Ejercicio 5.15.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Realizar un programa que calcule la derivada de la función:\n",
    "\\begin{equation}\n",
    "f(x)=1+\\frac{1}{2}tanh(2x)\n",
    "\\end{equation}\n",
    "\n",
    "Utilizando el método de derivadas hacia adelante y derivadas centrales, Por otra parte, compare dicha derivada numérica con la análica mediante un gráfico, además grafique el porcentaje de error entre las mísmas.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x189b1f75d48>]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math as mt\n",
    "import matplotlib.pyplot as plt\n",
    "def f(x):\n",
    "    return 1+(1/2)*mt.tanh(2*x)   # Función que se desea derivar \n",
    "\n",
    "def g(x):\n",
    "    return 1-mt.tanh(2*x)**2    # Derivada de la función \n",
    "\n",
    "a=-2\n",
    "b=2\n",
    "N=100\n",
    "h=(b-a)/N\n",
    "\n",
    "fp=[]\n",
    "for i in range(N):\n",
    "    fp.append(f(a+i*h))\n",
    "\n",
    "plt.plot(fp,'o') \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Derivadas numéricas por el método: $\\textbf{Derivadas}$ $\\textbf{hacia}$ $\\textbf{adelante}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dfn=[]\n",
    "dfa=[]\n",
    "\n",
    "for i in range(N-1):\n",
    "    dfn.append((fp[i+1]-fp[i])/h)\n",
    "    dfa.append(g(a+i*h))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparamos la derivada Analítica y Númerica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x189b2effc88>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(dfa)\n",
    "plt.plot(dfn,'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "diff=[]\n",
    "\n",
    "for i in range(N-1):\n",
    "    tmp=1-(dfn[i]/dfa[i])          # Diferencia entre la derivada numérica y analítica (Porcentaje de Error)\n",
    "    diff.append(tmp*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x189b2f6ce08>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(diff,'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Derivadas Númericas por el método de $\\textbf{Derivadas}$ $\\textbf{Centrales}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "dfn=[]\n",
    "dfa=[]\n",
    "\n",
    "for i in range(1,N-1):\n",
    "    dfn.append((fp[i+1]-fp[i-1])/(2*h)) \n",
    "    dfa.append(g(a+i*h))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparación entre la derivada analítica y númerica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x189b2feda88>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(dfa)\n",
    "plt.plot(dfn,'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "diff=[]\n",
    "\n",
    "for i in range(N-2):                    # Diferencia entre la derivada numérica y analítica (Porcentaje de Error)\n",
    "    tmp=1-(dfn[i]/dfa[i])\n",
    "    diff.append(tmp*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x189b3046688>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(diff,'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se concluye que el método de derivadas centrales es más preciso que el método de derivas hacia adelante. Ya que la diferencia porcentual de error es menor en el método de diferenciación central."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}