code/4_NonlinearEquations/jupyter/4_NonlinearEquations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non-linear equations and root-finding\n",
    "\n",
    "Often we may encounter a problem where we need to find a root of an equation\n",
    "$$\n",
    "f(x) = 0\n",
    "$$\n",
    "that we cannot solve explicitly.\n",
    "The solution can be obtained using numerical methods.\n",
    "\n",
    "The most common methods are:\n",
    "\n",
    "- Non-local (two-point) methods\n",
    "    - Bisection method\n",
    "    - False position method\n",
    "    - Secant method\n",
    "- Local methods\n",
    "    - Newton method\n",
    "    - Quasi-newton methods\n",
    "    - Iteration method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bisection method\n",
    "\n",
    "Let us consider an equation \n",
    "$$\n",
    "x+e^{-x}-2 = 0,\n",
    "$$\n",
    "i.e. $f(x) = x+e^{-x}-2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def func1(x):\n",
    "    return x + np.exp(-x) - 2.\n",
    "\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func1(xref)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "# Default style parameters (feel free to modify as you see fit)\n",
    "params = {'legend.fontsize': 'large',\n",
    "         'axes.labelsize': 'x-large',\n",
    "         'axes.titlesize':'x-large',\n",
    "         'xtick.labelsize':'x-large',\n",
    "         'ytick.labelsize':'x-large',\n",
    "         'xtick.direction':'in',\n",
    "         'ytick.direction':'in',\n",
    "         }\n",
    "plt.rcParams.update(params)\n",
    "\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref)\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--',label='max. error')\n",
    "#plt.plot([1.841406], [0], 'ro')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $x>0$ the equation $f(x) = 0$ has a root at $x \\approx 1.84...$\n",
    "\n",
    "The idea of the bisection method is to consider an interval $a<x<b$ such that $f(a) * f(b) < 0$, i.e. the function $f(x)$ has opposite signs at the edges of the interval. If the function is continuous, this implies that it has at least one root $f(x) = 0$ for $a < x < b$. The bisection method halves the initial $(a,b)$ interval at each step until the solution is found with the desired precision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "last_bisection_iterations = 0  # Count how many interactions it took\n",
    "bisection_verbose = True\n",
    "\n",
    "def bisection_method(\n",
    "    f,                    # The function whose root we are trying to find\n",
    "    a,                    # The left boundary\n",
    "    b,                    # The right boundary\n",
    "    tolerance = 1.e-10,   # The desired accuracy of the solution\n",
    "    ):\n",
    "    fa = f(a)                           # The value of the function at the left boundary\n",
    "    fb = f(b)                           # The value of the function at the right boundary\n",
    "    if (fa * fb > 0.):\n",
    "        return None                     # Bisection method is not applicable\n",
    "    \n",
    "    global last_bisection_iterations\n",
    "    last_bisection_iterations = 0\n",
    "    \n",
    "    \n",
    "    while ((b-a) > tolerance):\n",
    "        last_bisection_iterations += 1\n",
    "        c = (a + b) / 2.                # Take the midpoint\n",
    "        fc = f(c)                       # Calculate the function at midpoint\n",
    "        \n",
    "        \n",
    "        if bisection_verbose:\n",
    "            print(\"Iteration: {0:5}, c = {1:20.15f}, f(c) = {2:10.15f}\".format(last_bisection_iterations, c, fc))\n",
    "        \n",
    "        if (fc * fa < 0.):              \n",
    "            b = c                       # The midpoint is the new right boundary\n",
    "            fb = fc\n",
    "        else:                           \n",
    "            a = c                       # The midpoint is the new left boundary\n",
    "            fa = fc\n",
    "\n",
    "    return (a+b) / 2.                   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The default desired accuracy\n",
    "accuracy = 1.e-10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x + e^-x - 2 = 0 on an interval ( 0.0 , 3.0 ) using bisection method\n",
      "Iteration:     1, c =    1.500000000000000, f(c) = -0.276869839851570\n",
      "Iteration:     2, c =    2.250000000000000, f(c) = 0.355399224561864\n",
      "Iteration:     3, c =    1.875000000000000, f(c) = 0.028354966844928\n",
      "Iteration:     4, c =    1.687500000000000, f(c) = -0.127518600092696\n",
      "Iteration:     5, c =    1.781250000000000, f(c) = -0.050322518721816\n",
      "Iteration:     6, c =    1.828125000000000, f(c) = -0.011160374631956\n",
      "Iteration:     7, c =    1.851562500000000, f(c) = 0.008554175081233\n",
      "Iteration:     8, c =    1.839843750000000, f(c) = -0.001314006731460\n",
      "Iteration:     9, c =    1.845703125000000, f(c) = 0.003617373389399\n",
      "Iteration:    10, c =    1.842773437500000, f(c) = 0.001151003645707\n",
      "Iteration:    11, c =    1.841308593750000, f(c) = -0.000081671712691\n",
      "Iteration:    12, c =    1.842041015625000, f(c) = 0.000534623455207\n",
      "Iteration:    13, c =    1.841674804687500, f(c) = 0.000226465239541\n",
      "Iteration:    14, c =    1.841491699218750, f(c) = 0.000072394105009\n",
      "Iteration:    15, c =    1.841400146484375, f(c) = -0.000004639468506\n",
      "Iteration:    16, c =    1.841445922851562, f(c) = 0.000033877152093\n",
      "Iteration:    17, c =    1.841423034667969, f(c) = 0.000014618800253\n",
      "Iteration:    18, c =    1.841411590576172, f(c) = 0.000004989655488\n",
      "Iteration:    19, c =    1.841405868530273, f(c) = 0.000000175090895\n",
      "Iteration:    20, c =    1.841403007507324, f(c) = -0.000002232189455\n",
      "Iteration:    21, c =    1.841404438018799, f(c) = -0.000001028549442\n",
      "Iteration:    22, c =    1.841405153274536, f(c) = -0.000000426729314\n",
      "Iteration:    23, c =    1.841405510902405, f(c) = -0.000000125819220\n",
      "Iteration:    24, c =    1.841405689716339, f(c) = 0.000000024635835\n",
      "Iteration:    25, c =    1.841405600309372, f(c) = -0.000000050591693\n",
      "Iteration:    26, c =    1.841405645012856, f(c) = -0.000000012977929\n",
      "Iteration:    27, c =    1.841405667364597, f(c) = 0.000000005828953\n",
      "Iteration:    28, c =    1.841405656188726, f(c) = -0.000000003574488\n",
      "Iteration:    29, c =    1.841405661776662, f(c) = 0.000000001127232\n",
      "Iteration:    30, c =    1.841405658982694, f(c) = -0.000000001223628\n",
      "Iteration:    31, c =    1.841405660379678, f(c) = -0.000000000048198\n",
      "Iteration:    32, c =    1.841405661078170, f(c) = 0.000000000539517\n",
      "Iteration:    33, c =    1.841405660728924, f(c) = 0.000000000245659\n",
      "Iteration:    34, c =    1.841405660554301, f(c) = 0.000000000098731\n",
      "Iteration:    35, c =    1.841405660466990, f(c) = 0.000000000025266\n",
      "The solution is x =  1.8414056604233338  obtained with  35  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.\n",
    "b = 3.\n",
    "print(\"Solving the equation x + e^-x - 2 = 0 on an interval (\", a, \",\", b, \") using bisection method\")\n",
    "bisection_verbose = True\n",
    "xroot = bisection_method(func1,a,b,accuracy)\n",
    "print(\"The solution is x = \", xroot, \" obtained with \", last_bisection_iterations, \" iterations\")\n",
    "\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func1(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us try a polynomial equation with a single real root:\n",
    "$$\n",
    "f(x) = x^3 - x - 1\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:     1, c =    1.500000000000000, f(c) = 0.875000000000000\n",
      "Iteration:     2, c =    0.750000000000000, f(c) = -1.328125000000000\n",
      "Iteration:     3, c =    1.125000000000000, f(c) = -0.701171875000000\n",
      "Iteration:     4, c =    1.312500000000000, f(c) = -0.051513671875000\n",
      "Iteration:     5, c =    1.406250000000000, f(c) = 0.374664306640625\n",
      "Iteration:     6, c =    1.359375000000000, f(c) = 0.152614593505859\n",
      "Iteration:     7, c =    1.335937500000000, f(c) = 0.048348903656006\n",
      "Iteration:     8, c =    1.324218750000000, f(c) = -0.002127945423126\n",
      "Iteration:     9, c =    1.330078125000000, f(c) = 0.022973485291004\n",
      "Iteration:    10, c =    1.327148437500000, f(c) = 0.010388596914709\n",
      "Iteration:    11, c =    1.325683593750000, f(c) = 0.004121791920625\n",
      "Iteration:    12, c =    1.324951171875000, f(c) = 0.000994790971163\n",
      "Iteration:    13, c =    1.324584960937500, f(c) = -0.000567110148040\n",
      "Iteration:    14, c =    1.324768066406250, f(c) = 0.000213707162629\n",
      "Iteration:    15, c =    1.324676513671875, f(c) = -0.000176734802636\n",
      "Iteration:    16, c =    1.324722290039062, f(c) = 0.000018477852226\n",
      "Iteration:    17, c =    1.324699401855469, f(c) = -0.000079130557112\n",
      "Iteration:    18, c =    1.324710845947266, f(c) = -0.000030326872924\n",
      "Iteration:    19, c =    1.324716567993164, f(c) = -0.000005924640470\n",
      "Iteration:    20, c =    1.324719429016113, f(c) = 0.000006276573348\n",
      "Iteration:    21, c =    1.324717998504639, f(c) = 0.000000175958307\n",
      "Iteration:    22, c =    1.324717283248901, f(c) = -0.000002874343115\n",
      "Iteration:    23, c =    1.324717640876770, f(c) = -0.000001349192913\n",
      "Iteration:    24, c =    1.324717819690704, f(c) = -0.000000586617430\n",
      "Iteration:    25, c =    1.324717909097672, f(c) = -0.000000205329594\n",
      "Iteration:    26, c =    1.324717953801155, f(c) = -0.000000014685651\n",
      "Iteration:    27, c =    1.324717976152897, f(c) = 0.000000080636326\n",
      "Iteration:    28, c =    1.324717964977026, f(c) = 0.000000032975337\n",
      "Iteration:    29, c =    1.324717959389091, f(c) = 0.000000009144842\n",
      "Iteration:    30, c =    1.324717956595123, f(c) = -0.000000002770405\n",
      "Iteration:    31, c =    1.324717957992107, f(c) = 0.000000003187219\n",
      "Iteration:    32, c =    1.324717957293615, f(c) = 0.000000000208407\n",
      "Iteration:    33, c =    1.324717956944369, f(c) = -0.000000001280999\n",
      "Iteration:    34, c =    1.324717957118992, f(c) = -0.000000000536296\n",
      "Iteration:    35, c =    1.324717957206303, f(c) = -0.000000000163944\n",
      "The solution is x =  1.324717957249959  obtained with  35  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func2(x):\n",
    "    return x**3 - x - 1.\n",
    "\n",
    "a = 0.\n",
    "b = 3.\n",
    "xroot = bisection_method(func2, a, b, accuracy)\n",
    "print(\"The solution is x = \", xroot, \" obtained with \", last_bisection_iterations, \" iterations\")\n",
    "\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func2(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### False position method\n",
    "\n",
    "In the false position method instead of choosing the midpoint, we choose the point where the straight line between current interval edges crosses the $y = 0$ axis.\n",
    "\n",
    "![falseposition](falseposition.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "last_falseposition_iterations = 0\n",
    "falseposition_verbose = True\n",
    "\n",
    "def falseposition_method(\n",
    "    f,                    # The function whose root we are trying to find\n",
    "    a,                    # The left boundary\n",
    "    b,                    # The right boundary\n",
    "    tolerance = 1.e-10,   # The desired accuracy of the solution\n",
    "    max_iterations = 100  # Maximum number of iterations\n",
    "    ):\n",
    "    fa = f(a)                           # The value of the function at the left boundary\n",
    "    fb = f(b)                           # The value of the function at the right boundary\n",
    "    if (fa * fb > 0.):\n",
    "        return None                     # False position method is not applicable\n",
    "    \n",
    "    xprev = xnew = (a+b) / 2.                  # Estimate of the solution from the previous step  \n",
    "    \n",
    "    global last_falseposition_iterations\n",
    "    last_falseposition_iterations = 0\n",
    "    \n",
    "    for i in range(max_iterations):\n",
    "        last_falseposition_iterations += 1\n",
    "        \n",
    "        xprev = xnew\n",
    "        xnew = a - fa * (b - a) / (fb - fa) # Take the point where straight line between a and b crosses y = 0\n",
    "        fnew = f(xnew)                      # Calculate the function at midpoint\n",
    "\n",
    "        if falseposition_verbose:\n",
    "            print(\"Iteration: {0:5}, x = {1:20.15f}, f(x) = {2:10.15f}\".format(last_falseposition_iterations, xnew, fnew))\n",
    "        \n",
    "        if (fnew * fa < 0.):              \n",
    "            b = xnew                        # The intersection is the new right boundary\n",
    "            fb = fnew\n",
    "        else:                           \n",
    "            a = xnew                        # The midpoint is the new left boundary\n",
    "            fa = fnew\n",
    "    \n",
    "        if (abs(xnew-xprev) < tolerance):\n",
    "            return xnew\n",
    "    \n",
    "    print(\"False position method failed to converge to a required precision in \" + str(max_iterations) + \" iterations\")\n",
    "    print(\"The error estimate is \", abs(xnew - xprev))\n",
    "    \n",
    "    return xnew                   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x + e^-x - 2 = 0 on an interval ( 0.0 , 3.0 ) using the false position method\n",
      "Iteration:     1, x =    1.463566653481105, f(x) = -0.305023902720619\n",
      "Iteration:     2, x =    1.809481253839539, f(x) = -0.026779692379373\n",
      "Iteration:     3, x =    1.839095511827520, f(x) = -0.001943348598294\n",
      "Iteration:     4, x =    1.841240588240115, f(x) = -0.000138890519932\n",
      "Iteration:     5, x =    1.841393875903701, f(x) = -0.000009915561978\n",
      "Iteration:     6, x =    1.841404819191791, f(x) = -0.000000707828391\n",
      "Iteration:     7, x =    1.841405600384506, f(x) = -0.000000050528475\n",
      "Iteration:     8, x =    1.841405656150106, f(x) = -0.000000003606984\n",
      "Iteration:     9, x =    1.841405660130943, f(x) = -0.000000000257485\n",
      "Iteration:    10, x =    1.841405660415115, f(x) = -0.000000000018381\n",
      "Iteration:    11, x =    1.841405660435401, f(x) = -0.000000000001312\n",
      "The solution is x =  1.8414056604354012 obtained after  11  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.\n",
    "b = 3.\n",
    "print(\"Solving the equation x + e^-x - 2 = 0 on an interval (\", a, \",\", b, \") using the false position method\")\n",
    "xroot = falseposition_method(func1, a, b, accuracy)\n",
    "print(\"The solution is x = \", xroot, \"obtained after \", last_falseposition_iterations, \" iterations\")\n",
    "\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func1(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x^3 - x - 1 = 0 on an interval ( 0.0 , 3.0 ) using the false position method\n",
      "Iteration:     1, x =    0.125000000000000, f(x) = -1.123046875000000\n",
      "Iteration:     2, x =    0.258845437616387, f(x) = -1.241502544655680\n",
      "Iteration:     3, x =    0.399230727605107, f(x) = -1.335599268673875\n",
      "Iteration:     4, x =    0.541967526475374, f(x) = -1.382776055418208\n",
      "Iteration:     5, x =    0.681365453934702, f(x) = -1.365035490183169\n",
      "Iteration:     6, x =    0.811265467641601, f(x) = -1.277329754233812\n",
      "Iteration:     7, x =    0.926423756077868, f(x) = -1.131310399158622\n",
      "Iteration:     8, x =    1.023635980751716, f(x) = -0.951038855271058\n",
      "Iteration:     9, x =    1.102112700940041, f(x) = -0.763428857530277\n",
      "Iteration:    10, x =    1.163084623011103, f(x) = -0.589703475641066\n",
      "Iteration:    11, x =    1.209004461867383, f(x) = -0.441812567314840\n",
      "Iteration:    12, x =    1.242759715838447, f(x) = -0.323377345963561\n",
      "Iteration:    13, x =    1.267123755869329, f(x) = -0.232626542846002\n",
      "Iteration:    14, x =    1.284474915416815, f(x) = -0.165250826057421\n",
      "Iteration:    15, x =    1.296712725379603, f(x) = -0.116337099147602\n",
      "Iteration:    16, x =    1.305284823099690, f(x) = -0.081381697897300\n",
      "Iteration:    17, x =    1.311260149895704, f(x) = -0.056675277433967\n",
      "Iteration:    18, x =    1.315411216706803, f(x) = -0.039346415911536\n",
      "Iteration:    19, x =    1.318288144277179, f(x) = -0.027256756945956\n",
      "Iteration:    20, x =    1.320278742279728, f(x) = -0.018853392932333\n",
      "Iteration:    21, x =    1.321654503458967, f(x) = -0.013027238417732\n",
      "Iteration:    22, x =    1.322604583024956, f(x) = -0.008995024910972\n",
      "Iteration:    23, x =    1.323260335853139, f(x) = -0.006207779657019\n",
      "Iteration:    24, x =    1.323712771581656, f(x) = -0.004282733486323\n",
      "Iteration:    25, x =    1.324024847881927, f(x) = -0.002953948207525\n",
      "Iteration:    26, x =    1.324240069970690, f(x) = -0.002037106345411\n",
      "Iteration:    27, x =    1.324388478616892, f(x) = -0.001404674045584\n",
      "Iteration:    28, x =    1.324490806628938, f(x) = -0.000968508967562\n",
      "Iteration:    29, x =    1.324561357818050, f(x) = -0.000667741626827\n",
      "Iteration:    30, x =    1.324609998150458, f(x) = -0.000460359597848\n",
      "Iteration:    31, x =    1.324643531473506, f(x) = -0.000317376586783\n",
      "Iteration:    32, x =    1.324666649368313, f(x) = -0.000218798801115\n",
      "Iteration:    33, x =    1.324682586648379, f(x) = -0.000150837640515\n",
      "Iteration:    34, x =    1.324693573573097, f(x) = -0.000103985047874\n",
      "Iteration:    35, x =    1.324701147748373, f(x) = -0.000071685209996\n",
      "Iteration:    36, x =    1.324706369216883, f(x) = -0.000049418152359\n",
      "Iteration:    37, x =    1.324709968770709, f(x) = -0.000034067656374\n",
      "Iteration:    38, x =    1.324712450210734, f(x) = -0.000023485358447\n",
      "Iteration:    39, x =    1.324714160849362, f(x) = -0.000016190175755\n",
      "Iteration:    40, x =    1.324715340116887, f(x) = -0.000011161062609\n",
      "Iteration:    41, x =    1.324716153071144, f(x) = -0.000007694125345\n",
      "Iteration:    42, x =    1.324716713498952, f(x) = -0.000005304113208\n",
      "Iteration:    43, x =    1.324717099842002, f(x) = -0.000003656505113\n",
      "Iteration:    44, x =    1.324717366175894, f(x) = -0.000002520690342\n",
      "Iteration:    45, x =    1.324717549778863, f(x) = -0.000001737691789\n",
      "Iteration:    46, x =    1.324717676349487, f(x) = -0.000001197914878\n",
      "Iteration:    47, x =    1.324717763603640, f(x) = -0.000000825808104\n",
      "Iteration:    48, x =    1.324717823754144, f(x) = -0.000000569288357\n",
      "Iteration:    49, x =    1.324717865220170, f(x) = -0.000000392451009\n",
      "Iteration:    50, x =    1.324717893805655, f(x) = -0.000000270544424\n",
      "Iteration:    51, x =    1.324717913511665, f(x) = -0.000000186505532\n",
      "Iteration:    52, x =    1.324717927096420, f(x) = -0.000000128571540\n",
      "Iteration:    53, x =    1.324717936461359, f(x) = -0.000000088633515\n",
      "Iteration:    54, x =    1.324717942917278, f(x) = -0.000000061101390\n",
      "Iteration:    55, x =    1.324717947367803, f(x) = -0.000000042121538\n",
      "Iteration:    56, x =    1.324717950435866, f(x) = -0.000000029037373\n",
      "Iteration:    57, x =    1.324717952550901, f(x) = -0.000000020017529\n",
      "Iteration:    58, x =    1.324717954008944, f(x) = -0.000000013799507\n",
      "Iteration:    59, x =    1.324717955014078, f(x) = -0.000000009512983\n",
      "Iteration:    60, x =    1.324717955706987, f(x) = -0.000000006557976\n",
      "Iteration:    61, x =    1.324717956184660, f(x) = -0.000000004520880\n",
      "Iteration:    62, x =    1.324717956513953, f(x) = -0.000000003116564\n",
      "Iteration:    63, x =    1.324717956740958, f(x) = -0.000000002148470\n",
      "Iteration:    64, x =    1.324717956897449, f(x) = -0.000000001481093\n",
      "Iteration:    65, x =    1.324717957005330, f(x) = -0.000000001021022\n",
      "Iteration:    66, x =    1.324717957079699, f(x) = -0.000000000703863\n",
      "The solution is x =  1.3247179570796994 obtained after  66  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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5ORkjRozAnXfeWb1dr9cDAHQ6Xa2vq9peWFhY7/5DQkKg0+mqH6+88goAa++RTCZDSUmJHd4F2aqkpAQymaxG7x0RETW9/GIjvjmUAQB4PM71Jgj8O5cYQr1ixQq8/vrriI6Oxqefftqg11b1DMjqWkTzqoyMjBqDmapm/1UoFNDpdLh8+TKMRiO0Wi2USuUN90cNJwgCTCZTda+an5/fdWO1iIioaX2acB7llRbc2kaHPhHNb/wCJ+f0QWflypWYO3cuOnbsiF9++eW6FbGremyqenb+zmAw1GhXF61WW+eo7aCgIHh6eiI3N7d6f9R0FAoFWrVqdcO/MyIisq/SChM+TUgHAEwb2E4S/6l36qCzfPlyPPPMM+jcuTN27dqFwMDA69pER0fj0KFDSElJQffu3Ws8ZzKZkJaWBqVSiXbtGt/9JpPJ4OfnB51OB7PZDJPJ1Oh9Uf2USiUUCoUk/nEREbma9YcycaW0EqH+XhjRuZXY5diF0wadV155BQsWLEBMTAx27tx5XU9OlSFDhuDzzz/Htm3b8MADD9R4bu/evSgtLcWAAQNqLETZWDKZDEqlEkql0x42IiKiRjGZLfjoV+uNO48PaOeSyz3UxikHIy9ZsgQLFixA9+7dsWvXrjpDDgCMGzcOAQEB+Oqrr3Do0KHq7eXl5Xj++ecBADNmzGjymomIiFzZD8cvIfNKGZp7q3Gfiy73UBun65pYu3YtXnjhBSgUCsTFxeGtt966rk1YWBimTJkCwDq25qOPPsK4ceMwaNAgTJgwAf7+/vjuu+9w+vRpjBs3DuPHj3fwuyAiInIdgiDggz3W3pwpfcPgoZLOjSBOF3TS0qwzMZrNZqxYsaLWNgMHDqwOOgAwevRo7NmzB0uXLsW3336L8vJyREZG4o033sCTTz7J8R5ERET1+PVMHk5eMsBTpcCkPm3FLseunG6tK0ezda0MIiIiqXpo9e/YdzYfU/uFYdHdt4hdjk1cdq0rIiIicpzjmXrsO5sPhVyGxyQwQeDfMegQERG5sff2nAUA3N2lFdr4eYpcjf0x6BAREbmpc5eL8VOydfHOGYMiRa6maTDoEBERuakP9pyDIAC3dwxEdJBrL95ZFwYdIiIiN3RJX4ZNRy8CkG5vDsCgQ0RE5JY+2puGSrOAXuH+6N62mdjlNBkGHSIiIjdTUFKBLw9cAADMHCzd3hyAQYeIiMjtfLI/HWWVZtzSWosBUXUvsyQFDDpERERupNhowtr96QCAmYMiJb96AIMOERGRG/ky8QL0ZZVoF+CN4Z2DxC6nyTHoEBERuQmjyYzVv1kX75w2sB0Ucmn35gAMOkRERG5jw+FM5BiMCNJ6YHRsG7HLcQgGHSIiIjdQabbgvd3nAFh7czRKhcgVOQaDDhERkRvYkpSFzCtlCPBRY8JtoWKX4zAMOkRERBJntgh4d7d18c7H4trBU+0evTkAgw4REZHk/ZR8CamXS6DzVGFi77Zil+NQDDpEREQSJggC3vnF2psztV8YfDRKkStyLAYdIiIiCdt1Khd/ZhfBR6PElL5hYpfjcAw6REREEiUIAt6Ot/bmTOrTFn5eapErcjwGHSIiIon67WwejmUUwkMlx6P9w8UuRxQMOkRERBIkCALe2nUGADDhtlAE+GhErkgcDDpEREQSlJCaj4PpV6BWyjFjUITY5YiGQYeIiEiCVv5c1ZsTgpZaD5GrEQ+DDhERkcT8npqPxLQCqBXu3ZsDMOgQERFJTtXYnPt6BKOVzlPkasTFoENERCQhB9MLsP9cPlQKGWYOjhS7HNEx6BAREUlIVW/OuO7BaOPn3r05AIMOERGRZBw+fwW/nsmDUi7DzEHszQEYdIiIiCSjqjdnbLc2CPH3Erka58CgQ0REJAFHL1zBnpTLUMhleGJwlNjlOA0GHSIiIgl48+q8OWNi2yC0OXtzqjDoEBERubjD5wuwN+UylHIZnhzC3pxrMegQERG5uDd3/nWnFXtzamLQISIicmEH0grw21nrnVazOG/OdRh0iIiIXNibO1MAAPffFsI7rWrBoENEROSiEs7lIyHVOgsye3Nqx6BDRETkggRBwJs/W3tzJtwWylmQ68CgQ0RE5IL2n8vHgasrlM8c7N4rlNeHQYeIiMjFCIKA13ecBgA82CvU7Vcorw+DDhERkYvZffoyjlwohIdKjpmD2JtTHwYdIiIiF2KxCFh+tTdncp8wBGo9RK7IuTHoEBERuZDtJ7JxIssAH40S0wayN+dGGHSIiIhchNki4PWr8+Y80j8c/t5qkStyfgw6RERELuK7YxdxNrcYOk8VHosLF7scl8CgQ0RE5AIqzZbqNa2mDWwHrYdK5IpcA4MOERGRC1h/KBMXCkoR4KPBlL5hYpfjMhh0iIiInFx5pRlv/2LtzZk1OAJeaqXIFbkOBh0iIiInt+7387ikL0crnQce6BkqdjkuhUGHiIjIiRWVV+Ld3ecAAHNuj4KHSiFyRa6FQYeIiMiJrf41DQUlFWjXwhv3dgsWuxyXw6BDRETkpPKKjVj9ayoAYN6waCgV/NpuKB4xIiIiJ7Uq/ixKKsy4tY0OIzoHiV2OS2LQISIickKZV0rx+e8XAADzh3eATCYTuSLXxKBDRETkhFb8fAYVZgv6RjRH/6gAsctxWU4ZdDZs2IDZs2cjLi4OWq0WMpkMEydOrLVteno6ZDJZnY8JEyY4uHoiIqKbk5JThI1HMgEA/x7eQeRqXJtTzjj08ssv49ixY/Dx8UFwcDD+/PPPG76ma9euGD169HXbO3fu3AQVEhERNZ3l20/DIgDDbwlCTIif2OW4NKcMOm+++SaCg4MRGRmJPXv2YPDgwTd8TUxMDBYvXtz0xRERETWhQ+kF2HEyB3IZMO/O9mKX4/KcMujYEmyIiIikRhAEvPKT9SrG/T1CEBnoK3JFrs8pg05jZGVl4YMPPkB+fj6aN2+OPn36oEuXLmKXRUREZLMdJ3Nw+PwVeKjkmHsHe3PsQTJBZ+fOndi5c2eNbYMGDcLatWsRGnrjdUEMBkONP2s0Gmg0GrvWSEREVBeT2YLXtll7cx7tH46WWg+RK5IGp7zrqiG8vLywcOFCHD58GFeuXMGVK1eqx/Xs3r0bQ4cORUlJyQ33ExISAp1OV/145ZVXHFA9ERGR1TeHMnHucgmaeakwbWCE2OVIhsv36AQGBuKll16qsW3AgAHYsWMH+vfvj8TERKxevRpPPfVUvfvJyMiAVqut/jN7c4iIyFFKK0x48+cUAMDsIVHQeqhErkg6XL5Hpy5KpRKPPfYYAGDv3r03bK/Vams8GHSIiMhRPv41DZeLjAjx98RDvW883IJsJ9mgA1h7ewDYdOmKiIhIDPnFRnyw96+FOzVKhcgVSYukg05iYiIAoF27diJXQkREVLuVu86g2GhC5zZa3N2ltdjlSI7LB53ExERUVFRct33Pnj144403AKDO5SOIiIjEdDa3GJ8nWhfuXDCyI+RyLtxpb045GHnz5s3YvHkzACA7OxsAkJCQgClTpgAAAgICsHz5cgDA/PnzceLECQwaNAjBwcEAgOPHj2PXrl0AgCVLlqBv376OfQNEREQ2ePWnP2G2CLi9YyD6RnDhzqbglEEnKSkJa9eurbEtNTUVqanWa5ht27atDjqTJk3Cpk2bcPDgQfz000+orKxEy5Ytcf/99+OJJ55AXFycw+snIiK6kYRz+fj5VA4UchmeHdFR7HIkSyYIgiB2EWIyGAzQ6XTQ6/U1bi8nIiJqKhaLgHtW/YbkiwZM6t0WS0ZzAeqGsvX72+XH6BAREbmaLccuIvmiAT4aJZ66PUrsciSNQYeIiMiByivN+O+20wCAGYMiEODDeduaEoMOERGRA/1vXxqy9OVorfPAo/3DxS5H8hh0iIiIHORykRHvxp8DADwzPBoeKk4O2NQYdIiIiBzkjZ2nUWw0oUuwDqO6thG7HLfAoENEROQAJ7L0+OpgBgDghbs6cXJAB2HQISIiamKCIGDJ1pMQBOCuLq3QI8xf7JLcBoMOERFRE9txMge/pxZArZTj2REdxC7HrTDoEBERNSGjyYxlP54CAPwzrh2Cm3mJXJF7YdAhIiJqQmv3p+N8fila+GowY1CE2OW4HQYdIiKiJpJXbMTbu84CAP59ZzS8NU65xKSkMegQERE1kdd3nEaR0YTObbS4t1uw2OW4JQYdIiKiJnA886/byRfdfQtvJxcJgw4REZGdCYKAxd+fgCAAo2Ja4zbeTi4aBh0iIiI725KUhcPnr8BLrcBzIzqKXY5bY9AhIiKyoxKjCa/8ZL2dfNbgSATpPESuyL0x6BAREdnRqvizyDEYEervxdXJnQCDDhERkZ2czy/B6l/TAADP/6MjVyd3Agw6REREdrJk6ylUmC2IiwrAHZ1ail0OgUGHiIjILuJP5+LnUzlQymVYdHcnyGS8ndwZMOgQERHdpPJKMxZ/dwIAMLVfGCIDfUWuiKow6BAREd2kj/am4nx+KVpqNXjq9vZil0PXYNAhIiK6CRkFpVi127qe1YKRHeHD9aycCoMOERHRTViy9STKKy3o3c4f93RtLXY59DcMOkRERI0UfzoXO05aByC/NKozByA7IQYdIiKiRjCazHjx6gDkKX3D0L4lByA7IwYdIiKiRvhwTyrS80sR6KvBU7dHiV0O1YFBh4iIqIEu5JfinXjrAOT//KMjfD1UIldEdWHQISIiagBBELBwSzKMJgv6RTbnAGQnx6BDRETUAD8lZ2NPymWoFXIs4QBkp8egQ0REZKNiowkvfX8SADB9YDu0a+EjckV0Iww6RERENnpzZwqyDeUI9ffCzMGRYpdDNmDQISIissGJLD0+2Z8OAHhp1C3wUCnELYhswqBDRER0AxaLgOc3J8NsEfCPW1thUHSg2CWRjRh0iIiIbuDzAxdw9EIhvNUKLLyrk9jlUAM0euWxlJQU7Ny5E3v37kVGRgby8vLg6emJwMBAxMTEYPDgwRgyZAg8PDzsWS8REZFD5RjK8dpPfwIAnrkzGkE6fq+5EpkgCEJDXvDVV1/h3Xffxb59+wBY5xOodccyGfz8/DBlyhTMnj0bYWFhN11sUzAYDNDpdNDr9dBqtWKXQ0RETmbGusP4KTkbXUP8sHFGXyjkvJ3cGdj6/W3zpav4+HjExsbiwQcfxIkTJzBlyhR8+OGHSEpKQnZ2NioqKqDX65Gamooff/wRCxcuRHR0NN5880107NgR8+fPh8FgsMubIyIicoSdJ3PwU3I2FHIZXhlzK0OOC7L50tXQoUPRrVs3fPPNN7jnnnugVquva+Pr6wtfX1+EhYVh+PDhWLx4Mc6cOYP3338f77zzDnx8fLBw4UK7vgEiIqKmUGw04YUtyQCAx+LC0ak1e/1dkc2XrjZt2oQxY8Y0+gdlZ2cjPT0dvXv3bvQ+mgIvXRERUW1e/P4E1uxLR4i/J3bMGQhPNW8ndya2fn/b3KNzMyEHAIKCghAUFHRT+yAiInKEYxmFWHt1zpylo29lyHFhTX57udlsbuofQUREZDeVZgvmf/sHLAIwOqY1BrRvIXZJdBMaHXRmzJgBo9FYb5vz588jLi6usT+CiIjI4T7Ycw5/ZhehmZcKz3POHJfX6KDzwQcfoFevXjh9+nStz2/cuBGxsbFITExsdHFERESOdDa3CG/tOgsAWHT3LQjw0YhcEd2sRged//znP0hOTkaPHj2wdu3a6u0VFRWYNWsW7rvvPsjlcmzatMkuhRIRETUli0XA/G+Po8JsweDoFhgV01rsksgOGh10lixZgu3bt8PHxwePPPIIJk2ahEOHDqFXr15477330LdvXyQlJeGee+6xZ71ERERN4rPfz+Pw+SvwVivw8phbIZNxzhwpuKnByEOHDsWxY8dw++2344svvkCvXr2QnJyM559/Hnv27EFwcLC96iQiImoymVdK8X/brMs8PDuiA9r4eYpcEdlLo9e6quLj44MWLVpULwWh0+kwcOBAyOVcL5SIiJyfIAhYsCkZpRVm3BbWDA/1ait2SWRHN5VGjh07hm7duuHLL7/EnXfeiffffx8VFRW488478fzzz8NisdirTiIioiax4XAm9qZchlopx6v3doGcyzxISqODzqpVq9CnTx+kpqZi2bJl+Omnn/DPf/4Thw8fRpcuXfDKK69g4MCByMzMtGe9REREdpOtL8dLW08CAObcHoWIFj4iV0T21uDVy6vI5XKEhobiyy+/RJ8+fWo8V1FRgX/9619YtWoV/P39kZeXZ5dimwKXgCAick+CIODRtYfwy5+56Bqsw7cz+kKp4LALV2H31cv/btSoUTh69Oh1IQcA1Go13n77bWzcuBGNzFFERERNauORi/jlz1yoFXL8976uDDkS1ejByLbMjzN69Gh07969sT+CiIioSeQYyvHi9ycAAE/dHoX2LX1FroiaSpPH15CQkAa/ZsOGDZg9ezbi4uKg1Wohk8kwceLEel+zf/9+jBw5Ev7+/vDy8kKXLl2wYsUKrrVFREQ1CIKABRuPw1BuQpdgHaYNaCd2SdSEbA46WVlZN/3DLl26ZFO7l19+Ge+88w6SkpLQpk2bG7bfsmULBgwYgL1792LMmDGYNWsWKioqMHfuXEyYMOFmyyYiIgnZnHQRu6ouWY3jJSups/lvNyIiAvPmzUNOTk6DfoAgCNiyZQtiY2Px0Ucf2fSaN998EykpKTAYDHjvvffqbWswGPDYY49BoVBg9+7d+Pjjj/Hf//4XSUlJ6NOnDzZs2ICvvvqqQTUTEZE0ZevLsWjLX5esooN4yUrqbA46zzzzDN577z2EhITgnnvuwbp165Camlpr2+LiYvzyyy+YP38+QkJCMHbsWHh4eGDs2LE2/azBgwcjKirKpum3169fj7y8PDzwwAPo0aNH9XYPDw+8/PLLAIB3333Xpp9LRETSJQgC/v3tHzCUm9CVl6zchs2DkV966SU8/vjjWLJkCb744gv88MMPAKwzIQcGBqJZs2YoLy9Hfn4+Ll26BIvFAkEQEBsbi+XLlzfZJaT4+HgAwPDhw697bsCAAfDy8kJCQgKMRiM0Gq5CS0Tkrr44cAF7Uy5Do5Tj9ftjeMnKTTTorquQkBB8+OGHWL58Ob744gvs3LkT+/fvR0pKSnUbtVqNmJgYDBo0CPfeey969+5t96Kvdfr0aQBAVFTUdc8plUqEh4fjxIkTSE1NRceOHZu0FiIick7n80uw9IdTAIB/D++AyEBODOgubA46b731Fnr37o2ePXtCq9Vi+vTpmD59OgCgsrIS+fn58PT0hE6na7Jia6PX6wGgzp9btb2wsLDe/RgMhhp/1mg07AEiIpIAs0XAvPXHUFphRq9wf0ztGyZ2SeRANvfbzZkzB9u2bav+s0KhwJIlSwAAKpUKQUFBDg85tqiasPBG431CQkKg0+mqH6+88oojyiMioib2v9/ScDD9CrzVCiy/ryvXsnIzNvfoeHp6wmg0Vv9ZEASnmPW4KlxV9ez8XVVPzY1CWEZGRo0ppNmbQ0Tk+lJyivDfHdYhDgvv6oQQfy+RKyJHs7lHJzw8HNu3b69xe7ktd0U1tejoaACoMU6oislkQlpaGpRKJdq1q390vVarrfFg0CEicm1GkxlPfZWECpMFg6NbYPxtDZ/AllyfzUFnxowZOHLkCFq3bg2FQgEAWLx4MRQKRb0PpbLRq0zYZMiQIQBQ47Jalb1796K0tBR9+/ZlcCEicjNv7EzBqUsG+Hur8X/jujjFf87J8WxOIbNmzUKLFi3w/fffIysrC/Hx8QgNDUVYWFgTlndj48aNw/z58/HVV19h9uzZ1XPplJeX4/nnnwdgDWlEROQ+Es7l48O91rneXhl7KwJ9PUSuiMQiExo50EYul2Px4sV44YUX7F0TNm/ejM2bNwMAsrOzsX37drRr1w5xcXEAgICAACxfvrxG+3HjxsHDwwMTJkyAv78/vvvuO5w+fRrjxo3DN998U2eSt3WZdyIicg36skqMWLEXWfpyjO8Rgv8b10XskqgJ2Pr93ejrSosWLcKgQYMa+/J6JSUlYe3atTW2paamVs/E3LZt2xpBZ/To0dizZw+WLl2Kb7/9FuXl5YiMjMQbb7yBJ598kt2VRERu5IUtycjSl6Ntcy+8cHcnscshkTW6R0cq2KNDRCQdW5Iu4qmvkqCQy7B+eh90C20mdknURGz9/ub810REJAkZBaV4fnMyAGDW4EiGHALAoENERBJgMlsw9+skFJWbEBPih9lDIsUuiZwEgw4REbm8t385i0Pnr8BHo8RbE2Kh4oKddBXPBCIicmkH0grw9i9nAABLx3RGaHPOfkx/YdAhIiKXpS+txJyvjsIiAGNj22BUTBuxSyInw6BDREQuSRAELNh0vPpW8pdGdxa7JHJCDDpEROSSvj6YgR+OX4JSLsPKCbHw0TTtkkPkmhh0iIjI5ZzOLsLi708AAP41LBoxIX7iFkROi0GHiIhcSmmFCU98cQTllRYMaN8C0wa0E7skcmIMOkRE5FIWf3cCZ3KLEeirwRv3d4VczmV+qG4MOkRE5DI2Hc3EN4cyIZcBKyfEIsBHI3ZJ5OQYdIiIyCWkXi7GfzZZl3h4cmgU+kQ0F7kicgUMOkRE5PTKK82Y9cVRlFaY0budP2YPiRK7JHIRDDpEROT0Fn93AqcuGdDcW42VE2Kh4LgcshGDDhERObUNhzPx1cEMyK6Oy2mp9RC7JHIhDDpEROS0/sw24PnNxwEAc4a2R/+oAJErIlfDoENERE6p2GjCzM//mi9n9pBIsUsiF8SgQ0RETkcQBMz/9g+kXi5BK50HVoyP4Xw51CgMOkRE5HTW7k/HD39Y17F658Fu8PdWi10SuSgGHSIicioH0wvw8g+nAADPjeyI7m2biVwRuTIGHSIichq5hnLM/PwITBYBd3VphUf6hYldErk4Bh0iInIKlWYLZn1xBJeLjGjf0gf/d28XyGQcl0M3h0GHiIicwtIfTuFg+hX4apT4YFIPeGuUYpdEEsCgQ0REott0NBOf7E8HALwxPgbhAd7iFkSSwaBDRESiOpGlx3MbrZMCPjE4End0ailyRSQlDDpERCSa/GIj/vnpYZRXWjCwfQvMvaO92CWRxDDoEBGRKCrNFsz8/AguFpYhrLkX3uJindQEGHSIiEgUS7aeRGJaAbzVCnz0cA/ovFRil0QSxKBDREQO9/XBC/g04TwAYMWEWES19BW5IpIqBh0iInKow+ev4PnNyQCAp+9oz8HH1KQYdIiIyGEuFpZh2meHUGkWMPyWIDwxmCuSU9Ni0CEiIocoMZrw2NpDyCuuQMdWWrx+f1euSE5NjkGHiIianMUiYO7XSTh1yYAAHzVWT+bMx+QYDDpERNTkXt95GjtO5kCtkOODST3Qxs9T7JLITTDoEBFRk9p0NBOr4s8BAP5v3K3o3raZyBWRO2HQISKiJnMovQDzv7Uu7zBzUATGxAaLXBG5GwYdIiJqEul5JXj800OoMFkwrFNLzBsWLXZJ5IYYdIiIyO4KSyvwyCcHcaW0El2CdVgxIYZ3WJEoGHSIiMiujCYz/vnZYaTmlaCNnydWT+4BLzXvsCJxMOgQEZHdCIKA5749jgNpBfDVKPG/Kbch0NdD7LLIjTHoEBGR3az4+Qw2Hr0IhVyGVQ91Q3QQ17AicTHoEBGRXXx98AJW7joDAFgyqjMGtG8hckVEDDpERGQH8X/mYsEm60KdswZH4MFeoSJXRGTFoENERDflj8xCzPz8CMwWAWO7teFt5ORUGHSIiKjRLuSX4pFPDqKs0oz+kQF4dWwXyGS8jZycB4MOERE1SkFJBSavOYC84gp0aqXFexO7Qa3k1wo5F56RRETUYMVGE6asOYC0q3PlrJl6G3w9VGKXRXQdBh0iImoQo8mM6Z8dxh+ZejTzUmHtI7ehpZZz5ZBzYtAhIiKbmS0C/vXNMfx2Ng9eagXWTO2JyEDOlUPOi0GHiIhsIggCXvz+BLb+cQkqhQwfTOqOmBA/scsiqheDDhER2WTlrjP4NOE8ZDLgjftjEBfFCQHJ+THoEBHRDX38WxpW/Gyd9Xjx3bfg7q6tRa6IyDYMOkREVK+vD17Akq0nAQBzb2+PyX3DxC2IqAEYdIiIqE5b/8jCsxuPAwAejwvHk0MjRa6IqGEkE3TCwsIgk8lqfQQFBYldHhGRy4n/MxdzvkqCIAAP9AzBgpEdOesxuRyl2AXYk06nw5w5c67b7uPj4/hiiIhc2P5zeZi+7jBMFgH3dG2Nl0ffypBDLklSQcfPzw+LFy8WuwwiIpd2IK0Aj35yCEaTBbd3DMTr93eFQs6QQ65JMpeuiIjo5h0+fwVT1xxAWaUZcVEBeOfBblAp+FVBrktSPTpGoxHr1q3DhQsX4O3tjS5dumDAgAFQKBRil0ZE5PT+yCzElP8dQEmFGX0jmuOjh3vAQ8XPT3Jtkgo62dnZmDRpUo1t4eHhWLNmDQYOHChSVUREzi/5oh4TVyeiyGhCzzB/rJ7MkEPSIJn+yKlTp2LXrl3Izs5GSUkJjh8/jmnTpiE9PR0jRozAsWPH6n29wWCo8TAajQ6qnIhIXCey9Jj0cSIM5SZ0C/XD/6beBi+1pP4fTG5MJgiCIHYRTWnevHl4/fXXMXr0aGzatOm65w0GA3Q63XXbFy1axIHNRCR5yRf1mPhxIgpLK9E1WIfPHusFrYdK7LKIbqjq+1uv10Or1dbZTvJB5+zZs4iKioK/vz/y8/Ove77qQGVkZNQ4UBqNBhqNxpGlEhE5VPJFPR5anQh9WSViQvzw6aM9GXLIZdgadCTfNxkYGAgAKCkpqbedVqut90AREUnJ8Uw9Hlr9OwzlJsSG+mHtIww5JE2SGaNTl8TERABAu3btRK6EiMg5HMsorA453UL98ClDDkmYJILOiRMnUFBQcN32jIwMPPHEEwCAiRMnOrosIiKncyCtAA+ttg487tG2GT59tBd8GXJIwiRx6Wr9+vV49dVXMXjwYISHh8PX1xepqanYunUrysvLMXLkSMybN0/sMomIRPXbmTw89ulBlFda0LudP1ZPvg0+Gkl8DRDVSRJn+ODBg3H69GkcPXoUCQkJKCkpgZ+fH/r3749JkyZh0qRJXKOFiNzarlM5mPH5EVSYLBjYvgU+mNSd8+SQW5D8XVc3YuuobSIiV/Xj8Ut48sujMFkE3HlLS7z1QCw0SoYccm2864qIiPDNwQw8u/EPWATgnq6t8fr9Xbl2FbkVBh0iIon6cO85LPvxTwDAhNtCsHTMrVyFnNwOgw4RkcQIgoDXtp/Ge7vPAQCmD4zA/OHRHKtIbolBh4hIQswWAc9vPo4vD2QAAJ4d0QHTB0aIXBWReBh0iIgkorzSjLlfJ+Gn5GzIZcCyMbdiQs9QscsiEhWDDhGRBOhLK/H4Z4dwIK0AaoUcKybEYOStrcQui0h0DDpERC7ukr4Mk/93ACk5xfDVKPHBw93RNyJA7LKInAKDDhGRC0vJKcLk/x3AJX05An01WPtIT3RsxTnBiKow6BARuaiEc/mY9tkhGMpNiGjhjbWP9ERwMy+xyyJyKgw6REQu6NvDmXh24x+oNAvo3rYZVj/cA8281WKXReR0GHSIiFyIIAhY8fMZrNx1BgDwjy6t8Pp9XbluFVEdGHSIiFyE0WTGc98ex8ajFwEAMwZF4Jlh0ZBztmOiOjHoEBG5gIKSCkxfdxgH0gqgkMvw8ujOeIBz5BDdEIMOEZGTS8kpwqNrDyKjoAw+GiXefagbBrRvIXZZRC6BQYeIyIn98mcOnvwyCcVGE0L9vfDx5B6IaukrdllELoNBh4jICQmCgI9/S8PSH09BEIBe4f54f2J33llF1EAMOkRETqa80owFm45j4xHroOMHeobgxXs6Q62Ui1wZketh0CEiciJZhWWY9tlhHL+oh0Iuw39GdsTUfmGQyXhnFVFjMOgQETmJxNR8zPz8CPJLKtDMS4VVD3ZD30iuWUV0Mxh0iIhEJggCPk04jyVbT8JkEdCplRYfTOqOEH8u50B0sxh0iIhEVGI04bmNx/HdsSwAwD1dW+P/7u0CTzVnOiayBwYdIiKRnM0txox1h3EmtxgKuQzPjeiAR/uHczwOkR0x6BARiWDrH1mYv+EPlFSYEeirwaqHuuG2MH+xyyKSHAYdIiIHKq8045UfT2FtwnkAQO92/njrgVgE+nqIXBmRNDHoEBE5SFpeCZ744ghOZBkAANMGtsMzw6KhVHB+HKKmwqBDROQAW5IuYsHG4yipMKOZlwpv3B+DwR0CxS6LSPIYdIiImlBphQkvfX8SXx3MAAD0DPPHygdi0ErnKXJlRO6BQYeIqIkkX9Tjya+OIvVyCWQy4InBkXhqaBQvVRE5EIMOEZGdWSwCPvo1Fct3nEalWUBLrQZv3h/DWY6JRMCgQ0RkR9n6cvxrfRL2nc0HANx5S0u8OrYLVx0nEgmDDhGRHQiCgO+OZWHh5mQYyk3wVCmw6O5OGH9bCCcAJBIRgw4R0U0qKKnAws3J+OH4JQBA12Ad3hgfg4gWPiJXRkQMOkREN+GXP3Mw/9vjuFxkhFIuw5NDozBzUAQHHBM5CQYdIqJGKCytwEvfn8TGoxcBAFGBPnjj/hjcGqwTuTIiuhaDDhFRA20/kY3nNyfjcpERMhnwaL9wzLszGh4qrjhO5GwYdIiIbJRfbMSi705g6x/WsTgRLbzx3/u6oltoM5ErI6K6MOgQEd2AIAhYfzgTy348hcLSSijkMkwb0A5PDo1iLw6Rk2PQISKqR+rlYvxnUzISUq3z4nRspcVr93bhWBwiF8GgQ0RUC6PJjA/3pOLt+LOoMFngoZJj7u3t8Uj/cKh4RxWRy2DQISL6m1/PXMaiLSeQmlcCAIiLCsDS0bcitLmXyJURUUMx6BARXXVJX4aXt56qnvgvwEeDhXd1xD1dW3N2YyIXxaBDRG7PaDJjzb50vLXrDEorzJDLgMl9wzD3jvbQeqjELo+IbgKDDhG5LUEQ8POpXLz8w0mczy8FAHRv2wxLRnVGp9ZakasjIntg0CEit5SSU4QlW0/i1zN5AIBAXw3mD++AMbFtIJfzMhWRVDDoEJFbuVxkxIqfU/DVwQyYLQLUCjkeiwvHzMGR8NHwI5FIavivmojcQmmFCat/TcMHe86hpMIMABjWqSWe/0cn3k1FJGEMOkQkaSazBd8eycQbO1OQYzACALoG67BgZEf0atdc5OqIqKkx6BCRJFksAn5KzsbrO05Xz4cT3MwT/x7eAXfd2orjcIjcBIMOEUmKIAjYeyYP/93+J5IvGgAAzbxUmDU4EpP6tIVGybWpiNwJgw4RSYIgCNh3Nh8rfk7BofNXAADeagUei2uHx+LC4cv5cIjcEoMOEbk0QRCw/5w14BxMtwYctVKOSb3bYuagCDT30YhcIRGJiUGHiFySIAjYk3IZq+LP1gg4D/YMxYxBEWip9RC5QiJyBgw6RORSLBYB205kY1X8WZzIso7BqQo40wdGIEjHgENEf2HQISKXYDSZseVoFj7Yew7nLlvvovJUKfBQr1A8FteOAYeIaiWpoJOZmYkXXngB27ZtQ35+Plq1aoXRo0dj0aJFaNasmdjlEVEj6EsrsS7xPD7Zn47LRdZ5cLQeSkzpG4Yp/cLh760WuUIicmaSCTrnzp1D3759kZubi1GjRqFDhw44cOAAVq5ciW3btmHfvn1o3pyTgxG5ivS8EnyyPx3fHMpA6dWZjIO0HpjaLwwP9grlXVREZBPJBJ2ZM2ciNzcXb731FmbPnl29/emnn8abb76J//znP3j//fdFrJCIAABmM/Drr8ClS0CrVkBcHKCwzm0jCAJ+O5uHNfvSEX86F4JgfUmHIF/8c0A73NWlNdRKuYjFE5GrkQlC1UeJ6zp37hwiIyMRHh6Os2fPQi7/64OwqKgIrVq1gsViQW5uLnx8fGq81mAwQKfTQa/XQ6vVOrp0IveycSPw1FNAZuZf24KDUfrf17GhbU98mnAeZ3OLq58a0iEQU/qGIS4qADIZZzImor/Y+v0tiR6d+Ph4AMCwYcNqhBwA8PX1Rb9+/bBjxw4kJiZi6NChYpRIRBs3AuPGAX/7v5WQeREeD4zHvtELcDa6L3w0SozrHozJfcMQHuAtUrFEJBWSCDqnT58GAERFRdX6fFRUFHbs2IGUlJQ6g05JSQkUiuunhlcoFPDw8KjRri5yuRyenp6NaltaWoq6OtdkMhm8vLwa1basrAwWi6XOOry9vRvVtry8HGaz2S5tvby8qv+3bjQaYTKZ7NLW09OzOvhWVFSgsrLSLm09PDyqz5WGtK2srERFRUWdbTUaDZRKZYPbmkwmGI3GOtuq1WqoVKoGtzWbzSgvL6+zrUqlglqttq2tXA71U09dF3IAQAYBAoAl8R+hx4wJGNu7HZprreePxWJBWVlZnftVKpXQaKwTAgqCgNLSUru0bci/e35G1N6WnxH8jGjQZ8Q1bW/07/7atjYRJODxxx8XAAgfffRRrc8vWLBAACAsW7bsuuf0er0AoM7HyJEja7T38vKqs+3AgQNrtA0ICKizbY8ePWq0bdu2bZ1tO3XqVKNtp06d6mzbtm3bGm179OhRZ9uAgIAabQcOHFhnWy8vrxptR44cWe9xu9a4cePqbVtcXFzddvLkyfW2zc3NrW47c+bMetumpaVVt503b169bZOTk6vbLlq0qN62Bw4cqG772muv1ds2Pj6+uu0777xTb9utW7dWt12zZk29bb/55pvqtt988029bdesWVPdduvWrfW2feedd6rbxsfH19v2tddeq2574MCBetv+7+GHBQG44WMgIMybN696v2lpafXud+bMmdVtc3Nz6207efLk6rbFxcX1th03blyNc7i+tvyMsD74GfHXg58R1kdDPiMWLVpU3TY5ObnetlWfEVXf33q9XqiPW4zqE67+z4bX+InEceRImk3tWjVxHUTkfiQxGPmZZ57B8uXLsXz5cvzrX/+67vknnngCq1atwrvvvosZM2bUeK5qMNPp06fh6+tbvV2j0UCj0bBbuo627JZmt3Rd3dL5xUbsOJmD75IuIilDDwDoc/EUvv5mYZ37qlL2449QDB1qcxc2L11Z8TOicW35GWHlqpeu3GowcnR0NAAgJSWl1ufPnDkDAGjfvn2d+wgKCrLprqtr/3Has+21Hzz2bHvtB6U92177wW7PtlUB095t1Wq1zdd0m6qtSqWq/oCwZ1ulUln9gWbPtgqFwuZzuLjCgh2nCvD9H5ew72wezBbrl6xS44H+US1w70O3wbLvA8izLqK2cTqQyYDgYHgOG1Z9qzlg/bK3tQaZTNYkbYGm+3fPz4iGt+VnRMPbOsNnREPaNuTfvS0kEXQGDx4MANixYwcsFst1t5fv27cPnp6e6N27t1glEknOlZIK/HwqB9uSs/HrmTxUmP/6n37nNlqM6toGo2JaI7Bqcc23VlrvupLJaoadqkvKK1bUCDlERPYgiaATERGBYcOGYceOHVi1alWNCQMXLVqEkpISTJs2za4JkcgdZevLsfNUDrYnZyMhNb+65wYA2rf0wd1dWuOurq1rvy187Fhgw4Za59HBihXW54mI7EwSY3SA65eA6NixIxITExEfH4/27dtj//79tS4BwQkDieomCAJOZBnw86kc/HwqB8kXDTWe79hKi+G3BGHErUFo39K3jr38TT0zIxMR2crW72/JBB0AyMjIqHNRT39//1pfw6BDVJO+tBK/nc3D7tO52JNyGblFfw1MlMmA2BA/DLslCMNvCUIYJ/QjIpG4ZdBpDAYdcncVJguSMgqx72wefjubh6MXruCaK1LwVCkwoH0AhnZsiSEdAhHgY9vgTiKipuRWd10Rke1MZgtOZBmQmJaP/efycSCtoHp18CqRgT4Y1L4FBka3wG1h/vBQ8dISEbkmBh0iiSuvNOP4RT0OphcgMbUAh89fQbGx5twi/t5q9I1ojn6RAYiLCkBwM9tvTyYicmYMOkQSIggCMq+U4VhmIY6cL8ThC1dwMkuPSnPNK9RaDyV6hvujV7g13HQI8oVczpnDiUh6GHSIXJQgCMg2lOPERQOSs/Q4llGIY5l6FJRcP1tqC18Nuoc2s4abdv7oEKSFgsGGiNwAg04T+en4JSSmFaCFrwYtfDQI8FWjhY8HAnzVaO6tgVrpFsuMkZ0YTWacyy3B6RwD/swuwsksA05mGZBfS6hRKWToEKRFTIgfeoQ1Q7fQZghu5sm13ojILTHoNJHfzubh88QLdT7v56VCgI8GAT7qq79q0MK35p8DfDVo7q3mQFA3UlZhxrnLxdZHbjHOXi5GSk4x0vJKakzOV0UhlyGyhQ9uaa1F1xA/dAnWoWMrLc8ZIqKrGHSayJAOgdB6qnC5yIi8YuvjcpER+cUVMFkEFJZWorC0Emdzb7wvX42yOvQ091GjuY8GAd7WX/2rtnlbf9/MSwWlgr1FzkxfWomMK6XIKCjFhYJSpOeXIC2vBOfzS3FJX/eid1oPJToEaREd5IuOrbS4pbX19ww1RER14zw6Dp5Hx2IRUFhWaQ0/RUZcvhqA8oorqgNRXrE1EOUVG68bRHojMhmg81RZA5C3Gs28rj681fD3VsHv6p/9vFRo5mX9s85TBRXDkV0UG03INZQjt8iIbH05svRluFRYjkv6MlwsLEfmlVIUlde9mjIANPNSITLQB5GBPoho4YOIQB90CPJFkNaDl5+IiK7iPDpOSi6Xwd9bDX9v9Q2nzBcEAYYyEy4XG5FfbER+SQXyi/8KRQUlFdXb8ksqUFhaCUFAdW9R6uUSm+vy0Sih81TVeGg9ldB6qKD1VMHXQwlfj6pflfDVqODjoYS3RgEfjRKeKoXkvoRNZguKjSYYyky4UlqBwrJKFJZaj3P1cS+uQH6J9e8k11COkr/NR1OXAB81gpt5IcTfC+HNvRAW4G19NPeGv7dtKx0TEdGNMeg4MZlMBp2XCrqr/8O/EZPZgsKySly5GoAKSipwpbQCV0oqUFBSiYISo/X50r++sPVllQCsPRHFRhMuFpY1qla5DPBWK+GlUcBLrYSXWgFvtRIalRyeKgU81Qp4KBXwUMmhUSmgUcqhUcqhVsqhUlgfaoUcKqUMSrkcCrkMCrkMSrkMcrkMcpkMMlh7rORXA5VFECAIgABrKLQIAkxmAWaLAPPV31eYLKgwW1BptqDCZEF5pQXlJjPKK62PsgozSirMKK0wodhoRqnRhKJyE4rKK20OLX/no1Ei0FeDQK0GrXWeaOXngVY6T7T280BwMy8EN/OEl5r/9IiIHIGfthKiVMirBzJH2fgas0WAocwaeKp6LPRllTCUm2Aoq4ShvPLqr38FgKJyE4rLTSgxmlBcYYIgABYBKDKaUGQ0ATDe8Oe6Eg+VHM2uXuKruuznf3WMVNXgcX9vNVpqPRDoq4G3hv+siIicBT+R3ZxCLkMzb+sYnsYQBAGlFWaUGE0oufprWeXVXyvMKKs0o7zSgrJKM8oqTDCaLNZHpbn695XmqoeASrOlZq+MRYDZYqkOU38fUia7pqdHebUX6K/eoKoeIxnUSgVUChk0SgU8VdaeJQ+V9ffeGuslOC+1Et5qBXw8rJfsqi7XcSoAIiLXxaBDN0Umk10NCjyViIjI+fC/qkRERCRZDDpEREQkWQw6REREJFkMOkRERCRZDDpEREQkWQw6REREJFkMOkRERCRZDDpEREQkWQw6REREJFkMOkRERCRZDDpNxGg0YvHixTAapbXAZVPh8bIdj5XteKxsx2NlOx4r2znDsZIJf18l0c0YDAbodDro9XpotVqn369U8XjZjsfKdjxWtuOxsh2Ple2a8ljZum/26BAREZFkMegQERGRZCnFLkBsVVfuDAaDXfdbtT9771eqeLxsx2NlOx4r2/FY2Y7HynZNeayq9nmjEThuP0YnMzMTISEhYpdBREREjZCRkYHg4OA6n3f7oGOxWJCVlQVfX1/IZDKxyyEiIiIbCIKAoqIitG7dGnJ53SNx3D7oEBERkXRxMDIRERFJFoMOERERSRaDTgNkZmbikUceQevWraHRaBAWFoY5c+bgypUrouzHmdnjPYaFhUEmk9X6CAoKasLqHWfDhg2YPXs24uLioNVqIZPJMHHixEbtS+rnlb2OlTucV/n5+Vi9ejXGjBmDyMhIeHp6QqfToX///vj4449hsVgatD8pn1v2PFbucG7Nnz8fQ4cORUhICDw9PeHv74/Y2Fi8+OKLyM/Pb9C+HHVecYyOjc6dO4e+ffsiNzcXo0aNQocOHXDgwAHEx8cjOjoa+/btQ/PmzR22H2dmr/cYFhaGwsJCzJkz57rnfHx8MG/evCao3rFiYmJw7Ngx+Pj4IDg4GH/++SceeughrFu3rkH7cYfzyl7Hyh3Oq/fffx8zZsxAUFAQhgwZgtDQUOTk5GDjxo3Q6/UYO3YsNmzYYNMNGFI/t+x5rNzh3FKr1ejWrRs6deqEwMBAlJSU4Pfff8ehQ4fQunVrJCQkIDQ09Ib7ceh5JZBNhg0bJgAQ3nrrrRrb586dKwAQpk2b5tD9ODN7vce2bdsKbdu2bYIKnccvv/wipKSkCBaLRYiPjxcACA899FCD9+MO55W9jpU7nFe7du0SNm/eLJhMphrbL126JISEhAgAhPXr19u0L6mfW/Y8Vu5wbpWVldW6fcGCBQIAYfr06Tbtx5HnFYOODc6ePSsAEMLDwwWz2VzjOYPBIHh7ewuenp5CUVGRQ/bjzOz5Ht3hQ+Najf3ydofz6u8YdBpv6dKlAgBh1qxZN2zrjufWtRpyrATBvc+tpKQkAYBwxx133LCto88rjtGxQXx8PABg2LBh192r7+vri379+qGsrAyJiYkO2Y8zs/d7NBqNWLduHZYtW4aVK1ciPj4eZrPZ7nW7Mnc4r+zNnc8rtVoNAFCpVDds6+7nVkOOVRV3Pbe+//57AECXLl1u2NbR55XbLwFhi9OnTwMAoqKian0+KioKO3bsQEpKCoYOHdrk+3Fm9n6P2dnZmDRpUo1t4eHhWLNmDQYOHHjzBUuAO5xX9uau55XJZMLatWsBAMOHD79he3c+txp6rKq4y7m1fPlyFBcXQ6/X49ChQ/jtt98QGxuL55577oavdfR5xR4dG+j1egCATqer9fmq7YWFhQ7ZjzOz53ucOnUqdu3ahezsbJSUlOD48eOYNm0a0tPTMWLECBw7dsxudbsydziv7Mmdz6tnn30WycnJGDFiBO68884btnfnc6uhxwpwr3Nr+fLlePHFF7FixQr89ttvGDFiBLZt22bTAGJHn1cMOnYgXL1x7WaXkLDXfpxZQ97jokWLMGTIELRs2RJeXl7o3Lkz3n//fTz99NMoKyvD4sWLm7haaXCH86oh3PW8WrFiBV5//XVER0fj008/tcs+pXpuNfZYudO5lZ2dDUEQkJ2djY0bN+LcuXOIiYnBkSNHbnrf9j6vGHRsUJUuq1Lo31WtoFpXOrX3fpyZI97j9OnTAQB79+5t9D6kxB3OK0eQ8nm1cuVKzJ07Fx07dsTu3bsREBBg0+vc8dxq7LGqj5TPrZYtW2LMmDHYuXMn8vPz8fDDD9/wNY4+rxh0bBAdHQ0ASElJqfX5M2fOAADat2/vkP04M0e8x8DAQABASUlJo/chJe5wXjmCVM+r5cuXY86cOejcuTN2797doInr3O3cupljVR+pnlvXCg0NRadOnXDixAnk5eXV29bh55Vd7t2SuKpb4cLCwuq9Fa64uNgh+3FmjniPO3bsEAAIHTt2vNlyncrN3l4u5fPq727m9vK6SPG8WrZsmQBAiImJES5fvtzg17vTuXWzx6o+Ujy3ahMYGCgAEAoKCupt5+jzikHHRg2Z3KiiokI4deqUcPbs2Zvaj6uyx7FKTk4W8vPzr9v3hQsXhPbt2wsAhKVLlzbNGxDJjb683f28ulZjj5U7nVcvvfSSAEDo3r17re/5Wu5+btnjWLnDuXXq1Cnh0qVL1203m83VEwb27du3eruznFdcAsJGf5+uumPHjkhMTER8fDzat2+P/fv3V482T09PR3h4ONq2bYv09PRG78dV2eNYLV68GK+++ioGDx6M8PBw+Pr6IjU1FVu3bkV5eTlGjhyJTZs2Vc9z4ao2b96MzZs3A7AO7tu+fTvatWuHuLg4AEBAQACWL18OgOeVPY6Vu5xXa9euxZQpU6BQKDB79uxaxzqEhYVhypQpANz73LLXsXKHc2vFihV45plnMGDAAERERKB58+bIycnBnj17kJqaiqCgIOzatQudOnUC4ETnld0ikxu4cOGCMGXKFCEoKEhQqVRCaGio8OSTT16X4tPS0gQAdc6Qaet+XNnNHqvdu3cLEyZMEKKjowWdTicolUohICBAuP3224W1a9cKFovFge+m6SxatEgAUOfj2uPi7ueVPY4Vz6u/HgMHDqxu787nlr2OlTucW8ePHxdmzpwpdO3aVWjevLmgUCgErVYr9OjRQ1i0aJHTfheyR4eIiIgki3ddERERkWQx6BAREZFkMegQERGRZDHoEBERkWQx6BAREZFkMegQERGRZDHoEBERkWQx6BAREZFkMegQERGRZDHoEBERkWQx6BAREZFkMegQERGRZDHoEBERkWQx6BCRpIwePRoymQxvv/32dc8tXLgQMpkM06ZNE6EyIhKDTBAEQewiiIjspaCgALGxscjJyUFCQgJiY2MBALt27cKwYcPQqVMnHDhwAJ6eniJXSkSOwKBDRJKzf/9+DBw4EOHh4Thy5AhKS0vRtWtXGAwGHDx4EJ06dRK7RCJyEF66IiLJ6du3L5YsWYIzZ85g2rRpmDhxIrKzs/H2228z5BC5GfboEJEkCYKAESNGYPv27QCABx54AF988YXIVRGRo7FHh4gkSSaTYcyYMdV/njNnjnjFEJFo2KNDRJJ05swZdOvWDSqVCnq9Hp07d0ZiYiI8PDzELo2IHIg9OkQkOUajEePHj0dJSQm+/vprPPfcc/jjjz8wd+5csUsjIgdj0CEiyZk3bx6OHj2K+fPn44477sCLL76Ifv364f3338eGDRvELo+IHIiXrohIUjZv3owxY8agT58+2Lt3L5RKJQAgIyMDMTExMJvNSEpKQlhYmLiFEpFDMOgQkWRcuHABMTExEAQBSUlJaNu2bY3nt2zZgtGjR6NXr1749ddfoVKpRKqUiByFQYeIiIgki2N0iIiISLIYdIiIiEiyGHSIiIhIshh0iIiISLIYdIiIiEiyGHSIiIhIshh0iIiISLIYdIiIiEiyGHSIiIhIshh0iIiISLIYdIiIiEiyGHSIiIhIshh0iIiISLL+H/+oKMLd8oqDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.\n",
    "b = 3.\n",
    "print(\"Solving the equation x^3 - x - 1 = 0 on an interval (\", a, \",\", b, \") using the false position method\")\n",
    "xroot = falseposition_method(func2, a, b, accuracy)\n",
    "print(\"The solution is x = \", xroot, \"obtained after \", last_falseposition_iterations, \" iterations\")\n",
    "\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func2(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "last_secant_iterations = 0\n",
    "secant_verbose = True\n",
    "\n",
    "def secant_method(\n",
    "    f,                    # The function whose root we are trying to find\n",
    "    a,                    # The left boundary\n",
    "    b,                    # The right boundary\n",
    "    tolerance = 1.e-10,   # The desired accuracy of the solution\n",
    "    max_iterations = 100  # Maximum number of iterations\n",
    "    ):\n",
    "    fa = f(a)                           # The value of the function at the left boundary\n",
    "    fb = f(b)                           # The value of the function at the right boundary\n",
    "    \n",
    "    xprev = xnew = a                           # Estimate of the solution from the previous step  \n",
    "    \n",
    "    global last_secant_iterations\n",
    "    last_secant_iterations = 0\n",
    "    \n",
    "    for i in range(max_iterations):\n",
    "        last_secant_iterations += 1\n",
    "        \n",
    "        xprev = xnew\n",
    "        xnew = a - fa * (b - a) / (fb - fa) # Take the point where straight line between a and b crosses y = 0\n",
    "        fnew = f(xnew)                      # Calculate the function at midpoint\n",
    "        \n",
    "        if secant_verbose:\n",
    "            print(\"Iteration: {0:5}, x = {1:20.15f}, f(x) = {2:10.15f}\".format(last_secant_iterations, xnew, fnew))\n",
    "        \n",
    "        b = a\n",
    "        fb = fa\n",
    "        a = xnew\n",
    "        fa = fnew\n",
    "    \n",
    "        if (abs(xnew-xprev) < tolerance):\n",
    "            return xnew\n",
    "    \n",
    "    print(\"Secant method failed to converge to a required precision in \" + str(max_iterations) + \" iterations\")\n",
    "    print(\"The error estimate is \", abs(xnew - xprev))\n",
    "    \n",
    "    return xnew                   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x + e^-x - 2 = 0 on an interval ( 0.0 , 3.0 ) using the secant method\n",
      "Iteration:     1, x =    1.463566653481105, f(x) = -0.305023902720619\n",
      "Iteration:     2, x =    2.105923727751964, f(x) = 0.227656901758072\n",
      "Iteration:     3, x =    1.831393427201715, f(x) = -0.008416373991634\n",
      "Iteration:     4, x =    1.841180853051291, f(x) = -0.000189150198961\n",
      "Iteration:     5, x =    1.841405873494811, f(x) = 0.000000179268085\n",
      "Iteration:     6, x =    1.841405660432446, f(x) = -0.000000000003799\n",
      "Iteration:     7, x =    1.841405660436961, f(x) = 0.000000000000000\n",
      "The solution is x =  1.8414056604369606 obtained after  7  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.\n",
    "b = 3.\n",
    "print(\"Solving the equation x + e^-x - 2 = 0 on an interval (\", a, \",\", b, \") using the secant method\")\n",
    "xroot = secant_method(func1, a, b, accuracy)\n",
    "print(\"The solution is x = \", xroot, \"obtained after \", last_secant_iterations, \" iterations\")\n",
    "\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func1(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x^3 - x - 1 = 0 on an interval ( 0.0 , 3.0 ) using the secant method\n",
      "Iteration:     1, x =    0.125000000000000, f(x) = -1.123046875000000\n",
      "Iteration:     2, x =   -1.015873015873016, f(x) = -1.032505888892888\n",
      "Iteration:     3, x =  -14.026092564115256, f(x) = -2746.344947419933305\n",
      "Iteration:     4, x =   -1.010979901305751, f(x) = -1.022322801027050\n",
      "Iteration:     5, x =   -1.006133240911884, f(x) = -1.012379562467959\n",
      "Iteration:     6, x =   -0.512666258317272, f(x) = -0.622076118670072\n",
      "Iteration:     7, x =    0.273834681149844, f(x) = -1.253301069122821\n",
      "Iteration:     8, x =   -1.287767830907429, f(x) = -1.847796782789951\n",
      "Iteration:     9, x =    3.565966235528240, f(x) = 40.779271189538719\n",
      "Iteration:    10, x =   -1.077368321415013, f(x) = -1.173157330026346\n",
      "Iteration:    11, x =   -0.947522156044583, f(x) = -0.903161564408282\n",
      "Iteration:    12, x =   -0.513174359589628, f(x) = -0.621969042319750\n",
      "Iteration:    13, x =    0.447558454314033, f(x) = -1.357908660326462\n",
      "Iteration:    14, x =   -1.325124217388110, f(x) = -2.001733206403897\n",
      "Iteration:    15, x =    4.186373891812861, f(x) = 68.182869385339558\n",
      "Iteration:    16, x =   -1.167930924631363, f(x) = -1.425200021260205\n",
      "Iteration:    17, x =   -1.058303471905222, f(x) = -1.127003019010034\n",
      "Iteration:    18, x =   -0.643978481189561, f(x) = -0.623084729828961\n",
      "Iteration:    19, x =   -0.131674045244213, f(x) = -0.870608926487776\n",
      "Iteration:    20, x =   -1.933586024088406, f(x) = -6.295618222310159\n",
      "Iteration:    21, x =    0.157497929951306, f(x) = -1.153591099624717\n",
      "Iteration:    22, x =    0.626623389695762, f(x) = -1.380575409253824\n",
      "Iteration:    23, x =   -2.226715128003442, f(x) = -9.813918004365664\n",
      "Iteration:    24, x =    1.093727500240917, f(x) = -0.785367085117557\n",
      "Iteration:    25, x =    1.382563036703896, f(x) = 0.260179317740376\n",
      "Iteration:    26, x =    1.310687668369503, f(x) = -0.059054486528599\n",
      "Iteration:    27, x =    1.323983763313963, f(x) = -0.003128925829655\n",
      "Iteration:    28, x =    1.324727653842468, f(x) = 0.000041352804288\n",
      "Iteration:    29, x =    1.324717950607204, f(x) = -0.000000028306680\n",
      "Iteration:    30, x =    1.324717957244686, f(x) = -0.000000000000256\n",
      "Iteration:    31, x =    1.324717957244746, f(x) = 0.000000000000000\n",
      "The solution is x =  1.324717957244746 obtained after  31  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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5ORkjRozAnXfeWb1dr9cDAHQ6Xa2vq9peWFhY7/5DQkKg0+mqH6+88goAa++RTCZDSUmJHd4F2aqkpAQymaxG7x0RETW9/GIjvjmUAQB4PM71Jgj8O5cYQr1ixQq8/vrriI6Oxqefftqg11b1DMjqWkTzqoyMjBqDmapm/1UoFNDpdLh8+TKMRiO0Wi2USuUN90cNJwgCTCZTda+an5/fdWO1iIioaX2acB7llRbc2kaHPhHNb/wCJ+f0QWflypWYO3cuOnbsiF9++eW6FbGremyqenb+zmAw1GhXF61WW+eo7aCgIHh6eiI3N7d6f9R0FAoFWrVqdcO/MyIisq/SChM+TUgHAEwb2E4S/6l36qCzfPlyPPPMM+jcuTN27dqFwMDA69pER0fj0KFDSElJQffu3Ws8ZzKZkJaWBqVSiXbtGt/9JpPJ4OfnB51OB7PZDJPJ1Oh9Uf2USiUUCoUk/nEREbma9YcycaW0EqH+XhjRuZXY5diF0wadV155BQsWLEBMTAx27tx5XU9OlSFDhuDzzz/Htm3b8MADD9R4bu/evSgtLcWAAQNqLETZWDKZDEqlEkql0x42IiKiRjGZLfjoV+uNO48PaOeSyz3UxikHIy9ZsgQLFixA9+7dsWvXrjpDDgCMGzcOAQEB+Oqrr3Do0KHq7eXl5Xj++ecBADNmzGjymomIiFzZD8cvIfNKGZp7q3Gfiy73UBun65pYu3YtXnjhBSgUCsTFxeGtt966rk1YWBimTJkCwDq25qOPPsK4ceMwaNAgTJgwAf7+/vjuu+9w+vRpjBs3DuPHj3fwuyAiInIdgiDggz3W3pwpfcPgoZLOjSBOF3TS0qwzMZrNZqxYsaLWNgMHDqwOOgAwevRo7NmzB0uXLsW3336L8vJyREZG4o033sCTTz7J8R5ERET1+PVMHk5eMsBTpcCkPm3FLseunG6tK0ezda0MIiIiqXpo9e/YdzYfU/uFYdHdt4hdjk1cdq0rIiIicpzjmXrsO5sPhVyGxyQwQeDfMegQERG5sff2nAUA3N2lFdr4eYpcjf0x6BAREbmpc5eL8VOydfHOGYMiRa6maTDoEBERuakP9pyDIAC3dwxEdJBrL95ZFwYdIiIiN3RJX4ZNRy8CkG5vDsCgQ0RE5JY+2puGSrOAXuH+6N62mdjlNBkGHSIiIjdTUFKBLw9cAADMHCzd3hyAQYeIiMjtfLI/HWWVZtzSWosBUXUvsyQFDDpERERupNhowtr96QCAmYMiJb96AIMOERGRG/ky8QL0ZZVoF+CN4Z2DxC6nyTHoEBERuQmjyYzVv1kX75w2sB0Ucmn35gAMOkRERG5jw+FM5BiMCNJ6YHRsG7HLcQgGHSIiIjdQabbgvd3nAFh7czRKhcgVOQaDDhERkRvYkpSFzCtlCPBRY8JtoWKX4zAMOkRERBJntgh4d7d18c7H4trBU+0evTkAgw4REZHk/ZR8CamXS6DzVGFi77Zil+NQDDpEREQSJggC3vnF2psztV8YfDRKkStyLAYdIiIiCdt1Khd/ZhfBR6PElL5hYpfjcAw6REREEiUIAt6Ot/bmTOrTFn5eapErcjwGHSIiIon67WwejmUUwkMlx6P9w8UuRxQMOkRERBIkCALe2nUGADDhtlAE+GhErkgcDDpEREQSlJCaj4PpV6BWyjFjUITY5YiGQYeIiEiCVv5c1ZsTgpZaD5GrEQ+DDhERkcT8npqPxLQCqBXu3ZsDMOgQERFJTtXYnPt6BKOVzlPkasTFoENERCQhB9MLsP9cPlQKGWYOjhS7HNEx6BAREUlIVW/OuO7BaOPn3r05AIMOERGRZBw+fwW/nsmDUi7DzEHszQEYdIiIiCSjqjdnbLc2CPH3Erka58CgQ0REJAFHL1zBnpTLUMhleGJwlNjlOA0GHSIiIgl48+q8OWNi2yC0OXtzqjDoEBERubjD5wuwN+UylHIZnhzC3pxrMegQERG5uDd3/nWnFXtzamLQISIicmEH0grw21nrnVazOG/OdRh0iIiIXNibO1MAAPffFsI7rWrBoENEROSiEs7lIyHVOgsye3Nqx6BDRETkggRBwJs/W3tzJtwWylmQ68CgQ0RE5IL2n8vHgasrlM8c7N4rlNeHQYeIiMjFCIKA13ecBgA82CvU7Vcorw+DDhERkYvZffoyjlwohIdKjpmD2JtTHwYdIiIiF2KxCFh+tTdncp8wBGo9RK7IuTHoEBERuZDtJ7JxIssAH40S0wayN+dGGHSIiIhchNki4PWr8+Y80j8c/t5qkStyfgw6RERELuK7YxdxNrcYOk8VHosLF7scl8CgQ0RE5AIqzZbqNa2mDWwHrYdK5IpcA4MOERGRC1h/KBMXCkoR4KPBlL5hYpfjMhh0iIiInFx5pRlv/2LtzZk1OAJeaqXIFbkOBh0iIiInt+7387ikL0crnQce6BkqdjkuhUGHiIjIiRWVV+Ld3ecAAHNuj4KHSiFyRa6FQYeIiMiJrf41DQUlFWjXwhv3dgsWuxyXw6BDRETkpPKKjVj9ayoAYN6waCgV/NpuKB4xIiIiJ7Uq/ixKKsy4tY0OIzoHiV2OS2LQISIickKZV0rx+e8XAADzh3eATCYTuSLXxKBDRETkhFb8fAYVZgv6RjRH/6gAsctxWU4ZdDZs2IDZs2cjLi4OWq0WMpkMEydOrLVteno6ZDJZnY8JEyY4uHoiIqKbk5JThI1HMgEA/x7eQeRqXJtTzjj08ssv49ixY/Dx8UFwcDD+/PPPG76ma9euGD169HXbO3fu3AQVEhERNZ3l20/DIgDDbwlCTIif2OW4NKcMOm+++SaCg4MRGRmJPXv2YPDgwTd8TUxMDBYvXtz0xRERETWhQ+kF2HEyB3IZMO/O9mKX4/KcMujYEmyIiIikRhAEvPKT9SrG/T1CEBnoK3JFrs8pg05jZGVl4YMPPkB+fj6aN2+OPn36oEuXLmKXRUREZLMdJ3Nw+PwVeKjkmHsHe3PsQTJBZ+fOndi5c2eNbYMGDcLatWsRGnrjdUEMBkONP2s0Gmg0GrvWSEREVBeT2YLXtll7cx7tH46WWg+RK5IGp7zrqiG8vLywcOFCHD58GFeuXMGVK1eqx/Xs3r0bQ4cORUlJyQ33ExISAp1OV/145ZVXHFA9ERGR1TeHMnHucgmaeakwbWCE2OVIhsv36AQGBuKll16qsW3AgAHYsWMH+vfvj8TERKxevRpPPfVUvfvJyMiAVqut/jN7c4iIyFFKK0x48+cUAMDsIVHQeqhErkg6XL5Hpy5KpRKPPfYYAGDv3r03bK/Vams8GHSIiMhRPv41DZeLjAjx98RDvW883IJsJ9mgA1h7ewDYdOmKiIhIDPnFRnyw96+FOzVKhcgVSYukg05iYiIAoF27diJXQkREVLuVu86g2GhC5zZa3N2ltdjlSI7LB53ExERUVFRct33Pnj144403AKDO5SOIiIjEdDa3GJ8nWhfuXDCyI+RyLtxpb045GHnz5s3YvHkzACA7OxsAkJCQgClTpgAAAgICsHz5cgDA/PnzceLECQwaNAjBwcEAgOPHj2PXrl0AgCVLlqBv376OfQNEREQ2ePWnP2G2CLi9YyD6RnDhzqbglEEnKSkJa9eurbEtNTUVqanWa5ht27atDjqTJk3Cpk2bcPDgQfz000+orKxEy5Ytcf/99+OJJ55AXFycw+snIiK6kYRz+fj5VA4UchmeHdFR7HIkSyYIgiB2EWIyGAzQ6XTQ6/U1bi8nIiJqKhaLgHtW/YbkiwZM6t0WS0ZzAeqGsvX72+XH6BAREbmaLccuIvmiAT4aJZ66PUrsciSNQYeIiMiByivN+O+20wCAGYMiEODDeduaEoMOERGRA/1vXxqy9OVorfPAo/3DxS5H8hh0iIiIHORykRHvxp8DADwzPBoeKk4O2NQYdIiIiBzkjZ2nUWw0oUuwDqO6thG7HLfAoENEROQAJ7L0+OpgBgDghbs6cXJAB2HQISIiamKCIGDJ1pMQBOCuLq3QI8xf7JLcBoMOERFRE9txMge/pxZArZTj2REdxC7HrTDoEBERNSGjyYxlP54CAPwzrh2Cm3mJXJF7YdAhIiJqQmv3p+N8fila+GowY1CE2OW4HQYdIiKiJpJXbMTbu84CAP59ZzS8NU65xKSkMegQERE1kdd3nEaR0YTObbS4t1uw2OW4JQYdIiKiJnA886/byRfdfQtvJxcJgw4REZGdCYKAxd+fgCAAo2Ja4zbeTi4aBh0iIiI725KUhcPnr8BLrcBzIzqKXY5bY9AhIiKyoxKjCa/8ZL2dfNbgSATpPESuyL0x6BAREdnRqvizyDEYEervxdXJnQCDDhERkZ2czy/B6l/TAADP/6MjVyd3Agw6REREdrJk6ylUmC2IiwrAHZ1ail0OgUGHiIjILuJP5+LnUzlQymVYdHcnyGS8ndwZMOgQERHdpPJKMxZ/dwIAMLVfGCIDfUWuiKow6BAREd2kj/am4nx+KVpqNXjq9vZil0PXYNAhIiK6CRkFpVi127qe1YKRHeHD9aycCoMOERHRTViy9STKKy3o3c4f93RtLXY59DcMOkRERI0UfzoXO05aByC/NKozByA7IQYdIiKiRjCazHjx6gDkKX3D0L4lByA7IwYdIiKiRvhwTyrS80sR6KvBU7dHiV0O1YFBh4iIqIEu5JfinXjrAOT//KMjfD1UIldEdWHQISIiagBBELBwSzKMJgv6RTbnAGQnx6BDRETUAD8lZ2NPymWoFXIs4QBkp8egQ0REZKNiowkvfX8SADB9YDu0a+EjckV0Iww6RERENnpzZwqyDeUI9ffCzMGRYpdDNmDQISIissGJLD0+2Z8OAHhp1C3wUCnELYhswqBDRER0AxaLgOc3J8NsEfCPW1thUHSg2CWRjRh0iIiIbuDzAxdw9EIhvNUKLLyrk9jlUAM0euWxlJQU7Ny5E3v37kVGRgby8vLg6emJwMBAxMTEYPDgwRgyZAg8PDzsWS8REZFD5RjK8dpPfwIAnrkzGkE6fq+5EpkgCEJDXvDVV1/h3Xffxb59+wBY5xOodccyGfz8/DBlyhTMnj0bYWFhN11sUzAYDNDpdNDr9dBqtWKXQ0RETmbGusP4KTkbXUP8sHFGXyjkvJ3cGdj6/W3zpav4+HjExsbiwQcfxIkTJzBlyhR8+OGHSEpKQnZ2NioqKqDX65Gamooff/wRCxcuRHR0NN5880107NgR8+fPh8FgsMubIyIicoSdJ3PwU3I2FHIZXhlzK0OOC7L50tXQoUPRrVs3fPPNN7jnnnugVquva+Pr6wtfX1+EhYVh+PDhWLx4Mc6cOYP3338f77zzDnx8fLBw4UK7vgEiIqKmUGw04YUtyQCAx+LC0ak1e/1dkc2XrjZt2oQxY8Y0+gdlZ2cjPT0dvXv3bvQ+mgIvXRERUW1e/P4E1uxLR4i/J3bMGQhPNW8ndya2fn/b3KNzMyEHAIKCghAUFHRT+yAiInKEYxmFWHt1zpylo29lyHFhTX57udlsbuofQUREZDeVZgvmf/sHLAIwOqY1BrRvIXZJdBMaHXRmzJgBo9FYb5vz588jLi6usT+CiIjI4T7Ycw5/ZhehmZcKz3POHJfX6KDzwQcfoFevXjh9+nStz2/cuBGxsbFITExsdHFERESOdDa3CG/tOgsAWHT3LQjw0YhcEd2sRged//znP0hOTkaPHj2wdu3a6u0VFRWYNWsW7rvvPsjlcmzatMkuhRIRETUli0XA/G+Po8JsweDoFhgV01rsksgOGh10lixZgu3bt8PHxwePPPIIJk2ahEOHDqFXr15477330LdvXyQlJeGee+6xZ71ERERN4rPfz+Pw+SvwVivw8phbIZNxzhwpuKnByEOHDsWxY8dw++2344svvkCvXr2QnJyM559/Hnv27EFwcLC96iQiImoymVdK8X/brMs8PDuiA9r4eYpcEdlLo9e6quLj44MWLVpULwWh0+kwcOBAyOVcL5SIiJyfIAhYsCkZpRVm3BbWDA/1ait2SWRHN5VGjh07hm7duuHLL7/EnXfeiffffx8VFRW488478fzzz8NisdirTiIioiax4XAm9qZchlopx6v3doGcyzxISqODzqpVq9CnTx+kpqZi2bJl+Omnn/DPf/4Thw8fRpcuXfDKK69g4MCByMzMtGe9REREdpOtL8dLW08CAObcHoWIFj4iV0T21uDVy6vI5XKEhobiyy+/RJ8+fWo8V1FRgX/9619YtWoV/P39kZeXZ5dimwKXgCAick+CIODRtYfwy5+56Bqsw7cz+kKp4LALV2H31cv/btSoUTh69Oh1IQcA1Go13n77bWzcuBGNzFFERERNauORi/jlz1yoFXL8976uDDkS1ejByLbMjzN69Gh07969sT+CiIioSeQYyvHi9ycAAE/dHoX2LX1FroiaSpPH15CQkAa/ZsOGDZg9ezbi4uKg1Wohk8kwceLEel+zf/9+jBw5Ev7+/vDy8kKXLl2wYsUKrrVFREQ1CIKABRuPw1BuQpdgHaYNaCd2SdSEbA46WVlZN/3DLl26ZFO7l19+Ge+88w6SkpLQpk2bG7bfsmULBgwYgL1792LMmDGYNWsWKioqMHfuXEyYMOFmyyYiIgnZnHQRu6ouWY3jJSups/lvNyIiAvPmzUNOTk6DfoAgCNiyZQtiY2Px0Ucf2fSaN998EykpKTAYDHjvvffqbWswGPDYY49BoVBg9+7d+Pjjj/Hf//4XSUlJ6NOnDzZs2ICvvvqqQTUTEZE0ZevLsWjLX5esooN4yUrqbA46zzzzDN577z2EhITgnnvuwbp165Camlpr2+LiYvzyyy+YP38+QkJCMHbsWHh4eGDs2LE2/azBgwcjKirKpum3169fj7y8PDzwwAPo0aNH9XYPDw+8/PLLAIB3333Xpp9LRETSJQgC/v3tHzCUm9CVl6zchs2DkV966SU8/vjjWLJkCb744gv88MMPAKwzIQcGBqJZs2YoLy9Hfn4+Ll26BIvFAkEQEBsbi+XLlzfZJaT4+HgAwPDhw697bsCAAfDy8kJCQgKMRiM0Gq5CS0Tkrr44cAF7Uy5Do5Tj9ftjeMnKTTTorquQkBB8+OGHWL58Ob744gvs3LkT+/fvR0pKSnUbtVqNmJgYDBo0CPfeey969+5t96Kvdfr0aQBAVFTUdc8plUqEh4fjxIkTSE1NRceOHZu0FiIick7n80uw9IdTAIB/D++AyEBODOgubA46b731Fnr37o2ePXtCq9Vi+vTpmD59OgCgsrIS+fn58PT0hE6na7Jia6PX6wGgzp9btb2wsLDe/RgMhhp/1mg07AEiIpIAs0XAvPXHUFphRq9wf0ztGyZ2SeRANvfbzZkzB9u2bav+s0KhwJIlSwAAKpUKQUFBDg85tqiasPBG431CQkKg0+mqH6+88oojyiMioib2v9/ScDD9CrzVCiy/ryvXsnIzNvfoeHp6wmg0Vv9ZEASnmPW4KlxV9ez8XVVPzY1CWEZGRo0ppNmbQ0Tk+lJyivDfHdYhDgvv6oQQfy+RKyJHs7lHJzw8HNu3b69xe7ktd0U1tejoaACoMU6oislkQlpaGpRKJdq1q390vVarrfFg0CEicm1GkxlPfZWECpMFg6NbYPxtDZ/AllyfzUFnxowZOHLkCFq3bg2FQgEAWLx4MRQKRb0PpbLRq0zYZMiQIQBQ47Jalb1796K0tBR9+/ZlcCEicjNv7EzBqUsG+Hur8X/jujjFf87J8WxOIbNmzUKLFi3w/fffIysrC/Hx8QgNDUVYWFgTlndj48aNw/z58/HVV19h9uzZ1XPplJeX4/nnnwdgDWlEROQ+Es7l48O91rneXhl7KwJ9PUSuiMQiExo50EYul2Px4sV44YUX7F0TNm/ejM2bNwMAsrOzsX37drRr1w5xcXEAgICAACxfvrxG+3HjxsHDwwMTJkyAv78/vvvuO5w+fRrjxo3DN998U2eSt3WZdyIicg36skqMWLEXWfpyjO8Rgv8b10XskqgJ2Pr93ejrSosWLcKgQYMa+/J6JSUlYe3atTW2paamVs/E3LZt2xpBZ/To0dizZw+WLl2Kb7/9FuXl5YiMjMQbb7yBJ598kt2VRERu5IUtycjSl6Ntcy+8cHcnscshkTW6R0cq2KNDRCQdW5Iu4qmvkqCQy7B+eh90C20mdknURGz9/ub810REJAkZBaV4fnMyAGDW4EiGHALAoENERBJgMlsw9+skFJWbEBPih9lDIsUuiZwEgw4REbm8t385i0Pnr8BHo8RbE2Kh4oKddBXPBCIicmkH0grw9i9nAABLx3RGaHPOfkx/YdAhIiKXpS+txJyvjsIiAGNj22BUTBuxSyInw6BDREQuSRAELNh0vPpW8pdGdxa7JHJCDDpEROSSvj6YgR+OX4JSLsPKCbHw0TTtkkPkmhh0iIjI5ZzOLsLi708AAP41LBoxIX7iFkROi0GHiIhcSmmFCU98cQTllRYMaN8C0wa0E7skcmIMOkRE5FIWf3cCZ3KLEeirwRv3d4VczmV+qG4MOkRE5DI2Hc3EN4cyIZcBKyfEIsBHI3ZJ5OQYdIiIyCWkXi7GfzZZl3h4cmgU+kQ0F7kicgUMOkRE5PTKK82Y9cVRlFaY0budP2YPiRK7JHIRDDpEROT0Fn93AqcuGdDcW42VE2Kh4LgcshGDDhERObUNhzPx1cEMyK6Oy2mp9RC7JHIhDDpEROS0/sw24PnNxwEAc4a2R/+oAJErIlfDoENERE6p2GjCzM//mi9n9pBIsUsiF8SgQ0RETkcQBMz/9g+kXi5BK50HVoyP4Xw51CgMOkRE5HTW7k/HD39Y17F658Fu8PdWi10SuSgGHSIicioH0wvw8g+nAADPjeyI7m2biVwRuTIGHSIichq5hnLM/PwITBYBd3VphUf6hYldErk4Bh0iInIKlWYLZn1xBJeLjGjf0gf/d28XyGQcl0M3h0GHiIicwtIfTuFg+hX4apT4YFIPeGuUYpdEEsCgQ0REott0NBOf7E8HALwxPgbhAd7iFkSSwaBDRESiOpGlx3MbrZMCPjE4End0ailyRSQlDDpERCSa/GIj/vnpYZRXWjCwfQvMvaO92CWRxDDoEBGRKCrNFsz8/AguFpYhrLkX3uJindQEGHSIiEgUS7aeRGJaAbzVCnz0cA/ovFRil0QSxKBDREQO9/XBC/g04TwAYMWEWES19BW5IpIqBh0iInKow+ev4PnNyQCAp+9oz8HH1KQYdIiIyGEuFpZh2meHUGkWMPyWIDwxmCuSU9Ni0CEiIocoMZrw2NpDyCuuQMdWWrx+f1euSE5NjkGHiIianMUiYO7XSTh1yYAAHzVWT+bMx+QYDDpERNTkXt95GjtO5kCtkOODST3Qxs9T7JLITTDoEBFRk9p0NBOr4s8BAP5v3K3o3raZyBWRO2HQISKiJnMovQDzv7Uu7zBzUATGxAaLXBG5GwYdIiJqEul5JXj800OoMFkwrFNLzBsWLXZJ5IYYdIiIyO4KSyvwyCcHcaW0El2CdVgxIYZ3WJEoGHSIiMiujCYz/vnZYaTmlaCNnydWT+4BLzXvsCJxMOgQEZHdCIKA5749jgNpBfDVKPG/Kbch0NdD7LLIjTHoEBGR3az4+Qw2Hr0IhVyGVQ91Q3QQ17AicTHoEBGRXXx98AJW7joDAFgyqjMGtG8hckVEDDpERGQH8X/mYsEm60KdswZH4MFeoSJXRGTFoENERDflj8xCzPz8CMwWAWO7teFt5ORUGHSIiKjRLuSX4pFPDqKs0oz+kQF4dWwXyGS8jZycB4MOERE1SkFJBSavOYC84gp0aqXFexO7Qa3k1wo5F56RRETUYMVGE6asOYC0q3PlrJl6G3w9VGKXRXQdBh0iImoQo8mM6Z8dxh+ZejTzUmHtI7ehpZZz5ZBzYtAhIiKbmS0C/vXNMfx2Ng9eagXWTO2JyEDOlUPOi0GHiIhsIggCXvz+BLb+cQkqhQwfTOqOmBA/scsiqheDDhER2WTlrjP4NOE8ZDLgjftjEBfFCQHJ+THoEBHRDX38WxpW/Gyd9Xjx3bfg7q6tRa6IyDYMOkREVK+vD17Akq0nAQBzb2+PyX3DxC2IqAEYdIiIqE5b/8jCsxuPAwAejwvHk0MjRa6IqGEkE3TCwsIgk8lqfQQFBYldHhGRy4n/MxdzvkqCIAAP9AzBgpEdOesxuRyl2AXYk06nw5w5c67b7uPj4/hiiIhc2P5zeZi+7jBMFgH3dG2Nl0ffypBDLklSQcfPzw+LFy8WuwwiIpd2IK0Aj35yCEaTBbd3DMTr93eFQs6QQ65JMpeuiIjo5h0+fwVT1xxAWaUZcVEBeOfBblAp+FVBrktSPTpGoxHr1q3DhQsX4O3tjS5dumDAgAFQKBRil0ZE5PT+yCzElP8dQEmFGX0jmuOjh3vAQ8XPT3Jtkgo62dnZmDRpUo1t4eHhWLNmDQYOHChSVUREzi/5oh4TVyeiyGhCzzB/rJ7MkEPSIJn+yKlTp2LXrl3Izs5GSUkJjh8/jmnTpiE9PR0jRozAsWPH6n29wWCo8TAajQ6qnIhIXCey9Jj0cSIM5SZ0C/XD/6beBi+1pP4fTG5MJgiCIHYRTWnevHl4/fXXMXr0aGzatOm65w0GA3Q63XXbFy1axIHNRCR5yRf1mPhxIgpLK9E1WIfPHusFrYdK7LKIbqjq+1uv10Or1dbZTvJB5+zZs4iKioK/vz/y8/Ove77qQGVkZNQ4UBqNBhqNxpGlEhE5VPJFPR5anQh9WSViQvzw6aM9GXLIZdgadCTfNxkYGAgAKCkpqbedVqut90AREUnJ8Uw9Hlr9OwzlJsSG+mHtIww5JE2SGaNTl8TERABAu3btRK6EiMg5HMsorA453UL98ClDDkmYJILOiRMnUFBQcN32jIwMPPHEEwCAiRMnOrosIiKncyCtAA+ttg487tG2GT59tBd8GXJIwiRx6Wr9+vV49dVXMXjwYISHh8PX1xepqanYunUrysvLMXLkSMybN0/sMomIRPXbmTw89ulBlFda0LudP1ZPvg0+Gkl8DRDVSRJn+ODBg3H69GkcPXoUCQkJKCkpgZ+fH/r3749JkyZh0qRJXKOFiNzarlM5mPH5EVSYLBjYvgU+mNSd8+SQW5D8XVc3YuuobSIiV/Xj8Ut48sujMFkE3HlLS7z1QCw0SoYccm2864qIiPDNwQw8u/EPWATgnq6t8fr9Xbl2FbkVBh0iIon6cO85LPvxTwDAhNtCsHTMrVyFnNwOgw4RkcQIgoDXtp/Ge7vPAQCmD4zA/OHRHKtIbolBh4hIQswWAc9vPo4vD2QAAJ4d0QHTB0aIXBWReBh0iIgkorzSjLlfJ+Gn5GzIZcCyMbdiQs9QscsiEhWDDhGRBOhLK/H4Z4dwIK0AaoUcKybEYOStrcQui0h0DDpERC7ukr4Mk/93ACk5xfDVKPHBw93RNyJA7LKInAKDDhGRC0vJKcLk/x3AJX05An01WPtIT3RsxTnBiKow6BARuaiEc/mY9tkhGMpNiGjhjbWP9ERwMy+xyyJyKgw6REQu6NvDmXh24x+oNAvo3rYZVj/cA8281WKXReR0GHSIiFyIIAhY8fMZrNx1BgDwjy6t8Pp9XbluFVEdGHSIiFyE0WTGc98ex8ajFwEAMwZF4Jlh0ZBztmOiOjHoEBG5gIKSCkxfdxgH0gqgkMvw8ujOeIBz5BDdEIMOEZGTS8kpwqNrDyKjoAw+GiXefagbBrRvIXZZRC6BQYeIyIn98mcOnvwyCcVGE0L9vfDx5B6IaukrdllELoNBh4jICQmCgI9/S8PSH09BEIBe4f54f2J33llF1EAMOkRETqa80owFm45j4xHroOMHeobgxXs6Q62Ui1wZketh0CEiciJZhWWY9tlhHL+oh0Iuw39GdsTUfmGQyXhnFVFjMOgQETmJxNR8zPz8CPJLKtDMS4VVD3ZD30iuWUV0Mxh0iIhEJggCPk04jyVbT8JkEdCplRYfTOqOEH8u50B0sxh0iIhEVGI04bmNx/HdsSwAwD1dW+P/7u0CTzVnOiayBwYdIiKRnM0txox1h3EmtxgKuQzPjeiAR/uHczwOkR0x6BARiWDrH1mYv+EPlFSYEeirwaqHuuG2MH+xyyKSHAYdIiIHKq8045UfT2FtwnkAQO92/njrgVgE+nqIXBmRNDHoEBE5SFpeCZ744ghOZBkAANMGtsMzw6KhVHB+HKKmwqBDROQAW5IuYsHG4yipMKOZlwpv3B+DwR0CxS6LSPIYdIiImlBphQkvfX8SXx3MAAD0DPPHygdi0ErnKXJlRO6BQYeIqIkkX9Tjya+OIvVyCWQy4InBkXhqaBQvVRE5EIMOEZGdWSwCPvo1Fct3nEalWUBLrQZv3h/DWY6JRMCgQ0RkR9n6cvxrfRL2nc0HANx5S0u8OrYLVx0nEgmDDhGRHQiCgO+OZWHh5mQYyk3wVCmw6O5OGH9bCCcAJBIRgw4R0U0qKKnAws3J+OH4JQBA12Ad3hgfg4gWPiJXRkQMOkREN+GXP3Mw/9vjuFxkhFIuw5NDozBzUAQHHBM5CQYdIqJGKCytwEvfn8TGoxcBAFGBPnjj/hjcGqwTuTIiuhaDDhFRA20/kY3nNyfjcpERMhnwaL9wzLszGh4qrjhO5GwYdIiIbJRfbMSi705g6x/WsTgRLbzx3/u6oltoM5ErI6K6MOgQEd2AIAhYfzgTy348hcLSSijkMkwb0A5PDo1iLw6Rk2PQISKqR+rlYvxnUzISUq3z4nRspcVr93bhWBwiF8GgQ0RUC6PJjA/3pOLt+LOoMFngoZJj7u3t8Uj/cKh4RxWRy2DQISL6m1/PXMaiLSeQmlcCAIiLCsDS0bcitLmXyJURUUMx6BARXXVJX4aXt56qnvgvwEeDhXd1xD1dW3N2YyIXxaBDRG7PaDJjzb50vLXrDEorzJDLgMl9wzD3jvbQeqjELo+IbgKDDhG5LUEQ8POpXLz8w0mczy8FAHRv2wxLRnVGp9ZakasjIntg0CEit5SSU4QlW0/i1zN5AIBAXw3mD++AMbFtIJfzMhWRVDDoEJFbuVxkxIqfU/DVwQyYLQLUCjkeiwvHzMGR8NHwI5FIavivmojcQmmFCat/TcMHe86hpMIMABjWqSWe/0cn3k1FJGEMOkQkaSazBd8eycQbO1OQYzACALoG67BgZEf0atdc5OqIqKkx6BCRJFksAn5KzsbrO05Xz4cT3MwT/x7eAXfd2orjcIjcBIMOEUmKIAjYeyYP/93+J5IvGgAAzbxUmDU4EpP6tIVGybWpiNwJgw4RSYIgCNh3Nh8rfk7BofNXAADeagUei2uHx+LC4cv5cIjcEoMOEbk0QRCw/5w14BxMtwYctVKOSb3bYuagCDT30YhcIRGJiUGHiFySIAjYk3IZq+LP1gg4D/YMxYxBEWip9RC5QiJyBgw6RORSLBYB205kY1X8WZzIso7BqQo40wdGIEjHgENEf2HQISKXYDSZseVoFj7Yew7nLlvvovJUKfBQr1A8FteOAYeIaiWpoJOZmYkXXngB27ZtQ35+Plq1aoXRo0dj0aJFaNasmdjlEVEj6EsrsS7xPD7Zn47LRdZ5cLQeSkzpG4Yp/cLh760WuUIicmaSCTrnzp1D3759kZubi1GjRqFDhw44cOAAVq5ciW3btmHfvn1o3pyTgxG5ivS8EnyyPx3fHMpA6dWZjIO0HpjaLwwP9grlXVREZBPJBJ2ZM2ciNzcXb731FmbPnl29/emnn8abb76J//znP3j//fdFrJCIAABmM/Drr8ClS0CrVkBcHKCwzm0jCAJ+O5uHNfvSEX86F4JgfUmHIF/8c0A73NWlNdRKuYjFE5GrkQlC1UeJ6zp37hwiIyMRHh6Os2fPQi7/64OwqKgIrVq1gsViQW5uLnx8fGq81mAwQKfTQa/XQ6vVOrp0IveycSPw1FNAZuZf24KDUfrf17GhbU98mnAeZ3OLq58a0iEQU/qGIS4qADIZZzImor/Y+v0tiR6d+Ph4AMCwYcNqhBwA8PX1Rb9+/bBjxw4kJiZi6NChYpRIRBs3AuPGAX/7v5WQeREeD4zHvtELcDa6L3w0SozrHozJfcMQHuAtUrFEJBWSCDqnT58GAERFRdX6fFRUFHbs2IGUlJQ6g05JSQkUiuunhlcoFPDw8KjRri5yuRyenp6NaltaWoq6OtdkMhm8vLwa1basrAwWi6XOOry9vRvVtry8HGaz2S5tvby8qv+3bjQaYTKZ7NLW09OzOvhWVFSgsrLSLm09PDyqz5WGtK2srERFRUWdbTUaDZRKZYPbmkwmGI3GOtuq1WqoVKoGtzWbzSgvL6+zrUqlglqttq2tXA71U09dF3IAQAYBAoAl8R+hx4wJGNu7HZprreePxWJBWVlZnftVKpXQaKwTAgqCgNLSUru0bci/e35G1N6WnxH8jGjQZ8Q1bW/07/7atjYRJODxxx8XAAgfffRRrc8vWLBAACAsW7bsuuf0er0AoM7HyJEja7T38vKqs+3AgQNrtA0ICKizbY8ePWq0bdu2bZ1tO3XqVKNtp06d6mzbtm3bGm179OhRZ9uAgIAabQcOHFhnWy8vrxptR44cWe9xu9a4cePqbVtcXFzddvLkyfW2zc3NrW47c+bMetumpaVVt503b169bZOTk6vbLlq0qN62Bw4cqG772muv1ds2Pj6+uu0777xTb9utW7dWt12zZk29bb/55pvqtt988029bdesWVPdduvWrfW2feedd6rbxsfH19v2tddeq2574MCBetv+7+GHBQG44WMgIMybN696v2lpafXud+bMmdVtc3Nz6207efLk6rbFxcX1th03blyNc7i+tvyMsD74GfHXg58R1kdDPiMWLVpU3TY5ObnetlWfEVXf33q9XqiPW4zqE67+z4bX+InEceRImk3tWjVxHUTkfiQxGPmZZ57B8uXLsXz5cvzrX/+67vknnngCq1atwrvvvosZM2bUeK5qMNPp06fh6+tbvV2j0UCj0bBbuo627JZmt3Rd3dL5xUbsOJmD75IuIilDDwDoc/EUvv5mYZ37qlL2449QDB1qcxc2L11Z8TOicW35GWHlqpeu3GowcnR0NAAgJSWl1ufPnDkDAGjfvn2d+wgKCrLprqtr/3Has+21Hzz2bHvtB6U92177wW7PtlUB095t1Wq1zdd0m6qtSqWq/oCwZ1ulUln9gWbPtgqFwuZzuLjCgh2nCvD9H5ew72wezBbrl6xS44H+US1w70O3wbLvA8izLqK2cTqQyYDgYHgOG1Z9qzlg/bK3tQaZTNYkbYGm+3fPz4iGt+VnRMPbOsNnREPaNuTfvS0kEXQGDx4MANixYwcsFst1t5fv27cPnp6e6N27t1glEknOlZIK/HwqB9uSs/HrmTxUmP/6n37nNlqM6toGo2JaI7Bqcc23VlrvupLJaoadqkvKK1bUCDlERPYgiaATERGBYcOGYceOHVi1alWNCQMXLVqEkpISTJs2za4JkcgdZevLsfNUDrYnZyMhNb+65wYA2rf0wd1dWuOurq1rvy187Fhgw4Za59HBihXW54mI7EwSY3SA65eA6NixIxITExEfH4/27dtj//79tS4BwQkDieomCAJOZBnw86kc/HwqB8kXDTWe79hKi+G3BGHErUFo39K3jr38TT0zIxMR2crW72/JBB0AyMjIqHNRT39//1pfw6BDVJO+tBK/nc3D7tO52JNyGblFfw1MlMmA2BA/DLslCMNvCUIYJ/QjIpG4ZdBpDAYdcncVJguSMgqx72wefjubh6MXruCaK1LwVCkwoH0AhnZsiSEdAhHgY9vgTiKipuRWd10Rke1MZgtOZBmQmJaP/efycSCtoHp18CqRgT4Y1L4FBka3wG1h/vBQ8dISEbkmBh0iiSuvNOP4RT0OphcgMbUAh89fQbGx5twi/t5q9I1ojn6RAYiLCkBwM9tvTyYicmYMOkQSIggCMq+U4VhmIY6cL8ThC1dwMkuPSnPNK9RaDyV6hvujV7g13HQI8oVczpnDiUh6GHSIXJQgCMg2lOPERQOSs/Q4llGIY5l6FJRcP1tqC18Nuoc2s4abdv7oEKSFgsGGiNwAg04T+en4JSSmFaCFrwYtfDQI8FWjhY8HAnzVaO6tgVrpFsuMkZ0YTWacyy3B6RwD/swuwsksA05mGZBfS6hRKWToEKRFTIgfeoQ1Q7fQZghu5sm13ojILTHoNJHfzubh88QLdT7v56VCgI8GAT7qq79q0MK35p8DfDVo7q3mQFA3UlZhxrnLxdZHbjHOXi5GSk4x0vJKakzOV0UhlyGyhQ9uaa1F1xA/dAnWoWMrLc8ZIqKrGHSayJAOgdB6qnC5yIi8YuvjcpER+cUVMFkEFJZWorC0Emdzb7wvX42yOvQ091GjuY8GAd7WX/2rtnlbf9/MSwWlgr1FzkxfWomMK6XIKCjFhYJSpOeXIC2vBOfzS3FJX/eid1oPJToEaREd5IuOrbS4pbX19ww1RER14zw6Dp5Hx2IRUFhWaQ0/RUZcvhqA8oorqgNRXrE1EOUVG68bRHojMhmg81RZA5C3Gs28rj681fD3VsHv6p/9vFRo5mX9s85TBRXDkV0UG03INZQjt8iIbH05svRluFRYjkv6MlwsLEfmlVIUlde9mjIANPNSITLQB5GBPoho4YOIQB90CPJFkNaDl5+IiK7iPDpOSi6Xwd9bDX9v9Q2nzBcEAYYyEy4XG5FfbER+SQXyi/8KRQUlFdXb8ksqUFhaCUFAdW9R6uUSm+vy0Sih81TVeGg9ldB6qKD1VMHXQwlfj6pflfDVqODjoYS3RgEfjRKeKoXkvoRNZguKjSYYyky4UlqBwrJKFJZaj3P1cS+uQH6J9e8k11COkr/NR1OXAB81gpt5IcTfC+HNvRAW4G19NPeGv7dtKx0TEdGNMeg4MZlMBp2XCrqr/8O/EZPZgsKySly5GoAKSipwpbQCV0oqUFBSiYISo/X50r++sPVllQCsPRHFRhMuFpY1qla5DPBWK+GlUcBLrYSXWgFvtRIalRyeKgU81Qp4KBXwUMmhUSmgUcqhUcqhVsqhUlgfaoUcKqUMSrkcCrkMCrkMSrkMcrkMcpkMMlh7rORXA5VFECAIgABrKLQIAkxmAWaLAPPV31eYLKgwW1BptqDCZEF5pQXlJjPKK62PsgozSirMKK0wodhoRqnRhKJyE4rKK20OLX/no1Ei0FeDQK0GrXWeaOXngVY6T7T280BwMy8EN/OEl5r/9IiIHIGfthKiVMirBzJH2fgas0WAocwaeKp6LPRllTCUm2Aoq4ShvPLqr38FgKJyE4rLTSgxmlBcYYIgABYBKDKaUGQ0ATDe8Oe6Eg+VHM2uXuKruuznf3WMVNXgcX9vNVpqPRDoq4G3hv+siIicBT+R3ZxCLkMzb+sYnsYQBAGlFWaUGE0oufprWeXVXyvMKKs0o7zSgrJKM8oqTDCaLNZHpbn695XmqoeASrOlZq+MRYDZYqkOU38fUia7pqdHebUX6K/eoKoeIxnUSgVUChk0SgU8VdaeJQ+V9ffeGuslOC+1Et5qBXw8rJfsqi7XcSoAIiLXxaBDN0Umk10NCjyViIjI+fC/qkRERCRZDDpEREQkWQw6REREJFkMOkRERCRZDDpEREQkWQw6REREJFkMOkRERCRZDDpEREQkWQw6REREJFkMOkRERCRZDDpNxGg0YvHixTAapbXAZVPh8bIdj5XteKxsx2NlOx4r2znDsZIJf18l0c0YDAbodDro9XpotVqn369U8XjZjsfKdjxWtuOxsh2Ple2a8ljZum/26BAREZFkMegQERGRZCnFLkBsVVfuDAaDXfdbtT9771eqeLxsx2NlOx4r2/FY2Y7HynZNeayq9nmjEThuP0YnMzMTISEhYpdBREREjZCRkYHg4OA6n3f7oGOxWJCVlQVfX1/IZDKxyyEiIiIbCIKAoqIitG7dGnJ53SNx3D7oEBERkXRxMDIRERFJFoMOERERSRaDTgNkZmbikUceQevWraHRaBAWFoY5c+bgypUrouzHmdnjPYaFhUEmk9X6CAoKasLqHWfDhg2YPXs24uLioNVqIZPJMHHixEbtS+rnlb2OlTucV/n5+Vi9ejXGjBmDyMhIeHp6QqfToX///vj4449hsVgatD8pn1v2PFbucG7Nnz8fQ4cORUhICDw9PeHv74/Y2Fi8+OKLyM/Pb9C+HHVecYyOjc6dO4e+ffsiNzcXo0aNQocOHXDgwAHEx8cjOjoa+/btQ/PmzR22H2dmr/cYFhaGwsJCzJkz57rnfHx8MG/evCao3rFiYmJw7Ngx+Pj4IDg4GH/++SceeughrFu3rkH7cYfzyl7Hyh3Oq/fffx8zZsxAUFAQhgwZgtDQUOTk5GDjxo3Q6/UYO3YsNmzYYNMNGFI/t+x5rNzh3FKr1ejWrRs6deqEwMBAlJSU4Pfff8ehQ4fQunVrJCQkIDQ09Ib7ceh5JZBNhg0bJgAQ3nrrrRrb586dKwAQpk2b5tD9ODN7vce2bdsKbdu2bYIKnccvv/wipKSkCBaLRYiPjxcACA899FCD9+MO55W9jpU7nFe7du0SNm/eLJhMphrbL126JISEhAgAhPXr19u0L6mfW/Y8Vu5wbpWVldW6fcGCBQIAYfr06Tbtx5HnFYOODc6ePSsAEMLDwwWz2VzjOYPBIHh7ewuenp5CUVGRQ/bjzOz5Ht3hQ+Najf3ydofz6u8YdBpv6dKlAgBh1qxZN2zrjufWtRpyrATBvc+tpKQkAYBwxx133LCto88rjtGxQXx8PABg2LBh192r7+vri379+qGsrAyJiYkO2Y8zs/d7NBqNWLduHZYtW4aVK1ciPj4eZrPZ7nW7Mnc4r+zNnc8rtVoNAFCpVDds6+7nVkOOVRV3Pbe+//57AECXLl1u2NbR55XbLwFhi9OnTwMAoqKian0+KioKO3bsQEpKCoYOHdrk+3Fm9n6P2dnZmDRpUo1t4eHhWLNmDQYOHHjzBUuAO5xX9uau55XJZMLatWsBAMOHD79he3c+txp6rKq4y7m1fPlyFBcXQ6/X49ChQ/jtt98QGxuL55577oavdfR5xR4dG+j1egCATqer9fmq7YWFhQ7ZjzOz53ucOnUqdu3ahezsbJSUlOD48eOYNm0a0tPTMWLECBw7dsxudbsydziv7Mmdz6tnn30WycnJGDFiBO68884btnfnc6uhxwpwr3Nr+fLlePHFF7FixQr89ttvGDFiBLZt22bTAGJHn1cMOnYgXL1x7WaXkLDXfpxZQ97jokWLMGTIELRs2RJeXl7o3Lkz3n//fTz99NMoKyvD4sWLm7haaXCH86oh3PW8WrFiBV5//XVER0fj008/tcs+pXpuNfZYudO5lZ2dDUEQkJ2djY0bN+LcuXOIiYnBkSNHbnrf9j6vGHRsUJUuq1Lo31WtoFpXOrX3fpyZI97j9OnTAQB79+5t9D6kxB3OK0eQ8nm1cuVKzJ07Fx07dsTu3bsREBBg0+vc8dxq7LGqj5TPrZYtW2LMmDHYuXMn8vPz8fDDD9/wNY4+rxh0bBAdHQ0ASElJqfX5M2fOAADat2/vkP04M0e8x8DAQABASUlJo/chJe5wXjmCVM+r5cuXY86cOejcuTN2797doInr3O3cupljVR+pnlvXCg0NRadOnXDixAnk5eXV29bh55Vd7t2SuKpb4cLCwuq9Fa64uNgh+3FmjniPO3bsEAAIHTt2vNlyncrN3l4u5fPq727m9vK6SPG8WrZsmQBAiImJES5fvtzg17vTuXWzx6o+Ujy3ahMYGCgAEAoKCupt5+jzikHHRg2Z3KiiokI4deqUcPbs2Zvaj6uyx7FKTk4W8vPzr9v3hQsXhPbt2wsAhKVLlzbNGxDJjb683f28ulZjj5U7nVcvvfSSAEDo3r17re/5Wu5+btnjWLnDuXXq1Cnh0qVL1203m83VEwb27du3eruznFdcAsJGf5+uumPHjkhMTER8fDzat2+P/fv3V482T09PR3h4ONq2bYv09PRG78dV2eNYLV68GK+++ioGDx6M8PBw+Pr6IjU1FVu3bkV5eTlGjhyJTZs2Vc9z4ao2b96MzZs3A7AO7tu+fTvatWuHuLg4AEBAQACWL18OgOeVPY6Vu5xXa9euxZQpU6BQKDB79uxaxzqEhYVhypQpANz73LLXsXKHc2vFihV45plnMGDAAERERKB58+bIycnBnj17kJqaiqCgIOzatQudOnUC4ETnld0ikxu4cOGCMGXKFCEoKEhQqVRCaGio8OSTT16X4tPS0gQAdc6Qaet+XNnNHqvdu3cLEyZMEKKjowWdTicolUohICBAuP3224W1a9cKFovFge+m6SxatEgAUOfj2uPi7ueVPY4Vz6u/HgMHDqxu787nlr2OlTucW8ePHxdmzpwpdO3aVWjevLmgUCgErVYr9OjRQ1i0aJHTfheyR4eIiIgki3ddERERkWQx6BAREZFkMegQERGRZDHoEBERkWQx6BAREZFkMegQERGRZDHoEBERkWQx6BAREZFkMegQERGRZDHoEBERkWQx6BAREZFkMegQERGRZDHoEBERkWQx6BCRpIwePRoymQxvv/32dc8tXLgQMpkM06ZNE6EyIhKDTBAEQewiiIjspaCgALGxscjJyUFCQgJiY2MBALt27cKwYcPQqVMnHDhwAJ6eniJXSkSOwKBDRJKzf/9+DBw4EOHh4Thy5AhKS0vRtWtXGAwGHDx4EJ06dRK7RCJyEF66IiLJ6du3L5YsWYIzZ85g2rRpmDhxIrKzs/H2228z5BC5GfboEJEkCYKAESNGYPv27QCABx54AF988YXIVRGRo7FHh4gkSSaTYcyYMdV/njNnjnjFEJFo2KNDRJJ05swZdOvWDSqVCnq9Hp07d0ZiYiI8PDzELo2IHIg9OkQkOUajEePHj0dJSQm+/vprPPfcc/jjjz8wd+5csUsjIgdj0CEiyZk3bx6OHj2K+fPn44477sCLL76Ifv364f3338eGDRvELo+IHIiXrohIUjZv3owxY8agT58+2Lt3L5RKJQAgIyMDMTExMJvNSEpKQlhYmLiFEpFDMOgQkWRcuHABMTExEAQBSUlJaNu2bY3nt2zZgtGjR6NXr1749ddfoVKpRKqUiByFQYeIiIgki2N0iIiISLIYdIiIiEiyGHSIiIhIshh0iIiISLIYdIiIiEiyGHSIiIhIshh0iIiISLIYdIiIiEiyGHSIiIhIshh0iIiISLIYdIiIiEiyGHSIiIhIshh0iIiISLL+H/+oKMLd8oqDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.\n",
    "b = 3.\n",
    "print(\"Solving the equation x^3 - x - 1 = 0 on an interval (\", a, \",\", b, \") using the secant method\")\n",
    "xroot = secant_method(func2, a, b, accuracy)\n",
    "print(\"The solution is x = \", xroot, \"obtained after \", last_secant_iterations, \" iterations\")\n",
    "\"\"\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func2(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "31 iterations!\n",
    "\n",
    "Why so many compared to the previous example?\n",
    "\n",
    "See the animation\n",
    "\n",
    "![img-secant2](secant-func2.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The method is not convergent during the initial phase.\n",
    "The reasons is that the interval (0,3) covers a point $x = 1/\\sqrt{3} = 0.577...$ where the derivative is zero $f'(x) = 0$. In this case we can go far outside the initial interval and lose convergence.\n",
    "\n",
    "Let us try to reduce the interval to (1,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x^3 - x - 1 = 0 on an interval ( 1.0 , 3.0 ) using the secant method\n",
      "Iteration:     1, x =    1.083333333333333, f(x) = -0.811921296296297\n",
      "Iteration:     2, x =    1.443076923076923, f(x) = 0.562088928538917\n",
      "Iteration:     3, x =    1.295910704621766, f(x) = -0.119578283458892\n",
      "Iteration:     4, x =    1.321726650403328, f(x) = -0.012721292233753\n",
      "Iteration:     5, x =    1.324800030879539, f(x) = 0.000350040702043\n",
      "Iteration:     6, x =    1.324717728006158, f(x) = -0.000000977618237\n",
      "Iteration:     7, x =    1.324717957227214, f(x) = -0.000000000074767\n",
      "Iteration:     8, x =    1.324717957244746, f(x) = 0.000000000000000\n",
      "The solution is x =  1.324717957244746 obtained after  8  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1.\n",
    "b = 3.\n",
    "print(\"Solving the equation x^3 - x - 1 = 0 on an interval (\", a, \",\", b, \") using the secant method\")\n",
    "xroot = secant_method(func2, a, b, accuracy)\n",
    "print(\"The solution is x = \", xroot, \"obtained after \", last_secant_iterations, \" iterations\")\n",
    "\"\"\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func2(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Newton-Raphson method\n",
    "\n",
    "Newton's method is a local method. \n",
    "\n",
    "Let us assume that a given point $x$ is close to the root $x^*$, where $f(x^*) = 0$.\n",
    "\n",
    "We can express $f(x^*)$ by expanding it around x:\n",
    "$$\n",
    "f(x^*) \\approx f(x) + f'(x) (x^* - x)\n",
    "$$\n",
    "\n",
    "Given that $f(x^*) = 0$, we can express the root $x^*$ as\n",
    "$$\n",
    "x^* \\approx x - \\frac{f(x)}{f'(x)}\n",
    "$$\n",
    "which is accurate is $x$ is sufficiently close to $x^*$.\n",
    "\n",
    "Newton-Raphson method is an iterative procedure to find $x^*$.\n",
    "The $(n+1)$th approximation is\n",
    "$$\n",
    "x_{n+1} = x_n - \\frac{f(x_n)}{f'(x_n)}.\n",
    "$$\n",
    "\n",
    "The method is expected to work well if the initial guess $x_0$ is not too far from $x$ and/or we avoid regions where $f'(x) = 0$. The method converges faster than other methods considered so far but requires the evaluation of the derivative $f'$ at each step.\n",
    "\n",
    "![newton](newton.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "last_newton_iterations = 0\n",
    "newton_verbose = False\n",
    "\n",
    "def newton_method(\n",
    "    f,                    # The function whose root we are trying to find\n",
    "    df,                   # The derivative of the function\n",
    "    x0,                   # The initial guess\n",
    "    tolerance = 1.e-10,   # The desired accuracy of the solution\n",
    "    max_iterations = 100  # Maximum number of iterations\n",
    "    ):\n",
    "    \n",
    "    xprev = xnew = x0\n",
    "    \n",
    "    global last_newton_iterations\n",
    "    last_newton_iterations = 0\n",
    "    \n",
    "    if newton_verbose:\n",
    "        print(\"Iteration: {0:5}, x = {1:20.15f}, f(x) = {2:10.15f}\".format(last_newton_iterations, x0, f(x0)))\n",
    "    \n",
    "    for i in range(max_iterations):\n",
    "        last_newton_iterations += 1\n",
    "           \n",
    "        xprev = xnew\n",
    "        fval  = f(xprev)                       # The current function value\n",
    "        dfval = df(xprev)                      # The current function derivative value\n",
    "        \n",
    "        xnew = xprev - fval / dfval            # The next iteration\n",
    "        \n",
    "        if newton_verbose:\n",
    "            print(\"Iteration: {0:5}, x = {1:20.15f}, f(x) = {2:10.15f}\".format(last_newton_iterations, xnew, f(xnew)))\n",
    "\n",
    "        if (abs(xnew-xprev) < tolerance):\n",
    "            return xnew\n",
    "        \n",
    "    \n",
    "    print(\"Newton-Raphson method failed to converge to a required precision in \" + str(max_iterations) + \" iterations\")\n",
    "    print(\"The error estimate is \", abs(xnew-xprev))\n",
    "    \n",
    "    return xnew                   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x + e^-x - 2 = 0 with an initial guess of x0 =  0.5\n",
      "Iteration:     0, x =    0.500000000000000, f(x) = -0.893469340287367\n",
      "Iteration:     1, x =    2.770747041268399, f(x) = 0.833362252387609\n",
      "Iteration:     2, x =    1.881718050961633, f(x) = 0.034046224211712\n",
      "Iteration:     3, x =    1.841553658165603, f(x) = 0.000124527863398\n",
      "Iteration:     4, x =    1.841405662500950, f(x) = 0.000000001736652\n",
      "Iteration:     5, x =    1.841405660436960, f(x) = -0.000000000000000\n",
      "Iteration:     6, x =    1.841405660436961, f(x) = 0.000000000000000\n",
      "The solution is x =  1.8414056604369606 obtained after  6  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Recall function 1\n",
    "def func1(x):\n",
    "    return x + np.exp(-x) - 2.\n",
    "\n",
    "# Now we have to define the derivative\n",
    "def dfunc1(x):\n",
    "    return 1. - np.exp(-x)\n",
    "\n",
    "# Initial guess\n",
    "x0 = 0.5\n",
    "\n",
    "print(\"Solving the equation x + e^-x - 2 = 0 with an initial guess of x0 = \", x0)\n",
    "newton_verbose = True\n",
    "xroot = newton_method(func1, dfunc1, x0, accuracy)\n",
    "print(\"The solution is x = \", xroot, \"obtained after \", last_newton_iterations, \" iterations\")\n",
    "\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func1(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x^3 - x - 1 = 0 with an initial guess of x0 =  0.5\n",
      "Iteration:     0, x =    0.500000000000000, f(x) = -1.375000000000000\n",
      "Iteration:     1, x =   -5.000000000000000, f(x) = -121.000000000000000\n",
      "Iteration:     2, x =   -3.364864864864865, f(x) = -35.733196947860939\n",
      "Iteration:     3, x =   -2.280955053664953, f(x) = -10.586297439073974\n",
      "Iteration:     4, x =   -1.556276567967263, f(x) = -3.213020231094429\n",
      "Iteration:     5, x =   -1.043505227179037, f(x) = -1.092770911285728\n",
      "Iteration:     6, x =   -0.561409518771311, f(x) = -0.615535897017610\n",
      "Iteration:     7, x =  -11.864344921350634, f(x) = -1659.192647549701178\n",
      "Iteration:     8, x =   -7.925964323903187, f(x) = -490.990330807181920\n",
      "Iteration:     9, x =   -5.306828631368327, f(x) = -145.146361872742261\n",
      "Iteration:    10, x =   -3.568284222599895, f(x) = -42.865438067273487\n",
      "Iteration:    11, x =   -2.415924209768375, f(x) = -12.685075952386104\n",
      "Iteration:    12, x =   -1.647600608320907, f(x) = -3.824955843874735\n",
      "Iteration:    13, x =   -1.112174714899762, f(x) = -1.263510442920995\n",
      "Iteration:    14, x =   -0.646071913773210, f(x) = -0.623604264554248\n",
      "Iteration:    15, x =    1.826323485985127, f(x) = 3.265300837953712\n",
      "Iteration:    16, x =    1.463768987529280, f(x) = 0.672531206531874\n",
      "Iteration:    17, x =    1.339865398074654, f(x) = 0.065513601104520\n",
      "Iteration:    18, x =    1.324927455582133, f(x) = 0.000893607955833\n",
      "Iteration:    19, x =    1.324717998133174, f(x) = 0.000000174374144\n",
      "Iteration:    20, x =    1.324717957244748, f(x) = 0.000000000000007\n",
      "Iteration:    21, x =    1.324717957244746, f(x) = 0.000000000000000\n",
      "The solution is x =  1.324717957244746 obtained after  21  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Recall function 1\n",
    "def func2(x):\n",
    "    return x**3 - x - 1.\n",
    "\n",
    "# Now we have to define the derivative\n",
    "def dfunc2(x):\n",
    "    return 3. * x**2 - 1.\n",
    "\n",
    "# Initial guess\n",
    "x0 = 0.50\n",
    "\n",
    "print(\"Solving the equation x^3 - x - 1 = 0 with an initial guess of x0 = \", x0)\n",
    "newton_verbose = True\n",
    "xroot = newton_method(func2, dfunc2, x0, accuracy)\n",
    "print(\"The solution is x = \", xroot, \"obtained after \", last_newton_iterations, \" iterations\")\n",
    "\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func2(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For an unfortunate choice of initial guess the Newton-Raphson method can enter a loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x^3 - 2x - 2 = 0 with an initial guess of x0 =  0.2\n",
      "Iteration:     0, x =    0.200000000000000, f(x) = 1.608000000000000\n",
      "Iteration:     1, x =    1.055319148936170, f(x) = 1.064669061768587\n",
      "Iteration:     2, x =    0.261439035839439, f(x) = 1.494991383012186\n",
      "Iteration:     3, x =    1.094327030585932, f(x) = 1.121859079804777\n",
      "Iteration:     4, x =    0.389931467644111, f(x) = 1.279424798892584\n",
      "Iteration:     5, x =    1.218649426200272, f(x) = 1.372525239026891\n",
      "Iteration:     6, x =    0.659648706939285, f(x) = 0.967739760651828\n",
      "Iteration:     7, x =    2.052900431402751, f(x) = 6.545943087393848\n",
      "Iteration:     8, x =    1.437865220849364, f(x) = 2.096993201890540\n",
      "Iteration:     9, x =    0.938862607780933, f(x) = 0.949847431796620\n",
      "Iteration:    10, x =   -0.535165422191687, f(x) = 2.917058381558375\n",
      "Iteration:    11, x =    2.021876957818959, f(x) = 6.221651656230159\n",
      "Iteration:    12, x =    1.415712077796703, f(x) = 2.006003592114745\n",
      "Iteration:    13, x =    0.915801154166546, f(x) = 0.936472567945143\n",
      "Iteration:    14, x =   -0.898803491799477, f(x) = 3.071510634833125\n",
      "Iteration:    15, x =   -8.150746134217721, f(x) = -523.190576643922441\n",
      "Iteration:    16, x =   -5.499048198867083, f(x) = -153.290542596360382\n",
      "Iteration:    17, x =   -3.771219375974292, f(x) = -44.092203672807059\n",
      "Iteration:    18, x =   -2.686974730056577, f(x) = -12.025559903409908\n",
      "Iteration:    19, x =   -2.075282665245400, f(x) = -2.787258193548728\n",
      "Iteration:    20, x =   -1.820048459791015, f(x) = -0.388952647875359\n",
      "Iteration:    21, x =   -1.771047966241150, f(x) = -0.012992420597823\n",
      "Iteration:    22, x =   -1.769294563549005, f(x) = -0.000016329450484\n",
      "Iteration:    23, x =   -1.769292354242137, f(x) = -0.000000000025907\n",
      "Iteration:    24, x =   -1.769292354238631, f(x) = 0.000000000000000\n",
      "The solution is x =  -1.7692923542386314 obtained after  24  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The method ends up in a cycle\n",
    "def func3(x):\n",
    "    return x**3 - 2. * x + 2.\n",
    "\n",
    "# Now we have to define the derivative\n",
    "def dfunc3(x):\n",
    "    return 3. * x**2 - 2.\n",
    "\n",
    "# Initial guess\n",
    "x0 = 0.2\n",
    "\n",
    "print(\"Solving the equation x^3 - 2x - 2 = 0 with an initial guess of x0 = \", x0)\n",
    "newton_verbose = True\n",
    "xroot = newton_method(func3, dfunc3, x0, accuracy)\n",
    "print(\"The solution is x = \", xroot, \"obtained after \", last_newton_iterations, \" iterations\")\n",
    "\n",
    "# Plotting\n",
    "xref = np.linspace(-3,3,100)\n",
    "fref = func3(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![newton-3](newton-func3.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Relaxation method\n",
    "\n",
    "Another local method is iteration (or relaxation) method\n",
    "\n",
    "The idea is to rewrite the equation\n",
    "$$\n",
    "f(x) = 0\n",
    "$$\n",
    "in a form\n",
    "$$\n",
    "x = \\varphi(x).\n",
    "$$\n",
    "This is always possible to do, for instance by choosing $\\varphi(x) = f(x) + x$, although this choice of $\\varphi(x)$ is not unique.\n",
    "\n",
    "The root $x^*$ of this equation is approximated iteratively starting from some initial guess $x_0$\n",
    "$$\n",
    "x_{n+1} = \\varphi(x_n).\n",
    "$$\n",
    "\n",
    "It turns out that this iterative procedure in some cases converges quickly (as a geometric progression) to the root $x^*$.\n",
    "Namely, this is the case if the derivative\n",
    "$$\n",
    "|\\varphi'(x)| < 1\n",
    "$$\n",
    "for all $x$ in the interval of value covered by all $x_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "last_relaxation_iterations = 0\n",
    "relaxation_verbose = True\n",
    "\n",
    "def relaxation_method(\n",
    "    phi,                  # The function from the equation x = phi(x)\n",
    "    x0,                   # The initial guess\n",
    "    tolerance = 1.e-10,   # The desired accuracy of the solution\n",
    "    max_iterations = 100  # Maximum number of iterations\n",
    "    ):\n",
    "    \n",
    "    xprev = xnew = x0\n",
    "    \n",
    "    global last_relaxation_iterations\n",
    "    last_relaxation_iterations = 0\n",
    "    \n",
    "    if relaxation_verbose:\n",
    "        print(\"Iteration: {0:5}, x = {1:20.15f}, phi(x) = {2:10.15f}\".format(last_relaxation_iterations, x0, phi(x0)))\n",
    "    \n",
    "    for i in range(max_iterations):\n",
    "        last_relaxation_iterations += 1\n",
    "        \n",
    "        xprev = xnew\n",
    "        xnew = phi(xprev) # The next iteration\n",
    "        \n",
    "        if relaxation_verbose:\n",
    "            print(\"Iteration: {0:5}, x = {1:20.15f}, phi(x) = {2:10.15f}\".format(last_relaxation_iterations, xnew, phi(xnew)))\n",
    "\n",
    "        if (abs(xnew-xprev) < tolerance):\n",
    "            return xnew\n",
    "        \n",
    "    \n",
    "    print(\"The iteration method failed to converge to a required precision in \" + str(max_iterations) + \" iterations\")\n",
    "    print(\"The error estimate is \", abs(xnew - xprev))\n",
    "    \n",
    "    return xnew                   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x = 2 - e^-x with relaxation method an initial guess of x0 =  0.5\n",
      "Iteration:     0, x =    0.500000000000000, phi(x) = 1.393469340287367\n",
      "Iteration:     1, x =    1.393469340287367, phi(x) = 1.751787325113973\n",
      "Iteration:     2, x =    1.751787325113973, phi(x) = 1.826536369684999\n",
      "Iteration:     3, x =    1.826536369684999, phi(x) = 1.839029855597129\n",
      "Iteration:     4, x =    1.839029855597129, phi(x) = 1.841028423293983\n",
      "Iteration:     5, x =    1.841028423293983, phi(x) = 1.841345821475382\n",
      "Iteration:     6, x =    1.841345821475382, phi(x) = 1.841396170032424\n",
      "Iteration:     7, x =    1.841396170032424, phi(x) = 1.841404155305379\n",
      "Iteration:     8, x =    1.841404155305379, phi(x) = 1.841405421731432\n",
      "Iteration:     9, x =    1.841405421731432, phi(x) = 1.841405622579610\n",
      "Iteration:    10, x =    1.841405622579610, phi(x) = 1.841405654432999\n",
      "Iteration:    11, x =    1.841405654432999, phi(x) = 1.841405659484766\n",
      "Iteration:    12, x =    1.841405659484766, phi(x) = 1.841405660285948\n",
      "Iteration:    13, x =    1.841405660285948, phi(x) = 1.841405660413011\n",
      "Iteration:    14, x =    1.841405660413011, phi(x) = 1.841405660433162\n",
      "Iteration:    15, x =    1.841405660433162, phi(x) = 1.841405660436358\n",
      "The solution is x =  1.8414056604331623 obtained after  15  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Recall the equation x + e^-x - 2 = 0, rewrite as x = phi(x), where phi(x) = 2 - e^-x\n",
    "def phi1(x):\n",
    "    return 2. - np.exp(-x)\n",
    "\n",
    "# Initial guess\n",
    "x0 = 0.5\n",
    "\n",
    "print(\"Solving the equation x = 2 - e^-x with relaxation method an initial guess of x0 = \", x0)\n",
    "xroot = relaxation_method(phi1, x0, accuracy)\n",
    "print(\"The solution is x = \", xroot, \"obtained after \", last_relaxation_iterations, \" iterations\")\n",
    "\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func1(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "phiref = phi1(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,phiref, label = '${\\\\varphi(x)}$')\n",
    "plt.plot(xref,xref, label = 'x')\n",
    "plt.plot([xroot], [xroot], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x = x^3 - 1 with relaxation method an initial guess of x0 =  0.0\n",
      "Iteration:     0, x =    0.000000000000000, phi(x) = -1.000000000000000\n",
      "Iteration:     1, x =   -1.000000000000000, phi(x) = -2.000000000000000\n",
      "Iteration:     2, x =   -2.000000000000000, phi(x) = -9.000000000000000\n",
      "Iteration:     3, x =   -9.000000000000000, phi(x) = -730.000000000000000\n",
      "Iteration:     4, x = -730.000000000000000, phi(x) = -389017001.000000000000000\n",
      "Iteration:     5, x = -389017001.000000000000000, phi(x) = -58871587162270591457689600.000000000000000\n",
      "Iteration:     6, x = -58871587162270591457689600.000000000000000, phi(x) = -204040901322752646989478259680513109526757826056202557355691431285390611316736.000000000000000\n",
      "Iteration:     7, x = -204040901322752646989478259680513109526757826056202557355691431285390611316736.000000000000000, phi(x) = -8494771472237387691242611538599472199333045034070888643295870583150028612258583145101302119543367284932616097722814131127104275290993706669943943557518825041720139256751756296514363510463501782805696167407096791414943273033163341824.000000000000000\n"
     ]
    },
    {
     "ename": "OverflowError",
     "evalue": "(34, 'Result too large')",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mOverflowError\u001b[0m                             Traceback (most recent call last)",
      "Input \u001b[0;32mIn [19]\u001b[0m, in \u001b[0;36m<cell line: 9>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      6\u001b[0m x0 \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.\u001b[39m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mSolving the equation x = x^3 - 1 with relaxation method an initial guess of x0 = \u001b[39m\u001b[38;5;124m\"\u001b[39m, x0)\n\u001b[0;32m----> 9\u001b[0m xroot \u001b[38;5;241m=\u001b[39m \u001b[43mrelaxation_method\u001b[49m\u001b[43m(\u001b[49m\u001b[43mphi2\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx0\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maccuracy\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mThe solution is x = \u001b[39m\u001b[38;5;124m\"\u001b[39m, xroot, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mobtained after \u001b[39m\u001b[38;5;124m\"\u001b[39m, last_relaxation_iterations, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m iterations\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m     12\u001b[0m \u001b[38;5;66;03m# Plotting\u001b[39;00m\n",
      "Input \u001b[0;32mIn [17]\u001b[0m, in \u001b[0;36mrelaxation_method\u001b[0;34m(phi, x0, tolerance, max_iterations)\u001b[0m\n\u001b[1;32m     23\u001b[0m xnew \u001b[38;5;241m=\u001b[39m phi(xprev) \u001b[38;5;66;03m# The next iteration\u001b[39;00m\n\u001b[1;32m     25\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m relaxation_verbose:\n\u001b[0;32m---> 26\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mIteration: \u001b[39m\u001b[38;5;132;01m{0:5}\u001b[39;00m\u001b[38;5;124m, x = \u001b[39m\u001b[38;5;132;01m{1:20.15f}\u001b[39;00m\u001b[38;5;124m, phi(x) = \u001b[39m\u001b[38;5;132;01m{2:10.15f}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(last_relaxation_iterations, xnew, \u001b[43mphi\u001b[49m\u001b[43m(\u001b[49m\u001b[43mxnew\u001b[49m\u001b[43m)\u001b[49m))\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m (\u001b[38;5;28mabs\u001b[39m(xnew\u001b[38;5;241m-\u001b[39mxprev) \u001b[38;5;241m<\u001b[39m tolerance):\n\u001b[1;32m     29\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m xnew\n",
      "Input \u001b[0;32mIn [19]\u001b[0m, in \u001b[0;36mphi2\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mphi2\u001b[39m(x):\n\u001b[0;32m----> 3\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mx\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m3\u001b[39;49m \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m\n",
      "\u001b[0;31mOverflowError\u001b[0m: (34, 'Result too large')"
     ]
    }
   ],
   "source": [
    "# Recall the equation x^3 - x - 1 = 0, rewrite as x = phi(x), where phi(x) = x^3 - 1\n",
    "def phi2(x):\n",
    "    return x**3 - 1\n",
    "\n",
    "# Initial guess\n",
    "x0 = 0.\n",
    "\n",
    "print(\"Solving the equation x = x^3 - 1 with relaxation method an initial guess of x0 = \", x0)\n",
    "xroot = relaxation_method(phi2, x0, accuracy)\n",
    "print(\"The solution is x = \", xroot, \"obtained after \", last_relaxation_iterations, \" iterations\")\n",
    "\n",
    "# Plotting\n",
    "xref = np.linspace(0,3,100)\n",
    "fref = func2(xref)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.plot(xref,fref, label = 'f(x)')\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot([xroot], [0], 'ro',label='root')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
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