",
      "x970 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 971\n",
      "x971 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 972\n",
      "x972 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 973\n",
      "x973 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 974\n",
      "x974 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 975\n",
      "x975 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 976\n",
      "x976 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 977\n",
      "x977 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 978\n",
      "x978 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 979\n",
      "x979 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 980\n",
      "x980 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 981\n",
      "x981 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 982\n",
      "x982 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 983\n",
      "x983 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 984\n",
      "x984 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 985\n",
      "x985 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 986\n",
      "x986 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 987\n",
      "x987 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 988\n",
      "x988 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 989\n",
      "x989 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 990\n",
      "x990 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 991\n",
      "x991 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 992\n",
      "x992 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 993\n",
      "x993 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 994\n",
      "x994 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 995\n",
      "x995 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 996\n",
      "x996 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 997\n",
      "x997 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 998\n",
      "x998 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n",
      "\n",
      "Iteration 999\n",
      "x999 = 0.2599210498948732\n",
      "f(0.2599210498948732) = 0.0\n",
      "df(0.2599210498948732)/dx = 4.762203155904598\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def y(x):\n",
    "    return x**3 + 3*x + 3*x**2 - 1\n",
    "\n",
    "xg = 0.24\n",
    "for i in range(1000):\n",
    "    print()\n",
    "    print('Iteration',i)\n",
    "    print(f'x{i} = {xg}')\n",
    "    print(f'f({xg}) = {y(xg)}')\n",
    "    y1 = grad(y)\n",
    "    print(f'df({xg})/dx = {y1(xg)}')\n",
    "    xg = xg - (y(xg)/y1(xg))\n",
    "    \n",
    "          \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x18ca63dde48>"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Ar\n",
    "Tr = 1.64\n",
    "Pc = 48.64\n",
    "Vc = 0.07530\n",
    "\n",
    "V = np.array([40.506, 10.106, 1.999, 0.9857, 0.4795, 0.3114, 0.2279, 0.1785, 0.1462, 0.1076, 0.08630, 0.07348, 0.06208, 0.05626,0.05219, 0.04919, 0.04687, 0.04348, 0.04108])\n",
    "P = np.array([0.5, 2, 10, 20, 40, 60, 80, 100, 120, 160, 200, 240, 300, 350, 400, 450, 500, 600, 700])\n",
    "\n",
    "Vr = V/Vc\n",
    "Pr = P/Pc\n",
    "\n",
    "# Z1 = Vr/(Vr - 0.25992) - 1.2824/((Tr**1.5)*(Vr + 0.25992))\n",
    "Z1 = Vr/(Vr - 1/3) - 9/(8*Vr*Tr)\n",
    "\n",
    "plt.plot(Vr, Z1, label = 'Argon')\n",
    "plt.title('Compressibility vs Vr for Argon')\n",
    "plt.xlabel('Vr')\n",
    "plt.ylabel('Z')\n",
    "plt.legend()\n",
    "# plt.xlim(-5,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.639344262295082"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Ethane\n",
    "Tr = 1.64\n",
    "Pc = 48.714\n",
    "Vc = 0.1480\n",
    "\n",
    "V = np.array([83.076, 20.723, 4.105, 2.028, 0.9907, 0.6461, 0.4750, 0.3734, 0.3068, 0.2265, 0.1819, 0.1548, 0.1303, 0.1175, 0.1085,0.1019, 0.09676, 0.08937, 0.8421])\n",
    "\n",
    "# P = np.array([0.5, 2, 10, 20, 40, 60, 80, 100, 120, 160, 200, 240, 300, 350, 400, 450, 500, 600, 700])\n",
    "print(len(V))\n",
    "Vr = V/Vc\n",
    "Pr = P/Pc\n",
    "\n",
    "Z2 = Vr/(Vr - 1/3) - 9/(8*Vr*Tr)\n",
    "\n",
    "plt.plot(Vr, Z2,'o',label = 'Argon')\n",
    "plt.plot(Vr, Z1,label = 'Ethane')\n",
    "plt.xlabel('Vr')\n",
    "plt.title('Compressibility vs Vr')\n",
    "plt.ylabel('Z')\n",
    "plt.legend()\n",
    "247/150.9\n",
    "500/305"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.75534603e+09 -1.56087393e+12  5.55111512e-17]\n",
      "[0.22307545 0.64088259 0.13604195]\n",
      "6252641110775.731 6249633587451.924 6251087043055.529 6247328799290.3 6245951342781.14 6248430983215.014\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "27.023253623991675"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import fsolve\n",
    "\n",
    "kb = 1.381e-23\n",
    "h = 6.626e-34\n",
    "R = 8.314\n",
    "\n",
    "def fk(Gi):\n",
    "    kth = kb * T / h\n",
    "    rt = R * T\n",
    "    Gts1, Gts2, Gts3, Gas, Gbs, Gab = Gi\n",
    "    k1 = kth * np.exp(-(Gts1 - 0) / rt)\n",
    "    k_1 = kth * np.exp(-(Gts1 -Gas) / rt)\n",
    "    k2 = kth * np.exp(-(Gts2 - 0) / rt)\n",
    "    k_2 = kth * np.exp(-(Gts2 - 2*Gbs) / rt)\n",
    "    k3 = kth * np.exp(-(Gts3 - (Gas + Gbs)) / rt)\n",
    "    k_3 = kth * np.exp(-(Gts3 - Gab) / rt)\n",
    "#     print(0,-Gbs, Gts2,Gts2 - 2*Gas, (Gts3 - (Gas + Gbs), (Gts3 - Gab)))\n",
    "    return np.array([k1, k_1, k2, k_2, k3, k_3])\n",
    "\n",
    "def rsys(theta, Gi):\n",
    "    \"Steady state mole balance, returns 0 at the steady state coverages.\"\n",
    "    thetastar, thetaa, thetab = theta\n",
    "\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(Gi)\n",
    "\n",
    "    # balance on A*\n",
    "    z1 = (k1 * pa * thetastar**2 - k_1 * thetaa**2\n",
    "          - k3 * thetaa * thetab + k_3 * pab * thetastar**2)\n",
    "    # balance on B*\n",
    "    z2 = (k2 * pb * thetastar - k_2 * thetab\n",
    "          - k3 * thetaa * thetab + k_3 * pab * thetastar**2)\n",
    "    # site balance\n",
    "    z3 = 1 - thetastar - thetaa - thetab\n",
    "    return np.array([z1, z2, z3])\n",
    "\n",
    "T = 300.0\n",
    "\n",
    "\n",
    "# pressures of each species, consistent with the earlier limiting conditions.\n",
    "pb = 1 # bar\n",
    "pa = 10 # bar\n",
    "pab = 0.0\n",
    "\n",
    "#             Gts1, Gts2, Gts3, Gas, Gbs, Gabs\n",
    "# G = np.array([])\n",
    "G = np.array([0, 0.62, 0.72, -1.2, -0.75,-0.96])\n",
    "k1, k_1, k2, k_2, k3, k_3= fk(G)\n",
    "\n",
    "print(rsys([0.2,0.5,0.3], G))\n",
    "\n",
    "# Solve for the thetas\n",
    "[thetas, thetaa, thetab] = fsolve(rsys,\n",
    "                                [0.2,0.5,0.3], # initial guess\n",
    "                                args=(G,))\n",
    "\n",
    "# Make sure these are all positive.\n",
    "print(np.array([thetas, thetaa, thetab]))\n",
    "\n",
    "# Now we can compute the rate from any one of these expressions\n",
    "# r = k2 * pb * thetas - k_2 * thetab\n",
    "r = k3 * thetas * thetab\n",
    "print(k1, k_1, k2, k_2, k3, k_3)\n",
    "\n",
    "def lnrate_s(Gi):\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(Gi)\n",
    "    [thetas, thetaa, thetab] = fsolve(rsys,[0.3, 0.5, 0.2], # initial guess\n",
    "                                args=(Gi,))\n",
    "    r = k2 * pb * thetas - k_2 * thetab\n",
    "    ret = np.log(r)\n",
    "    return ret\n",
    "\n",
    "char = ['GTS1', 'GTS2', 'GTS3', 'GAS', 'GBS', 'GABS']\n",
    "lnrate_s(G)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numdifftools as nd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dlndG_s = nd.Gradient(lnrate_s)\n",
    "dlndGi_s = dlndG_s(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GTS1: -0.0379\n",
      "GTS2: 0.3158\n",
      "GTS3: 0.7221\n",
      "GAS: -0.9007\n",
      "GBS: 0.2638\n",
      "GABS: -0.0000\n"
     ]
    }
   ],
   "source": [
    "DRCi = -dlndGi_s.T * R * T\n",
    "for i in range(len(char)):\n",
    "    print(f'{char[i]}: {DRCi[i]:1.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.27048146e+09 3.43955100e+12]\n",
      "[0.22307074 0.13604192 0.64088734]\n",
      "27.023260768680235\n"
     ]
    }
   ],
   "source": [
    "## unicorn\n",
    "from scipy.optimize import fsolve\n",
    "\n",
    "kb = 1.381e-23\n",
    "h = 6.626e-34\n",
    "R = 8.314\n",
    "\n",
    "def fk(Gi):\n",
    "    kth = kb * T / h\n",
    "    rt = R * T\n",
    "    Gts1, Gts2, Gts3, Gas, Gbs, Gab = Gi\n",
    "    k1 = kth * np.exp(-(Gts1 - 0) / rt)\n",
    "    k_1 = kth * np.exp(-(Gts1 -Gas) / rt)\n",
    "    k2 = kth * np.exp(-(Gts2 - 0) / rt)\n",
    "    k_2 = kth * np.exp(-(Gts2 - 2*Gbs) / rt)\n",
    "    k3 = kth * np.exp(-(Gts3 - (Gas + Gbs)) / rt)\n",
    "    k_3 = kth * np.exp(-(Gts3 - Gab) / rt)\n",
    "#     print((Gts1 - 0),(Gts1 -Gas),(Gts2 - 0),(Gts2 - 2*Gbs),(Gts3 - (Gas + Gbs)),(Gts3 - Gab))\n",
    "    return np.array([k1, k_1, k2, k_2, k3, k_3])\n",
    "\n",
    "def rsys_s(theta, Gi):\n",
    "    \"Steady state mole balance, returns 0 at the steady state coverages.\"\n",
    "    thetaa, thetab = theta\n",
    "\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(Gi)\n",
    "#     print(k1, k_1, k2, k_2, k3, k_3)\n",
    "#     print(k1)\n",
    "#     print(k_1)\n",
    "#     print( k2)\n",
    "#     print(k_2)\n",
    "#     print(k3)\n",
    "#     print(k_3)\n",
    "\n",
    "#     print(Gi)\n",
    "\n",
    "    thetastar  = 1 - thetaa - thetab\n",
    "    # balance on A*\n",
    "    z1 = (k1 * pa * thetastar - k_1 * thetaa\n",
    "          - k3 * thetaa * thetab + k_3 * pab * thetastar**2)\n",
    "#     z1 = (k1 * pa * thetastar - k_1 * thetaa \n",
    "#          - k3* thetaa * thetab)\n",
    "#     print('Z1:',pa * thetastar**2, thetaa**2,thetaa * thetab, pab * thetastar**2)\n",
    "    # balance on B*\n",
    "    z2 = (k2 * pb * thetastar**2 - k_2 * thetab**2\n",
    "          - k3 * thetaa * thetab + k_3 * pab * thetastar**2)\n",
    "#     z2 = (k2 * pb * thetastar**2 - k3 * thetaa * thetab)\n",
    "#     print('Z2',pb * thetastar , thetab**2, thetaa * thetab, pab * thetastar**2)\n",
    "    return np.array([z1, z2])\n",
    "\n",
    "T = 300\n",
    "\n",
    "\n",
    "# pressures of each species, consistent with the earlier limiting conditions.\n",
    "pa = 1 # bar\n",
    "pb = 10 # bar\n",
    "pab = 0.0\n",
    "\n",
    "#             Gts1, Gts2, Gts3, Gas, Gbs, Gabs\n",
    "G = np.array([0, 0.62, 0.72, -1.2, -0.75,-0.96])\n",
    "k1, k_1, k2, k_2, k3, k_3= fk(G)\n",
    "\n",
    "print(rsys_s([0.2,0.5], G))\n",
    "\n",
    "# Solve for the thetas\n",
    "[thetaa, thetab] = fsolve(rsys_s,\n",
    "                                [0.2, 0.5], # initial guess\n",
    "                                args=(G,))\n",
    "\n",
    "thetas = 1 - thetaa - thetab\n",
    "\n",
    "# Make sure these are all positive.\n",
    "print(np.array([thetas, thetaa, thetab]))\n",
    "\n",
    "# Now we can compute the rate from any one of these expressions\n",
    "r = k2 * pb * thetas - k_2 * thetab\n",
    "# r = k3 * thetas * thetab\n",
    "# print(k1)\n",
    "# print(k_1)\n",
    "# print( k2)\n",
    "# print(k_2)\n",
    "# print(k3)\n",
    "# print(k_3)\n",
    "\n",
    "def lnrate_s2(Gi):\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(Gi)\n",
    "    [thetaa, thetab] = fsolve(rsys_s,[0.2, 0.5], # initial guess\n",
    "                                args=(Gi,))\n",
    "    thetas = 1 - thetaa - thetab\n",
    "#     r = k2 * pb * thetas**2 - k_2 * thetab**2\n",
    "#     r = k1 * pa * thetas - k_1 *thetaa\n",
    "    r = k3 * thetaa * thetab\n",
    "    ret = np.log(r)\n",
    "    return ret\n",
    "\n",
    "print(lnrate_s2(G))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "dlndG_s = nd.Gradient(lnrate_s2)\n",
    "dlndGi_s = dlndG_s(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GTS1: 0.3158\n",
      "GTS2: -0.0379\n",
      "GTS3: 0.7221\n",
      "GAS: -0.2291\n",
      "GBS: -1.0794\n",
      "GABS: -0.0000\n"
     ]
    }
   ],
   "source": [
    "DRCi = -dlndGi_s.T * R * T\n",
    "for i in range(len(char)):\n",
    "    print(f'{char[i]}: {DRCi[i]:1.4f}')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GTS1 0.3158\n",
      "GTS2 -0.0379\n",
      "GTS3 0.7221\n",
      "GAS -0.2291\n",
      "GBS -1.0794\n",
      "GABS -0.0000\n"
     ]
    }
   ],
   "source": [
    "from autograd import jacobian\n",
    "\n",
    "def rsys(theta, Gi):\n",
    "    \"Steady state mole balance, returns 0 at the steady state coverages.\"\n",
    "    thetastar, thetaa, thetab = theta\n",
    "\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(Gi)\n",
    "\n",
    "    # balance on A*\n",
    "    z1 = (k1 * pa * thetastar - k_1 * thetaa\n",
    "          - k3 * thetaa * thetab)# + k_3 * pab * thetastar**2)\n",
    "    # balance on B*\n",
    "    z2 = (k2 * pb * thetastar**2 - k_2 * thetab**2\n",
    "          - k3 * thetaa * thetab)# + k_3 * pab * thetastar**2)\n",
    "    # site balance\n",
    "    z3 = 1 - thetastar - thetaa - thetab\n",
    "    return np.array([z1, z2, z3])\n",
    "\n",
    "\n",
    "# These are jacobian functions\n",
    "dsysdtheta = jacobian(rsys, 0)\n",
    "dsysdG = jacobian(rsys, 1)\n",
    "\n",
    "# Now we evaluate them at the conditions we care about\n",
    "dSdth = dsysdtheta(np.array([thetas, thetaa, thetab]), np.array(G))\n",
    "dSdG = dsysdG(np.array([thetas, thetaa, thetab]), np.array(G))\n",
    "\n",
    "# And then compute the desired derivative\n",
    "dthdG = -np.linalg.inv(dSdth) @ dSdG\n",
    "\n",
    "# this gives an idea of how sensitive theta is to G, you can see they are all very small.\n",
    "# print('dthdG: ', dthdG)\n",
    "\n",
    "# Integers by name for indexing the derivatives\n",
    "THETAS, THETAA, THETAB = np.arange(3)\n",
    "GTS1, GTS2, GTS3, GAS, GBS, GABS = np.arange(6)\n",
    "\n",
    "# I have left out  - k_4 * pab * dthdG[THETAS, GTS3] since pab=0 here\n",
    "# print('\\n'.join([f'XRC G_A*: {-(k4 * dthdG[THETAAB, GAS]) * R * T / r:1.3f}',\n",
    "#                  f'XRC G_B*: {-(k4 * dthdG[THETAAB, GBS]) * R * T / r:1.3f}',\n",
    "#                  f'XRC G_3TS: {-(k4 * dthdG[THETAAB, GTS3]) * R * T / r:1.3f}']))\n",
    "\n",
    "dkdG = jacobian(fk)\n",
    "\n",
    "r = k1 * pa * thetas - k_1 *thetaa\n",
    "# r = k3 * pa * pb\n",
    "\n",
    "for label, i in zip(['GTS1', 'GTS2', 'GTS3', 'GAS', 'GBS', 'GABS'], range(6)):\n",
    "#     print((pb*dkdG(np.array(G))[2,i] * thetas + k2 * dthdG[THETAS,i] * pb - (dkdG(np.array(G))[3,i] * thetas + k_2*dthdG[THETAS,i]))* R * T /r)\n",
    "    term1 = pa*(dkdG(np.array(G))[0,i] * thetas +  k1 * dthdG[THETAS,i]) # pb*(dk2/dG * t* + k2 * dt*/dG)\n",
    "    term2 = dkdG(np.array(G))[1,i] * thetaa + k_1*dthdG[THETAA,i] # k_2()\n",
    "    print(label, f'{-(term1 - term2)* R * T /r:1.4f}')\n",
    "#     print(label, f'{-(pb*dkdG(np.array(G))[2,i] * thetas + k2 * dthdG[THETAS,i] * pb - (dkdG(np.array(G))[3,i] * thetaa + k_2*dthdG[THETAA,i]))* R * T /r:1.4f}')\n",
    "#     print(label, f'{-(dkdG(np.array(G))[4,i] * thetas + k2 * dthdG[THETAS,i] * pb - (dkdG(np.array(G))[3,i] * thetas + k_2*dthdG[THETAS,i]))* R * T /r:1.4f}')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lnrate_s(G_i):\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(G_i)\n",
    "    thetaa, thetab = fsolve(rsys_s,\n",
    "                                [0.2, 0.5], # initial guess\n",
    "                                args=(G_i,))\n",
    "    thetas = 1 - thetaa - thetab\n",
    "#     r = k2 * pb * thetas - k_2 * thetab\n",
    "    r = k3 * thetaa * thetab - k_3 * thetas**2 * pab\n",
    "#     r = k3 * pa * pb\n",
    "#     print(r)\n",
    "    ret = np.log(r)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.    0.62  0.72 -1.2  -0.75 -0.96]\n",
      "[ 0.31577669 -0.03791007  0.72213338 -0.22912497 -1.0793974  -0.        ]\n"
     ]
    }
   ],
   "source": [
    "dlndG_s = nd.Gradient(lnrate_s)\n",
    "dlndGi_s = dlndG_s(G)\n",
    "print(G)\n",
    "print(-dlndGi_s.T * R * T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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u9fuw/sNw5k2D7gOh/1gYf2p47T8O+u0fkkFpj8LFLiLtlhJER7NjM6x6C1bOgspZoX/bml3je+4HgyfC2BNh0ISQCPrvH7YSRET2ghJEe+YOGxfD0r/D8n/Cypmwfv6u8QPGw5iTYL+PhaQwaCJ071+4eEWkU1GCaG82LYUlfw9JYemrULUylHcfCMMmwce+AsOOgKEfh259ChqqiHRuShCFVrcjJIQFz8GCv4QziSAcGB79CRj1CRj9yXDcIF8X0IiIZKAEUQjb18MHT8L852Dxy+EK4eLusP8UOOY7ITEMPFAJQUQKSgmirVRvhHl/hvf/CEteCReZ9RkBH/8ajP80jDw+XPkrItJO5DVBmNlpwC1AHPi1u9+Yoc5XgGmE2xTOdvfz8hlTm0rUha2Et++FhX+FZB30HQXHXQYHfyFccKatBBFpp/KWIMwsDtwGnAJUAjPM7Al3n5tSZxzwQ+A4d99kZoPyFU+b2rgE3vodvPNAuEVFjyFw9MUw8Qsw9HAlBRHpEPK5BTEZWOjuiwHM7EHgDGBuSp1vAbe5+yYAd1+7RysdhTssehFe/2V4tRiMOxU+/o3wqiuRRaSDyee/1jBgRcpwJXBUWp3xAGb2D8JuqGnu/mx6Q2Z2EXARwIgRI/IS7D5L1MP7j8Brt4armXsMgSk/gsOnQu9hhY5ORGSf5TNBZNqPkv7IoyJgHDAFqAD+bmYHu/vm3SZyvxO4E2DSpEm5f2zSvkgmwgHnl/8bNi6CgQfBGbfDIV8Kt5IWEeng8pkgKoHhKcMVwKoMdd5w9zpgiZl9SEgYM/IYV+steB7+8l+w7oNw9fLZ98OBn9OxBRHpVPKZIGYA48xsNLASOAdIP0PpT8C5wHQzG0DY5bQ4jzG1zsYl8OwPYf4z0G8MfOk3MOFMPb9ARDqlvCUId683s0uA5wjHF+5x9zlmdh0w092fiMadamZzgQTwA3ffkK+Y9lmiHl69GV75WXhU5CnXwVH/Hp5UJiLSSZl7+9iln61Jkyb5zJkz226GGxbBY/8GlTNg4lnw6Rug19C2m7+ISA6Y2Sx3n7Q30+jcy+a8dS88c2U4RfWLd4cD0CIiXYQSRCaJenjuR/Dm/4Yb5Z35K52yKiJdjhJEupoqeORfYeHzcPS34dSfQCxe6KhERNqcEkSqravh3i/AunnwLzfDpH8tdEQiIgWjBNFg62qY/rnwOvURGHNioSMSESkoJQgIt+L+7edDcvjqIzDymEJHJCJScEoQdTXw+3PDoz6/9piSg4hIpGsnCHf483dhxRvhquhRxxc6IhGRdqNr3yNi1m9g9u9hyg/DA3xERKRR100Qa+aEi+DGngKfvKLQ0YiItDtdM0Ek6uCxi6GsN5z1v7rZnohIBl3zGMSrN8Pqd+Hs+6B7/0JHIyLSLnW9VefNy+Hv/zfceO+gzxc6GhGRdqvrJYjnrwEMTr2+0JGIiLRrXStBLH8D5jwGx10GvSsKHY2ISLvWtRLEyzdC94Fw3KWFjkREpN3rOgmiciYsfgmO/Q6UdC90NCIi7V7XSRCv/BzK+ugOrSIiWeoaCWL9Qpj/DBx1MZT2LHQ0IiIdQtdIELN+A7EimHRBoSMREekwOn+CqKuBdx6AAz4LPYcUOhoRkQ6j8yeID56EHRu19SAispc6f4J4537oOwpGTyl0JCIiHUrnThDbN8CSV+DgL+qGfCIie6lz/2vOexI8ARPOLHQkIiIdTudOEHP+BH1Hw5BDCh2JiEiH03kTRMPupYlnglmhoxER6XA6b4JY+HzYvXTQ6YWORESkQ+q8CWLRS1A+APY7rNCRiIh0SJ0zQbjD4pdh/xN09pKIyD7K67+nmZ1mZh+a2UIzuyrD+PPNbJ2ZvRN138zJjNd+ANtWw/6fyklzIiJdUd6eSW1mceA24BSgEphhZk+4+9y0qn9w90tyOvPFL4XX/afktFkRka4kn1sQk4GF7r7Y3WuBB4Ez8ji/XRa9BP3HQp/hbTI7EZHOKJ8JYhiwImW4MipL90Uze9fMHjGzjP/oZnaRmc00s5nr1q1rfq6JOlj2mnYviYi0Uj4TRKaLDzxt+ElglLt/DHgB+G2mhtz9Tnef5O6TBg4c2Pxc48Vw6Vtw/Hf3IWQREWmQzwRRCaRuEVQAq1IruPsGd98ZDd4FHJGTOfccAr0rctKUiEhXlc8EMQMYZ2ajzawEOAd4IrWCme2XMng68EEe4xERkb2Qt7OY3L3ezC4BngPiwD3uPsfMrgNmuvsTwKVmdjpQD2wEzs9XPCIisnfMPf2wQPs2adIknzlzZqHDEBHpUMxslrtP2ptpdJmxiIhkpAQhIiIZKUGIiEhGShAiIpKREoSIiGSkBCEiIhkpQYiISEZKECIikpEShIiIZKQEISIiGSlBiIhIRkoQIiKSkRKEiIhkpAQhIiIZ5e15ECIi7VVdXR2VlZXU1NQUOpScKysro6KiguLi4la3pQQhIl1OZWUlPXv2ZNSoUZhZocPJGXdnw4YNVFZWMnr06Fa3p11MItLl1NTU0L9//06VHADMjP79++dsy2ivEoSZdc/JXEVECqyzJYcGuXxfWSUIMzvWzOYCH0TDh5rZ7TmLQkRE2p1styBuBj4NbABw99nAJ/MVlIhIV7B69WrOOeccxowZw4QJE/jsZz/L/PnzmTNnDieeeCLjx49n3Lhx/OQnP8HdgXCcYenSpUyfPj3v8WW9i8ndV6QVJXIci4hIl+HunHXWWUyZMoVFixYxd+5cbrjhBtasWcPpp5/OVVddxfz585k9ezavvfYat98edtpcfPHFvPrqqyxfvpwLL7yQlStX5i3GbM9iWmFmxwJuZiXApUS7m0REZO+99NJLFBcXc/HFFzeWHXbYYdx9990cd9xxnHrqqQCUl5fzy1/+kilTpvDtb3+bO+64g9NPP53333+fN998k0GDBuUtxmwTxMXALcAwoBL4C/DtfAUlItJWrn1yDnNXVeW0zQlDe/Hjz09sts7777/PEUccsUf5nDlz9igfM2YM27Zto6qqiiuvvJKzzz6byZMnc/XVV3PttdcydOjQnMbfIKsE4e7rga/mJQIREWnk7k2eiWRm3H777SxbtoxEIsE111yT11iyShBm9v8yFG8BZrr747kNSUSk7bS0pp8vEydO5JFHHslY/sorr+xWtnjxYnr06EHPnj0BGDVqFOeff37eY8z2IHUZcBiwIOo+BvQDLjSzX+QpNhGRTuvEE09k586d3HXXXY1lM2bMYNy4cbz66qu88MILAOzYsYNLL72UK664os1jzDZBjAVOdPdb3f1W4GTgIOAs4NR8BSci0lmZGY899hjPP/88Y8aMYeLEiUybNo2hQ4fy+OOPc/3113PAAQdwyCGHcOSRR3LJJZe0eYzZHqQeBnQn7FYi6h/q7gkz25mXyEREOrmhQ4fy0EMPZRz38ssvt20wGWSbIG4C3jGzlwEjXCR3Q3TrjRfyFJuIiBRQtmcx3W1mTwOTCQniR+6+Khr9g3wFJyIihbM3N+urAT4CNgJjzazFW22Y2Wlm9qGZLTSzq5qp9yUzczObtBfxiIhIHmV7mus3gcuACuAd4GjgdeDEZqaJA7cBpxAurpthZk+4+9y0ej0JV2b/c1/egIiI5Ee2WxCXAUcCy9z9U8DhwLoWppkMLHT3xe5eCzwInJGh3k8Ixzg636OdREQ6sGwTRI271wCYWam7zwMOaGGaYUDqDf4qo7JGZnY4MNzd/5xlHCIi0kayTRCVZtYH+BPwvJk9DqxqYZpM14p740izGOE24pe3NHMzu8jMZprZzHXrWtpwERHpGCorKznjjDMYN24cY8aM4bLLLqO2trbx1t7Tpk0DaBxua1klCHc/y903u/s04L+Au4EzW5isEhieMlzB7kmlJ3Aw8LKZLSUc13gi04Fqd7/T3Se5+6SBAwdmE7KISLvm7nzhC1/gzDPPZMGCBcyfP59t27Zx9dVXc/XVV/P444+zYcMGLr30UmbPnl2QGFs8SB2t6b/r7gcDuPvfsmx7BjDOzEYDK4FzgPMaRrr7FmBAynxeBr7v7jOzjl5EpIN68cUXKSsr44ILLgAgHo9z8803M3r0aFasWMHll1/Ogw8+yBtvvMEBB7S0Rz8/WkwQ7p40s9lmNsLdl2fbsLvXm9klwHNAHLjH3eeY2XWEm/w9se9hi4jkyDNXwer3ctvmkEPgMzc2WyXTbb179erFiBEjmDp1Kl//+tcpKiritttu48ILL+TQQw/NbYxZyPZK6v2AOWb2JrC9odDdT29uInd/Gng6rSzj/WndfUqWsYiIdHhN3dbb3bn22ms55JBDeOedd5g2bVrBjkFkmyCuzWsUIiKF0sKafr5MnDiRRx99dLeyqqoqVqxYwZgxY4BdB6mbej5EvmV7kPpvwFKgOOqfAbyVx7hERDq1k046ierqan73u98BkEgkuPzyyzn//PMpLy8vcHRBVgnCzL4FPAL8b1Q0jHDKq4iI7IOG230//PDDjBs3jvHjx1NWVsYNN9xQ6NAaZbuL6duEK6P/CeDuC8wsf0/KFhHpAoYPH86TTz5Z6DCalO2Fcjuj22UAYGZFpFz0JiIinU+2CeJvZvYjoJuZnQI8DLTftCciIq2WbYK4inBzvveAfyOcuvqf+QpKREQKL9tjEGcAv3P3u1qsKSIinUK2WxCnA/PN7F4z+1x0DEJERDqxbK+DuAAYSzj2cB6wyMx+nc/ARESksLJ+5Ki71wHPEB78M4vMD/8REZEstJdbejcn20eOnka4G+ungJeBXwNfyV9YIiKd2/3338+qVauoqanhpptuYujQoUydOrXQYe0m2y2I8wlXTo9392+4+9PuXp+/sEREOrepU6cyfPhwbrrppsY7uLY3WW1BuPs5ZjYYOCW6adSb7r42r5GJiLSBn775U+ZtnJfTNg/sdyBXTr6y2ToPPPAAlZWVXHHFFSxfvpwHHniA8847r9lp2lq2u5i+DPycsHvJgFvN7Afu/kgeYxMR6bTOPfdczIxp06ZxxRVXdNxjEISL4o5s2Gows4HAC4Qb+ImIdFgtrennS8MtvAt9S+/mZHsMIpa2S2nDXkwrIiIdULZbEM+a2XPA76Phs0l7UpyIiHQuzSYIMxsLDHb3H5jZF4DjCccgXgfub4P4RESkQFraTfQLYCuAu//R3f/D3b9H2Hr4Rb6DExGRwmkpQYxy93fTC919JjAqLxGJiEi70FKCKGtmXLdcBiIi0pba42mluZDL99VSgpgRPY96N2Z2IeF+TCIiHU5ZWRkbNmzodEnC3dmwYQNlZc2t22evpbOYvgs8ZmZfZVdCmASUAGflJAIRkTZWUVFBZWUl69atK3QoOVdWVkZFRUVO2mo2Qbj7GuBYM/sUcHBU/JS7v5iTuYuIFEBxcTGjR48udBjtXrb3YnoJeCnPsYiISDuiq6FFRCQjJQgREclICUJERDJSghARkYyUIEREJKO8JggzO83MPjSzhWZ2VYbxF5vZe2b2jpm9amYT8hmPiIhkL28JwsziwG3AZ4AJwLkZEsAD7n6Iux8G3AT8Ty7mXZeoo6q2KhdNiYh0WfncgpgMLHT3xe5eCzwInJFawd1T/8W7A62+7r0uWceJD5/IXe/e1dqmRES6tHwmiGHAipThyqhsN2b2bTNbRNiCuDRTQ2Z2kZnNNLOZLV0aXxwr5oC+B/Daqtf2PXIREclrgsj0gNU9thDc/TZ3HwNcSXj29Z4Tud/p7pPcfdLAgQNbnPExQ49h/qb5rKvufPdZERFpK/lMEJXA8JThCmBVM/UfBM7MxYyPHXosAG989EYumhMR6ZLymSBmAOPMbLSZlQDnAE+kVjCzcSmDnwMW5GLGB/Q7gH5l/bSbSUSkFbK6Wd++cPd6M7sEeA6IA/e4+xwzuw6Y6e5PAJeY2clAHbAJ+EYu5h2zGEfvdzSvr3qdpCeJmS73EBHZW3lLEADu/jTh+dWpZdek9F+Wr3kfO/RYnl7yNB9s/ICJ/SfmazYiIp1Wp121PqHiBIqsiGeXPFvoUEREOqROmyD6lPXh+GHH8/SSp0kkE4UOR0Skw+m0CQLgs/t/lrXVa3lr7VuFDkVEpMPp1AliyvAplBeV89Tipwodijmbak8AABK6SURBVIhIh9OpE0S3om6cPPJknlnyjO7NJCKylzp1ggCYetBUquureXT+o4UORUSkQ+n0CeKg/gdx1JCjuO+D+6hL1BU6HBGRDqPTJwiAb0z8Bmur1/LUEh2LEBHJVpdIEMcPO56J/Sdy69u3Ul1XXehwREQ6hC6RIMyMKydfydrqtdzz/j2FDkdEpEPoEgkC4PBBh/OZ0Z9h+pzpLNmypNDhiIi0e10mQQB8f9L36VbUjSteuYLaRG2hwxERade6VIIYVD6I64+7nnkb5/HTN3+Ke6ufcCoi0ml1qQQBcMLwE7hg4gU8NP8h7npPz60WEWlKXm/33V5994jvsm7HOm59+1ZiFuPCgy/ELNMTUkVEuq4umSBiFuO6464jkUxwy1u3ULm1kh8e9UNK46WFDk1EpN3ocruYGhTHirnxkzfyzUO+yaMLHuWcP5/DnA1zCh2WiEi70WUTBIQtics+fhl3nHwHW3Zu4dw/n8vVr17NsqplhQ5NRKTgrKOdyTNp0iSfOXNmztvdWruVu967i/vm3kd9sp4TKk7gM6M/E24ZXlye8/mJiLQlM5vl7pP2aholiN2t37GeBz54gMcXPs7aHWspjZdy/LDjOXLIkRw28DDG9xtPcaw4b/MXEckHJYgcSnqSt9e+zXNLn+OlFS+xevtqIDxjYv/e+zO692j2770/FT0rGFQ+qLHTgW4RaY+UIPJo9fbVvLPuHWavnc2izYtYvGUxa6rX7FGvb2lf+pb1pVdJL3qV9qJnSc/QXxL6uxV1a+zKisp2vcZ3lZXGSymOF1NkRTr9VkRyQgmijW2v285H2z5ibfVa1lSvYU31GtZWr2Xzzs1U7ayiqjbqdlaxtW7rXrdvGMWxYorjxRTHiimJlTT2F8WKKImXhPFRlzocj8WJWYyiWBFx29UfsxhFFl7jsfhu/XGLuljaa3p/1F7MYpgZhjX2xyy2azilvKG/oTy1rpkRY9/aa5i+cZlF/UbaazTNbss3pSzjdEaLbSmBS0exLwmiS14HkSvdi7sztu9YxvYd22LdRDLB9vrt1NTXsKN+R+NrQ39Nooaa+hqq66vZmdhJXaKOumToahO11CXrqE/W7zZcl6yjLlFHbbKW7fXb2bxzc2N5Ipkg4VGX1p/0JPVeTyKZwOlYKwjtXWrCam2ySU9++xJLIabd10lbFW8BllOh4m1LShBtJB6LN+5qak+SniThIWkkkgnqvZ5kMiSQhrKMicYT4GH6JEncHcfDsCcb20767uMaX90bp2sob+hPby+97fT2gMayhn5gt+SXXtYwv/R6LbXlOA3VdytrYrr08S22lVKnNcm7UHsG9jXm1sRbiOVUqBWr1sT7Cq/s9XRKEF1cw24fAOKFjUVE8ufH/Hivp+nSF8qJiEjTlCBERCQjJQgREclICUJERDLKa4Iws9PM7EMzW2hmV2UY/x9mNtfM3jWzv5rZyHzGIyIi2ctbgjCzOHAb8BlgAnCumU1Iq/Y2MMndPwY8AtyUr3hERGTv5PM018nAQndfDGBmDwJnAHMbKrj7Syn13wCm5mLGn73l79QlkvTrXsL4wT05bHgfphwwkP49dJ8kEZFs5TNBDANWpAxXAkc1U/9C4JlMI8zsIuAigBEjRrQ44yNG9mXd1p2s27aTx95eyb1vLMMMPj6iL6dMGMxZhw9jcK+yrN+IiEhXlM8Ekela8oyXAZrZVGAScEKm8e5+J3AnhHsxtTTjn5x5cGN/MunMWVXFCx+s4cV5a7nxmXnc9Ow8PnXAIM4+cjgnHjiIoriO1YuIpMtngqgEhqcMVwCr0iuZ2cnA1cAJ7r4z10HEYsYhFb05pKI33ztlPEvXb+ehmSt4ZFYlf523liG9yjjvqBGcM3k4g3pqq0JEpEHe7uZqZkXAfOAkYCUwAzjP3eek1DmccHD6NHdfkE27ubqba30iyYvz1nLvG8v4+4L1FMWM0w4ewtePGcWRo/p2mJtpiYhko13dzdXd683sEuA5wl1+7nH3OWZ2HTDT3Z8Afgb0AB6O/pCXu/vp+YopVVE8xqkTh3DqxCEsWb+d+95YxsMzV/Dndz/iwCE9mXr0SM46fBjdS3W7KhHpmvQ8iBQ7ahM8MXslv3t9GXNWVdGjtIgvfnwYU48eybjBPfMyTxGRtqAHBuWIu/P2is3c+/oynnr3I2oTSY7Zvz9fO2Ykp0wYTLEOaotIB6MEkQcbtu3kDzNXcP8by1m5eQeDe5Vy3uSRnDt5OIN0qqyIdBBKEHmUSDovRQe1/zZ/HUUx49MHD+FrR4/kqNH9dFBbRNq1dnWQurOJx4yTJwzm5AmDWbp+O/f/cxkPzazkqXc/YvzgHnzx4xV8/tChDO3TrdChiojkhLYgWmFHbYInZ6/i/jeXM3vFZgAmj+7H6YcO5bOH7Ee/7iUFjlBEJNAupgJaun47T85exZ/eWcmiddspihmTR/fjlAmDOfmgwQzvV17oEEWkC1OCaAfcnbkfVfHndz/i+blrWLh2GwAHDunJqdEuqkOG9dYxCxFpU0oQ7dCS9dt5Ye4anp+7hpnLNpJ0GNizlGPH9Oe4sQM4buwAhum4hYjkmRJEO7dh205enLeWvy9Yz2uL1rN+Wy0Aowd0b0wYk0b11T2hRCTnlCA6EHfnwzVbeXXBel5btIF/Lt7A9toEABV9u3HEyL58fEToDtyvpy7OE5FWUYLowOoSSd6t3MJbyzbx1vLQrakKN7ftVhzn4GG9mDi0NxOG9mLCfr0YP7gnJUVKGiKSHV0H0YEVx2McMbIvR4zsC4QtjFVbanhr2SZmLdvEeyu38NDMFVRHWxnFcWPsoJ5MHNqLcYN6MHZQD8YM7MHwfuXEYzoALiKtpwTRTpkZw/p0Y1ifbnz+0KFAuJp72YbtzFlVxZxVVcz9qIqXP1zHI7MqG6criccYPaA7YwZ1Z+zAHowZ1IOR/btT0bcb/buX6OwpEcmaEkQHEo8Z+w/swf4DezQmDYDN1bUsWredRWu3sWhd6D74aCvPvr+aZMoexPKSOBV9u1HRt5zhfbsxvF85FX27MbRPNwb3KqN/9xI9XU9EGilBdAJ9yks4YmRJ4+6pBjvrEyzbUM3yDdWs2FRN5aYdrNhYzYpNO5ixZCNbd9bvVj9mMKBHKYN7lTG4VymDepUxuGfoH9yrjP49SuhbXkK/7iWUl8S1NSLSySlBdGKlRXHGD+7J+CaeZbGluo4Vm6r5aEsNa6pqWFtVw5qqnazZWsPKzTW8vXwzG7bXZpy2pChGvyhZ9OteQt/uJfQrL6ZPeQm9uxXTs6yInmXF9OpWRK+yMNzwqq0UkY5BCaIL611eTO/y3hw8rHeTdWrrk6zbtpM1VTVs3FbLxupaNm0Prxu31bKpupaN22tZuXkHG7fXsmVHXYvz7VYcp1e3kEC6lxZRXhyne2mcbiWhv1tJnPKSON1Li+hWHPpDWRHlJXHKiuOUFsUoK45REo9TWhyjJB5rfFUCEskNJQhpVklRrPFgeTbqE0m27axna009W3bUsbWmnq01dVQ1vO4Ir1tr6qmqqWPbznp21CZYtbmOHXUJtkfD1XUJEsl9OwU7HjNKi2KUFMUoLYpRWhRv7C8pCkmkOB6jKG4UxWIUxYyiuIWyqL8o1jDeKIrHKI4Z8aiseLfxu+rFY0bMQhePhRMN4hbKzdhtfCwaNmuYjpRpo+GoftzSpo+FukaYR3gFw8Aa+neNi0XTk1IvvY4Z2mUoe1CCkJwqisfoU15Cn/IShreiHXenNpEMyaI2QXVtffSaYEddgtr6JLX1SXbWJ9lZn2jsr00b3lmXpDaxZ1l1bT31Sacu4SSSSeoTTl0ySSLh1CWd+kSS+qRTn3Dqk0nqEh3reqHWyJg8GpIPTSeZhvGx2J7JK8Nc9phn8zUy17MMtfask6mdlpPhHu1kjDE3889iEe3z+2gNJQhpl8yM0qI4pUVx+rSDG+G6O0kPFzTWJz1KJFFiicqS7rg7iWQ4JTnpDV0YDuPCcMO4UJ65fuNwEhIpbTeUu4e4HEJ/FCeNw95Y3lC/4b3sqr97PXZrb896pMwnUxupyyq1bLdluceyzbjEM3wGLU/nadPt6/zT28kQTqYi0i88zlwnN+1kLszMcf6affVGShAiWQi7iyAeixc6FJF9csfUvZ9GR/NERCQjJQgREclICUJERDJSghARkYyUIEREJCMlCBERyUgJQkREMlKCEBGRjDrcI0fNbB2wLIuqA4D1eQ6nvdMy0DIALQPQMgA4wN0z39q5CR3uSmp3H5hNPTObubfPX+1stAy0DEDLALQMICyDvZ1Gu5hERCQjJQgREcmoMyeIOwsdQDugZaBlAFoGoGUA+7AMOtxBahERaRudeQtCRERaQQlCREQy6nQJwsxOM7MPzWyhmV1V6HjampkNN7OXzOwDM5tjZpcVOqZCMbO4mb1tZn8udCyFYGZ9zOwRM5sXfR+OKXRMbc3Mvhf9Dt43s9+bWVmhY2oLZnaPma01s/dTyvqZ2fNmtiB67dtSO50qQZhZHLgN+AwwATjXzCYUNqo2Vw9c7u4HAUcD3+6Cy6DBZcAHhQ6igG4BnnX3A4FD6WLLwsyGAZcCk9z9YCAOnFPYqNrMdOC0tLKrgL+6+zjgr9FwszpVggAmAwvdfbG71wIPAmcUOKY25e4fuftbUf9Wwp/CsMJG1fbMrAL4HPDrQsdSCGbWC/gkcDeAu9e6++bCRlUQRUA3MysCyoFVBY6nTbj7K8DGtOIzgN9G/b8Fzmypnc6WIIYBK1KGK+mCf44NzGwUcDjwz8JGUhC/AK4AkoUOpED2B9YBv4l2s/3azLoXOqi25O4rgZ8Dy4GPgC3u/pfCRlVQg939IwgrksCglibobAnCMpR1yfN4zawH8CjwXXevKnQ8bcnM/gVY6+6zCh1LARUBHwfucPfDge1ksUuhM4n2sZ8BjAaGAt3NbGpho+pYOluCqASGpwxX0EU2KVOZWTEhOdzv7n8sdDwFcBxwupktJexmPNHM7itsSG2uEqh094atx0cICaMrORlY4u7r3L0O+CNwbIFjKqQ1ZrYfQPS6tqUJOluCmAGMM7PRZlZCOCD1RIFjalNmZoT9zh+4+/8UOp5CcPcfunuFu48ifAdedPcutebo7quBFWZ2QFR0EjC3gCEVwnLgaDMrj34XJ9HFDtSneQL4RtT/DeDxlibocHdzbY6715vZJcBzhDMW7nH3OQUOq60dB3wNeM/M3onKfuTuTxcwJimM7wD3RytLi4ELChxPm3L3f5rZI8BbhLP73qaL3HLDzH4PTAEGmFkl8GPgRuAhM7uQkDy/3GI7utWGiIhk0tl2MYmISI4oQYiISEZKECIikpEShIiIZKQEISKSZ5luntfK9p41s83pN6I0s7vNbLaZvRvdqLFHa+ajBCFdnpn1N7N3om61ma1MGX4th/M508yuaWb8IWY2PVfzk3ZlOnvePK81fkY4nT3d99z9UHf/GOFU1ktaM5NOdR2EyL5w9w3AYQBmNg3Y5u4/z8OsrgBObyaO98yswsxGuPvyPMxfCsTdX4nujdbIzMYQ7j49EKgGvuXu87Js769mNiVDeVXUtgHdaOWthrQFIdIMM9sWvU4xs7+Z2UNmNt/MbjSzr5rZm2b2XvRjx8wGmtmjZjYj6o6LyscDO919fTT85egZBbPN7JWUWT5J17kldVd3J/Addz8C+D5wey4aNbPfAKuBA4FbW9OWtiBEsncocBDhNsqLgV+7++TooUzfAb5LeAbDze7+qpmNIFzVfxDhCve3Utq6Bvi0u680sz4p5TMJN9W7Ke/vRgomOjZwLPBwWNkHoDQa9wXgugyTrXT3T7fUtrtfED0b51bgbOA3+xqnEoRI9mY03C7ZzBYBDbeOfg/4VNR/MjAh5Uffy8x6AvsRbr/d4B/AdDN7iHATuQZrCXcelc4tBmx298PSR0Q32GzVTTbdPWFmfwB+QCsShHYxiWRvZ0p/MmU4ya6VrRhwjLsfFnXDogc37QAaH3fp7hcD/0m4+/A7ZtY/GlUW1ZVOLDpWsMTMvgzhmIGZHdqaNqM2xjb0A58Hsjqm0RQlCJHc+gspZ46YWcMa4gfA2JTyMe7+T3e/BljPrtvUjwdyciqktB/RzfNeBw4ws8rohnlfBS40s9nAHPbi6Zdm9nfgYeCkqL1PE56H81sze4+wVbsfmXdVZU27mERy61LgNjN7l/D7egW4OHr9v2ZmHu6Q+TMzG0f4Uf8VmB1N/yngqbYPW/LJ3c9tYtQ+nfrq7p9oYtRx+9JeU3Q3V5E2Yma3AE+6+wtNjC8F/gYc7+71bRqcSAbaxSTSdm4AypsZPwK4SslB2gttQYiISEbaghARkYyUIEREJCMlCBERyUgJQkREMlKCEBGRjP4/+PjGMlsgWhAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[29.03322478 28.85754012 28.70125022 28.56237934 28.43920946 28.33018052\n",
      " 28.2338339  28.14879032 28.07374469 28.00747324 27.94884369 27.8968232\n",
      " 27.85048386 27.80900387 27.77166467 27.73784518 27.70701403 27.6787204\n",
      " 27.65258446 27.62828835 27.60556736 27.58420188 27.56401042 27.54484333\n",
      " 27.5265774  27.50911139 27.49236204 27.47626092 27.46075182 27.44578816\n",
      " 27.43133142 27.41734966 27.40381618 27.39070842 27.37800726 27.36569629\n",
      " 27.35376116 27.34218938 27.33096975 27.32009214 27.30954727 27.29932652\n",
      " 27.28942178 27.27982534 27.2705298  27.26152799 27.25281287 27.24437769\n",
      " 27.23621574 27.22832037 27.22068505 27.21330325 27.20616856 27.19927461\n",
      " 27.19261513 27.18618386 27.17997461 27.17398128 27.1681978  27.16261821\n",
      " 27.15723661 27.15204719 27.14704422 27.14222207 27.13757518 27.1330981\n",
      " 27.12878553 27.12463225 27.12063314 27.11678317 27.11307739 27.10951096\n",
      " 27.10607926 27.10277773 27.09960192 27.0965475  27.09361025 27.09078607\n",
      " 27.08807097 27.08546107 27.0829526  27.0805419  27.0782254  27.07599967\n",
      " 27.07386138 27.07180731 27.06983435 27.06793947 27.06611976 27.0643724\n",
      " 27.06269466 27.0610839  27.05953757 27.0580532  27.05662841 27.05526087\n",
      " 27.05394835 27.0526887  27.05147986 27.05031986 27.04920677 27.04813871\n",
      " 27.04711393 27.04613076 27.04518758 27.04428285 27.0434151  27.04258286\n",
      " 27.04178472 27.0410193  27.0402853  27.03958144 27.03890641 27.03825916\n",
      " 27.0376384  27.03704298 27.0364718  27.03592383 27.03539833 27.03489455\n",
      " 27.0344117  27.03394886 27.03350523 27.03307999 27.0326723  27.03228134\n",
      " 27.03190641 27.03154694 27.03120228 27.03087205 27.0305555  27.03025214\n",
      " 27.02996138 27.02968263 27.02941541 27.02915926 27.02891373 27.0286784\n",
      " 27.02845284 27.02823664 27.02802943 27.02783083 27.02764046 27.02745802\n",
      " 27.02728314 27.02711555 27.02695492 27.02680097 27.02665342 27.02651201\n",
      " 27.02637648 27.02624658 27.02612208 27.02600276 27.0258884  27.02577882\n",
      " 27.02567378 27.0255731  27.02547662 27.02538417 27.02529559 27.02521071\n",
      " 27.02512937 27.02505141 27.0249767  27.02490511 27.02483651 27.02477076\n",
      " 27.02470775 27.02464737 27.02458951 27.02453407 27.02448093 27.02443\n",
      " 27.0243812  27.02433443 27.02428962 27.02424667 27.02420551 27.02416607\n",
      " 27.02412826 27.02409204 27.02405733 27.02402406 27.02399218 27.02396164\n",
      " 27.02393238 27.02390435 27.0238775  27.02385177 27.02382712 27.0238035\n",
      " 27.02378086 27.02375917 27.02373839 27.02371848 27.02369942 27.02368116\n",
      " 27.02366367 27.02364691]\n"
     ]
    }
   ],
   "source": [
    "tspan = np.linspace(0,1e-12,200)\n",
    "char = ['TS1', 'TS2', 'TS3', 'CO*', 'O*', 'CO2']\n",
    "# tspan = np.linspace(0,0.01,200)\n",
    "\n",
    "def rsys_t(theta, t, Gi):\n",
    "    \"Steady state mole balance, returns 0 at the steady state coverages.\"\n",
    "    thetaa, thetab = theta\n",
    "\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(Gi)\n",
    "    \n",
    "    thetastar = 1 - thetaa - thetab\n",
    "\n",
    "    # balance on A*\n",
    "    z1 = (k1 * pa * thetastar - k_1 * thetaa\n",
    "          - k3 * thetaa * thetab + k_3 * pab * thetastar**2)\n",
    "    # balance on B*\n",
    "    z2 = (k2 * pb * thetastar**2 - k_2 * thetab**2\n",
    "          - k3 * thetaa * thetab + k_3 * pab * thetastar**2)\n",
    "    # site balance\n",
    "    \n",
    "    return np.array([z1, z2])\n",
    "\n",
    "Theta = odeint(rsys_t, [0.2, 0.5], tspan, args = ((G,)))\n",
    "plt.plot(tspan, Theta[:,0], label = 'CO*')\n",
    "# plt.show()\n",
    "plt.plot(tspan, Theta[:,1],label = 'O*')\n",
    "plt.plot(tspan, 1- Theta[:,0] - Theta[:,1], label = '*')\n",
    "plt.legend()\n",
    "plt.xlabel('Time(s)')\n",
    "plt.ylabel('Coverage')\n",
    "plt.xlim(-0.3e-13,1e-12)\n",
    "plt.title(f'Final Coverages for CO* = {Theta[:,0][-1]:1.2f} | O* = {Theta[:,1][-1]:1.2f} | * = {(1- Theta[:,0] - Theta[:,1])[-1]:1.2f}')\n",
    "plt.show()\n",
    "\n",
    "def lnrate(G_i):\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(G_i)\n",
    "\n",
    "    Theta = odeint(rsys_t, [0.2, 0.5], tspan, args = ((G_i,)))\n",
    "    thetas = 1 -Theta[:,0] - Theta[:,1]\n",
    "    r = k2 * pb * thetas**2 - k_2 * Theta[:,1]**2\n",
    "#     r = k1 * pa * thetas - k_1 * Theta[:,0]\n",
    "#     r = k3 * Theta[:,0] * Theta[:,1] - k_3 * thetas * pab\n",
    "#     print(r)\n",
    "#     r = k3 * pa * pb\n",
    "    ret = np.log(r)\n",
    "    return ret\n",
    "\n",
    "lnr = lnrate(G)\n",
    "plt.plot(tspan, lnr)\n",
    "plt.title(f'log(Rate): steady state value: {lnr[-1]:1.4f}')\n",
    "plt.xlim(-0.3e-13,1e-12)\n",
    "# plt.grid()\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('log(Rate)')\n",
    "plt.show()\n",
    "print(lnr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numdifftools as nd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "dlndG = nd.Gradient(lnrate)\n",
    "dlndGi = dlndG(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 523,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00000000e+00, 2.51256281e-14, 5.02512563e-14, 7.53768844e-14,\n",
       "       1.00502513e-13, 1.25628141e-13, 1.50753769e-13, 1.75879397e-13,\n",
       "       2.01005025e-13, 2.26130653e-13, 2.51256281e-13, 2.76381910e-13,\n",
       "       3.01507538e-13, 3.26633166e-13, 3.51758794e-13, 3.76884422e-13,\n",
       "       4.02010050e-13, 4.27135678e-13, 4.52261307e-13, 4.77386935e-13,\n",
       "       5.02512563e-13, 5.27638191e-13, 5.52763819e-13, 5.77889447e-13,\n",
       "       6.03015075e-13, 6.28140704e-13, 6.53266332e-13, 6.78391960e-13,\n",
       "       7.03517588e-13, 7.28643216e-13, 7.53768844e-13, 7.78894472e-13,\n",
       "       8.04020101e-13, 8.29145729e-13, 8.54271357e-13, 8.79396985e-13,\n",
       "       9.04522613e-13, 9.29648241e-13, 9.54773869e-13, 9.79899497e-13,\n",
       "       1.00502513e-12, 1.03015075e-12, 1.05527638e-12, 1.08040201e-12,\n",
       "       1.10552764e-12, 1.13065327e-12, 1.15577889e-12, 1.18090452e-12,\n",
       "       1.20603015e-12, 1.23115578e-12, 1.25628141e-12, 1.28140704e-12,\n",
       "       1.30653266e-12, 1.33165829e-12, 1.35678392e-12, 1.38190955e-12,\n",
       "       1.40703518e-12, 1.43216080e-12, 1.45728643e-12, 1.48241206e-12,\n",
       "       1.50753769e-12, 1.53266332e-12, 1.55778894e-12, 1.58291457e-12,\n",
       "       1.60804020e-12, 1.63316583e-12, 1.65829146e-12, 1.68341709e-12,\n",
       "       1.70854271e-12, 1.73366834e-12, 1.75879397e-12, 1.78391960e-12,\n",
       "       1.80904523e-12, 1.83417085e-12, 1.85929648e-12, 1.88442211e-12,\n",
       "       1.90954774e-12, 1.93467337e-12, 1.95979899e-12, 1.98492462e-12,\n",
       "       2.01005025e-12, 2.03517588e-12, 2.06030151e-12, 2.08542714e-12,\n",
       "       2.11055276e-12, 2.13567839e-12, 2.16080402e-12, 2.18592965e-12,\n",
       "       2.21105528e-12, 2.23618090e-12, 2.26130653e-12, 2.28643216e-12,\n",
       "       2.31155779e-12, 2.33668342e-12, 2.36180905e-12, 2.38693467e-12,\n",
       "       2.41206030e-12, 2.43718593e-12, 2.46231156e-12, 2.48743719e-12,\n",
       "       2.51256281e-12, 2.53768844e-12, 2.56281407e-12, 2.58793970e-12,\n",
       "       2.61306533e-12, 2.63819095e-12, 2.66331658e-12, 2.68844221e-12,\n",
       "       2.71356784e-12, 2.73869347e-12, 2.76381910e-12, 2.78894472e-12,\n",
       "       2.81407035e-12, 2.83919598e-12, 2.86432161e-12, 2.88944724e-12,\n",
       "       2.91457286e-12, 2.93969849e-12, 2.96482412e-12, 2.98994975e-12,\n",
       "       3.01507538e-12, 3.04020101e-12, 3.06532663e-12, 3.09045226e-12,\n",
       "       3.11557789e-12, 3.14070352e-12, 3.16582915e-12, 3.19095477e-12,\n",
       "       3.21608040e-12, 3.24120603e-12, 3.26633166e-12, 3.29145729e-12,\n",
       "       3.31658291e-12, 3.34170854e-12, 3.36683417e-12, 3.39195980e-12,\n",
       "       3.41708543e-12, 3.44221106e-12, 3.46733668e-12, 3.49246231e-12,\n",
       "       3.51758794e-12, 3.54271357e-12, 3.56783920e-12, 3.59296482e-12,\n",
       "       3.61809045e-12, 3.64321608e-12, 3.66834171e-12, 3.69346734e-12,\n",
       "       3.71859296e-12, 3.74371859e-12, 3.76884422e-12, 3.79396985e-12,\n",
       "       3.81909548e-12, 3.84422111e-12, 3.86934673e-12, 3.89447236e-12,\n",
       "       3.91959799e-12, 3.94472362e-12, 3.96984925e-12, 3.99497487e-12,\n",
       "       4.02010050e-12, 4.04522613e-12, 4.07035176e-12, 4.09547739e-12,\n",
       "       4.12060302e-12, 4.14572864e-12, 4.17085427e-12, 4.19597990e-12,\n",
       "       4.22110553e-12, 4.24623116e-12, 4.27135678e-12, 4.29648241e-12,\n",
       "       4.32160804e-12, 4.34673367e-12, 4.37185930e-12, 4.39698492e-12,\n",
       "       4.42211055e-12, 4.44723618e-12, 4.47236181e-12, 4.49748744e-12,\n",
       "       4.52261307e-12, 4.54773869e-12, 4.57286432e-12, 4.59798995e-12,\n",
       "       4.62311558e-12, 4.64824121e-12, 4.67336683e-12, 4.69849246e-12,\n",
       "       4.72361809e-12, 4.74874372e-12, 4.77386935e-12, 4.79899497e-12,\n",
       "       4.82412060e-12, 4.84924623e-12, 4.87437186e-12, 4.89949749e-12,\n",
       "       4.92462312e-12, 4.94974874e-12, 4.97487437e-12, 5.00000000e-12])"
      ]
     },
     "execution_count": 523,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tspan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steady state DRC: 0.314\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steady state DRC: -0.039\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steady state DRC: 0.721\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steady state DRC: -0.227\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steady state DRC: -1.077\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steady state DRC: -0.000\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "DRCi = -dlndGi.T * R * T\n",
    "for i in range(len(DRCi)):\n",
    "    plt.plot(tspan, DRCi[i],'.--')\n",
    "    print(f'Steady state DRC: {DRCi[i][-1]:1.3f}')\n",
    "    plt.xlim(-0.3e-13,1e-12)\n",
    "    plt.xlabel('Time(s)')\n",
    "    plt.ylabel('DRC')\n",
    "#     plt.xlim(0,2)\n",
    "    plt.title(f'Steady state DRC for {char[i]} DRC: {DRCi[i][-1]:1.3f}')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sigma at steady state:  -1.68057728705165\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(tspan, -DRCi[3]/Theta[:,0],label = 'sigma = -(XA*) / (theta_A*)')\n",
    "plt.plot(tspan, -DRCi[4]/Theta[:,1], label = 'sigma = -(XB*) / (theta_B*)')\n",
    "plt.legend()\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Sigma')\n",
    "print('Sigma at steady state: ',(DRCi[4]/Theta[:,1])[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sigma at steady state:  1.6793419481427085\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x21fb38a09b0>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma_A = -DRCi[3]/Theta[:,0]\n",
    "sigma_B = -DRCi[4]/Theta[:,1]\n",
    "\n",
    "n1 = 1\n",
    "n2 = 2\n",
    "n3 = 2\n",
    "X1 = DRCi[0]\n",
    "X2 = DRCi[1]\n",
    "X3 = DRCi[2]\n",
    "\n",
    "plt.plot(tspan, (n1 * DRCi[0] + n2 * DRCi[1] + n3 * DRCi[2]), label = 'sum (X_i * n_i)')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Sigma')\n",
    "\n",
    "print('Sigma at steady state: ',(n1 * DRCi[0] + n2 * DRCi[1] + n3 * DRCi[2])[-1])\n",
    "plt.plot(tspan, (sigma_A + sigma_B)/2, label = '(sigma_A + sigma_B)/2')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:  1\n",
      "Iteration:  2\n",
      "Iteration:  3\n",
      "Iteration:  4\n",
      "Iteration:  5\n",
      "Iteration:  6\n",
      "Iteration:  7\n",
      "Iteration:  8\n",
      "Iteration:  9\n",
      "Iteration:  10\n",
      "Iteration:  11\n",
      "Iteration:  12\n",
      "Iteration:  13\n",
      "Iteration:  14\n",
      "Iteration:  15\n",
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    }
   ],
   "source": [
    "## Testing odeint with autograd()\n",
    "\n",
    "# def fk(G_i):\n",
    "#     kth = kb * T / h\n",
    "#     rt = R * T\n",
    "#     Gts1, Gts2, Gts3, Gas, Gbs, Gab = G_i\n",
    "#     k1 = kth * np.exp(-(0 / rt))\n",
    "#     k_1 = kth * np.exp(-(-Gbs) / rt)\n",
    "#     k2 = kth * np.exp(-(Gts2 - 2*Gas) / rt)\n",
    "#     k_2 = kth * np.exp(-(Gts2 - Gas - Gbs) / rt)\n",
    "#     k3 = kth * np.exp(-(Gts3 - (Gas + Gbs)) / rt)\n",
    "#     k_3 = kth * np.exp(-(Gts3 - Gab) / rt)\n",
    "#     return np.array([k1, k_1, k2, k_2, k3, k_3])\n",
    "\n",
    "def solver(k1, k_1, k2, k_2, k3, k_3):\n",
    "    def inside(theta, t, k1, k_1, k2, k_2, k3, k_3):\n",
    "        thetaa, thetab = theta\n",
    "        thetastar = 1 - thetaa - thetab\n",
    "\n",
    "\n",
    "        # balance on A*\n",
    "        z1 = (k1 * pa * thetastar - k_1 * thetaa\n",
    "              - k3 * thetaa * thetab )#+ k_3 * pab * thetastar**2)\n",
    "        # balance on B*\n",
    "        z2 = (k2 * pb * thetastar**2 - k_2 * thetab**2\n",
    "              - k3 * thetaa * thetab )#+ k_3 * pab * thetastar**2)\n",
    "        \n",
    "        return np.array([z1, z2])\n",
    "    Th = odeint(inside, [0.2, 0.5], tspan, tuple((k1, k_1, k2, k_2, k3, k_3,)))\n",
    "    return Th\n",
    "\n",
    "def outside(G_i,i):\n",
    "    Gts1, Gts2, Gts3, Gas, Gbs, Gab = G_i\n",
    "    k1, k_1, k2, k_2, k3, k_3 = fk(G_i)\n",
    "    thet = solver(k1, k_1, k2, k_2, k3, k_3)\n",
    "    theta_a, theta_b = thet[i,0], thet[i,1]\n",
    "    theta_s = 1 - theta_a - theta_b\n",
    "    r = k2 * pb * theta_s**2 - k_2 * theta_b**2\n",
    "    return r\n",
    "\n",
    "drdg = elementwise_grad(outside)\n",
    "ri = []\n",
    "drc = []\n",
    "for i in range(len(tspan)):\n",
    "    print('Iteration: ',i+1)\n",
    "    ri.append(outside(G,i))\n",
    "    drci = -np.array(drdg(G,i))*R*T\n",
    "    drc.append(drci/ri[i])  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steady state drc: 0.314\n",
      "Steady state drc: -0.039\n",
      "Steady state drc: 0.721\n",
      "Steady state drc: -0.227\n",
      "Steady state drc: -1.077\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.plot(tspan, drci[:,0])\n",
    "drc = np.squeeze([np.array([drc])])\n",
    "for i in range(len(char)-1):\n",
    "    plt.plot(tspan,drc[:,i],label = char[i])\n",
    "    plt.xlabel('Time(s)')\n",
    "#     plt.ylabel(f'DRC for {char[i]}' )\n",
    "    plt.ylabel(f'DRC' )\n",
    "    plt.xlim(-0.9e-13,1e-12)\n",
    "    print('Steady state drc:',f'{drc[:,i][-1]:1.3f}')\n",
    "#     plt.title(f'Steady state DRC: {drc[:,i][-1]:1.3f}')\n",
    "    plt.legend(bbox_to_anchor=(1.04,0.38), loc='upper left', ncol=1)\n",
    "#     plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DRC is nan for all energies till: 5.527638190954774e-14\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Comparision of \n",
    "print('DRC is nan for all energies till:',tspan[11]) \n",
    "for i in range(len(char)):\n",
    "    plt.plot(tspan,DRCi[i],'yo', label = 'FD')\n",
    "    plt.plot(tspan,drc[:,i] ,'r', label = 'AD')\n",
    "    plt.title(f'Steady state DRC for {char[i]} DRC: {DRCi[i][-1]:1.3f}')\n",
    "    plt.xlabel('Time(s)')\n",
    "    plt.ylabel('DRC')\n",
    "    plt.xlim(-0.9e-13,1e-12)\n",
    "    plt.legend()\n",
    "#     plt.grid()\n",
    "    plt.show()\n",
    "\n",
    "plt.plot(tspan, sum(DRCi[0:3]),'r.--')\n",
    "plt.title(f'Steady state sum is: {sum(DRCi[0:3])[-1]:1.4f}')\n",
    "plt.xlabel('Time(s)')\n",
    "plt.ylabel('sum of GTS')\n",
    "# plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(tspan, sum(DRCi[3:-1]),'r.--')\n",
    "plt.title(f'Steady state sum is: {sum(DRCi[3:-1])[-1]:1.4f}')\n",
    "plt.xlabel('Time(s)')\n",
    "plt.ylabel('sum of GIS')\n",
    "# plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lnrate1(G_i):\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(G_i)\n",
    "\n",
    "    Theta = odeint(rsys_t, [0.2, 0.5], tspan, args = ((G_i,)))\n",
    "    thetas = 1 -Theta[:,0] - Theta[:,1]\n",
    "#     r = k2 * pb * thetas**2 - k_2 * Theta[:,1]**2\n",
    "    r = k1 * pa * thetas - k_1 * Theta[:,0]\n",
    "#     r = k3 * Theta[:,0] * Theta[:,1]\n",
    "#     print(r)\n",
    "    ret = np.log(r)\n",
    "    return ret\n",
    "\n",
    "def lnrate2(G_i):\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(G_i)\n",
    "\n",
    "    Theta = odeint(rsys_t, [0.2, 0.5], tspan, args = ((G_i,)))\n",
    "    thetas = 1 -Theta[:,0] - Theta[:,1]\n",
    "    r = k2 * pb * thetas**2 - k_2 * Theta[:,1]**2\n",
    "#     r = k1 * pa * thetas - k_1 * Theta[:,0]\n",
    "#     r = k3 * Theta[:,0] * Theta[:,1]\n",
    "#     print(r)\n",
    "    ret = np.log(r)\n",
    "    return ret\n",
    "\n",
    "def lnrate3(G_i):\n",
    "    k1, k_1, k2, k_2, k3, k_3= fk(G_i)\n",
    "\n",
    "    Theta = odeint(rsys_t, [0.2, 0.5], tspan, args = ((G_i,)))\n",
    "    thetas = 1 -Theta[:,0] - Theta[:,1]\n",
    "#     r = k2 * pb * thetas**2 - k_2 * Theta[:,1]**2\n",
    "#     r = k1 * pa * thetas - k_1 * Theta[:,0]\n",
    "    r = k3 * Theta[:,0] * Theta[:,1]\n",
    "#     print(r)\n",
    "    ret = np.log(r)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "dlndG = nd.Gradient(lnrate1)\n",
    "dlndGi1 = dlndG(G)\n",
    "\n",
    "dlndG = nd.Gradient(lnrate2)\n",
    "dlndGi2 = dlndG(G)\n",
    "\n",
    "dlndG = nd.Gradient(lnrate3)\n",
    "dlndGi3 = dlndG(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 200)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "DRCi1 = -dlndGi1.T * R * T\n",
    "DRCi2 = -dlndGi2.T * R * T\n",
    "DRCi3 = -dlndGi3.T * R * T\n",
    "\n",
    "print(DRCi1.shape)\n",
    "\n",
    "for i in range(len(char)):\n",
    "    plt.plot(tspan,DRCi1.T[:,i] ,'y', label = 'CO consumption')\n",
    "    plt.plot(tspan,DRCi2.T[:,i] ,'g', label = 'O2 consumption')\n",
    "    plt.plot(tspan,DRCi3.T[:,i] ,'r', label = 'CO2 production')\n",
    "    plt.title(f'Steady state DRC for {char[i]} DRC: {DRCi1[i][-1]:1.3f}')\n",
    "    plt.xlabel('Time(s)')\n",
    "    plt.ylabel('DRC')\n",
    "    plt.xlim(-0.9e-13,1.5e-12)\n",
    "    plt.legend()\n",
    "#     plt.grid()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "DRCi1 = -dlndGi1.T * R * T\n",
    "DRCi2 = -dlndGi2.T * R * T\n",
    "DRCi3 = -dlndGi3.T * R * T\n",
    "\n",
    "# plt.plot(tspan, sum(DRCi1[0:3]),'r', label = 'Rate based on CO consumption')\n",
    "plt.plot(tspan, sum(DRCi2[0:3]),'b', label = 'Rate based on O2 consumption')\n",
    "# plt.plot(tspan, sum(DRCi3[0:3]),'g', label = 'Rate based on CO2 production')\n",
    "# plt.title(f'Steady state sum is: {sum(DRCi[0:3])[-1]:1.4f}')\n",
    "plt.xlabel('Time(s)')\n",
    "plt.ylabel('sum of G_TS')\n",
    "plt.title(f'Steady state sum = {sum(DRCi1[0:3])[-1]:1.2f}')\n",
    "plt.xlim(-0.05e-12, 1.5e-12)\n",
    "# plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(0, -1/2 - sqrt(3)*I/2), (0, -1/2 + sqrt(3)*I/2)}"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Getting analytical expression for rate\n",
    "from sympy import Symbol, Derivative, exp\n",
    "from sympy.solvers import solve\n",
    "from sympy.solvers.solveset import nonlinsolve\n",
    "\n",
    "G0 = np.array([0, 0.62, 0.72, -0.75, -1.2,-0.96])\n",
    "pa = 1e-5\n",
    "pb = 1e-6\n",
    "T = 300\n",
    "\n",
    "# k1, k_1, k2, k_2, k3, k_3 = fk(G0)\n",
    "# A = k1*pa\n",
    "# B = -k_1\n",
    "# C = -k_3\n",
    "# D = k_3*pb\n",
    "# E = k2*pb\n",
    "# F = -k_2\n",
    "# G = D+A\n",
    "# H = -2*G\n",
    "# I = G+B\n",
    "# J = 2*G + C\n",
    "# K = E + 2*D\n",
    "# L = D + E\n",
    "# M = F - K\n",
    "# N = C + 2*D\n",
    "\n",
    "G = Symbol('G')\n",
    "H = Symbol('H')\n",
    "I = Symbol('I')\n",
    "J = Symbol('J')\n",
    "L = Symbol('L')\n",
    "K = Symbol('K')\n",
    "M = Symbol('M')\n",
    "N = Symbol('N')\n",
    "D = Symbol('D')\n",
    "x = Symbol('x')\n",
    "y = Symbol('y')\n",
    "\n",
    "dxdt = G + H*x + H*y + I*x**2 + J*x*y + G*y**2\n",
    "dydt = L - K*x + M*y + N*x*y + D*x**2 + D*y**2\n",
    "\n",
    "\n",
    "# dxdt = 1 + 1*x + 1*y + 1*x**2 + 1*x*y + 1*y**2\n",
    "# dydt = 1 - 1*x + 1*y + 1*x*y + 1*x**2 + 1*y**2\n",
    "\n",
    "sol = nonlinsolve([dxdt, dydt], [x,y])\n",
    "sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(-(-1/2 - sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3)) - sqrt(5/6 - 2*(1619/13824 + sqrt(5862)*I/384)**(1/3) + 1/(2*sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))) - 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3))))*(11/4 + 2*(1/4 - sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))/2 - sqrt(5/6 - 2*(1619/13824 + sqrt(5862)*I/384)**(1/3) + 1/(2*sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))) - 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)))/2)**2 - 3*sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))/2 - 3*sqrt(5/6 - 2*(1619/13824 + sqrt(5862)*I/384)**(1/3) + 1/(2*sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))) - 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)))/2)/6, 1/4 - sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))/2 - sqrt(5/6 - 2*(1619/13824 + sqrt(5862)*I/384)**(1/3) + 1/(2*sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))) - 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)))/2), (-(-1/2 + sqrt(5/6 - 2*(1619/13824 + sqrt(5862)*I/384)**(1/3) + 1/(2*sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))) - 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3))) - sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3)))*(11/4 + 3*sqrt(5/6 - 2*(1619/13824 + sqrt(5862)*I/384)**(1/3) + 1/(2*sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))) - 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)))/2 - 3*sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))/2 + 2*(1/4 + sqrt(5/6 - 2*(1619/13824 + sqrt(5862)*I/384)**(1/3) + 1/(2*sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))) - 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)))/2 - sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))/2)**2)/6, 1/4 + sqrt(5/6 - 2*(1619/13824 + sqrt(5862)*I/384)**(1/3) + 1/(2*sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))) - 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)))/2 - sqrt(5/12 + 217/(288*(1619/13824 + sqrt(5862)*I/384)**(1/3)) + 2*(1619/13824 + sqrt(5862)*I/384)**(1/3))/2)}\n"
     ]
    }
   ],
   "source": [
    "## Simple example: \n",
    "\n",
    "def something(p):\n",
    "    return 2*p\n",
    "\n",
    "def find_rate(pin):\n",
    "    \n",
    "    pout = something(pin)\n",
    "    x = Symbol('x')\n",
    "    y = Symbol('y')\n",
    "\n",
    "    dxdt = 1 + 1*x + pout*y + 1*x**2 + 1*x*y + pout*y**2\n",
    "    dydt = 1 - 1*x + 1*y + pout*x*y + 1*x**2 + 1*y**2\n",
    "    \n",
    "    sol = nonlinsolve([dxdt, dydt], [x,y])\n",
    "    print(sol)\n",
    "\n",
    "find_rate(1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.        ,  3.        ],\n",
       "       [-0.39317367,  2.30774435],\n",
       "       [-2.46680856, -0.26005301],\n",
       "       [-2.53562764, -2.61650105],\n",
       "       [-0.54370045, -2.84647573],\n",
       "       [ 1.89010111, -0.76307279],\n",
       "       [ 2.78778646,  1.94049203],\n",
       "       [ 1.41979197,  3.06698706],\n",
       "       [-1.10209066,  1.70089145],\n",
       "       [-2.7282862 , -1.04754657],\n",
       "       [-2.13715871, -2.94462629],\n",
       "       [ 0.19087265, -2.4485599 ],\n",
       "       [ 2.36377872,  0.03749124],\n",
       "       [ 2.61560303,  2.4930727 ],\n",
       "       [ 0.74168383,  2.92249299],\n",
       "       [-1.73501396,  0.97675535],\n",
       "       [-2.8016375 , -1.76280747],\n",
       "       [-1.59132418, -3.06970768],\n",
       "       [ 0.91228432, -1.88180612],\n",
       "       [ 2.67446444,  0.83547014],\n",
       "       [ 2.26306338,  2.87374613],\n",
       "       [ 0.01243351,  2.57648147],\n",
       "       [-2.2483014 ,  0.18526793],\n",
       "       [-2.68180488, -2.35651602],\n",
       "       [-0.93576144, -2.98312069],\n",
       "       [ 1.57079065, -1.18529421],\n",
       "       [ 2.80073544,  1.57584037],\n",
       "       [ 1.7544765 ,  3.0562636 ],\n",
       "       [-0.71767422,  2.05281125],\n",
       "       [-2.60655936, -0.61899447],\n",
       "       [-2.37705093, -2.78773326],\n",
       "       [-0.21567412, -2.69083547],\n",
       "       [ 2.12098469, -0.40705145],\n",
       "       [ 2.73388444,  2.20755009],\n",
       "       [ 1.12491136,  3.02803938],\n",
       "       [-1.39829559,  1.38759139],\n",
       "       [-2.78508482, -1.38057494],\n",
       "       [-1.90838985, -3.02672535],\n",
       "       [ 0.51928482, -2.21300638],\n",
       "       [ 2.52492823,  0.39925916],\n",
       "       [ 2.47852103,  2.68704029],\n",
       "       [ 0.41777908,  2.79101961],\n",
       "       [-1.98249869,  0.62669162],\n",
       "       [-2.77156731, -2.04695893],\n",
       "       [-1.30813771, -3.05701244],\n",
       "       [ 1.21843699, -1.58258166],\n",
       "       [ 2.75476794,  1.17803928],\n",
       "       [ 2.05225373,  2.98124836],\n",
       "       [-0.31816084,  2.36154796],\n",
       "       [-2.43000098, -0.17742133]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def Gii(A, t):\n",
    "    a,b = A\n",
    "    z1 = 0\n",
    "    z2 = 0\n",
    "    for i in range(3):\n",
    "        z1 += i*a - i**2*b\n",
    "        z2 += 2*i*a - i*b\n",
    "        \n",
    "    return z1, z2\n",
    "tt = np.linspace(0,10)\n",
    "\n",
    "odeint(Gii,[2,3],tt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.010648"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = np.array([-1,2,0,0,0,-2])\n",
    "pi = np.array([0.55, 0.33, 0.22, 0.11, 0.44, 0.66])\n",
    "result = np.array([i for i in l if i < 0])\n",
    "neg = np.where(l==0)\n",
    "p = 1\n",
    "prod = np.prod([p*pi[i] for i in neg])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  4.,  9., 16., 25., 36., 49., 64., 81.])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ff = np.arange(0,10)\n",
    "ll = np.ones(10)*2\n",
    "\n",
    "print(ff)\n",
    "(ff**ll)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1  4  0  0  0 64]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0., 0.],\n",
       "       [0., 0.],\n",
       "       [0., 0.],\n",
       "       [0., 0.]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = np.array([-1,2,0,0,0,-2])\n",
    "pi = np.array([1, 2, 3, 4, 5, 6])\n",
    "print(l**pi)\n",
    "neg = np.where(l<0)\n",
    "np.prod([l[i]**pi[i] for i in neg])\n",
    "np.zeros([4,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 521,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.282\n",
      "0.546\n",
      "0.173\n",
      "-0.333\n",
      "-1.053\n",
      "-0.000\n"
     ]
    }
   ],
   "source": [
    "## Simple equation for rate: \n",
    "\n",
    "def fk(Gi):\n",
    "    kth = kb * T / h\n",
    "    rt = R * T\n",
    "    Gts1, Gts2, Gts3, Gas, Gbs, Gab = Gi\n",
    "    k1 = kth * np.exp(-(Gts1 - 0) / rt)\n",
    "    k_1 = kth * np.exp(-(Gts1 -Gas) / rt)\n",
    "    k2 = kth * np.exp(-(Gts2 - 0) / rt)\n",
    "    k_2 = kth * np.exp(-(Gts2 - 2*Gbs) / rt)\n",
    "    k3 = kth * np.exp(-(Gts3 - (Gas + Gbs)) / rt)\n",
    "    k_3 = kth * np.exp(-(Gts3 - Gab) / rt)\n",
    "#     print((Gts1 - 0),(Gts1 -Gas),(Gts2 - 0),(Gts2 - 2*Gbs),(Gts3 - (Gas + Gbs)),(Gts3 - Gab))\n",
    "    return np.array([k1, k_1, k2, k_2, k3, k_3])\n",
    "\n",
    "G = np.array([0, 0.62, 0.72, -1.2, -0.75,-0.96])\n",
    "\n",
    "def simple_rate(G_i):\n",
    "    k1, k_1, k2, k_2, k3, k_3 = fk(G_i)\n",
    "    K1 = k1/k_1\n",
    "    K2 = k2/k_2\n",
    "    K3 = k3/k_3\n",
    "    ts = 1/(1 + K1*pa + (K2*pb)**0.5)\n",
    "#     rf = k1*pa*ts\n",
    "#     rb = k_1*(ts**2 * pab)/(K3 * (K2*ts**2*pb)**0.5)\n",
    "#     print(rb, '.', rf)\n",
    "    r1 = ts*(k1*pa - (k_1*pab)/(K3 * (K2*pb)**0.5))\n",
    "    r3 = k3*K1*pa*ts**2*(K2*pb)**0.5 - k_3*ts**2*pab\n",
    "#     r = rf - rb\n",
    "    r2 = k2 * pb * (1/(1 + (k1/k_1)*pa + (k2*pb/k_2)**0.5))**2\n",
    "    ret = np.log(r1+r2+r3)\n",
    "    return ret\n",
    "\n",
    "pab = 0\n",
    "r = simple_rate(G)\n",
    "drdg = grad(simple_rate)\n",
    "dd = -drdg(G)*R*T\n",
    "for i in dd:\n",
    "    print(f'{i:1.3f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.000\n",
      "-0.000\n",
      "1.000\n",
      "0.000\n",
      "1.000\n",
      "-0.000\n"
     ]
    }
   ],
   "source": [
    "def fk(Gi):\n",
    "    kth = kb * T / h\n",
    "    rt = R * T\n",
    "    Gts1, Gts2, Gts3, Gas, Gbs, Gab = Gi\n",
    "    k1 = kth * np.exp(-(Gts1 - 0) / rt)\n",
    "    k_1 = kth * np.exp(-(Gts1 -Gas) / rt)\n",
    "    k2 = kth * np.exp(-(Gts2 - 0) / rt)\n",
    "    k_2 = kth * np.exp(-(Gts2 - 2*Gbs) / rt)\n",
    "    k3 = kth * np.exp(-(Gts3 - (Gas + Gbs)) / rt)\n",
    "    k_3 = kth * np.exp(-(Gts3 - Gab) / rt)\n",
    "#     print((Gts1 - 0),(Gts1 -Gas),(Gts2 - 0),(Gts2 - 2*Gbs),(Gts3 - (Gas + Gbs)),(Gts3 - Gab))\n",
    "    return np.array([k1, k_1, k2, k_2, k3, k_3])\n",
    "\n",
    "G = np.array([0, 0.62, 0.72, -1.2, -0.75,-0.96])\n",
    "\n",
    "def simple_rate(G_i):\n",
    "    k1, k_1, k2, k_2, k3, k_3 = fk(G_i)\n",
    "    K1 = k1/k_1\n",
    "    K2 = k2/k_2\n",
    "    K3 = k3/k_3\n",
    "#     ret1 = k3*pa*pb*K1*K2\n",
    "#     ret2 = (1 + K1*pa + K2*pb)**2\n",
    "#     ret = k3*np.exp(1.2/R/T)*pb/pa\n",
    "    ts = 1/(1 + K1*pa + K2*pb**0.5)\n",
    "    ta = K1*pa*thetas\n",
    "    tb = K2*pb*thetas\n",
    "    ret = k3*ta*tb\n",
    "    return np.log(ret)\n",
    "\n",
    "r = simple_rate(G)\n",
    "drdg = grad(simple_rate)\n",
    "dd = -drdg(G)*R*T\n",
    "for i in dd:\n",
    "    print(f'{i:1.3f}')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000\n",
      "-0.000\n",
      "1.000\n",
      "-0.388\n",
      "-1.225\n",
      "-0.000\n"
     ]
    }
   ],
   "source": [
    "def simple_rate(G_i):\n",
    "    k1, k_1, k2, k_2, k3, k_3 = fk(G_i)\n",
    "    a = k1*pa\n",
    "    b = a\n",
    "    c = (k_1 + k1*pa)\n",
    "    d = k2*pb\n",
    "    e = k_2\n",
    "#     print(a,b,c,d,e)\n",
    "    ta_n = -(e**0.5 * b * (d*c**2*(c - a)**2)**0.5 - a*b*c*d + d*a*c**2 - e*a*c**2 + c*d*b**2 - d*b*c**2)\n",
    "    ta_d = c*(b**2*(-d) + 2*b*c*d - d*c**2 + e*c**2)\n",
    "    ta = ta_n / ta_d\n",
    "\n",
    "    tb_n = a*b*d - e**0.5*(c**2*d*(a-c)**2)**0.5 - a*c*d - b*c*d + d*c**2\n",
    "    tb_d = (d*b**2 - 2*b*c*d + d*c**2 - e*c**2)\n",
    "    tb = tb_n / tb_d\n",
    "\n",
    "    r = k3*ta*tb\n",
    "    return np.log(r)\n",
    "\n",
    "G = np.array([0, 0.62, 0.72, -1.2, -0.75,-0.96])\n",
    "\n",
    "r = simple_rate(G)\n",
    "drdg = grad(simple_rate)\n",
    "dd = -drdg(G)*R*T\n",
    "for i in dd:\n",
    "    print(f'{i:1.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$G_{TS_1},G_{TS_2},G_{TS_3},G_{CO*}$ and $G_{O*}$"
   ]
  }
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