{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "ChEn-3170: Computational Methods in Chemical Engineering Spring 2024 UMass Lowell; Prof. V. F. de Almeida **25Mar24**\n",
    "\n",
    "# 13. Non-Linear Equation Root Finding w/ Newton's Method\n",
    "$  \n",
    "  \\newcommand{\\Amtrx}{\\boldsymbol{\\mathsf{A}}}\n",
    "  \\newcommand{\\Bmtrx}{\\boldsymbol{\\mathsf{B}}}\n",
    "  \\newcommand{\\Mmtrx}{\\boldsymbol{\\mathsf{M}}}\n",
    "  \\newcommand{\\Imtrx}{\\boldsymbol{\\mathsf{I}}}\n",
    "  \\newcommand{\\Pmtrx}{\\boldsymbol{\\mathsf{P}}}\n",
    "  \\newcommand{\\Lmtrx}{\\boldsymbol{\\mathsf{L}}}\n",
    "  \\newcommand{\\Umtrx}{\\boldsymbol{\\mathsf{U}}}\n",
    "  \\newcommand{\\Smtrx}{\\boldsymbol{\\mathsf{S}}}\n",
    "  \\newcommand{\\xvec}{\\boldsymbol{\\mathsf{x}}}\n",
    "  \\newcommand{\\avec}{\\boldsymbol{\\mathsf{a}}}\n",
    "  \\newcommand{\\bvec}{\\boldsymbol{\\mathsf{b}}}\n",
    "  \\newcommand{\\cvec}{\\boldsymbol{\\mathsf{c}}}\n",
    "  \\newcommand{\\rvec}{\\boldsymbol{\\mathsf{r}}}\n",
    "  \\newcommand{\\mvec}{\\boldsymbol{\\mathsf{m}}}\n",
    "  \\newcommand{\\gvec}{\\boldsymbol{\\mathsf{g}}}\n",
    "  \\newcommand{\\zerovec}{\\boldsymbol{\\mathsf{0}}}\n",
    "  \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n",
    "  \\newcommand{\\abs}[1]{\\left\\lvert{#1}\\right\\rvert}\n",
    "  \\newcommand{\\transpose}[1]{{#1}^\\top}\n",
    "  \\DeclareMathOperator{\\rank}{rank}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Table of Contents <a id=\"toc\"></a>\n",
    " * [Introduction](#intro)\n",
    " * [Algorithm](#algo)\n",
    " * [Input Data 1](#data1)\n",
    "   - [Plot Root Function](#prf1)\n",
    "   - [Plot Root 1](#prf11)\n",
    "   - [Plot Root 2](#prf12)\n",
    " * [Input Data 2](#data2)\n",
    "   - [Plot Root Function](#prf2)\n",
    "   - [Plot Root 1](#prf21)\n",
    " * [Inverse Problem (Forensics and/or Reverse Engineering)](#inv)\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Introduction](#toc)<a id=\"intro\"></a>\n",
    "Newton's method for computing roots of a single non-linear equation, $f(x)=0$, arising from chemical reaction equilibrium is described in the course notes OneNote [ChEn-3170-nonlinalg-a](https://studentuml-my.sharepoint.com/:o:/g/personal/valmor_dealmeida_uml_edu/Egp74fd_7GVCinMOYNy_QsABVyVlMd-lGwRy1kTLMW7HVA?e=QV1YfO). The reaction\n",
    "\n",
    "\\begin{equation*}\n",
    "\\text{A} + \\text{B} \\overset{K_x}{\\longleftrightarrow} \\text{C}   ,\n",
    "\\end{equation*}\n",
    "\n",
    "is used as a model, that is, compute $x_A$, $x_B$, $x_C$ for the given stoichiometry and molar equilibrium reaction constant $K_x$, where \n",
    "\n",
    "\\begin{equation*}\n",
    "K_x = \\frac{x_C}{x_A\\,x_B}.\n",
    "\\end{equation*}\n",
    "\n",
    "\n",
    "Note that this information is not sufficient for computing the equilibrium molar fraction. In addition, it is required that the molar fraction of **any two species is known** at some point in time or as a reference, say $x_{A_0}$, and $x_{B_0}$; note $x_{A_0} + x_{B_0} + x_{C_0} = 1$.\n",
    "\n",
    "The normalized extent of reaction, $\\widehat{\\varepsilon}$, at equilibrium, satisfies the equilibrium condition\n",
    "\n",
    "\\begin{equation*}\n",
    "\\bigl(K_x+1\\bigr) {\\widehat{\\varepsilon}}^2  - \n",
    "\\bigl(1-x_{C_0}\\bigr) \\bigl(K_x+1\\bigr) \\widehat{\\varepsilon} + x_{A_0}\\,x_{B_0}\\,K_x - x_{C_0} = 0 ,\n",
    "\\end{equation*}\n",
    "\n",
    "**for this particular stoichiometry**. Therefore this can be casted as $f_\\text{eq} (\\widehat{\\varepsilon}) = 0$, which is the form we need to use Newton's method on, thus \n",
    "\n",
    "\\begin{equation*}\n",
    "f_\\text{eq} (\\widehat{\\varepsilon}; x_{A_0}, x_{B_0}, x_{C_0}, K_x) = \n",
    "\\bigl(K_x+1\\bigr) {\\widehat{\\varepsilon}}^2  - \n",
    "\\bigl(1-x_{C_0}\\bigr) \\bigl(K_x+1\\bigr) \\widehat{\\varepsilon} + x_{A_0}\\,x_{B_0}\\,K_x - x_{C_0} = 0 .\n",
    "\\end{equation*}\n",
    "\n",
    "Note that if the stoichiometry changes, this function will be different.\n",
    "\n",
    "Once the values of $\\widehat{\\varepsilon}$ are found, the equilibrium molar fractions are computed from\n",
    "\n",
    "\\begin{equation*}\n",
    "x_A = \\frac{x_{A_0} - \\widehat{\\varepsilon}}{1 - \\widehat{\\varepsilon}} \\ \\qquad  ; \\qquad \\\n",
    "x_B = \\frac{x_{B_0} - \\widehat{\\varepsilon}}{1 - \\widehat{\\varepsilon}} \\ \\qquad  ; \\qquad \\\n",
    "x_C = \\frac{x_{C_0} + \\widehat{\\varepsilon}}{1 - \\widehat{\\varepsilon}}.\n",
    "\\end{equation*}\n",
    "\n",
    "Note the bounds on the normalized extent of reaction: $-x_{C_0} \\le \\widehat{\\varepsilon} \\le \\min(x_{A_0},x_{B_0})$, showing that the extent of reaction can be either positive (forward reaction) or negative (reverse reaction)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:15:42.823201Z",
     "start_time": "2022-03-29T16:15:42.812117Z"
    },
    "code_folding": [
     2
    ]
   },
   "outputs": [],
   "source": [
    "'''Equilibrium function at values or array values'''\n",
    "\n",
    "# Note: this function allows for either:\n",
    "#     1) a single ext_hat value passed (evaluation of function for Newton's method)\n",
    "#     2) a vector of values of ext_hat values passed (for plotting the function wrt to ext_hat)\n",
    "\n",
    "def f_eq(ext_hat, x_a_0, x_b_0, x_c_0, eq_kx_cte):\n",
    "    \"\"\"Root function f(ext_hat) for A + B <=> C.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    ext_hat: float or numpy.ndarray, required\n",
    "        Normalized extent of reaction. If `ext_hat` is an array, \n",
    "        the return value is also an array of values.\n",
    "    x_a_0: float, required\n",
    "        Mole fraction of species A.\n",
    "    x_b_0: float, required\n",
    "        Mole fraction of species B.\n",
    "    x_c_0: float, required\n",
    "        Mole fraction of species B.\n",
    "    eq_kx_cte: float, required\n",
    "        Mole equilibrium reaction constant.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    value: float or numpy.ndarray\n",
    "        Value or array of values of the equilibrium function \n",
    "        evaluated at `ext_hat`.\n",
    "\n",
    "    Examples\n",
    "    --------\n",
    "    \"\"\"\n",
    "    # Sanity checks\n",
    "    assert x_a_0 >= 0. and x_b_0 >= 0. and x_c_0 >= 0 and eq_kx_cte >= 0.\n",
    "    assert abs(x_a_0 + x_b_0 + x_c_0 - 1.0) <= 1e-12\n",
    "           \n",
    "    value =   (eq_kx_cte+1)*ext_hat**2  \\\n",
    "            - (1-x_c_0)*(eq_kx_cte+1)*ext_hat \\\n",
    "            + x_a_0 * x_b_0 * eq_kx_cte - x_c_0\n",
    "        \n",
    "    return value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:15:46.936674Z",
     "start_time": "2022-03-29T16:15:46.932589Z"
    },
    "code_folding": [
     2
    ]
   },
   "outputs": [],
   "source": [
    "'''Equilibrium function derivative'''\n",
    "\n",
    "def f_eq_prime(ext_hat, x_c_0, eq_kx_cte):\n",
    "    \"\"\"Derivative of equilibrium function f'(ext_hat) for A + B <=> C.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    ext_hat: float or numpy.ndarray, required\n",
    "        Normalized extent of reaction\n",
    "    x_c_0: float, required\n",
    "        Mole fraction of species B\n",
    "    eq_kx_cte: float, required\n",
    "        Mole equilibrium reaction constant.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    value: float or numpy.ndarray\n",
    "        Value or values of the root function evaluated at `ext_hat`.\n",
    "\n",
    "    Examples\n",
    "    --------\n",
    "    \"\"\"\n",
    "    # Sanity check\n",
    "    assert x_c_0 >= 0.0 and eq_kx_cte >= 0.0\n",
    "    \n",
    "    # f_eq = (eq_kx_cte+1)*ext_hat**2 - (1-x_c_0)*(eq_kx_cte+1)*ext_hat + x_a_0 * x_b_0 * eq_kx_cte - x_c_0       \n",
    "    value = 2.0*(eq_kx_cte+1)*ext_hat - (1-x_c_0)*(eq_kx_cte+1)\n",
    "        \n",
    "    return value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function f_eq in module __main__:\n",
      "\n",
      "f_eq(ext_hat, x_a_0, x_b_0, x_c_0, eq_kx_cte)\n",
      "    Root function f(ext_hat) for A + B <=> C.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    ext_hat: float or numpy.ndarray, required\n",
      "        Normalized extent of reaction. If `ext_hat` is an array, \n",
      "        the return value is also an array of values.\n",
      "    x_a_0: float, required\n",
      "        Mole fraction of species A.\n",
      "    x_b_0: float, required\n",
      "        Mole fraction of species B.\n",
      "    x_c_0: float, required\n",
      "        Mole fraction of species B.\n",
      "    eq_kx_cte: float, required\n",
      "        Mole equilibrium reaction constant.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    value: float or numpy.ndarray\n",
      "        Value or array of values of the equilibrium function \n",
      "        evaluated at `ext_hat`.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(f_eq)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Algorithm](#toc)<a id=\"algo\"></a>\n",
    "\n",
    "Given $f(\\cdot)$, find the roots \n",
    "\n",
    "\\begin{equation*}\n",
    "f(\\widehat{\\varepsilon}) = 0 ,\n",
    "\\end{equation*}\n",
    "\n",
    "using an iterative method based on the initial guess $\\widehat{\\varepsilon}_0$. Compute the updates\n",
    "\n",
    "\\begin{equation*}\n",
    "\\delta \\widehat{\\varepsilon}_k = - \\frac{f(\\widehat{\\varepsilon}_{k-1})}{f'(\\widehat{\\varepsilon}_{k-1})} \\ \\qquad \\  \\forall \\ \\qquad \\ k = 1,\\ldots,k_\\text{max} , \n",
    "\\end{equation*}\n",
    "\n",
    "then compute the approximation to the root\n",
    "\n",
    "\\begin{equation*}\n",
    " \\widehat{\\varepsilon}_k = \\widehat{\\varepsilon}_{k-1} + \\delta \\widehat{\\varepsilon}_k \\ \\qquad \\  \\forall \\ \\qquad\\ \\ k = 1,\\ldots,k_\\text{max} ,\n",
    "\\end{equation*}\n",
    "\n",
    "until convergence, say, $\\abs{\\delta \\widehat{\\varepsilon}_k} \\le 10^{-8}$ and $\\abs{f(\\widehat{\\varepsilon}_k)} \\le 10^{-8}$, or no convergence achieved , say $k>k_\\text{max}$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:15:51.912648Z",
     "start_time": "2022-03-29T16:15:51.903070Z"
    },
    "code_folding": [
     2
    ]
   },
   "outputs": [],
   "source": [
    "'''Newton's method'''\n",
    "\n",
    "def newton_solve(x_a_0, x_b_0, x_c_0, eq_kx_cte,\n",
    "                 ext_hat_0=0.0, k_max=30, tolerance=1.0e-10, verbose=True):\n",
    "\n",
    "    # Other initialization\n",
    "    delta_k = 1e+10   # Newton's update\n",
    "    f_k     = 1e+10\n",
    "    ext_hat = ext_hat_0\n",
    "\n",
    "    if verbose is True:\n",
    "        print('\\n')\n",
    "        print('******************************************************')\n",
    "        print(\"          Newton's Method Iterations                  \")\n",
    "        print('******************************************************')\n",
    "        print(\"k |  f(e_k)  |  f'(e_k) | |del e_k| |    e_k   |convg|\")\n",
    "        print('------------------------------------------------------')\n",
    "\n",
    "    import math\n",
    "    \n",
    "    k = 0 # step counter\n",
    "    \n",
    "    while (abs(delta_k) > tolerance or abs(f_k) > tolerance) and k <= k_max:\n",
    "        \n",
    "        f_k       = f_eq(ext_hat, x_a_0, x_b_0, x_c_0, eq_kx_cte)\n",
    "        \n",
    "        f_prime_k = f_eq_prime(ext_hat, x_c_0, eq_kx_cte)\n",
    "        \n",
    "        delta_k_old = delta_k\n",
    "        \n",
    "        delta_k = -f_k / f_prime_k # Newton's update\n",
    "        \n",
    "        ext_hat += delta_k # do the update\n",
    "        \n",
    "        if k > 0:\n",
    "            if delta_k != 0.0 and delta_k_old != 0.0:\n",
    "                convergence_factor = math.log(abs(delta_k), 10) / math.log(abs(delta_k_old), 10)\n",
    "            else:\n",
    "                convergence_factor = 0.0  \n",
    "        else:\n",
    "            convergence_factor = 0.0\n",
    "            \n",
    "        k += 1 # increment counter\n",
    "        \n",
    "        if verbose is True:\n",
    "            print('%2i %+5.3e %+5.3e %+5.3e  %+5.3e %5.2f'%\\\n",
    "                  (k,f_k, f_prime_k, abs(delta_k), ext_hat, convergence_factor))\n",
    "            \n",
    "    # Exit the while loop here\n",
    "    if verbose is True:\n",
    "        print('******************************************************') \n",
    "        print('Root = %8.5e'%ext_hat)\n",
    "    \n",
    "    return ext_hat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Input Data 1](#toc)<a id=\"data1\"></a>\n",
    "\n",
    "Reversible reaction: \n",
    "$\\text{A} + \\text{B} \\overset{K_x}{\\longleftrightarrow} \\text{C}$\n",
    "\n",
    "Name                        | Parameter    | Value |\n",
    "----------------------------|--------------|-------| \n",
    "initial mole fraction of A  | $x_{A_0}$    | 0.5   | \n",
    "initial mole fraction of B  | $x_{B_0}$    | 0.5   |\n",
    "initial mole fraction of C  | $x_{C_0}$    | 0.0   |\n",
    "molar equilibrium constant   | $K_\\text{x}$ | 108   | "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:16:44.564061Z",
     "start_time": "2022-03-29T16:16:44.557925Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min. ext_hat = -0.00\n",
      "Max. ext_hat =  0.50\n"
     ]
    }
   ],
   "source": [
    "'''Parameters for chemical equilibrium of A + B <-> C'''\n",
    "\n",
    "x_a_0 = 0.5 # initial (or ref) equimolar\n",
    "x_b_0 = 0.5 # initial (or ref) equimolar\n",
    "x_c_0 = 0.0 # initial (or ref) no product\n",
    "\n",
    "eq_kx_cte = 108.0\n",
    "\n",
    "# Sanity check\n",
    "assert abs(x_a_0 + x_b_0 + x_c_0 - 1.0) <= 1e-12\n",
    "assert x_a_0 >= 0. and x_b_0 >= 0. and x_c_0 >= 0 and eq_kx_cte >= 0.\n",
    "\n",
    "ext_hat_min = -x_c_0\n",
    "ext_hat_max = min(x_a_0, x_b_0)\n",
    "\n",
    "print('Min. ext_hat = %5.2f'%ext_hat_min)\n",
    "print('Max. ext_hat = %5.2f'%ext_hat_max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:17:33.445173Z",
     "start_time": "2022-03-29T16:17:33.421227Z"
    },
    "code_folding": [
     2
    ]
   },
   "outputs": [],
   "source": [
    "'''Function: plot equilibrium function'''\n",
    "\n",
    "def plot_function(ex_min, ex_max, n_pts,\n",
    "                  x_a_0, x_b_0, x_c_0, eq_kx_cte,\n",
    "                  ext_hat_root=None  ):\n",
    "    \n",
    "    import matplotlib.pyplot as plt\n",
    "    %matplotlib inline\n",
    "    \n",
    "    plt.figure(1, figsize=(8, 6))\n",
    "    \n",
    "    import numpy as np\n",
    "    ex_vec = np.linspace(ex_min, ex_max, n_pts)\n",
    "    \n",
    "    # Note here that f_eq(ex_vec, ...) receives a vector of values of ex_vec (see definition of f_eq())\n",
    "    plt.plot(ex_vec, f_eq(ex_vec, x_a_0, x_b_0, x_c_0, eq_kx_cte),'b-',label='$f_{eq}$')\n",
    "    \n",
    "    plt.xlabel(r'$\\hat{\\varepsilon}$',fontsize=18)\n",
    "    plt.ylabel(r'$f_{eq}(\\hat{\\varepsilon})$',fontsize=18)\n",
    "    plt.title('Computing the Roots of $f(x)$',fontsize=20)\n",
    "    plt.legend(loc='best',fontsize=12)\n",
    "    plt.xticks(fontsize=16)\n",
    "    plt.yticks(fontsize=16)\n",
    "    \n",
    "    (x_min,x_max) = plt.xlim()\n",
    "    dx = abs(x_max-x_min)\n",
    "    x_text = (x_max+x_min)/2\n",
    "    \n",
    "    (y_min,y_max) = plt.ylim()\n",
    "    dy = abs(y_max-y_min)\n",
    "    y_text = y_max - dy*0.05\n",
    "    \n",
    "    plt.text(x_text, y_text, r'$x_{A_0}=$%8.2e'%x_a_0,fontsize=16)\n",
    "    y_text -= dy*0.06\n",
    "    plt.text(x_text, y_text, r'$x_{B_0}=$%8.2e'%x_b_0,fontsize=16)\n",
    "    y_text -= dy*0.06\n",
    "    plt.text(x_text, y_text, r'$x_{C_0}=$%8.2e'%x_c_0,fontsize=16)\n",
    "    y_text -= dy*0.06\n",
    "    plt.text(x_text, y_text, r'$K_x=$%8.2e'%eq_kx_cte,fontsize=16)\n",
    "    \n",
    "    \n",
    "    if ext_hat_root is not None:\n",
    "        \n",
    "        plt.plot(ext_hat_root, 0.0,'r*',label='root',markersize=14)\n",
    "               \n",
    "        (x_min,x_max) = plt.xlim()\n",
    "        dx = abs(x_max-x_min)\n",
    "        x_text = ext_hat_root + dx*0.01\n",
    "    \n",
    "        (y_min,y_max) = plt.ylim()\n",
    "        dy = abs(y_max-y_min)\n",
    "        y_text = 0.0 + dy*0.01\n",
    "    \n",
    "        plt.text(x_text, y_text, r'$\\hat{\\varepsilon}^*=$%8.2e'%ext_hat_root,fontsize=16)\n",
    "    \n",
    "    \n",
    "    plt.grid(True)\n",
    "    plt.show()\n",
    "    print('')\n",
    "    \n",
    "    return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Plot Root Function](#toc)<a id=\"prf1\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:17:40.891892Z",
     "start_time": "2022-03-29T16:17:39.227294Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "'''Plot equilibrium function'''\n",
    "\n",
    "n_pts = 100\n",
    "\n",
    "plot_function(ext_hat_min, ext_hat_max, n_pts, x_a_0, x_b_0, x_c_0, eq_kx_cte)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:18:36.143384Z",
     "start_time": "2022-03-29T16:18:36.135643Z"
    },
    "code_folding": [],
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "******************************************************\n",
      "          Newton's Method Iterations                  \n",
      "******************************************************\n",
      "k |  f(e_k)  |  f'(e_k) | |del e_k| |    e_k   |convg|\n",
      "------------------------------------------------------\n",
      " 1 +6.562e+00 -5.450e+01 +1.204e-01  +3.704e-01  0.00\n",
      " 2 +1.580e+00 -2.825e+01 +5.594e-02  +4.264e-01  1.36\n",
      " 3 +3.411e-01 -1.605e+01 +2.125e-02  +4.476e-01  1.34\n",
      " 4 +4.922e-02 -1.142e+01 +4.309e-03  +4.519e-01  1.41\n",
      " 5 +2.024e-03 -1.048e+01 +1.931e-04  +4.521e-01  1.57\n",
      " 6 +4.063e-06 -1.044e+01 +3.892e-07  +4.521e-01  1.73\n",
      " 7 +1.651e-11 -1.044e+01 +1.581e-12  +4.521e-01  1.84\n",
      "******************************************************\n",
      "Root = 4.52109e-01\n"
     ]
    }
   ],
   "source": [
    "'''Find root'''\n",
    "\n",
    "ext_hat_0 = (ext_hat_max + ext_hat_min)/2.0  # initial guess\n",
    "\n",
    "k_max = 20         # maximum # of Newton iterations\n",
    "tolerance = 1.0e-8 # convergence tolerance\n",
    "\n",
    "ext_hat = newton_solve(x_a_0, x_b_0, x_c_0, eq_kx_cte,\n",
    "                       ext_hat_0, k_max, tolerance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:18:36.143384Z",
     "start_time": "2022-03-29T16:18:36.135643Z"
    },
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Equilibrium mole fractions:\n",
      "\n",
      "x_a = 8.741e-02 ( 8.7%)\n",
      "x_b = 8.741e-02 ( 8.7%)\n",
      "x_c = 8.252e-01 (82.5%)\n"
     ]
    }
   ],
   "source": [
    "'''Post-process root result and find equilibrium molar fractions'''\n",
    "\n",
    "x_a = (x_a_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_b = (x_b_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_c = (x_c_0 + ext_hat)/(1.0-ext_hat)\n",
    "\n",
    "# Sanity checks\n",
    "assert x_a >= 0. and x_b >= 0. and x_c >= 0.\n",
    "assert abs(x_a + x_b + x_c - 1.0) <= 1e-12\n",
    "assert abs(x_c/x_a/x_b - eq_kx_cte) <= 1e-10,'%r'%(abs(x_c/x_a/x_b - eq_kx_cte))\n",
    "\n",
    "print('')\n",
    "print('Equilibrium mole fractions:\\n')\n",
    "print('x_a = %5.3e (%4.1f%%)'%(x_a,round(x_a*100,1)))\n",
    "print('x_b = %5.3e (%4.1f%%)'%(x_b,round(x_b*100,1)))\n",
    "print('x_c = %5.3e (%4.1f%%)'%(x_c,round(x_c*100,1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Plot Root 1](#toc)<a id=\"prf11\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:19:31.626466Z",
     "start_time": "2022-03-29T16:19:31.329821Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "'''Plot equilibrium function with root'''\n",
    "\n",
    "n_pts = 100\n",
    "\n",
    "plot_function(ext_hat_min, ext_hat_max, n_pts, x_a_0, x_b_0, x_c_0, eq_kx_cte, ext_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:20:20.807513Z",
     "start_time": "2022-03-29T16:20:20.799229Z"
    },
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "******************************************************\n",
      "          Newton's Method Iterations                  \n",
      "******************************************************\n",
      "k |  f(e_k)  |  f'(e_k) | |del e_k| |    e_k   |convg|\n",
      "------------------------------------------------------\n",
      " 1 +4.110e+00 +4.360e+01 +9.427e-02  +6.057e-01  0.00\n",
      " 2 +9.686e-01 +2.305e+01 +4.202e-02  +5.637e-01  1.34\n",
      " 3 +1.925e-01 +1.389e+01 +1.386e-02  +5.499e-01  1.35\n",
      " 4 +2.093e-02 +1.087e+01 +1.926e-03  +5.479e-01  1.46\n",
      " 5 +4.042e-04 +1.045e+01 +3.869e-05  +5.479e-01  1.62\n",
      " 6 +1.631e-07 +1.044e+01 +1.563e-08  +5.479e-01  1.77\n",
      " 7 +2.132e-14 +1.044e+01 +2.042e-15  +5.479e-01  1.88\n",
      "******************************************************\n",
      "Root = 5.47891e-01\n"
     ]
    }
   ],
   "source": [
    "'''Find root'''\n",
    "\n",
    "ext_hat_0 = 0.7 # not valid; we know in advance but let's do it anyway\n",
    "\n",
    "k_max = 20\n",
    "\n",
    "tolerance = 1.0e-8\n",
    "\n",
    "ext_hat = newton_solve( x_a_0, x_b_0, x_c_0, eq_kx_cte,\n",
    "                        ext_hat_0,k_max,tolerance )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:20:20.807513Z",
     "start_time": "2022-03-29T16:20:20.799229Z"
    },
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Equilibrium mole fractions:\n",
      "\n",
      "x_a = -1.059e-01 (-10.6%)\n",
      "x_b = -1.059e-01 (-10.6%)\n",
      "x_c = 1.212e+00 (121.2%)\n"
     ]
    }
   ],
   "source": [
    "'''Post-process result and find equilibrium molar fractions'''\n",
    "\n",
    "x_a = (x_a_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_b = (x_b_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_c = (x_c_0 + ext_hat)/(1.0-ext_hat)\n",
    "\n",
    "# Sanity check is not going to pass\n",
    "#assert x_a >= 0. and x_b >= 0. and x_c >= 0.\n",
    "assert abs(x_a + x_b + x_c - 1.0) <= 1e-12\n",
    "assert abs(x_c/x_a/x_b - eq_kx_cte) <= 1e-10,'%r'%(abs(x_c/x_a/x_b - eq_kx_cte))\n",
    "\n",
    "print('')\n",
    "print('Equilibrium mole fractions:\\n')\n",
    "print('x_a = %5.3e (%4.1f%%)'%(x_a,round(x_a*100,1)))\n",
    "print('x_b = %5.3e (%4.1f%%)'%(x_b,round(x_b*100,1)))\n",
    "print('x_c = %5.3e (%4.1f%%)'%(x_c,round(x_c*100,1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Plot Root 2](#toc)<a id=\"prf12\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:21:16.561340Z",
     "start_time": "2022-03-29T16:21:16.317267Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "'''Plot equilibrium function with root'''\n",
    "\n",
    "ext_hat_min = 0.0\n",
    "ext_hat_max = 1.0\n",
    "\n",
    "n_pts = 100\n",
    "\n",
    "plot_function(ext_hat_min, ext_hat_max, n_pts, x_a_0, x_b_0, x_c_0, eq_kx_cte, ext_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:21:50.683604Z",
     "start_time": "2022-03-29T16:21:50.678246Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "******************************************************\n",
      "          Newton's Method Iterations                  \n",
      "******************************************************\n",
      "k |  f(e_k)  |  f'(e_k) | |del e_k| |    e_k   |convg|\n",
      "------------------------------------------------------\n",
      " 1 +0.000e+00 +1.044e+01 +0.000e+00  +5.479e-01  0.00\n",
      "******************************************************\n",
      "Root = 5.47891e-01\n"
     ]
    }
   ],
   "source": [
    "'''Find root at the root'''\n",
    "\n",
    "ext_hat_0 = ext_hat\n",
    "\n",
    "k_max = 20\n",
    "tolerance = 1.0e-8\n",
    "\n",
    "ext_hat = newton_solve(x_a_0, x_b_0, x_c_0, eq_kx_cte,\n",
    "                       ext_hat_0, k_max, tolerance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Input Data 2](#toc)<a id=\"data2\"></a>\n",
    "\n",
    "Reversible reaction: A + B <=> C \n",
    "\n",
    "Name                        | Parameter    | Value    |\n",
    "----------------------------|--------------|----------| \n",
    "initial mole fraction of A  | $x_{A0}$     | 0.5      |\n",
    "initial mole fraction of B  | $x_{B0}$     | 0.2      |\n",
    "initial mole fraction of C  | $x_{C0}$     | 0.3      |\n",
    "mole equilibrium constant   | $K_\\text{x}$ | 108      |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:22:42.541623Z",
     "start_time": "2022-03-29T16:22:42.536726Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min. ext_hat = -0.30\n",
      "Max. ext_hat =  0.20\n"
     ]
    }
   ],
   "source": [
    "'''Parameters for chemical equilibrium of A + B <-> C'''\n",
    "\n",
    "x_a_0 = 0.5 # initial (or ref)\n",
    "x_b_0 = 0.2 # initial (or ref)\n",
    "x_c_0 = 0.3 # initial (or ref)\n",
    "\n",
    "eq_kx_cte = 108.0\n",
    "\n",
    "# Sanity checks\n",
    "assert abs(x_a_0 + x_b_0 + x_c_0 - 1.0) <= 1e-12\n",
    "assert x_a_0 >= 0. and x_b_0 >= 0. and x_c_0 >= 0. and eq_kx_cte >= 0.\n",
    "\n",
    "ext_hat_min = -x_c_0\n",
    "ext_hat_max = min(x_a_0,x_b_0)\n",
    "\n",
    "print('Min. ext_hat = %5.2f'%ext_hat_min)\n",
    "print('Max. ext_hat = %5.2f'%ext_hat_max)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Plot Root Function](#toc)<a id=\"prf2\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:22:50.826237Z",
     "start_time": "2022-03-29T16:22:50.561685Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "'''Plot equilibrium function'''\n",
    "\n",
    "n_pts = 100\n",
    "\n",
    "plot_function( ext_hat_min, ext_hat_max, n_pts, x_a_0, x_b_0, x_c_0, eq_kx_cte )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:23:07.239037Z",
     "start_time": "2022-03-29T16:23:07.230669Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "******************************************************\n",
      "          Newton's Method Iterations                  \n",
      "******************************************************\n",
      "k |  f(e_k)  |  f'(e_k) | |del e_k| |    e_k   |convg|\n",
      "------------------------------------------------------\n",
      " 1 +1.459e+01 -8.720e+01 +1.673e-01  +1.173e-01  0.00\n",
      " 2 +3.050e+00 -5.073e+01 +6.013e-02  +1.774e-01  1.57\n",
      " 3 +3.941e-01 -3.762e+01 +1.047e-02  +1.879e-01  1.62\n",
      " 4 +1.196e-02 -3.534e+01 +3.384e-04  +1.882e-01  1.75\n",
      " 5 +1.248e-05 -3.527e+01 +3.539e-07  +1.882e-01  1.86\n",
      " 6 +1.365e-11 -3.527e+01 +3.872e-13  +1.882e-01  1.92\n",
      "******************************************************\n",
      "Root = 1.88229e-01\n"
     ]
    }
   ],
   "source": [
    "'''Find root'''\n",
    "\n",
    "ext_hat_0 = (ext_hat_max+ext_hat_min)/2.0\n",
    "\n",
    "k_max = 20\n",
    "tolerance = 1.0e-8\n",
    "\n",
    "ext_hat = newton_solve( x_a_0, x_b_0, x_c_0, eq_kx_cte,\n",
    "                        ext_hat_0,k_max,tolerance )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:23:07.239037Z",
     "start_time": "2022-03-29T16:23:07.230669Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Equilibrium mole fractions:\n",
      "\n",
      "x_a = 3.841e-01 (38.4%)\n",
      "x_b = 1.450e-02 ( 1.4%)\n",
      "x_c = 6.014e-01 (60.1%)\n"
     ]
    }
   ],
   "source": [
    "'''Post-process result and find equilibrium molar fractions'''\n",
    "\n",
    "x_a = (x_a_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_b = (x_b_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_c = (x_c_0 + ext_hat)/(1.0-ext_hat)\n",
    "\n",
    "# Sanity checks\n",
    "assert x_a >= 0. and x_b >= 0. and x_c >= 0.\n",
    "assert abs(x_a + x_b + x_c - 1.0) <= 1e-12\n",
    "assert abs(x_c/x_a/x_b - eq_kx_cte) <= 1e-10,'%r'%(abs(x_c/x_a/x_b - eq_kx_cte))\n",
    "\n",
    "print('')\n",
    "print('Equilibrium mole fractions:\\n')\n",
    "print('x_a = %5.3e (%4.1f%%)'%(x_a,round(x_a*100,1)))\n",
    "print('x_b = %5.3e (%4.1f%%)'%(x_b,round(x_b*100,1)))\n",
    "print('x_c = %5.3e (%4.1f%%)'%(x_c,round(x_c*100,1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Plot Root 1](#toc)<a id=\"prf21\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:23:34.436714Z",
     "start_time": "2022-03-29T16:23:34.152820Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "'''Plot equilibrium function with root'''\n",
    "\n",
    "n_pts = 100\n",
    "\n",
    "plot_function(ext_hat_min, ext_hat_max, n_pts, x_a_0, x_b_0, x_c_0, eq_kx_cte, ext_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Inverse Problem (Forensics and Reverse Engineering)](#toc)<a id=\"inv\"></a>\n",
    "Someone is interested in the answers to the questions:\n",
    "\n",
    "1. If we know equilibrium molar fractions $x_A$, $x_B$ and $x_C$, could a unique initial (reference) $x_{A_0} , x_{B_0}, x_{C_0}$ be computed? if not unique, how many exist?\n",
    "2. What could we say about the initial (reference)  values $x_{A_0} , x_{B_0}, x_{C_0}$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:36:32.052214Z",
     "start_time": "2022-03-29T16:36:32.046911Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "'''Let us compute an equilibrium molar fraction'''\n",
    "\n",
    "x_a_0 = 0.34\n",
    "x_b_0 = 0.64\n",
    "x_c_0 = 0.02\n",
    "\n",
    "# Sanity checks\n",
    "assert abs(x_a_0 + x_b_0 + x_c_0 - 1.0) <= 1e-12\n",
    "assert x_a_0 >= 0. and x_b_0 >= 0. and x_c_0 >= 0.\n",
    "\n",
    "eq_kx_cte = 56.8 #108.0\n",
    "\n",
    "ext_hat_min = -x_c_0\n",
    "ext_hat_max = min(x_a_0,x_b_0)\n",
    "\n",
    "print('Min. ext_hat = %5.2f'%ext_hat_min)\n",
    "print('Max. ext_hat = %5.2f'%ext_hat_max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:36:51.120519Z",
     "start_time": "2022-03-29T16:36:51.112571Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "'''Find root and the \"gold\" equilibrium molar fractions'''\n",
    "\n",
    "ext_hat_0 = (ext_hat_max+ext_hat_min)/2.0\n",
    "\n",
    "k_max = 20\n",
    "tolerance = 1.0e-8\n",
    "\n",
    "ext_hat = newton_solve(x_a_0, x_b_0, x_c_0, eq_kx_cte,\n",
    "                       ext_hat_0,k_max,tolerance)\n",
    "\n",
    "x_a_gold = (x_a_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_b_gold = (x_b_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_c_gold = (x_c_0 + ext_hat)/(1.0-ext_hat)\n",
    "\n",
    "# Sanity checks\n",
    "assert x_a_gold > 0. and x_b_gold > 0. and x_c_gold >= 0.\n",
    "assert abs(x_a_gold + x_b_gold + x_c_gold - 1.0) <= 1e-12\n",
    "assert abs(x_c_gold/x_a_gold/x_b_gold - eq_kx_cte) <= 1e-12,'%r'%(abs(x_c_gold/x_a_gold/x_b_gold - eq_kx_cte)) \n",
    "\n",
    "print('')\n",
    "print('Equilibrium mole fractions:\\n')\n",
    "print('x_a_gold = %5.3e\\n'%x_a_gold)\n",
    "print('x_b_gold = %5.3e\\n'%x_b_gold)\n",
    "print('x_c_gold = %5.3e\\n'%x_c_gold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:37:26.378696Z",
     "start_time": "2022-03-29T16:37:26.367301Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "'''Find the reference molar fractions'''\n",
    "\n",
    "try:\n",
    "    from chen_3170.toolkit import magic_molar_fractions\n",
    "except ModuleNotFoundError:\n",
    "    assert False, 'You need to provide your own magic_molar_fractions function here. Bailing out.'\n",
    "\n",
    "# this magic function returns reference molar fractions for given equilibrium molar fractions\n",
    "(x_a_0, x_b_0, x_c_0) = magic_molar_fractions(x_a_gold, x_b_gold, x_c_gold)\n",
    "\n",
    "print('x_A_0 = %5.3e\\n'%x_a_0)\n",
    "print('x_B_0 = %5.3e\\n'%x_b_0)\n",
    "print('x_C_0 = %5.3e\\n'%x_c_0)\n",
    "\n",
    "# Sanity checks\n",
    "assert abs(x_a_0 + x_b_0 + x_c_0 - 1.0) <= 1e-12\n",
    "assert x_a_0 >= 0. and x_b_0 >= 0. and x_c_0 >= 0.\n",
    "\n",
    "ext_hat_min = -x_c_0\n",
    "ext_hat_max = min(x_a_0,x_b_0)\n",
    "\n",
    "print('Min. ext_hat = %5.2f'%ext_hat_min)\n",
    "print('Max. ext_hat = %5.2f'%ext_hat_max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:37:35.383676Z",
     "start_time": "2022-03-29T16:37:35.150325Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "'''Plot equilibrium function'''\n",
    "\n",
    "n_pts = 100\n",
    "\n",
    "plot_function(ext_hat_min, ext_hat_max, n_pts, x_a_0, x_b_0, x_c_0, eq_kx_cte)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:37:40.942828Z",
     "start_time": "2022-03-29T16:37:40.934188Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "'''Find root and equilibrium molar fractions'''\n",
    "\n",
    "ext_hat_0 = (ext_hat_max+ext_hat_min)/2.0\n",
    "\n",
    "k_max = 20\n",
    "tolerance = 1.0e-8\n",
    "\n",
    "ext_hat = newton_solve( x_a_0, x_b_0, x_c_0, eq_kx_cte,\n",
    "                        ext_hat_0,k_max,tolerance )\n",
    "\n",
    "x_a = (x_a_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_b = (x_b_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_c = (x_c_0 + ext_hat)/(1.0-ext_hat)\n",
    "\n",
    "# Sanity checks\n",
    "assert x_a >= 0. and x_b >= 0. and x_c >= 0.\n",
    "assert abs(x_a + x_b + x_c - 1.0) <= 1e-12\n",
    "assert abs(x_c/x_a/x_b - eq_kx_cte) <= 1e-10,'%r'%(abs(x_c/x_a/x_b - eq_kx_cte))\n",
    "\n",
    "print('')\n",
    "print('Equilibrium mole fractions:\\n')\n",
    "print('x_a = %5.3e\\n'%x_a)\n",
    "print('x_b = %5.3e\\n'%x_b)\n",
    "print('x_c = %5.3e\\n'%x_c)\n",
    "\n",
    "if abs(x_a - x_a_gold) + abs(x_b - x_b_gold) + abs(x_c - x_c_gold) <= 1e-12:\n",
    "    print('This matches the gold values.')\n",
    "else:\n",
    "    print('This DOES NOT match the gold values.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:37:59.298246Z",
     "start_time": "2022-03-29T16:37:59.290330Z"
    },
    "code_folding": [
     2
    ],
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "'''Function: reference states'''\n",
    "\n",
    "def plot_ref_states(x_a_0, x_b_0, x_c_0,\n",
    "                     x_a, x_b, x_c ):\n",
    "    \n",
    "    import matplotlib.pyplot as plt\n",
    "    \n",
    "    plt.figure(1, figsize=(15, 6))\n",
    "    \n",
    "    plt.subplot(121) \n",
    "    \n",
    "    plt.plot(x_a_0, x_b_0,'b*',markersize=14)\n",
    "    \n",
    "    plt.xlim(0,1)\n",
    "    plt.ylim(0,1)\n",
    "    plt.xlabel(r'$x_{A_0}$',fontsize=18)\n",
    "    plt.ylabel(r'$x_{B_0}$',fontsize=18)\n",
    "    plt.title('Reference',fontsize=20)   \n",
    "    plt.xticks(fontsize=16)\n",
    "    plt.yticks(fontsize=16)\n",
    "    plt.grid(True)\n",
    "    \n",
    "    plt.subplot(122)\n",
    "    plt.plot(x_a, x_b,'go',markersize=14)\n",
    "    \n",
    "    plt.xlim(0,1)\n",
    "    plt.ylim(0,1)  \n",
    "    plt.xlabel(r'$x_{A}$',fontsize=18)\n",
    "    plt.ylabel(r'$x_{B}$',fontsize=18)\n",
    "    plt.title('Gold Equilibrium',fontsize=20)  \n",
    "    plt.xticks(fontsize=16)\n",
    "    plt.yticks(fontsize=16)\n",
    "    plt.grid(True)\n",
    "    \n",
    "    plt.show()\n",
    "    print('')\n",
    "    \n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:38:02.153656Z",
     "start_time": "2022-03-29T16:38:01.909480Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "'''Plot reference state'''\n",
    "\n",
    "plot_ref_states(x_a_0, x_b_0, x_c_0, x_a_gold, x_b_gold, x_c_gold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:38:27.813470Z",
     "start_time": "2022-03-29T16:38:27.534846Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "'''Let us do this one more time'''\n",
    "\n",
    "import numpy as np\n",
    "x_0 = np.zeros((3,2))\n",
    "\n",
    "x_0[:,0] = np.array([x_a_0, x_b_0, x_c_0]) # save previous reference molar fractions\n",
    "\n",
    "(x_a_0,x_b_0,x_c_0) = magic_molar_fractions(x_a_gold, x_b_gold, x_c_gold)\n",
    "\n",
    "ext_hat_min = -x_c_0\n",
    "ext_hat_max = min(x_a_0,x_b_0)\n",
    "\n",
    "ext_hat_0 = (ext_hat_max+ext_hat_min)/2.0\n",
    "\n",
    "ext_hat = newton_solve(x_a_0, x_b_0, x_c_0, eq_kx_cte,\n",
    "                       ext_hat_0, k_max, tolerance )\n",
    "\n",
    "x_a = (x_a_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_b = (x_b_0 - ext_hat)/(1.0-ext_hat)\n",
    "x_c = (x_c_0 + ext_hat)/(1.0-ext_hat)\n",
    "\n",
    "if abs(x_a-x_a_gold) + abs(x_b-x_b_gold) + abs(x_c-x_c_gold) <= 1e-12:\n",
    "    print('This matches the gold values.')\n",
    "else:\n",
    "    print('This DOES NOT match the gold values.')\n",
    "\n",
    "x_0[:,1] = np.array([x_a_0,x_b_0,x_c_0])\n",
    "\n",
    "plot_ref_states( x_0[0,:], x_0[1,:], x_0[2,:], x_a_gold, x_b_gold, x_c_gold )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Could a unique $x_{A_0} , x_{B_0}, x_{C_0}$ be computed?** <br>\n",
    "**If not unique, how many exist?** <br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**So is it hopeless? or can we say something about the reference molar fractions?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-29T16:41:03.042244Z",
     "start_time": "2022-03-29T16:41:02.762826Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "'''Plot reference states'''\n",
    "\n",
    "npts = 50\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "x_0  = np.zeros((3,npts))\n",
    "x_eq = np.zeros((3,npts))\n",
    "\n",
    "for i in range(npts):\n",
    "    \n",
    "    (x_a_0, x_b_0, x_c_0) = magic_molar_fractions(x_a_gold, x_b_gold, x_c_gold)\n",
    "    \n",
    "    x_0[0,i] = x_a_0\n",
    "    x_0[1,i] = x_b_0\n",
    "    x_0[2,i] = x_c_0\n",
    "    \n",
    "    ext_hat_min = -x_c_0\n",
    "    ext_hat_max = min(x_a_0,x_b_0)\n",
    "\n",
    "    ext_hat_0 = (ext_hat_max+ext_hat_min)/2.0\n",
    "    \n",
    "    ext_hat = newton_solve(x_a_0, x_b_0, x_c_0, eq_kx_cte,\n",
    "                           ext_hat_0,k_max, tolerance, verbose=False)\n",
    "    \n",
    "    x_eq[0,i] = (x_a_0 - ext_hat)/(1.0-ext_hat)\n",
    "    x_eq[1,i] = (x_b_0 - ext_hat)/(1.0-ext_hat)\n",
    "    x_eq[2,i] = (x_c_0 + ext_hat)/(1.0-ext_hat)\n",
    "    \n",
    "    if abs(x_eq[0,i]-x_a_gold) + abs(x_eq[1,i]-x_b_gold) + abs(x_eq[2,i]-x_c_gold) <= 1e-12:\n",
    "        print('This matches the gold value.')\n",
    "    else:\n",
    "        print('This DOES NOT match the gold value.')\n",
    "    \n",
    "plot_ref_states(x_0[0,:], x_0[1,:], x_0[2,:], x_eq[0,:], x_eq[1,:], x_eq[2,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}