{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical integration\n",
    "\n",
    "Consider a generic problem of integrating a function over some interval:\n",
    "$$\n",
    "I = \\int_{a}^b f(x) \\, dx\n",
    "$$\n",
    "\n",
    "We may need to resort to numerical integration when:\n",
    "- we have no explicit expression for $f(x)$ but only know its values at certain points\n",
    "- we do not know how to evaluate the antiderivative of $f(x)$ even if we know $f(x)$ itself\n",
    "\n",
    "There are two main types of numerical integration methods:\n",
    "- direct evaluation of the integral over the interval (a,b)\n",
    "- composite methods where the integration interval is separated into sub-intervals\n",
    "\n",
    "The most common methods are:\n",
    "\n",
    "- Rectangle, trapezoidal and Simpson rules\n",
    "- Quadratures (Newton-Cotes, Gaussian)\n",
    "\n",
    "\n",
    "Adaptive quadratures: divide the integration range into subintervals to control the error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rectangle rule\n",
    "\n",
    "Approximate the integral by an area of a rectangle:\n",
    "\n",
    "$$\n",
    "\\int_{a}^b f(x) \\, dx \\approx (b - a) \\, f\\left(\\frac{a+b}{2}\\right)\n",
    "$$\n",
    "\n",
    "To improve the accuracy, separate the integration interval into $N$ subintervals of length $h = (b-a)/N$ and apply the rectangle rule to each of them\n",
    "$$\n",
    "\\int_a^b f(x) \\approx h \\sum_{k=1}^N f(x_k), \\qquad k = 1,\\ldots, N\n",
    "$$\n",
    "with\n",
    "$$\n",
    "x_k = a + \\frac{2k-1}{2} h~.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rectangle rule for numerical integration \n",
    "# of function f(x) over (a,b) using n subintervals\n",
    "def rectangle_rule(f, a, b, n):\n",
    "    h = (b - a) / n\n",
    "    ret = 0.0\n",
    "    xk = a + h / 2.\n",
    "    for k in range(n):\n",
    "        ret += f(xk) * h\n",
    "        xk += h\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Visualize\n",
    "def rectangle_rule_plot(f, a, b, n, numpoints = 100):\n",
    "    xplot = np.linspace(0,2,numpoints)\n",
    "    yplot = f(xplot)\n",
    "\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"f(x)\")\n",
    "    plt.xlim(0,2)\n",
    "    plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "    plt.plot(xplot,yplot, color = 'red',label='f(x)')\n",
    "    \n",
    "    labelrec = \"rectangle rule, (N = \" + str(n) + \")\"\n",
    "    \n",
    "    xks = []\n",
    "    fks = []\n",
    "    h = (b - a) / n\n",
    "    xk = a + h / 2.\n",
    "    for k in range(1,n+1):\n",
    "        fval = f(xk)\n",
    "        if (k == 1):\n",
    "            plt.plot([xk - h/2., xk - h/2., xk + h/2., xk + h/2.,xk - h/2.], [0.,fval,fval,0.,0.], \n",
    "                     color = 'blue', label=labelrec)\n",
    "        else:\n",
    "            plt.plot([xk - h/2., xk - h/2., xk + h/2., xk + h/2.,xk - h/2.], [0.,fval,fval,0.,0.], \n",
    "                     color = 'blue')\n",
    "        \n",
    "        xks.append(xk)\n",
    "        fks.append(fval)\n",
    "        \n",
    "        xk += h\n",
    "    \n",
    "    plt.plot(xks,fks,'.', color = 'blue')\n",
    "    plt.legend()\n",
    "    \n",
    "    return plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a function $f(x) = x^4 - 2x + 2$ and its integral over $(0,2)$:\n",
    "$$\n",
    "\\int_0^2 ( x^4 - 2x + 2) dx = \\left. \\frac{x^5}{5} - x^2 + 2x \\right|_0^2 = 6.4\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The function example we will use\n",
    "# Overwrite as applicable\n",
    "\n",
    "flabel = 'x^4 - 2x + 2'\n",
    "def f(x):\n",
    "    return x**4 - 2*x + 2\n",
    "flimit_a = 0.\n",
    "flimit_b = 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Preliminaries: import numpy, matplotlib and set default styles\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\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",
    "numpoints = 100\n",
    "xplot = np.linspace(0,2,numpoints)\n",
    "\n",
    "yplot = f(xplot)\n",
    "\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.xlim(0,2)\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "plt.plot(xplot,yplot, color = 'red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us evaluate the performance of numerical integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using rectangle rule\n",
      "N = 1 , I =  2.0\n",
      "N = 2 , I =  5.125\n",
      "N = 3 , I =  5.818930041152262\n",
      "N = 4 , I =  6.0703125\n",
      "N = 5 , I =  6.188159999999999\n",
      "N = 6 , I =  6.252572016460903\n",
      "N = 7 , I =  6.291545189504369\n",
      "N = 8 , I =  6.31689453125\n",
      "N = 9 , I =  6.334298633338417\n",
      "N = 10 , I =  6.346759999999996\n",
      "N = 11 , I =  6.355986612936278\n",
      "N = 12 , I =  6.363007973251031\n",
      "N = 13 , I =  6.368474493190009\n",
      "N = 14 , I =  6.37281341107871\n",
      "N = 15 , I =  6.376314732510287\n",
      "N = 16 , I =  6.379180908203125\n",
      "N = 17 , I =  6.381556734234506\n",
      "N = 18 , I =  6.383547985571311\n",
      "N = 19 , I =  6.385233385256395\n",
      "N = 20 , I =  6.386672500000006\n",
      "N = 21 , I =  6.387911072718333\n",
      "N = 22 , I =  6.388984700498595\n",
      "N = 23 , I =  6.3899214196633\n",
      "N = 24 , I =  6.3907435538837385\n",
      "N = 25 , I =  6.391469056000005\n",
      "N = 26 , I =  6.392112496061053\n",
      "N = 27 , I =  6.392685798298071\n",
      "N = 28 , I =  6.393198797376085\n",
      "N = 29 , I =  6.393659662849694\n",
      "N = 30 , I =  6.394075226337445\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"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = flimit_a\n",
    "b = flimit_b\n",
    "print(\"Computing the integral of\",flabel, \"over the interval (\",a,\",\",b,\") using rectangle rule\")\n",
    "for n in range(1,31):\n",
    "    print(\"N =\",n,\", I = \",rectangle_rule(f,a,b,n))\n",
    "    \n",
    "rectangle_rule_plot(f,a,b,5).show()\n",
    "rectangle_rule_plot(f,a,b,10).show()\n",
    "rectangle_rule_plot(f,a,b,30).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Animate\n",
    "\n",
    "import os\n",
    "import matplotlib.animation as animation\n",
    "import imageio.v2 as imageio\n",
    "\n",
    "def integrate_animate(f, flabel, a, b, rule, rule_plot, filename = 'rectangle.gif', nstart = 1, iterations = 8):\n",
    "    labelgif = filename\n",
    "\n",
    "    filenames = []\n",
    "    n = nstart\n",
    "    for ind in range(1,iterations):\n",
    "        # create file name and append it to a list\n",
    "        filename = f'{ind}.png'\n",
    "        filenames.append(filename)\n",
    "\n",
    "        plot = rule_plot(f,a,b,n)\n",
    "        val = rule(f,a,b,n)\n",
    "        plot.title('I = ' + str(val))\n",
    "        plot.savefig(filename)\n",
    "        plot.close()\n",
    "\n",
    "        n *= 2\n",
    "\n",
    "    # build gif\n",
    "    with imageio.get_writer(labelgif, mode='I', loop=0, duration=2000) as writer:\n",
    "        for filename in filenames:\n",
    "            image = imageio.imread(filename)\n",
    "            writer.append_data(image)\n",
    "\n",
    "    # Remove files\n",
    "    for filename in set(filenames):\n",
    "        os.remove(filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/gif": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "integrate_animate(f,flabel,flimit_a,flimit_b,rectangle_rule,rectangle_rule_plot,'rectangle_rule.gif', 1, 8)\n",
    "\n",
    "from IPython.display import display, Image, clear_output\n",
    "display(Image(filename='rectangle_rule.gif'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The error for a rectangle rule can be shown to be equal to (using the Taylor theorem):\n",
    "$$\n",
    "\\int_a^b f(x) dx -  (b - a) \\, f\\left(\\frac{a+b}{2}\\right) \\approx \\frac{(b-a)^3}{24} f''(a)\n",
    "$$\n",
    "to leading order in $(b-a)$.\n",
    "\n",
    "For the composite rectangle rule, we have this rule for each subinterval $h = (b-a) / N$ and we have to sum up the errors from each interval. We have\n",
    "$$\n",
    "I - I_{\\rm rect} = (b-a) \\frac{h^2}{24} \\, f''(a) + \\mathcal{O}(h^4).\n",
    "$$\n",
    "\n",
    "The rectangle rule is exact for the integration of linear functions ($f'' = 0$ and all higher-order derivatives)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N = 1 , I =  10.0\n",
      "N = 2 , I =  10.0\n",
      "N = 3 , I =  9.999999999999998\n",
      "N = 4 , I =  10.0\n",
      "N = 5 , I =  10.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "flabellinear = 'f(x) = 2*x + 3'\n",
    "def flinear(x):\n",
    "    return 2. * x + 3.\n",
    "\n",
    "a = 0.\n",
    "b = 2.\n",
    "for n in range(1,6):\n",
    "    print(\"N =\",n,\", I = \",rectangle_rule(flinear,a,b,n))\n",
    "    \n",
    "rectangle_rule_plot(flinear,a,b,1).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Trapezoidal rule\n",
    "\n",
    "Approximate the integral by an area of a trapezoid.\n",
    "This is achieved by linear interpolation of the function between (sub)interval endpoints:\n",
    "\n",
    "$$\n",
    "\\int_{a}^b f(x) \\, dx \\approx (b-a) \\, \\frac{f(a) + f(b)}{2}~.\n",
    "$$\n",
    "\n",
    "As for rectangle rule, to improve the accuracy, separate the integration interval into $N$ subintervals of length $h = (b-a)/N$ and apply the trapezoidal rule to each of them\n",
    "$$\n",
    "\\int_a^b f(x) \\approx h \\sum_{k=0}^N \\frac{f(x_k) + f(x_{k+1})}{2}, \\qquad i = 0,\\ldots, N\n",
    "$$\n",
    "with\n",
    "$$\n",
    "x_k = a +  k h~.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Trapezoidal rule for numerical integration \n",
    "# of function f(x) over (a,b) using n subintervals\n",
    "def trapezoidal_rule(f, a, b, n):\n",
    "    h = (b - a) / n\n",
    "    ret = 0.0\n",
    "    xk = a\n",
    "    fk = f(xk)\n",
    "    for k in range(n):\n",
    "        xk += h\n",
    "        fk1 = f(xk)\n",
    "        ret += h * (fk + fk1) / 2.\n",
    "        fk = fk1\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Visualize\n",
    "def trapezoidal_rule_plot(f, a, b, n, numpoints = 100):\n",
    "    xplot = np.linspace(0,2,numpoints)\n",
    "    yplot = f(xplot)\n",
    "\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"f(x)\")\n",
    "    plt.xlim(0,2)\n",
    "    plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "    plt.plot(xplot,yplot, color = 'red',label='f(x)')\n",
    "    \n",
    "    labelrec = \"trapezoidal rule, (N = \" + str(n) + \")\"\n",
    "    \n",
    "    xks = []\n",
    "    fks = []\n",
    "    h = (b - a) / n\n",
    "    xk = a\n",
    "    fk = f(xk)\n",
    "    for k in range(1,n+1):\n",
    "        xk += h\n",
    "        fk1 = f(xk)\n",
    "        if (k == 1):\n",
    "            plt.plot([xk - h, xk - h, xk, xk,xk - h], [0.,fk,fk1,0.,0.], \n",
    "                     color = 'blue', label=labelrec)\n",
    "        else:\n",
    "            plt.plot([xk - h, xk - h, xk, xk,xk - h], [0.,fk,fk1,0.,0.], \n",
    "                     color = 'blue')\n",
    "                    \n",
    "        xks.append(xk)\n",
    "        fks.append(fk1)\n",
    "        \n",
    "        fk = fk1\n",
    "    \n",
    "    plt.plot(xks,fks,'.', color = 'blue')\n",
    "    plt.legend()\n",
    "    \n",
    "    return plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using trapezoidal rule\n",
      "N = 1 , I =  16.0\n",
      "N = 2 , I =  9.0\n",
      "N = 3 , I =  7.572016460905349\n",
      "N = 4 , I =  7.0625\n",
      "N = 5 , I =  6.824960000000001\n",
      "N = 6 , I =  6.695473251028805\n",
      "N = 7 , I =  6.61724281549354\n",
      "N = 8 , I =  6.56640625\n",
      "N = 9 , I =  6.531524665955397\n",
      "N = 10 , I =  6.506559999999999\n",
      "N = 11 , I =  6.488081415203885\n",
      "N = 12 , I =  6.474022633744856\n",
      "N = 13 , I =  6.463079023843701\n",
      "N = 14 , I =  6.454394002498951\n",
      "N = 15 , I =  6.447386337448559\n",
      "N = 16 , I =  6.441650390625\n",
      "N = 17 , I =  6.4368961099603705\n",
      "N = 18 , I =  6.432911649646909\n",
      "N = 19 , I =  6.429539368175497\n",
      "N = 20 , I =  6.426660000000005\n",
      "N = 21 , I =  6.424181968075723\n",
      "N = 22 , I =  6.422034014070073\n",
      "N = 23 , I =  6.420160019439603\n",
      "N = 24 , I =  6.418515303497934\n",
      "N = 25 , I =  6.417063936000004\n",
      "N = 26 , I =  6.41577675851685\n",
      "N = 27 , I =  6.4146299087449545\n",
      "N = 28 , I =  6.41360370678883\n",
      "N = 29 , I =  6.412681805392758\n",
      "N = 30 , I =  6.411850534979421\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"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = flimit_a\n",
    "b = flimit_b\n",
    "print(\"Computing the integral of\",flabel, \"over the interval (\",a,\",\",b,\") using trapezoidal rule\")\n",
    "for n in range(1,31):\n",
    "    print(\"N =\",n,\", I = \",trapezoidal_rule(f,a,b,n))\n",
    "    \n",
    "trapezoidal_rule_plot(f,a,b,5).show()\n",
    "trapezoidal_rule_plot(f,a,b,10).show()\n",
    "trapezoidal_rule_plot(f,a,b,30).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/gif": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "integrate_animate(f,flabel,flimit_a,flimit_b,trapezoidal_rule,trapezoidal_rule_plot,'trapezoidal_rule.gif', 1, 8)\n",
    "\n",
    "from IPython.display import display, Image, clear_output\n",
    "display(Image(filename='trapezoidal_rule.gif'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The error for the trapezoidal rule can be shown to be equal to (using the Taylor theorem):\n",
    "$$\n",
    "I - I_{\\rm trap} = \\int_a^b f(x) dx ~~ - ~~ (b-a) \\, \\frac{f(a) + f(b)}{2} \\approx -\\frac{(b-a)^3}{12} f''(a)\n",
    "$$\n",
    "to leading order in $(b-a)$.\n",
    "\n",
    "For the composite trapezoidal rule we have:\n",
    "$$\n",
    "I - I_{\\rm trap} = -(b-a) \\frac{h^2}{12} \\, f''(a) + \\mathcal{O}(h^4).\n",
    "$$\n",
    "\n",
    "Just like the rectangle rule, the trapezoidal rule is exact for the integration of linear functions ($f'' = 0$ and all higher-order derivatives)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N = 1 , I =  10.0\n",
      "N = 2 , I =  10.0\n",
      "N = 3 , I =  9.999999999999998\n",
      "N = 4 , I =  10.0\n",
      "N = 5 , I =  10.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "flabellinear = 'f(x) = 2*x + 3'\n",
    "def flinear(x):\n",
    "    return 2. * x + 3.\n",
    "\n",
    "a = 0.\n",
    "b = 2.\n",
    "for n in range(1,6):\n",
    "    print(\"N =\",n,\", I = \",trapezoidal_rule(flinear,a,b,n))\n",
    "    \n",
    "trapezoidal_rule_plot(flinear,a,b,1).show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simpson's rule\n",
    "\n",
    "Recall the error estimate for rectangle and trapezoidal rules:\n",
    "$$\n",
    "I - I_{\\rm rect} = \\frac{(b-a)^3}{24} f''(a) + \\mathcal{O}(h^4)\n",
    "$$\n",
    "and\n",
    "$$\n",
    "I - I_{\\rm trap} = -\\frac{(b-a)^3}{12} f''(a) + \\mathcal{O}(h^4).\n",
    "$$\n",
    "\n",
    "Simpson's rule is a combination rectangle and trapezoidal rules:\n",
    "\n",
    "$$\n",
    "I_S = \\frac{2I_{\\rm rect} + I_{\\rm trap}}{3}.\n",
    "$$\n",
    "\n",
    "This combination is chosen such that $O[(b-a)^3]$ error term vanishes. \n",
    "Another way to derive Simpson's rule is to interpolate the integrand by a quadratic polynomial through the endpoints and the midpoint.\n",
    "\n",
    "Simpson's rule reads\n",
    "$$\n",
    "\\int_{a}^b f(x) \\, dx \\approx \\frac{(b-a)}{6} \\, \\left[f(a) + 4 f \\left( \\frac{a+b}{2} \\right) + f(b)\\right].\n",
    "$$\n",
    "\n",
    "In the composite Simpson's rule one splits the integration interval into an even number $N$ of subintervals.\n",
    "With $h = (b-a)/N$ one has\n",
    "$$\n",
    "\\int_a^b f(x) \\approx \\frac{h}{3} \\left[f(x_0) + 4 \\sum_{k=1}^{N/2} f(x_{2k-1}) + 2 \\sum_{k=1}^{N/2-1} f(x_{2k}) + f(x_N) \\right] , \\qquad i = 0,\\ldots, N\n",
    "$$\n",
    "with\n",
    "$$\n",
    "x_k = a +  k h~.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simpson's rule for numerical integration \n",
    "# of function f(x) over (a,b) using n subintervals\n",
    "def simpson_rule(f, a, b, n):\n",
    "    if n % 2 == 1:\n",
    "        raise ValueError(\"Number of subintervals must be even for Simpson's rule.\")\n",
    "\n",
    "    h = (b - a) / n\n",
    "    ret = f(a) + f(b)\n",
    "    for k in range(1, n, 2):\n",
    "        xk = a + k * h \n",
    "        ret += 4 * f(xk)\n",
    "    for k in range(2, n-1, 2):\n",
    "        xk = a + k * h\n",
    "        ret += 2 * f(xk)\n",
    "    ret *= h / 3.0\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Visualize\n",
    "def simpson_rule_plot(f, a, b, n, numpoints = 100):\n",
    "    tn = n\n",
    "    if (tn == 1):\n",
    "        tn = 2\n",
    "    if tn % 2 == 1:\n",
    "        raise ValueError(\"Number of subintervals must be even for Simpson's rule.\")\n",
    "    \n",
    "    xplot = np.linspace(0,2,numpoints)\n",
    "    yplot = f(xplot)\n",
    "\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"f(x)\")\n",
    "    plt.xlim(0,2)\n",
    "    plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "    plt.plot(xplot,yplot, color = 'red',label='f(x)')\n",
    "    \n",
    "    def PolySimpson(x,a,b,m,fa,fb,fm):\n",
    "        ret = 0.\n",
    "        ret += fa * (x - m) * (x - b) / (a - m) / (a - b)\n",
    "        ret += fm * (x - a) * (x - b) / (m - a) / (m - b)\n",
    "        ret += fb * (x - a) * (x - m) / (b - a) / (b - m)\n",
    "        return ret\n",
    "    \n",
    "    labelrec = \"Simpson's rule, (N = \" + str(n) + \")\"\n",
    "    \n",
    "    xks = []\n",
    "    fks = []\n",
    "    h = (b - a) / tn\n",
    "    for k in range(1,tn,2):\n",
    "        x1 = a + h * (k-1)\n",
    "        x2 = a + h * k\n",
    "        x3 = a + h * (k+1)\n",
    "        f1 = f(x1)\n",
    "        f2 = f(x2)\n",
    "        f3 = f(x3)\n",
    "        \n",
    "        xks.append([x1,x2,x3])\n",
    "        fks.append([f1,f2,f3])\n",
    "        \n",
    "        numpointssubplot = 50\n",
    "        xsubplot = np.linspace(x1,x3,numpointssubplot)\n",
    "        ysubplot = PolySimpson(xsubplot, x1, x3, x2, f1, f3, f2)\n",
    "        \n",
    "        if (k == 1):\n",
    "            plt.plot(xsubplot, ysubplot, \n",
    "                     color = 'blue', label=labelrec)\n",
    "        else:\n",
    "            plt.plot(xsubplot, ysubplot, \n",
    "                     color = 'blue')\n",
    "    \n",
    "    plt.plot(xks,fks,'.', color = 'blue')\n",
    "    plt.legend()\n",
    "    \n",
    "    return plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using Simpson's rule\n",
      "N = 2 , I =  6.666666666666666\n",
      "N = 4 , I =  6.416666666666666\n",
      "N = 6 , I =  6.403292181069957\n",
      "N = 8 , I =  6.401041666666666\n",
      "N = 10 , I =  6.400426666666667\n",
      "N = 12 , I =  6.4002057613168715\n",
      "N = 14 , I =  6.400111064834095\n"
     ]
    },
    {
     "data": {
      "image/png": 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G8vq1fp//+fPnUt26dSUAEgDJ1tZWql27thQYGChFR0frbNugQQOpQYMGKY/v3r0rAZAqVaokJScnpzw/d+5cCYDUunVrnfcPGTIk1b91kSJFJJVKJQUHB+ts27hxY8nFxUWKiYmRJEmSWrZsKfn6+mb4WWrWrCnlz59fJ+6kpCSpQoUKkpeXl6RWqyVJkqSVK1dKAKRvvvlG5/0zZ86UAEhPnjxJ9xiZiSMtQUFBEgCpfv36qV6bOHGilNalqInz7t27Kc+9ew42bNggAZC2bdum897z589LAKTFixdnOdazZ89KAKSNGzemeq1BgwZS+fLlJUmSpD/++EMCIC1YsECSJO3vw6xZs957jCJFiqT8zmW0TJw4McvxX7x4UXJ0dJTatWuX5uvjxo2TrKyspNcZXDTpXfdEZFitW4vvsJSvi+RkSfLyEk9u3pzhe9/3/W0K7M7L4fLmzYsTJ07g/Pnz+OGHH9CmTRvcvHkTY8aMwYcffojnz5+/dx8tWrTQaS0oW7YsAOCTTz7R2U7z/IMHD3SeL1++PCpVqqTzXOfOnREVFYV//vkHgOieuXjxIr755hscOHAAUVFROtvHxMTg7Nmz6NChA5ydnVOet7a2Rrdu3fDw4UPcuHFD5z2tW7fWeVyxYkUA0Lkb7V3vi+N92rdvn6Xt32fPnj1wc3NDq1atkJSUlLL4+vrC09MzVUtaZmi6NN/XStaoUSM0adIEkydPRnR0dJaOsXv3bpw/f/69S58+fbK033v37qFly5bw9vbG8uXL09wmf/78UKvVCAsLy9K+iciwjh8Hdu0SvXYzZvz35JEjwMOHos5Bq1Zyhpcp7M7Tk5OT6MNVCien7L2/WrVqqFatGgAx4Pm7777DnDlzMHPmzFQDzN/l7u6u89jOzi7D59+99dzT0zPVPjXPvXjxAoDoBsuVKxfWrVuHpUuXwtraGvXr18eMGTNQrVo1vHr1CpIkoWDBgqn2VahQIZ19aeTNm1fnsb29PQAgNjY23c/6vjjeJ634suPp06eIiIhI+bd9V2aS4HdpPr+Dg8N7t50xYwaqVKmC2bNno2fPnpk+Rrly5TLdnZdZ9+/fh7+/P2xsbHD48OFUv38ams+V0XkmIuNSq4H/Rmvg66+BMmX+e2HFCvGzc2cxX57CsSVKTyoVkCuXchZD3iBla2uLiRMnAgCuXLliuB2nI60WAc1zmkTHxsYGw4YNwz///IOXL19iw4YNCA0NRdOmTfHmzRvkyZMHVlZWePLkSap9aVpWPDw8sh3r++J4n7QGkGu+1OPj43Wez0wCpBkUn15Ljj4lKTT/Ti9fvnzvtr6+vvjiiy/w008/4enTp5k+RvHixWFra/veJbPjlu7fvw8/Pz9IkoSgoCB4eXmlu63mcxni94GI9LN5M3D+PODsLAaWAwBevRIzDwNAFv5TJie2ROVwT548SbN15N9//wWgbcUxpqtXr+LixYs6XXrr169H7ty5UaVKlVTbu7m5oUOHDnj06BGGDBmCe/fuoVy5cqhRowZ+++03zJ49O2UwtVqtxrp16+Dl5YVSpUoZNO704sgqHx8fAMClS5fw0UcfpTy/W1NoLgMtW7bExo0bkZycjBo1amT52GnRdLveuXMnU9tPnToVW7duxaRJkzJ9jN27d6dKGtOSmd+/Bw8ewM/PD8nJyTh69Giada3eFhISgrx586KA0gesElmo+HhgzBixPmrUW2PHN24UL374IVC1qmzxZQWTqByuadOm8PLyQqtWrVCmTBmo1WoEBwfjxx9/hLOzMwYPHmz0GAoVKoTWrVsjICAABQsWxLp163Do0CHMmDEDTv/1U7Zq1QoVKlRAtWrVkC9fPty/fx9z585FkSJFULJkSQBAYGAgGjduDH9/f4wYMQJ2dnZYvHgxrly5gg0bNhiknlFm4siqFi1awN3dHb169cLkyZNhY2ODVatWpbo9Py2dOnXC//73P7Ro0QKDBw9G9erVYWtri4cPHyIoKAht2rRBu3btAIiSCT179sTKlSszrMLu5eWFYsWK4cyZMxg0aNB7YyhatCj69+//3jIPb/vQQMXzwsPD4e/vjydPnuDXX39FeHi4ThkNLy+vVK1SZ86cQYMGDWStb0WUky1aBNy7BxQsCAwb9tYLmq68nj0N271iREyicrjx48dj586dmDNnDp48eYL4+HgULFgQH3/8McaMGZPSKmFMvr6+6NmzJyZOnIhbt26hUKFC+OmnnzB06NCUbfz9/bFt2zYsX74cUVFR8PT0ROPGjTFhwoSU2+sbNGiAI0eOYOLEiejRowfUajUqVaqEXbt2oWXLlgaJNTNxZJWLiwv279+PIUOGoGvXrnBzc0Pv3r3RvHlz9O7dO8P3WltbY9euXZg3bx7Wrl2LwMBA2NjYwMvLCw0aNNBJVl7/N4gvM+OyunTpgoULFyI+Pj5lrFhGxo8fj5UrV2Z5oH12Xbt2DSEhIQCArl27pnp94sSJCEjpKxCta5cvX9Z5johM59UrYOpUsT5lihiOAgC4fBn46y8xR14a17JSqaTMjO60YFFRUXB1dUVkZCRcXFxSvR4XF4e7d++iaNGimRpoS1nj4+ODChUqYM+ePXKHYvE+//xz3L17F+fPn3/vto8fP0bRokWxZs2aVPW1zNmECROwZs0a3LlzJ8NK8bzuiYxjxAjgxx+BChWA4GBxZx4A0SQ1Zw7w6afAtm2Z2tf7vr9NgQPLiXIASZJw9OhRTJs2LVPbFypUCEOGDMG0adOgVquNHJ1pREREYNGiRZg+fboip9ohsnR37wILFoj1mTPfSqASEoC1a8W6mQwo1+BfEqIcQKVSpZpy533Gjx8PJycnPHr0yCLmmbt79y7GjBmDzp07yx0KUY40bpzIlxo1Apo1e+uFPXuA588BT893XlA+JlEkq/fNC0fyyZ07d0qpC0tQuXJlVK5cWe4wiHKk8+eBDRvEePFZs94ZN75ypfjZvbsYE2VG2J1HRERERiNJgOY+oa5dAZ3/yzx+DOzbJ9bNrCsPYBJFRERERrR1K3DyJODoCEyf/s6La9eK8uW1awOlS8sSX3YwiSIiIiKjiIsTBTUB8VOnbJskabvyvvrK5LEZgiKTqK1bt2LgwIGoV68eXFxcoFKp0qwBAwC3bt3CjBkz0LBhQ3h7e8POzg4FChRA69atERQUZLCYcnglCKIchdc7kWHMnSsKa37wATBy5DsvnjwJ3LghJn/9/HMZoss+RY7gmjp1Ki5evAhnZ2d4eXnh+vXr6W47YcIEbNq0CWXLlk2p/Hzjxg3s2rULu3fvxty5c7NVddvW1hYqlQoxMTEpU4kQkWXTzIOobwFVIgKePtV23wUGvlVYU2PZMvGzY0cgd26TxmYoikyi5syZAy8vL5QoUQLHjh2Dv79/uts2bdoUI0eORNV35tk5duwYGjdujJEjR+Lzzz/PVJXmtFhbW8PV1RXPnj1DfHw8XFxcYGNjwykjiCyQJEl48+YNwsPD4ebmBuuUQjZElFUTJgDR0UC1akCXLu+8GBEBbNki1r/+2tShGYwik6iMkqZ39UxnNH+DBg3g5+eHQ4cO4eTJk+jQoYPe8Xh6esLR0RHh4eEmn9aCiEzPzc0Nnp6ecodBZLYuXgSWLxfrc+cCVu8OHvrf/4DYWKB8eaBmTVOHZzCKTKIMxc7ODkD2m+RVKhXc3Nzg6uqK5ORkJCUlGSI8IlIgW1tbtkARZYMkiVlcJEkMdapTJ40NNF15X39tNpMNp8Vik6j79+/jjz/+gJOTE+rXr2+QfapUKtjY2HDKCCIionTs3g0cOQLY2wMzZqSxwd9/i6Yqe3ugWzeTx2dIFpkNxMfHo0uXLoiPj8eMGTOQJ0+e977n3W46e3v7TM1eT0REREJCAjB8uFgfNgzw8UljI00rVPv2gLu7qUIzCkWWOMiOpKQkdOnSJWUc1MhU91SmzdvbG66urilLYGCgkSMlIiKyLIsWAbdvAwUKAGPGpLHB69fA+vVi3YwHlGtYVEtUUlISOnfujG3btuGzzz7D+vXrM30XXWhoKFxcXFIesxWKiIgo854/ByZPFutTp6ZTtWDTJpFIlSwJNGhg0viMwWKSqMTERHTs2BHbt29H586dsWbNmiwNDnVxcdFJooiIiCjzAgJE5YJKlTKYBk/Tlde7t1kPKNewiO68hIQEtG/fHtu3b8eXX36JtWvX8u4aIiIiE7l2DVi6VKzPmQOk+RV8+TJw9ixgYwN0727S+IzF7JOo+Ph4tGvXDrt370avXr2wcuVKWKUqSEFERETGMmIEkJwMtGkDpFvqUdMK1aaNGDRlARTZnbdjxw7s2LEDABAWFgYAOH36NHr06AEA8PDwwOzZswEA/fr1w759++Dh4YEPPvgAkzUdsm/x8/ODn5+fKUInIiLKUfbvB37/HbC1BWbNSmej2Fhg7VqxbgEDyjUUmUQFBwdj9erVOs+FhIQgJCQEAFCkSJGUJOru3bsAgOfPn6eZQGkwiSIiIjKspCRtSYOBA8V48TRt2SIGTBUpAjRubKrwjE4l5fDpyqOiouDq6orIyEgOLCciIsqCRYuAb78F8uYVpQ3c3NLZsFYt4MwZYNo0YOxYgxxbCd/fHDxEREREWfbihZhkGBClDdJNoIKDRQJlYwP06mWi6EyDSRQRERFl2YQJwKtXQMWKQJ8+GWyouW3v008tZkC5BpMoIiIiypLgYODnn8X6/PmikSlN0dHA//4n1vv3N0VoJsUkioiIiDJNkoBBgwC1GujY8T2Fx9etExXKy5SxiArl72ISRURERJm2aRNw4gTg6JhBSQNAZFtLloj1fv0sokL5u5hEERERUabExIjCmoC4yc7bO4ONT58WVcodHYEvvzRJfKbGJIqIiIgyJTAQePQIKFpUm0ylS9MK1akTkCeP0WOTA5MoIiIieq87d7Tddz/9BDg4ZLDx8+eiwCYguvIsFJMoIiIieq/hw4GEBFFwvE2b92y8ahUQHw9UqQJ89JEpwpMFkygiIiLK0IEDwM6dopTBvHnvGSOuVmvrH1jogHINJlFERESUroQEYPBgsT5wIFC27Hve8McfYg4YFxfgiy+MHp+cmEQRERFRuhYuBG7cAPLnByZOzOQbAKBHD8DZ2ZihyY5JFBEREaUpLAwICBDrgYGAq+t73nD3LrBnj1j/5htjhqYITKKIiIgoTWPHiplbPvpINCy915IloshmkyZA6dLGDk92TKKIiIgolXPngJUrxfqCBYDV+zKGN2+A5cvF+rffGjU2pWASRURERDrUajGIHBAtUDVqZOJNGzYAr14BPj5AixZGjE45mEQRERGRjtWrRUtU7txiLNR7SZJ2QPmAAYC1tVHjUwomUURERJTi1Svgu+/E+vffA56emXjTqVNAcLAoY/7VV8YMT1GYRBEREVGKceOAZ8+AcuW09aHeS9MK1aUL4O5utNiUhkkUERERAQD++gtYulSsL1oE2Npm4k1PngBbt4r1AQOMFpsSMYkiIiIiJCeL0k6SJBqU/Pwy+cZffgGSkoA6dYDKlY0ZouIwiSIiIiL8+itw/ryYrWXWrEy+KTFRO09eDilr8DYmUURERDnc8+fAmDFiffJkoGDBTL5x61bRnefpCXz6qdHiUyomUURERDnc6NHAy5dApUpZGNYkScCcOWJ9wADAzs5o8SkVkygiIqIc7PRp0ZUHAIsXAzY2mXzjmTOi/8/eHujb12jxKRmTKCIiohwqKUk7T3DPnkDt2ll489y54mfXrkC+fIYOzSwwiSIiIsqhliwRNTLd3IAZM7LwxgcPgG3bxHqmi0lZHiZRREREOVBYGDB+vFifPj2LjUmLFomaCI0aAR9+aJT4zAGTKCIiohxo1CggKgqoVg3o0ycLb4yJEbWhAGDIEGOEZjaYRBEREeUwx48Da9cCKpUYTJ6l+YLXrAEiIoASJYAWLYwVollgEkVERJSDJCZqB5P36QN89FEW3qxWA/PmifXBgwGrnJ1G5OxPT0RElMPMnw9cvQp4eIixUFly4ABw4wbg6gr06GGM8MyKIpOorVu3YuDAgahXrx5cXFygUqnQtWvXDN9z6tQptGjRAu7u7nByckLFihUxd+5cJCcnmyhqIiIiZXv0CAgIEOszZgDu7lncgaasQe/egLOzASMzT5ktqWVSU6dOxcWLF+Hs7AwvLy9cv349w+137tyJ9u3bw8HBAR07doS7uzt2796NoUOH4uTJk9iyZYuJIiciIlKuoUOB16+BWrX0aEi6ehU4eFB04eXAefLSosiWqDlz5uDmzZuIiorCkiVLMtw2KioKvXv3hrW1NY4ePYpff/0Vs2bNQnBwMGrVqoWtW7di48aNJoqciIhImfbtA7ZsEYPIFy/WYzjTjz+Kn+3aAT4+hg7PLCkyifL390fJkiWhUqneu+2WLVvw/PlzfPHFF6hWrVrK8w4ODpg6dSoAYPHixUaLlYiISOliYrSDyYcMAXx9s7iDJ0+AdevE+siRBozMvCkyicqKoKAgAECzZs1SvVa/fn04OTnh9OnTiI+PN3VoREREijB5MnD/PlC4sHZMVJYsWCBu66tbF6hRw9DhmS2zT6Ju3LgBAChZsmSq12xsbFC0aFEkJSUhJCTE1KERERHJ7tIlbU/cokV6jAd//VrMDwMAI0YYNDZzp8iB5VkRGRkJAHB1dU3zdc3zERERGe4nKipK57G9vT3s7e2zHyAREZFM1GpRCyo5GWjfHmjZUo+drFghimuWLAm0amXoEM2a2bdEvY8kSQDw3vFV3t7ecHV1TVkCAwNNER4REZHR/PwzcPYskDu3tkZmliQlAXPmiPXhw3N8cc13mX1LlKalSdMi9S5NC1N6LVUaoaGhcHFxSXnMVigiIjJnjx8Do0eL9enTgQ8+0GMnv/0G3LsnKnN++aUhw7MIZp9Sli5dGgBw8+bNVK8lJSXh7t27sLGxQbFixTLcj4uLi87CJIqIiMzZkCFiguHq1YH+/fXYgSQBs2eL9W+/BRwdDRmeRTD7JKphw4YAgP3796d67fjx43jz5g1q167NpIiIiHKMvXu1NaF+/jmLEwxrnDgBnD8PODho6yOQDrNPojp06AAPDw9s3LgRf/31V8rzcXFxGD9+PACgv14pOBERkfmJiQEGDBDrQ4fqURNKQ9MK1aMHkC+fASKzPCpJM/JaQXbs2IEdO3YAAMLCwnDgwAEUK1YM9erVAwB4eHhgtubk/rd9hw4d4ODggE6dOsHd3R27du3CjRs30KFDB2zevDndgeVRUVFwdXVFZGSkzpgoIiIiczRqFDBrlqgJde0akCuXHjv591+gXDlApQKuXwdKlTJ4nNmlhO9vRQ4sDw4OxurVq3WeCwkJSan1VKRIEZ0kqm3btjh27BimTZuGbdu2IS4uDiVKlMBPP/2EQYMGZaryORERkbm7eBH46SexvmiRngkUAMycKX62aaPIBEopFNkSZUpKyGSJiIiyKzkZqFNHlDTo0EGMidJLaChQrJgob3DmjGIrlCvh+9vsx0QRERGRAWpCafz0k0ig/P0Vm0ApBZMoIiIiM/f4MTBmjFgPDAQKFdJzR8+fA7/8ItY1RaYoXUyiiIiIzNzgwaImVI0aQL9+2djRwoXAmzdAlSpA48YGi89SMYkiIiIyY9u3A1u3ZrMmFCAmGl6wQKyPHi3uzKMMMYkiIiIyUxER2ppQo0YBlSplY2fLlwMvXwIlSgCffmqI8CwekygiIiIzNXIk8OSJqELw/ffZ2FFCAvDjj2J91KhsNGflLEyiiIiIzNDhw6LxCAB+/VXMzqK3//0PePgQKFiQEw1nAZMoIiIiMxMTA/TpI9YHDADq1s3GztRqYMYMsT5sGMC5ZjONSRQREZGZ+f57ICQE8PYWJQ2yZft24MYNwM1Nm5lRpjCJIiIiMiPnzgFz54r1pUtFcU29SRIwdapYHzgQ4MwdWcIkioiIyEwkJAC9eokeuK5dgRYtsrnDPXuA4GDA2RkYMsQAEeYsTKKIiIjMxA8/AFeuAPnyAXPmZHNnkgRMmSLWBwwA3N2zHV9OwySKiIjIDFy9qu15mz8f8PDI5g4PHQLOnwccHcWAcsoyJlFEREQKl5wM9O4NJCYCrVoBHTtmc4dvt0L17Qvkz5/tGHMiJlFEREQKt3AhcOaMGPe9eLEBZmQ5dgz4809RzmDkSIPEmBMxiSIiIlKwu3eBsWPF+qxZgJeXAXaqaYXq1QsoVMgAO8yZmEQREREplCSJ0k1v3gB+fqJLL9tOnQKOHAFsbMQUL6Q3JlFEREQKtXo18McfYkqXZcsAK0N8a2tGp3fvDhQpYoAd5lxMooiIiBTo8WNg6FCxPnkyUKKEAXb611/A77+LbGzMGAPsMGdjEkVERKQwmm68iAigWjVtMpVtEyeKn126AMWLG2inOReTKCIiIoVZvRrYuxewsxPrNjYG2OnZs8C+fYC1tZh8j7KNSRQREZGCPHyonYFl8mSgXDkD7VjTCtWtm4H6BolJFBERkUJIEvD110BkJFCjBjB8uIF2fOoUcOCAaIWaMMFAOyUmUURERAqxYgWwf7+ogblqlYG68QBtK1SPHkCxYgbaKTGJIiIiUoAHD7QDyKdNA8qUMdCO//xT1EmwsQHGjzfQTglgEkVERCQ7SRKFNKOjgdq1tWOiDELTCvXVV4CPjwF3TEyiiIiIZLZsGXDokCiquXKlGLpkEMeOierktrbAuHEG2ilpMIkiIiKS0b172gHkgYFAqVIG2rEkaUsZ9O4NFC5soB2TBpMoIiIimajVYg7g16+BevWAQYMMuPMjR4Djx0WxKc0MxmRQTKKIiIhksnSpyHWcnMSdeQaZGw8QrVCaxKlvX8DLy0A7prcxiSIiIpJBSAgwcqRY/+EHA9e/3LkTOHdOZGccC2U0TKKIiIhMTK0WN8u9eQM0aAAMGGDAnScna0sZDBkCFChgwJ3T2ywqidq1axc+/vhjeHl5wdHREcWKFcNnn32G06dPyx0aERFRikWLxI1zuXIZuBsPADZsAK5eBdzctE1dZBQWk0SNGDECbdq0QXBwMJo1a4bBgwejSpUq2LlzJ+rUqYM1a9bIHSIRERFu3gS++06sz5pl4ALiCQnaO/K++04kUmQ0KkmSJLmDyK6wsDB88MEHyJcvHy5duoT8+fOnvBYUFISGDRvCx8cHd+/eTfXeqKgouLq6IjIyEi4uLqYMm4iIcpjERKBOHeD8eaBRI+DgQQO3Qi1ZAnzzjejCu3NHNHVZKCV8f1tES9T9+/ehVqtRo0YNnQQKAPz9/ZE7d248f/5cpuiIiIiE6dNFAuXmJubGM2gC9eYNMGWKWB8/3qITKKWwiCSqZMmSsLe3x9mzZxEeHq7zWlBQEKKjo9G4cWOZoiMiIgLOntXmOEuWGKHqwMKFwJMnYmqXPn0MvHNKi6Hmh5aVu7s7Zs2ahSFDhqBcuXJo164dPDw8cPv2bezatQtNmjTB0qVL5Q6TiIhyqJgYoFs3cePcF18AnToZ+ACRkaJOAgAEBIgCm2R0FpFEAcDAgQNRpEgR9OjRA8uXL095vkSJEujevXuqbr53RUVF6Ty2t7eHvb29UWIlIqKcZeRI4NYt4IMPxJ15BjdjBvDqFVC2LNC1qxEOQGmxiO48AAgMDES7du3Qo0cP3LlzBzExMfj7779RrFgxdOnSBaNGjcrw/d7e3nB1dU1ZAgMDTRQ5ERFZst9/F913ALB6NZAnj4EP8PAhMGeOWA8MNODsxfQ+FnF33pEjR9CoUSO0a9cOv/32m85rb968QalSpfDkyRPcvHkTxYsX13ldM7o/NDRUZ3Q/W6KIiCi7nj8HPvwQCAsTdS81uY5B9eolik3VrSvmylOpjHAQ5eHdeQayd+9eAOJOvHc5OTmhevXqUKvVuHDhQrr7cHFx0VmYQBERUXZIkhjfHRYGlCsn7swzuCtXxG1+gCg6lUMSKKWwiCQqISEBAPDs2bM0X9c8z8SIiIhMZc0aYPt2wNYWWLcOcHQ0wkFGjxZzyLRvD9SsaYQDUEYsIomqV68eAOCXX37Bo0ePdF77/fffcfLkSTg4OKB27dpyhEdERDnM3bvAwIFifdIkoHJlIxzk6FFg717AxsZIzVz0PhZxd16HDh3w8ccf448//kDZsmXRrl07eHp64t9//8WePXsgSRJ++OEH5M2bV+5QiYjIwiUnA927A9HRojr5e+5r0o9arZ0Xr08foFQpIxyE3sciBpYDQGJiIhYtWoSNGzfi2rVrePPmDdzd3VG9enUMGjQITZo0SfN9ShiYRkRElmPmTDFtnbMzcPGigefG09i0SRSbcnYGbt8W07zkMEr4/raYJEpfSjgJRERkGYKDgerVxRx5v/4KfPWVEQ6SkCDqQYWEiL5CzYTDOYwSvr8tYkwUERGR3OLiRJ3LxESgbVugZ08jHWjRIpFAeXoCw4YZ6SCUGUyiiIiIDGDkSODqVSB/fuCXX4xUbeDFC2DyZLE+ZYroziPZMIkiIiLKpt27xfy/gCjblC+fkQ4UEABERACVKhmxqYsyi0kUERFRNjx+rM1nhg4Fmjc30oH+/Vc7f8xPP3F6FwVgEkVERKSn5GSgWzfRy1a5spi6zmhGjBAHbN0aaNjQiAeizNK7TtTNmzdx6NAhHD9+HKGhoXj+/DkcHR2RP39++Pr6wt/fHw0bNoSDg4Mh4yUiIlKMWbOAI0cAJydgwwbAaBNjHDwI7NsnCmvOmmWkg1BWZbnEwcaNG7F48WKcPHkSAJDe21UqFdzc3NCjRw8MHDgQPj4+2Q7WGJRwiyQREZmfc+dEMc2kJGD5cjEPsFEkJQG+vmLUutFmMTY/Svj+znQSFRQUhGHDhuHixYvIkycP2rZti9q1a+Ojjz6Cp6cn3N3dERsbixcvXuD69es4c+YMDh48iDNnzsDe3h6DBg3CuHHjFJeoKOEkEBGReYmKEt13ISHA558DGzcace7fpUuB/v0Bd3dRWDNPHiMdyLwo4fs700mUlZUVqlSpgtGjR6N169aws7PL1AFu3bqFpUuXYunSpRg9ejQmTJiQrYANTQkngYiIzEu3bmJS4SJFRIFNNzcjHSgyEihZEnj2DFiwAPj2WyMdyPwo4fs700nU9u3b0a5dO70PFBYWhnv37qGmwmaZVsJJICIi87F2LfDll4CVFXD8uOjSM5phw0T3XZkywKVLgK2tEQ9mXpTw/c1pXxRwEoiIyDzcvi268V6/NsGMK9euiXpQSUnAgQNAOnPA5lRK+P42eomD5ORkYx+CiIjI6BISgM6dRQJVvz4wbpwRDyZJwKBBIoFq04YJlELpnUT1798f8fHxGW5z//591KtXT99DEBERKcb33wPnz4tx3evWGbnW5fbtwOHDombCTz8Z8UCUHXonUT///DNq1KiBGzdupPn6b7/9hsqVK+Ps2bN6B0dERKQEhw8DM2eK9eXLAW9vIx7szRvtxMKjRgHFihnxYJQdeidR48aNw5UrV1CtWjWsXr065fmEhAQMGDAAn332GaysrLB9+3aDBEpERCSHZ8/E3XiSBPTpA3z6qZEPOHMmcP8+ULgwMHq0kQ9G2ZGtgeWHDx9G165dER4ejs6dO2Pw4MH4+uuvcfHiRdSpUwcbNmyAl5eXIeM1OCUMTCMiImVSq4EWLcS47rJlgb/+EtXJjebePXGguDhgyxagQwcjHsy8KeH7O1sDyxs1aoSLFy/i448/xvr161GjRg1cuXIF48ePx7FjxxSfQBEREWXkhx9EAuXoCGzebOQEChDdeHFxYm689u2NfDDKLr3nztNwdnZGvnz5UqZ/cXV1RYMGDWBlxbmNiYjIfB07BmjqQy9aBFSoYOQDHjwoBpRbWwPz5xuxBDoZSrYynYsXL6JKlSrYsGEDmjZtiqVLlyIhIQFNmzbF+PHjoVarDRUnERGRyTx9CnzxhejO+/JLoEcPIx8wLg4YMECsDxwIlC9v5AOSIeidRC1atAi1atVCSEgIpk+fjt9//x19+vTB33//jYoVKyIwMBANGjTAw4cPDRkvERGRUSUnA127Ak+eAOXKAYsXm6BR6IcfRCXPQoWAyZONfDAyFL0HlltZWaFw4cLYsGEDatWqpfNaQkIChg8fjkWLFsHd3R3Pnz83SLDGoISBaUREpByTJwMTJ4rxT+fPi0TKqG7dEn2FCQli4NVnnxn5gJZBCd/ferdEtWnTBhcuXEiVQAGAnZ0dFixYgN9++w05fFYZIiIyI0eOAAEBYn3JEhMkUJIkuvESEoCmTXk3npkx+tx5oaGh8DZqVbLsUUImS0RE8gsLA3x9xXior74Cfv3VBAfdtAno1ElUJr9yBShRwgQHtQxK+P42+i10Sk6giIiIADEOqnNnkUBVqAAsWGCCg0ZFAUOHivWxY5lAmaFMJ1GPHz/O9sGePHmS7X0QEREZ2uTJQFAQkCuXqHFp9HpQgKif8OSJSJ5GjTLBAcnQMp1EFS9eHCNGjMDTp0+zdABJkrBz505UrlwZy5Yty3KARERExnToEDBlilj/+WegTBkTHPSff4CFC8X64sWAg4MJDkqGlukkauTIkViyZAm8vb3RunVrrFu3DiEhIWlu+/r1axw5cgTfffcdvL298emnn8LBwQGfGn3CISIiosx7/Bjo0kWM7/76a7FudElJQO/eoghVp05A48YmOCgZQ5YGloeGhmLKlClYv349YmNjAYgK5fnz50eePHkQFxeHFy9e4MmTJ1Cr1ZAkCZUrV8bIkSPRqVMno32I7FDCwDQiIjK9pCSgUSPg+HGgUiXg9GkxvYvRzZoluu/y5AH+/RcoUMAEB7U8Svj+1uvuvKioKKxfvx6HDh3CqVOndLr47Ozs8OGHH8LPzw/t27dHzZo1DRqwoSnhJBARkemNGSNqXDo7A3//DZQqZYKD3rkDfPghEBsLrFgB9OxpgoNaJiV8f2c6iZo/fz5q1qyJ6tWrp3otMTERL168gKOjI1xdXQ0epDEp4SQQEZFpbd8OaEaYbNwIdOxogoNKkui6O3xYTDD8xx+cHy8blPD9nekxUUOGDMH+/ftTHltbW2PKfyPxbG1t4enpaXYJFBER5TzXrwPdu4v1oUNNlEABwJo1IoFycBAj2JlAmb1MJ1GOjo6Ij49PeSxJEquRExGRWYmOFi1Q0dFA/frAjBkmOnB4ODBsmFgPCGBNKAuR6SSqaNGiOHDggM74J5UCs+gTJ06gffv2KFiwIOzt7VGwYEE0adIE+/btkzs0IiKSkSSJSuT//ivm+d28GbC1NdHBhwwBXr4UJdE1yRSZvUwnUf3798c///yDQoUKwdraGgAQEBAAa2vrDBcbGxujBf+uqVOnon79+jh+/DiaNWuG4cOHo1WrVnj16hWOHj1qsjiIiEh5fvwR2LpVJE5bt5rwpri9e4ENGwArK2D5chNmbmRsmc5wBgwYgHz58mH37t14/PgxgoKCULhwYfj4+BgxvMzbvHkzJkyYgI8//hi//fYbcufOrfN6YmKiTJEREZHcgoKA774T63PnArVqmejAr14BffqI9aFDgapVTXRgMgW9JyC2srJCQEAAvv/+e0PHlGVqtRrFixfH06dPcf/+feTLly/T71XC6H4iIjKe0FCRuzx7Bnz5JbBqlQnHdPfsKQ5YqhQQHGyiQlQ5gxK+v/Xua5s4cSL8/PwMGIr+Tp06hXv37qFDhw7IkycP9u7diytXrsDBwQHVq1dHLZP9l4OIiJQkPh7o0EEkUL6+wNKlJkyg9u3TZmwrVzKBskDZSqKU4vz58wAAT09PVK1aFZcuXdJ5vX79+ti6dWuWWqiIiMj8DR4MnDsnioP/9psJ85iICDGPDCC68WrXNtGByZQyPbBcycLDwwEAS5YsQWxsLI4cOYLo6GhcuXIFTZs2xfHjx/HZZ59luI+oqCid5e1yDkREZH5WrtSWY1q/Hiha1IQHHzZMTMxXsqR2dmOyOBaRRCUnJwMQtau2bdsGf39/ODs7o3z58ti+fTu8vLxw7NgxnD59Ot19eHt7w9XVNWUJDAw0VfhERGRgf/8N9O8v1idNApo1M+HBf/9dZHAqlZjaxcnJhAcnU7KIJCpPnjwAgGLFiuHDDz/Uec3R0RFNmzYFAJw7dy7dfYSGhiIyMjJlGTNmjPECJiIio3nxAmjfXoyHatUKGDfOhAePjNR24w0eDNSta8KDk6mZroiTEZUuXRoA4ObmlubrmiQrNjY23X24uLjw7jwiIjOXlCSmcbl/XxQFX7NGlGcymYEDgUePxMGnTTPhgUkOFtESVb9+fdjY2OD27dtISEhI9fqVK1cAQDE1rYiIyDiGDxfT0+XKJQaSp/N/a+PYuhVYu1ZkbatXsxsvB7CIJMrDwwMdO3ZEREQEpk+frvPaoUOHcODAAbi6uqKZSTvFiYjIlJYvB+bPF+vr1gHvjO4wridPgL59xfro0bwbL4fQu9im0oSHh6NOnTq4ffs26tevj48++gj379/H9u3boVKpsH79+jTv0FNCsS4iIsqeP/8EGjYEEhPFzXDjx5vw4JIEfPKJGFBeuTJw5gxgZ2fCAHImJXx/W0wSBQAvX77E1KlTsX37djx69Ai5c+dG3bp1MWbMGNSsWTPN9yjhJBARkf4ePACqVRMFNT/7DNi0yYQFNQFRwbN/f8DeHvjnH6BcORMePOdSwve3RSVR+lDCSSAiIv3ExIgb4IKDRSPQiRNiPJTJ3LolSqG/eQPMmQMMGWLCg+dsSvj+togxUURElPNIEtCjh0ig8ucHduwwcQKVlAR06yYSqIYNgUGDTHhwUgImUUREZJamThU3xNnaijvxChc2cQBTpgBnzwKurmKOPJPWUiAl4BknIiKzs3078P33Yn3pUqBOHRMHcPy4yOIAYMkSwNvbxAGQEjCJIiIis3LpkuhFA0RR8K++MnEAL18CXboAajXQvTvwxRcmDoCUgkkUERGZjWfPgNatxYDyjz8GZs82cQCSJKZ1efhQTC68YIGJAyAlYRJFRERmISEB6NBBO6XLpk2AjaknL1u2TAzAsrUFNmwAcuc2cQCkJEyiiIhI8SRJTEt3/LjIW3btAtzdTRzEtWvaEgbTpwNVq5o4AFIaJlFERKR4P/4I/PKLKKK5YQNQtqyJA4iLE2OfYmOBJk2AYcNMHAApEZMoIiJStG3bgJEjxfqcOWKGFZMbNkyMaM+XT0wuzHIGBCZRRESkYOfOAV27ivVvv5WpnuWGDaKMgUoFrF0LeHrKEAQpEZMoIiJSpHv3gFatRE/aJ5+IViiTzokHADduAH36iPVx44CmTU0cACkZkygiIlKciAiROIWHA5UqicYgk9+J9+aNmNH49WvAzw8ICDBxAKR0TKKIiEhREhNF7nLtGlCoELBnj0yVBAYOBC5fBgoUANavB6ytZQiClIxJFBERKYYkAd98A/zxh5hMeM8ewMtLhkBWrwZWrBADyNevBwoWlCEIUjomUUREpBizZgHLl4vcZeNGoHJlGYK4cgXo31+sBwQADRvKEASZAyZRRESkCFu3At99J9bnzgVatpQhiIgIoF07UQ+qcWNg7FgZgiBzwSSKiIhkd/asdlLhQYPEcCSTU6tFELdvA4ULcxwUvReTKCIiktW9e2JS4bg40fr0008yBTJ1qhiEZW8v5sfz8JApEDIXTKKIiEg2L14AzZuLUgaVK4tSBrI0/uzdqy1hsHQp58WjTGESRUREsnjzRhTTvH5d3IG3ezfg7CxDILdvi7LomlsDe/SQIQgyR0yiiIjI5JKSgI4dgdOngTx5gAMHgA8+kCGQmBjg00/FgPJatURZdKJMYhJFREQmJUlAv35i+JGDg2iBKldOhkDUaqB7d21Bza1bATs7GQIhc8UkioiITOr774Fff9XWgqpTR6ZAJk8Gtm0DbG3Fz0KFZAqEzBWTKCIiMpnFi8VNcIAYv92mjUyBbNkCTJok1n/+WcZMjswZkygiIjKJbduAb78V65MmAV9/LVMg//wjuvEAYNgwoGdPmQIhc8ckioiIjO7YMaBzZzEeqm9fYMIEmQIJCxPNX7GxQLNmwMyZMgVCloBJFBERGdXlyyJvSUgA2rYFFi0CVCoZAomLE1O6PHwIlCkjBmSxIjllA5MoIiIymvv3RYNPZCRQr56MM6mo1aLb7swZUVNh1y7A1VWGQMiSMIkiIiKjePECaNoUePwYKF8e2LkTcHSUKZgJE0TLk42NGFResqRMgZAlYRJFREQG9/q1mAfvxg1RjXz/ftEAJIsVK4Dp08X6smVAo0YyBUKWhkkUEREZVFycGAOl6Tk7cEAkUrI4dEiMZAdEaxSndCEDYhJFREQGk5gIfP45cOSImAdv/36ZqpEDwJUrQIcOYo6Zrl21daGIDIRJFBERGURysii/tHu3djqX6tVlCubxY6BFCyAqCqhfH1i+XKZbAsmSWWwStXbtWqhUKqhUKixfvlzucIiILJpmPrwNG8TY7W3bAD8/mYKJiACaNwdCQ4HSpYHt2wF7e5mCIUtmkUlUaGgoBg4cCGdnZ7lDISKyeJIEDB8uGnusrEQZgxYtZApGMyDr0iXA0xP4/XfA3V2mYMjSWVwSJUkSevbsibx586Jfv35yh0NEZPEmTwbmzBHry5cDn30mUyDJyaIs+vHjgIuLGJBVtKhMwVBOYHFJ1Pz583HkyBGsXLkSuXLlkjscIiKL9tNPQECAWJ83T8Zp6CQJ+OYbbdfdrl1ApUoyBUM5hUUlUf/++y9Gjx6NwYMHo379+nKHQ0Rk0ZYtE914ADB1KjBokIzBTJoE/PKLGDy+fj3QoIGMwVBOYSN3AIaSlJSEbt26oXDhwpiuKaqWBVFRUTqP7e3tYc+BiEREadqwQVt+adQoYOxYGYNZuFBbvmDxYuDTT2UMhnISi2mJmjx5Mi5cuIBVq1bBUY95Bby9veHq6pqyBAYGGiFKIiLzt2sX0K2b6EHr3x/44QcZqwesXAkMHCjWJ04UtwgSmYhFtESdO3cO06dPx/Dhw1GrVi299hEaGgoXF5eUx2yFIiJKbf9+MXA8OVkkUgsXyphAbd4M9O4t1ocOFUkUkQmZfRKl6cYrVaoUpkyZovd+XFxcdJIoIiLStX8/0LYtkJAgesxWrBAlDWSxZw/QpQugVgNffw38+COLaZLJqSRJkuQOIjsiIiKQJ5OzWg4ePBhz587VeS4qKgqurq6IjIxkEkVElI4DB0T5pfh4oF07YNMmwNZWpmCOHBGFqOLjRUmDNWsAa2uZgiG5KOH72+xbouzt7dGrV680X/vnn39w4cIF1K1bF6VLl9a7q4+IKCd7N4HauFHGBOrkSaB1axFMmzbAqlVMoEg2Zp9EOTo6pjutS0BAAC5cuIDu3bujt6bfnIiIMu3tBKptW5FA2dnJFMzJk0CzZkBMDNC4sczNYUQWdHceEREZ1sGD2gSqTRuRs8ieQL1+DTRsCOzYwfnwSHZMooiIKJV3E6jNm2VMoE6d0k2gdu8GnJxkCoZIy+wHlmeXEgamEREpyaFDYtiRZi5fRSRQ0dFMoEiHEr6/2RJFREQp/vhDm0C1bi1zAqXpwouOBvz9mUCR4jCJIiIiACKBatVKJFCtWgFbtsiYQP3xB9CkiTaB2rOHCRQpDpMoIiLC/v26CdTWrTImULt3Ay1bAm/eiJYoJlCkUEyiiIhyuG3btF14srdAbdokyqFrilLt2MEEihSLSRQRUQ62ejXw+edAYiLQsaNIqGSrHLBypahAnpQkpnTZvJllDEjRmEQREeVQixcDPXqI6ee++gr43/9krF05d64IQq0G+vQRU7nYmH09aLJwTKKIiHKgGTOAAQPE+uDBwLJlMs2eIknA6NHA0KHi8dChwNKlMs5sTJR5/C0lIspBJAkYP17kLYBYnzNHppwlMRHo2VNkdAAQGAj8+COgUskQDFHWsa2UiCiHUKtFQ8/8+eLxjBnAqFEyBfPmjRiMtXevaAJbtkwkVERmhEkUEVEOkJwshhqtWCEeL14M9O8vUzAvXogSBmfOAA4OYgB5q1YyBUOkPyZRREQWLiEB6NZN5CpWVsCqVeKxLG7dAlq0AG7fBvLkETWgateWKRii7GESRURkwWJjRa/Znj3izruNG0UZJlmcOAG0bQu8fAkUKQLs2weUKydTMETZx4HlREQW6uVL4OOPRQLl6CgKgcuWQK1fL4J5+RKoXh04e5YJFJk9JlFERBbo/n2gTh3g1CnAzQ04cABo2lSGQCQJmDpVFM9MSBBZXFAQUKCADMEQGRa784iILMylS0Dz5sDjx4CXl5gXr3x5GQKJjQV69xatUAAwYoS4JZA1oMhCMIkiIrIgQUFi2FFUFFChAvD77yKRMrmHD8Xcd3/9JSqPL1gA9OsnQyBExsMkiojIQmzaBHz5peg1q18f2LlTdOWZ3KlTotvu6VMgb15g61bAz0+GQIiMi22qREQWYO5coFMnkUB16CDGQMmSQK1YAfj7iwSqYkXREsUEiiwUkygiIjOmVouhRpqp5wYOFGUMHBxMHEh8PPDNN0CvXiKTa98eOHkS8PExcSBEpsPuPCIiM5WQIGZK0Yzb/uEHMY2Lyaeeu38f+Owz4Px5cfCAADEpHweQk4VjEkVEZIaiosSwo8OHxbjtFStkqkJ+4ADQubOo/+TuDvzvf0CzZjIEQmR6/G8CEZGZuXsXqFVLJFC5cok5fE2eQKnVwKRJopbCy5dAtWrAP/8wgaIchS1RRERm5M8/ReWA58+BQoWAXbuAqlVNHMTjx+I2wMOHxeN+/cTIdnt7EwdCJC+2RBERmYm1a4FGjUQCVaUKcO6cDAnUvn1ApUoigXJyAtasAZYsYQJFORKTKCIihVOrgbFjtTWgPv0UOH4c+OADEwYRHw8MGwZ88onI4nx9RfedLAOxiJSBSRQRkYLFxIgb3wIDxeOxY4EtW8RYKJO5cQOoXRuYM0c8HjQIOH0aKF3ahEEQKQ/HRBERKdSjR0Dr1qLBx84OWL7cxA0/ajWwaBHw3XdiHry8eYGVK4FWrUwYBJFyMYkiIlKgv/4SCdSTJ4CHB7BjB1CnjgkDCA0FvvoK+OMP8fjjj0UCJctEfETKxO48IiKF2bpVzH335AlQvrwYQG6yBEqSRK2nDz8UCZSjI7BwoagHxQSKSAeTKCIihdCUXvrsM9F71ry5mMu3aFETBfD4saif0LUrEBkJ1KgBBAcDAwaw+jhRGnhVEBEpwKtXovsuIEA8HjxY1IBycTHBwSUJ+PVXoFw5YOdOwNYWmDJFFKUqVcoEARCZJ46JIiKS2aVLogEoJERMHPzzz6KcgUmEhABffw0cOSIef/SRSKg+/NBEARCZL4toiXrx4gWWL1+Odu3aoUSJEnB0dISrqyvq1q2LX3/9FWq1Wu4QiYjS9L//ATVrilzGx0d035kkgUpMBGbNEsnSkSNi7NPs2aJ0ARMookyxiJaoLVu2oH///vD09ETDhg1RuHBhPH36FL/99ht69+6Nffv2YevWrVCZfGpzIqK0JSQAI0YACxaIx82aiYTK3d0EBz9+HPjmG+DqVfHYzw9YtgwoUcIEByeyHCpJkiS5g8iuI0eOIDo6Gi1btoS1tXXK82FhYahevTpCQ0OxZcsWdOjQIdV7o6Ki4OrqisjISLiYZPABEeV0T56IweMnT4rHEyYAEycCb/35Mo7wcGDUKGD1avHYw0O0Rn35JQeOk9lRwve3RVw1DRs2RJs2bXQSKADw9PREv379AABHjx7NcB+PHhkrOiIirT//FPPenTwpBo3v3AlMnmzkBCopSZQpKFNGm0D16QNcvw706MEEikhPFn/l2NnZAQBsbW0z3K58eTGWkojIGCQJmD8f8PcHwsKAChW0BTWN6uBBMWHwwIHiFkBfXzHu6eefRQVyItKbRSdRSUlJWP3f/7qaNWuW4baSBPT9Ohm3Zq7H6zNnEB8TY4oQiSgHiIwEvvhClC1ISgI6dQLOnAFKljTiQW/eFNOzNG0KXLsmEqbFi4Hz58VIdiLKNosYWJ6e0aNH48qVK2jevDmaNm363u2TJWs8/O4XlMQxJFlbA5UraxdfX6BiRRPP+klE5u7cOZE03b0ruuxmzxbJlNHucwkPB6ZOBZYsERmbjQ3w7bfA998DefIY6aBEOZNFDCxPy9y5czF06FCULl0af/75Jzw8PNLcTjMwDYgE4ILWbsewJvELuMY8Sb2xlZUoPOfrq02sKlcG8uUz4ichInOkVouEadw4kcv4+AAbNhixESg6GvjpJ3HQ16/Fcy1aAD/+KMZCEVkYJQwst8gkat68eRgyZAjKli2LI0eOwNPTM91t306iVCoXSBJQrJiEjbMe4qPkM8CFC2LagwsXxECGtBQqpJtU+fqKeRo4WJMoR3r6VNzwdvCgePzZZ8AvvwBubkY4WEKC2PmUKaIVCgCqVgVmzAAaNTLCAYmUgUmUEcyePRsjR45EhQoVcPjwYeTPnz/D7TUn4dq1SLx65YLOnYH790ULeGAgMGzYW7lQWJg2odL8vH1bDKh6l4uLGMz5dnJVrhzw30B3IrJMBw+KBOrpU1G/ct48oHdvI3TfJSQAq1YB06YBDx6I54oXB6ZPBzp04H/iyOIxiTKwwMBAjB07Fr6+vjh06FC6XXhve/ckRESIGRC2bhWvN2sm7ghONxeLjhZzNmiSqgsXgCtXxB+4d9naikRKk1hpFldXvT4vESlHYqKo9zRjhnhcoQKwaZO45A1+IE3ydP++eM7TExg/XpQteM+dyESWgkmUAU2ZMgXff/89qlatioMHD8I9k2V/0zoJkiSK9w4eDMTFib9Pa9cCH3+cyWASE0X9lbdbrIKDgYiItLcvWlS3K9DXF/DyMuLIUyIypLt3xd13Z8+Kx/36ieFJjo4GPEhcnEieZswA7t0TzxUoAIweDfTta+CDESkfkygDWb16NXr06AFra2sMHDjwvzFOunx8fNCjR49Uz2d0Eq5cATp2FHcHq1Si0O+kSYC9vR5BSpJocn+7xeriRe3/JN+VN69ua5WvrxgcamPRN1QSmRVJAjZuFElTVJQY87R8OdC+vQEPEhkJLF0KzJkj+ggBkTx9951InpycDHgwIvPBJMpAAgICMGnSpAy3adCgQZpVy993Et68AYYOFeM2AVHlYPVqkdMYxMuXIrF6u8Xq33+B5OTU29rbi4lB306sKlYEcuc2UDBElFnPnonp5zRd/7VrA+vXA0WKGOgAjx+LifUWLxYZGgB4ewPDh4sxB0yeKIdjEqUAmT0Jv/0m/tP3/LloDPr+e9GKbpThB3FxYmJQTWJ18aJYoqPT3r5ECZFQVaqk/cnuQCKj2bFD/D0IDxd/D8aNE0OSDNJQ/NdfwNy5YkBVUpJ4rlw50fL0xRcc80T0HyZRCpCVkxAeLprtt28Xj6tVE61SBh84mha1Wgy8eDuxCg4GHj5Me3t3d5FMvZ1Y8e5Aomx59UqMlVy7VjwuX178DahaNZs7TkwUmdm8edpZiQGgTh0xjqBlS95tR/QOJlEKkNWTIEmiyf7bb8U4cXt7URx46FATzMCelufPRUL1dovVtWtpdwfa2gJly2qTK83CYqFE77V/P9Crl+hls7ICRo7MxhhJjQcPxCCq5cuBJ/8V+LW1FYMxBw8W/1MjojQxiVIAfU/Co0diWMLvv4vHdeqIG2dKlDBOnFkSFycSqeBgbYvVxYtigGpaChbUTaoqVgRKl+YgdiKIXvThw8Udu4CY7271aqBWLT13mJwsMrKlS4F9+0QrMyD+M9OvH9C/v7gmiShDTKIUIDsnQZKAFStEK1R0tBjnOWOGGGyquJb3t+8O1LRYXbokioWmxd5edP9VrKhNrCpWZKsV5ShBQcBXX2krCgweLGpZ6jWm+99/Rfa1dq1oztLw9xfJU9u27G4nygImUQpgiJNw/774Q3vkiHjs7y/u5lNEq9T7vH4NXL6sm1hduqSde+tdnp7iDsGKFbU/y5YFHBxMGzeREUVFicHiCxeKxz4+wMqVgJ9fFnf04gWwZYtoptYUkQLEmMUePURxzNKlDRIzUU7DJEoBDHUS1GoxafqoUaIsgr29uFtn5MhsjpmQg2YQuyah0ix37qQ9xY21tejj+PBD3YXzB5KZkSRxJ+6gQdrGor59gVmzslBJJCoK2LlTFJA6eFB7h521NfDJJ0D37uKn2f1hIFIWJlEKYOiTcOeO6M7TTDxapgzw889A/frZ3rX8Xr8WpRcuXxZJlebny5dpb+/kJG5fqlBBdylYkOUXSHHu3RM3jOzdKx6XKCH+Y5SpmQoiI8X4pm3bxA7i4rSv+fqKyfQ6dxZFMonIIJhEKYAxToKmivGQIdpJ1Xv2FP+bzZvXIIdQDkkSdxVdvqxdLl0S4z/i49N+j5ubSKbKl9dd8udnckUml5goyjIFBIhWZFtbUQNu7Nj39FI/fSpanLZvBw4fFjvSKF1a1HTq2FH8T4qIDI5JlAIY8yS8egWMGSNaogDAwwP48UegW7cckCskJYlmuStXtMnV1avArVvau5He5e4ukqly5cRStqz4WahQDvgHIzmcOSO66y5dEo/r1xc3zZUtm8bGajXwzz+ixWnfPuDcOd3u7TJlgHbtgM8/Fzdj8HeWyKiYRCmAKU7CqVPiD/WVK+Kxv7/oJsiR40nj4oAbN0RCdeWK+HntWvrjrQDAxUV8QZUtq7sULcoyDKSXiAjR0rR0qfi1c3cHZs8WY711cp+wMHHHyMGDop6JpmlZo1o1kTi1a5dO5kVExsIkSgFMdRISE8Ws7pMmAbGx4k7mMWPETA6cfB3iH0WTXF27JroDr10TJRjSKhwKiH6XEiVEglW6tPZnqVLiW5HoHZIkZlMZOlTkR4AY5z1r1n/VOyIigBMnRPfcH3+I38e3OTsDjRsDLVoAzZqJ6ZWISBZMohTA1Cfh7l1gwABtkc7ChUVtqY4d2fqfpvh40QX477/A9evi57//ioQrNjb99+XNK5Kp0qXFnYOapUQJ8UVIOc5ff4lxippZVUqVApZOeQZ/9WGROP35p+h2fvtPokolBoY3agQ0bw7UrctaTkQKwSRKAeQ4CZIkZn4fPhwIDRXP1aoFzJkD1KhhkhDMn1ot/vGuXxcJ1Y0bYv3mzfTnE9Tw9BQJVfHiIqkqXly7sAXLojx8KLrTN28WN84BgJNtAkaX/A2jIsfB/lFI6jeVLAk0bChuy/P3t8C7QYgsA5MoBZDzJMTGioHmP/wAxMSI57p2BQID2UuQLTExovXq5k3tcuuW6Bp8/jzj97q6AsWKifFWmp8+PmIpUgTIlcsUn4Cy68ULLJkUjgELykCCton3S6zGdIzFB/ivCJSVlWhpqldPLHXrsgwBkZlgEqUASjgJjx+L6sirVonHjo6iaOfIkfzONrhXr0Qydfu2GMx+5452XTMBbEby5RPJVJEioi9Ws3h7i8y3QAEWGDUVSRJJ8dtj6a5ehfrKNSx82h6DMR94K4GyQjLue9aEV50iQPXqotm3alV27xKZKSV8fzOJUsBJ0Pj7bzFm488/xeMPPhCtUl268HvZJN68ERUXQ0LE4LWQELHcvy+WiIj378PGRpRk8PISS6FCorhooULadU9PUSuLg+DeLylJzPZ9755Y7t7VtjLeupVqUu0zqIEhmIuzqJnm7oKC9Ji6hYgUSQnf30yiFHAS3iZJYuzGyJHaSU8/+kh0+TVsKGtoFBEhkql798R4rPv3xaTOmiUsLP0aWO+ysxOtVp6e4me+fLqLh4cYi+PuLn66uYlpQyyFWi0q3YeHiyUsTCRLmuXxYzGgKTQ0/bszAZGIenvjdpFG+P7Zt9hwvQoAwNFRQlycSmeMuLW1OHXsKieyDEr4/mYSpYCTkJa4OFFFedo07VzA/v7A1KlA7dqyhkbpSUoSycDDh9rlyROxPH6sXd5pPck0NzexuLpqf7q6iknd3l6cncWUO46O2p+OjmKuNjs77U9bW5FZvL1YWYlMXvNnQZJEwpOUJOp0aH4mJIhf0thY7fLmjfhljY7WLlFRogv11SuRNL16JSblff488wmnra3oPtWMTdPcaVmqFO7bFMeUWQ5YtUrkWiqVmB1g6lRRD7NvX/G8tbUoeturl37/9ESkPEr4/mYSpYCTkJGwMGD6dPEFkJAgnmveHJgyRQznIDMUFyemDHn6VJzg8HDg2TPtz2fPRJLx8qVYoqLkjth43N3FdD/584v+6w8+EN2emnUfH9EF+k5/9uPH4rr45RftbCstWojkqXJl7XYPH4ohbyVKsAWKyNIo4fubSZQCTkJmPHggviBWrND2brRrJ4p3fvihvLGRkSUmaltyIiNFt2JEhHb93daf1691W4c0PxMStEt8fOZbgt5mZSXGfdnaalu4HB3FJHOOjqlbxVxcgDx5xOLurv2ZP7/osrS1zdLhw8NFXbXFi7Vz/DZsKP5TwRZaopxFCd/fTKIUcBKy4vZtYPJkYN060dOiUolCnQEBOXQaGdJfcrJIpJKTtYtaLX6pNAsgEidbW5E8yXSHw6tXYlqWefO05UBq1xb/sfD3lyUkIpKZEr6/mUQp4CTo49o1kTht2SIeW1kBX34pppIpVUrW0IgM5tUrYMECMWWSZihZ1aoieWralDc4EuVkSvj+5o3zZqpcOVGF+cIFoHVr0YCwapWYPq59e+DsWbkjJNLfgwfAsGGi/NbEiSKBqlAB2L4dOH9eTFvHBIqI5MYkysz5+gI7d4qk6ZNPRBffb78BNWsCDRoAe/fqN/SFSA6XL4sW1eLFxTRIMTFizN+GDcDFi0DbtkyeiEg5mERZiOrVgT17gCtXgB49xBCW48eBli2BihWB1au1d/cRKYkkiSKYLVqI39W1a0UlhYYNxUTdFy8CnTqx4CwRKQ//LFmY8uWBlStFoe0RI8QNUlevisSqWDExV58l3zFP5iM5WYzpq15dmzBZWQGffy667A4fZrcdESkbB5YrYGCaMUVGihpTc+dqp4ZzdRVFB/v25SB0Mr0XL0TL6OLFYspCQFRI+OorMQ6qeHF54yMi86CE728mUQo4CaYQHw/873/ArFnA9eva5xs2BPr1A9q0EUWsiYxBkoBTp0RCv3mz+H0ERMmogQOBAQPEbDdERJmlhO9vJlEKOAmmpFYD+/cDS5fqDjovUEC0Tn39tSgSTWQIkZGiptnSpWK8nkblykD//kDnzkCuXPLFR0TmSwnf30yiFHAS5PLgAbB8uVg0XX0qlZhWpl8/MdDXkua8JdP5+2+ROK1fL4qlA6Kg+RdfiN+tatU41omIskcJ399MohRwEuSWmAjs3i2+9A4d0j7v7Q107w506SLqTxFlJDxcDBRftQr46y/t8+XKicSpWzcxbzIRkSEo4fubSZQCToKS3L4tJnVdsUIMANaoXFl0vXTqxIlcSSs6WtQp+9//RAKumdfR1hbo0EF02dWty1YnIjI8JXx/W1SJg4cPH+Krr75CoUKFYG9vDx8fHwwZMgSvXr2SOzSzUaIEMHMm8PChKHDYsqWYMu3CBWDkSKBwYTFX2bJlYj5cynkSEoBdu0RCXaCAaGHav18kUNWqiTIaDx+Krrx69ZhAEZHlspiWqDt37qB27doIDw9HmzZtUKZMGZw7dw5BQUEoXbo0Tp48ibx586Z6nxIyWaV7/hzYulV8KZ44oX3e1laMn+rSRSRbTk7yxUjGlZwM/Pmn+B3YskXMaadRsqT4HfjiC5bMICLTUcL3t8UkUU2bNsXBgwcxf/58DBw4MOX5YcOGYc6cOejbty+WLl2a6n1KOAnm5MEDYONG8WV68aL2eQcHoFEjoFUrMf0Mu/zMX1QUcPCgqIS/bx/w7Jn2tYIFRUtU585iQmC2NhGRqSnh+9sikqg7d+6gRIkSKFq0KG7fvg2rt+aHiI6ORsGCBaFWqxEeHg5nZ2ed9yrhJJirq1dFMrVhA3D3ru5rvr4ioWrZUnTxcMoO8xASIpKm3buBY8fETQcabm5icuvOncW8jLxzk4jkpITvbxtZjmpgQUFBAIAmTZroJFAAkDt3btSpUwcHDx7E2bNn0ahRozT3ERMTA+s0vhWsra3h4OCgs116rKys4OjoqNe2b968QXr5rEqlgtNbfWVZ2TY2NhbqDGYgzvVWkZ6sbBsXFwcfn2SMHQuMGQNcu6bC77/bYP9+a5w9a4XgYBWCg4EpU4ACBSQ0bZqEZs2S4e+fjNy5dffr5OQE1X9NGfHx8UhKSko3hqxs6+jomPL7kJCQgMS3M4JsbOvg4JDyu5KVbRMTE5GQwQSG9vb2sLGxyfK2SUlJiNdUr0yDnZ0dbG1t09w2KQk4e9YK+/dbY98+G9y4oXv9lCypRrNmyWjePAm1aqnx324QFwfY2trC7r8KrcnJyYiLi0s3hre3VavViI2NNci2NjY2sLe3BwBIkoQ3mnoK2dw2K9c9/0akvW1cXBySNXcaZHNb/o0Q5PgbkdG2WbnujfU3QnaSBRgxYoQEQJo9e3aarw8YMEACIC1evDjVa5GRkRKAdJcWLVrobO/k5JTutg0aNNDZ1sPDI91tq1WrprNtkSJF0t22XLlyOtuWK1cu3W2LFCmis221atXS3dbDw0Nn2wYNGqS7rZOTk862LVq0yODfzUNavVqSPvtMknLnliRRr1qzJErAGQmYKQEtJcBNev36dcp+u3fvnuH5CA8PT9n2m2++yXDbu3fvpmyr+R1Jb7ly5UrKthMnTsxw23PnzqVsO3PmzAy3DQoKStl24cKFGW67Z8+elG1XrlyZ4babN29O2Xbz5s0Zbrty5cqUbbdv3ycBdSRgrATsl4BonfNjZZUk+ftL0o8/StKaNWcy3O/MmTNT9nvu3LkMt504cWLKtleuXMlw2xEjRqRse/fu3Qy3/eabb1K2DQ8Pz3Db7t27p2z7+vXrDLft0KGDzu97Rtvyb4Q+fyN0v3o6dOiQ4bb8GyEWU/yN2LNnT4bbLly4MGXboKCgDLc19t8Izfd3ZGSkJBeLaImKjIwEALi6uqb5uub5iIgIU4WUwz3Hl18CX34p7uT6+ONJOHHCFUBLACUA1PhvGQlAjVq1JPj5iS6i2NjcGeyXss4J164VxMSJonvu1KkmAJq/s80LAPsA7MEPP3yMkSO/BgAcPZr+/wSJiMhCxkT16dMHy5Ytw7Jly9C7d+9Ur48dOxaBgYEIDAzE6NGjdV7T9KneuHEDud/qZ7K3t4e9vT2b6tPZVt+m+gcPVDh1ygp//mmNkyetcetW6sFSpUurUatWMipWVKNSJTUqVFCnTA3CpvrU22qa35OSgBs3VLh0yRoXL1rh/Hkr/P23FZKSdEd958snoU6dZNStK5Zy5aSUMWtKa6pnd17O+xuRFnbnCezO092WY6IMRNPSpGmReldUVJTOdmnx9PTM1EnIlYWJvrKyrVMW6gNkZdu3/wgbctu3vzSysm3ZsmLp1Us8fvJElE04fly0lFy5Aty4YaUzNkelErfOV64sBqxXriyWfPnsU74U38fOzi7TfejG2tbW1jblj092t339Grh0CQgOBi5csEFwsA0uX9ZO7Ps2Ly/Ryle/vlhKl1ZBpbLB+y5/a2vrTP8OZ2VbKysro2yrUqmMsi1gvOuefyOyvq3mP7iG3tbS/ka8zcbGJiWhMuS2SvgbITeLSKJKly4NALh582aar9+6dQsAUIpFbBSnYEHg88/FAogq6SdOAOfOiQKfwcFAWBhw44ZYNm7UvrdQIaBiRVEgtHhxsRQrJpYs/K1XrKQkUVIiJAS4c0e7XL0K3LwJpNXQ4OwsEk1fX3FXZP36YkJpliAgIjI8i+jO05Q48PHxwZ07d9ItcfDs2bNU2a0SmgMpY2FhmhYX7c//8uJ0FSokkilNclW0KJA/P5Avn3bJ5H9QjSIpSSSMz55plwcPtIlSSAhw/77YLj0FC2pb5jQ/ixVjOQkiyhmU8P1tES1RxYsXR5MmTXDw4EEsWrRIp9jmxIkTERMTg759+5pN8yDp8vQEmjUTi0Z0tOjOunpVm3RoEpCoKODxY7H8+Wf6+3V21k2q8uUDPDxEK5adnUiy0lvs7ESCEx///uXlS5EkPX+uTZhevUq7Jeld9vYiAdS0shUvDpQuLRKmAgWy/29LRET6s4iWKCD1tC9ly5bF2bNnERQUhFKlSuHUqVOc9iUHkCSRtLzdonPnDnDvnjaJef484xYeU3J31yZwXl66yVLx4qJFjS1LRESpKeH722KSKAAIDQ3F999/j/379+PFixcoWLAg2rZti4kTJ8Ld3T3N9yjhJJBpSRIQEaFtFXq7hejFC1FIMq0WpYQE3XUbm7RbqN59zs0tdYtXvnwigcrk+E0iInqHEr6/LSqJ0ocSTgIRERFljRK+v9lRQERERKQHJlFEREREemASRURERKQHJlFEREREemASRURERKQHJlFEREREemASRURERKQHJlFEREREemASRURERKQHJlFEREREesjxSVR8fLzOz5wiPj4eAQEB/Nw5BD83P3dOwM+d8z732z/lkOPnznv48CG8vb0RGhoKLy8vucMxGSXMOSQHfm5+7pyAn5ufOydQwvd3jm+JIiIiItIHkygiIiIiPdjIHYDcNL2Z0dHRiIqKkjka09F81pz0mQF+bn7unIGfm587J4iOjgag/R6XQ44fExUSEoLixYvLHQYRERHp4c6dOyhWrJgsx87xSZRarcbjx4+RO3duqFQqucMhIiKiTJAkCdHR0ShUqBCsrOQZnZTjkygiIiIifXBgOREREZEemEQRERER6cFsk6iHDx/iq6++QqFChWBvbw8fHx8MGTIEr169Mvp+Tp06hRYtWsDd3R1OTk6oWLEi5s6di+Tk5Ox+LKPE+7YXL15g+fLlaNeuHUqUKAFHR0e4urqibt26+PXXX6FWq1O95969e1CpVOkunTp1MvTHTMUQ59vHxyfdz+Dp6Znu+8z5fK9atSrDc6dSqWBtba3zHrnP99atWzFw4EDUq1cPLi4uUKlU6Nq1q177Mqfr2xCf2xyvb0Odb3O7vg3xuc3t+tbn9zMjSri+zbLEwZ07d1C7dm2Eh4ejTZs2KFOmDM6dO4d58+Zh//79OHnyJPLmzWuU/ezcuRPt27eHg4MDOnbsCHd3d+zevRtDhw7FyZMnsWXLFmN9bIN87i1btqB///7w9PREw4YNUbhwYTx9+hS//fYbevfujX379mHr1q1pDrKvVKkS2rZtm+r5ChUqGOojpslQ5xsAXF1dMWTIkFTPOzs7p7m9uZ9vX19fTJw4Mc3XTpw4gSNHjqB58+Zpvi7X+Z46dSouXrwIZ2dneHl54fr163rtx9yub0N8bnO8vg11vgHzur4N8bnN7frOzu/nuxRzfUtmqEmTJhIAaf78+TrPDx06VAIg9e3b1yj7iYyMlDw8PCQ7Ozvp/PnzKc/HxsZKtWrVkgBIGzZs0PNTGT7etBw+fFjasWOHlJSUpPP8kydPJG9vbwmAtGXLFp3X7t69KwGQunfvnu3PoA9Dne8iRYpIRYoUyfRxLeF8Z6RmzZoSAGnnzp06z8t9vo8cOSLdvHlTUqvVUlBQkARA6tKlS5b3Y27XtyE+tzle34Y63+Z2fRvqc6dHide3Pr+f6VHK9W12SdTt27clAFLRokWl5ORkndeioqKkXLlySY6OjlJ0dLTB97N8+fJ0f/kOHz4sAZDq1aun/4czcLxZNW3aNAmANGDAAJ3n5bzoDPm5s/pH1pLP9+XLlyUA0gcffJDqD5rcX6pv0/fLxdyu73cZ40tVidf3u0yZRFny+TaX6/tt6f1+pkVJ17fZjYkKCgoCADRp0iRVXYjcuXOjTp06iI2NxdmzZw2+H817mjVrlmp/9evXh5OTE06fPm2UGaUN9bkzYmdnBwCwtbVN8/XHjx/j559/xvTp0/Hzzz/j0qVLeh8rswz9uePj47Fu3TpMnz4d8+bNQ1BQULp94ZZ8vn/++WcAQK9evVKNmdCQ43wbirld36agxOvb0Mzl+jY2c7y+3/f7+TYlXd9ml0TduHEDAFCyZMk0X9c8f/PmTYPvJ6P32NjYoGjRokhKSkJISEiGx9aHoT53epKSkrB69WoAaf+SAcChQ4fQr18/jBs3Dv369UOlSpXg7++PBw8e6HXMzDD05w4LC0O3bt0wbtw4DBkyBA0bNkTJkiVx7NixLB3bnM93bGws1q1bBysrK/Tu3Tvd7eQ434Zibte3sSn1+jY0c7m+jckcr+/M/H6+TUnXt9klUZGRkQDEAMK0aJ6PiIgw+H4MdWx9GPvYo0ePxpUrV9C8eXM0bdpU5zUnJydMmDABf//9N169eoVXr17h2LFj8Pf3x9GjR9GoUSPExMToddz3MeTn7tmzJw4fPoywsDDExMTg8uXL6Nu3L+7du4fmzZvj4sWLRjt2Vhnz2Js3b0ZERASaN28Ob2/vVK/Leb4Nxdyub2NT6vVtSOZ0fRuTOV7fGf1+pkVJ17fZJVHvI/1XgD27U7josx9DHVsf2Tn23Llz8eOPP6J06dJYs2ZNqtfz58+PyZMno0qVKnBzc4Obmxvq16+PgwcPokaNGrh9+zaWL1+e7c+gj6x87okTJ6Jhw4YoUKAAnJycUKFCBSxduhTDhg1DbGwsAgICjHZsQ8vOsX/55RcAQN++fdN8Xcnn21DM7frODnO+vrPCkq7v7DC36/t9v5/6MOX1bXZJlCZb1GSV79LMYp1etpmd/Rjq2Pow1rHnzZuHoUOHomzZsjh69Cg8PDwy/V4bG5uU5uLjx49n6biZZYp/8379+gFI/Rks8Xxfu3YNp06dgpeXF1q0aJGl95rifBuKuV3fxqL069sUlHh9G4u5Xd/6/n4q6fo2uySqdOnSANIfC3Lr1i0AQKlSpQy+n4zek5SUhLt378LGxsYos0kb6nO/bfbs2RgyZAgqVKiAo0ePZliQLj358+cHAKM1/xrjc78rvc9gaecbyNyA04wY+3wbirld38ZgDte3KSjx+jYWc7q+s/P7qaTr2+ySKH9/fwDAwYMHU1U3jY6OxsmTJ+Ho6IiaNWsafD8NGzYEAOzfvz/V/o4fP443b96gdu3asLe3z/oHew9DfW6NwMBAjBw5Er6+vggKCkq5eLJKc/eDsf7QGPpzpyW9z2BJ5xsA4uLisHbtWlhZWaFXr156xWXs820o5nZ9G5q5XN+moMTr2xjM6frO7u+noq7vLBdFUICsFNlKSEiQ/v33X+n27dvZ2o8kyV+czVCfe/LkyRIAqWrVqtKLFy/ee9wzZ85I8fHxqZ4/evSo5ODgIAGQTp48qccnyhxDfO4rV66k+VkfPHgglSpVSgIgTZs2Tec1SznfGmvWrJEASC1btszwuHKf77e9r36OJV3fb8vO5za36/tt+n5uc7y+35ad861hLtd3Vn4/zeH6VknSf6OpzMi75d7Lli2Ls2fPIigoCKVKlcKpU6dSyr3fu3cPRYsWRZEiRXDv3j2996OxY8cOdOjQAQ4ODujUqRPc3d2xa9cu3LhxAx06dMDmzZuNNhDREJ979erV6NGjB6ytrTFw4MA0+399fHzQo0ePlMd+fn64evUq/Pz84OXlBQC4fPkyDh8+DACYMmUKxo8fb5TPbKjPHRAQgB9++AH+/v4oWrQocufOjZCQEOzZswdxcXFo0aIFtm/fnlKrRMPcz/fb6tWrhz///BO7du1Cq1at0j2u3Od7x44d2LFjBwBxy/qBAwdQrFgx1KtXDwDg4eGB2bNnA7Cs69sQn9scr29DfG5zvL4N9XuuYQ7Xd1Z/P83i+s5y2qUQDx48kHr06CF5enpKtra2UuHChaVBgwalymw11VnTq2Sb2f287c8//5SaN28uubm5SQ4ODlKFChWkn376KVVlWGPI7ueeOHGiBCDDpUGDBjrvWb58ufTJJ59IRYoUkXLlyiXZ2dlJ3t7e0ueffy4dP37cyJ9YyO7nPnr0qNSpUyepdOnSkqurq2RjYyN5eHhIH3/8sbR69WpJrVane2xzPt8a165dkwBIXl5e741b7vP9vt/Rtz+jJV3fhvjc5nh9G+Jzm+P1bcjfc3O5vrP6+2kO17dZtkQRERERyc3sBpYTERERKQGTKCIiIiI9MIkiIiIi0gOTKCIiIiI9MIkiIiIi0gOTKCIiIiI9MIkiIiIi0gOTKCIiIiI9MIkiIiIi0gOTKCIiIiI9MIkiIiIi0gOTKCIiIiI9MIkiIiIi0gOTKCKyKG3btoVKpcKCBQtSvTZhwgSoVCr07dtXhsiIyNKoJEmS5A6CiMhQXr58icqVK+Pp06c4ffo0KleuDAA4fPgwmjRpgnLlyuHcuXNwdHSUOVIiMndMoojI4pw6dQoNGjRA0aJF8c8//+DNmzeoVKkSoqKicP78eZQrV07uEInIArA7j4gsTu3atTFlyhTcunULffv2RdeuXREWFoYFCxYwgSIig2FLFBFZJEmS0Lx5cxw4cAAA8MUXX2D9+vUyR0VEloQtUURkkVQqFdq1a5fyeMiQIfIFQ0QWiS1RRGSRbt26hSpVqsDW1haRkZGoUKECzp49CwcHB7lDIyILwZYoIrI48fHx6NixI2JiYrBp0yaMGTMGly5dwtChQ+UOjYgsCJMoIrI4I0aMwIULF/Ddd9+hcePGmDRpEurUqYOlS5di69atcodHRBaC3XlEZFF27NiBdu3aoVatWjh+/DhsbGwAAKGhofD19UVycjKCg4Ph4+Mjb6BEZPaYRBGRxXjw4AF8fX0hSRKCg4NRpEgRndd37tyJtm3bokaNGjhx4gRsbW1lipSILAGTKCIiIiI9cEwUERERkR6YRBERERHpgUkUERERkR6YRBERERHpgUkUERERkR6YRBERERHpgUkUERERkR6YRBERERHpgUkUERERkR6YRBERERHpgUkUERERkR6YRBERERHpgUkUERERkR7+D6NjgNKp4GZPAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gnDp1KsPvyEoc6Vm9erUBGE2bNk2zbtSoUUZ6p2JynIcOHUpZdv0x+OKLLwzA+Prrr1N9dsuWLQZgTJ8+Pduxbtq0yQCMBQsWpFnXrFkz47bbbjMMwzB++uknAzDef/99wzCu/h7efvvtG35H6dKlU35zmU2jRo264ba2bdtm+Pr6GsuXL89SHCNGjDC8vLyMy5mcNBmd9yKSs+6807ymjeFVw3j55UzL3uj6nRvUnJfHFS5cmF9++YUtW7bw5ptv0qlTJ/bu3cvw4cOpUaMG586du+E22rVrl6q2oGrVqgDcd999qcolLz969Giq5bfddhu1atVKtezRRx8lMjKSrVu3AlC/fn127NjBM888w4oVK4iMjExVPjo6mk2bNtGlSxeCg4NTlnt7e9OjRw+OHz/Onj17Un2mY8eOqd7XrFkTINXdaNe7URw38uCDD2ar/I18++23FChQgA4dOpCYmJgy1a5dm2LFiqWpScuK5CbNG9WStWrVijZt2jBmzBiioqKy9R3Lli1jy5YtN5yeeuqpTLeTmJjIE088QdeuXWnbtm2WvrtIkSLY7XZOnz6drZhFJGft2gUbNoA3ifRltss35YGa8xwWFASXL1sdxVVBQTf3+Xr16qX0JUlISOCll15i8uTJTJw4MU0H8+sVKlQo1Xs/P79Ml1+5ciXV8mLFiqXZZvKy8+fPA2YzWL58+fj888+ZMWMG3t7eNG3alLfeeot69epx8eJFDMOgePHiabZVokSJVNtKVrhw4VTv/f39AfM2+YzcKI4bSS++m3HmzBkuXbqU8m97vawkwddL3v+AgIAbln3rrbeoW7cukyZNonfv3ln+jmrVqmW5OS8zU6ZM4eDBgyxcuDClSTU5sb1y5QqXLl0if/78eHt7p3wmeb8yO84ikvtmzDBf72cxxeuWADe4mUk1UQ6y2SBfPteZnHmDlK+vL6NGjQJg9+7dzttwBtKrEUhelpzo+Pj48Pzzz7N161YuXLjAF198wbFjx2jbti0xMTEULFgQLy8vTp06lWZbyTUrYU4YrO1GcdxIeh3Iky/qcXFxqZZnJQFK7hSfUU2OI0NSJP87Xbhw4YZla9euzSOPPMK7777LmTNnsvwd5cuXx9fX94bTjfot7d69m4iICCpWrEjBggUpWLBgSq3myJEjKViwILt27Ur1meT9csbvQUSc4/Jl+Owzc74/H4ILjc+XGdVE5XGnTp1Kt3bk77//Bq7W4uSkP//8kx07dqRq0ps/fz758+enbt26acoXKFCALl26cOLECQYPHszhw4epVq0aDRo04JtvvmHSpEkpnantdjuff/454eHhVKpUyalxZxRHdpUpUwaAnTt3cscdd6QsX7Zs2Q0/2759exYsWEBSUhINGjTI9nenJ7nZ9cCBA1kqP27cOL766itef/31LH/HsmXL0iSN6bnR7+/ll19OMxjq6dOneeSRR+jXrx9du3alQoUKqdYfPHiQwoULU7Ro0SzHKyI5a/58iIqCiuylhc96eMQ17vy9ESVReVzbtm0JDw+nQ4cOVKlSBbvdzvbt23nnnXcIDg7mueeey/EYSpQoQceOHRk9ejTFixfn888/58cff+Stt94i6L92yg4dOlC9enXq1avHLbfcwpEjR5gyZQqlS5em4n9P9p4wYQKtW7emRYsWDB06FD8/P6ZPn87u3bv54osvnDKeUVbiyK527dpRqFAh+vTpw5gxY/Dx8eHTTz/l2LFjN/xst27d+L//+z/atWvHc889R/369fH19eX48eOsXr2aTp060blzZ8AcMqF3797MmTMn01HYw8PDKVeuHL/99huDBg26YQxly5alf//+Nxzm4Vo1atTIctnMVKlShSpVqqRaljwkRPny5dMd3f23336jWbNmLjO+lUheZxhXm/L6MQOvDve57GNerqckKo979dVXWbJkCZMnT+bUqVPExcVRvHhx7r77boYPH55SK5GTateuTe/evRk1ahT79u2jRIkSvPvuuwwZMiSlTIsWLfj666+ZPXs2kZGRFCtWjNatWzNy5MiU2+ubNWvGqlWrGDVqFL169cJut1OrVi2WLl1K+/btnRJrVuLIrpCQEJYvX87gwYPp3r07BQoUoG/fvtx777307ds30896e3uzdOlSpk6dymeffcaECRPw8fEhPDycZs2apUpWLv/XiS8r/bIee+wxPvjgA+Li4lL6imXm1VdfZc6cOdnuaJ/bDhw4wK5duxg9erTVoYjIf7ZsgW3bwJ8r9GQu9JpjdUhZZjOy0rvTg0VGRhIaGkpERAQhISFp1l+5coVDhw5RtmzZLHW0lewpU6YM1atX59tvv7U6FI/38MMPc+jQIbZs2XLDsidPnqRs2bLMmzcvzfha7mzkyJHMmzePAwcOZDpSvM57kdzTuzd8+in0YB7zbhkKJ05AFv5TeqPrd25Qx3KRPMAwDNasWcMbb7yRpfIlSpRg8ODBvPHGG9jt9hyOLndcunSJadOmMX78eJd81I5IXnTxIixYYM7350Po3j1LCZSr0F8SkTzAZrOleeTOjbz66qsEBQVx4sQJj3jO3KFDhxg+fDiPPuq6T4QXyWvmzTMf9VLTtpOGxm/Qc4bVIWWLkiix1I2eCyfWyZ8/f8pQF56gTp061KlTx+owROQ/13Yo729Mx1a7Nlw38LKrU3OeiIiI5Lo1a+CffyDYK5rH+D+3GRvqWkqiREREJNcljwXc3T6P/D5XwA2b2pVEiYiISK46cQIWLTLnn2E63Hcf3HKLtUE5QElUFuXxkSBE8hSd7yI5a+ZMSEqCJn6/UYPdbtmUBy6aRH311VcMHDiQJk2aEBISgs1mo3v37umW3bdvH2+99RYtW7akZMmS+Pn5UbRoUTp27Mjq1atvOhZfX19sNhvR0dE3vS0RcQ/Jz0F0dABVEclYfLyZRAEMiJ9sjk7erp21QTnIJe/OGzduHDt27CA4OJjw8HD++eefDMuOHDmS//3vf1StWjXl8Rl79uxh6dKlLFu2jClTptzUo0u8vb0JDQ3l33//JS4ujpCQEHx8fPTICBEPZBgGMTExnD17lgIFCuDt7W11SCIeZ/FiOH0aivlfpHPcIujxLPj5WR2WQ1wyiZo8eTLh4eFUqFCBtWvX0qJFiwzLtm3blmHDhnH77benWr527Vpat27NsGHDePjhh7P0qIuMFCtWjMDAQM6ePevyj7UQkZtXoEABihUrZnUYIh5p2jTz9cn4afiRAH36WBvQTXDJJCqzpOl6vXv3Tnd5s2bNaN68OT/++CMbNmygS5cuDsdjs9koUKAAoaGhJCUlkZiY6PC2RMS1+fr6qgZKJIfs2gXr1oG3l52n7R9CgwZw221Wh+Uwl0yinMXvv+pBZ/VrsNls+Pj46JERIiIiDkge1uD+fD9ya9RJ6DPa0nhulkt2LHeGI0eO8NNPPxEUFETTpk2tDkdERCRPi4yEzz4z55+JeguCgsDNH3DukVUqcXFxPPbYY8TFxfHWW29RsGDBG37m+r5O/v7++Pv751SIIiIiecq8eRAdDVULnKTFpdXwcC8ICbE6rJvicTVRiYmJPPbYYyn9oIYNG5alz5UsWZLQ0NCUacKECTkcqYiISN5gGFeb8p6JeQcbuHWH8mQeVROVmJjIo48+ytdff81DDz3E/PnzszwUwbFjxwi5JiNWLZSIiIhzrF4Nf/8N+fwT6BE3GypXhjvvtDqsm+YxSVRCQgJdu3Zl0aJFPProo8ybNy9bd9iEhISkSqJERETEOd5/33ztUWAZoWci4YkR4AHjLXpEc158fDwPPvggixYt4vHHH+ezzz7TLcoiIiIu4MgRWLrUnH/2zEjw9obHH7c2KCdx+yQqLi6Ozp07s2zZMvr06cOcOXPw8nL73RIREfEI06eD3Q6tSu3lNv6C9u3BQwazdcnmvMWLF7N48WIATp8+DcDGjRvp9d8DCsPCwpg0aRIA/fr14/vvvycsLIxbb72VMWPGpNle8+bNad68eW6ELiIiIv+JjYXZs835gZfGmTMe0KE8mUsmUdu3b2fu3Lmplh08eJCDBw8CULp06ZQk6tChQwCcO3cu3QQqmZIoERGR3DV/Ply4AGVuiab9v/8HxYvDvfdaHZbT2AzDMKwOwkqRkZGEhoYSERGhjuUiIiJOYhhQuzbs3AlvV5zJ0H1Pw4gRMG6cU7bvCtdvdR4SERERp/vlFzOBCgyw88S+l8278fr2tTosp1ISJSIiIk6XPKxB98q/U4iL0LYtlCljaUzOpiRKREREnOrYMVi0yJwfeOxFc+app6wLKIcoiRIRERGnmjEDkpKg+W1nqXFhrTmkQfv2VofldEqiRERExGmuXIGZM835gd4fmjNPPAG+vtYFlUOURImIiIjTLFgA585ByeKJdNw51iM7lCdTEiUiIiJOYRgwdao5P6Dyj/iQBG3aQNmy1gaWQ5REiYiIiFOsWwfbt0NgoMGTuwebCz2wQ3kyJVEiIiLiFFOmmK89mxyi0Lm9ZofyDh0sjSknKYkSERGRm3bwICxZYs4PinrDnPHQDuXJlESJiIjITfvgA7NPVNsmMVTd+IlHdyhPpiRKREREbkpkJMyebc4PLjrfnPHgDuXJlESJiIjITfn0U4iKgiqV7bT5+WVz4YABlsaUG5REiYiIiMOSkuC998z5QQ0243XxPJQqBe3aWRtYLlASJSIiIg77/ns4cAAKFIDH//qvFqpfP/D2tjSu3KAkSkRERByWPKzBUx1Pk+/3tebdeH36WBpTblESJSIiIg7ZuRNWrTIrnQbEvWsufOghKFLE2sByiZIoERERcUhyLdQD7eMptfQD880zz1gWT25TEiUiIiLZdvo0/N//mfPPl/kGYmOhZk1o3NjawHKRkigRERHJtmnTID4eGjUyaPj9a+bCZ54xB9nMI5REiYiISLbExMCHH5rzL9y9E/btg/z54bHHrA0slymJEhERkWyZNw/OnzcHJL9/5xhzYc+eEBxsbWC5TEmUiIiIZJndDpMnm/ODe17Ee9li803//pbFZBUlUSIiIpJl330He/dCaCj0jpxqZlXNm0O1alaHluuURImIiEiWvfOO+fp0nwTyz/1vWINBg6wLyEJKokRERCRL/vgD1q4FHx8YWPxrs2NU6dLQoYPVoVlCSZSIiIhkybv/DUretatB+Odvmm8GDDCzqjxISZSIiIjc0LFjsHChOf98822wYwcEBuaZ5+SlR0mUiIiI3NB770FiotmHvO6KCebC7t2hUCFL47KSkigRERHJVEQEfPSROf/C42dh0SLzzcCB1gXlApREiYiISKZmzoSoKHMUg3Z7pkBSErRoATVqWB2apZREiYiISIbi42HKFHN+6KB4vGbPNN/k0WENrqUkSkRERDI0fz6cPAklSsCjzM/zwxpcyyWTqK+++oqBAwfSpEkTQkJCsNlsdO/ePdPP/Prrr7Rr145ChQoRFBREzZo1mTJlCklJSbkUtYiIiGex22HSJHP+uUEG/h9OMd8MGADe3pbF5SpccmCHcePGsWPHDoKDgwkPD+eff/7JtPySJUt48MEHCQgIoGvXrhQqVIhly5YxZMgQNmzYwJdffplLkYuIiHiOH36AP/+E/Pnh6eobNKzBdVyyJmry5Mns3buXyMhIPvzww0zLRkZG0rdvX7y9vVmzZg0ff/wxb7/9Ntu3b6dRo0Z89dVXLFiwIJciFxER8Rxvv22+Pv00hM78783jj+fpYQ2u5ZJJVIsWLahYsSI2m+2GZb/88kvOnTvHI488Qr169VKWBwQEMG7cOACmT5+eY7GKiIh4os2brz7i5bmOh2DZMnPFkCHWBuZCXDKJyo7Vq1cDcM8996RZ17RpU4KCgti4cSNxcXG5HZqIiIjbSq6FevRRCP/fO2AYcN99ULmytYG5ELdPovbs2QNAxYoV06zz8fGhbNmyJCYmcvDgwdwOTURExC3t3w/ffGPOD30yAubMMd88/7x1Qbkgl+xYnh0REREAhIaGprs+efmlS5cy3U5kZGSq9/7+/vj7+998gCIiIm7m3XfNO/PuvRdqbJgBMTFQs6Y5wKakcPuaqBsxDAPghv2rSpYsSWhoaMo0YcKE3AhPRETEpZw5A598Ys6/OCTBfGgemLVQWeirnJe4fU1Uck1Tco3U9ZJrmDKqqUp27NgxQkJCUt6rFkpERPKiKVMgLg4aNoRmZxaaI20WKwbdulkdmstx+5qoyv91cNu7d2+adYmJiRw6dAgfHx/KlSuX6XZCQkJSTUqiREQkr4mIgOQb2l9+ycA2+V3zzbPPgq6Labh9EtWyZUsAli9fnmbdunXriImJoXHjxkqKREREbmDGDIiMNB803KHAL7B1KwQEmANFSRpun0R16dKFsLAwFixYwO+//56y/MqVK7z66qsA9O/f36rwRERE3EJsLEyebM6/9BJ4TfmvFqpnTwgLsy4wF+aSfaIWL17M4sWLATh9+jQAGzdupFevXgCEhYUx6b+H+YSEhDBr1iy6dOlC8+bN6datG4UKFWLp0qXs2bOHLl260LVrVyt2Q0RExG3MnWt2Ki9VCh65Yz/0WmquGDzY0rhcmUsmUdu3b2fu3Lmplh08eDBlrKfSpUunJFEA999/P2vXruWNN97g66+/5sqVK1SoUIF3332XQYMGZWnkcxERkbwqMfHq4JpDh4Lve9cMrlmlirXBuTCbkTwGQB4VGRlJaGgoERERqe7OExERySsWLIBHHjFb7Y5sPkNQ1dLmLXpr10LTplaHly5XuH67fZ8oERERcZxhwJtvmvODBkHQJx+YCVSDBtCkibXBuTiXbM4TERGR3LF8OezYAcHB8Gyvy1BrmrnixRc1uOYNqCZKREQkDxs/3nx9+mko+M3HcPEiVKgAnTpZG5gbUE2UiIhIHrVuHaxfD35+8PzABGj637AGQ4eCt7e1wbkB1USJiIjkUePGma9PPAElNnwJR49CkSLw+OPWBuYmVBMlIiKSB23eDD/+aFY4vfSiAZ0nmisGDYLAQGuDcxOqiRIREcmD3njDfO3eHcrs+9HsXZ4vH+gpH1mmmigREZE8ZudOWLrUvPlu+HBgwH+1UH37QqFClsbmTlQTJSIiksck35H30ENQOep3+Plns11vyBBrA3MzSqJERETykD17YOFCc37ECGDCBPPNI49A6dKWxeWOlESJiIjkIW++aY5S3qED1PT5C775xlzx8svWBuaGlESJiIjkEYcPw2efmfMjRgBvvWW+6dwZbrvNqrDclpIoERGRPGLiREhKgrvvhgZFDsH//Z+5YvhwawNzU0qiRERE8oDjx+Hjj835ESOAt982M6rWreGOOyyNzV0piRIREckD3nwT4uOhaVNoXvkUfPKJueKVV6wNzI0piRIREfFwJ07ArFnm/KhRwOTJEBcHjRpBs2aWxubONNimiIiIh5s40ayFuusuaFHrAnT60FwxYoQ54qY4RDVRIiIiHuzUKZg505x/7TWwffA+XL4MNWtCu3bWBufmVBMlIiLiwSZOhCtXzJa7uxtehq5TzRWvvKJaqJukmigREREPdfo0zJhhzo8aBbbp0+DiRahYEbp0sTY4D6CaKBEREQ81aZJZC9WgAbS5Mxq6TzJXjBhhPitPbopqokRERDzQ2bMwfbo5P2oU2GZ8COfOQfny8Nhj1gbnIVQTJSIi4oEmTYLYWHMczXuaxkCvt80VI0aAjy7/zqCaKBEREQ9z5gxMm2bOv/Ya2D6aYVZNlS0L3btbG5wHUSoqIiLiYSZOhJgYsxbqvhYx0HeiueKVV8DX19rgPIhqokRERDzIqVNX+0KNGQO22bPMqqnSpeHxx60NzsOoJkpERMSDTJhg3pHXuDG0bXYFnnjLXPHKK+DnZ21wHkY1USIiIh7i+HH46CNzPqUW6tQpKFUKevWyNDZPpJooERERDzF+vPmMvKZNoWXjK/D4m+aK4cNVC5UDVBMlIiLiAY4cgdmzzfmUWqiTJyE8HHr3tjY4D6WaKBEREQ8wbhwkJECrVtDsjhjo+oa54tVXwd/f2uA8lGqiRERE3NyBAzBnjjk/ZgzmIFFnzpjjQqkWKseoJkpERMTNjR0LSUlwzz3QuEYUdPzvjrzXXlNfqBzkUTVRS5cu5e677yY8PJzAwEDKlSvHQw89xMaNG60OTUREJEf8/Td89pk5//rrwNSpcP48VKqk0clzmMckUUOHDqVTp05s376de+65h+eee466deuyZMkS7rzzTubNm2d1iCIiIk732mtgt0OnTlC/4kXzoXkAo0frGXk5zGYYhmF1EDfr9OnT3Hrrrdxyyy3s3LmTIkWKpKxbvXo1LVu2pEyZMhw6dCjNZyMjIwkNDSUiIoKQkJDcDFtEROSm/PEH1KsHNhvs3AnV/zfS7GFevTrs2AFeHlNXkoYrXL894l/3yJEj2O12GjRokCqBAmjRogX58+fn3LlzFkUnIiKSM1591Xx97DGoXuwcTJliLhgzxqMTKFfhEf/CFStWxN/fn02bNnH27NlU61avXk1UVBStW7e2KDoRERHnW7cOli83W+xGj8Z86vDly1C3Ltx/v8XR5Q0e0VhaqFAh3n77bQYPHky1atXo3LkzYWFh7N+/n6VLl9KmTRtmzJhhdZgiIiJOYRgwYoQ537cvlA86BR98YC4YO9Zs35Mc5xFJFMDAgQMpXbo0vXr1YnbykK1AhQoV6NmzZ5pmvutFRkameu/v74+/BicTEREXtHw5rF8PAQH/NemNHQuxsdCoEdx7r9Xh5Rke0ZwHMGHCBDp37kyvXr04cOAA0dHR/PHHH5QrV47HHnuMF198MdPPlyxZktDQ0JRpwoQJuRS5iIhI1tntV2uhnn0Wbo3dD7NmmQsmTFAtVC7yiLvzVq1aRatWrejcuTPffPNNqnUxMTFUqlSJU6dOsXfvXsqXL59qfXLv/mPHjqXq3a+aKBERcUULF0LXrpA/Pxw8CGHPdoP//c+sgfr+e6vDyzW6O89JvvvuO8C8E+96QUFB1K9fH7vdzrZt2zLcRkhISKpJCZSIiLiaxEQYOdKcHzoUwo5uNRMom82shZJc5RF9ouLj4wH4999/012fvFyJkYiIuLNPPoG9eyEsDAYPBh4abq549FGoVcvK0PIkj6iJatKkCQAzZ87kxIkTqdb98MMPbNiwgYCAABo3bmxFeCIiIjctOvq/oQwwa6NCfl8FK1eCr+9/Tx2W3OYRNVFdunTh7rvv5qeffqJq1ap07tyZYsWK8ffff/Ptt99iGAZvvvkmhQsXtjpUERERh0ydCqdOQdmy8PRTBjR92Vzx9NNQrpy1weVRHtGxHCAhIYFp06axYMEC/vrrL2JiYihUqBD169dn0KBBtGnTJt3PuULHNBERkcycOwfly0NkJPzf/8Gj/l9Dly6QLx8cOABFi1odYq5zheu3R9REAfj6+jJ48GAGDx5sdSgiIiJONX68mUDVrg3duiRCzf/GOHjhhTyZQLkKj+gTJSIi4qkOH4Zp08z5t94Crzkfw549Zu/yF16wNLa8zmNqokRERDzRa69BfDy0agWtG0ZBj9fMFSNHgrqhWMrhJGrv3r38+OOPrFu3jmPHjnHu3DkCAwMpUqQItWvXpkWLFrRs2ZKAgABnxisiIpJn7NgBn39uzr/5Jtjenghnz0LFitCvn7XBSfY7li9YsIDp06ezYcMGADL6uM1mo0CBAvTq1YuBAwdSpkyZmw42J7hCxzQREZH0tGsHP/xgjlC+YNJxqFTJfEbeN99A585Wh2cpV7h+ZzmJWr16Nc8//zw7duygYMGC3H///TRu3Jg77riDYsWKUahQIWJjYzl//jz//PMPv/32GytXruS3337D39+fQYMGMWLECJdLVFzhIIiIiFzvp5+gdWvw8YG//4YK43rB3LnQpAmsXZvnn5HnCtfvLCdRXl5e1K1bl5dffpmOHTvi5+eXpS/Yt28fM2bMYMaMGbz88suMTB6v3kW4wkEQERG5VlIS3H672Zw3aBBM7bXNXGAYsGkT1K9vdYiWc4Xrd5aTqEWLFtH5JqoOT58+zeHDh2nYsKHD28gJrnAQRERErjV3LvTqBaGhsH+fQVi3u2HVKnjkEZg/3+rwXIIrXL89ZrBNR7nCQRAREUkWE2N2fTpxAiZOhGHVvoP27cHPzxzawEX7GOc2V7h+5/gQB0lJSXh7e+f014iIiHiEyZPNBKp0aRjYPxHqDzNXPPecEigX4/Bgm/379ycuLi7TMkeOHEl5OLCIiIhk7swZcygDgAkTIGDeTLNXeaFC8Mor1gYnaTicRH300Uc0aNCAPXv2pLv+m2++oU6dOmzatMnh4ERERPKS0aPh8mW44w7o2vqCOdImwOuvQ4ECVoYm6XA4iRoxYgS7d++mXr16zJ07N2V5fHw8AwYM4KGHHsLLy4tFixY5JVARERFP9tdfMHOmOT9pEniNfR3On4fbbtPAmi7K4SRq7NixrFixguDgYJ544gl69OjB77//ToMGDfjwww9p3Lgx27dvp2PHjs6MV0RExCO9+CLY7XD//dA07K+rD8ybMsUcLEpczk3fnXf27Fl69OjBTz/9BJjjSQ0fPpzRo0fj5eX6zzd2hd79IiKSt/34I7RpY+ZKf+42qDToHli5Ejp1gsWLrQ7PJbnC9fumU9vg4GBuueWWlMe/hIaG0qxZM7dIoERERKyWmAhDhpjzAwZApX3fmQmUr6/Zricu66YynR07dlC3bl2++OIL2rZty4wZM4iPj6dt27a8+uqr2O12Z8UpIiLikWbOhD//NG/Ae+3l+KsZ1ZAhUKGCtcFJphxOoqZNm0ajRo04ePAg48eP54cffuCpp57ijz/+oGbNmkyYMIFmzZpx/PhxZ8YrIiLiMS5evHoD3pgxUOjz92D/fihaFEaMsDY4uSGH+0R5eXlRqlQpvvjiCxo1apRqXXx8PC+88ALTpk2jUKFCnDt3zinB5gRXaFMVEZG8acgQs994tWqwY+UZfKpWhKgo+OQT6N3b6vBcmitcvx2uierUqRPbtm1Lk0AB+Pn58f777/PNN9+Qx58qIyIikq5//oEPPjDnJ08GnxEvmQnU7bdDz57WBidZ4nDH8qyM/3T//fdz++23O/oVIiIiHmvoULNTefv20CZovfnUYTCHNtDNWW4hxweeKFmyZE5/hYiIiFtZsQK++84c0uCdtxLhkQHmir59oUEDa4OTLMtyqnvy5Mmb/rJTp07d9DZERETcWUICPP+8OT9wIFT6+UPYuRMKFjQfmCduI8tJVPny5Rk6dChnzpzJ1hcYhsGSJUuoU6cOs2bNynaAIiIinmTaNPMRL2Fh8Fq/s/Dqq+aK8ePNheI2spxEDRs2jA8//JCSJUvSsWNHPv/8cw4ePJhu2cuXL7Nq1SpeeuklSpYsyQMPPEBAQAAPPPCA0wIXERFxN2fOwKhR5vz48VDgjWEQGWl2Jn/ySWuDk2zL1hAHx44dY+zYscyfP5/Y2FjAHKG8SJEiFCxYkCtXrnD+/HlOnTqF3W7HMAzq1KnDsGHD6NatW47txM1whVskRUQkb3jiCZgzx8yZNk36Be8WTcFmg99+g/r1rQ7PrbjC9duhcaIiIyOZP38+P/74I7/++muqJj4/Pz9q1KhB8+bNefDBB2nYsKFTA3Y2VzgIIiLi+TZtguRL4sZfEmn4TF3YtcusgZo509rg3JArXL+znES99957NGzYkPrpZMoJCQmcP3+ewMBAQkNDnR5kTnKFgyAiIp7Nbjdvuvv9d+jVC+bUnGz2Li9UCPbsUV8oB7jC9TvLfaIGDx7M8uXLU957e3szduxYAHx9fSlWrJjbJVAiIiK54ZNPzAQqJATefPY4jBxprnjzTSVQbizLSVRgYCBxcXEp7w3D0GjkIiIiN3DxIgwfbs6PHmVQdHR/iI6Gu+6CPn2sDU5uSpaTqLJly7JixYpU/Z9sNluOBCUiIuIpRo2Cc+fM5+M9G74Yvv0WfH3ho480Mrmby/LR69+/P1u3bqVEiRJ4e3sDMHr0aLy9vTOdfHxyfFB0ERERl7RzJ0yfbs6/NyEa3yHPmm9eesnMqsStZTnDGTBgALfccgvLli3j5MmTrF69mlKlSlGmTJkcDE9ERMQ92e3Qvz8kJUGXLtDqp+Fw8iRUqACvvGJ1eOIEDg1xAODl5cXo0aN57bXXnB1TrnKF3v0iIuJ5Pv7YfBRecDD8s2A7t3aoC4YBP/0ErVpZHZ7bc4Xrt8ONsaNGjaJ58+ZODMU5fvnlFx588EGKFy+Ov78/xYsXp02bNnz//fdWhyYiInnEuXPw4ovm/OuvJXHrq73NBKpHDyVQHsThDkujksetdyHjxo1j5MiRhIWF0b59e4oXL865c+fYtm0ba9asoV27dlaHKCIiecDw4XDhAtSoAQMTJ8P27eaYUO+8Y3Vo4kQe0+t74cKFjBw5krvvvptvvvmG/Pnzp1qfkJBgUWQiIpKX/PorzJ5tzn84/Ci+T/w3JtQ778Att1gXmDidw32iXIndbqd8+fKcOXOGI0eOcEs2fqSu0KYqIiKeITHRfC7ezp3wRG+Dj/c1hfXroW1b+OEH8zl54hSucP32iJqoX3/9lcOHD9OlSxcKFizId999x+7duwkICKB+/fo0atTI6hBFRCQP+OADM4EqVAjeqvwJzFlv9iz/6CMlUB7II5KoLVu2AFCsWDFuv/12du7cmWp906ZN+eqrr7JVQyUiIpIdJ05cfZrLWy+eJ2zcYPPNm29C6dKWxSU5xyOGSj179iwAH374IbGxsaxatYqoqCh2795N27ZtWbduHQ899FCm24iMjEw1XfuIGxERkRsZOBAuX4aGDQ2e+Pkx881dd5mDRYlH8ogkKikpCTCf5/f111/TokULgoODue2221i0aBHh4eGsXbuWjRs3ZriNkiVLEhoamjJNmDAht8IXERE3t3gxLFoEPj4w876leP24Avz9zR7merSLx/KII1uwYEEAypUrR40aNVKtCwwMpG3btgBs3rw5w20cO3aMiIiIlGl48tMiRUREMhEZCc/+9zSXYf0vU+Pd3uab11+HypWtC0xynEf0iar834+0QIEC6a5PTrJiY2Mz3EZISIjuzhMRkWwbMcLsD1W+vMHI/T3h4kXzFr0XXrA6NMlhHlET1bRpU3x8fNi/fz/x8fFp1u/evRtAz/kTERGn2rQJpk0z5z/qvILAH74BPz/49FOzbU88mkckUWFhYXTt2pVLly4xfvz4VOt+/PFHVqxYQWhoKPfcc49FEYqIiKdJSIAnnzSf5vL4A5dp9dHD5oqxY6F6dWuDk1zhMWnyu+++y6ZNm3j99ddZvXo1d9xxB0eOHGHRokV4e3sza9asDJv7REREsuvdd2HXLihc2OCdsz0gKgoaNVIzXh7iESOWJ7tw4QLjxo1j0aJFnDhxgvz583PXXXcxfPhwGjZsmO5nXGHEUxERcS8HDpiVTVeuwLzHf6THvDYQGAg7dkDFilaHlye4wvXbo5IoR7jCQRAREfdht0OrVrBmDdzdOIaV227BFhsD771nDhYlucIVrt8e0SdKREQkt8ycaSZQQUEGM688biZQLVrAgAFWhya5TEmUiIhIFh07Bi++aM5PaPkTZbd+DfnzwyefaFDNPEhHXEREJAsMA55+2uw/3rjmZZ794T5zxdSpoCF08iQlUSIiIlnw2Wfwww/g72/wceRDeCUlQJcu0KuX1aGJRZREiYiI3MDp0zB4sDk/utYiqhxeDrfeCh99BDabpbGJdZREiYiI3MCAAebTXOqWu8TQzQ+bidO8eVCokNWhiYWURImIiGRi4UL45hvw8TH45HwnfEgyB9Rs2dLq0MRiSqJEREQycPo0PPOMOT+81HxqRayD2rVh3DhL4xLXoCRKREQkHcl3450/D7VLnOXVg70hIADmzwd/f6vDExfgMc/OExERcabPPoOlS8HXx868M23xIwEmvwdVq1odmrgI1USJiIhc5/hxGDTInH89/zvUSNpuDmfw9NOWxiWuRUmUiIjINQwD+vSBiAioX3Afwy4Oh7JlYdYsDWcgqSiJEhERucbMmbByJQT4JjL3Ygd8fGywYAEUKGB1aOJi1CdKRETkP4cOmaMXAIy3D6cKe+Ctd6B+fWsDE5ekmigREREgMRF69IDoaGgSuIXnkt6B++6DIUOsDk1clJIoERER4K23YMMGyO8Tw9zYh/G6tQR8+qn6QUmG1JwnIiJ53pYtMHq0Of9BYj/K+hyH/62BsDArwxIXpyRKRETytOho6N7dbM572LaQHsZn8PZkuPNOq0MTF6fmPBERydOGDoW9e+FWr1N8aPTD9vDD8NxzVoclbkBJlIiI5FnLlsGMGeb8XHt3ClUpCrNnqx+UZIma80REJE86c8YcVBPged6hVb5N8PVmyJ/f2sDEbSiJEhGRPMduh5494d9/oQY7eYMRMPtTqFbN6tDEjag5T0RE8px334UVKyCAWObzKAHP9YNu3awOS9yMkigREclTtmyB4cMNAKYwmOotisDbb1sclbgjNeeJiEieERkJ3boZJCbaeJCveKr0Sli4BXx9rQ5N3JCSKBERyRMMA/r1g4MHbZTmMLMCn8O25HsNqCkOU3OeiIjkCZ9+Cl98Ad4k8gWPUPDTyVCrltVhiRtTEiUiIh7vn3/g2WeSABjDazQa3gIeftjiqMTdqTlPREQ8WkwMPHR/PDFX/GjFT7zUbjeMXWR1WOIBlESJiIjHMgx45skEdu/xoyin+azyG3h/sQS8va0OTTyAmvNERMRjfTLbztz5vniRxIKCz1B8xacQEmJ1WOIhlESJiIhH2rEDnu1v9oMa6/06zX94CUqXtjgq8SRKokRExONERECX1hFcSfKlHd/x8me3QYMGVoclHsZjk6jPPvsMm82GzWZj9uzZVocjIiK5xDCgT/vT7P83lFIcYd7Lf+P1SFerwxIP5JFJ1LFjxxg4cCDBwcFWhyIiIrls6rBjfL2+GL7E8+U9n1B4/AtWhyQeyuOSKMMw6N27N4ULF6Zfv35WhyMiIrnk+HGY/Op5XninOADvVJpJ/SUjwGazODLxVB43xMF7773HqlWrWLNmDatWrbI6HBERyQUffwxPPWVgtxcGoGHgDp7d1AP8/CyOTDyZR9VE/f3337z88ss899xzNG3a1OpwREQkFxw/npxAXa1x2hJXkxOXQy2MSvICj0miEhMT6dGjB6VKlWL8+PFWhyMiIrlk7z9JqRIogCS7jf37LQpI8gyPac4bM2YM27ZtY/369QQGBmb785GRkane+/v74+/v76zwREQkJxgGv728BHgg1WJvb6hQwZqQJO/wiJqozZs3M378eF544QUaNWrk0DZKlixJaGhoyjRhwgQnRykiIs62ofuHjP6jPQA2mwGYCdRHH0F4uJWRSV7g9jVRyc14lSpVYuzYsQ5v59ixY4Rc8ygA1UKJiLi2Iy9N54H5D5KAHw/XO8ikb8px4IBZA6UESnKDzTAMw+ogbsalS5coWLBglso+99xzTJkyJdWyyMhIQkNDiYiISJVEiYiI67o8ZTZ3DanHDmpTq8RZ1u8pgoYGzFtc4frt9jVR/v7+9OnTJ911W7duZdu2bdx1111UrlzZ4aY+ERFxHfb5C+gxpDA7qE3RfFEs3agESqzh9klUYGBgho91GT16NNu2baNnz5707ds3lyMTERGn+/ZbRnY/xGKG4+eVwKKVwZQqZXVQkle5fRIlIiJ5xPLlzL9/IeONeQB8PMebRo01GrlYR0mUiIi4vp9+YlPHN3gi6UcAXh6WRPfHvS0OSvI6t+9YfrNcoWOaiIhkYs0aDt3Tn4ZxazhLUTq2t7NoiRdeHjFIjzjKFa7fqokSERHXtX49F+/rTru4HzlLUWrXsvP5fCVQ4hqURImIiGvauJG4e++nc8xX/ENVwm81+O57L/LntzowEZNyeRERcT3r1mG/uw1PXJ7KWpoTEmLw/Q82SpSwOjCRq5REiYiIa/n5Z7jnHkbGvMx8HsPHx+Drr23UqGF1YCKpKYkSERHXsXw5tG/PrNjHGM8IAGbOtHH33RbHJZIOJVEiIuIali2DTp1YfKUt/ZgBwMiR0Lu3xXGJZEBJlIiIWO/LL+GBB1gX34BuXgux403v3vD661YHJpIxJVEiImKtjz6Crl3ZkViNDr7LibP70bEjzJwJNg1ILi5MSZSIiFjDMGD8eOjXj4NGGdoGriMyIYgmTWDBAvDRIDzi4vQTFRGR3Ge3w7Bh8O67nKEIbQpu4czFUGrWhKVLITDQ6gBFbkxJlIiI5K7EROjbF+bO5SIFaFtiFwdOFqZsWfPmvAIFrA5QJGuURImISO65fBkefhh++IFIrwLcU2YvOw7eQtGisHIlFC9udYAiWackSkREcsfp03DffbB1K9EBhWlfbg+b/ypM4cLw009QoYLVAYpkjzqWi4hIzvv7b2jYELZu5UpYOPfXOMAvfxUmNNSsgape3eoARbJPSZSIiOSsX36BO++EI0eIr1CNLjX+4actoeTLBz/8AHXrWh2giGOURImISM6ZPx/uvhsuXiShwV08WmUr363OR0AAfPstNGpkdYAijlMSJSIizme3w4gR8NhjEB9PfKeH6Fp0DV9/64+vLyxaBM2bWx2kyM1REiUiIs51+TJ06WIOpAnEDxvBw8b/WLTUGz8/WLwY7rnH2hBFnEF354mIiPMcPQodO8KOHeDnR9yHn9Bl0WN8+y34+yuBEs+imigREXGODRugfn0zgSpShCsr1tL5KzOBCgiAZcuUQIlnURIlIiI3xzDggw/MTk5nzkCtWkSv/Z1OExryww/mI1y++w5at7Y6UBHnUhIlIiKOi4mBnj1h4EDzcS7dunHx2w206VOSlSshKAi+/x5atrQ6UBHnU58oERFxzMGD8MADZvOdtze8/TZnHhlMm7Y2du40n4H3/fcaxkA8l5IoERHJvu++gx494OJFuOUWWLiQw2Wa07oJ7N9PyrPwata0OlCRnKPmPBERybqEBBg6FNq3NxOo+vVh61b+KtKcu+4yE6gyZWD9eiVQ4vmURImISNYcPgxNmsA775jvBw2CdevYcCScJk3gxAmoVs1MoPQwYckLlESJiMiNLV4MderApk1mZ6dFi2DqVL7+1p9WreDCBbjjDli3Dm691epgRXKHkigREclYTAw88wx07gyXLkGDBrBtG9x/P5Mnw0MPQVwcdOgAq1dD4cJWByySe5REiYhI+v74A+rWhQ8/NN+/8AKsW0dSyTIMHgzPP28OEfXMM2bFVL58lkYrkut0d56IiKSWlAQTJ8Jrr5ljP5UoAXPnwt13Ex0Njz8C33xjFn3rLRg2DGw2a0MWsYKSKBERuergQXPwzPXrzfddusBHH0GhQhw9Cp06wfbt4OcHn34KjzxiZbAi1lJznoiIgN0O778PNWqYCVRwsJklLVwIhQqxYYPZcXz7dnNYqJ9+UgIlopooEZG8bv9+6NPHvLUOoFkz+OQTKFcOgDlz4OmnzSGiatWCJUugdGkL4xVxER5RE3X+/Hlmz55N586dqVChAoGBgYSGhnLXXXfx8ccfY7fbrQ5RRMT1JCXBe++Zo2KuW2f2DJ82DVatgnLlSEw0O48/8YSZQD3wgFlJpQRKxOQRNVFffvkl/fv3p1ixYrRs2ZJSpUpx5swZvvnmG/r27cv333/PV199hU09H0VETDt2mNVLmzaZ71u2hNmzoWxZAE6dgm7drlZOjRpl9jP38oj/eos4h80wDMPqIG7WqlWriIqKon379nh7e6csP336NPXr1+fYsWN8+eWXdOnSJc1nIyMjCQ0NJSIigpCQkNwMW0Qk90VHw+jRMHmyWRMVEmLeiffUUym32K1dC127wpkzkD+/2Zz34IPWhi1yPVe4fnvE/ylatmxJp06dUiVQAMWKFaNfv34ArFmzxoLIRERcyLffwm23waRJZgL10EPw999mjZTNhmGYQxa0bGkmUNWrw++/K4ESyYhHJFGZ8fPzA8DX1zfTcidO5EY0IiIWOHDAHJugQwc4csTs1PTtt+addyVKAOZjWzp3hpdfNm/U69EDfvsNKlWyOHYRF+bRSVRiYiJz584F4J577sm07G23GXz8cW5EJSKSSy5fhhEjzKcCL10KPj7myJh//gn33ZdSbPVqs2/5kiXm+E8zZphja2oEcpHMeUTH8oy8/PLL7N69m3vvvZe2bdtmWtYwbDzZ107k7AXcf18Mt7a6Db+6dcHfP5eiFRFxEsOABQvMhCm5mr11a5g6FapWTSkWH292Fp840fxIpUowfz7cfrtFcYu4GY/oWJ6eKVOmMGTIECpXrsz69esJCwtLt1xyxzSIAK52TKvGn7S0raFFqQM0bxxPoUaVzSeY16pl9rQUEXFFv/xiJk/Jd92VLWt2Iu/YMdWzWfbuhUcfNR+PB/Dkk2Yx1T6Ju3CFjuUemURNnTqVwYMHU7VqVVatWkWxYsUyLHttEmUjP9UKneKvC8UwrmnptGGnFjtowWqas5Ym5U9S8I4KZlJVt675qkeXi4iV/vnH7NC0ZIn5Pl8+8/3QoRAQkFLMbofp0+GllyAmBgoWNEc2eOABi+IWcZCSqBwwadIkhg0bRvXq1fn5558pUqRIpuWTD4KXVwQzZ4bQpw+cPw9r1xisWnqZ1asN/jqW+uDYsFOb7TRjLc1Zw12sp3Cp4NRJVd26ZodNjU0lIjnp1CkYMwZmzTLvuPPygr59zWEMihdPVXTfPnNg8l9+Md+3aAHz5kF4eO6HLXKzlEQ52YQJE3jllVeoXbs2P/74Y4ZNeNdKPgh//RVB1arpH4TTp2HNmv+mnxPZsz9tV7Lq7KIp62jKOprwCyU4ZT5g6tqkqk4d8zEKGq1ORG7Wv/+a4xFMmwZXrpjLOnaEN99M1e8Jrg5MPmIExMaalVQTJ0K/fvpzJO5LSZQTjR07ltdee43bb7+dlStXUqhQoSx9zpGDcOqUORjdmjXmaL5//522TDkOcBfrU6Yq/IMNzIHtatdOnVxVqWLeNSMiciMXLsA775idxKOjzWWNGsGECeYz766za5c5DNTGjeb7Vq3MSqv/BiYXcVtKopxk7ty59OrVC29vbwYOHPhfH6fUypQpQ69evdIsd8ZBOHvWfJ7UunXmtGOH2e/gWoV9LtHIvoE77b/QmF+px+8EEWuuDAgwn5x+bY1VjRoQGOhQPCLigc6dMxOn996DyEhz2e23w9ixcM89aboOREWZLXpTp5o1Ufnzm2NsPvmkehmIZ1AS5SSjR4/m9ddfz7RMs2bN0h21PCcOQmSkOUjd+vXm9NtvZhX6tXy8kqgTtJdGcatplLCOhvxGaY6Q8rfN29usoapT5+pUu7bZC1RE8o4TJ8yap48+MnuCg/mfrDFjzAE0r8uIDMMcQ/P55+HkSXPZAw/AlClQsmTuhi6Sk5REuYDcOAjx8bB9O/z6K2zYYE6nTqUtVyxfJA3z7aJB9CoaRK+iHr+Tn8upC5Upc7W2qnZt81Ud2EU8z969ZvL06afmHxEwz/1XXjGHFk+nM9Pu3TBkCPz0k/m+fHn44AOzokrE0yiJcgFWHATDgKNHzaRq40azpmrbNkhMTF3Oy8ugWti/NAjcSf3Lq7jj/A9UZze+XFfwllvS1lhVrKgeoyLuxjDMPgHvvgvLlpnvAZo0MXuFt2mT7n+YTp40B82cM8fsSuDvD8OHm8MYXDO6gYhHURLlAlzhIIDZ3Ld1q5lUbd5sjpN39GjacgF+SdQufoY7AnZxe9Ra6p1aRhXjL7y5rhNWvnzmcxySk6ratc2niaqflYjriY+HL780k6etW68uv+8+MxNq0iTdj12+DG+/bfZ1Sm7pe/BB86a98uVzIW4RC7nC9VtJlAschIycOmUmVJs3w5Yt5nTpUtpyQQFJ1C7xL7cH/cXtMeupc+JbqsZtS1tjldzPKjmpSp6yMBSEiOSAo0dh5kxztMszZ8xlAQHQqxcMHgyVK6f7sdhY82MTJlz9WKNGZjLVuHGuRC5iOVe4fiuJcoGDkFWGAfv3X02o/vjDbAa8fDltWX8/OzXDL1IneB+14zdT+9QP1Ij4hWCi0xa+9VYzmapV6+prhQpqDhTJCXa72Wlp+nSzyS75Vt7ixeGZZ8zBmzL4j01srNm//K23zPHrwKxxevNNswZKXSMlL3GF67eSKBc4CDcjKcnsf/rHH/D772ZStX371Tugr2WzGVQsEU2tgkepZeyg5oU11Dy1nFIcJc3f3nz5zDuAatW6mlzVqAHBwTm/UyKe6PBhs5P4p5/CkSNXl7doYSZPnTqBr2+6H42ONmueJk68mjyVKmX2Me/dG/z8cjp4EdfjCtdvJVEucBCczW6HgwfNhGrrVnPcqu3b078jECA0OJEaRc9Sw28P1WM2U/3Uj1SP30ohLqYuaLOZ/+2tWdNMrJJfy5TRf4FF0hMTA4sXwyefwM8/X10eGgqPPw79+6cZXfxax4+bd9d99NHVpvzSpc0+5j17KnmSvM0Vrt9KolzgIOSWM2euJlS7dsHOneZo6wkJ6ZcvUTCG20KPU834i9suradaxEZu408KEJG6YP78Zi1VzZpXpxo1zNHZRfKahASzuW7+fFi06Oqo4mAOF/7EE+YQBZnc5PHHH2Yf84ULr961W768+Tzhxx9X8iQCrnH9VhLlAgfBSvHxsGePmVz9+aeZXO3enbq14XrF8l+mar6jVE3cRdWLG6mStJsq/MOtnEjdLFi6tJlMXTtVrpxhk4WI20pKMkfW/fJLM/P599+r68qWNauNevY0a20zEBkJCxaYfcy3bLm6vFkzc+yn9u3Ne0NExOQK128lUS5wEFxRZKSZVP31lzklzx87lvFn8vnGUSnwGJUTdlM5djuV2EtF9lGRfVdrr3x9zUSqenUzqapeHW67zbzQqCO7uJP4eFi9Gr7+2myyuzZxKlIEunaFRx+FBg0ybO42DHO8uNmzzdwreZgCX1/z40OGmONrikharnD9VhLlAgfBnURGwj//mM2Af/99df7AAfM/4xkJ87lIRWMvFZP+oQL7Kc8BynOACuynEBewBQWZfUOSk6pq1czXUqWUXInrOH8eli+H776DH35IPeZIwYJm5/Bu3cxmuwweKm4YZnPdwoVmxdXhw1fXVa0KffpAjx5mHiYiGXOF67eSKBc4CJ4gPt7szL53r9k8uGePOb9v39W7iTISyiXKcohyHKQcBynLoZSpdNA5AquVNZOqqlWvvpYrp7YNyXl2u9nWvWKFmTj9+mvqp4sXLWr2b3rgAWjePMOm6sREc7y3pUvN5OnQoavrgoLMWqe+fc2xnnSPhkjWuML1W0mUCxwETxcVZY5vtW+f+bp/v1lztX//1QekZqYIZyjDYUpzhNIcoRRHKeVzilJlvChZLT+Fa4Vjq1rFHEi0UiVzeIYMHD9uxlGxIoSHO3EnxXMcOWJ2DP/xR/OOunPnUq+vUcMcSfy++8ysJ4Nk/vhxM/dascLc1LWVVkFBZh+nhx6Cdu3M9yKSPa5w/VYS5QIHIS+LiTGbMw4eNKdDh66+Hj5sEBV14/+WBxBLOMcpyTHCOU54/khKFDe4tZw/JaqGcmvdohRrUJq5a0rzVD8v7HazhXDmTLPpRPIwwzAz+nXrrk7XVhOBOTZa8+ZmtnPffWYT83WSksw+g7/+evWZmPv2pS5TsKD56LsHHzQ3lUmuLyJZ4ArXbyVRLnAQJH2GYf7v/fDhq9OxY3D0iMHR/fEcPQpnLvlncWt2wPbfZLJhMLrnQSrXC6Fo1UIULeFN0aJQoIC6YXmKLVvgl1/MR8/dcQdm1v7HH+bDKX/7zcx2rq8O9faG+vWhdWtzatAgVTPdxYvmjRa7d1+9mzW9AW5tNnMz99xjTnfcoRZoEWdyheu3kigXOAjiuCtXzGvgsWNm88nxvdEc2x3JycPxnDxl48SlIE7FFiCJ9Dv5psfblkRY8BWKFErilmJe3BLuT1gxXwoXNp/GERYGhQtDoULmVLCgOXaiEi/XEBcHFy7A030TWfa9N2bibNA5dBXTonoSbI/Ah0TseJGEN3bfAOx16xFzRzMuVb+LS2XrcCk+iEuXzLHVjh5NPV3fupcsXz5o2NBs4Wvc2JwvWDAXd1wkj3GF67eSKBc4CJKzkpJg57Yk6tX3wm5cWxNlp12+tUTFeHPGKMIZinIJx656Xl5mDdb1U2ioOYWEXH0NCTHHJ82f32wpSn7Nl8/sG5NXk7H4eHNcysuXzSkq6uprVBRERJi1PcnTpUvmFHHJ4NK/8Vy6YOdipDcxCTk/EmWpUuaNpMlT8mgdGdyQJyI5wBWu3zrlxeN5e0Odet7MnAVPP20mVd7e8NFHXvTp08JccPw47N9K3J7DnPvzDP/uu8i/h6I5ezKRf2OCOE9hzhHGOcJS5i9SkAsUIoZ82O1m7ceFCzcfb0DA1YQqKMgc2Dow0Fye/BoQAP7+Vyc/P3Py9TWn5Hlvb/PCfu2rzWYmal5e5nzydC3DMG9Cu/41MdH857r2NT7eHKQ7IeHqfFycOV25cnU+NvbqdOWK+RodbbawxcRcHZk7+2zA9c26SUB6bWcGpH1SJGD++1yfBIeFmWPGlip1dSpTRoPxi4hJNVEukMlK7jl+3LwrsEKFbNydFxFhdsgye7ub05EjZtvOkSPEnY9KSagiCOUSBVKmixQkkhBz8ipIhH8RInwKc9krhMvk47I9iMsJ/lyO88UwdG87gJ9PEsF+8QR7xZKfKPIlRhAa/y8h9ovJ/5KEEHnNv/IlCvjGEFquMIWqFqVgrVLsyV+PhkPv5PqEadMms9YoKelqIuntnTqpFBH34ArXbyVRLnAQxM1dvnxNp6zjV+ePHTOf+nziRMYdaf5jALEEEk0+Yggi2iuE6JDixIYUJTb4FmKDCpuTfyhXfEOI88tPnE8+4nyCiLMFEmfzJ8HmT4LNjwSbH/F2HxKSvEhKSltzlFyrdG0NU3rSq7Xy8Ulbs5VSA+Zj4OedhK8Rhz9x+Btx+Ntj8E+Ixj8+isCESALjLhEYe4HAqLMERpwmKOIU+S4cI1/0GYKIIYgY/MjgYY42G9x6qzmMxfVTOuOG9eoFc+defd+zJ3z6aZaPqoi4OFe4fiuJcoGDIHlAXJw56ujJk+br9dO//5rT2bNpb/NylI9P6vbA5Ha/a9v/vL1TT15eZmaV/GchOctKSDAzsGvb7ZLb5K6dHG+TM9sww8PNRCn5tWxZs/2sbFmzLS2bT97dsgU2bIA77/zv7jwR8RiucP1WEuUCB0Eklbg4s+bq/HlzunDh6mtyb+prp+Se18lTZs/fyS3JPeZDQq7ewph8O2OhQuYzTYoWNV+T50NC1J4mIlnmCtdvdSwXcTX+/mYtzK23Zv+zhnG1F3dMzNXXmBiz9iguLvWr3U5Km19Skvn++t7mXl5me52Pz9We676+V2u4knu7BwVdvdUwr95iKCJ5ipIoEU9is129fU+DFImI5Cj9d1FERETEAUqiRERERBygJEpERETEAUqiRERERBygJEpERETEAUqiRERERBygJEpERETEAUqiRERERBygJEpERETEAUqiRERERBzgUUnU8ePHeeKJJyhRogT+/v6UKVOGwYMHc/HiRatDExEREQ/jMc/OO3DgAI0bN+bs2bN06tSJKlWqsHnzZqZOncry5cvZsGEDhQsXtjpMERER8RAeUxP1zDPPcPbsWd577z0WL17Mm2++yapVqxgyZAh79uxhxIgRVocoIiIiHsRmGIZhdRA368CBA1SoUIGyZcuyf/9+vLyu5oZRUVEUL14cu93O2bNnCQ4OTvXZyMhIQkNDiYiIICQkJLdDFxEREQe4wvXbI2qiVq9eDUCbNm1SJVAA+fPn58477yQ2NpZNmzZZEZ6IiIh4II/oE7Vnzx4AKlasmO76ihUrsnLlSvbu3UurVq3SLRMdHY23t3ea5d7e3gQEBKQqlxEvLy8CAwMdKhsTE0NGlYI2m42goCCHysbGxmK32zOMI1++fA6VvXLlCklJSU4pGxQUhM1mAyAuLo7ExESnlA0MDExJquPj40lISHBK2YCAgJTfSnbKJiQkEB8fn2FZf39/fHx8sl02MTGRuLi4DMv6+fnh6+ub7bJJSUlcuXIlw7K+vr74+fllu6zdbic2NtYpZX18fPD39wfAMAxiYmKcUjY7573+RqRfVn8j9DciN/5GWM7wAE8++aQBGLNmzUp3/SuvvGIAxvjx49Osi4iIMIAMp3bt2qUqHxQUlGHZZs2apSobFhaWYdl69eqlKlu6dOkMy1arVi1V2WrVqmVYtnTp0qnK1qtXL8OyYWFhqco2a9Ysw7JBQUGpyrZr1y7Tf7drdenSJdOyly9fTinbs2fPTMuePXs2pewzzzyTadlDhw6llB06dGimZXfv3p1SdtSoUZmW3bx5c0rZiRMnZlp29erVKWU/+OCDTMt+++23KWXnzJmTadmFCxemlF24cGGmZefMmZNS9ttvv8207AcffJBSdvXq1ZmWnThxYkrZzZs3Z1p21KhRKWV3796dadmhQ4emlD106FCmZZ955pmUsmfPns20bM+ePVPKXr58OdOyXbp0SfUbzqys/kaYk/5GXJ30N8KccvpvRPL1OyIiwrCKRzTn3Yjx3//Ikv93IiIiInKzPKJj+bBhw5g0aRKTJk3ihRdeSLP+2WefZdq0aUyfPp3+/funWpfcMW3Pnj3kz58/Zbm/vz/+/v6qqs+grKrqVVWv5rzsl9XfCMfK6m+ESX8jUpd1hY7lHtEnqnLlygDs3bs33fX79u0DoFKlShluo1ixYlk6CNee+M4se+0fNWeWvfaPsDPLXnvRcGbZ5OTV2WX9/Pyy3IaeU2V9fX1T/vg4s6yPj0/KH0tnlvX29s7ybzg7Zb28vHKkrM1my5GykHPnvf5GZL+s/kZkv6wn/42wmkc057Vo0QKAlStXpvlfUlRUFBs2bCAwMJCGDRtaEZ6IiIh4II9IosqXL0+bNm04fPgw06ZNS7Vu1KhRREdH8/jjj7tNZisiIiKuzyP6REHax75UrVqVTZs2sXr1aipVqsSvv/6a7mNfXKFNVURERLLHFa7fHlETBWZt1O+//06vXr3YtGkT77zzDgcOHGDQoEFs3LhRz80TERERp/KYmihHuUImKyIiItnjCtdvj6mJEhEREclNSqJEREREHKAkSkRERMQBSqJEREREHJDnk6jk4e0zG+beE8XFxTF69Gjtdx6h/dZ+5wXa77y339e+WiHP3513/PhxSpYsybFjxwgPD7c6nFzjCnc1WEH7rf3OC7Tf2u+8wBWu33m+JkpERETEEUqiRERERByQtUc1e7Dk1syoqCgiIyMtjib3JO9rXtpn0H5rv/MG7bf2Oy+IiooCrl7HrZDn+0QdPHiQ8uXLWx2GiIiIOODAgQOUK1fOku/O80mU3W7n5MmT5M+fH5vNZnU4IiIikgWGYRAVFUWJEiXw8rKmd1KeT6JEREREHKGO5SIiIiIOUBIlIiIi4gC3TaKOHz/OE088QYkSJfD396dMmTIMHjyYixcv5vh2fv31V9q1a0ehQoUICgqiZs2aTJkyhaSkpJvdrRyJ91rnz59n9uzZdO7cmQoVKhAYGEhoaCh33XUXH3/8MXa7Pc1nDh8+jM1my3Dq1q2bs3czDWcc7zJlymS4D8WKFcvwc+58vD/99NNMj53NZsPb2zvVZ6w+3l999RUDBw6kSZMmhISEYLPZ6N69u0Pbcqfz2xn77Y7nt7OOt7ud387Yb3c7vx35fWbGFc5vtxzi4MCBAzRu3JizZ8/SqVMnqlSpwubNm5k6dSrLly9nw4YNFC5cOEe2s2TJEh588EECAgLo2rUrhQoVYtmyZQwZMoQNGzbw5Zdf5tRuO2W/v/zyS/r370+xYsVo2bIlpUqV4syZM3zzzTf07duX77//nq+++irdTva1atXi/vvvT7O8evXqztrFdDnreAOEhoYyePDgNMuDg4PTLe/ux7t27dqMGjUq3XW//PILq1at4t577013vVXHe9y4cezYsYPg4GDCw8P5559/HNqOu53fzthvdzy/nXW8wb3Ob2fst7ud3zfz+7yey5zfhhtq06aNARjvvfdequVDhgwxAOPpp5/Oke1EREQYYWFhhp+fn7Fly5aU5bGxsUajRo0MwPjiiy8c3Cvnx5uen3/+2Vi8eLGRmJiYavmpU6eMkiVLGoDx5Zdfplp36NAhAzB69ux50/vgCGcd79KlSxulS5fO8vd6wvHOTMOGDQ3AWLJkSarlVh/vVatWGXv37jXsdruxevVqAzAee+yxbG/H3c5vZ+y3O57fzjre7nZ+O2u/M+KK57cjv8+MuMr57XZJ1P79+w3AKFu2rJGUlJRqXWRkpJEvXz4jMDDQiIqKcvp2Zs+eneGP7+effzYAo0mTJo7vnJPjza433njDAIwBAwakWm7lSefM/c7uH1lPPt67du0yAOPWW29N8wfN6ovqtRy9uLjb+X29nLiouuL5fb3cTKI8+Xi7y/l9rYx+n+lxpfPb7fpErV69GoA2bdqkGRcif/783HnnncTGxrJp0yanbyf5M/fcc0+a7TVt2pSgoCA2btyYI0+UdtZ+Z8bPzw8AX1/fdNefPHmSjz76iPHjx/PRRx+xc+dOh78rq5y933FxcXz++eeMHz+eqVOnsnr16gzbwj35eH/00UcA9OnTJ02fiWRWHG9ncbfzOze44vntbO5yfuc0dzy/b/T7vJYrnd9ul0Tt2bMHgIoVK6a7Pnn53r17nb6dzD7j4+ND2bJlSUxM5ODBg5l+tyOctd8ZSUxMZO7cuUD6PzKAH3/8kX79+jFixAj69etHrVq1aNGiBUePHnXoO7PC2ft9+vRpevTowYgRIxg8eDAtW7akYsWKrF27Nlvf7c7HOzY2ls8//xwvLy/69u2bYTkrjrezuNv5ndNc9fx2Nnc5v3OSO57fWfl9XsuVzm+3S6IiIiIAswNhepKXX7p0yenbcdZ3OyKnv/vll19m9+7d3HvvvbRt2zbVuqCgIEaOHMkff/zBxYsXuXjxImvXrqVFixasWbOGVq1aER0d7dD33ogz97t37978/PPPnD59mujoaHbt2sXTTz/N4cOHuffee9mxY0eOfXd25eR3L1y4kEuXLnHvvfdSsmTJNOutPN7O4m7nd05z1fPbmdzp/M5J7nh+Z/b7TI8rnd9ul0TdiPHfAOw3+wgXR7bjrO92xM1895QpU3jnnXeoXLky8+bNS7O+SJEijBkzhrp161KgQAEKFChA06ZNWblyJQ0aNGD//v3Mnj37pvfBEdnZ71GjRtGyZUuKFi1KUFAQ1atXZ8aMGTz//PPExsYyevToHPtuZ7uZ7545cyYATz/9dLrrXfl4O4u7nd83w53P7+zwpPP7Zrjb+X2j36cjcvP8drskKjlbTM4qr5f8FOuMss2b2Y6zvtsROfXdU6dOZciQIVStWpU1a9YQFhaW5c/6+PikVBevW7cuW9+bVbnxb96vXz8g7T544vH+66+/+PXXXwkPD6ddu3bZ+mxuHG9ncbfzO6e4+vmdG1zx/M4p7nZ+O/r7dKXz2+2SqMqVKwMZ9wXZt28fAJUqVXL6djL7TGJiIocOHcLHxydHnibtrP2+1qRJkxg8eDDVq1dnzZo1mQ5Il5EiRYoA5Fj1b07s9/Uy2gdPO96QtQ6nmcnp4+0s7nZ+5wR3OL9zgyue3znFnc7vm/l9utL57XZJVIsWLQBYuXJlmtFNo6Ki2LBhA4GBgTRs2NDp22nZsiUAy5cvT7O9devWERMTQ+PGjfH398/+jt2As/Y72YQJExg2bBi1a9dm9erVKSdPdiXf/ZBTf2icvd/pyWgfPOl4A1y5coXPPvsMLy8v+vTp41BcOX28ncXdzm9nc5fzOze44vmdE9zp/L7Z36dLnd/ZHhTBBWRnkK34+Hjj77//Nvbv339T2zEM6wdnc9Z+jxkzxgCM22+/3Th//vwNv/e3334z4uLi0ixfs2aNERAQYADGhg0bHNijrHHGfu/evTvdfT169KhRqVIlAzDeeOONVOs85XgnmzdvngEY7du3z/R7rT7e17rR+DmedH5f62b2293O72s5ut/ueH5f62aOdzJ3Ob+z8/t0h/PbZhj/9aZyI9cP9161alU2bdrE6tWrqVSpEr/++mvKcO+HDx+mbNmylC5dmsOHDzu8nWSLFy+mS5cuBAQE0K1bNwoVKsTSpUvZs2cPXbp0YeHChTnWEdEZ+z137lx69eqFt7c3AwcOTLf9t0yZMvTq1SvlffPmzfnzzz9p3rw54eHhAOzatYuff/4ZgLFjx/Lqq6/myD47a79Hjx7Nm2++SYsWLShbtiz58+fn4MGDfPvtt1y5coV27dqxaNGilLFKkrn78b5WkyZNWL9+PUuXLqVDhw4Zfq/Vx3vx4sUsXrwYMG9ZX7FiBeXKlaNJkyYAhIWFMWnSJMCzzm9n7Lc7nt/O2G93PL+d9TtP5g7nd3Z/n25xfmc77XIRR48eNXr16mUUK1bM8PX1NUqVKmUMGjQoTWabPDprRiPZZnU711q/fr1x7733GgUKFDACAgKM6tWrG++++26akWFzws3u96hRowwg06lZs2apPjN79mzjvvvuM0qXLm3ky5fP8PPzM0qWLGk8/PDDxrp163J4j003u99r1qwxunXrZlSuXNkIDQ01fHx8jLCwMOPuu+825s6da9jt9gy/252Pd7K//vrLAIzw8PAbxm318b7Rb/TaffSk89sZ++2O57cz9tsdz29n/s7d5fzO7u/THc5vt6yJEhEREbGa23UsFxEREXEFSqJEREREHKAkSkRERMQBSqJEREREHKAkSkRERMQBSqJEREREHKAkSkRERMQBSqJEREREHKAkSkRERMQBSqJEREREHKAkSkRERMQBSqJEREREHKAkSkRERMQBSqJExKPcf//92Gw23n///TTrRo4cic1m4+mnn7YgMhHxNDbDMAyrgxARcZYLFy5Qp04dzpw5w8aNG6lTpw4AP//8M23atKFatWps3ryZwMBAiyMVEXenJEpEPM6vv/5Ks2bNKFu2LFu3biUmJoZatWoRGRnJli1bqFatmtUhiogHUHOeiHicxo0bM3bsWPbt28fTTz9N9+7dOX36NO+//74SKBFxGtVEiYhHMgyDe++9lxUrVgDwyCOPMH/+fIujEhFPopooEfFINpuNzp07p7wfPHiwdcGIiEdSTZSIeKR9+/ZRt25dfH19iYiIoHr16mzatImAgACrQxMRD6GaKBHxOHFxcXTt2pXo6Gj+97//MXz4cHbu3MmQIUOsDk1EPIiSKBHxOEOHDmXbtm289NJLtG7dmtdff50777yTGTNm8NVXX1kdnoh4CDXniYhHWbx4MZ07d6ZRo0asW7cOHx8fAI4dO0bt2rVJSkpi+/btlClTxtpARcTtKYkSEY9x9OhRateujWEYbN++ndKlS6dav2TJEu6//34aNGjAL7/8gq+vr0WRiognUBIlIiIi4gD1iRIRERFxgJIoEREREQcoiRIRERFxgJIoEREREQcoiRIRERFxgJIoEREREQcoiRIRERFxgJIoEREREQcoiRIRERFxgJIoEREREQcoiRIRERFxgJIoEREREQcoiRIRERFxwP8DuKiCYqlPYAEAAAAASUVORK5CYII=",
      "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": [
    "a = 0.\n",
    "b = 2.\n",
    "print(\"Computing the integral of\",flabel, \"over the interval (\",a,\",\",b,\") using Simpson's rule\")\n",
    "for n in range(2,15,2):\n",
    "    print(\"N =\",n,\", I = \",simpson_rule(f,a,b,n))\n",
    "    \n",
    "simpson_rule_plot(f,a,b,2).show()\n",
    "simpson_rule_plot(f,a,b,4).show()\n",
    "simpson_rule_plot(f,a,b,6).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/gif": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "integrate_animate(f,flabel,flimit_a,flimit_b,simpson_rule,simpson_rule_plot,'simpson_rule.gif', 2, 8)\n",
    "\n",
    "from IPython.display import display, Image, clear_output\n",
    "display(Image(filename='simpson_rule.gif'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using Simpson's rule\n",
      "    N            rectangle          trapezoidal              Simpson\n",
      "    2    5.125000000000000    9.000000000000000    6.666666666666666\n",
      "    4    6.070312500000000    7.062500000000000    6.416666666666666\n",
      "    6    6.252572016460903    6.695473251028805    6.403292181069957\n",
      "    8    6.316894531250000    6.566406250000000    6.401041666666666\n",
      "   10    6.346759999999996    6.506559999999999    6.400426666666667\n",
      "   12    6.363007973251031    6.474022633744856    6.400205761316871\n",
      "   14    6.372813411078710    6.454394002498951    6.400111064834095\n",
      "   16    6.379180908203125    6.441650390625000    6.400065104166666\n",
      "   18    6.383547985571311    6.432911649646909    6.400040644210740\n",
      "   20    6.386672500000006    6.426660000000005    6.400026666666668\n"
     ]
    }
   ],
   "source": [
    "a = flimit_a\n",
    "b = flimit_b\n",
    "print(\"Computing the integral of\",flabel, \"over the interval (\",a,\",\",b,\") using Simpson's rule\")\n",
    "print(\"{0:>5} {1:>20} {2:>20} {3:>20}\".format(\"N\", \"rectangle\", \"trapezoidal\", \"Simpson\"))\n",
    "for n in range(2,21,2):\n",
    "    print(\"{0:5} {1:20.15f} {2:20.15f} {3:20.15f}\".format(n, rectangle_rule(f,a,b,n), \n",
    "                                                          trapezoidal_rule(f,a,b,n), \n",
    "                                                          simpson_rule(f,a,b,n)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The error for the Simpson's rule can be shown to be of order $h^4$, i.e.\n",
    "$$\n",
    "I - I_S = C \\, h^4 + \\mathcal{O}(h^6)\n",
    "$$\n",
    "\n",
    "Simpson's rule is exact for polynomials up to 3rd order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simpson's rule:\n",
      "N = 2 , I =  16.0\n",
      "N = 4 , I =  16.0\n",
      "N = 6 , I =  16.0\n",
      "N = 8 , I =  16.0\n",
      "N = 10 , I =  16.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Trapezoidal rule:\n",
      "N = 2 , I =  17.0\n",
      "N = 4 , I =  16.25\n",
      "N = 6 , I =  16.111111111111107\n",
      "N = 8 , I =  16.0625\n",
      "N = 10 , I =  16.04\n"
     ]
    }
   ],
   "source": [
    "flabelquad = 'f(x) = 3 * x^2 + x + 3'\n",
    "def fquad(x):\n",
    "    return 3. * x**2 + x + 3.\n",
    "\n",
    "a = 0.\n",
    "b = 2.\n",
    "print(\"Simpson's rule:\")\n",
    "for n in range(2,11,2):\n",
    "    print(\"N =\",n,\", I = \",simpson_rule(fquad,a,b,n))\n",
    "    \n",
    "tplot =  simpson_rule_plot(fquad,a,b,2)\n",
    "tplot.title(flabelquad)\n",
    "tplot.show()\n",
    "\n",
    "print('')\n",
    "\n",
    "print(\"Trapezoidal rule:\")\n",
    "for n in range(2,11,2):\n",
    "    print(\"N =\",n,\", I = \",trapezoidal_rule(fquad,a,b,n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simpson's rule:\n",
      "N = 2 , I =  8.0\n",
      "N = 4 , I =  8.0\n",
      "N = 6 , I =  7.999999999999998\n",
      "N = 8 , I =  8.0\n",
      "N = 10 , I =  8.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Trapezoidal rule:\n",
      "N = 2 , I =  9.0\n",
      "N = 4 , I =  8.25\n",
      "N = 6 , I =  8.111111111111109\n",
      "N = 8 , I =  8.0625\n",
      "N = 10 , I =  8.04\n"
     ]
    }
   ],
   "source": [
    "flabelcubic = 'f(x) = 2*x^3 - 3 * x^2 + x + 3'\n",
    "def fcubic(x):\n",
    "    return 2. * x**3 - 3. * x**2 + x + 3.\n",
    "\n",
    "a = 0.\n",
    "b = 2.\n",
    "print(\"Simpson's rule:\")\n",
    "for n in range(2,11,2):\n",
    "    print(\"N =\",n,\", I = \",simpson_rule(fcubic,a,b,n))\n",
    "    \n",
    "tplot =  simpson_rule_plot(fcubic,a,b,2)\n",
    "tplot.title(flabelcubic)\n",
    "tplot.show()\n",
    "\n",
    "print('')\n",
    "\n",
    "print(\"Trapezoidal rule:\")\n",
    "for n in range(2,11,2):\n",
    "    print(\"N =\",n,\", I = \",trapezoidal_rule(fcubic,a,b,n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adaptive methods\n",
    "\n",
    "We would like to control the error of numerical integration\n",
    "\n",
    "For rectangle/trapezoidal method we know that the error scales with $h$ as $\\varepsilon = c h^2$.\n",
    "\n",
    "Let us double the number of steps. We have $h_2 = h_1 / 2$.\n",
    "Then, $\\varepsilon_2 = I - I_2 = c h_2^2$, and $\\varepsilon_1 = I - I_1 = 4 c h_2^2$.\n",
    "Therefore, $\\varepsilon_2 \\simeq (I_2 - I_1) / 3$.\n",
    "\n",
    "More generally,\n",
    "$$\n",
    "\\varepsilon_k \\simeq (I_k - I_{k-1}) / 3.\n",
    "$$\n",
    "\n",
    "We can continue to double the number of subintervals until the desired precision is reached.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rectangle rule for numerical integration with adaptive step\n",
    "def rectangle_rule_adaptive(f, a, b, nst = 1, tol = 1.e-8, max_iterations = 16):\n",
    "    Iprev = 0.\n",
    "    n = nst\n",
    "    Iprev = rectangle_rule(f, a, b, n)\n",
    "    print(\"Iteration: {0:5}, I = {1:20.15f}\".format(1, Iprev))\n",
    "    for k in range(1, max_iterations):\n",
    "        n *= 2\n",
    "        Inew = rectangle_rule(f, a, b, n)\n",
    "        ek = (Inew - Iprev) / 3.\n",
    "        print(\"Iteration: {0:5}, I = {1:20.15f}, error estimate = {2:10.15f}\".format(k+1, Inew, ek))\n",
    "        if (abs(ek) < tol):\n",
    "            return Inew\n",
    "        Iprev = Inew\n",
    "        \n",
    "    print(\"Failed to achieve the desired accuracy after\", max_iterations,\"iterations\")\n",
    "    return Inew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using adaptive rectangle rule\n",
      "Iteration:     1, I =    2.000000000000000\n",
      "Iteration:     2, I =    5.125000000000000, error estimate = 1.041666666666667\n",
      "Iteration:     3, I =    6.070312500000000, error estimate = 0.315104166666667\n",
      "Iteration:     4, I =    6.316894531250000, error estimate = 0.082194010416667\n",
      "Iteration:     5, I =    6.379180908203125, error estimate = 0.020762125651042\n",
      "Iteration:     6, I =    6.394792556762695, error estimate = 0.005203882853190\n",
      "Iteration:     7, I =    6.398697972297668, error estimate = 0.001301805178324\n",
      "Iteration:     8, I =    6.399674482643604, error estimate = 0.000325503448645\n",
      "Iteration:     9, I =    6.399918620008975, error estimate = 0.000081379121790\n",
      "Iteration:    10, I =    6.399979654961498, error estimate = 0.000020344984174\n",
      "Iteration:    11, I =    6.399994913737828, error estimate = 0.000005086258777\n",
      "Iteration:    12, I =    6.399998728434201, error estimate = 0.000001271565458\n",
      "Iteration:    13, I =    6.399999682108611, error estimate = 0.000000317891470\n",
      "Iteration:    14, I =    6.399999920527143, error estimate = 0.000000079472844\n",
      "Iteration:    15, I =    6.399999980131772, error estimate = 0.000000019868210\n",
      "Iteration:    16, I =    6.399999995032923, error estimate = 0.000000004967050\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "6.399999995032923"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = flimit_a\n",
    "b = flimit_b\n",
    "print(\"Computing the integral of\",flabel, \"over the interval (\",a,\",\",b,\") using adaptive rectangle rule\")\n",
    "rectangle_rule_adaptive(f,a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Trapezoidal rule for numerical integration with adaptive step\n",
    "def trapezoidal_rule_adaptive(f, a, b, nst = 1, tol = 1.e-8, max_iterations = 16):\n",
    "    Iprev = 0.\n",
    "    n = nst\n",
    "    Iprev = trapezoidal_rule(f, a, b, n)\n",
    "    print(\"Iteration: {0:5}, I = {1:20.15f}\".format(1, Iprev))\n",
    "    for k in range(1, max_iterations):\n",
    "        n *= 2\n",
    "        Inew = trapezoidal_rule(f, a, b, n)\n",
    "        ek = (Inew - Iprev) / 3.\n",
    "        print(\"Iteration: {0:5}, I = {1:20.15f}, error estimate = {2:10.15f}\".format(k+1, Inew, ek))\n",
    "        if (abs(ek) < tol):\n",
    "            return Inew\n",
    "        Iprev = Inew\n",
    "        \n",
    "    print(\"Failed to achieve the desired accuracy after\", max_iterations,\"iterations\")\n",
    "    return Inew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using adaptive trapezoidal rule\n",
      "Iteration:     1, I =   16.000000000000000\n",
      "Iteration:     2, I =    9.000000000000000, error estimate = -2.333333333333333\n",
      "Iteration:     3, I =    7.062500000000000, error estimate = -0.645833333333333\n",
      "Iteration:     4, I =    6.566406250000000, error estimate = -0.165364583333333\n",
      "Iteration:     5, I =    6.441650390625000, error estimate = -0.041585286458333\n",
      "Iteration:     6, I =    6.410415649414062, error estimate = -0.010411580403646\n",
      "Iteration:     7, I =    6.402604103088379, error estimate = -0.002603848775228\n",
      "Iteration:     8, I =    6.400651037693024, error estimate = -0.000651021798452\n",
      "Iteration:     9, I =    6.400162760168314, error estimate = -0.000162759174903\n",
      "Iteration:    10, I =    6.400040690088645, error estimate = -0.000040690026556\n",
      "Iteration:    11, I =    6.400010172525072, error estimate = -0.000010172521191\n",
      "Iteration:    12, I =    6.400002543131352, error estimate = -0.000002543131240\n",
      "Iteration:    13, I =    6.400000635782950, error estimate = -0.000000635782801\n",
      "Iteration:    14, I =    6.400000158945742, error estimate = -0.000000158945736\n",
      "Iteration:    15, I =    6.400000039736406, error estimate = -0.000000039736446\n",
      "Iteration:    16, I =    6.400000009934106, error estimate = -0.000000009934100\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "6.400000009934106"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = flimit_a\n",
    "b = flimit_b\n",
    "print(\"Computing the integral of\",flabel, \"over the interval (\",a,\",\",b,\") using adaptive trapezoidal rule\")\n",
    "trapezoidal_rule_adaptive(f,a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simpson's rule for numerical integration with adaptive step\n",
    "def simpson_rule_adaptive(f, a, b, nst = 2, tol = 1.e-8, max_iterations = 16):\n",
    "    Iprev = 0.\n",
    "    n = nst\n",
    "    Iprev = simpson_rule(f, a, b, n)\n",
    "    print(\"Iteration: {0:5}, I = {1:20.15f}\".format(1, Iprev))\n",
    "    for k in range(1, max_iterations):\n",
    "        n *= 2\n",
    "        Inew = simpson_rule(f, a, b, n)\n",
    "        ek = (Inew - Iprev) / 15.\n",
    "        \n",
    "        print(\"Iteration: {0:5}, I = {1:20.15f}, error estimate = {2:10.15f}\".format(k+1, Inew, ek))\n",
    "        if (abs(ek) < tol):\n",
    "            return Inew\n",
    "        Iprev = Inew\n",
    "        \n",
    "    print(\"Failed to achieve the desired accuracy after\", max_iterations,\"iterations\")\n",
    "    return Inew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using adaptive Simpson's rule\n",
      "Iteration:     1, I =    6.666666666666666\n",
      "Iteration:     2, I =    6.416666666666666, error estimate = -0.016666666666667\n",
      "Iteration:     3, I =    6.401041666666666, error estimate = -0.001041666666667\n",
      "Iteration:     4, I =    6.400065104166666, error estimate = -0.000065104166667\n",
      "Iteration:     5, I =    6.400004069010416, error estimate = -0.000004069010417\n",
      "Iteration:     6, I =    6.400000254313150, error estimate = -0.000000254313151\n",
      "Iteration:     7, I =    6.400000015894571, error estimate = -0.000000015894572\n",
      "Iteration:     8, I =    6.400000000993410, error estimate = -0.000000000993411\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "6.40000000099341"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = flimit_a\n",
    "b = flimit_b\n",
    "print(\"Computing the integral of\",flabel, \"over the interval (\",a,\",\",b,\") using adaptive Simpson's rule\")\n",
    "simpson_rule_adaptive(f,a,b,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "rungelabel = \"Runge function\"\n",
    "def runge(x):\n",
    "    return 1./(25*x**2 + 1.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of Runge function over the interval ( -2.0 , 2.0 ) using adaptive trapezoidal rule\n",
      "Iteration:     1, I =    1.086824067022087\n",
      "Iteration:     2, I =    0.698810316902099, error estimate = -0.129337916706663\n",
      "Iteration:     3, I =    0.596649043819530, error estimate = -0.034053757694190\n",
      "Iteration:     4, I =    0.588479663841841, error estimate = -0.002723126659230\n",
      "Iteration:     5, I =    0.588444691123849, error estimate = -0.000011657572664\n",
      "Iteration:     6, I =    0.588449474263155, error estimate = 0.000001594379768\n",
      "Iteration:     7, I =    0.588450670842736, error estimate = 0.000000398859860\n",
      "Iteration:     8, I =    0.588450970000918, error estimate = 0.000000099719394\n",
      "Iteration:     9, I =    0.588451044791294, error estimate = 0.000000024930125\n",
      "Iteration:    10, I =    0.588451063488940, error estimate = 0.000000006232549\n",
      "Iteration:    11, I =    0.588451068163354, error estimate = 0.000000001558138\n",
      "Iteration:    12, I =    0.588451069331961, error estimate = 0.000000000389535\n",
      "Iteration:    13, I =    0.588451069624111, error estimate = 0.000000000097383\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.588451069624111"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = -2.\n",
    "b = 2.\n",
    "print(\"Computing the integral of\",rungelabel, \"over the interval (\",a,\",\",b,\") using adaptive trapezoidal rule\")\n",
    "trapezoidal_rule_adaptive(runge,a,b,4,1.e-10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of Runge function over the interval ( -2.0 , 2.0 ) using adaptive trapezoidal rule\n",
      "Iteration:     1, I =    0.775831429296776\n",
      "Iteration:     2, I =    0.569472400195436, error estimate = -0.013757268606756\n",
      "Iteration:     3, I =    0.562595286125340, error estimate = -0.000458474271340\n",
      "Iteration:     4, I =    0.585756537182612, error estimate = 0.001544083403818\n",
      "Iteration:     5, I =    0.588433033551185, error estimate = 0.000178433091238\n",
      "Iteration:     6, I =    0.588451068642924, error estimate = 0.000001202339449\n",
      "Iteration:     7, I =    0.588451069702595, error estimate = 0.000000000070645\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.5884510697025954"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = -2.\n",
    "b = 2.\n",
    "print(\"Computing the integral of\",rungelabel, \"over the interval (\",a,\",\",b,\") using adaptive trapezoidal rule\")\n",
    "simpson_rule_adaptive(runge,a,b,4,1.e-10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Romberg method\n",
    "\n",
    "Romberg method is a generalization of the above procedure to cancel higher orders in the error\n",
    "\n",
    "We estimated the $\\mathcal{O}(h^2)$ error in the k$th$ step of the trapezoidal method as\n",
    "$$\n",
    "I - I_k = \\frac{I_k - I_{k-1}}{3} + \\mathcal{O}(h^4).\n",
    "$$\n",
    "\n",
    "The integral can therefore be estimated to $\\mathcal{O}(h^4)$ order as\n",
    "$$\n",
    "I = I_k + \\frac{I_k - I_{k-1}}{3} + \\mathcal{O}(h^4),\n",
    "$$\n",
    "which is in fact nothing else but the Simpson rule.\n",
    "\n",
    "We can denote $R_{k,0} = I_k$ and $R_{k,1} = R_{k,0} + \\frac{R_{k,0} - R_{k-1,0}}{3}$.\n",
    "As seen above \n",
    "$$\n",
    "I = R_{k,1} + \\mathcal{O}(h^4).\n",
    "$$\n",
    "\n",
    "Repeating this process to eliminate the $\\mathcal{O}(h^4)$ we get a higher-order estimate\n",
    "$$\n",
    "R_{k,2} = R_{k,1} + \\frac{R_{k,1} - R_{k-1,1}}{15}\n",
    "$$\n",
    "which accurate to order $\\mathcal{O}(h^6)$.\n",
    "\n",
    "The general formula for an estimate of order $m+1$ reads\n",
    "$$\n",
    "R_{k,m+1} = R_{k,m} + \\frac{R_{k,m} - R_{k-1,m}}{4^{m} - 1}~.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def romberg(\n",
    "    f, \n",
    "    a, \n",
    "    b, \n",
    "    accuracy=1e-8, \n",
    "    max_order=10\n",
    "):\n",
    "    R = np.zeros((max_order, max_order))\n",
    "    h = (b - a) / 2.\n",
    "    R[0, 0] = h * (f(a) + f(b)) # The initial trapezoidal rule   \n",
    "    for n in range(1, max_order):\n",
    "        trapezoid = 0.0\n",
    "        for j in range(2**(n-1)):\n",
    "            trapezoid += f(a + (2*j+1)*h)\n",
    "        R[n, 0] = 0.5 * R[n-1, 0] + h * trapezoid # The trapezoidal rule\n",
    "        l = 1\n",
    "        # The Romberg iterations\n",
    "        for m in range(1, n+1):\n",
    "            l *= 4\n",
    "            R[n, m] = (l * R[n, m-1] - R[n-1, m-1]) / (l-1)\n",
    "        print(\"Iteration: {0:5}, I = {1:20.15f}, error estimate = {2:10.15f}\".format(n, R[n, m], abs(R[n, m] - R[n-1, m-1])))\n",
    "        if abs(R[n, m] - R[n-1, m-1]) < accuracy:\n",
    "            return R[n, m]\n",
    "        h /= 2.\n",
    "    print(\"Romberg method did not converge to required accuracy\")\n",
    "    return R[-1, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of x^4 - 2x + 2 over the interval ( 0.0 , 2.0 ) using Romberg method\n",
      "Iteration:     1, I =    6.666666666666667, error estimate = 9.333333333333332\n",
      "Iteration:     2, I =    6.400000000000000, error estimate = 0.266666666666667\n",
      "Iteration:     3, I =    6.400000000000000, error estimate = 0.000000000000000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(6.4)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = flimit_a\n",
    "b = flimit_b\n",
    "print(\"Computing the integral of\",flabel, \"over the interval (\",a,\",\",b,\") using Romberg method\")\n",
    "romberg(f,a,b,1e-6,18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing the integral of Runge function over the interval ( -2.0 , 2.0 ) using Romberg method\n",
      "Iteration:     1, I =    2.679867986798680, error estimate = 2.640264026402640\n",
      "Iteration:     2, I =    0.648895658796649, error estimate = 2.030972328002031\n",
      "Iteration:     3, I =    0.554236075601252, error estimate = 0.094659583195396\n",
      "Iteration:     4, I =    0.562270126297315, error estimate = 0.008034050696062\n",
      "Iteration:     5, I =    0.587824850153293, error estimate = 0.025554723855978\n",
      "Iteration:     6, I =    0.588636945021199, error estimate = 0.000812094867906\n",
      "Iteration:     7, I =    0.588448788195693, error estimate = 0.000188156825505\n",
      "Iteration:     8, I =    0.588451058525226, error estimate = 0.000002270329532\n",
      "Iteration:     9, I =    0.588451069812733, error estimate = 0.000000011287507\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(0.5884510698127332)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = -2.\n",
    "b = 2.\n",
    "print(\"Computing the integral of\",rungelabel, \"over the interval (\",a,\",\",b,\") using Romberg method\")\n",
    "romberg(runge,a,b,1e-6,18)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discontinuous integrands\n",
    "\n",
    "Integrand can be discontinuous. Consider\n",
    "$$\n",
    "f(x) = 3 x^2 + x + 3 \\qquad {\\rm for} ~ x < 1,\n",
    "$$\n",
    "and\n",
    "$$\n",
    "f(x) = 2 x^3 - 3x^2 + x + 3. \\qquad {\\rm for} ~ x > 1,\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "I = \\int_0^2 f(x) = 9.5\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "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"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fdist1(x):\n",
    "    return 3*x**2 + x + 3\n",
    "\n",
    "def fdist2(x):\n",
    "    return 2*x**3 - 3*x**2 + x + 3\n",
    "\n",
    "# Discontinuity point\n",
    "xdistcont = 1.\n",
    "\n",
    "def fdist(x):\n",
    "    x = np.asarray(x)  # Ensure x is a numpy array\n",
    "    result = np.where(x < xdistcont, fdist1(x), fdist2(x))\n",
    "    return result\n",
    "\n",
    "xplot = np.linspace(0,2,1000)\n",
    "yplot = fdist(xplot)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"f(x)\")\n",
    "plt.xlim(0,2)\n",
    "plt.axhline(y = 0., color = 'black', linestyle = '--')\n",
    "\n",
    "# Fill the area under the curve\n",
    "plt.fill_between(xplot, yplot, where=(xplot < xdistcont), color='blue', alpha=0.5)\n",
    "plt.fill_between(xplot, yplot, where=(xplot >= xdistcont), color='blue', alpha=0.5)\n",
    "\n",
    "plt.plot(xplot,yplot, color = 'red')\n",
    "plt.show()\n",
    "\n",
    "trapezoidal_rule_plot(fdist,0,2,15).show()\n",
    "rectangle_rule_plot(fdist,0,2,15).show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rectangle rule:\n",
      "Iteration:     1, I =    6.000000000000000\n",
      "Iteration:     2, I =    8.750000000000000, error estimate = 0.916666666666667\n",
      "Iteration:     3, I =    9.312500000000000, error estimate = 0.187500000000000\n",
      "Iteration:     4, I =    9.453125000000000, error estimate = 0.046875000000000\n",
      "Iteration:     5, I =    9.488281250000000, error estimate = 0.011718750000000\n",
      "Iteration:     6, I =    9.497070312500000, error estimate = 0.002929687500000\n",
      "Iteration:     7, I =    9.499267578125000, error estimate = 0.000732421875000\n",
      "Iteration:     8, I =    9.499816894531250, error estimate = 0.000183105468750\n",
      "Iteration:     9, I =    9.499954223632812, error estimate = 0.000045776367188\n",
      "Iteration:    10, I =    9.499988555908203, error estimate = 0.000011444091797\n",
      "Iteration:    11, I =    9.499997138977051, error estimate = 0.000002861022949\n",
      "Iteration:    12, I =    9.499999284744263, error estimate = 0.000000715255737\n",
      "Iteration:    13, I =    9.499999821186066, error estimate = 0.000000178813934\n",
      "Iteration:    14, I =    9.499999955296516, error estimate = 0.000000044703484\n",
      "Iteration:    15, I =    9.499999988824127, error estimate = 0.000000011175870\n",
      "Iteration:    16, I =    9.499999997206030, error estimate = 0.000000002793968\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(9.49999999720603)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Adaptive rectangle rule\n",
    "print(\"Rectangle rule:\")\n",
    "rectangle_rule_adaptive(fdist,0,2,1,1.e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trapezoidal rule:\n",
      "Iteration:     1, I =   12.000000000000000\n",
      "Iteration:     2, I =    9.000000000000000, error estimate = -1.000000000000000\n",
      "Iteration:     3, I =    8.875000000000000, error estimate = -0.041666666666667\n",
      "Iteration:     4, I =    9.093750000000000, error estimate = 0.072916666666667\n",
      "Iteration:     5, I =    9.273437500000000, error estimate = 0.059895833333333\n",
      "Iteration:     6, I =    9.380859375000000, error estimate = 0.035807291666667\n",
      "Iteration:     7, I =    9.438964843750000, error estimate = 0.019368489583333\n",
      "Iteration:     8, I =    9.469116210937500, error estimate = 0.010050455729167\n",
      "Iteration:     9, I =    9.484466552734375, error estimate = 0.005116780598958\n",
      "Iteration:    10, I =    9.492210388183594, error estimate = 0.002581278483073\n",
      "Iteration:    11, I =    9.496099472045898, error estimate = 0.001296361287435\n",
      "Iteration:    12, I =    9.498048305511475, error estimate = 0.000649611155192\n",
      "Iteration:    13, I =    9.499023795127869, error estimate = 0.000325163205465\n",
      "Iteration:    14, I =    9.499511808156967, error estimate = 0.000162671009700\n",
      "Iteration:    15, I =    9.499755881726742, error estimate = 0.000081357856592\n",
      "Iteration:    16, I =    9.499877935275437, error estimate = 0.000040684516232\n",
      "Failed to achieve the desired accuracy after 16 iterations\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(9.499877935275437)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Adaptive trapezoidal rule\n",
    "print(\"Trapezoidal rule:\")\n",
    "trapezoidal_rule_adaptive(fdist,0,2,1,1.e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simpson's rule:\n",
      "Iteration:     1, I =    8.000000000000000\n",
      "Iteration:     2, I =    8.833333333333332, error estimate = 0.055555555555555\n",
      "Iteration:     3, I =    9.166666666666666, error estimate = 0.022222222222222\n",
      "Iteration:     4, I =    9.333333333333332, error estimate = 0.011111111111111\n",
      "Iteration:     5, I =    9.416666666666666, error estimate = 0.005555555555556\n",
      "Iteration:     6, I =    9.458333333333332, error estimate = 0.002777777777778\n",
      "Iteration:     7, I =    9.479166666666666, error estimate = 0.001388888888889\n",
      "Iteration:     8, I =    9.489583333333332, error estimate = 0.000694444444444\n",
      "Iteration:     9, I =    9.494791666666666, error estimate = 0.000347222222222\n",
      "Iteration:    10, I =    9.497395833333332, error estimate = 0.000173611111111\n",
      "Iteration:    11, I =    9.498697916666666, error estimate = 0.000086805555556\n",
      "Iteration:    12, I =    9.499348958333332, error estimate = 0.000043402777778\n",
      "Iteration:    13, I =    9.499674479166666, error estimate = 0.000021701388889\n",
      "Iteration:    14, I =    9.499837239583332, error estimate = 0.000010850694444\n",
      "Iteration:    15, I =    9.499918619791664, error estimate = 0.000005425347222\n",
      "Iteration:    16, I =    9.499959309895530, error estimate = 0.000002712673591\n",
      "Failed to achieve the desired accuracy after 16 iterations\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(9.49995930989553)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Adaptive Simpson rule\n",
    "print(\"Simpson's rule:\")\n",
    "simpson_rule_adaptive(fdist,0,2,2,1.e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Romberg method:\n",
      "Iteration:     1, I =    8.000000000000000, error estimate = 4.000000000000000\n",
      "Iteration:     2, I =    8.888888888888889, error estimate = 0.888888888888889\n",
      "Iteration:     3, I =    9.193650793650793, error estimate = 0.304761904761904\n",
      "Iteration:     4, I =    9.347514610782586, error estimate = 0.153863817131793\n",
      "Iteration:     5, I =    9.423831487774139, error estimate = 0.076316876991553\n",
      "Iteration:     6, I =    9.461925044409840, error estimate = 0.038093556635701\n",
      "Iteration:     7, I =    9.480963684231190, error estimate = 0.019038639821350\n",
      "Iteration:     8, I =    9.490481987353379, error estimate = 0.009518303122189\n",
      "Iteration:     9, I =    9.495241011830926, error estimate = 0.004759024477547\n",
      "Iteration:    10, I =    9.497620508184726, error estimate = 0.002379496353800\n",
      "Iteration:    11, I =    9.498810254376020, error estimate = 0.001189746191294\n",
      "Iteration:    12, I =    9.499405127223469, error estimate = 0.000594872847449\n",
      "Iteration:    13, I =    9.499702563616168, error estimate = 0.000297436392700\n",
      "Iteration:    14, I =    9.499851281808635, error estimate = 0.000148718192467\n",
      "Iteration:    15, I =    9.499925640904392, error estimate = 0.000074359095757\n",
      "Iteration:    16, I =    9.499962820452204, error estimate = 0.000037179547812\n",
      "Iteration:    17, I =    9.499981410226075, error estimate = 0.000018589773871\n",
      "Romberg method did not converge to required accuracy\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(9.499981410226075)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Romberg method\n",
    "print(\"Romberg method:\")\n",
    "romberg(fdist,0,2,1e-8,18)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The methods still work but with reduced accuracy\n",
    "\n",
    "A better solution is to split the integration into two separate integrals\n",
    "\n",
    "$$\n",
    "I = I_1 + I_2,\n",
    "$$\n",
    "where\n",
    "$$\n",
    "I_1 = \\int_a^{x_{\\rm distcont}} f_1(x)\n",
    "$$\n",
    "and\n",
    "$$\n",
    "I_2 = \\int_{x_{\\rm distcont}}^b f_2(x)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rectangle rule:\n",
      "Iteration:     1, I =    4.250000000000000\n",
      "Iteration:     2, I =    4.437500000000000, error estimate = 0.062500000000000\n",
      "Iteration:     3, I =    4.484375000000000, error estimate = 0.015625000000000\n",
      "Iteration:     4, I =    4.496093750000000, error estimate = 0.003906250000000\n",
      "Iteration:     5, I =    4.499023437500000, error estimate = 0.000976562500000\n",
      "Iteration:     6, I =    4.499755859375000, error estimate = 0.000244140625000\n",
      "Iteration:     7, I =    4.499938964843750, error estimate = 0.000061035156250\n",
      "Iteration:     8, I =    4.499984741210938, error estimate = 0.000015258789062\n",
      "Iteration:     9, I =    4.499996185302734, error estimate = 0.000003814697266\n",
      "Iteration:    10, I =    4.499999046325684, error estimate = 0.000000953674316\n",
      "Iteration:    11, I =    4.499999761581421, error estimate = 0.000000238418579\n",
      "Iteration:    12, I =    4.499999940395355, error estimate = 0.000000059604645\n",
      "Iteration:    13, I =    4.499999985098839, error estimate = 0.000000014901161\n",
      "Iteration:    14, I =    4.499999996274710, error estimate = 0.000000003725290\n",
      "Iteration:     1, I =    4.500000000000000\n",
      "Iteration:     2, I =    4.875000000000000, error estimate = 0.125000000000000\n",
      "Iteration:     3, I =    4.968750000000000, error estimate = 0.031250000000000\n",
      "Iteration:     4, I =    4.992187500000000, error estimate = 0.007812500000000\n",
      "Iteration:     5, I =    4.998046875000000, error estimate = 0.001953125000000\n",
      "Iteration:     6, I =    4.999511718750000, error estimate = 0.000488281250000\n",
      "Iteration:     7, I =    4.999877929687500, error estimate = 0.000122070312500\n",
      "Iteration:     8, I =    4.999969482421875, error estimate = 0.000030517578125\n",
      "Iteration:     9, I =    4.999992370605469, error estimate = 0.000007629394531\n",
      "Iteration:    10, I =    4.999998092651367, error estimate = 0.000001907348633\n",
      "Iteration:    11, I =    4.999999523162842, error estimate = 0.000000476837158\n",
      "Iteration:    12, I =    4.999999880790710, error estimate = 0.000000119209290\n",
      "Iteration:    13, I =    4.999999970197678, error estimate = 0.000000029802322\n",
      "Iteration:    14, I =    4.999999992549419, error estimate = 0.000000007450581\n",
      "Iteration:    15, I =    4.999999998137355, error estimate = 0.000000001862645\n",
      "I1 = 4.49999999627471\n",
      "I2 = 4.999999998137355\n",
      "I = 9.499999994412065\n"
     ]
    }
   ],
   "source": [
    "# Adaptive rectangle rule\n",
    "print(\"Rectangle rule:\")\n",
    "eps = 1.e-8\n",
    "a = 0\n",
    "b = xdistcont\n",
    "I1 = rectangle_rule_adaptive(fdist1,a,b,1,0.5*eps)\n",
    "\n",
    "a = xdistcont\n",
    "b = 2\n",
    "I2 = rectangle_rule_adaptive(fdist2,a,b,1,0.5*eps)\n",
    "\n",
    "print(\"I1 =\",I1)\n",
    "print(\"I2 =\",I2)\n",
    "print(\"I =\",I1 + I2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trapezoidal rule:\n",
      "Iteration:     1, I =    5.000000000000000\n",
      "Iteration:     2, I =    4.625000000000000, error estimate = -0.125000000000000\n",
      "Iteration:     3, I =    4.531250000000000, error estimate = -0.031250000000000\n",
      "Iteration:     4, I =    4.507812500000000, error estimate = -0.007812500000000\n",
      "Iteration:     5, I =    4.501953125000000, error estimate = -0.001953125000000\n",
      "Iteration:     6, I =    4.500488281250000, error estimate = -0.000488281250000\n",
      "Iteration:     7, I =    4.500122070312500, error estimate = -0.000122070312500\n",
      "Iteration:     8, I =    4.500030517578125, error estimate = -0.000030517578125\n",
      "Iteration:     9, I =    4.500007629394531, error estimate = -0.000007629394531\n",
      "Iteration:    10, I =    4.500001907348633, error estimate = -0.000001907348633\n",
      "Iteration:    11, I =    4.500000476837158, error estimate = -0.000000476837158\n",
      "Iteration:    12, I =    4.500000119209290, error estimate = -0.000000119209290\n",
      "Iteration:    13, I =    4.500000029802322, error estimate = -0.000000029802322\n",
      "Iteration:    14, I =    4.500000007450581, error estimate = -0.000000007450581\n",
      "Iteration:    15, I =    4.500000001862645, error estimate = -0.000000001862645\n",
      "Iteration:     1, I =    6.000000000000000\n",
      "Iteration:     2, I =    5.250000000000000, error estimate = -0.250000000000000\n",
      "Iteration:     3, I =    5.062500000000000, error estimate = -0.062500000000000\n",
      "Iteration:     4, I =    5.015625000000000, error estimate = -0.015625000000000\n",
      "Iteration:     5, I =    5.003906250000000, error estimate = -0.003906250000000\n",
      "Iteration:     6, I =    5.000976562500000, error estimate = -0.000976562500000\n",
      "Iteration:     7, I =    5.000244140625000, error estimate = -0.000244140625000\n",
      "Iteration:     8, I =    5.000061035156250, error estimate = -0.000061035156250\n",
      "Iteration:     9, I =    5.000015258789062, error estimate = -0.000015258789062\n",
      "Iteration:    10, I =    5.000003814697266, error estimate = -0.000003814697266\n",
      "Iteration:    11, I =    5.000000953674316, error estimate = -0.000000953674316\n",
      "Iteration:    12, I =    5.000000238418579, error estimate = -0.000000238418579\n",
      "Iteration:    13, I =    5.000000059604645, error estimate = -0.000000059604645\n",
      "Iteration:    14, I =    5.000000014901161, error estimate = -0.000000014901161\n",
      "Iteration:    15, I =    5.000000003725290, error estimate = -0.000000003725290\n",
      "I1 = 4.500000001862645\n",
      "I2 = 5.00000000372529\n",
      "I = 9.500000005587935\n"
     ]
    }
   ],
   "source": [
    "# Adaptive trapezoidal rule\n",
    "print(\"Trapezoidal rule:\")\n",
    "eps = 1.e-8\n",
    "a = 0\n",
    "b = xdistcont\n",
    "I1 = trapezoidal_rule_adaptive(fdist1,a,b,1,0.5*eps)\n",
    "\n",
    "a = xdistcont\n",
    "b = 2\n",
    "I2 = trapezoidal_rule_adaptive(fdist2,a,b,1,0.5*eps)\n",
    "\n",
    "print(\"I1 =\",I1)\n",
    "print(\"I2 =\",I2)\n",
    "print(\"I =\",I1 + I2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simpson's rule:\n",
      "Iteration:     1, I =    4.500000000000000\n",
      "Iteration:     2, I =    4.500000000000000, error estimate = 0.000000000000000\n",
      "Iteration:     1, I =    5.000000000000000\n",
      "Iteration:     2, I =    5.000000000000000, error estimate = 0.000000000000000\n",
      "I1 = 4.5\n",
      "I2 = 5.0\n",
      "I = 9.5\n"
     ]
    }
   ],
   "source": [
    "# Adaptive Simpson's rule\n",
    "print(\"Simpson's rule:\")\n",
    "eps = 1.e-8\n",
    "a = 0\n",
    "b = xdistcont\n",
    "I1 = simpson_rule_adaptive(fdist1,a,b,2,0.5*eps)\n",
    "\n",
    "a = xdistcont\n",
    "b = 2\n",
    "I2 = simpson_rule_adaptive(fdist2,a,b,2,0.5*eps)\n",
    "\n",
    "print(\"I1 =\",I1)\n",
    "print(\"I2 =\",I2)\n",
    "print(\"I =\",I1 + I2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Romberg method:\n",
      "Iteration:     1, I =    4.500000000000000, error estimate = 0.500000000000000\n",
      "Iteration:     2, I =    4.500000000000000, error estimate = 0.000000000000000\n",
      "Iteration:     1, I =    5.000000000000000, error estimate = 1.000000000000000\n",
      "Iteration:     2, I =    5.000000000000000, error estimate = 0.000000000000000\n",
      "I1 = 4.5\n",
      "I2 = 5.0\n",
      "I = 9.5\n"
     ]
    }
   ],
   "source": [
    "# Romberg method\n",
    "print(\"Romberg method:\")\n",
    "eps = 1.e-8\n",
    "a = 0\n",
    "b = xdistcont\n",
    "I1 = romberg(fdist1,a,b,0.5*eps)\n",
    "\n",
    "a = xdistcont\n",
    "b = 2\n",
    "I2 = romberg(fdist2,a,b,0.5*eps)\n",
    "\n",
    "print(\"I1 =\",I1)\n",
    "print(\"I2 =\",I2)\n",
    "print(\"I =\",I1 + I2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Improper integrals\n",
    "\n",
    "Some integrals may contain peculiarities like:\n",
    "- Integrable singularity (typically at endpoints)\n",
    "- (Semi-)infinite integration range\n",
    "\n",
    "#### Integrable singularities\n",
    "Consider\n",
    "$$\n",
    "\\int_0^1 \\frac{1}{\\sqrt{x}} dx = \\left. 2\\sqrt{x} \\right|_0^1 = 2\n",
    "$$\n",
    "\n",
    "The integrand diverges at $x = 0$, however, this singularity is integrable.\n",
    "\n",
    "The trapezoidal and any method that makes use of function evaluation at integration endpoints will fail, however, due to division by zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/3v/f0ynmrq5313979_z9dzqpvr00000gp/T/ipykernel_46468/847063500.py:2: RuntimeWarning: divide by zero encountered in scalar divide\n",
      "  return 1./np.sqrt(x)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(inf)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def fsing1(x):\n",
    "    return 1./np.sqrt(x)\n",
    "\n",
    "trapezoidal_rule(fsing1,0.,1.,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the other hand, the rectangular rule seems to work (albeit slowly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using rectangle rule to evaluate \\int_0^1 1/\\sqrt{x} dx\n",
      "Iteration:     1, I =    1.414213562373095\n",
      "Iteration:     2, I =    1.577350269189626, error estimate = 0.054378902272177\n",
      "Iteration:     3, I =    1.698844079579673, error estimate = 0.040497936796682\n",
      "Iteration:     4, I =    1.786461001734842, error estimate = 0.029205640718390\n",
      "Iteration:     5, I =    1.848856684639738, error estimate = 0.020798560968299\n",
      "Iteration:     6, I =    1.893088359706383, error estimate = 0.014743891688882\n",
      "Iteration:     7, I =    1.924392755699513, error estimate = 0.010434798664376\n",
      "Iteration:     8, I =    1.946535279970520, error estimate = 0.007380841423669\n",
      "Iteration:     9, I =    1.962194152677056, error estimate = 0.005219624235512\n",
      "Iteration:    10, I =    1.973267083679453, error estimate = 0.003690977000799\n",
      "Iteration:    11, I =    1.981096937261288, error estimate = 0.002609951193945\n",
      "Iteration:    12, I =    1.986633507070365, error estimate = 0.001845523269692\n",
      "Iteration:    13, I =    1.990548459938304, error estimate = 0.001304984289313\n",
      "Iteration:    14, I =    1.993316751362098, error estimate = 0.000922763807931\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(1.993316751362098)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Using rectangle rule to evaluate \\int_0^1 1/\\sqrt{x} dx')\n",
    "nst = 1\n",
    "rectangle_rule_adaptive(fsing1,0.,1.,1,1.e-3,20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Integrable singularities\n",
    "Consider\n",
    "$$\n",
    "\\int_a^\\infty f(x) dx\n",
    "$$\n",
    "\n",
    "The semi-infinite range can be mapped into (0,1) range by appropriate variable transformation.\n",
    "For instance, if\n",
    "$$\n",
    "x = a + \\frac{t}{1-t},\n",
    "$$\n",
    "then\n",
    "$dx = \\frac{dt}{1-t^2}$ \n",
    "and\n",
    "$$\n",
    "\\int_a^\\infty f(x) dx = \\int_0^1 f\\left(a + \\frac{t}{1-t}\\right) \\frac{dt}{1-t^2} = \\int_0^1 g(t) dt\n",
    "$$\n",
    "\n",
    "Let us try it with\n",
    "$$\n",
    "\\int_0^\\infty e^{-x} dx = 1\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fexp(x):\n",
    "    return np.exp(-x)\n",
    "\n",
    "def g(t, f, a = 0.):\n",
    "    return f(a + t / (1. - t)) / (1. - t)**2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using change of variable and the rectangle rule to evaluate \\int_0^\\infty \\exp(-x) dx\n",
      "Iteration:     1, I =    1.471517764685769\n",
      "Iteration:     2, I =    1.035213267452946, error estimate = -0.145434832410941\n",
      "Iteration:     3, I =    0.984670579385046, error estimate = -0.016847562689300\n",
      "Iteration:     4, I =    1.001784913275257, error estimate = 0.005704777963404\n",
      "Iteration:     5, I =    1.000155714391028, error estimate = -0.000543066294743\n",
      "Iteration:     6, I =    1.000040642390661, error estimate = -0.000038357333456\n",
      "Iteration:     7, I =    1.000010172618432, error estimate = -0.000010156590743\n",
      "Iteration:     8, I =    1.000002543136036, error estimate = -0.000002543160799\n",
      "Iteration:     9, I =    1.000000635783161, error estimate = -0.000000635784292\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(1.0000006357831608)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 0.\n",
    "def frect(x):\n",
    "    return g(x, fexp, a)\n",
    "\n",
    "print('Using change of variable and the rectangle rule to evaluate \\int_0^\\infty \\exp(-x) dx')\n",
    "rectangle_rule_adaptive(frect,0.,1.,1,1.e-6,20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using change of variable and the rectangle rule to evaluate \\int_ 3.0 ^\\infty \\exp(-x) dx\n",
      "Iteration:     1, I =    0.073262555554937\n",
      "Iteration:     2, I =    0.051540233722000, error estimate = -0.007240773944312\n",
      "Iteration:     3, I =    0.049023861455667, error estimate = -0.000838790755444\n",
      "Iteration:     4, I =    0.049875933967130, error estimate = 0.000284024170487\n",
      "Iteration:     5, I =    0.049794820930896, error estimate = -0.000027037678745\n",
      "Iteration:     6, I =    0.049789091833346, error estimate = -0.000001909699183\n",
      "Iteration:     7, I =    0.049787574832713, error estimate = -0.000000505666878\n",
      "Expected value: exp(-a) = 0.049787068367863944\n"
     ]
    }
   ],
   "source": [
    "# Try a > 0\n",
    "a = 3.\n",
    "def frect(x):\n",
    "    return g(x, fexp, a)\n",
    "\n",
    "print('Using change of variable and the rectangle rule to evaluate \\int_',a,'^\\infty \\exp(-x) dx')\n",
    "# nst = 1\n",
    "# for n in range(1,6):\n",
    "#     nst *= 10\n",
    "#     print(\"N =\",nst,\", I = \",rectangle_rule(frect,0.,1.,nst))\n",
    "rectangle_rule_adaptive(frect,0.,1.,1,1.e-6,20)\n",
    "\n",
    "print('Expected value: exp(-a) =', np.exp(-a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For an infinite interval\n",
    "$$\n",
    "\\int_{-\\infty}^\\infty f(x) dx\n",
    "$$\n",
    "\n",
    "one option is\n",
    "$$\n",
    "x = \\frac{t}{1-t^2}\n",
    "$$\n",
    "giving\n",
    "$dx = \\frac{1+t^2}{(1-t^2)^2} dt$ \n",
    "and\n",
    "$$\n",
    "\\int_{-\\infty}^\\infty f(x) dx = \n",
    "\\int_{-1}^1 f\\left(\\frac{t}{1-t^2}\\right) \\frac{1+t^2}{(1-t^2)^2} dt = \\int_{-1}^1 g(t) dt\n",
    "$$\n",
    "\n",
    "Let us try it with\n",
    "$$\n",
    "\\int_{-\\infty}^\\infty e^{-x^2} dx = \\sqrt{\\pi} = 1.772454\\ldots\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fexp2(x):\n",
    "    return np.exp(-x**2)\n",
    "\n",
    "def g2(t, f):\n",
    "    return f(t / (1. - t**2)) * (1.+t**2) / (1. - t**2)**2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using change of variable and the rectangle rule to evaluate \\int_{-\\infty}^\\infty \\exp(-x^2) dx\n",
      "Iteration:     1, I =    2.000000000000000\n",
      "Iteration:     2, I =    2.849690615244243, error estimate = 0.283230205081414\n",
      "Iteration:     3, I =    1.557994553948652, error estimate = -0.430565353765197\n",
      "Iteration:     4, I =    1.808005109208286, error estimate = 0.083336851753211\n",
      "Iteration:     5, I =    1.770118560572371, error estimate = -0.012628849545305\n",
      "Iteration:     6, I =    1.772492101507391, error estimate = 0.000791180311673\n",
      "Iteration:     7, I =    1.772453880915058, error estimate = -0.000012740197444\n",
      "Iteration:     8, I =    1.772453850905505, error estimate = -0.000000010003185\n",
      "Expected value: \\sqrt{\\pi} = 1.7724538509055159\n"
     ]
    }
   ],
   "source": [
    "def frect2(x):\n",
    "    return g2(x, fexp2)\n",
    "\n",
    "print('Using change of variable and the rectangle rule to evaluate \\int_{-\\infty}^\\infty \\exp(-x^2) dx')\n",
    "rectangle_rule_adaptive(frect2,-1.,1.,1,1.e-6,20)\n",
    "\n",
    "print('Expected value: \\sqrt{\\pi} =', np.sqrt(np.pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Relativistic quantum distribution\n",
    "\n",
    "In a relativistic \"ideal gas, the density of particles can be calculated as an integral over the momentum states\n",
    "$$\n",
    "n = \\frac{d}{2\\pi^2} \\int_0^\\infty dk \\, k^2 \\, \\left[\\exp\\left\\{\\frac{\\sqrt{m^2+k^2}-\\mu}{T} \\right\\} + \\eta \\right ]^{-1}.\n",
    "$$\n",
    "Here $d$ is the spin degeneracy, $m$ is the mass of the particle, and $T$ and $\\mu$ are the temperature and chemical potential. $\\eta$ is the statitics, such that $\\eta = +1$ corresponds to Fermi-Dirac distributio, $\\eta = -1$ to Bose-Einstein distribution, and $\\eta = 0$ to Maxwell-Boltzmann approximation.\n",
    "\n",
    "In general, the integral has to be evaluated numerically. First, it is useful to make the integration variable dimensionless through a change of variable $\\tilde k = k / T$. Then\n",
    "$$\n",
    "n = \\frac{d T^3}{2\\pi^2} \\int_0^\\infty d \\tilde k \\, \\tilde k^2 \\, \\left[\\exp\\left\\{\\sqrt{\\tilde m^2+\\tilde k^2}-\\tilde \\mu \\right\\} + \\eta \\right ]^{-1},\n",
    "$$\n",
    "where $\\tilde m = m/T$ and $\\tilde \\mu = \\mu / T$.\n",
    "This expression can be cast in a form\n",
    "$$\n",
    "\\tilde n = n/T^3 = \\int_0^\\infty d x f(x)\n",
    "$$\n",
    "with\n",
    "$$\n",
    "f(x) = \\frac{d}{2\\pi^2} x^2 \\, \\left[\\exp\\left\\{\\sqrt{\\tilde m^2+x^2}-\\tilde \\mu \\right\\} + \\eta \\right ]^{-1}~.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Steps\n",
    "\n",
    "1. Make a change of variables $x \\to t/(1-t)$ to convert the semi-infinite integration range $x \\in (0,\\infty)$ into a finite range $t \\in (0,1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fThermal(x):\n",
    "    return d * x**2 / (2 * np.pi**2) / (np.exp(np.sqrt((m/T)**2 + x**2) - mu/T) + eta)\n",
    "\n",
    "def g(t, f, a = 0.):\n",
    "    return f(a + t / (1. - t)) / (1. - t)**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Calculate the scaled density $\\tilde n = n/T^3$ using numerical integration for the following values of parameters, corresponding to an ideal gas of $\\pi$-mesons:\n",
    "$$\n",
    "m = 138~\\textrm{MeV}, \\qquad d = 1, \\qquad T = 150~\\textrm{MeV}, \\qquad \\mu = 0.\n",
    "$$\n",
    "Ignore quantum statisics for the time being by setting $\\eta = 0$.\n",
    "\n",
    "We will use the rectangle rule to avoid singularities at endpoints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:     1, I =    0.052071598602252\n",
      "Iteration:     2, I =    0.160089665256309, error estimate = 0.036006022218019\n",
      "Iteration:     3, I =    0.075406103813409, error estimate = -0.028227853814300\n",
      "Iteration:     4, I =    0.085410602578111, error estimate = 0.003334832921567\n",
      "Iteration:     5, I =    0.084623507486682, error estimate = -0.000262365030476\n",
      "Iteration:     6, I =    0.084721979027677, error estimate = 0.000032823846998\n",
      "Iteration:     7, I =    0.084722493628870, error estimate = 0.000000171533731\n",
      "Using adaptive rectangle rule: n/T^3 = 0.08472249362886973\n"
     ]
    }
   ],
   "source": [
    "T = 150 # MeV\n",
    "mu = 0  \n",
    "m = 138 # MeV\n",
    "d = 1\n",
    "eta = 0\n",
    "\n",
    "def nIntegral(eps = 1e-6):\n",
    "    def fInt(t):\n",
    "        return g(t, fThermal, 0)\n",
    "    return rectangle_rule_adaptive(fInt, 0., 1., 1, eps, 20)\n",
    "\n",
    "def nT3num(inT, inMu, eps):\n",
    "    global T, mu\n",
    "    T = inT\n",
    "    mu = inMu\n",
    "    return nIntegral(eps)\n",
    "\n",
    "print(\"Using adaptive rectangle rule:\", \"n/T^3 =\",nT3num(T,mu,1e-6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Compare the results to the analytic expression\n",
    "$$\n",
    "\\tilde n = n/T^3 = \\frac{d m^2}{2\\pi^2 T^2} K_2(m/T) e^{\\mu/T}.\n",
    "$$\n",
    "Here $K_2$ is the modified Bessel function of the second kind, which is accessbile through scipy package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Analytic result: n/T^3 = 0.08472249379368636\n"
     ]
    }
   ],
   "source": [
    "from scipy.special import kn\n",
    "\n",
    "# Analytic expression for the density in the Maxwell-Boltzmann limit\n",
    "def nT3analyt(T, mu, m, d = 1):\n",
    "    return d * m**2 / (2 * np.pi**2 * T**2) * kn(2,m/T) * np.exp(mu/T)\n",
    "\n",
    "print(\"Analytic result:\", \"n/T^3 =\", nT3analyt(T,mu,m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. Incorporate the effect of Bose statistics by setting $\\eta = -1$ and compare the results to the $\\eta = 0$ case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:     1, I =    0.052071598602252\n",
      "Iteration:     2, I =    0.160089665256309, error estimate = 0.036006022218019\n",
      "Iteration:     3, I =    0.075406103813409, error estimate = -0.028227853814300\n",
      "Iteration:     4, I =    0.085410602578111, error estimate = 0.003334832921567\n",
      "Iteration:     5, I =    0.084623507486682, error estimate = -0.000262365030476\n",
      "Iteration:     6, I =    0.084721979027677, error estimate = 0.000032823846998\n",
      "Iteration:     7, I =    0.084722493628870, error estimate = 0.000000171533731\n",
      "Maxwell-Boltzmann: n/T^3 = 0.08472249362886973\n",
      "Iteration:     1, I =    0.070079419142193\n",
      "Iteration:     2, I =    0.168395499279461, error estimate = 0.032772026712423\n",
      "Iteration:     3, I =    0.083996336251779, error estimate = -0.028133054342561\n",
      "Iteration:     4, I =    0.093987772319729, error estimate = 0.003330478689317\n",
      "Iteration:     5, I =    0.093223117309176, error estimate = -0.000254885003518\n",
      "Iteration:     6, I =    0.093321713544158, error estimate = 0.000032865411661\n",
      "Iteration:     7, I =    0.093322228547175, error estimate = 0.000000171667672\n",
      "    Bose-Einstein: n/T^3 = 0.09332222854717481\n"
     ]
    }
   ],
   "source": [
    "prec = 1.e-6\n",
    "eta = 0\n",
    "print(\"Maxwell-Boltzmann:\", \"n/T^3 =\",nT3num(T,mu,prec))\n",
    "\n",
    "eta = -1\n",
    "print(\"    Bose-Einstein:\", \"n/T^3 =\",nT3num(T,mu,prec))"
   ]
  }
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