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"cells": [
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"cell_type": "markdown",
"metadata": {},
"source": [
"ChEn-3170: Computational Methods in Chemical Engineering Spring 2024 UMass Lowell; Prof. V. F. de Almeida **26Mar24**\n",
"\n",
"# 16. Non-Linear Least-Squares Arrhenius Rate Constant Data Fitting\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{\\Jmtrx}{\\boldsymbol{\\mathsf{J}}}\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{\\fvec}{\\boldsymbol{\\mathsf{f}}}\n",
" \\newcommand{\\kvec}{\\boldsymbol{\\mathsf{k}}}\n",
" \\newcommand{\\alphabf}{\\boldsymbol{\\alpha}}\n",
" \\newcommand{\\betabf}{\\boldsymbol{\\beta}}\n",
" \\newcommand{\\zerovec}{\\boldsymbol{\\mathsf{0}}}\n",
" \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n",
" \\newcommand{\\transpose}[1]{{#1}^\\top}\n",
" \\DeclareMathOperator{\\rank}{rank}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## Table of Contents\n",
"* [Introduction](#intro)\n",
"* [Non-Linear Arrhenius Data Fitting](#adf)\n",
"* [Experimental Data (10 points)](#ed10)\n",
" * [Non-Linear System](#nls10)\n",
" * [NLLS Newton's Method Data Fitting](#nlls10)\n",
" * [Goodness of Fit](#gof10)\n",
" * [Objective Function](#of10)\n",
"* [Experimental Data (20 points)](#ed20)\n",
" * [Non-Linear System](#nls20)\n",
" * [NLLS Newton's Method Data Fitting](#nlls20)\n",
" * [Goodness of Fit](#gof20)\n",
" * [Objective Function](#of20)\n",
"* [Experimental Data (80 points)](#ed80)\n",
" * [Non-Linear System](#nls80)\n",
" * [NLLS Newton's Method Data Fitting](#nlls80)\n",
" * [Objective Function](#of80)\n",
"* [Results Comparison](#res)\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## [Introduction](#toc)\n",
"The non-linear least-squares method is an extension of the linear least-squares method, covered earlier in this course, to treat non-linear objective functions. Therefore Newton's method, also covered earlier, will be needed to solve an iterative version of the normal equations similarly obtained in the linear case. The theoretical notes we will need for this topic can be found in the course notes OneNote [ChEn-3170-nllsq](https://studentuml-my.sharepoint.com/:o:/g/personal/valmor_dealmeida_uml_edu/EhnksYqisMNIhij4WnIDh_4B5VUtoSDyvKgoC-PydKMouQ?e=ab00EQ). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Non-linear Arrhenius Data Fitting](#toc)\n",
"\n",
"This notebook will apply the previous developments in the course to fit experimental data to a non-linear model directly. Here the example is the Arrhenius function for the dependency of the reaction rate constant on temperature, namely\n",
"\n",
"\\begin{equation*}\n",
"k(\\beta) = k_0 \\, e^{-\\beta\\,E_\\text{a}}.\n",
"\\end{equation*}\n",
"\n",
"Therefore the methods and results here are to be compared to its linear counterpart in Notebook 10.\n",
"\n",
"The pre-exponential factor (frequency parameter), $k_0$, and the energy of activation, $E_\\text{a}$, are the sought parameters in this expression. These parameters will be computed by direct minimization of the non-linear residual of the differences between the values measured for $k_i$ and the predicted values of the Arrhenius function for all values of $\\beta_i$. To that end, evaluate the residuals, $r_i$, of the Arrhenius formula at each experimental point $(\\beta_i,k_i)$\n",
"\n",
"\\begin{equation*}\n",
"r_i = k_i - k(\\beta_i) = k_i - k_0\\,e^{-\\beta_i\\,E_a}.\n",
"\\end{equation*}\n",
"\n",
"If the residual vector is denoted\n",
"\n",
"$\\rvec = \\begin{pmatrix}\n",
" r_1 \\\\ \n",
" r_2 \\\\ \n",
" \\vdots \\\\ \n",
" r_m \\\\ \n",
"\\end{pmatrix}$, and the vector of parameters $\\alphabf = \\begin{pmatrix}\n",
" k_0 \\\\ \n",
" E_a \n",
"\\end{pmatrix}$, then find the optimum vector of parameters $\\alphabf^*$ such that it minimizes the\n",
"objective function\n",
"\n",
"\\begin{equation*}\n",
" \\phi(\\alpha^*) = \\min\\limits_{\\alphabf} \\norm{\\rvec(\\alpha)}^2 \\quad\\ \\forall \\quad\\ \\alphabf.\n",
"\\end{equation*}\n",
"\n",
"Note that $\\rvec$ is a vector-valued function of $\\alphabf$.\n",
"Find the optimal value $\\alphabf^*$ using Newton's method iterations on\n",
"the vector function leading to the minimum point of the objective function, that is, starting with an initial guess $\\alphabf^{(0)}$ compute the \n",
"sequence $\\alphabf^{(k)}, k = 1\\ldots N_\\text{max}$ solving the Jacobian normal equations\n",
"\n",
"\\begin{equation*}\n",
"{\\Jmtrx^{(k-1)}}^\\top\\Jmtrx^{(k-1)}\\,\\delta\\alphabf = -\\Jmtrx^\\top\\rvec^{(k-1)} ,\n",
"\\end{equation*}\n",
"\n",
"where $\\Jmtrx^{(k-1)} := \\partial_\\alphabf\\rvec^{(k-1)} = \\begin{pmatrix}\n",
" -e^{-\\beta_1 E_a^{(k-1)}} & k_0^{(k-1)}\\, \\beta_1 e^{-\\beta_1 E_a^{(k-1)}} \\\\\n",
" -e^{-\\beta_2 E_a^{(k-1)}} & k_0^{(k-1)}\\, \\beta_2 e^{-\\beta_2 E_a^{(k-1)}} \\\\\n",
" \\vdots & \\vdots \\\\\n",
" -e^{-\\beta_m E_a^{(k-1)}} & k_0^{(k-1)}\\, \\beta_m e^{-\\beta_m E_a^{(k-1)}}\n",
" \\end{pmatrix}$, and \n",
" $\\alphabf^{(k)} = \\alphabf^{(k-1)} + \\delta\\alphabf$,\n",
" \n",
" until $\\norm{\\delta\\alphabf^{(k)}}$ is less than a small value."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## [Experimental Data (10 points)](#toc)\n",
"Data will be provided for exercises as ASCII files in the `data/` directory of the course [repository](https://github.com/dpploy/chen-3170/tree/master/notebooks/data). The data is organized in two columns of $T$ versus $k$. For example `data/k_x_T_10pts.dat`:\n",
"```\n",
"#(T,k) [K x 1/s]\n",
"r_cte = 8.314 [J/(mol.K)]\n",
"n_pts = 10\n",
"3.00000e+02 6.79538e-01\n",
"3.22222e+02 7.08972e-01\n",
"3.44444e+02 6.34251e-01\n",
"3.66667e+02 7.25196e-01\n",
"3.88889e+02 6.59508e-01\n",
"4.11111e+02 7.42922e-01\n",
"4.33333e+02 6.65461e-01\n",
"4.55556e+02 7.01082e-01\n",
"4.77778e+02 6.74563e-01\n",
"5.00000e+02 7.98533e-01\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:50:10.570774Z",
"start_time": "2022-01-10T06:50:10.564579Z"
},
"code_folding": [
2
]
},
"outputs": [],
"source": [
"'''Function: read experimental data'''\n",
"\n",
"def read_experimental_data(filename):\n",
" import io # import io module\n",
" finput = open(filename, 'rt') # create file object\n",
"\n",
" import numpy as np\n",
"\n",
" for line in finput:\n",
" \n",
" line = line.strip() # original line\n",
" \n",
" if line[0] == '#': # skip comments in the file\n",
" continue\n",
" \n",
" var_line = line.split(' = ') # variable line\n",
" \n",
" if var_line[0] == 'r_cte':\n",
" r_cte = float(var_line[1].split(' ')[0])\n",
" r_cte_units = var_line[1].split(' ')[1]\n",
" elif var_line[0] == 'n_pts':\n",
" n_pts = int(var_line[1])\n",
" temp = np.zeros(n_pts) # reserve space\n",
" k_cte = np.zeros(n_pts) # reserve space\n",
" idx = 0 # counter\n",
" else:\n",
" data = line.split(' ') # original line\n",
" temp[idx] = float(data[0])\n",
" k_cte[idx] = float(data[1])\n",
" idx += 1\n",
" \n",
" return (r_cte, r_cte_units, n_pts, temp, k_cte)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:50:10.647053Z",
"start_time": "2022-01-10T06:50:10.572689Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"R = 8.314 [J/(mol.K)]\n",
"m = 10\n",
"T = [300. 322.22 344.44 366.67 388.89 411.11 433.33 455.56 477.78 500. ]\n",
"k = [0.64 0.65 0.67 0.67 0.71 0.7 0.69 0.7 0.75 0.76]\n"
]
}
],
"source": [
"'''Read experimental data'''\n",
"\n",
"import numpy as np\n",
"(r_cte, r_cte_units, n_pts, temp_vec, k_cte_vec) = read_experimental_data('data/k_x_T_10pts.dat')\n",
" \n",
"print('R = %4.3f %s'%(r_cte,r_cte_units))\n",
"print('m = ',n_pts)\n",
"np.set_printoptions(precision=2)\n",
"print('T =',temp_vec)\n",
"print('k =', k_cte_vec)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:50:10.652520Z",
"start_time": "2022-01-10T06:50:10.648255Z"
},
"code_folding": [
2
]
},
"outputs": [],
"source": [
"'''Function: plot experimental data'''\n",
"\n",
"def plot_experimental_data(temp, k_cte):\n",
" \n",
" import matplotlib.pyplot as plt\n",
"\n",
" plt.figure(1, figsize=(7, 7))\n",
"\n",
" plt.plot(temp, k_cte,'r*',label='experimental')\n",
" \n",
" plt.xlabel(r'$T$ [K]',fontsize=14)\n",
" plt.ylabel(r'$k$ [s$^{-1}$]',fontsize=14)\n",
" plt.title('Arrhenius Rxn Rate Constant Data',fontsize=20)\n",
" plt.legend(loc='best',fontsize=12)\n",
" plt.grid(True)\n",
" plt.show()\n",
" \n",
" return"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:50:11.659313Z",
"start_time": "2022-01-10T06:50:10.654564Z"
}
},
"outputs": [
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"'''Plot experimental data'''\n",
"\n",
"plot_experimental_data(temp_vec, k_cte_vec)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Non-linear System](#toc)\n",
"\n",
"Evaluate the residuals, $r_i, i =1,\\ldots m$, of the Arrhenius fit function at each experimental point\n",
"\n",
"\\begin{equation*}\n",
"r_i = k_i - f(\\alphabf;\\beta_i),\n",
"\\end{equation*}\n",
"\n",
"and form the residual vector $\\rvec = \\begin{pmatrix}\n",
" r_1 \\\\ \n",
" r_2 \\\\ \n",
" \\vdots \\\\ \n",
" r_m \\\\ \n",
"\\end{pmatrix} $.\n",
"\n",
"This should be done in elementary steps, first define the fit function\n",
"\n",
"\\begin{equation*}\n",
"f(\\alphabf;\\beta_i) = k_0\\,e^{-\\beta\\,E_a}.\n",
"\\end{equation*}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then evaluate the fit function at the $\\beta_i$ data points to form the fit vector function\n",
"\n",
"\\begin{equation*}\n",
"f_i(\\alphabf) = f(\\alphabf;\\beta_i)\n",
"\\end{equation*}\n",
"\n",
"$\\fvec = \\begin{pmatrix}\n",
" f_1 \\\\ \n",
" f_2 \\\\ \n",
" \\vdots \\\\ \n",
" f_m \\\\ \n",
"\\end{pmatrix} $.\n",
"\n",
"This should be done in one implementation as shown in the `arrhenius_func`. This allows a simple assembly of the residual vector using the $k_i$ values in a vector operation\n",
"\n",
"\\begin{equation*}\n",
"\\rvec = \\kvec - \\fvec .\n",
"\\end{equation*}"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:50:11.665935Z",
"start_time": "2022-01-10T06:50:11.661213Z"
},
"code_folding": [
2
]
},
"outputs": [],
"source": [
"'''Function: Arrhenius fit function'''\n",
"\n",
"def arrhenius_func(beta_vec, param_vec):\n",
" \n",
" import numpy as np\n",
" \n",
" k0 = param_vec[0]\n",
" ea = param_vec[1]\n",
" \n",
" k = k0 * np.exp(-beta_vec*ea)\n",
" \n",
" return k"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, build the elements needed to allow for the construction of the Jacobian matrix\n",
"\n",
"$\\Jmtrx = \\partial_\\alphabf\\rvec = - \\partial_\\alphabf\\fvec = - \\partial_\\alphabf f(\\alphabf;\\betabf)$. \n",
"Assemble the Jacobian column by column as follows. \n",
"\n",
" + First column: $\\Jmtrx_{\\bullet,1} = -\\partial_{\\alpha_1}\\fvec = - \\partial_{\\alpha_1}f(\\alphabf;\\betabf)$\n",
" + Second column: $\\Jmtrx_{\\bullet,2} = -\\partial_{\\alpha_2}\\fvec = - \\partial_{\\alpha_2}f(\\alphabf;\\betabf)$\n",
"\n",
"To compute the gradient of the fit **vector** function, $\\fvec$,\n",
"first implement the gradient of the **scalar** fit function, $f$, evaluated at the $\\betabf$ vector\n",
"\n",
"$ \\begin{pmatrix}\n",
" \\partial_{\\alpha_1}f(\\alphabf;\\betabf) \\\\ \n",
" \\partial_{\\alpha_2}f(\\alphabf;\\betabf) \n",
"\\end{pmatrix} \n",
"=\n",
"\\begin{pmatrix}\n",
" \\partial_{k_0}f(\\alphabf;\\betabf) \\\\ \n",
" \\partial_{E_a}f(\\alphabf;\\betabf) \n",
"\\end{pmatrix}\n",
"=\n",
"\\begin{pmatrix}\n",
" e^{-\\beta_1\\,E_a}, \\ldots, e^{-\\beta_m\\,E_a} \\\\ \n",
" -k_0\\,\\beta_1\\,e^{-\\beta_1\\,E_a}, \\ldots, -k_0\\,\\beta_m\\,e^{-\\beta_m\\,E_a}\n",
"\\end{pmatrix}\n",
"$.\n",
"\n",
"This is effectively the transpose of $\\Jmtrx$."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:50:11.673094Z",
"start_time": "2022-01-10T06:50:11.667412Z"
},
"code_folding": [
2
]
},
"outputs": [],
"source": [
"'''Function: Arrhenius parameter gradient'''\n",
"\n",
"def partial_p_arrhenius_func(beta_vec, param_vec):\n",
" \n",
" import numpy as np\n",
" \n",
" k0 = param_vec[0] # parameter 0: p0\n",
" ea = param_vec[1] # parameter 1: p1\n",
" \n",
" partial_p0_f = np.exp(-beta_vec*ea) # evaluated at all beta values\n",
" partial_p1_f = -k0*beta_vec*np.exp(-beta_vec*ea) # evaluated at all beta values\n",
" \n",
" # Columns of the Jacobian matrix (column 0, column 1)\n",
" return (partial_p0_f, partial_p1_f)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Jacobian matrix can be assembled simply from the gradient of the fit function, `partial_p_arrhenius_func`, directly\n",
"\n",
"$\\Jmtrx = \\partial_\\alphabf\\rvec = - \\partial_\\alphabf\\fvec = - \\begin{pmatrix}\n",
" \\partial_{\\alpha_1}f(\\alphabf;\\beta_1) & \\partial_{\\alpha_2}f(\\alphabf;\\beta_1) \\\\\n",
" \\partial_{\\alpha_1}f(\\alphabf;\\beta_2) & \\partial_{\\alpha_2}f(\\alphabf;\\beta_2) \\\\\n",
" \\vdots & \\vdots \\\\\n",
" \\partial_{\\alpha_1}f(\\alphabf;\\beta_m) & \\partial_{\\alpha_2}f(\\alphabf;\\beta_m)\n",
" \\end{pmatrix}$.\n",
" \n",
"This is easier than programming the construction of the Jacobian matrix directly as\n",
" \n",
"$\\Jmtrx = \\partial_\\alphabf\\rvec = - \\partial_\\alphabf\\fvec = - \\begin{pmatrix}\n",
" e^{-\\beta_1 E_a} & -k_0\\, \\beta_1 e^{-\\beta_1 E_a} \\\\\n",
" e^{-\\beta_2 E_a} & -k_0\\, \\beta_2 e^{-\\beta_2 E_a} \\\\\n",
" \\vdots & \\vdots \\\\\n",
" e^{-\\beta_m E_a} & -k_0\\, \\beta_m e^{-\\beta_m E_a}\n",
" \\end{pmatrix}$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Non-Linear Least-Squares Newton's Method Data Fitting](#toc)\n",
"\n",
"Find the optimal value $\\alphabf^*$ using Newton's method iterations on\n",
"the linearized residual vector, that is, starting with an initial guess $\\alphabf^{(0)}$ compute the \n",
"sequence $\\alphabf^{(k)}, k = 1\\ldots N_\\text{max}$ solving the normal equations\n",
"\n",
"\\begin{equation*}\n",
"{\\Jmtrx^{(k-1)}}^\\top\\Jmtrx^{(k-1)}\\,\\delta\\alphabf = -\\Jmtrx^\\top\\rvec^{(k-1)} ,\n",
"\\end{equation*}\n",
"\n",
"where $\\Jmtrx^{(k-1)} = \\begin{pmatrix}\n",
" -e^{-\\beta_1 E_a^{(k-1)}} & k_0^{(k-1)}\\, \\beta_1 e^{-\\beta_1 E_a^{(k-1)}} \\\\\n",
" -e^{-\\beta_2 E_a^{(k-1)}} & k_0^{(k-1)}\\, \\beta_2 e^{-\\beta_2 E_a^{(k-1)}} \\\\\n",
" \\vdots & \\vdots \\\\\n",
" -e^{-\\beta_m E_a^{(k-1)}} & k_0^{(k-1)}\\, \\beta_m e^{-\\beta_m E_a^{(k-1)}}\n",
" \\end{pmatrix}$, and \n",
" $\\alphabf^{(k)} = \\alphabf^{(k-1)} + \\delta\\alphabf$,\n",
" \n",
" until $\\norm{\\delta\\alphabf^{(k)}}$ and $\\norm{\\Jmtrx^\\top\\rvec^{(k)}}$ are less than a small value."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:56:52.212228Z",
"start_time": "2022-01-10T06:56:52.195647Z"
},
"code_folding": [
0
]
},
"outputs": [],
"source": [
"def newton_solve(x_vec, y_vec, \n",
" fit_func, partial_p_fit_func,\n",
" param_vec_0,\n",
" k_max=10, tolerance=1.0e-8, verbose=True):\n",
"\n",
" assert x_vec.size == y_vec.size\n",
" \n",
" import numpy as np\n",
" import numpy.linalg\n",
" \n",
" try: \n",
" from chen_3170.toolkit import solve \n",
" except ModuleNotFoundError:\n",
" assert False, 'You need to provide your own solve function here. Bailing out.'\n",
" \n",
" # Other initialization\n",
" delta_vec_k = np.ones(param_vec_0.size, dtype=np.float64)*1e10\n",
" r_vec_k = np.ones(x_vec.size, dtype=np.float64)*1e10\n",
" j_mtrx_k = np.ones((x_vec.size, param_vec_0.size),dtype=np.float64)*1e10\n",
" param_vec = np.copy(param_vec_0)\n",
" \n",
" if verbose is True:\n",
" print('\\n')\n",
" print('**************************************************************************')\n",
" print(\" Newton's Method Iterations \")\n",
" print('**************************************************************************')\n",
" print('k ||r(p_k)|| ||J(p_k)|| ||J^T r(p_k)|| ||del p_k|| ||p_k|| |convg| ')\n",
" print('--------------------------------------------------------------------------')\n",
" # 1234567890 12345678901 123456789012345 123456789012 123456789 12345678\n",
" \n",
" import math\n",
" assert k_max >= 1\n",
" k = 1\n",
" \n",
" while (np.linalg.norm(delta_vec_k) > tolerance or np.linalg.norm(j_mtrx_k.transpose()@r_vec_k) > tolerance) and k <= k_max:\n",
" \n",
" # Build the residual vector\n",
" r_vec_k = y_vec - fit_func(x_vec, param_vec)\n",
" \n",
" # Build the columns of the Jacobian matrix\n",
" partial_p_f = partial_p_fit_func(x_vec, param_vec)\n",
" \n",
" # Assemble the Jacobian matrix\n",
" j_mtrx_k = np.zeros((x_vec.size, param_vec.size), dtype=np.float64) # allocate space\n",
" \n",
" for (i, partial_p_f_i) in enumerate(partial_p_f):\n",
" j_mtrx_k[:, i] = - partial_p_f_i\n",
" \n",
" delta_vec_k_old = delta_vec_k\n",
" \n",
" delta_vec_k = solve(j_mtrx_k.transpose()@j_mtrx_k, -j_mtrx_k.transpose()@r_vec_k,\n",
" pivoting_option='partial', pivot_tol=1e-8)\n",
" #delta_vec_k = numpy.linalg.solve( j_mtrx_k.transpose()@j_mtrx_k, -j_mtrx_k.transpose()@r_vec_k )\n",
" \n",
" r_vec_k_old = r_vec_k\n",
" step_size = 1.0\n",
" r_vec_k = y_vec - fit_func(x_vec, param_vec+delta_vec_k)\n",
" \n",
" n_steps_max = 5\n",
" n_steps = 0\n",
" while (np.linalg.norm(r_vec_k) > np.linalg.norm(r_vec_k_old)) and n_steps <= n_steps_max:\n",
" step_size *= 0.5\n",
" #print('step reduced')\n",
" r_vec_k = y_vec - fit_func( x_vec, param_vec + step_size*delta_vec_k)\n",
" n_steps += 1\n",
" \n",
" param_vec += step_size * delta_vec_k\n",
" \n",
" if k > 0:\n",
" if np.linalg.norm(delta_vec_k) != 0.0 and np.linalg.norm(delta_vec_k_old) != 0.0:\n",
" convergence_factor = math.log(np.linalg.norm(delta_vec_k),10) / math.log(np.linalg.norm(delta_vec_k_old),10)\n",
" else:\n",
" convergence_factor = 0.0 \n",
" else:\n",
" convergence_factor = 0.0\n",
" \n",
" if verbose is True:\n",
" print('%2i %+10.2e %+11.2e %+15.2e %+12.2e %+9.2e %8.2f'%\\\n",
" (k,np.linalg.norm(r_vec_k),np.linalg.norm(j_mtrx_k), np.linalg.norm(j_mtrx_k.transpose()@r_vec_k),\n",
" np.linalg.norm(delta_vec_k), np.linalg.norm(param_vec), convergence_factor) )\n",
" \n",
" k = k + 1\n",
" \n",
" if verbose is True:\n",
" print('******************************************************') \n",
" print('Root = ',param_vec)\n",
" \n",
" return param_vec"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:56:53.539582Z",
"start_time": "2022-01-10T06:56:53.524142Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"**************************************************************************\n",
" Newton's Method Iterations \n",
"**************************************************************************\n",
"k ||r(p_k)|| ||J(p_k)|| ||J^T r(p_k)|| ||del p_k|| ||p_k|| |convg| \n",
"--------------------------------------------------------------------------\n",
" 1 +1.36e-01 +3.16e+00 +3.90e-01 +6.78e+02 +6.78e+02 0.28\n",
" 2 +4.86e-02 +2.57e+00 +4.88e-03 +2.95e+02 +9.72e+02 0.87\n",
" 3 +4.85e-02 +2.35e+00 +6.25e-05 +1.96e+01 +9.92e+02 0.52\n",
" 4 +4.85e-02 +2.33e+00 +8.97e-09 +1.60e-01 +9.92e+02 -0.62\n",
" 5 +4.85e-02 +2.33e+00 +3.03e-13 +1.14e-03 +9.92e+02 3.70\n",
" 6 +4.85e-02 +2.33e+00 +8.68e-17 +8.10e-06 +9.92e+02 1.73\n",
" 7 +4.85e-02 +2.33e+00 +3.06e-16 +5.76e-08 +9.92e+02 1.42\n",
"******************************************************\n",
"Root = [9.43e-01 9.92e+02]\n",
"k_0 = 9.42649e-01 [1/s] \n",
"E_a = 9.91923e+02 [J/mol]\n"
]
}
],
"source": [
"k_0 = 1.0\n",
"energy_a = 0.0\n",
"\n",
"beta_vec = 1./r_cte/temp_vec\n",
"\n",
"param_vec_0 = np.array([k_0, energy_a])\n",
"\n",
"k_max = 8\n",
"tolerance = 1.0e-6\n",
"\n",
"param_vec = newton_solve(beta_vec, k_cte_vec, \n",
" arrhenius_func, partial_p_arrhenius_func,\n",
" param_vec_0, k_max, tolerance)\n",
"\n",
"k_0 = param_vec[0]\n",
"energy_a = param_vec[1]\n",
"\n",
"print('k_0 = %8.5e [1/s] '%k_0)\n",
"print('E_a = %8.5e [J/mol]'%energy_a)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:56:58.806967Z",
"start_time": "2022-01-10T06:56:58.796759Z"
},
"code_folding": [
2
]
},
"outputs": [],
"source": [
"'''Function: plot the fit in the Cartesian plane'''\n",
"\n",
"def plot_fit(r_cte, temp,k_cte, k_0, energy_a):\n",
" \n",
" import matplotlib.pyplot as plt\n",
" \n",
" plt.figure(2, figsize=(6, 6))\n",
"\n",
" # plot experimental data\n",
" plt.plot(temp, k_cte,'r*',label='experimental')\n",
"\n",
" # plot Arrhenius expression\n",
" n_plot_pts = 100\n",
" temp_plot = np.linspace( temp[0], temp[-1], n_plot_pts)\n",
" k_plot = k_0 * np.exp(-energy_a/temp_plot/r_cte) # Arrhenius expression\n",
" \n",
" plt.plot(temp_plot,k_plot,'b-',label='LS fitting' )\n",
"\n",
" plt.xlabel(r'$T$ [K]',fontsize=16)\n",
" plt.ylabel(r'$k$ [s$^{-1}$]',fontsize=16)\n",
" plt.title('Arrhenius Rxn Rate Constant Data',fontsize=20)\n",
"\n",
" (x_min,x_max) = plt.xlim()\n",
" dx = abs(x_max-x_min)\n",
" x_text = x_min + dx*0.07\n",
" \n",
" (y_min,y_max) = plt.ylim()\n",
" dy = abs(y_max-y_min)\n",
" y_text = y_min + dy*0.05\n",
" plt.text(x_text, y_text, r'$k_0=$%8.2e [1/s], $E_a$=%8.2e [J/mol]'%(k_0,energy_a),fontsize=16)\n",
" \n",
" plt.xticks(fontsize=14)\n",
" plt.yticks(fontsize=14)\n",
" plt.legend(loc='best',fontsize=12)\n",
" plt.grid(True)\n",
" plt.show()\n",
"\n",
" return"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:56:59.630412Z",
"start_time": "2022-01-10T06:56:59.448389Z"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"'''Plot the fit in the Cartesian plane'''\n",
"\n",
"plot_fit(r_cte, temp_vec, k_cte_vec, k_0, energy_a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Goodness of Fit](#toc)\n",
"\n",
"There are different ways to evaluate the goodness of fit. Below is the most direct and relevant error evaluation.\n",
"That is, the error on fitting the data as given."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:01.835785Z",
"start_time": "2022-01-10T06:57:01.831141Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Relative Error:\n",
"mean [%] = 1.89\n",
"std [%] = 1.05\n",
"max, min [%] = 3.81, 0.77\n"
]
}
],
"source": [
"'''Local relative error on reaction rate constant values'''\n",
"\n",
"print('Relative Error:')\n",
"\n",
"local_error = np.abs(k_cte_vec - arrhenius_func(beta_vec, param_vec))/k_cte_vec*100\n",
"\n",
"mean = np.mean(local_error)\n",
"std = np.std(local_error)\n",
"emax = np.max(local_error)\n",
"emin = np.min(local_error)\n",
"print('mean [%%] = %1.2f'%(mean))\n",
"print('std [%%] = %1.2f'%(std))\n",
"print('max, min [%%] = %1.2f, %1.2f'%(emax,emin))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Note**: An ideal fit should have an equal distribution of residual signs. That is the same number of experimental points above and below the fit. Verify this on your own."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Objective Function](#toc)\n",
"\n",
"Let's show graphically that \n",
"\n",
"\\begin{equation*}\n",
"\\phi(\\alphabf^*) = \\min\\limits_{\\alphabf} \\norm{\\rvec}^2 ,\n",
"\\end{equation*}\n",
"\n",
"that is, the minimum sits at the bottom of the objective function surface.\n",
"\n",
"Information on `matplotlib` plots in 3D is found [here](https://matplotlib.org/tutorials/toolkits/mplot3d.html#sphx-glr-tutorials-toolkits-mplot3d-py)."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:05.387890Z",
"start_time": "2022-01-10T06:57:05.382509Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"phi(x_LS) = 2.35459e-03\n",
"sqrt(phi(x_LS)) = 4.85241e-02\n",
"Mean(r_vec) = 5.97872e-06\n",
"STD(r_vec) = 1.53447e-02\n",
"Goodness of fit = 1.53447e-02\n"
]
}
],
"source": [
"'''Examining the residual'''\n",
"\n",
"r_vec = k_cte_vec - arrhenius_func( beta_vec, param_vec )\n",
"phi = np.linalg.norm(r_vec)**2\n",
"# phi_ls = np.dot(r_vec,r_vec) # alternative dot product\n",
"\n",
"import math\n",
"print('phi(x_LS) = %8.5e'%phi)\n",
"print('sqrt(phi(x_LS)) = %8.5e'%math.sqrt(phi)) # norm of the residual vector\n",
"print('Mean(r_vec) = %8.5e'%np.mean(r_vec))\n",
"print('STD(r_vec) = %8.5e'%np.std(r_vec))\n",
"print('Goodness of fit = %8.5e'%math.sqrt(phi/n_pts))"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:06.287999Z",
"start_time": "2022-01-10T06:57:06.279950Z"
},
"code_folding": [
2
]
},
"outputs": [],
"source": [
"'''Function: objective function around the minimum'''\n",
"\n",
"def get_objective_function_data(n_plot_pts, arrhenius_func, beta_vec, k_cte_vec, params_vec):\n",
" \n",
" import numpy as np\n",
" \n",
" # create the objective function array\n",
" k_0_pts = np.linspace( 0.95*params_vec[0], params_vec[0]*1.05, n_plot_pts )\n",
" energy_pts = np.linspace( 0.95*params_vec[1], params_vec[1]*1.05, n_plot_pts )\n",
" \n",
" phi = np.zeros((n_plot_pts,n_plot_pts))\n",
" \n",
" i = -1\n",
" for k_0 in k_0_pts:\n",
" i += 1\n",
" j = -1\n",
" for e_a in energy_pts:\n",
" j += 1\n",
" res = k_cte_vec - arrhenius_func( beta_vec, np.array( [k_0,e_a] ) )\n",
" phi[i,j] = np.dot(res,res)\n",
" \n",
" return (k_0_pts, energy_pts, phi)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:07.303008Z",
"start_time": "2022-01-10T06:57:07.292330Z"
},
"code_folding": [
2
]
},
"outputs": [],
"source": [
"'''Function: plot the objective function around the minimum'''\n",
"\n",
"def plot_objective_function( objective_function_data, param_vec, delta_factor=1.0 ):\n",
" \n",
" (k_0_pts, energy_pts, phi) = objective_function_data # unpack the data\n",
" \n",
" # 3D-plot the surface of the objective function\n",
" import numpy as np\n",
" import matplotlib.pyplot as plt\n",
" from matplotlib import cm\n",
" from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
" #fig = plt.figure(3,figsize=(6, 6))\n",
" \n",
" #ax = Axes3D(fig)\n",
" \n",
" #ax.plot_surface( k_0_pts, energy_pts, phi, rstride=1, cstride=1, cmap=cm.viridis )\n",
" #ax.plot_surface( k_0_pts, energy_pts, phi, cmap=cm.viridis )\n",
" \n",
" #ax.view_init(azim=10)\n",
"\n",
" #ax.set_xlabel(r'$\\ln k_0$ [ ]',fontsize=16)\n",
" #ax.set_ylabel(r'$E_a$ [J/mol]',fontsize=16)\n",
" #ax.set_zlabel(r'$\\phi$',fontsize=16)\n",
"\n",
" #plt.show()\n",
" \n",
" # plot the contour curves of the objective function\n",
" from matplotlib import ticker, cm\n",
" fig, ax = plt.subplots(figsize=(6, 6))\n",
" \n",
" delta = np.min(np.min(phi))/100.0 * delta_factor # % variation near the minimum\n",
" \n",
" cv = np.linspace( np.min(np.min(phi))+delta, np.max(np.max(phi)), 10 );\n",
" \n",
" cs = ax.contour(k_0_pts, energy_pts, phi, cv)\n",
" \n",
" xpos = param_vec[0]\n",
" ypos = param_vec[1]\n",
" \n",
" plt.text(xpos,ypos,r'* ($k_0$=%5.2e, $E_a$=%5.2e)'%(param_vec[0],param_vec[1]),color='r',fontsize=12);\n",
" \n",
" plt.xlabel(r'$k_0$ []',fontsize=14)\n",
" plt.ylabel(r'$E_a$ [J/mol]',fontsize=14)\n",
"\n",
" plt.show()\n",
" return"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:08.511598Z",
"start_time": "2022-01-10T06:57:08.145330Z"
}
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"'''Plot the objective function surface around the minimum'''\n",
"\n",
"n_plot_pts = 150\n",
"\n",
"objective_function_data = get_objective_function_data(n_plot_pts, arrhenius_func, beta_vec, k_cte_vec, param_vec)\n",
"\n",
"plot_objective_function( objective_function_data, param_vec )"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:11.468969Z",
"start_time": "2022-01-10T06:57:10.933341Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"linkText": "Export to plot.ly",
"plotlyServerURL": "https://plot.ly",
"showLink": false
},
"data": [
{
"type": "surface",
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""
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"source": [
"'''Plot the objective function around the minimum'''\n",
"#!pip install plotly\n",
"\n",
"(x_vec, y_vec, z_mtrx) = objective_function_data\n",
"\n",
"import plotly\n",
"import plotly.graph_objs as go\n",
"\n",
"plotly.offline.init_notebook_mode(connected=True)\n",
"\n",
"data = [ go.Surface(z=z_mtrx) ]\n",
"layout = go.Layout(\n",
" title='Objective Function Surface',\n",
" autosize=False,\n",
" width=500,\n",
" height=500,\n",
" margin=dict(\n",
" l=65,\n",
" r=50,\n",
" b=65,\n",
" t=90\n",
" )\n",
" )\n",
"\n",
"plotly.offline.iplot({\n",
" \"data\": data,\n",
" \"layout\": layout\n",
"})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## [Experimental Data (20 points)](#toc)\n",
"Data will be provided for exercises as ASCII files in the `data/` directory of the course [repository](https://github.com/dpploy/chen-3170/data). The data is organized in two columns of $T$ versus $k$. For example `data/k_x_T_20pts.dat`:\n",
"```\n",
"#(T,k) [K x 1/s]\n",
"r_cte = 8.314 [J/(mol.K)]\n",
"n_pts = 20\n",
"3.00000e+02 6.46842e-01\n",
"3.10526e+02 6.51310e-01\n",
"3.21053e+02 6.30482e-01\n",
"3.31579e+02 6.07467e-01\n",
"3.42105e+02 6.85455e-01\n",
"3.52632e+02 7.00184e-01\n",
"3.63158e+02 7.39440e-01\n",
"3.73684e+02 6.89361e-01\n",
"3.84211e+02 7.06639e-01\n",
"3.94737e+02 6.56265e-01\n",
"4.05263e+02 6.97063e-01\n",
"4.15789e+02 7.27683e-01\n",
"4.26316e+02 6.89620e-01\n",
"4.36842e+02 7.26620e-01\n",
"4.47368e+02 6.98762e-01\n",
"4.57895e+02 7.24678e-01\n",
"4.68421e+02 7.63007e-01\n",
"4.78947e+02 8.17275e-01\n",
"4.89474e+02 7.30909e-01\n",
"5.00000e+02 7.32861e-01\n",
"```"
]
},
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"cell_type": "code",
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"end_time": "2022-01-10T06:57:17.090943Z",
"start_time": "2022-01-10T06:57:17.086042Z"
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},
"outputs": [
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"R = 8.314 [J/(mol.K)]\n",
"m = 20\n",
"T = [300. 310.53 321.05 331.58 342.11 352.63 363.16 373.68 384.21 394.74\n",
" 405.26 415.79 426.32 436.84 447.37 457.89 468.42 478.95 489.47 500. ]\n",
"k = [0.64 0.67 0.67 0.68 0.68 0.69 0.69 0.71 0.66 0.68 0.73 0.73 0.7 0.7\n",
" 0.7 0.74 0.75 0.7 0.75 0.73]\n"
]
}
],
"source": [
"'''Read experimental data'''\n",
"\n",
"(r_cte, r_cte_units, n_pts, temp_vec, k_cte_vec) = read_experimental_data('data/k_x_T_20pts.dat')\n",
" \n",
"print('R = %4.3f %s'%(r_cte,r_cte_units))\n",
"print('m = ',n_pts)\n",
"np.set_printoptions(precision=2)\n",
"print('T =',temp_vec)\n",
"print('k =', k_cte_vec)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:17.539724Z",
"start_time": "2022-01-10T06:57:17.353310Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"'''Plot experimental data'''\n",
"\n",
"plot_experimental_data(temp_vec, k_cte_vec)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Non-Linear System](#toc)\n",
"\n",
"Similar as [before](#nls10) with 10 points."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Non-Linear Least-Squares Newton's Method Data Fitting](#toc)\n",
"\n",
"Similar as [before](#nlls10) with 10 points."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:18.719984Z",
"start_time": "2022-01-10T06:57:18.710143Z"
},
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"**************************************************************************\n",
" Newton's Method Iterations \n",
"**************************************************************************\n",
"k ||r(p_k)|| ||J(p_k)|| ||J^T r(p_k)|| ||del p_k|| ||p_k|| |convg| \n",
"--------------------------------------------------------------------------\n",
" 1 +1.64e-01 +4.47e+00 +6.30e-01 +4.80e+02 +4.80e+02 0.26\n",
" 2 +7.87e-02 +3.86e+00 +9.94e-03 +2.00e+02 +6.80e+02 0.86\n",
" 3 +7.86e-02 +3.63e+00 +1.87e-05 +9.38e+00 +6.89e+02 0.42\n",
" 4 +7.86e-02 +3.62e+00 +6.57e-11 +7.06e-03 +6.89e+02 -2.21\n",
" 5 +7.86e-02 +3.62e+00 +6.47e-11 +1.18e-06 +6.89e+02 2.75\n",
" 6 +7.86e-02 +3.62e+00 +3.24e-11 +1.17e-06 +6.89e+02 1.00\n",
" 7 +7.86e-02 +3.62e+00 +2.83e-11 +5.83e-07 +6.89e+02 1.05\n",
"******************************************************\n",
"Root = [ 0.87 689.5 ]\n",
"k_0 = 8.65108e-01 [1/s]\n",
"E_a = 6.89497e+02 [J/mol]\n"
]
}
],
"source": [
"k_0 = 1.0\n",
"energy_a = 0.0\n",
"\n",
"beta_vec = 1./r_cte/temp_vec\n",
"param_vec_0 = np.array([k_0,energy_a])\n",
"\n",
"k_max = 8\n",
"tolerance = 1.0e-6\n",
"\n",
"param_vec = newton_solve(beta_vec, k_cte_vec, \n",
" arrhenius_func, partial_p_arrhenius_func,\n",
" param_vec_0, k_max, tolerance)\n",
"\n",
"k_0 = param_vec[0]\n",
"energy_a = param_vec[1]\n",
"\n",
"print('k_0 = %8.5e [1/s]'%k_0)\n",
"print('E_a = %8.5e [J/mol]'%energy_a)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:19.352587Z",
"start_time": "2022-01-10T06:57:19.151048Z"
}
},
"outputs": [
{
"data": {
"image/png": 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PKxZXZCyuyFhckYnHuICl6vH3t1U/GmOMiRuW1IwxxsQNS2rGGGPihiU1Y4wxccNaP0Zoz549bN++ncOHgw1+7VSoUIGff/455HyvWFzhKV68ONWr58UgB8aYvGZJLQJ79uxh27Zt1KlTh4SEBEKNXLJ3717KlSuXz9Flz+LKnqqyf/9+tmzZQtGi+T1gsTEmt6z6MQLbt2+nTp06lC5dOmRCMwWbiFC6dGnq1KkTk/cQGWOyZkktAocPHyYhIcHrMEw+yOpM3BgTuyypRci+6AoH+5yNKZgsqRljjIkbltRMVPXp04dhw4Z5HUa2Fi5cyDHHHON1GCbeJCVBYiL8+afXkRRa1vrRRNXYsWM92e/gwYP59ddfef311z3ZvzEADBsGX3wBQ4fC6NFeR1Mo2ZlaforzX3EpKSleh2CMNxISQATGjIHUVPcs4qabfGVJLT/5/4rLA1u3bqVr165Uq1aNBg0a8OKLL7Jz506OOeYYZs2aBUBycjKNGzdmypQpAPTo0YM+ffrQoUMHypUrR2JiIps2bUrf5po1a+jQoQOVK1fmhBNO4K233kqf16NHD/r27UunTp0oU6YMCxYsoEePHjzyyCPA0Sq+//u//6N69erUqlWLmTNn8vHHH3P88cdTuXJlhg8fnr691NRUnn76aRo1akSVKlW4+uqr2blzJwAbN25ERJg8eTLHHnssVatW5cknnwRgzpw5DB8+nOnTp1O2bFmaN28OwMSJEznxxBMpV64cDRs2ZNy4cXly3I1h/Xq4/nooXdq9Ll0auneHDRu8jasQsqSWH/LhV1xqaiqXXnopzZs3Z8uWLcybN48XXniB7777jgkTJnDrrbfy119/MWDAAFq0aMFNN92Uvu7UqVN59NFH2bFjBy1atKB79+6AG1epQ4cOXH/99Wzfvp0333yTfv368dNPP6Wv+8YbbzBo0CD27t3LeeedlymuP//8kwMHDrBlyxaGDh3Krbfeyuuvv86yZctYvHgxQ4cOZYPvH//FF19k5syZLFq0iK1bt1KpUiVuv/32DNv74osv+OWXX5g3bx5Dhw7l559/5qKLLuLhhx/mmmuuITk5me+//x6A6tWr8+GHH7Jnzx4mTpzIgAEDWL58edSOuTHpatWC8uXhwAEoVco9ly8PNWt6HVmhY0ktP+TDr7jvvvuOv/76i8cee4wSJUrQsGFDbr31VqZNm8aFF15It27duPTSS/noo48ynbF07tyZ888/n5IlS/Lkk0/y9ddf88cff/Dhhx9Sv359brnlFooVK8app55K165dmTFjRvq6Xbp04dxzz6VIkSKUKlUqU1zFixdn0KBBFC9enGuvvZYdO3bQv39/ypUrR9OmTWnatGl6khw3bhxPPvkkxxxzDCVLlmTw4MHMmDGDI0eOpG/v8ccfJyEhgebNm9O8efP0BBZM586dadSoESJCYmIiF154IYsXL87toTYmuG3boE8f+OYb9xynlxlinTUUyQ/58Ctu06ZNbN26lYoVK6ZPS0lJoXXr1gD07t2bl156iYcffpgqVapkWLdu3brpf5ctW5bKlSuzdetWNm3axJIlSzJs88iRI9x4441B1w2mSpUq6d1Npd24XqNGjfT5CQkJJCcnp7+HK664giJFjv7WKlq0KNu2bUt/XdPvmJUuXTp93WBmz57NkCFDWLt2Lampqfz777+cfPLJWcZrTI69++7Rv0eN8i6OQs6SWn5J+xXXuze8/LJrNBJFdevWpUGDBqxbty7TvJSUFG677Tauu+46xowZwy233ELjxo3T5//xxx/pfycnJ7Nz505q165N3bp1SUxM5NNPPw2532jepFy3bl0mTJjAueeem2nexo0bs1w3MI6DBw/StWtXpkyZQpcuXShevDiXX345bnBeY0y8surH/PLuu+7XW/Pm7tn/V10UnHHGGZQvX57//ve/7N+/n5SUFFatWsV3332X3hhj9OjR3Hfffdx0000ZWip+/PHHfPHFFxw6dIhHH32UM888k7p163LJJZewdu1aXnvtNQ4fPszhw4f57rvv8qxH/T59+jBo0KD0hip//fUX77//fljr1qhRg40bN5KamgrAoUOHOHjwINWqVaNYsWLMnj2buXPn5kncxpjYYUktThQtWpRZs2axcuVKGjRoQNWqVenVqxfz58/n+eefZ8qUKRQtWpQHH3wQEeHpp59OX/f6669nyJAhVK5cmWXLljF16lQAypUrx9y5c5k2bRq1a9emZs2aPPjggxw8eDBP3kP//v257LLLuPDCCylXrhxnnXUWS5YsCWvdbt26Aa6689RTT6VcuXK8+OKLXH311VSqVIk33niDyy67LE/iNsbEEFW1R8CjVatWGszq1auDTg+0Z8+esJbLb8Hiuvnmm3XQoEEeRHNUrB6v5cuXex1CUAsWLPA6hKAsrsjEY1zAUvX4+9vO1IwxxsQNS2rGGGPihrV+LOQmTZrkdQjGGBM1dqZmjDHxIs77lw2HJTVjjIkXedy/bEFgSc0YYwo6GyUgnSU1Y4wp6GyUgHSW1IwxpqCzUQLSWVIzmfzyyy+0bNkyvVeOPn36MGzYsIi2cfHFFzN58uQ8itAYk4mNEgBYk/64Ur9+fV555RXat2+fad7w4cN5+eWX2bFjBxUrVuTcc89l+vTpQbfzf//3f7Rp04YVK1Zkmrdw4UJuuOEGNm/enD5t8ODB/Prrr7z++uvp02bPnh2Fd2SMCZuNEgDYmVqhMHnyZF577TXef/99kpOTWbp0Ke3atQu5/KZNm2jatGk+RmiMMdFhSa0Q+O677+jYsSMNGzYE3JhkvXv3DrrsBRdcwIIFC7jjjjsoW7Ysa9eupUePHjzyyCPs27ePiy++mK1bt1K2bFnKli3LG2+8wfDhw5k+fTply5alefPmALRp04ZXXnkFcDd4n3feedx3331UqlSJBg0aZDiT27hxI+effz7lypWjffv23H777dxwww15fFSMMfHIqh9z4e67YeXKzNNTUhLwjYuZay1awAsv5G4bZ511FnfddRdVq1bloosuomXLlukDdwaaP38+bdq04YYbbqBXr14Z5pUpU4bZs2dnqn5cu3ZtpurHQEuWLOHmm29mx44dvPzyy/Ts2ZMtW7YgIvTs2ZPzzz+fzz77jG+//ZZOnTpZj/rGmByxM7VC4IYbbuB///sf8+bNIzExkerVq2cYeiY/1KtXj1tvvZWiRYty8803k5SUxLZt2/j9999Zvnw5Q4cOpUSJEpx33nmW0IwxOWZnarkQ6gxq7979lCtXLl9jyU737t257LLLKFWqFDNnzqR79+60bNmSjh075sv+a/o1LS7tu5cmOTmZHTt2UKlSpfRp4EbA9h+N2xhjwmVnaoVM8eLF6datG6eccgqrVq2KeH0RCWtauGrVqsWuXbv4999/06dZQjPG5FTMJDUR6SciG0TkgIgsE5HWWSw7WEQ0xKN6kOXPE5EjIhL5t3gBc/jwYQ4cOJD+OHLkCJMmTeKjjz5i7969pKamMnv2bH766SfOPPPMiLdfo0YN/v77b3bv3p1h2saNG0lNTY14e/Xq1aNly5YMHjyYQ4cO8fXXXzNr1qyIt2OMMRAjSU1ErgFGAsOBlsBXwGwROTbEKs8CtQIei4CFqro9YNuVgCnAvLyJPrZ06tSJhISE9MfgwYMpX748w4cPp2nTplSsWJEHHniAMWPGcN5550W8/SZNmnDdddfRsGFDKlasyNatW+nWrRsAVapU4dRTT414m6+88gpff/01VapU4ZFHHuGaa66hZMmSEW/HGGNi5ZraPcAkVR3ve32niFwE9AUGBi6sqslActprEakLtAZuDLLtV4HJgABXRTnumLJx48aQ86688kr27t0b1rW+hQsXZngdOObahAkTMq3zxRdfhNxGjx496NGjR4b5buR3p2HDhixevDj99TXXXEOTJk2yjdMYYwJ5fqYmIiWAVsDcgFlzgXPC3ExP4B/gnYBt9wNqAk/kLkqTl5YtW8Zvv/1Gamoqc+bM4f333+fyyy/3OixjTAEUC2dqVYGiwLaA6duAzP09BRCRIsB/gCmqetBv+snA48BZqpqSXWMGEekN9AZ3jSjwbAWgQoUK7N27N7uQSElJCWu5/BarcSUlJXHDDTewc+dOateuzYgRI2jcuLHnsapq0HLgteTkZIsrAhZXZGI1rrCpqqcPoDagQOuA6Y8Da8JYv7Nv/aZ+00oCPwE3+k0bDKwKJ6ZWrVppMKtXrw46PdCePXvCWi6/WVyRWb58udchBLVgwQKvQwjK4opMPMYFLFWPc0osnKntAFJw1YT+qpP57C2Y3sBXqvqT37RawEnARBGZ6JtWBBAROQJ0UtXA6s6wqGqumrCbgkH9rvkZYwoOz6+pqeohYBnQIWBWB1wryJBEpDbuTG18wKwtwMlAC7/HWOBX399ZbjeU4sWLs3///pysagqY/fv3W2IzpgCKhTM1gOeB10TkW+BLoA+uWnIsgIg8BZyhqoFdy/8H2Ae85T9RVQ8DGe5JE5HtwEFVzfG9atWrV2fLli3UqVOHhIQEO2OLQ6rK/v372bJlC/v27fM6HGNMhGIiqanqdBGpAjyCqzpchasi3ORbpBbQyH8dcRmlJzBVVf8lH5QvXx6ArVu3cvjw4ZDLHThwgFKlSuVHSBGxuMJTvHhxatSowZYtW7wOxRgToZhIagCqOhoYHWJejyDTFGgQwfYH4xqL5Er58uXTk1soCxcupGXLlrndVdRZXMZkIykJrr0Wpk+HmoGX+U1B4Pk1NWOMiRnDhsEXX8DQoV5HYnLIkpoxxiQkgAiMGQOpqe5ZxE03BYolNWOMWb8err8e0oZAKl0auneHDRu8jctEzJKaMcbUqgXly8OBA1CqlHsuX96uqxVAltSMMQZg2zbo0we++cY9//mn1xGZHIiZ1o/GmBhQmFv/vfvu0b9HjfIuDpMrdqZmjDnKWv+ZAs6SmjHGWv+ZuGFJzRhjrf9M3LCkZoyx1n8mblhSM8Y41vrPxAFr/WiMcaz1X6F35Ajs3FnC6zByxc7UjDGmkNu7F0aOhOMaHmHkzUUL9Fm6JTVjjCmkNm+GBx6AunXh7rvhmMMb6Z/8X3RIwb2lw5KaMcYUMitXwo03QoMG8Nxz0HHvDJZwBov/PI4reQ8ZW3Bv6bCkZowxhYAqfPIJdOgALVvCzJlwxx3w228wffO5nHH9cXFxS4c1FDHGmDh26JDr9ezZZ+GHH9zdG08/DbfdBhUrpi119JaOlBIlKFqAb+mwpGaMMXFozx4YPx5GjIAtW6BZM5g40d1jXyJYA0ffLR3LW7bk9BUrXD+gBZAlNWOMiSNJSfDii66ns927oU0bl9wuushdJgvJd0vHvoULoVev/Ag1T1hSM8aYOLB2LTzzDEyZ4u43u+oquP9+OO00ryPLX5bUjDGmAPv2W/jvf+G996BkSejZE+69Fxo18joyb1hSM8aYAkYVPv3UNfhYsMA1+Hj4YbjrLqhe3evovGVN+o2JJ0lJkJhYoHuEMKGlpMDbb7sqxY4d4ZdfXKvG33+HJ56whAaW1IyJLzbIZ1w6dAgmTICTToKrr3bdWo0f70YMuvdeKFfO6whjh1U/GhMPEhLccDFpxoxxj1KlYP9+7+IyubJvH7zyijsb27zZ3TT91ltw5ZVQtKjX0cUmO1MzJh7YIJ9x5Z9/4MknoX591ydjw4YwZw4sWwbdullCy4qdqRkTD2yQz7jw11/wwgvw0kvu5ulOnVwDkHPP9TqygsPO1IyJFzbIZ4G1dSvcc487M3vqKbjwQli+HD76yBJapOxMzZh4YYN8FjibNrl7zF591bVs7N4dHnoITjzR68gKLktqxhiTz377DZ555gTmznVdV/XoAQ8+WHhvmI4mS2rGGJNPfvkFhg+HqVOhSJEa9OlzdJBOEx2W1IwxJo+tXu1aM06b5rqy6t8fzjnnG7p2Pcfr0OKONRQxxpg88tNPcO21btiX99+H++6DjRvdaNNVqhzyOry4ZGdqxhgTZatWuc5d3n4bypRxjT/uuQeqVvU6svhnSc0YY6Lkp59cD2Vvvw1ly8LAgS6ZVanidWSFhyU1Y4zJpdWrYciQo2dmDz8MAwZYMvOCJTVjjMmhNWvcmdm0aS6Z2ZmZ9yypGWNMhH791SWzqVNdr2QPPuh6y7drZt6zpGaMMWHauNE1AJk8GUqUcGdl999v45jFEktqxhiTjS1b3H1mr7wCRYrAHXe4Fo3WX3TssaRmjDEhbN8OTz8No0dDair06gWDBkGdOl5HZkKxpGaMMQF27XIDc44c6cZYvflmeOwx14u+iW2W1Iwxxic52SWyZ56B3btdbyCDB8MJJ3gdmQmXJTVjTKF34ACMG+c6G96+HS691DUIad7c68hMpCypGWMKrSNHYMoUdzb2xx/Qtq3ro/Gss7yOzORUzHRoLCL9RGSDiBwQkWUi0jqLZQeLiIZ4VPctc6WIzBWRv0Rkr4gsEZHL8u8dGWNilaobU/Xkk6FnT9eK8dNPYf58S2gFXUwkNRG5BhgJDAdaAl8Bs0Xk2BCrPAvUCngsAhaq6nbfMonAfKCzb5sfA+9llSyNMfFv/nw480zo2tUN0PnOO7BkCbRv73VkJhpipfrxHmCSqo73vb5TRC4C+gIDAxdW1WQgOe21iNQFWgM3+i3TP2C1ISLSGbgcWBzV6I0xMW/5cndv2aefukE5J0yAG2+EYrHyLWiiwvMzNREpAbQC5gbMmguEO4JeT+Af4J1slisH7IokPmNMwbZlSymuuw5atYJly9xYZmvXwi23WEKLR6Kq3gYgUhvYAiSq6ud+0x8Duqtqlo1pRaQIsBF4R1UHZLHc7cDTQDNV3RRkfm+gN0CNGjVaTZs2LQfvxklOTqZs2bI5Xj+vWFyRsbgiE2tx7dpVnNdeq8cHH9SmWDHlqqs2c+21v1O2bIrXoQGxd7zS5Cautm3bLlPV06IcUmRU1dMHUBtQoHXA9MeBNWGs39m3ftMslukK/AtcFk5MrVq10txYsGBBrtbPKxZXZCyuyMRKXHv3qg4Zolq2rGrRoqqXXrpFt271OqrMYuV4BcpNXMBS9TinxMLJ9w4gBQjsRa06sC2M9XsDX6nqT8FmikhX4DXgJlX9IDeBGmNi15Ej8Oqr8PjjsG0bXHmlu+8sKWkttWrV9jo8k088v6amqoeAZUCHgFkdcK0gQ/JVXXYGxoeYfzXwOtBDVWfkPlpjTKxRhQ8+cM3z+/SB446Dr75yrRqtJ5DCx/Ok5vM80ENEeonIiSIyElctORZARJ4SkXlB1vsPsA94K3CGiFwLTAUeAj4XkZq+R+U8exfGmHz13XfQpg106eKS28yZ8PnncPbZXkdmvBITSU1VpwN3A48AK4HzgE56tEFHLaCR/zoiIrhWj1NV9d8gm+2Du2XhBSDJ7/Fu1N+AMSZfbdgA110HZ5zhRp8ePRp+/NElNxGvozNeioVragCo6mhgdIh5PYJMU6BBFttrE63YjDGx4Z9/3LhmL74IRYvCI4/AAw9AuXJeR2ZiRcwkNWOMCeXwYRg71vXRuGuXGwrmiSdsXDOTWUxUPxpjTDBpjUCaNYO77oIWLVzPIBMnWkIzwVlSM8bEpJUroV07d52sSBH48EP47DOX2IwJxZKaMSamJCW5nvNPPRV++AH+9z/33LmzNQIx2bNrasaYmHDgAIwY4W6YPngQ7rnHNQSpWNHryExBYknNGOMpVZgxA+6/HzZtgssvh2eegcaNvY7MFERW/WiM8cyKFZCYCFdfDRUqwLx58N57ltBMzllSM8bku+3boXdvNxzMzz+75vrLl8MFF3gdmSnorPrRGJNvDh2Cl16CIUPg339hwAB49FG7bmaix5KaMSZfzJkDd98Nv/wCF1/sGoVYh8Mm2qz60RiTp377zd1rdvHFkJLi7jf7+GNLaCZvWFIzxuSJfftg0CA46SSYPx/++19Ytcrdb2ZMXrGkZoy/pCTXHO/PP72OpMBShenToUkTd8/Z1Ve7KscHHoCSJb2OzsQ7S2rG+Bs2DL74AoYO9TqSAumnn1zXVtdeC1WrukP52mtQ2waeNvnEGooYA5CQ4Lq0SDNmDG3GjIFSpWD/fu/iKiD27IFRoxrx3ntQvrwb36x3bzc8jDH5yc7UjAFYvx6uvx5Kl3avS5dmW/v2bjRKE5IqvPGGa/TxzjvH0LMnrF0LfftaQjPesKRmDECtWu4U48ABd3Z24ABHSpeGmjW9jixm/fQTtG0L3bvDMcfA6NHLGTfOVTsa4xVLasak2bYN+vSBb76BPn0osWuX1xHFpORk109jixbw448wbpw7ZE2a7PU6NGPsmpox6d599+jfo0bx08KFtPEsmNijCu+8426g3rIFevWCp56yMzMTW+xMzRiTrV9/dTdPd+sG1arBV1/B+PGW0EzssaRmjAnpwAHXT2OzZi6RjRwJ330HZ5/tdWTGBGfVj8aYoD77DPr1g3Xr3H1nzz/v2tMYE8vsTM0Yk8G2ba5FY4cO7jra3Lnw5puW0EzBYEnNGANAaqprydikiRuJ+rHHXOvGDh28jsyY8Fn1ozGGVavgttvcdbM2bdygndaLvimI7EzNmEJs/354+GFo2dJ1OjxpkutR3xKaKajsTM2YQuqzz9y95r/9Bj16wDPPWBN9U/DZmZoxhcyOHXDzze5aWZEi7sxs4kRLaCY+WFIzppBQhddfdw1B3ngDHnkEfvjB9d9oTLyw6kdjCoGNG11V4yefwFlnud5AmjXzOipjos/O1IyJYykprheQZs3gyy/hf/9zA3daQjPxys7UjIlTq1a5ToeXLIFOnWDMGDj2WK+jMiZv2ZmaMXHm0CEYPBhOPdW1bJw6FT780BKaKRzsTM2YOPLtt/Cf/7gBPK+/Hl54wfWqb0xhEVZSE5Hfc7BtBTqr6qocrGuMicD+/a5bq7ROh2fNgksu8ToqY/JfuGdqxwAfA3+FuXwR4AagRE6CMsaEb/Fi6NnT9abfu7e7ibp8ea+jMsYbkVQ/DlXVb8NZUESKATfmLCRjTDj27YOBA+Gll6B+fZg3Dy64wOuojPFWuA1FHgX+CHejqnrEt86WnARljMnaggVw8smuif4dd7je9C2hGRPmmZqqPhnphnOyjjEma8nJ8MILx/H++9C4MXz+ObRu7XVUxsQOa9JvTAGRdnb2wQe1uftu+P57S2jGBMpxUhOR6tEMxBgTXHKyq2K84AIoVgxGjlzJiBFQurTXkRkTe3JzprY0alEYY4JavBiaN4fRo6F/f3d2dvLJu70Oy5iYleU1NRG5LIvZpaIcizHGZ/9+14v+iBHQoAEsXAjnn+91VMbEvuwairwHLAIkyLxy0Q/HGPPtt268szVroG9f+L//g7JlvY7K5IukJLj2Wpg+HWrW9DqaAim7pLYO6KmqGwJniEjYTfyNMdk7dAiGDYOnnnK9gsyd6wbyNIXIsGFuGIWhQ12ds4lYdtfUJgOhxsMdG81ARKSfiGwQkQMiskxEQrbrEpHBIqIhHtX9lkv0beuAiKwXkT7RjNmYaFm1yo1z9sQTcMMN7r4zS2iFSEICiLihFFJT3bOIm24ikmVSU9WnVPW7EPOidh+aiFwDjASGAy2Br4DZIhKqX/FngVoBj0XAQlXd7ttmA1zXXl/5tvkU8D8R6RqtuI3JrZQUeO45aNUKNm+G996DSZOgYkWvIzP5av161wN1WpPW0qWhe3fYkKmSzGQjotaPIlInj+K4B5ikquNV9WdVvRNIAvoGW1hVk1X1z7QHUBxoDYz3W6wPsFVV7/RtczzuzPO+PHoPxkRk0yZo1w7uuw8uvtidrV1+uddRGU/UquU67DxwAEqVcs/ly9t1tRwQVQ1/YZHtqhrV+9NEpATwL3Cdqr7tN30U0ExVE8PYxmDgTqC2qh70Tfsc+FFVb/dbrhvwBlBaVQ8HbKM30BugRo0araZNm5bj95ScnEzZGLyyb3FFJq/iUoVPPqnB//53HAB33vkrHTv+iQRrjpWPceVWcnIylQ8e5KShQ1n9+OMcqlzZ65CA2D5e/nE1fewxDlWuzNZLLqH2hx9SYudOfho61PO4ItG2bdtlqnpalEOKjKqG/QD+imT5MLdZGzdMzfkB0x8Dfglj/SLA78CIgOlrgccCpp3v21etrLbZqlUrzY0FCxbkav28YnFFJi/i2rFDtWtXVVBt3Vp1w4bItxHTx6tvX9UiRdxzjIjp4xWDchMXsFSjnCMifUQ6SGj4p3WRC9y2hLm/i4G6wCthbjPYdGPy3Ny50KMH7NgB//0v3HsvFC3qdVRRkpBAmwMHjr4eM8Y9SpVyN90Zk09ioe/HHUAKEFh5XB3YFsb6vYGvVPWngOl/htjmEeDvHMRpTI7s3+96A+nYESpVcvehPfBAHCU0gPXr2daunTV0MJ7zPKmp6iFgGRDYgLkDruViSCJSG+hMxgYiab4G2gfZ5lINuJ5mTF75/ns4/XR48UWX2JYuhRYtvI4qD9SqxZEyZbxv6JCUBImJ8Oef+btfEzM8T2o+zwM9RKSXiJwoIiNx19rGAojIUyIyL8h6/wH2AW8FmTcWOEZEXvBtsxfQA3c7gDF5KjXVdXF1xhnw998wZw688EJ833ZUYtcu6NMHvvnGPXuRWPxvXjaFUqTX1PKkFxFVnS4iVYBHcPecrQI6qeom3yK1gEb+64iIAD2Bqar6b5BtbhCRTsAI3K0BW4G7VPWdvHgPxqRJSnLXzubOhS5d4JVXoGqoLgziyE9Dh9KmTRv3YtSonG0kp91EJSS4s8M0/tf0Zs/OWSymQIroTE1VW+VVIKo6WlXrq2pJVW2lqp/7zeuhqvUDlldVbaCq/bLY5iJVPdW3zQaqGtVeUIwJNGsWnHKK611/7Fh3M3VhSGhRk9MzLbt52fjESvWjMQXa/v1uzLPLLoNjjoFly+C22wj73rNCL7fdRNnNy8Yn4qQmIkVEpFjAtI4icq+ItIxeaMYUDKtWucYgo0bBPfe4S0onnuh1VAVMNM60tm3z/pqe8Vyk19QA3gQOAjcB+DoJTutO+rCIdFbVz6IUnzExS9VVMd5zD1So4BqDdOzodVQFVDTOtN599+jfOb2mZwq8nFQ/noXrKDjN/bgbnysA7wKDohCXMTFt507o2hX69YM2beCHHyyh5ZqdaZkoyMmZWnVgC4CINAYaAC+p6l4RmYjrW9GYuPXFF66m7M8/4dlnYcAAKGJXp3PPzrRMFOTkX3EPUMX3dxtgh6r+4HudApSKQlzGxJyUFNc4LzERSpSAr75yXV1ZQjMmduTkTO0r4CEROQLcTcaqyMbA5ijEZUxMSUpy7RYWLHBnaWPGuEs+xpjYkpPfmA8AlYEPcGdlg/3mXYPrnsqYuPHJJ9C8ubvU8+qr8PrrltCMiVURn6mp6jrgeBGpoqqBHQP3x3UkbEyBl5IiDBwITz8NzZrBwoVw0kleR2WMyUpOqh8BCJLQUNUfcxeOMbFh82YYMKA5P/4IvXrByJFHb6EyxsSusKofRWS+iDQJd6O+G7Tni8hxOQ/NGG/Mnu160v/117JMnQrjx1tCM6agCPeaWhugXATblRysY4ynjhyBgQOhUyeoUwfGjVvG9dd7HZUxJhKRVD/OFJGDESxvo0ubAmPrVtc5/OLF0Lu3GyZmyRIbsdmYgibcpDY5h9vfkcP1jMk3n33mmun/+69r2di9u9cRGWNyKqykpqq35HUgxuS3lBR44gkYMsR1QDxjhnVEbExBl+PWj8YUZDt2wA03uHvQbrzR3UxdpozXURljcsuSmil0liyBbt1g+3YYNw5uvdXGPTMmXlivdabQUHX95LZuDUWLwpdfukYhltCMiR+W1EyhsG+fq2684w648EI3MnWrVl5HZYyJtpyMfN06LwIxJq+sXQtnnQVvvukahnzwAVSu7HVUxpi8kJMztekiEnI4WhEpm4t4TGGXlOTGdonSAJEzZ8Jpp7nNfvIJDBpkQ8UYE89y8u/9FTBDRDI1MhGRusCXuY7KFF7DhrlROIcOzdn6vqSYsuVPHn4YrrgCTjgBli+HDh2iG6oxJvbkJKndAlQDRvhPFJFWwBLcQKHGRCYhwbXYGDMGUlPds4ibHolhw/h78WouPmsXTz3lWjYuXgzHHps3YRtjYkvESU1V9wJXAbeISHcAEbkc+BxYCtg1NxO59etdtx5pPQeXLu269tiwIbz1fUlxxZivOU2/ZdHmhoynFy+/lkApG4vdmEIj3F7624lIxbTXviFm+gHjROQ5YAYwHuiiqvvyIlAT52rVciNvHjgApUq55/LloWbIy7cZrV/P62eP4hy+4gjFWFyyA726Hwg/KRpj4kK4Z2qfAn+LyK8iMk1E7gV+Bz4E7gTuUNW7VdU6MTY5t20b9Onjhpju0yfsxiKHD8Pd/63FjV/34yy+YVnJcznj8JeRJUVjTFwIt0eRpsCpQCvf4zGODivzD3C+iJQHVgIrVXV7dMM0hcK77x79e9SosFb56y+4+mo3KvXdjWbxTIe5FOszC15+2TUaMcYUKuF2aPwz8DMwNW2aiByPS3BpyW4gUAE35EzRqEdqTIDly13rxu3bYcoUuPHGS4FL3cwwk6IxJr7kuO9HVV0LrAXeTJsmIo1xSc6YPPXGG9CzJ1Sr5u4AsN5BjDEQ5W6yVPVXVX0rmts0xl9KCtx/v2sYecYZsHSpJTRjzFHWS78pMP75B667DubMgX793OjUxYt7HZUxJpZYUjMFwi+/wGWXuRb6L7/sbqo2xphAltRMzJszB669FkqUgPnz4bzzvI7IGBOrrGtXE7NU4fnnoXNnqF8fvvvOEpoxJmuW1ExMOngQ/vMfuPde12z/yy+hXj2vo8oHUR6lwJjCxpKaiTnbt0O7djBpEjz+OLz1FpQp43VU+SS3oxQYU8jZNTUTU374wTUI2b7dJbNu3byOKJ8kJLj+LtOMGeMepUrB/v3exWVMAWNnaiZmzJoF55zj+nL8/PNClNAg96MUGGMAS2omBqjCs89Cly5w4omuQchpp3kdVT7L7SgFxhjAkprx2KFD8OyzJ3D//XDVVbBoEdSu7XVUHsnhKAXGmKPsmpqJrqQkd1PZ9OnZnmXs3Aldu8LChbV49FEYPBiKFOafWTkYpcAYk1Fh/goxeSHM1nvr1sHZZ8NXX8HDD//M0KGFPKEZY6LCztRMdETQem/xYrj8cpfE5s2DI0e2ASfma7jGmPhkv41NdITZeu/11909aNWquUtH1kOIMSaaLKmZ6Mim9Z6qu2Z2440ukX39NTRq5G3Ixpj4EzNJTUT6icgGETkgIstEpHU2y4uI3C0ia0TkoIgkicjTActcLyIrReRfEflTRF4XEWsjnVdCtN47dAhuvhmGDIEePVwHxZUqeRuqMSY+xcQ1NRG5BhgJ9AO+8D3PFpGTVPX3EKs9B1wC3A/8CFQAavlt81zgNeA+YCZQAxgNTAXa5ckbKeyCtN7btQuuvBIWLnRtRx55BES8Cc8YE/9iIqkB9wCTVHW87/WdInIR0BcYGLiwiJwA3Amcoqo/+81a4ff32cBmVR3he71BRP4H/C/q0ZugNm6ETp3gt9/ctbTu3b2OyBgT70RVvQ1ApATwL3Cdqr7tN30U0ExVE4Os8wDQExiLS25FgEXA/aq63bfM2b5pXYEPgSq4s7Tdqnp1kG32BnoD1KhRo9W0adNy/J6Sk5MpW7ZsjtfPK/kZ1y+/lGPgwJM5ckQYOnQVLVrsjom4ImFxRcbiikw8xtW2bdtlquptf0Cq6ukDqA0ocH7A9MeAX0KsMxY4ACwBzgda+/5eAhTxW64rsAc47NvHXCAhu5hatWqlubFgwYJcrZ9X8iuuWbNUS5dWrV9fdfXq7Jcv7McrUhZXZCyuyOQmLmCpepxTYqahCC7p+JMg09IUAUoCN6rq56q6GLgROAM4HUBETgJeBIYBrYCLgJrAuOiHbtKMG3e0D8evv3bPxhiTX2Ihqe0AUnAJx191YFuIdZKAI6q61m/aOuAIcKzv9UDgW1V9RlV/UNVPcA1QbhSRulGL3gCuyf6gQa7R40UXuYYh1hevMSa/eZ7UVPUQsAzoEDCrA/BViNW+BIqJiP+dTg1xDV82+V6XxiVLf2mvrf1dFKU12R8+HG69Fd5/H2LwUoExphDwPKn5PA/0EJFeInKiiIzEXWsbCyAiT4nIPL/lPwOWAxNEpKWItAQm4K6pLfUtMwvoIiJ9RaShr4n/i8ByDX2bgElKgsTEsHuI37sXLrkEXnvNNdkfNw6KxUqbWmNMoRMTSU1VpwN3A48AK4HzgE6qmnbWVQto5Ld8Ku4ete3A58AnwGagi28eqjoJd6vAHcAqYAauirJLXr+fAi3MDonB5b02bWD+fJgwAR591O5BM8Z4K2Z+U6vqaNzN0cHm9QgyLQnIcmxkVbX70sIVQYfE4HrZ79jRdSIyaxZcfHE+xmqMMSHExJmaiQFhdkgMbmTqc86B5GTXIMQSmjEmVlhSM042HRKn+eQTaNsWypWDL7+E00/3KF5jjAnCkpo5KkSHxGmmTnWNQo47zg3uedxxHsVpjDEhxMw1NRMDgnRInOaFF2DAAHeWNnOmO4kzxphYY2dqJkuqMHCgS2hdu8LHH1tCM8bELjtTMyEdOeJqIV99FW67zZ28FS3qdVTGGBOanamZoA4cgKuvdgntkUdc635LaMaYWGdnaiaTPXvg8sthwQJ3La1/f68jMsaY8FhSMxns2OHuO1uxAqZMgRtv9DoiY4wJnyU1k27zZrjwQne/9XvvwaWXeh2RMcZExpKaAeDXX6F9e9i5E+bMcX0aG2NMQWNJzfDjj9ChA6SkuOtorVp5HZExxuSMtX4s5JYscWdlxYrB4sWW0IwxBZsltXgTwXhoCxZAu3ZQubIbbaZJk3yIzxhj8pAltXgT5nhoH33kWjnWr+/O0OrXz5fojDEmT1lSixcJCW6EzjFjIDXVPYu46QHeftvdh9asmRs6platfI/WGGPyhCW1eBHmeGiTJ8O118JZZ8G8eVC1qgexGmNMHrGkFi/CGA/tgw9q06MHXHCBa7ZfoYJ34RpjTF6wpBZPshgPbcQIGDHieC65BGbNgjJlPIzTGGPyiN2nFmuSklz94PTpmUadzlaI8dCefNJ1SpyYuJ133qlOiRJRitUYY2KMnanFmjBbL4ZDFR591CW0G26ARx/92RKaMSauWVKLFRG0XgyHKjz4IDzxBPTsCZMmQdGiGt2YjTEmxlhSixVhtl4Mh6obqfqZZ6BvX3j5ZRsLzRhTOFhSixVhtF4MR2oq3HEHjBzpxkEbNQqK2KdsjCkk7OsulmTRejEcqanQrx+MHg333edaPIrkUazGGBODrPVjLAnRejEcqalw223wyivw0EMwfLglNGNM4WNnanEgNRV69XIJ7ZFHLKEZYwovS2oFXEqKa904cSI89pi7E8ASmjGmsLLqxwIsLaFNngyDB8Pjj3sdkTHGeMuSWgHln9CGDHFnacYYU9hZ9WMBlHYNzRKaMcZkZEmtgElLaJMmuSpHS2jGGHOUJbUCJK3ZflqjELuGZowxGVlSKyBU4fbbXbP9QYPcWZoxxpiMLKkVAKpw110wdqzrpHjYMGu2b4wxwVhSi3GqcO+98NJLcM898NRTltCMMSYUS2oxTBUeftj14XjnnfDss5bQjDEmK5bUYtiQIfD0065xyMiRltCMMSY7ltRi1NNPu6TWo4frdd8SmjHGZM+SWgwaORIGDoTrrnOtHW08NGOMCY99XcaYl1+Gu++GK6+EKVNsxGpjjImEJbUY8vrrbmzQTp3gzTehmPXMWfAkJUFiYsQDvBpjosOSWox47z13/axtW5gxA0qU8DoikyPDhsEXX7gxgIwx+c6SWgz45BO45ho480x4/31ISPA6IhOxhATXmmfMGNef2Zgx7rV9mMbkK0tqHvv8c7jiCmjWDD76CMqW9ToikyPr18P110Pp0u516dLQvTts2OBtXMYUMjGT1ESkn4hsEJEDIrJMRFpns7yIyN0iskZEDopIkog8HbBMCREZ6tvuQRH5XUTuytt3Er6lS+GSS6BePXe2VrGi1xGZHKtVC8qXhwMHoFQp91y+PNSs6XVkxhQqMdEUQUSuAUYC/YAvfM+zReQkVf09xGrPAZcA9wM/AhWAWgHLvAnUBXoD64AaQEzUB61eDRddBFWqwGefQbVqXkdkcm3bNtfSp3dv14w1KcnriIwpdGIiqQH3AJNUdbzv9Z0ichHQFxgYuLCInADcCZyiqj/7zVrht8yFQHugkaru8E3emAexR2z9emjf3jUG+ewzqFPH64hMVLz77tG/R43yLg5jCjFRVW8DECkB/Atcp6pv+00fBTRT1cQg6zwA9ATG4pJbEWARcL+qbvctMxo4HvgWuAnYD8wGHlbV5CDb7I07o6NGjRqtpk2bluP3lJycTNkQF8f+/rsEd93VkuTkYrzwwkoaNNiX4/1EMy4vWVyRsbgiY3FFJjdxtW3bdpmqnhblkCKjqp4+gNqAAucHTH8M+CXEOmOBA8AS4Hygte/vJUAR3zJzfMt8BJwJdATWAjOyi6lVq1aaGwsWLAg6/e+/VZs1Uy1TRnXJklztIkdCxeU1iysyFldkLK7I5CYuYKl6nFNipfoRXGLzJ0GmpSkClARuVNW1ACJyI/ALcDq+5OZb/3pV3e1b5g7gExGpoarbov8WQtu3Dzp3hrVr4eOP4Ywz8nPvxhhTOMRC68cdQAoQ2EysOhAq8SQBR9ISms864AhwrN8yW9ISmk/a9bdjyUeHDrlur779FqZNg3bt8nPvxhhTeHie1FT1ELAM6BAwqwPwVYjVvgSKiUgjv2kNcQ1fNvktU1tE/CuHj/c9byKfpKTATTfB3Lmuc+IrrsivPRtjTOHjeVLzeR7oISK9ROREERmJu9Y2FkBEnhKReX7LfwYsByaISEsRaQlMwFU7LvUt8wbwNzBRRJqKyLm42wZmqK8xSV5ThbvugunT4f/+D265JT/2aowxhVdMJDVVnQ7cDTwCrATOAzqpatoZVS2gkd/yqbh71LYDnwOfAJuBLr55qGvh2B53/9p3wFu4FpL/yfM35DNkiBsL7f773cMYY0zeipmGIqo6GhgdYl6PINOSgG7ZbPMX4MJoxBep0aNdUrvlFvjvf72IwBhjCp+YOFOLNwsXVuOOO+DSS13HEjZqtTHG5A9LalE2fz4MH34i55zjWjramGjGGJN/LKlF0Zo1cPnlUKfOfmbNOtphuzHGmPxh5xFR1KiR68v2zDO/p1Klc7wOxxhjCh07U4ui4sXh2WehWrVDXodijDGFkiU1Y4wxccOSmjHGmLhhSc0YY0zcsKRmjDEmblhSM8YYEzcsqRljjIkbltSMMcbEDUtqxhhj4oYlNWOMMXHDkpoxxpi4YUnNGGNM3LCkZowxJm5YUjPGGBM3LKkZY4yJG5bUjDHGxA1LasYYY+KGJTVjjDFxw5KaMcaYuGFJzRhjTNywpGaMMSZuWFLz2OrVqxERPv30U69DAeDLL7/kwgsvpHr16pQvX55TTz2VCRMmhL3+xx9/zPnnn0/ZsmUpX748p512GvPnz0+fv3DhQkQkw6Nt27ZUrFgx6u/ljz/+4KqrrqJChQqUL1+eK6+8kt9//z3DMps3b+bOO+/k7LPPpnTp0ogIGzduDHsfPXr0SH8fbdq0yfF2k5KSKFKkCF9++WVY+33iiSfS93vMMceEHW9OjB8/PtNnlvYoU6YMKSkpebr/7MpUKGll+YorrsiyLC9YsIDzzjuPhIQEKleuzI033si2bdvy4q1kKZzyOmPGDLp27Uq9evVISEjghBNOYODAgezduzfb7Ycqq4MHD0ZEOHLkSKZ1Ii2X0SAig0VE/V4/IiLqe2zObn1Lah5bvnw5AK1atfI4Evjhhx9o3749hw8fZvz48bzzzjucfvrp9OzZkzFjxmS7/rhx4+jSpQutWrXivffe4+2336Zbt278+++/mZZ98cUX+frrr/n6668ZNWoUn332WVTfy7///ssFF1zAmjVrmDx5Mq+99hrr1q2jbdu27Nu3L325X3/9lbfeeotKlSrRunXrHO2rZs2afP3114wePTrH2505cybVqlXj7LPPDmuft9xyC19//TWdOnXKUcyRWLlyJWXKlEn/vPwfX331FUWLFs2zfUdSpvz5l+V77703ZFlevHgxF154IRUrVuSdd95h5MiRfP7557Rr146DBw/m2fsKFG55ffbZZylatCjDhw9nzpw59O3blzFjxtChQwdSU1Oz3U+wspqVSMtlHpkInA18HNbSqmqPgEerVq00NxYsWBD2snfffbc2aNAgV/sLV3ZxDRw4UIsXL6579+7NMP3MM8/Us846K8t1N2zYoKVKldIRI0ZkGwOgn376adhx5cQLL7ygRYoU0XXr1qVPW79+vRYtWlSfe+659GkpKSnpf48fP14B3bBhQ9hx3XzzzVqvXr1M07PabjAXXnih9urVK9v9BcZ18803a506dcJaL6fOOeccPeOMM7JdLtqfY7hlKhj/suwfV2BZbteunTZq1EgPHz6cPu3bb79VQEeNGpWb8NPVq1dPH3/88UzT/eMKt7xu374903YmT56sgM6bNy/LOEKV1ccff1yB9GPgH1ck5VJVFViqufz+BQa71JRp+iRgc3br25max5YtW8Zpp52W/nrPnj1cddVV1KxZk0WLFuVrLIcOHaJ48eIkJCRkmF6xYsVsfwVOmDCBIkWK0KdPn6jG9P3333PZZZdRqVIlEhISOPfcc1m8eHG2633wwQecddZZNG7cOH1agwYNOPfcc3n//ffTpxUpkjf/ApFsd8+ePSxcuJDLL78cgLVr13LFFVdQvXp1SpUqxbHHHku3bt2CVg/lNVXlhx9+4JRTTsn3feemTIVblr/55hs6dOhAsWLF0qedfvrpVKlShffeey/Dujkti+EIt7xWq1Yt07qnn346AFu2bIlKLGkCyyUcrapcs2YNHTt2pEyZMhx77LFMnDgxbZHKIrJGRJJFZIGINPLfpohcJCJfi8h+EdktIjNF5IRoxm1JzUOqysqVK9OT2o8//shpp53Gli1bWLZsGYmJiRFt68iRI1k+UlJSsrz+0aNHDwDuuusutm7dyj///MP48eOZN28eAwYMyHL/X3zxBU2aNGHatGk0atSIYsWK0bhxY0aNGhV0+e7du1O0aFGqVKnCsGHDMl07AFc1e84557Bz58706tAqVarQvn17li1blmU8P/30E82aNcs0vWnTpqxevTrLdfPbRx99RIkSJWjfvj0Al1xyCVu2bGHMmDF88sknPP3005QsWTKs6qVoW7duHcnJyTRt2jRoeQpXOOUzcJuRlil//mV5x44dIcty0aJFKVGiRKb1S5YsyapVq9Jf56YshiM35TXtx++JJ56Y6zj8BZZLf926daNz587MnDmTVq1a8Z///IeHH34YoDrwEHALcALwRto6InIR8BGQDFwD9AWaAV+ISJ2oBZ7bU8V4fORX9eOaNWvSqw0mT56spUuX1r59++rBgwdztE8g20diYmKW2/n222+1Tp066csXL15cX3nllWz3f8IJJ2i5cuW0atWq+vLLL+u8efO0T58+CugLL7yQvtzy5cv13nvv1Q8++EAXLlyoI0aM0IoVK2rt2rV127ZtGbZ5wQUXaJMmTTIcjyNHjmiTJk20S5cuWcZTvHhxffDBBzNNHzRokBYtWjToOtGsfsxqu4Guvvpqveqqq1RV9a+//lJA33///ZDby8/qx+nTp4csSy1atAgZV6CclM9wy1Qo4ZTl008/PVPV6saNG1VEtESJEunTwi2Lqampevjw4QyPevXq6aOPPpph2pEjRzIcr5yUV1XVzZs3a7Vq1bR9+/bZHo9Iqx/9y2XgspMnT06ftnPnTi1atKhWrlxZgeV6tLrwLt+xr+d7vRRYBxTzW6YBcBh43m/aYHJR/Xj0nNvku7RfeOPGjWPWrFmMHTuWm266KcMyv/32GzfffDPbt2+nTJkyjB8/PkN1ZZpWrVrx3XffZbs//1ZPgdatW0fXrl1p2rQpY8eOJSEhgffff58+ffpQqlQpunfvHnLd1NRU9u7dy6RJk7jyyisBuOCCC9i4cSNPPfUUd911FyJCy5YtadmyZfp6iYmJlC5dmn79+vHiiy/yxBNPALB//34WLVrEww8/TJEiRTJUvbVv356pU6eiqpnOFvyrkUQkU5y+f46YcejQIebMmZN+4b5KlSo0bNiQhx56iG3bttGmTRuOO+44z+JbsWIFIsIXX3yR6YymUqVKYW8nnPIJUK5cufS/wy1TwfiX5dtvv50zzjgjaFnu378/N9xwA4888gh33XUXO3fupHfv3hQpUiS9Cjmcsphm0aJFtG3bNlM8w4YNY9iwYemvExMTGTx4cIZlIi2vycnJdOnShWLFivlX/0VFYLkMdPHFF6f/XalSJapXr07Lli35+OOP/asT1vie64rIDuBUYLiqph9AVd0gIl8C4VdLZcOSmoeWL1+e3urqzjvvzJTQAPr06UOPHj3o1asXn376Kd27d2fNmjWZ/gHKli1LixYtstzf7t27M9TZB3r44YcpXrw4H374IcWLFwegXbt2/P333/Tv35/rrrsu5LWiKlWqsG7dOjp06JBh+oUXXsicOXNISkqidu3aQdc9/vjjOf744zN86e3cuZOUlJRMXwb+FixYQLt27TJMS/sSqFSpEjt37sy0zq5duyL6Ms5r8+bNY//+/XTu3Bkg/faOwYMHM3DgQP7++28aNGjA/fffT9++ffM9vpUrV9KwYUPOOeecXG0nnPIJGb/Yc1Om/Mvyl19+SZs2bYKW5bT/p2effZYnn3wSEeGaa66hU6dO6dWP4ZTF1NRUihQpEjR5X3bZZVxyySX07t07fVq5cuVISkpKfx1peT1w4ACXXXYZ69evZ9GiRVG/rSOwXAYKjKlEiRLB4jzkey4FVAIESApcCPgTqJebeP1ZUvPQsmXL6NixI+effz533nknrVu3Tv9FCvDXX3/xzTff8PHHriVr2j93YOMSCP0LMVBiYiILFy4MOu/HH3+kefPm6QktzRlnnMEbb7zB9u3bqVmzZtB1mzZtyjfffJNpelqSya7hhKpm+EKrWLEiRYoU4fbbbw+a7AFOOOGEkL/+mzZtyk8//ZRp+urVqznppJOyjCU/zZw5k8TExAz36TVs2JApU6agqnz//fe89NJL9OvXj/r162f4hZwfVq5cyVlnnRXWsr/88guPPfYY+/btY/fu3dx88808+uijQM7KZ27KVCRlediwYTz00EOsX7+e6tWrU6NGDU488UTOO+88ILyymBZLuXLlMv1vlihRgtq1a2ea7p/UIimvhw8fpmvXrnz77bd89tlnnHzyySGPQ04FK5e5tAtXFRnsC6Qm8He0dmRJzSOqyooVK3jooYfo168fv/zyCzfccAOLFi1Kb830+++/U7t27Qz/mPXq1eP333/P9A8SjerHmjVrsnLlSg4dOpShqmnJkiWUKlWKypUrh1z3iiuu4NVXX+WTTz7hqquuSp/+ySefcMwxx4RMhuC+DNeuXcvVV1+dPq1MmTK0bt2a77//nlNPPTXkF1iwqlhwv47vu+8+1q9fT8OGDQHYuHEjX375JU8//XTIWPKTqjJr1iwGDRoUdL6I0KJFC55//nleffVVVq1ala9Jbdu2bfz5559ht3ysXbs28+fPp1ixYuzfv59jjz2WO+64g0qVKuWo+jE3Zcq/LPsLVZbLlCmTnhzmzJnDmjVrePXVV9PnhVMWcyPc8pqamkr37t2ZN28eH330Udg/OCKRXbnM4Tb3icgyoJuIDFbVFAARqQecA/wvWvuypBZtSUm06N8fPvkEsvin++2339i9e3d6lcyIESNYv349l112GUuWLOHYY48Nul6oOvZgvxADJScnc8IJoVvP3nHHHXTr1o1LL72Ufv36kZCQwAcffMCbb77JgAED0hPdokWLaNeuHRMmTEj/5dqpUyfatm3Lbbfdxo4dO2jYsCEzZsxg7ty5Ger7u3fvToMGDTj11FOpWLEiK1asYOjQodSpU4c777wzQzzPP/88559/Ph07dqRnz57UqlWLHTt2sHz5clJSUrJMTrfeeisvvfQSXbp0Se9949FHH6Vu3brcdtttGZadMWMGcPQa5+zZs6lWrRqbN2/O8kdAdkJtt1q1aiQmJvLNN9+QlJREly5d0tf54Ycf6N+/P9dccw2NGzcmJSWFSZMmUaxYMS644IJs97lx40YaNGjA448/numaTaRWrFgBuOuUwc6YTjnlFEqXLp3++ttvv+W5555j165dqCr//PNPepkJp3wGCrdMBSuP/mW5devWHDp0KGhZXrFiBbNnz+bUU08FXIvLZ555hgceeCBDlWtuymI4wi2vt99+O2+//TaDBg2iTJkyGT6XY445JlfVkGk1JatXr85ULqPkUVzrxw9FZDRQFhgC7Aaei9pesmtJUhgfuWr92Levpoqo9u2b5WLTpk1TQJOSktKn7d27V5s3b67NmjXT3bt36/bt27Vs2bJ66NCh9GWOO+44/e6773IUWjit+T7++GNNTEzUqlWratmyZbV58+Y6atQoPXLkSIbtADpx4sQM6+7evVv79eun1atX1+LFi+vJJ5+sU6dOzbDM8OHD9eSTT9by5ctrsWLF9JhjjtHOnTvr1q1bg8azevVqveaaa7RatWpaokQJrVOnjl566aX60UcfZfteNm3apFdeeaWWK1dOy5Ytq126dAnaApEQLfGaN2+e7T6yav0YartpLfweeOABPe200zKss23bNr3pppv0uOOO04SEBK1UqZKef/75OmfOnPRlsmr9uGrVKgV0zJgx2caenaeeeirkexAR3bVrV/qyH374oTZp0iT9c5w3b542adIk1zGEU6ZClce0slyhQoWQZXnVqlV67rnnaoUKFbRUqVLasmVLnTBhQtBYcloWw7n5WjW88lqvXr2Qn0mwffgLVVYfeOCBDC0sr7322kzlMk1gS0n/uLp3757h5mugjS+29n7TLgK+Bvb7ktn7wAnq9/1LLls/ep5AYvGRo6RWqpQ7nIGPUqUi35afCy64QF9++WVVVZ07d642btxYU1NTc7StvOi5IxoKclxpXxRpzbQjccIJJ+gTTzyRo7jSmo7fdNNNGZLauHHjtGrVqrpv376It5sbQ4YM0c6dO6uq6/WiVatWeuONN+ZrDKEU5PIVTaHK6hVXXKGNGjVKf123bt0clUtVjUqPIoEPXAOTYsDkcJKa3XwdLevXw/XXQ1p1TOnS0L07bNiQq82OHTuWiRMncvzxx3P//fczderUkM2YjTc2bdpE8eLFM7XEzM6aNWtyfN3iySefpHjx4kyZMiXD9EWLFjFgwIAM1YL54aabbuLnn3/mlFNOYcCAAdSvXz/i6kaT9/zL6tKlSxkxYgQfffQR3bp1S19mypQpUb2eFgWDcPeyBW+lE8CuqUVLrVpQvjwcOEBKiRIUPXDAvc7iulo4jjvuOL766qsoBWmibfDgwdxxxx1AxkYOea1nz55cdNFFABka9fjfM5Wf6tevz6uvvpqra5AmbwWW1YsvvpjU1FT69+/PkCFDPI4uS68Cc3x/H8pqQbCkFl3btkGfPixv2ZLTV6yApGC3ZJh4Ur9+ferXr5/v+61Vqxa1atXK9/2agiuwrK5fv967YCKgqkkEv78tKEtq0fTuuwDsW7gQevXyNhZjjCmE7JqaMcaYuGFJzRhjTNyImaQmIv1EZIOIHBCRZSKS5XDB4tztG7vnoIgkiUjQOyBF5DwROSIiq4LNN8YYEx9i4pqaiFwDjAT6AV/4nmeLyEmqmnmgLec54BLgfuBHoAKQ6cq5iFQCpgDzgOiN2WOMMSbmxERSA+4BJqnqeN/rO30DyvUFBgYu7Bsp9U7gFFX92W/WiiDbfhV3054AVwWZb4wxJk54Xv0oIiWAVsDcgFlzcR1dBtMFWA9cJCLrRWSjiEwWkeoB2+6H6wH6iSiHbYwxJgaJrxsS7wIQqQ1sARJV9XO/6Y8B3VU1Uw+8IjIW6AF8j6t+VOBZ3+yzVTVVRE4GPgPOUjcQ3WDgKlXNPGa622ZvoDdAjRo1Wk2bNi3H7yk5OZmyZcvmeP28YnFFxuKKjMUVmXiMq23btstU1duuZKLdT1cO+vWqjUtKrQOmPw6sCbHOy751jvebdrxv2plASeAn4Ea/+YOBVeHElKsOjdX6mouUxRUZiysyFldkchMXedD3Y6SPWLimtgNIIfPgcdWBbSHWSQKOqOpav2nrgCPAsb71TgImikjaGBVFcI0mjwCdVDWwutMYY0wB5/k1NVU9BCwDOgTM6gCE6vTwS6CYiDTym9YQ1/BlE64682Sghd9jLPCr72/rTNEYY+KQ59fUIL1J/2u4pvxfAn2AnkBTVd0kIk8BZ6hqO9/yRYDvgGTgbt9mXsBVO56jqqlB9jGYLK6pBSz7Fy455lRV3BlorLG4ImNxRcbiikw8xlVPVatFM5hIxUL1I6o6XUSqAI/g7jVbhasiTEsstYBGfsunisglwIvA57gB5z4F7gmW0HIQT64+FBFZql5fLA3C4oqMxRUZiysyFlfeiImkBqCqo4HRIeb1CDItCeiWeemQ2x+MayxijDEmTnl+Tc0YY4yJFktqeeNlrwMIweKKjMUVGYsrMhZXHoiJhiLGGGNMNNiZmjHGmLhhSc0YY0zcsKRmjDEmblhSy4aI3C4iP4jIHt/jaxHp7DdfRGSwiGwVkf0islBEmgZso6SI/E9EdojIPhH5QESOyau4RKS4iPzXN3+fbwDVN0Tk2IBtLBQRDXjkvCfnbOLyzZ8UZJ/fBGwj6scrzNgC40p7jPJbJurHLCDGh33bfMlvmidlLKu4vCxjWcXlm+ZZGcsmLk/Kl6/sBG7zT7/5npevqPK688lYf+CGubkYaIzrNPlJ4DBuLDeAB4G9QFegGfAWsBUo57eNMb5pHYBTgYXASqBoXsSFGzD1U+Aa4ATgDGAxsBoo5reNhcAEXL+baY8KeXy8Jvli899n5YBtRP14hRlbzYDHJbhOshPz8pj5bfssYANu9ImX/KZ7UsayisvLMhbG8fKsjGUTlyflC3d/7pqAbVaLlfIV7YfnARTEB7ATuA038GgSMMhvXoKvgNzme10BOIQbRidtmbpAKtAxL+IKMe8k3z/QyX7TFvr/0+X18fL9PQn4MItl8+14hXHMxgO/BEzLk2Pme9+/ARf478PrMhYqLq/LWFZxeVnGIjxe+VK+yGKEEq/LV148rPoxAiJSVESuBcriOkVugPvVk97jv6rux3XdlTbAaSugeMAyfwA/E3oQ1NzGFUx53/OugOnX+qoUfhKRZ0WkXDRiyiau80Rku4isFZHxknFw1zw/XtnElja/LHAt7osnUF4cs5eBGao6P2C612UsVFzB5GcZyy4ur8pYWMfLg/LVUES2iMgGEZkmIg19070uX1EXM91kxTJxA45+DZTCdaJ8har+KCJpH2jgEDnbgDq+v2vihtYJ7CB0G5mH24lKXEGWKwE8B8xS1c1+s97Addy8FWgKPAU0J/OICdGMaw7wLq56pj5uVPL5ItJKVQ+Sh8crjNj8XY/rIHtywPSoHzMRuRVXJXpjkNlp7znfy1g2cQUum29lLIy4PCljkRwv8rF8AUtwgyqvwQ3p9Qjwle+6mWflK69YUgvPL7ghayri6p0ni0gbv/mBd7BLkGmBwlkmR3Gp6qr0nYgUA173LXOZ/8qq6t9zwI8ish5YIiKnquryvIhLVf0vev8oIstw/8SdcV9EoUTjeGUZW8BytwIzVfUv/4nRPmYicgIwHDdI7qEsFs3XMhZBXPlaxsKJy4syFsnx8smX8uXb5uyAWL8B1gM3A2kNaLz6Dos6q34Mg6oeUtVfVXWpqg7EXSAdAKS1IMpqgNM/gaK44RxCLRPtuID0L5s3cY1H2qnq39lscinuF9lxeRlXwLJbgc1++8yz4xVubCLSAjiN4FVDgXJ7zM7GvddVInJE3CC2iUA/399pn1l+l7Es4xKRkuBJGQsrLn/5VMbCjiufy1cmqpoM/OTbpqffYXnBklrOFMFVHWzAfeDpVQMiUgpozdHrNMtwLez8lzkGOJHoD1aaFhciUhyYjvuyaauqf2a1os/JuMKblFdxBRKRqrhqjrR95ufxChVbb2Aj8FkY6+f2mM0k84C2S4Fpvr/X4k0Zyy6uQx6VsWzjClwhn8pYJHHlZ/nKxFd+mvi2GWvfYbnndUuVWH8AT+M+4Pq4AvYUrtXPxb75DwJ7gCtxzWGnEbw57BagPdASWEDum/SHjAtXrTzTt89TydiUN8G3fiPgMdwvxvpAJ9yF3+V5GFdZ4Fncr9r6QBvc9a3NeX28wvksfcuUBnbj1xrMb16eHLMg+1lI5ib9+V7GsorLyzKWTVyelrGsPkevypfveCTiGoWcCXzoK0/1Yql8Re24ex1ArD9wzYM3AQeB7bhfVx395guuyWwScABYBDQL2EYp4H+4qqR/gVlA3byKy/cPoSEePXzL1PXF+rdvG78CIwm4nyfKcSUAn/imH/ItNynwWOTF8Qrns/QtcwtwBKgdZP08OWZB9rOQjEnNkzKWVVxelrFs4vK0jGX1OXpVvjiapA7hEtM7wEmxVr6i9bBe+o0xxsQNu6ZmjDEmblhSM8YYEzcsqRljjIkbltSMMcbEDUtqxhhj4oYlNWOMMXHDkpoxxpi4YUnNGGNM3LCkZkw+EZEmIqJhPD4Ksu4kv/kLA+b18E1vHDD9dBHZKSIrRKSqiDzit43NGBOHbOgZY/LPn7g+CdOchut6aBAwP2C5UOtfgeunL0u+sf5m48bQukhVd4nIRFzXYI/ixugyJu5YUjMmn6jqPxwdvwoROd3350xVXR3GJg6q6jfZLSQiibhOa78HOqnqHt/+twBbROSvrNY3piCz6kdjvNMC14HsL9HaoIh0wJ2hfYfrrDnbszpj4oklNWO80xxYpaopUdpeZ1zv6Z8DnVV1X5S2a0yBYUnNGA+ISFGgKa6KMFpewI0b1kVV90dxu8YUGJbUjPFGE9wYVSujuM2PcANNDoziNo0pUKyhiDHeaOF7juaZ2gBcC8nHReSAqj4dxW0bUyBYUjPGG2lN6qOZ1BToDZQEnvIltheiuH1jYp4lNWO80QLYEO3WiaqaKiI9gBLACF9iGxvNfRgTyyypGeON5sCXebFhVU0Rke64M7bRInJQVSfmxb6MiTXWUMSYfCYiNYHqRLfqMQNVPQJcDcwBXhGR6/NqX8bEEjtTMyafqeqfgORkXREp5jZx9N42VZ0ETAqyn0NAJ791BSia030bUxDYmZoxBUc94DAwL4frD/Ktf1PUIjImxoiqeh2DMSYbIlIfqOp7uVdVI+5aS0RqAXV8Lw+p6g9RCs+YmGFJzRhjTNyw6kdjjDFxw5KaMcaYuGFJzRhjTNywpGaMMSZuWFIzxhgTNyypGWOMiRv/D49HthdFg5mDAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"'''Plot the fit in the Cartesian plane'''\n",
"\n",
"plot_fit(r_cte, temp_vec, k_cte_vec, k_0, energy_a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Goodness of Fit](#toc)\n",
"\n",
"There are different ways to evaluate the goodness of fit. Below is the most direct and relevant error evaluation.\n",
"That is, the error on fitting the data as given."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:20.644395Z",
"start_time": "2022-01-10T06:57:20.639315Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Relative Error:\n",
"mean [%] = 2.07\n",
"std [%] = 1.40\n",
"max, min [%] = 5.41, 0.06\n"
]
}
],
"source": [
"'''Relative error on reaction rate constant values'''\n",
"\n",
"print('Relative Error:')\n",
"error = np.abs(k_cte_vec - arrhenius_func( beta_vec, param_vec ))/k_cte_vec*100\n",
"mean = np.mean(error)\n",
"std = np.std(error)\n",
"emax = np.max(error)\n",
"emin = np.min(error)\n",
"print('mean [%%] = %1.2f'%(mean))\n",
"print('std [%%] = %1.2f'%(std))\n",
"print('max, min [%%] = %1.2f, %1.2f'%(emax,emin))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Objective Function](#toc)\n",
"\n",
"Let's show graphically that \n",
"\n",
"\\begin{equation*}\n",
"\\phi(\\alphabf^*) = \\min\\limits_{\\alphabf} \\norm{\\rvec}^2 ,\n",
"\\end{equation*}\n",
"\n",
"that is, the minimum sits at the bottom of the objective function surface.\n",
"\n",
"Information on `matplotlib` plots in 3D is found [here](https://matplotlib.org/tutorials/toolkits/mplot3d.html#sphx-glr-tutorials-toolkits-mplot3d-py)."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:21.921853Z",
"start_time": "2022-01-10T06:57:21.914003Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"phi(x_LS) = 6.18303e-03\n",
"sqrt(phi(x_LS)) = 7.86323e-02\n",
"Mean(r_vec) = -7.72050e-08\n",
"STD(r_vec) = 1.75827e-02\n",
"Goodness of fit = 1.75827e-02\n"
]
}
],
"source": [
"'''Examining the residual'''\n",
"\n",
"r_vec = k_cte_vec - arrhenius_func( beta_vec, param_vec )\n",
"phi = np.linalg.norm(r_vec)**2\n",
"# phi_ls = np.dot(r_vec,r_vec) # alternative dot product\n",
"\n",
"import math\n",
"print('phi(x_LS) = %8.5e'%phi)\n",
"print('sqrt(phi(x_LS)) = %8.5e'%math.sqrt(phi)) # norm of the residual vector\n",
"print('Mean(r_vec) = %8.5e'%np.mean(r_vec))\n",
"print('STD(r_vec) = %8.5e'%np.std(r_vec))\n",
"print('Goodness of fit = %8.5e'%math.sqrt(phi/n_pts))"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:22.814270Z",
"start_time": "2022-01-10T06:57:22.350300Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"'''Plot the objective function surface around the minimum'''\n",
"\n",
"n_plot_pts = 150\n",
"\n",
"objective_function_data = get_objective_function_data(n_plot_pts, arrhenius_func, beta_vec, k_cte_vec, param_vec)\n",
"\n",
"plot_objective_function( objective_function_data, param_vec, delta_factor = 0.4 )"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:23.624211Z",
"start_time": "2022-01-10T06:57:23.520716Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"linkText": "Export to plot.ly",
"plotlyServerURL": "https://plot.ly",
"showLink": false
},
"data": [
{
"type": "surface",
"z": [
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""
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"source": [
"'''Plot the objective function around the minimum'''\n",
"#!pip install plotly\n",
"\n",
"(x_vec, y_vec, z_mtrx) = objective_function_data\n",
"\n",
"import plotly\n",
"import plotly.graph_objs as go\n",
"\n",
"plotly.offline.init_notebook_mode(connected=True)\n",
"\n",
"data = [ go.Surface(z=z_mtrx) ]\n",
"layout = go.Layout(\n",
" title='Objective Function Surface',\n",
" autosize=False,\n",
" width=500,\n",
" height=500,\n",
" margin=dict(\n",
" l=65,\n",
" r=50,\n",
" b=65,\n",
" t=90\n",
" )\n",
" )\n",
"\n",
"plotly.offline.iplot({\n",
" \"data\": data,\n",
" \"layout\": layout\n",
"})"
]
},
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"metadata": {},
"source": [
"## [Experimental Data (80 points)](#toc)\n",
"Data will be provided for exercises as ASCII files in the `data/` directory of the course [repository](https://github.com/dpploy/chen-3170/data). The data is organized in two columns of $T$ versus $k$. For example `data/k_x_T_80pts.dat`."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:29.132852Z",
"start_time": "2022-01-10T06:57:29.123631Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"R = 8.314 [J/(mol.K)]\n",
"m = 80\n",
"T = [300. 302.53 305.06 307.6 310.13 312.66 315.19 317.72 320.25 322.79\n",
" 325.32 327.85 330.38 332.91 335.44 337.98 340.51 343.04 345.57 348.1\n",
" 350.63 353.17 355.7 358.23 360.76 363.29 365.82 368.35 370.89 373.42\n",
" 375.95 378.48 381.01 383.54 386.08 388.61 391.14 393.67 396.2 398.73\n",
" 401.27 403.8 406.33 408.86 411.39 413.92 416.46 418.99 421.52 424.05\n",
" 426.58 429.11 431.65 434.18 436.71 439.24 441.77 444.3 446.83 449.37\n",
" 451.9 454.43 456.96 459.49 462.02 464.56 467.09 469.62 472.15 474.68\n",
" 477.21 479.75 482.28 484.81 487.34 489.87 492.4 494.94 497.47 500. ]\n",
"k = [0.66 0.64 0.65 0.67 0.66 0.64 0.68 0.66 0.67 0.67 0.67 0.67 0.68 0.68\n",
" 0.67 0.68 0.69 0.68 0.68 0.66 0.69 0.66 0.69 0.68 0.68 0.69 0.68 0.68\n",
" 0.7 0.69 0.7 0.7 0.7 0.73 0.69 0.72 0.7 0.69 0.71 0.69 0.7 0.7\n",
" 0.7 0.7 0.71 0.72 0.71 0.69 0.73 0.73 0.71 0.71 0.7 0.73 0.74 0.73\n",
" 0.73 0.71 0.72 0.72 0.71 0.73 0.75 0.72 0.73 0.74 0.73 0.72 0.73 0.73\n",
" 0.73 0.75 0.71 0.76 0.75 0.77 0.74 0.73 0.74 0.74]\n"
]
}
],
"source": [
"'''Read experimental data'''\n",
"\n",
"import numpy as np\n",
"\n",
"(r_cte, r_cte_units, n_pts, temp_vec, k_cte_vec) = read_experimental_data('data/k_x_T_80pts.dat')\n",
" \n",
"print('R = %4.3f %s'%(r_cte,r_cte_units))\n",
"print('m = ',n_pts)\n",
"np.set_printoptions(precision=2)\n",
"print('T =',temp_vec)\n",
"print('k =', k_cte_vec)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:29.611264Z",
"start_time": "2022-01-10T06:57:29.428796Z"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"'''Plot experimental data'''\n",
"\n",
"plot_experimental_data(temp_vec, k_cte_vec)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Non-Linear System](#toc)\n",
"\n",
"Similar as [before](#nls10) with 10 points."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Non-Linear Least-Squares Newton's Method Data Fitting](#toc)\n",
"\n",
"Similar as [before](#nlls10) with 10 points."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:30.386138Z",
"start_time": "2022-01-10T06:57:30.376423Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
"**************************************************************************\n",
" Newton's Method Iterations \n",
"**************************************************************************\n",
"k ||r(p_k)|| ||J(p_k)|| ||J^T r(p_k)|| ||del p_k|| ||p_k|| |convg| \n",
"--------------------------------------------------------------------------\n",
" 1 +3.28e-01 +8.94e+00 +2.73e+00 +5.67e+02 +5.67e+02 0.27\n",
" 2 +1.03e-01 +7.52e+00 +3.93e-02 +2.34e+02 +8.01e+02 0.86\n",
" 3 +1.03e-01 +7.00e+00 +1.69e-04 +1.24e+01 +8.13e+02 0.46\n",
" 4 +1.03e-01 +6.98e+00 +5.44e-09 +4.10e-02 +8.13e+02 -1.27\n",
" 5 +1.03e-01 +6.98e+00 +1.91e-14 +9.66e-05 +8.13e+02 2.89\n",
" 6 +1.03e-01 +6.98e+00 +1.90e-15 +2.28e-07 +8.13e+02 1.65\n",
"******************************************************\n",
"Root = [ 0.9 813.49]\n",
"k_0 = 9.02980e-01 [1/s]\n",
"E_a = 8.13495e+02 [J/mol]\n"
]
}
],
"source": [
"k_0 = 1.0\n",
"energy_a = 0.0\n",
"\n",
"beta_vec = 1./r_cte/temp_vec\n",
"param_vec_0 = np.array([k_0,energy_a])\n",
"\n",
"k_max = 8\n",
"tolerance = 1.0e-6\n",
"\n",
"param_vec = newton_solve(beta_vec, k_cte_vec, \n",
" arrhenius_func, partial_p_arrhenius_func,\n",
" param_vec_0, k_max, tolerance)\n",
"\n",
"k_0 = param_vec[0]\n",
"energy_a = param_vec[1]\n",
"\n",
"print('k_0 = %8.5e [1/s]'%k_0)\n",
"print('E_a = %8.5e [J/mol]'%energy_a)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:30.894610Z",
"start_time": "2022-01-10T06:57:30.688169Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"'''Plot the fit in the Cartesian plane'''\n",
"\n",
"plot_fit(r_cte, temp_vec, k_cte_vec, k_0, energy_a)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Goodness of Fit](#toc)\n",
"\n",
"There are different ways to evaluate the goodness of fit. Below is the most direct and relevant error evaluation.\n",
"That is, the error on fitting the data as given."
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:31.428128Z",
"start_time": "2022-01-10T06:57:31.423354Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Relative Error:\n",
"mean [%] = 1.30\n",
"std [%] = 0.97\n",
"max, min [%] = 3.64, 0.00\n"
]
}
],
"source": [
"'''Relative error on reaction rate constant values'''\n",
"\n",
"print('Relative Error:')\n",
"error = np.abs(k_cte_vec - arrhenius_func(beta_vec, param_vec))/k_cte_vec*100\n",
"mean = np.mean(error)\n",
"std = np.std(error)\n",
"emax = np.max(error)\n",
"emin = np.min(error)\n",
"print('mean [%%] = %1.2f'%(mean))\n",
"print('std [%%] = %1.2f'%(std))\n",
"print('max, min [%%] = %1.2f, %1.2f'%(emax,emin))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Objective Function](#toc)\n",
"\n",
"Let's show graphically that \n",
"\n",
"\\begin{equation*}\n",
"\\phi(\\alphabf^*) = \\min\\limits_{\\alphabf} \\norm{\\rvec}^2 ,\n",
"\\end{equation*}\n",
"\n",
"that is, the minimum sits at the bottom of the objective function surface.\n",
"\n",
"Information on `matplotlib` plots in 3D is found [here](https://matplotlib.org/tutorials/toolkits/mplot3d.html#sphx-glr-tutorials-toolkits-mplot3d-py)."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:32.262920Z",
"start_time": "2022-01-10T06:57:32.254541Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"phi(x_LS) = 1.05684e-02\n",
"sqrt(phi(x_LS)) = 1.02803e-01\n",
"Mean(r_vec) = 1.13956e-06\n",
"STD(r_vec) = 1.14937e-02\n",
"Goodness of fit = 1.14937e-02\n"
]
}
],
"source": [
"'''Examining the residual'''\n",
"\n",
"r_vec = k_cte_vec - arrhenius_func(beta_vec, param_vec)\n",
"phi = np.linalg.norm(r_vec)**2\n",
"# phi_ls = np.dot(r_vec,r_vec) # alternative dot product\n",
"\n",
"import math\n",
"print('phi(x_LS) = %8.5e'%phi)\n",
"print('sqrt(phi(x_LS)) = %8.5e'%math.sqrt(phi)) # norm of the residual vector\n",
"print('Mean(r_vec) = %8.5e'%np.mean(r_vec))\n",
"print('STD(r_vec) = %8.5e'%np.std(r_vec))\n",
"print('Goodness of fit = %8.5e'%math.sqrt(phi/n_pts))"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:33.140927Z",
"start_time": "2022-01-10T06:57:32.639046Z"
}
},
"outputs": [
{
"data": {
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"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"'''Plot the objective function surface around the minimum'''\n",
"\n",
"n_plot_pts = 150\n",
"\n",
"objective_function_data = get_objective_function_data(n_plot_pts, arrhenius_func, beta_vec, k_cte_vec, param_vec)\n",
"\n",
"plot_objective_function(objective_function_data, param_vec, delta_factor = 0.4)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"ExecuteTime": {
"end_time": "2022-01-10T06:57:33.253486Z",
"start_time": "2022-01-10T06:57:33.142956Z"
},
"scrolled": false
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"linkText": "Export to plot.ly",
"plotlyServerURL": "https://plot.ly",
"showLink": false
},
"data": [
{
"type": "surface",
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"'''Plot the objective function around the minimum'''\n",
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" l=65,\n",
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" b=65,\n",
" t=90\n",
" )\n",
" )\n",
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"## [Results Comparison NLLSq Method](#toc)\n",
"\n",
"| Parameters | 10 pts | 20 pts | 80 pts |\n",
"| ------------------------------------- | -------- | ------- | -------- |\n",
"| Pre-exponential factor, $k_0$, 1/s | 9.42e-01 | 8.65e-01 | 9.03e-01 |\n",
"| Energy of activation, $E_a$, J/mol | 9.92e+02 | 6.89e+02 | 8.13e+02 |\n",
"| Relative error mean [%] | 1.89 | 2.07 | 1.30 |\n",
"| Relative error std [%] | 1.05 | 1.40 | 0.97 |\n",
"| Max. relative error [%] | 3.81 | 5.41 | 3.64 |"
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"## [Results Comparison LLSq Method Notebook 11](#toc)\n",
"\n",
"| Parameters | 10 pts | 20 pts | 80 pts |\n",
"| ------------------------------------- | -------- | ------- | -------- |\n",
"| Pre-exponential factor, $k_0$, 1/s | 9.38e-01 | 8.64e-01 | 9.02e-01 |\n",
"| Energy of activation, $E_a$, J/mol | 9.76e+02 | 6.88e+02 | 8.09e+02 |\n",
"| Relative error mean [%] | 1.89 | 2.08 | 1.29 |\n",
"| Relative error std [%] | 1.05 | 1.40 | 0.97 |\n",
"| Max. relative error [%] | 3.74 | 5.38 | 3.65 |"
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