{
 "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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",
      "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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",
      "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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",
      "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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",
      "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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",
      "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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",
      "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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",
      "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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",
      "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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",
      "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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",
      "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 =  0.0\n",
      "Iteration:     0, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:     1, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:     2, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:     3, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:     4, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:     5, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:     6, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:     7, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:     8, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:     9, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    10, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    11, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    12, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    13, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    14, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    15, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    16, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    17, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    18, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    19, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    20, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    21, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    22, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    23, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    24, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    25, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    26, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    27, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    28, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    29, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    30, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    31, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    32, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    33, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    34, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    35, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    36, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    37, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    38, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    39, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    40, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    41, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    42, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    43, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    44, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    45, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    46, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    47, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    48, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    49, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    50, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    51, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    52, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    53, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    54, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    55, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    56, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    57, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    58, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    59, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    60, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    61, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    62, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    63, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    64, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    65, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    66, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    67, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    68, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    69, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    70, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    71, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    72, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    73, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    74, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    75, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    76, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    77, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    78, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    79, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    80, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    81, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    82, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    83, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    84, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    85, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    86, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    87, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    88, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    89, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    90, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    91, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    92, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    93, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    94, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    95, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    96, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    97, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:    98, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Iteration:    99, x =    1.000000000000000, f(x) = 1.000000000000000\n",
      "Iteration:   100, x =    0.000000000000000, f(x) = 2.000000000000000\n",
      "Newton-Raphson method failed to converge to a required precision in 100 iterations\n",
      "The error estimate is  1.0\n",
      "The solution is x =  0.0 obtained after  100  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "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 = 0.0\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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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 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)",
      "Cell \u001b[0;32mIn[19], line 9\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",
      "Cell \u001b[0;32mIn[17], line 26\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",
      "Cell \u001b[0;32mIn[19], line 3\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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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) = 1.259921049894873\n",
      "Iteration:     2, x =    1.259921049894873, phi(x) = 1.312293836683289\n",
      "Iteration:     3, x =    1.312293836683289, phi(x) = 1.322353819138825\n",
      "Iteration:     4, x =    1.322353819138825, phi(x) = 1.324268744551578\n",
      "Iteration:     5, x =    1.324268744551578, phi(x) = 1.324632625250920\n",
      "Iteration:     6, x =    1.324632625250920, phi(x) = 1.324701748510359\n",
      "Iteration:     7, x =    1.324701748510359, phi(x) = 1.324714878440951\n",
      "Iteration:     8, x =    1.324714878440951, phi(x) = 1.324717372435671\n",
      "Iteration:     9, x =    1.324717372435671, phi(x) = 1.324717846162146\n",
      "Iteration:    10, x =    1.324717846162146, phi(x) = 1.324717936144965\n",
      "Iteration:    11, x =    1.324717936144965, phi(x) = 1.324717953236911\n",
      "Iteration:    12, x =    1.324717953236911, phi(x) = 1.324717956483471\n",
      "Iteration:    13, x =    1.324717956483471, phi(x) = 1.324717957100144\n",
      "Iteration:    14, x =    1.324717957100144, phi(x) = 1.324717957217279\n",
      "Iteration:    15, x =    1.324717957217279, phi(x) = 1.324717957239529\n",
      "Iteration:    16, x =    1.324717957239529, phi(x) = 1.324717957243755\n",
      "The solution is x =  1.324717957239529 obtained after  16  iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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 (1+x)**(1/3)\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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving the equation x = x^3 - 1 with relaxation method an initial guess of x0 =  1.2\n",
      "Iteration:     0, x =    1.200000000000000, phi(x) = 2.272727272727273\n",
      "Iteration:     1, x =    2.272727272727273, phi(x) = 0.240079365079365\n",
      "Iteration:     2, x =    0.240079365079365, phi(x) = -1.061163446475196\n",
      "Iteration:     3, x =   -1.061163446475196, phi(x) = 7.932235852407031\n",
      "Iteration:     4, x =    7.932235852407031, phi(x) = 0.016149775441666\n",
      "Iteration:     5, x =    0.016149775441666, phi(x) = -1.000260883289156\n",
      "Iteration:     6, x =   -1.000260883289156, phi(x) = 1916.315871752755584\n",
      "Iteration:     7, x = 1916.315871752755584, phi(x) = 0.000000272311464\n",
      "Iteration:     8, x =    0.000000272311464, phi(x) = -1.000000000000074\n",
      "Iteration:     9, x =   -1.000000000000074, phi(x) = 6741915609836.072265625000000\n",
      "Iteration:    10, x = 6741915609836.072265625000000, phi(x) = 0.000000000000000\n",
      "Iteration:    11, x =    0.000000000000000, phi(x) = -1.000000000000000\n"
     ]
    },
    {
     "ename": "ZeroDivisionError",
     "evalue": "float division by zero",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[21], line 9\u001b[0m\n\u001b[1;32m      6\u001b[0m x0 \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1.2\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",
      "Cell \u001b[0;32mIn[17], line 26\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",
      "Cell \u001b[0;32mIn[21], line 3\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[38;5;241;43m1\u001b[39;49m\u001b[38;5;241;43m/\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1.\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "\u001b[0;31mZeroDivisionError\u001b[0m: float division by zero"
     ]
    }
   ],
   "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 1/(x**2 - 1.)\n",
    "\n",
    "# Initial guess\n",
    "x0 = 1.2\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()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.16"
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 },
 "nbformat": 4,
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}