raices de funciones.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Raíces de funciones. Ceros de Funciones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from math import ceil, log, sqrt\n",
    "import matplotlib.pyplot as plt\n",
    "from beautifultable import BeautifulTable\n",
    "import scipy.optimize as opt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Métodos Cerrados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Método de Bisección"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bisection(func, x_a, x_b, error, table):\n",
    "    if func(x_a) * func(x_b) >= 0:\n",
    "        raise ValueError(\"The bisection method cannot be applied\")\n",
    "\n",
    "    # The bisection method\n",
    "    while x_b - x_a > error:\n",
    "        # calculate middle point\n",
    "        x_m = (x_a + x_b) / 2\n",
    "\n",
    "        table.append([x_a, x_b, x_m, func(x_a), func(x_b), func(x_m), x_b - x_a])\n",
    "\n",
    "        if func(x_m) == 0:\n",
    "            return x_m\n",
    "\n",
    "        if func(x_a) * func(x_m) < 0:\n",
    "            x_b = x_m\n",
    "        else:\n",
    "            x_a = x_m\n",
    "\n",
    "    table.append([x_a, x_b, (x_a + x_b) / 2, func(x_a), func(x_b), func(x_m), x_b - x_a])\n",
    "\n",
    "    return (x_a + x_b) / 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ejercicio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f(x) = x^3 + 4 x^2 - 10$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "func = lambda x: x ** 3 + 4 * x ** 2 - 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Tiempos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.36474609375"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bisection(func, 1, 2, 0.001)  # own function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3642578125"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt.bisect(func, 1, 2, xtol=0.001)  # scipy function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Raíz: 1.36474609375'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Raíz: {bisection(func, 1, 2, 0.001, table:=[])}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "table = np.array(table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_a</th>\n",
       "      <th>x_b</th>\n",
       "      <th>x_m</th>\n",
       "      <th>f(x_a)</th>\n",
       "      <th>f(x_b)</th>\n",
       "      <th>f(x_m)</th>\n",
       "      <th>tramo</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>-5.000000</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>2.375000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>1.250000</td>\n",
       "      <td>-5.000000</td>\n",
       "      <td>2.375000</td>\n",
       "      <td>-1.796875</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.250000</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>1.375000</td>\n",
       "      <td>-1.796875</td>\n",
       "      <td>2.375000</td>\n",
       "      <td>0.162109</td>\n",
       "      <td>0.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.250000</td>\n",
       "      <td>1.375000</td>\n",
       "      <td>1.312500</td>\n",
       "      <td>-1.796875</td>\n",
       "      <td>0.162109</td>\n",
       "      <td>-0.848389</td>\n",
       "      <td>0.125000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.312500</td>\n",
       "      <td>1.375000</td>\n",
       "      <td>1.343750</td>\n",
       "      <td>-0.848389</td>\n",
       "      <td>0.162109</td>\n",
       "      <td>-0.350983</td>\n",
       "      <td>0.062500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.343750</td>\n",
       "      <td>1.375000</td>\n",
       "      <td>1.359375</td>\n",
       "      <td>-0.350983</td>\n",
       "      <td>0.162109</td>\n",
       "      <td>-0.096409</td>\n",
       "      <td>0.031250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.359375</td>\n",
       "      <td>1.375000</td>\n",
       "      <td>1.367188</td>\n",
       "      <td>-0.096409</td>\n",
       "      <td>0.162109</td>\n",
       "      <td>0.032356</td>\n",
       "      <td>0.015625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.359375</td>\n",
       "      <td>1.367188</td>\n",
       "      <td>1.363281</td>\n",
       "      <td>-0.096409</td>\n",
       "      <td>0.032356</td>\n",
       "      <td>-0.032150</td>\n",
       "      <td>0.007812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.363281</td>\n",
       "      <td>1.367188</td>\n",
       "      <td>1.365234</td>\n",
       "      <td>-0.032150</td>\n",
       "      <td>0.032356</td>\n",
       "      <td>0.000072</td>\n",
       "      <td>0.003906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.363281</td>\n",
       "      <td>1.365234</td>\n",
       "      <td>1.364258</td>\n",
       "      <td>-0.032150</td>\n",
       "      <td>0.000072</td>\n",
       "      <td>-0.016047</td>\n",
       "      <td>0.001953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.364258</td>\n",
       "      <td>1.365234</td>\n",
       "      <td>1.364746</td>\n",
       "      <td>-0.016047</td>\n",
       "      <td>0.000072</td>\n",
       "      <td>-0.016047</td>\n",
       "      <td>0.000977</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x_a       x_b       x_m    f(x_a)     f(x_b)    f(x_m)     tramo\n",
       "0   1.000000  2.000000  1.500000 -5.000000  14.000000  2.375000  1.000000\n",
       "1   1.000000  1.500000  1.250000 -5.000000   2.375000 -1.796875  0.500000\n",
       "2   1.250000  1.500000  1.375000 -1.796875   2.375000  0.162109  0.250000\n",
       "3   1.250000  1.375000  1.312500 -1.796875   0.162109 -0.848389  0.125000\n",
       "4   1.312500  1.375000  1.343750 -0.848389   0.162109 -0.350983  0.062500\n",
       "5   1.343750  1.375000  1.359375 -0.350983   0.162109 -0.096409  0.031250\n",
       "6   1.359375  1.375000  1.367188 -0.096409   0.162109  0.032356  0.015625\n",
       "7   1.359375  1.367188  1.363281 -0.096409   0.032356 -0.032150  0.007812\n",
       "8   1.363281  1.367188  1.365234 -0.032150   0.032356  0.000072  0.003906\n",
       "9   1.363281  1.365234  1.364258 -0.032150   0.000072 -0.016047  0.001953\n",
       "10  1.364258  1.365234  1.364746 -0.016047   0.000072 -0.016047  0.000977"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(table, columns=['x_a', 'x_b', 'x_m', 'f(x_a)', 'f(x_b)', 'f(x_m)', 'tramo'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xi = table[:, 2]\n",
    "yi = table[:, 5]\n",
    "\n",
    "orden = np.argsort(xi)\n",
    "xi = xi[orden]\n",
    "yi = yi[orden]\n",
    "\n",
    "\n",
    "plt.plot(xi, yi)\n",
    "plt.plot(xi,yi,'o')\n",
    "plt.axhline(0, color=\"black\")\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Bisección en f(x)')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Método de Falsa Posición"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regula_falsi(func, a, b, error_total, table):\n",
    "    error = np.abs(b - a)\n",
    "    f_a = func(a)\n",
    "    f_b = func(b)\n",
    "\n",
    "    while error > error_total:\n",
    "        x_i = b - f_b * (a - b) / (f_a - f_b)\n",
    "        f_x_i = func(x_i)\n",
    "\n",
    "        table.append([a, b, x_i, f_a, f_b, f_x_i, error])\n",
    "\n",
    "        c = np.sign(f_a) * np.sign(f_x_i)\n",
    "\n",
    "        if c >  0:\n",
    "            error = np.abs(x_i - a)\n",
    "            a = x_i\n",
    "            f_a = f_x_i\n",
    "        else:\n",
    "            error = np.abs(b - x_i)\n",
    "            b = x_i\n",
    "            f_b = f_x_i\n",
    "\n",
    "    table.append([a, b, x_i, f_a, f_b, f_x_i, error])\n",
    "\n",
    "    return x_i"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ejercicio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f(x) = \\cos{2x} - x^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dada $f(x) = \\cos{2x} - x^2$ y sabiendo que la raíz se encuentra en el intervalo (0, 0.5). Encontrar un valor aproximado de la raíz. $e = 0.0001$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x = lambda x: np.cos(2 * x) - x ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [],
   "source": [
    "root = regula_falsi(f_x, 0, 0.5, 0.0001, table:=[])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Raíz: 0.6007685997975323'"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Raíz: {root}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "      <th>x_i</th>\n",
       "      <th>f(a)</th>\n",
       "      <th>f(b)</th>\n",
       "      <th>f(x_i)</th>\n",
       "      <th>error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.704525</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.290302</td>\n",
       "      <td>-0.335315</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.704525</td>\n",
       "      <td>0.527610</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.335315</td>\n",
       "      <td>0.214664</td>\n",
       "      <td>0.204525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.527610</td>\n",
       "      <td>0.704525</td>\n",
       "      <td>0.596662</td>\n",
       "      <td>0.214664</td>\n",
       "      <td>-0.335315</td>\n",
       "      <td>0.012565</td>\n",
       "      <td>0.527610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.596662</td>\n",
       "      <td>0.704525</td>\n",
       "      <td>0.600558</td>\n",
       "      <td>0.012565</td>\n",
       "      <td>-0.335315</td>\n",
       "      <td>0.000646</td>\n",
       "      <td>0.069052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.600558</td>\n",
       "      <td>0.704525</td>\n",
       "      <td>0.600758</td>\n",
       "      <td>0.000646</td>\n",
       "      <td>-0.335315</td>\n",
       "      <td>0.000033</td>\n",
       "      <td>0.003896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.600758</td>\n",
       "      <td>0.704525</td>\n",
       "      <td>0.600769</td>\n",
       "      <td>0.000033</td>\n",
       "      <td>-0.335315</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>0.000200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.600769</td>\n",
       "      <td>0.704525</td>\n",
       "      <td>0.600769</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>-0.335315</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>0.000010</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          a         b       x_i      f(a)      f(b)    f(x_i)     error\n",
       "0  0.000000  0.500000  0.704525  1.000000  0.290302 -0.335315  0.500000\n",
       "1  0.000000  0.704525  0.527610  1.000000 -0.335315  0.214664  0.204525\n",
       "2  0.527610  0.704525  0.596662  0.214664 -0.335315  0.012565  0.527610\n",
       "3  0.596662  0.704525  0.600558  0.012565 -0.335315  0.000646  0.069052\n",
       "4  0.600558  0.704525  0.600758  0.000646 -0.335315  0.000033  0.003896\n",
       "5  0.600758  0.704525  0.600769  0.000033 -0.335315  0.000002  0.000200\n",
       "6  0.600769  0.704525  0.600769  0.000002 -0.335315  0.000002  0.000010"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = np.array(table)\n",
    "pd.DataFrame(table, columns=['a', 'b', 'x_i', 'f(a)', 'f(b)', 'f(x_i)', 'error'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xi = np.linspace(0, 1, len(table))\n",
    "\n",
    "plt.plot(xi, f_x(xi))\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('Falsa Posición')\n",
    "\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Métodos Abiertos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Método de punto fijo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fixed_point(g_x, x0, error_total, table):\n",
    "    error = 1\n",
    "    x_a = sum(x0) / 2\n",
    "    while (error >= error_total):\n",
    "        x_i = g_x(x_a)\n",
    "        error = np.abs((x_i - x_a) / x_i)\n",
    "        table.append([x_a, x_i, error * 100])\n",
    "        x_a = x_i\n",
    "    return x_a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ejercicio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f(x) = 4x^2 + x^3 - 10$$\n",
    "$$4 x^2 + x^3 - 10 = 0$$\n",
    "$$g(x) = \\sqrt{\\frac{10 - x^3}{4}}$$\n",
    "\n",
    "Intervalo de confianza:\n",
    "$$f(1) = -5$$\n",
    "$$f(2) = 14$$\n",
    "$$x_a = \\frac{1 + 2}{2} = 1.5$$\n",
    "\n",
    "Convergencia:\n",
    "$$g'(x) = - \\frac{3x^2}{4 \\sqrt{10 - x^3}}$$\n",
    "$$|g'(1.5)| = |-0.655| < 1$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x = lambda x: 4 * x ** 2 + x ** 3 - 10\n",
    "g_x = lambda x: np.sqrt((10 - x ** 3) / 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "root = fixed_point(g_x, [1, 2], 10e-6, table := [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Raíz: 1.3652332557424998'"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Raíz: {root}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "table = np.array(table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_a</th>\n",
       "      <th>x_i</th>\n",
       "      <th>error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.500000</td>\n",
       "      <td>1.286954</td>\n",
       "      <td>16.554303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.286954</td>\n",
       "      <td>1.402541</td>\n",
       "      <td>8.241260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.402541</td>\n",
       "      <td>1.345458</td>\n",
       "      <td>4.242601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.345458</td>\n",
       "      <td>1.375170</td>\n",
       "      <td>2.160596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.375170</td>\n",
       "      <td>1.360094</td>\n",
       "      <td>1.108457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.360094</td>\n",
       "      <td>1.367847</td>\n",
       "      <td>0.566787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.367847</td>\n",
       "      <td>1.363887</td>\n",
       "      <td>0.290344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.363887</td>\n",
       "      <td>1.365917</td>\n",
       "      <td>0.148598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.365917</td>\n",
       "      <td>1.364878</td>\n",
       "      <td>0.076089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.364878</td>\n",
       "      <td>1.365410</td>\n",
       "      <td>0.038951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.365410</td>\n",
       "      <td>1.365138</td>\n",
       "      <td>0.019942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.365138</td>\n",
       "      <td>1.365277</td>\n",
       "      <td>0.010209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.365277</td>\n",
       "      <td>1.365206</td>\n",
       "      <td>0.005227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1.365206</td>\n",
       "      <td>1.365242</td>\n",
       "      <td>0.002676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.365242</td>\n",
       "      <td>1.365224</td>\n",
       "      <td>0.001370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.365224</td>\n",
       "      <td>1.365233</td>\n",
       "      <td>0.000701</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x_a       x_i      error\n",
       "0   1.500000  1.286954  16.554303\n",
       "1   1.286954  1.402541   8.241260\n",
       "2   1.402541  1.345458   4.242601\n",
       "3   1.345458  1.375170   2.160596\n",
       "4   1.375170  1.360094   1.108457\n",
       "5   1.360094  1.367847   0.566787\n",
       "6   1.367847  1.363887   0.290344\n",
       "7   1.363887  1.365917   0.148598\n",
       "8   1.365917  1.364878   0.076089\n",
       "9   1.364878  1.365410   0.038951\n",
       "10  1.365410  1.365138   0.019942\n",
       "11  1.365138  1.365277   0.010209\n",
       "12  1.365277  1.365206   0.005227\n",
       "13  1.365206  1.365242   0.002676\n",
       "14  1.365242  1.365224   0.001370\n",
       "15  1.365224  1.365233   0.000701"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(table, columns=['x_a', 'x_i', 'error'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xi = np.linspace(1, 2, len(table))\n",
    "fi = f_x(xi)\n",
    "gi = g_x(xi)\n",
    "yi = xi\n",
    "\n",
    "plt.plot(xi, fi, label='f(x)')\n",
    "plt.plot(xi ,gi, label='g(x)')\n",
    "plt.plot(xi, yi, label='y=x')\n",
    "plt.axvline(root)\n",
    "\n",
    "plt.axhline(0, color='k')\n",
    "plt.title('Punto Fijo')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Método de Newton - Raphson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [],
   "source": [
    "def newton_raphson(fx, dfx, x0, error_total, table):\n",
    "    error = np.abs(2 * error_total)\n",
    "    x_i = x0\n",
    "    while error >= error_total:\n",
    "        x_ip1 = x_i - fx(x_i) / dfx(x_i)\n",
    "        error = np.abs((x_ip1 - x_i) / x_ip1)\n",
    "\n",
    "        table.append([x_i, x_ip1, error])\n",
    "\n",
    "        x_i = x_ip1\n",
    "\n",
    "    return x_i"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ejercicio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f(x) = \\frac{1}{e^x} - x$$\n",
    "$$f'(x) = - e^{-x} - 1$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dada la función $f(x) = \\frac{1}{e^x} - x$ obtener una raíz aproximada, con el método **Newton - Raphson**. Valor inicial $x_0 = 0$ y $e = 0.0001$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [],
   "source": [
    "fx = lambda x: np.exp(-x) - x\n",
    "dfx = lambda x: - np.exp(-x) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [],
   "source": [
    "root = newton_raphson(fx, dfx, 0, 0.0001, table:=[])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Raíz: 0.5671432904097811'"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Raíz: {root}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.440892098500626e-15"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fx(root)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x_i</th>\n",
       "      <th>x_i + 1</th>\n",
       "      <th>error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.566311</td>\n",
       "      <td>1.170929e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.566311</td>\n",
       "      <td>0.567143</td>\n",
       "      <td>1.467287e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.567143</td>\n",
       "      <td>0.567143</td>\n",
       "      <td>2.210639e-07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        x_i   x_i + 1         error\n",
       "0  0.000000  0.500000  1.000000e+00\n",
       "1  0.500000  0.566311  1.170929e-01\n",
       "2  0.566311  0.567143  1.467287e-03\n",
       "3  0.567143  0.567143  2.210639e-07"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = np.array(table)\n",
    "pd.DataFrame(table, columns=['x_i', 'x_i + 1', 'error'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_plot = np.linspace(-2, 2, len(table))\n",
    "y_plot = fx(x_plot)\n",
    "\n",
    "plt.plot(x_plot, y_plot, c='blue')\n",
    "plt.plot(root, fx(root), c='red', marker='o', fillstyle='none')\n",
    "\n",
    "plt.xlim([-5, 5])\n",
    "plt.ylim([-5, 10])\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Método de la Secante"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [],
   "source": [
    "def secant(fx, x1, x0, error_total, table):\n",
    "    error = np.abs(4 * error_total)\n",
    "    while error >= error_total:\n",
    "        f_x1 = fx(x1)\n",
    "        f_x0 = fx(x0)\n",
    "        x_i = x1 - f_x1 * (x0 - x1) / (f_x0 - f_x1)\n",
    "        error = np.abs((x_i - x1) / x_i)\n",
    "\n",
    "        table.append([x1, x0, x_i, error])\n",
    "\n",
    "        x0 = x1\n",
    "        x1 = x_i\n",
    "\n",
    "    return x1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ejercicio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f(x) = x^3 + 4x^2 - 10$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = lambda x: x ** 3 + 4 * x ** 2 - 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [],
   "source": [
    "root = secant(f, 1, 2, 0.0001, table:=[])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Raíz: 1.3652300201877012'"
      ]
     },
     "execution_count": 304,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Raíz: {root}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1</th>\n",
       "      <th>x0</th>\n",
       "      <th>x_i</th>\n",
       "      <th>error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.263158</td>\n",
       "      <td>0.208333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.263158</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.387256</td>\n",
       "      <td>0.089456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.387256</td>\n",
       "      <td>1.263158</td>\n",
       "      <td>1.364095</td>\n",
       "      <td>0.016979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.364095</td>\n",
       "      <td>1.387256</td>\n",
       "      <td>1.365218</td>\n",
       "      <td>0.000823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.365218</td>\n",
       "      <td>1.364095</td>\n",
       "      <td>1.365230</td>\n",
       "      <td>0.000009</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x1        x0       x_i     error\n",
       "0  1.000000  2.000000  1.263158  0.208333\n",
       "1  1.263158  1.000000  1.387256  0.089456\n",
       "2  1.387256  1.263158  1.364095  0.016979\n",
       "3  1.364095  1.387256  1.365218  0.000823\n",
       "4  1.365218  1.364095  1.365230  0.000009"
      ]
     },
     "execution_count": 305,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = np.array(table)\n",
    "pd.DataFrame(table, columns=['x1', 'x0', 'x_i', 'error'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1185523263179675e-07"
      ]
     },
     "execution_count": 306,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(root)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 313,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xi = np.linspace(1, 2, len(table) + 1)\n",
    "fi = f(xi)\n",
    "dx = (2 - 1.5) / 2\n",
    "\n",
    "xa = 1.5\n",
    "fxa = f(xa)\n",
    "xb = xa + dx\n",
    "fxb = f(xb)\n",
    "\n",
    "descent = (f((root) + dx) - f(root)) / (root + dx - root)\n",
    "b0 = f(root) - descent * (root)\n",
    "tan_i = descent * xi + b0\n",
    "\n",
    "plt.plot(xi, fi, label='f(x)')\n",
    "\n",
    "plt.plot(xi, tan_i, label='secante')\n",
    "plt.plot(xa, fxa, 'go', label='x1')\n",
    "plt.plot(xb, fxb, 'ro', label='x0')\n",
    "plt.plot((-b0 / descent), 0, 'yo', label='xi')\n",
    "\n",
    "plt.plot([xa, xa], [0, fxa], 'm')\n",
    "plt.plot([xb, xb], [0, fxb], 'm')\n",
    "\n",
    "plt.axhline(0, color='k')\n",
    "plt.title('Método de la Secante')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.7 ('venv': venv)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.7"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "1dc376ffec5caecdc0a86d966f5e97e45537af940d2aef553cd87bae54f46a19"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}