gauss_newton_noise_ep.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f4191d0b",
   "metadata": {},
   "source": [
    "# Advancement of project\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3260080d",
   "metadata": {},
   "source": [
    "\n",
    "The provided Python code demonstrates the application of the Gauss-Newton algorithm for parameter estimation in a nonlinear model. To assess the model's robustness, Gaussian noise is incorporated into the data. The algorithm iteratively updates parameter values to minimize the sum of squared residuals, aided by the Jacobian matrix. Parameters such as convergence threshold, maximum iterations, and initial values are set. Synthetic data is generated by applying the model function to time values and introducing Gaussian noise. The algorithm converges to optimal parameter values, reflecting the model's performance amidst noise. Visualization of original measurements and fitted curves offers insight into the model's efficacy in capturing underlying trends. This code exemplifies practical implementation of Gauss-Newton optimization, robustness assessment, and result visualization using Python."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "584a43a3",
   "metadata": {},
   "source": [
    "## Import Librairies\n",
    "To start, we import essential libraries: NumPy, which facilitates numerical computations, and Matplotlib, enabling plotting functionalities. These libraries provide fundamental tools necessary for data manipulation, mathematical operations, and visualization, laying the groundwork for subsequent analyses and visualizations within the Python environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e81b41aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "956b18e2",
   "metadata": {},
   "source": [
    "## Define function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f789ff46",
   "metadata": {},
   "source": [
    "This function represents the residual or error function. It calculates the difference between the model prediction (x[0] * np.exp(-x[1] * t)) and the actual measurements N."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f9a56fa1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define your function f(x)\n",
    "def f(x, t, N):\n",
    "    # Example function, replace it with your actual function\n",
    "    return x[0] * np.exp(-x[1] * t) - N"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57b2bc8e",
   "metadata": {},
   "source": [
    "g(x, t): This function defines the model function. It computes the model predictions based on the parameters x and the time values t."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7de90fb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the model function g(x)\n",
    "def g(x, t):\n",
    "    return x[0] * np.exp(-x[1] * t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92d22872",
   "metadata": {},
   "source": [
    "jacobian_f(x, t): This function calculates the Jacobian matrix of the residual function f(x, t, N) with respect to the parameters x."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "08ff4010",
   "metadata": {},
   "outputs": [],
   "source": [
    "def jacobian_f(x, t):\n",
    "    return np.column_stack((np.exp(-x[1] * t), -x[0] * t * np.exp(-x[1] * t)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66c1404b",
   "metadata": {},
   "source": [
    "This function calculates the cost function, which represents the sum of squared residuals. It evaluates how well the model fits the data using the initial parameter values x_init."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ffa6629a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_function(x_init,cost_init,t,N,k_max):\n",
    "    cost= cost_init\n",
    "    x = x_init\n",
    "    k=0\n",
    "    for i in range(k_max):\n",
    "          f_x = f(x, t, N)\n",
    "    return 0.5*np.sum(f_x**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee4530db",
   "metadata": {},
   "source": [
    "## Gauss Newton Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7156bafe",
   "metadata": {},
   "source": [
    "This function implements the Gauss-Newton algorithm to iteratively update the parameter values until convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "90904b7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gauss-Newton algorithm\n",
    "def Gauss_Newton(x_init, eps, t, N, k_max):\n",
    "    x = x_init\n",
    "    k = 0\n",
    "    while k < k_max:\n",
    "        J_f = jacobian_f(x, t)\n",
    "        f_x = f(x, t, N)\n",
    "        A = np.dot(J_f.T, J_f)\n",
    "        b = np.dot(J_f.T, -f_x.reshape((-1, 1)))\n",
    "        dk = np.linalg.solve(A, b).flatten()\n",
    "        x = x + dk\n",
    "        if np.linalg.norm(dk) < eps:\n",
    "            break\n",
    "        k += 1\n",
    "    \"\"\"\n",
    "    Returns:\n",
    "    - Approximation of a zero of G\n",
    "    - Value of G at the approximation\n",
    "    - Number of iterations\n",
    "    \"\"\"\n",
    "    return x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0c32479",
   "metadata": {},
   "source": [
    "## Setting parameter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f7147d4",
   "metadata": {},
   "source": [
    "These lines set various parameters such as the convergence threshold eps, maximum number of iterations k_max, initial parameter values x_init, number of data points p, time values t, and Gaussian noise d to simulate measurement errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "02d2dd16",
   "metadata": {},
   "outputs": [],
   "source": [
    "eps = 1e-6\n",
    "k_max = 1000\n",
    "x_init = [0.8, 0.3]\n",
    "cost_init=[0, 0]\n",
    "p=10\n",
    "t=np.linspace(0,10,p)\n",
    "d=np.random.normal(0,0.01,p) # adding Gaussian noise"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0840a587",
   "metadata": {},
   "source": [
    "These lines generate synthetic data by applying the model function g(x_init, t) to the time values t and adding Gaussian noise d to simulate measurement errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c64156a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.81383044 0.58142906 0.40681388 0.28340257 0.23295061 0.15654182\n",
      " 0.11424276 0.08308591 0.04542801 0.03801367]\n"
     ]
    }
   ],
   "source": [
    "N=g(x_init,t)\n",
    "N=N+d\n",
    "print(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9db7b4a2",
   "metadata": {},
   "source": [
    "## Optimization\n",
    "This line applies the Gauss-Newton algorithm to find the optimal parameters x_op that minimize the sum of squared residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "eb469baf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal parameters: [0.81067285 0.30042979]\n"
     ]
    }
   ],
   "source": [
    "x_op = Gauss_Newton(x_init, eps, t, N,k_max)\n",
    "print(\"Optimal parameters:\", x_op)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dc8c8db",
   "metadata": {},
   "source": [
    "This line calculates the cost function using the initial parameter values x_init"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "23da2b9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cost function: 0.0005410696322970726\n"
     ]
    }
   ],
   "source": [
    "cost=cost_function(x_init,cost_init,t,N,k_max)\n",
    "print(\"cost function:\",cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4781e511",
   "metadata": {},
   "source": [
    "## Plotting results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9bad492d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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Y2CA+Ph7jxo1D586d8cYbb+Djjz/G2LFjAWiHxp588knMmDEDw4YNg7e3N0aMGPHAunv27Ik9e/bg7NmzCAoKQp8+ffDmm282eJ2exjiviYkJPvnkE3zxxRdwc3PDxIkTYWlpiVOnTuGRRx5B586dMXv2bLz44ot47rnnGlRvTQSxNoOhTaSsrAyWlpb48ccf8fDDD+va58+fj5SUFOzZs6fSMdOnT8ft27fx448/6tr27t2LoKAgXL58uVb/EQoLC2Fra4uCggLY2Ng0zpu5z+r483h/2ym0t7fEnwuHwVRuEDmSiJrA7du3kZ6eDm9vb5ibmzfsZEZ4E9733nsPq1atavJ/WJJxqOnnqbbf35J+4yoUCgQEBCAuLk6vPS4uDoMGDarymJKSEshk+mXL7/7gS5jTKnligCcc2yiQea0EPx1l7w0R1dLdIW5MmaL9swUGm8jISBw+fBgXLlzAN998g48++ghPPvmk1GVRKyJ5d0J4eDi++uorrF27FmlpaViwYAEyMzN1w0yLFy/GjBkzdPtPmDABsbGxiIqKwoULF7Bv3z7MmzcP/fr1g5ubm1RvoxJLhQmeG6qdXf7prrO4w7k3RNRKnD17FhMnTkS3bt3w73//GwsXLuQ9m6hZ1f5mIE1k8uTJyM/Px9KlS3U3X9u2bRs8PT0BaFd4vHcdg5kzZ6KoqAifffYZFi5cCDs7Ozz00EP4z3/+I9VbqNYTAzzxRfx5ZF27hdijlzC5b3upSyIianLLly/H8uXLpS6DWjFJ59xIpTnm3FT4KuEC3v01DR5tLbBz4XAoTCTvLCOiRtaoc26IWrkWP+emNZjW3xOObcxw6fotbD566cEHEBERUYMw3DQxC4Uczw/Xzr35bOc5lJVz7g0REVFTYrhpBtP6t0c7azNk37iFmCT23hARETUlhptmYG4qx/PDtL03n+9i7w0REVFTYrhpJlP7t4fT3d6bH5O4kBUREVFTYbhpJuamcrxwd+7N5zvPobS88k3FiIikkJOTg5deegkdOnSAmZkZlEolJkyYUO19l6R2+/ZtzJw5Ez169ICJiYneLQ+IAIabZvV4v/ZwtjHD5YLb+OEI594QkfQyMjIQEBCAnTt34sMPP8Tx48exfft2jBgxAnPnzq33eUVRRHl5eSNW+je1Wg0LCwvMmzcPo0aNapLXoJaN4aYZaXtvfAAAkbvYe0NE0nvhhRcgCAIOHTqESZMmoXPnzujevTvCw8Nx4MABANoAJAgCUlJSdMfduHEDgiBg9+7dAIDdu3dDEAT8/vvvCAwMhJmZGdasWQNBEHDq1Cm911y2bBm8vLx0t8xJTU3FuHHj0KZNGzg7O2P69OnIy8urtmYrKytERUXh2WefhYuLS+N+IGQUGG6a2eS+SrjYmENVcBs/HObcGyJjJYoiSsrKJdlquzbrtWvXsH37dsydO7fKu2Pb2dnV+X2/+uqriIiIQFpaGiZNmoSAgAB89913evts3LgRU6dOhSAIUKlUGDZsGHr37o0jR45g+/btuHLlCh577LE6vzZRBclvv9DamJvKMXdER7z580l8vus8Hg1Uwty05d0Yj4hqduuOGt3+9bskr526dAwsFQ/+9X7u3DmIooiuXbs22msvXboUo0eP1j2eNm0aPvvsM/z73/8GAJw5cwZJSUnYsGEDACAqKgr+/v54//33dcesXbsWSqUSZ86cQefOnRutNmo92HMjgcf6KuFqa46cwtuIZu8NEUmkoodHEIRGO2dgYKDe48cffxwXL17UDXF999136N27N7p16wYASEpKwq5du9CmTRvdVhG2zp8/32h1UevCnhsJmJnI8cIIH7y55QQid5/D5L7svSEyNhamcqQuHSPZa9dGp06dIAgC0tLSarziSCbT/jv43uGuO3fuVLnv/cNbrq6uGDFiBDZu3IgBAwZg06ZNeO6553TPazQaTJgwocqbH7u6utbqfRDdjz03Enks0ANutua4UliK7w9lPvgAImpRBEGApcJEkq22PTH29vYYM2YMPv/8cxQXF1d6/saNGwCAdu3aAQBUKpXuuXsnFz/ItGnTEB0djf379+P8+fN4/PHHdc/5+/vj5MmT8PLygo+Pj95W1TwgotpguJFIRe8NAETuPo/bd3jlFBE1v8jISKjVavTr1w+bN2/G2bNnkZaWhk8++QQDBw4EAFhYWGDAgAH44IMPkJqaivj4eLzxxhu1fo3Q0FAUFhbi+eefx4gRI+Du7q57bu7cubh27RqmTJmCQ4cO4cKFC9ixYwdmzZoFtbr634upqalISUnBtWvXUFBQgJSUlDoFLjJuDDcSeixQCXc7C+QWlWLjQfbeEFHz8/b2xtGjRzFixAgsXLgQfn5+GD16NP78809ERUXp9lu7di3u3LmDwMBAzJ8/H++++26tX8PGxgYTJkzAsWPHMG3aNL3n3NzcsG/fPqjVaowZMwZ+fn6YP38+bG1tdcNhVRk3bhz69OmD//3vf9i9ezf69OmDPn361P0DIKMkiLW9ZtCIFBYWwtbWFgUFBbCxsZG0lo0HM/H6T8fRztoMCa+O4Nwbohbo9u3bSE9Ph7e3N8zNzaUuh6hFq+nnqbbf3+y5kdikAA+421ngalEpvmPvDRERUYMx3EhMYSLDiw9p595E7T6PW2Wce0NERNQQDDcGYFKABzzaWiDvZim+O3hR6nKIiIhaNIYbA2Aql+Glu703q/aw94aIiKghGG4MRKi/B5T2Fsi7WYZvD7D3hqglaoXXZxA1usb4OWK4MRCmchleGtEJgLb3pqSsXOKKiKi2TE1NAQAlJSUSV0LU8lX8HFX8XNUHb79gQB72d8dnu84h81oJvj1wEbOHdpS6JCKqBblcDjs7O+Tm5gIALC0tG/V+TUStgSiKKCkpQW5uLuzs7CCX139pFIYbA1Ix9+aVmL/wxZ4LeGKAZ63u7EtE0nNxcQEAXcAhovqxs7PT/TzVF785DczDfbS9NxfzS7Bh/0XMGcbeG6KWQBAEuLq6wsnJqdqbShJRzUxNTRvUY1OB4cbAmMhleOmhTnj5x2NYHX8B0wd4wsqM/5mIWgq5XN4ov5yJqP44odgAhfR2g5eDJa4Vl2HDfl45RUREVBcMNwaoovcGAFbHn8fNUl45RUREVFsMNwZqYm83eDta4XrJHXydmCF1OURERC0Gw42BMpHLMG+kdtXiLxMusPeGiIiolhhuDNiEnm7o4GiFG+y9ISIiqjWGGwOm7b2pmHtzAUW3eXkpERHRgzDcGLgJvdzQsZ0VCm7dwfp9GVKXQ0REZPAMItxERkbC29sb5ubmCAgIQEJCQrX7zpw5E4IgVNq6d+/ejBU3H7lM0PXefLU3HYXsvSEiIqqR5OEmOjoaYWFhWLJkCZKTkxEUFISxY8ciMzOzyv1XrlwJlUql27KysmBvb49HH320mStvPv/X0w0+Tm3Ye0NERFQLgtgY9xZvgP79+8Pf3x9RUVG6Nl9fX4SEhCAiIuKBx2/ZsgWhoaFIT0+Hp6dnlfuUlpaitLRU97iwsBBKpRIFBQWwsbFp+JtoBluPXca8TcmwMTdBwqKHYGtR/7ulEhERtUSFhYWwtbV94Pe3pD03ZWVlSEpKQnBwsF57cHAwEhMTa3WONWvWYNSoUdUGGwCIiIiAra2tblMqlQ2qWwrje7iik1MbFN4uZ+8NERFRDSQNN3l5eVCr1XB2dtZrd3Z2Rk5OzgOPV6lU+O233/DMM8/UuN/ixYtRUFCg27KyshpUtxT0595cQMEtzr0hIiKqiuRzbgDt3XTvJYpipbaqrF+/HnZ2dggJCalxPzMzM9jY2OhtLdH4Hq7o7NwGRbfLsXZvutTlEBERGSRJw42joyPkcnmlXprc3NxKvTn3E0URa9euxfTp06FQKJqyTIMhkwmYP7IzAGDt3nQUlLD3hoiI6H6ShhuFQoGAgADExcXptcfFxWHQoEE1Hrtnzx6cO3cOTz/9dFOWaHDG+rmgi7M1ikrLsWYfe2+IiIjuJ/mwVHh4OL766iusXbsWaWlpWLBgATIzMzFnzhwA2vkyM2bMqHTcmjVr0L9/f/j5+TV3yZKSyQTMH6Wde7OOvTdERESVmEhdwOTJk5Gfn4+lS5dCpVLBz88P27Zt0139pFKpKq15U1BQgM2bN2PlypVSlCy5f3R3QVcXa5zKKcJXey9gYXAXqUsiIiIyGJKvcyOF2l4nb8i2n1BhzrdH0cbMBHsXjYCdZeuYd0RERK1Xi1jnhuovuJu29+ZmaTm+SuDcGyIiogoMNy2UTCYgbJT2yql1+9JxvbhM4oqIiIgMA8NNCzamuzO6udqguEyNLxMuSF0OERGRQWC4acEEQUDY3Sunvk7MwDX23hARETHctHSjuzmjuxt7b4iIiCow3LRw2t4b7dybrxMzkH+z9AFHEBERGTeGGyMwytcJfu42KClT40teOUVERK0cw40REAQBYXfvObVhP3tviIiodWO4MRIjfZ3Q08MWJWVqrI7n3BsiImq9GG6MxL1XTm3YfxF57L0hIqJWiuHGiIzo4oReHra4dYe9N0RE1Hox3BiRe6+c2rA/A1eL2HtDREStD8ONkRnepR16K+1w+44GX+w5L3U5REREzY7hxsjcO/fm24MXkVt0W+KKiIiImhfDjREa1vne3hvOvSEiotaF4cYICYKABaO1c2++PXARuYXsvSEiotaD4cZIDe3kCP/2digt1yCKc2+IiKgVYbgxUvf23mw8mMneGyIiajUYbozYEB9HBHi2RWm5BpG72XtDREStA8ONERMEAQvurnuz8VAmcgrYe0NERMaP4cbIDfZxQF+vtigr12AV594QEVErwHBj5O5dtZi9N0RE1Bow3LQCgzo6oJ+XPcrKNYjcfU7qcoiIiJoUw00rIAgCwkZrVy3+/lAWLt+4JXFFRERETYfhppUY2MEB/bztUabWIIpXThERkRFjuGkl7r1yKvowe2+IiMh4Mdy0IgM7OmBAB23vzee7OPeGiIiME8NNK1Nx5dQPR7KQzd4bIiIyQgw3rcyADg4Y2MEBd9Qie2+IiMgoMdy0QhX3nPrxSBYuXS+RuBoiIqLGxXDTCvXztsdgH/beEBGRcWK4aaUq5t78eOQSsq6x94aIiIyHQYSbyMhIeHt7w9zcHAEBAUhISKhx/9LSUixZsgSenp4wMzNDx44dsXbt2maq1jj09bLHEB9HlGvYe0NERMZF8nATHR2NsLAwLFmyBMnJyQgKCsLYsWORmZlZ7TGPPfYY/vzzT6xZswanT5/Gpk2b0LVr12as2jgsuLtqcUwSe2+IiMh4CKIoilIW0L9/f/j7+yMqKkrX5uvri5CQEERERFTaf/v27Xj88cdx4cIF2Nvb1+s1CwsLYWtri4KCAtjY2NS7dmMwfc1BJJzNw+RAJf4zqafU5RAREVWrtt/fkvbclJWVISkpCcHBwXrtwcHBSExMrPKYrVu3IjAwEB9++CHc3d3RuXNnvPzyy7h1q/o1W0pLS1FYWKi3kVbF3JuYo5eQmc/eGyIiavkkDTd5eXlQq9VwdnbWa3d2dkZOTk6Vx1y4cAF79+7FiRMn8NNPP2HFihWIiYnB3Llzq32diIgI2Nra6jalUtmo76MlC/Bsi6Gd20GtEfHpzrNSl0NERNRgks+5AbT3PbqXKIqV2ipoNBoIgoDvvvsO/fr1w7hx47Bs2TKsX7++2t6bxYsXo6CgQLdlZWU1+ntoycJGaefexCZnIyOvWOJqiIiIGkbScOPo6Ai5XF6plyY3N7dSb04FV1dXuLu7w9bWVtfm6+sLURRx6dKlKo8xMzODjY2N3kZ/82/fFsPu9t58xiuniIiohZM03CgUCgQEBCAuLk6vPS4uDoMGDarymMGDB+Py5cu4efOmru3MmTOQyWTw8PBo0nqNWcWqxT8lZyPj153Apk3A7t2AWi1tYURERHUk+bBUeHg4vvrqK6xduxZpaWlYsGABMjMzMWfOHADaIaUZM2bo9p86dSocHBzw1FNPITU1FfHx8XjllVcwa9YsWFhYSPU2WrzeSjuMsFVDrRHxSeQvwNSpwIgRgJcXEBsrdXlERES1Jnm4mTx5MlasWIGlS5eid+/eiI+Px7Zt2+Dp6QkAUKlUemvetGnTBnFxcbhx4wYCAwMxbdo0TJgwAZ988olUb8E4xMYi7NNXAABbug9Hels3bXt2NjBpEgMOERG1GJKvcyMFrnNzH7Va20Nz6RJmPfIv7PTph9ATO7Hs12Xa5wUB8PAA0tMBuVzSUomIqPVqEevckIFISADuTsYO27cRALCl2zCcdPLWPi+KQFaWdj8iIiIDx3BDgEql+2vPnHMYd2ovNDI5Fvzfy7gtN61yPyIiIkPFcEOAq6vew3/viITjzes4084THw57str9iIiIDBHDDQFBQdo5NXcXTnS4VYiPflsJAFjbNwQJXn0ApVK7HxERkYFjuCHtJOGV2jBTEXBGXDiC6Ud/AQC8PC4M1z9awcnERETUIjDckFZoKBATA7i765pe37UOHQpycMXaAUvKPdEKL6wjIqIWiOGG/hYaCmRkALt2ARs3wiJuO1YufhgmMgHbjucg9mi21BUSERE9kInUBZCBkcuB4cN1D3tAe2uGj34/jbe2nkQ/b3so7S0lK4+IiOhB2HNDDzRnWEcEerbFzdJyLIhOgVrD4SkiIjJcDDf0QHKZgOWTe6ONmQmOXLyOVXvOS10SERFRtRhuqFaU9pZ4+5/dAQDL487g+KUCiSsiIiKqGsMN1doj/u4Y18MF5RoR86OTcatMLXVJRERElTDcUK0JgoD3QnrA2cYMF64W4/1taVKXREREVAnDDdVJWysF/vtoLwDANwcuYtepXIkrIiIi0sdwQ3UW1KkdnhrsBQB4JeYv5N8slbYgIiKiezDcUL0s+kdXdHZug7ybpXgt9jhXLyYiIoPBcEP1Ym4qx4rJfaCQyxCXegXRh7OkLomIiAgAww01QDc3GywM7gwAWPpLKjLyiiWuiIiIiOGGGuiZoA4Y0MEeJWVqhEWnoFytkbokIiJq5RhuqEHkMgEfP9Yb1uYmSMm6gc92nZO6JCIiauUYbqjB3O0s8G6IHwDg053nkJx5XeKKiIioNWO4oUYxsbc7/tnLDWqNiAXRKSguLZe6JCIiaqUYbqjR/HuiH9xszZGRX4J3f02VuhwiImqlGG6o0dhamuK/j/WCIACbDmUhLvWK1CUREVErxHBDjWpQR0c8G9QBALBo81/ILbotcUVERNTaMNxQo1sY3BldXaxxrbgMi2L+4urFRETUrBhuqNGZmcix8vE+UJjIsOv0VXx7MFPqkoiIqBVhuKEm0cXFGov+0RUA8N6vqTh/9abEFRERUWvBcENN5qlBXhji44jbdzQI+z4Fd7h6MRERNQOGG2oyMpmA/z7aC7YWpjieXYCVf5yVuiQiImoFGG6oSbnYmiMitAcAIHL3ORzJuCZxRUREZOwYbqjJjevhilB/d2hEYMEPKSi6fUfqkoiIyIgZRLiJjIyEt7c3zM3NERAQgISEhGr33b17NwRBqLSdOnWqGSumunrnn93h0dYCWddu4Z3/cfViIiJqOpKHm+joaISFhWHJkiVITk5GUFAQxo4di8zMmi8fPn36NFQqlW7r1KlTM1VM9WFtboplj/WGTABiki5h23GV1CUREZGRkjzcLFu2DE8//TSeeeYZ+Pr6YsWKFVAqlYiKiqrxOCcnJ7i4uOg2uVzeTBVTffXztsecYR0BAK//dBxXCrl6MRERNT5Jw01ZWRmSkpIQHBys1x4cHIzExMQaj+3Tpw9cXV0xcuRI7Nq1q8Z9S0tLUVhYqLeRNMJGdYafuw1ulNzByz8eg0bD1YuJiKhxSRpu8vLyoFar4ezsrNfu7OyMnJycKo9xdXXF6tWrsXnzZsTGxqJLly4YOXIk4uPjq32diIgI2Nra6jalUtmo74NqT2Eiw4rJfWBuKkPC2Tx8vT9D6pKIiMjISD4sBQCCIOg9FkWxUluFLl264Nlnn4W/vz8GDhyIyMhIjB8/Hv/973+rPf/ixYtRUFCg27Kyshq1fqobH6c2WDLOFwAQ8dspnLlSJHFFRERkTCQNN46OjpDL5ZV6aXJzcyv15tRkwIABOHu2+gXizMzMYGNjo7eRtJ4Y4InhXdqhrFy7enFpuVrqkoiIyEhIGm4UCgUCAgIQFxen1x4XF4dBgwbV+jzJyclwdXVt7PKoCQmCgA8n9YS9lQKpqkIsizsjdUlERGQkTKQuIDw8HNOnT0dgYCAGDhyI1atXIzMzE3PmzAGgHVLKzs7Ghg0bAAArVqyAl5cXunfvjrKyMnz77bfYvHkzNm/eLOXboHpwstauXvzcN0lYHX8Bwzs7YWBHB6nLIiKiFk7ycDN58mTk5+dj6dKlUKlU8PPzw7Zt2+Dp6QkAUKlUemvelJWV4eWXX0Z2djYsLCzQvXt3/Prrrxg3bpxUb4EaYEx3F0wOVCL6SBYW/pCC38KGwtbCVOqyiIioBRNEUWx11+IWFhbC1tYWBQUFnH9jAIpLyzHukwRczC9BSG83rHi8j9QlERGRAart97dBXC1FrZuVmQmWT+4NuUzAlpTL+DklW+qSiIioBWO4IYPg374tXhzhAwB4Y8sJZN+4JXFFRETUUjHckMF48SEf9FLaoeh2OV7+gasXExFR/TDckMEwlcuwYnJvWJjKsf9CPtbsTZe6JCIiaoEYbsigeDta4V8TugEAPvr9NFIv8z5gRERUNww3ZHAe76vEKF9nlKk1CItOxu07XL2YiIhqj+GGDI4gCPjgkR5wbKPAmSs38dHvp6UuiYiIWhCGGzJIjm3M8OGkngCANXvTsfdsnsQVERFRS8FwQwbroa7OeGJAewDAwh9TcKOkTOKKiIioJWC4IYO2ZFw3dHC0wpXCUiz56QRa4YLaRERURww3ZNAsFHKseLw3TGQCfj2uwk/JXL2YiIhqxnBDBq+nhx3CRnUCAPzr55PIulYicUVERGTIGG6oRXh+uA8CPdviZmk5wn9IgZqrFxMRUTUYbqhFkMsELJ/cG1YKOQ5nXMeqPeelLomIiAwUww21GEp7S7z9z+4AgOVxZ3Aiu0DiioiIyBAx3FCLMinAA2P9XFCuETH/+2TcKuPqxUREpI/hhloUQRDw/sM94GRthvNXixHxW5rUJRERkYFhuKEWp62VAh892gsAsGH/Rew6nStxRUREZEjqFW7++OOPap/74osv6l0MUW0N69wOMwd5AQBejfkL+TdLpS2IiIgMRr3Czfjx47Fw4UKUlf29HP7Vq1cxYcIELF68uNGKI6rJa2O7opNTG1wtKsXi2ONcvZiIiADUM9zEx8fjf//7H/r27YuTJ0/i119/hZ+fH27evIljx441do1EVTI31a5ebCoXsCP1Cn44kiV1SUREZADqFW769++P5ORk9OzZEwEBAXj44YexcOFC7Ny5E0qlsrFrJKpWdzdbLAzuAgB453+puJhfLHFFREQktXpPKD59+jQOHz4MDw8PmJiY4NSpUygp4bL41PyeDeqA/t72KClTIyw6BeVqjdQlERGRhOoVbj744AMMHDgQo0ePxokTJ3D48GFdT87+/fsbu0aiGsllAj5+rBeszUyQnHkDn+/i6sVERK1ZvcLNypUrsWXLFnz66acwNzdH9+7dcejQIYSGhmL48OGNXCLRg3m0tcS/Q/wAAJ/sPIvkzOsSV0RERFKpV7g5fvw4xo4dq9dmamqKjz76CDt27NC1Xbp0CRoNhwioeUzs7YYJvdyg1ohYEJ2C4tJyqUsiIiIJ1CvcODo6VvvcsGHDdH/v1q0bMjIy6vMSRHUmCALenegHV1tzZOSX4N1fuXoxEVFr1KQrFHPdEWputpam+Pju6sWbDmUiLvWKxBUREVFz4+0XyOgM8nHEs0O8AACvbTwE1fadgJo32CQiai0Ybsj4xMbi5bn/h6656cgvl2Fq7Dlc8e0FxMZKXRkRETUDhhsyLrGxwKRJMMvMwJqYpXAvuIJ0e3dMHfYirs54hgGHiKgVqHW4+euvv+p85ZMgCHUuiKje1Gpg/nzg7lwv96Kr+H7T63ArzMV5ByWmTX4X+Yve4BAVEZGRq3W46dOnD/Ly8gAAHTp0QH5+/gOP4YRialYJCcClS3pNyoIr2LhpCZyL8nGmnSemBb2A63/GS1QgERE1h1qHGzs7O6SnpwMAMjIyatWLk5qaCk9PzwfuFxkZCW9vb5ibmyMgIAAJCQm1qmnfvn0wMTFB7969a7U/GTmVqspmrxsqbPz+dbS7eQ2nnLzxxP4iFJTcaebiiIioudQ63DzyyCMYNmwYvL29IQgCAgMD0aFDhyq3CkqlEnK5vMbzRkdHIywsDEuWLEFycjKCgoIwduxYZGZm1nhcQUEBZsyYgZEjR9b2LZCxc3Wt9qmO17Kx8fslcCi+gZO35Jix9iAKbzPgEBEZI0Gsw9jR9u3bce7cOcybNw9Lly6FtbV1lfvNnz+/1gX0798f/v7+iIqK0rX5+voiJCQEERER1R73+OOPo1OnTpDL5diyZQtSUlKq3be0tBSlpaW6x4WFhVAqlSgoKICNjU2tayUDp1YDXl5AdrZu3o0eQcDp7v3w+KNLcb3kDvq0t8OGWf1gbW7a7KUSEVHdFRYWwtbW9oHf3yZ1Oek//vEPAEBSUhLmz59fbbiprbKyMiQlJeG1117Taw8ODkZiYmK1x61btw7nz5/Ht99+i3ffffeBrxMREYF33nmnQbVSCyCXAytXApMmAYKgH3DuTm7v8s6r+HZAf0z98iCSM2/gqXWH8fWsfrAyq9OPAhERGbB6XQq+bt26BgcbAMjLy4NarYazs7Neu7OzM3Jycqo85uzZs3jttdfw3XffwcSkdl9IixcvRkFBgW7LyspqcO1koEJDgZgYwN1dv93DQ9seGorubrb49un+sDY3wZGL1zFr/WGUlPE+VERExsIg1rm5/5JxURSrvIxcrVZj6tSpeOedd9C5c+dan9/MzAw2NjZ6Gxmx0FAgIwPYtQvYuFH7Z3q6tv2uHh62+Obp/rA2M8HB9Gt45usjuH2Hl4gTERkDSfviHR0dIZfLK/XS5ObmVurNAYCioiIcOXIEycnJePHFFwEAGo0GoijCxMQEO3bswEMPPdQstZOBk8uB4cNr3KW30g7rZ/XDjDUHkXg+H89uOIIvZwTC3LTmSfBERGTYJO25USgUCAgIQFxcnF57XFwcBg0aVGl/GxsbHD9+HCkpKbptzpw56NKlC1JSUtC/f//mKp2MRIBnW6x7qh8sTOVIOJuH579NQmk5e3CIiFoyyWdRhoeHY/r06QgMDMTAgQOxevVqZGZmYs6cOQC082Wys7OxYcMGyGQy+Pn56R3v5OQEc3PzSu1EtdXP2x5rZ/bFU+sPYdfpq5j7XTIip/lDYWIQo7ZERFRHkv/2njx5MlasWIGlS5eid+/eiI+Px7Zt23SL/6lUqgeueUPUUAM7OuCrGX1hZiLDH2lXMG9TMu6o63a7ESIiMgx1WufGWNT2OnlqffacuYpnvz6CMrUG43u6YuXk3jCRS/5vACIiQu2/v/lbm+gewzq3w6rp/jCVC/j1LxUW/ngMak2ry/9ERC0aww3RfR7q6ozPp/rDRCbg55TLeDXmL2gYcIiIWgyGG6IqBHd3wadT+kAuE7D56CUsjj3OgENE1EIw3BBVY2wPVyyf3BsyAYg+koU3fz6BVjhFjYioxWG4IarBP3u54ePHekEQgO8OZuKd/6Uy4BARGTiGG6IHeLiPB/7zSE8AwPrEDLz3axoDDhGRAWO4IaqFxwKViAjtAQD4am86/rP9NAMOEZGBYrghqqUp/drj3xO7AwBW7TmPZXFnJK6IiIiqwnBDVAfTB3rhrQndAACf7jyHlX+clbgiIiK6H8MNUR09NdgbS8b5AgCW/3EGn+86J3FFRER0L4Ybonp4dmgHvPqPLgCAj34/jdXx5yWuiIiIKjDcENXTC8N9ED66MwDg/W2nsGZvusQVERERwHBD1CDzRnbCvId8AAD//iUVG/ZnSFsQEREx3BA11ILRnfH88I4AgH/9fBIbD2ZKXBERUevGcEPUQIIg4NUxXfBskDcA4PWfjuOHw1kSV0VE1Hox3BA1AkEQ8Po4Xzw12AsAsCj2L2xOuiRtUURErRTDDVEjEQQB//q/bpg+wBOiCLwScww/p2RLXRYRUavDcEPUiARBwDv/7I4p/ZTQiMCC6BT8+pdK6rKIiFoVhhuiRiaTCXgvpAcmBXhAIwLzvk/G9hM5UpdFRNRqMNwQNQGZTMB/HumJh/u4Q60R8dKmo/gj9YrUZRERtQoMN0RNRC4T8NGknpjQyw131CJe+O4odp3OlbosIiKjx3BD1IRM5DIsf6wXxvq5oEytwXPfJCHh7FWpyyIiMmoMN0RNzEQuwydT+mB0N2eUlWvwzNdHkHg+T+qyiIiMFsMNUTMwlcvw2dQ+eKirE0rLNXh6/REcvJAvdVlEREaJ4YaomZiZyBE5zR9DO7fDrTtqPLX+MJIuXpO6LCIio8NwQ9SMzE3lWD09AEN8HFFSpsaTaw8jOfO61GURERkVhhuiZmZuKseXMwIxoIM9bpaWY8baQ/jr0g2pyyIiMhoMN0QSsFDIsebJvujr1RZFt8sxfc0hnMgukLosIiKjwHBDJBErMxOse6of/NvboeDWHUxfcxCncgqlLouIqMVjuCGSUBszE6yf1Q+9lHa4XnIH0748iLNXiqQui4ioRWO4IZKYjbkpNszqBz93G+QXl2HKlwdxLvem1GUREbVYDDdEBsDWwhTfPt0fvq42yLtZiqlfHkB6XrHUZRERtUgGEW4iIyPh7e0Nc3NzBAQEICEhodp99+7di8GDB8PBwQEWFhbo2rUrli9f3ozVEjUNO0sFvnumP7o4WyO3SBtwMvNLpC6LiKjFkTzcREdHIywsDEuWLEFycjKCgoIwduxYZGZmVrm/lZUVXnzxRcTHxyMtLQ1vvPEG3njjDaxevbqZKydqfPZWCnz7TH90bGcFVcFtTPnyALKuMeAQEdWFIIqiKGUB/fv3h7+/P6KionRtvr6+CAkJQURERK3OERoaCisrK3zzzTdVPl9aWorS0lLd48LCQiiVShQUFMDGxqZhb4CoCeQW3sbjqw/gQl4xlPYWiJ49EG52FlKXRUQkqcLCQtja2j7w+1vSnpuysjIkJSUhODhYrz04OBiJiYm1OkdycjISExMxbNiwaveJiIiAra2tblMqlQ2qm6ipOdmYY+OzA+DpYImsa7cwhUNURES1Jmm4ycvLg1qthrOzs167s7MzcnJyajzWw8MDZmZmCAwMxNy5c/HMM89Uu+/ixYtRUFCg27KyshqlfqKm5GKrDTgebS1wMb8E4z9JwNZjl6Uui4jI4Ek+5wYABEHQeyyKYqW2+yUkJODIkSNYtWoVVqxYgU2bNlW7r5mZGWxsbPQ2opbA3c4CP84ZiEDPtigqLce8Tcl4NeYYSsrKpS6NiMhgmUj54o6OjpDL5ZV6aXJzcyv15tzP29sbANCjRw9cuXIFb7/9NqZMmdJktRJJQq2Ga/JBfG+rwicdHfDphTv44cglJF28jk+n+KObG4M6EdH9JO25USgUCAgIQFxcnF57XFwcBg0aVOvziKKoN2GYyCjExgJeXsCIETCZNhXhs8fgu7hlcDYVcf5qMUIi9+HrxAxIfE0AEZHBkbTnBgDCw8Mxffp0BAYGYuDAgVi9ejUyMzMxZ84cANr5MtnZ2diwYQMA4PPPP0f79u3RtWtXANp1b/773//ipZdekuw9EDW62Fhg0iTgvuAy6Ogu/JaWhFfe3IA/bwBvbT2Jvefy8NGknrCzVEhTKxGRgZE83EyePBn5+flYunQpVCoV/Pz8sG3bNnh6egIAVCqV3po3Go0GixcvRnp6OkxMTNCxY0d88MEHeO6556R6C0SNS60G5s+vFGwAAKII+1uF+CryRaz7bhc+2H4GcalXMHZlAlZM7o3+HRyav14iIgMj+To3UqjtdfJEkti9Gxgx4sH77dqFE5364KVNyUjPK4ZMAOaN7ISXHuoEuazmCflERC1Ri1jnhoiqoFLVej8/d1v88tIQPOLvAY0IrPjjLKZ8eQCqgltNWyMRkQFjuCEyNK6uddrPyswEHz/WCysm94aVQo5D6dcwdmUCdpysea0oIiJjxXBDZGiCggAPD6C6tZ4EAVAqtfvdI6SPO36dF4Qe7ra4UXIHs79Jwls/n8DtO+pmKJqIyHAw3BAZGrkcWLlS+/f7A07F4xUrtPvdx8vRCpufH4Rng7TrQH29/yIejkzEudybTVgwEZFhYbghMkShoUBMDODurt/u4aFtDw2t9lCFiQxLxnfDuqf6wsFKgTRVISZ8uhc/HM7imjhE1CrwaileLUWGTK0GEhK0k4xdXbVDUVX02FQnt/A2wn84hr3n8gAAE3q54b2H/WBjbtpUFRMRNZnafn8z3DDckJHTaESsij+Pj3ecgVojQmlvgU+n+KO30k7q0oiI6oSXghMRAEAmE/DCcB/8OGcgPNpaIOvaLUyKSsSqPeeh0bS6f9sQUSvAcEPUSvi3b4tf5wVhfE9XlGtEfPDbKTy57hCuFvG+bERkXBhuiFoRWwtTfDalDz4I7QFzUxkSzuZh7Mp4xJ+5KnVpRESNhuGGqJURBAGP92uP/704BF2crZF3swwz1h5CxLY0lJVrpC6PiKjBGG6IWqlOztb4+cXBmD5Ae5PaL+Iv4NEv9iMzv0TiyoiIGobhhqgVMzeV498hflj1RABszE1wLOsGxn+SgK3HLktdGhFRvTHcEBH+4eeC38KGoq9XWxSVlmPepmS8GnMMJWXlUpdGRFRnDDdEBABwt7PApmcHYN7IThAE4IcjlzDh071IvVwodWlERHXCcENEOiZyGcJHd8bGZwbA2cYM568WIyRyH75OzOCtG4ioxWC4IaJKBnZ0wG/zh2KUrxPKyjV4a+tJzP4mCdeLy+p3QrUa2L0b2LRJ+6eadyonoqbDcENEVbK3UuDLGYF4a0I3KOQyxKVewbhPEnDwQn7dThQbC3h5ASNGAFOnav/08tK2ExE1AYYbIqqWIAh4arA3Yl8YhA6OVlAV3MaULw9gedwZlKtrsSZObCwwaRJw6ZJ+e3a2tp0Bh4iaAG+cyRtnEtVKcWk53tp6EjFJ2qDSz8seKx7vDTc7i6oPUKu1PTT3B5sKggB4eADp6XW60zkRtV68cSYRNSorMxP899FeWPl4b7QxM8GhjGsY90kCdpzMqfqAhITqgw0AiCKQlaXdj4ioETHcEFGdTOztjl/nDUFPD1vcKLmD2d8k4V8/n8DtO/dNElapanfC2u5HRFRLDDdEVGeeDlaImTMIs4d2AABs2H8RIZ/vw7ncor93cnWt3clqux8RUS0x3BBRvShMZHh9nC/WP9UXDlYKnMopwoRP9yH6cKZ2TZygIO2cGkGo+gSCACiV2v2IiBoRww0RNcjwLk74LSwIQ3wcceuOGos2H8dLm5JReEcDrFyp3en+gFPxeMUKTiYmokbHcENEDeZkbY4Ns/ph0T+6wkQm4Je/VBj/SQJS+j4ExMQA7u76B3h4aNtDQ6UpmIiMGi8F56XgRI3qaOZ1zNuUjEvXb8FEJuDlMV0we5AnZPv2aicPu7pqh6LYY0NEdVTb72+GG4YbokZXePsOXo89jl/+0l4JFdTJER8/1gtO1uYSV0ZELRnXuSEiydiYm+LTKX3wn0d6wNxUhoSzeRi3MgHxZ65KXRoRtQIMN0TUJARBwOS+7fHLS0PQ1cUaeTfLMGPtIYRHpyAzv0Tq8ojIiDHcEFGT8nGyxpa5gzFjoCcAIDY5Gw99vBtvbDmOK4W3Ja6OiIwR59xwzg1Rszl+qQD/3XEae+4OT5mZyDBzkBfmDOuItlYKiasjIkPXoubcREZGwtvbG+bm5ggICEBCDfeaiY2NxejRo9GuXTvY2Nhg4MCB+P3335uxWiKqrx4etvh6Vj9Ezx6Avl5tUVquwRfxFxD04S6s+OMMim7fkbpEIjICkoeb6OhohIWFYcmSJUhOTkZQUBDGjh2LzMzMKvePj4/H6NGjsW3bNiQlJWHEiBGYMGECkpOTm7lyIqqv/h0c8MNzA7Huqb7o7maDm6XlWPHHWQz9cBe+jL9Q+T5VRER1IPmwVP/+/eHv74+oqChdm6+vL0JCQhAREVGrc3Tv3h2TJ0/Gv/71r1rtz2EpIsOh0Yj47UQOPo47jQtXiwEAzjZmmDeyEx4LVMJULvm/wYjIQLSIYamysjIkJSUhODhYrz04OBiJiYm1OodGo0FRURHs7e2r3ae0tBSFhYV6GxEZBplMwPiertgRNhQfTuoJdzsLXCksxZKfTmDUsj3YkpwNtabVTQ0kogaQNNzk5eVBrVbD2dlZr93Z2Rk5OTm1OsfHH3+M4uJiPPbYY9XuExERAVtbW92mVCobVDcRNT4TuQyPBSqx8+VheHtCNzi2UeBifgnColMwbmUCdpzMQSu8/oGI6sEg+nuF+26qJ4pipbaqbNq0CW+//Taio6Ph5ORU7X6LFy9GQUGBbsvKympwzUTUNMxM5Jg52Bvxr47AK2O6wMbcBKevFGH2N0kIiUzEvnN5UpdIRAZO0nDj6OgIuVxeqZcmNze3Um/O/aKjo/H000/jhx9+wKhRo2rc18zMDDY2NnobERk2S4UJ5o7wQcKih/DiCB9YmMpxLOsGpn11EFO/PICjmdelLpGIDJSk4UahUCAgIABxcXF67XFxcRg0aFC1x23atAkzZ87Exo0bMX78+KYuk4gkZGthipfHdEH8qyMwc5AXFHIZEs/nIzQyEc98fQRpKs6hIyJ9kl8tFR0djenTp2PVqlUYOHAgVq9ejS+//BInT56Ep6cnFi9ejOzsbGzYsAGANtjMmDEDK1euRGhoqO48FhYWsLW1rdVr8mopopbr0vUSfPLnWcQkXYJGBAQB+GcvNywY1RlejlZSl0dETahF3RU8MjISH374IVQqFfz8/LB8+XIMHToUADBz5kxkZGRg9+7dAIDhw4djz549lc7x5JNPYv369bV6PYYbopbv/NWbWB53RnfncblMwGOBSswb6QNXWwuJqyOiptCiwk1zY7ghMh4nLxfg4x1nsPNULgBAYSLDjAGeeH54Rzi0MZO4OiJqTAw3NWC4ITI+RzKu4cPfT+NQ+jUAgJVCjqeHeOOZoR1gY24qcXVE1BgYbmrAcENknERRRMLZPHz0+2kczy4AoJ2Q/PzwjnhyoBcsFHKJKySihmC4qQHDDZFxE0URv5/MwX93nMG53JsAgHbWZpj3kA8m920PhYlBLPFFRHXEcFMDhhui1kGtEbElORvL/ziDS9dvAQA82lpgwajOCOnjDrnswYuFEpHhYLipAcMNUetSVq5B9OFMfLLzHK4WlQIAfJza4OXgzhjT3aVWK6ITkfQYbmrAcEPUOt0qU+Pr/RmI2n0eBbfuAAB6uNvilTFdENTJkSGHyMAx3NSA4YaodSu8fQdfxV/AV3vTUVKmBgD097bHK2O6INDLXuLqiKg6DDc1YLghIgDIu1mKqN3n8c2Biygr1wAAHurqhIXBndHdrZoVz9VqICEBUKkAV1cgKAiQ8yosoubAcFMDhhsiupeq4BY++fMcfjiSBbVG+ytxfE9XhI/ujI7t2vy9Y2wsMH8+cOnS320eHsDKlcA9t4MhoqbBcFMDhhsiqkp6XjFW/HEGW49dhigCMgGYFOCB+aM6w33nb8CkScD9vzIr5unExDDgEDUxhpsaMNwQUU3SVIX4eMdp/JF295YOcgFTT/6JuXFr0a7kRuUDBEHbg5OeziEqoibEcFMDhhsiqo2jmdfx0fbT2H8hHwBgUXYbs478jNmHYmFbWlz5gF27gOHDm7dIolaktt/fXKaTiKga/u3bYtPsAfiuQzF6XT6NWwpzfD5oMoLmrMH7w5/CaUdP/QNUKmkKJSI97Llhzw0RPcju3RBHjECcT3/8d+gMnGn3d6jpqTqDScf/xIS0eLT9bSt7boiaEIelasBwQ0R1olYDXl5AdjbUEPBnx76I6TEKOzv2RbncBACgUN/BqF4emBSoxNBO7WAiZ8c4UWNjuKkBww0R1VlsrPZqKUB3xVS+hQ1+7j4cMX4jkercUberYxszPNzHDZMClOjiYi1FtURGieGmBgw3RFQvVa1zo1QCK1bg5ICR2JyUjZ9TspFfXKZ7uoe7LSYFeOCfvdzQ1kohQdFExoPhpgYMN0RUbw9YofiOWoPdp68iJikLf6blovzuooCmcgGjfJ0xKcADQzu3gymHrYjqjOGmBgw3RNQc8m+WYuuxy4hJuoSTlwt17RXDVo8EeKCrC38HEdUWw00NGG6IqLmlXi7E5qOXsCWZw1ZE9cVwUwOGGyKSSk3DViO7aoethnXhsBVRVRhuasBwQ0SGoGLYavPRSziRfe+wlQIhvd0xKZDDVkT3YripAcMNERmaNFUhNiddwpaUbOTd/HvYys/dBpP8PfDP3u6w57AVtXIMNzVguCEiQ3VHrcGe01cRk3QJf566gjtqDlsRVWC4qQHDDRG1BNeKy7A1JRsx1QxbPRLgAV9X/g6j1oPhpgYMN0TU0lQ3bNXdzQaTAjwwsa7DVg9Yr4fIEDHc1IDhhohaqpqGrR7q6oRJAUoMf9CwVVUrLXt4ACtXAqGhTfwOiOqP4aYGDDdEZAyuF5fpFgk8nl2ga3ewUiCkjzsmVTVsVXGPrPt/9QuC9s+YGAYcMlgMNzVguCEiY3MqRzts9VNyDcNW5nLt3c3v7bG5lyBoe3DS0zlERQaJ4aYGDDdEZKzuqDWIP6Mdtvoj7b5hK0cZJkW+heEXkmCqUVd/kl27gOHDm6dgojqo7fe3STPWRERETcxULsNIX2eM9HWuNGz1+xU1fn/kX3AovoGQ1N2YdPwP+F7NqHwSlarZ6yZqTOy5Yc8NEbUCp3IKsXnLfvx04iry2rTVtXtev4zBGccQlJGMQRePwba0mD03ZLBq+/1tEKtARUZGwtvbG+bm5ggICEBCQkK1+6pUKkydOhVdunSBTCZDWFhY8xVKRNRCdXWxwZJnR+HA1iVYG/MOxp3aC0X5HVxs64aNfcbi+YdfR595GzHx6U/x0S1n7D+fj9LyGoauiAyY5MNS0dHRCAsLQ2RkJAYPHowvvvgCY8eORWpqKtq3b19p/9LSUrRr1w5LlizB8uXLJaiYiKiFksthsmI5Hpo0CQ9dOIKbpuY4oOyBvV69sderN845tscxR28c23MBn++5AAtTOfp52yOokyOGdHJEF2drCBVXVREZMMmHpfr37w9/f39ERUXp2nx9fRESEoKIiIgajx0+fDh69+6NFStW1Ok1OSxFRK1aVevcKJVQfbgCe336Yt+5POw9l4+8m6V6hzm2McMQHwcM6dQOQ3wc4WJr3syFU2vXIiYUl5WVISkpCa+99ppee3BwMBITExvtdUpLS1Fa+vcPaWFhYQ17ExEZudBQYOLESisUu8rleBTAo4FKiKKIUzlF2HcuDwln83AwXRt2tqRcxpaUywCATk5tMNjHEUGdHNG/gwPamEk+GEAEQOJwk5eXB7VaDWdnZ712Z2dn5OTkNNrrRERE4J133mm08xERtXhyeY2ThgVBgK+rDXxdbfBMUAeUlquRdPG6tlfnbB7+yi7A2dybOJt7E+sTM2AiE9CnvR2G+LTDkE6O6OVhCxPe3JMkYhAx+/4xXFEUG3Vcd/HixQgPD9c9LiwshFKpbLTzExEZOzMTOQZ1dMSgjo54ZQxwo6QMiefzsfdu2Mm8VoLDGddxOOM6lv9xBtZmJhjQ0UE7X8fHEd6OVpyvQ81G0nDj6OgIuVxeqZcmNze3Um9OQ5iZmcHMzKzRzkdE1NrZWSowrocrxvVwBQBk5pdog865q9h3Lh8Ft+4gLvUK4lKvAADcbM0xpJMjhnRqh8EdHeDQppF+J/MGoFQFScONQqFAQEAA4uLi8PDDD+va4+LiMHHiRAkrIyKiumjvYImpDu0xtX97qDUiTl4uQMJZba9O0sXruFxwGz8cuYQfjmgnMXdztdFdhdXXyx7mpvUIJLwBKFVD8mGp8PBwTJ8+HYGBgRg4cCBWr16NzMxMzJkzB4B2SCk7OxsbNmzQHZOSkgIAuHnzJq5evYqUlBQoFAp069ZNirdARET3kMsE9PSwQ08PO8wd4YNbZWocyriGvWevIuFsHk7lFCFVVYhUVSG+iL8AhYkMfb3aYohPOwR1ckQ3VxvIZA8YwqruBqDZ2dp23gC0VZP8UnBAu4jfhx9+CJVKBT8/PyxfvhxDhw4FAMycORMZGRnYvXu3bv+qxm09PT2RkZFRq9fjpeBERNK5WlSKxPN5up6dnMLbes+3tTTFIB9HBPk4YrCPI5T2lvonUKt5A9BWijfOrAHDDRGRYRBFEeevFmPv2avYey4PBy5cw83Scr19vBwstfN1fNphYEcH2B7cB4wY8eCT8zYSRqdFrHNDREStmyAI8HFqAx+nNpg52Bt31Bocy7qh7dU5l4eUrBvIyC9BRn4mvj2QCZkA9LQoR1DQExickQL/7FNQaMqrPjlvANpqseeGPTdERAar6PYdHLhwTdezc/5qsd7zlmW30D/rBAIvpaJb7gX45ZxHu5Ib2ifZc2N0OCxVA4YbIqKW6fKNW9h7Jhd7l63FvnadkW9lV2kfp5v56F5wGd2nTUR3dzv4udvCo60F19kxAgw3NWC4ISJq4WJjoZn0KE6180SiZy/85eKDk84dccHeHaJQeWVkG3MTdHOzQXc3W/i5a//s4GjFVZRbGIabGjDcEBEZgSrWuSn29sGptz7Eyc59cDK7ECdVBTidU4Q76spfdWYmMnR1tUF3Nxv4udmiu5sNurhY12/NHWoWDDc1YLghIjIStVihuKxcg7O5RTh5uRCplwtxIrsAaapCFJepK51OLhPg064NurvZoLu7NvB0c7OBjblpc70jqgHDTQ0YboiIWjeNRkRGfjFOXi68uxXg5OVCXCsuq3L/9vaW2h4ed9u7w1s2cLI2b+aqieGmBgw3RER0P1EUkVN4GyezC3HibthJvVyI7Bu3qty/nbWZ3pBWdzdbKO05cbkpMdzUgOGGiIhq63pxGVJV2uGsil6eC3nFle78AADW5ibo5qrt4akIPB3bceJyY2G4qQHDDRERNURJWTnSVEXa4ay7E5fP5NxEmVpTaV8zExm6uljr5vB0d7NFV05crheGmxow3BARUWO7f+LyycsFSL1c/cTlju2s4Odmq7tEvZubDWwtOHG5Jgw3NWC4ISKi5lDXicsuNubwdLC8u1mhvb0lvBys0N7BksEHDDc1YrghIiKp3Dtx+e/AU4DsG7drPM7O0hSe9trQ4+lgifZ3/+7lYIl21matYiIzw00NGG6IiMhg3F2M8EbeDVywd0emnSsyPLsgc8Q4XGzjiIv5Jci7WVrjKSxM5Whvb4n2DpbwcrBEeweru0HIEu52FkYzoZnhpgYMN0REZBBiY4FJk1Dp0quKXpiYGCA0FDdLy5GZX4LMa8W4mF+CjHv+fvnGLWhq+CY3kQlwb2txt6fn7jCX/d/DXhaKljOxmeGmBgw3REQkObUa8PLSu32EHkEAPDyA9PRKqy7fq6xcg0vXS3DxWgky80twMb8EF/OLtY+vlaCsvPIVXPdytjGDp712Xo+nrvdHO/RlZ6mo+3t6wIrRDVHb72+TRntFIiIiqr2EhOqDDaDtzcnK0u43fHi1uylMZOjQrg06tGtT6TmNRsSVott/B558bQiq+HvR7XJcKSzFlcJSHMq4Vul4G3MT3RwfTwdLXQjycrCCk7UZZLJ75vlUca8veHgAK1cCoaG1+UQaDcMNERGRFFSqxt2vCjKZAFdbC7jaWmBABwe950RRxI2SO3ph5+I9w125RaUovF2O49kFOJ5dUOncZiYy3VCX57XL8Px2LdqbOsGzrQYeBVdgqlED2dnaYbe7w2vNheGGiIhICq6ujbtfHQmCgLZWCrS1UqC30q7S8yVl5ci8djfw5JcgI79Y9zj7xi2UlmtwNvcmzubeBGACjH5ed6xMo8b+qKfgfPOadngtLAyYOLFRh6hqwnBDREQkhaAg7bBNdnblCcXA33NugoKavzYAlgoTdHWxQVeXynNb7qg1yL5+Szuv50AKLq6PRkZbV2TauSLTzhkaQYZ2N69rd67l8FpjYrghIiKSglyunY8yaZI2yNwbcCqullqxotl6O+rCVC6Dl6MVvBytgKQ8YNca3XMigHxLW8hwX2BrwPBaXRnHhe9EREQtUWiodj6Ku7t+u4dHs89Tqbf7hs0EAI4llefoNNXwWlV4KTgvBSciIqk18SXUTarikvYHDa894JL22uCl4ERERC2FXN5s81EanQEOr3FYioiIiBrGwIbX2HNDREREDRcaqr3c2wCG1xhuiIiIqHEYyPAah6WIiIjIqDDcEBERkVFhuCEiIiKjwnBDRERERoXhhoiIiIwKww0REREZFYMIN5GRkfD29oa5uTkCAgKQkJBQ4/579uxBQEAAzM3N0aFDB6xataqZKiUiIiJDJ3m4iY6ORlhYGJYsWYLk5GQEBQVh7NixyMzMrHL/9PR0jBs3DkFBQUhOTsbrr7+OefPmYfPmzc1cORERERkiyW+c2b9/f/j7+yMqKkrX5uvri5CQEERERFTaf9GiRdi6dSvS0tJ0bXPmzMGxY8ewf//+Kl+jtLQUpaWluseFhYVQKpW8cSYREVEL0iJunFlWVoakpCS89tpreu3BwcFITEys8pj9+/cjODhYr23MmDFYs2YN7ty5A1NT00rHRERE4J133qnUXlhY2IDqiYiIqDlVfG8/qF9G0nCTl5cHtVoNZ2dnvXZnZ2fk5ORUeUxOTk6V+5eXlyMvLw+urq6Vjlm8eDHCw8N1j7Ozs9GtWzcolcpGeBdERETUnIqKimBra1vt8wZxbymh4pbod4miWKntQftX1V7BzMwMZmZmusdt2rRBVlYWrK2ta3yduqoY7srKyuJwVxPi59w8+Dk3H37WzYOfc/Noys9ZFEUUFRXBzc2txv0kDTeOjo6Qy+WVemlyc3Mr9c5UcHFxqXJ/ExMTODg41Op1ZTIZPDw86ld0LdjY2PAHpxnwc24e/JybDz/r5sHPuXk01edcU49NBUmvllIoFAgICEBcXJxee1xcHAYNGlTlMQMHDqy0/44dOxAYGFjlfBsiIiJqXSS/FDw8PBxfffUV1q5di7S0NCxYsACZmZmYM2cOAO18mRkzZuj2nzNnDi5evIjw8HCkpaVh7dq1WLNmDV5++WWp3gIREREZEMnn3EyePBn5+flYunQpVCoV/Pz8sG3bNnh6egIAVCqV3po33t7e2LZtGxYsWIDPP/8cbm5u+OSTT/DII49I9RZ0zMzM8NZbb+nN76HGx8+5efBzbj78rJsHP+fmYQifs+Tr3BARERE1JsmHpYiIiIgaE8MNERERGRWGGyIiIjIqDDdERERkVBhuGlFkZCS8vb1hbm6OgIAAJCQkSF2SUYmIiEDfvn1hbW0NJycnhISE4PTp01KXZfQiIiIgCALCwsKkLsXoZGdn44knnoCDgwMsLS3Ru3dvJCUlSV2WUSkvL8cbb7wBb29vWFhYoEOHDli6dCk0Go3UpbV48fHxmDBhAtzc3CAIArZs2aL3vCiKePvtt+Hm5gYLCwsMHz4cJ0+ebJbaGG4aSXR0NMLCwrBkyRIkJycjKCgIY8eO1buMnRpmz549mDt3Lg4cOIC4uDiUl5cjODgYxcXFUpdmtA4fPozVq1ejZ8+eUpdidK5fv47BgwfD1NQUv/32G1JTU/Hxxx/Dzs5O6tKMyn/+8x+sWrUKn332GdLS0vDhhx/io48+wqeffip1aS1ecXExevXqhc8++6zK5z/88EMsW7YMn332GQ4fPgwXFxeMHj0aRUVFTV+cSI2iX79+4pw5c/TaunbtKr722msSVWT8cnNzRQDinj17pC7FKBUVFYmdOnUS4+LixGHDhonz58+XuiSjsmjRInHIkCFSl2H0xo8fL86aNUuvLTQ0VHziiSckqsg4ARB/+ukn3WONRiO6uLiIH3zwga7t9u3boq2trbhq1aomr4c9N42grKwMSUlJCA4O1msPDg5GYmKiRFUZv4KCAgCAvb29xJUYp7lz52L8+PEYNWqU1KUYpa1btyIwMBCPPvoonJyc0KdPH3z55ZdSl2V0hgwZgj///BNnzpwBABw7dgx79+7FuHHjJK7MuKWnpyMnJ0fve9HMzAzDhg1rlu9FyVcoNgZ5eXlQq9WVbvbp7Oxc6Saf1DhEUUR4eDiGDBkCPz8/qcsxOt9//z2OHj2Kw4cPS12K0bpw4QKioqIQHh6O119/HYcOHcK8efNgZmamd8sZaphFixahoKAAXbt2hVwuh1qtxnvvvYcpU6ZIXZpRq/juq+p78eLFi03++gw3jUgQBL3HoihWaqPG8eKLL+Kvv/7C3r17pS7F6GRlZWH+/PnYsWMHzM3NpS7HaGk0GgQGBuL9998HAPTp0wcnT55EVFQUw00jio6OxrfffouNGzeie/fuSElJQVhYGNzc3PDkk09KXZ7Rk+p7keGmETg6OkIul1fqpcnNza2UWqnhXnrpJWzduhXx8fHw8PCQuhyjk5SUhNzcXAQEBOja1Go14uPj8dlnn6G0tBRyuVzCCo2Dq6srunXrptfm6+uLzZs3S1SRcXrllVfw2muv4fHHHwcA9OjRAxcvXkRERATDTRNycXEBoO3BcXV11bU31/ci59w0AoVCgYCAAMTFxem1x8XFYdCgQRJVZXxEUcSLL76I2NhY7Ny5E97e3lKXZJRGjhyJ48ePIyUlRbcFBgZi2rRpSElJYbBpJIMHD660lMGZM2d0Nw2mxlFSUgKZTP+rTi6X81LwJubt7Q0XFxe978WysjLs2bOnWb4X2XPTSMLDwzF9+nQEBgZi4MCBWL16NTIzMzFnzhypSzMac+fOxcaNG/Hzzz/D2tpa11Nma2sLCwsLiaszHtbW1pXmMVlZWcHBwYHzmxrRggULMGjQILz//vt47LHHcOjQIaxevRqrV6+WujSjMmHCBLz33nto3749unfvjuTkZCxbtgyzZs2SurQW7+bNmzh37pzucXp6OlJSUmBvb4/27dsjLCwM77//Pjp16oROnTrh/fffh6WlJaZOndr0xTX59VityOeffy56enqKCoVC9Pf35yXKjQxAldu6deukLs3o8VLwpvG///1P9PPzE83MzMSuXbuKq1evlroko1NYWCjOnz9fbN++vWhubi526NBBXLJkiVhaWip1aS3erl27qvyd/OSTT4qiqL0c/K233hJdXFxEMzMzcejQoeLx48ebpTZBFEWx6SMUERERUfPgnBsiIiIyKgw3REREZFQYboiIiMioMNwQERGRUWG4ISIiIqPCcENERERGheGGiIiIjArDDRERERkVhhsiIiIyKgw3RGQ0hg8fjrCwMKnLICKJMdwQERGRUeG9pYjIKMycORNff/21Xlt6ejq8vLykKYiIJMNwQ0RGoaCgAGPHjoWfnx+WLl0KAGjXrh3kcrnElRFRczORugAiosZga2sLhUIBS0tLuLi4SF0OEUmIc26IiIjIqDDcEBERkVFhuCEio6FQKKBWq6Uug4gkxnBDREbDy8sLBw8eREZGBvLy8qDRaKQuiYgkwHBDREbj5ZdfhlwuR7du3dCuXTtkZmZKXRIRSYCXghMREZFRYc8NERERGRWGGyIiIjIqDDdERERkVBhuiIiIyKgw3BAREZFRYbghIiIio8JwQ0REREaF4YaIiIiMCsMNERERGRWGGyIiIjIqDDdERERkVP4flAzlFkuXsNkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting\n",
    "plt.scatter(t, N, label='Original Measurements', color='red')\n",
    "plt.plot(t, g(x_op, t), label=\"Curve 1\")\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('f_x')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "# Plotting the cost function for each variation of noise\n",
    "plt.plot(t, [cost_function(x_init, cost_init, t, g(x_init, t) + d, k_max) for d in d], label=\"Cost Function Curve\")\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('Cost')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7cccd853",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.8, 0.3],\n",
       "       [0.8, 0.3]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_init = np.array([[0.8, 0.3],[0.8, 0.3]])\n",
    "A_init"
   ]
  },
  {
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