{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyOxMDsoLaGYO/x73HFv2lW+",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jmmarinr/ComputationalMethods/blob/master/Raices/Trascendentales_Librerias.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "PQUM5GvSJX6F"
      },
      "outputs": [],
      "source": [
        "#@title Librerias\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Ecuaciones trascendentales\n",
        "\n",
        "Las ecuaciones trascendentales son aquellas que no pueden expresarse únicamente con operaciones algebraicas, es decir, contienen funciones trascendentales como logaritmos, exponenciales, senos, cosenos, etc. Resolver este tipo de ecuaciones generalmente requiere métodos numéricos, ya que no siempre es posible encontrar soluciones exactas de forma algebraica.\n",
        "\n",
        "Supongamos que queremos resolver:\n",
        "\n",
        "$$xe^x = 1$$\n",
        "\n",
        "Graficamente tendriamos que la raiz seria equivalente al punto de corte entre $e^x$ y $1/x$. Esta ecuación vemos que no tiene solución algebraica, por ende, se hace necesario utilizar métodos númericos."
      ],
      "metadata": {
        "id": "uQPxsYPVKUSl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "f = lambda x: np.exp(x)\n",
        "g = lambda x: 1/x\n",
        "\n",
        "\n",
        "x = np.linspace(.1, 2, 100)\n",
        "plt.plot(x, f(x), label='$e^x$')\n",
        "plt.plot(x, g(x), label='$1/x$')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('f(x)')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "3QJgHUbBKPTd",
        "outputId": "e27e931a-b8dd-45ff-eef4-6767eacf06b3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "f = lambda x: x*np.exp(x) - 1\n",
        "x = np.linspace(-2, 2, 100)\n",
        "plt.plot(x, f(x), label = '$f(x)=x*e^x-1$')\n",
        "plt.axhline(y=0, color='m', linestyle = '--')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "wtdazarOKbvp",
        "outputId": "b64503d2-c4d1-4c87-d8e0-4195d3bd57f8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Ejemplo: Ecuación de Kepler\n",
        "\n",
        "En mecánica celeste, la **Ecuación de Kepler** describe el movimiento de un cuerpo en una órbita elíptica:\n",
        "\n",
        "$$\n",
        "M = E - e \\sin E\n",
        "$$\n",
        "\n",
        "donde:\n",
        "- $M$ es la **anomalía media** (proporcional al tiempo),\n",
        "- $E$ es la **anomalía excéntrica** (ángulo auxiliar),\n",
        "- $e$ es la **excentricidad orbital**, con $0 < e < 1$.\n",
        "\n",
        "La ecuación es **trascendental** en $E$ y debe resolverse numéricamente para obtener la posición del cuerpo.\n",
        "\n",
        "\n",
        "Dado $M = 1$ rad y $e = 0.6$, resolver:\n",
        "\n",
        "$$\n",
        "E - 0.6 \\sin E = 1\n",
        "$$\n",
        "\n"
      ],
      "metadata": {
        "id": "4YSo-wjoRwEU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.optimize import newton\n",
        "\n",
        "# Parámetros\n",
        "M = 1.0\n",
        "e = 0.6\n",
        "\n",
        "# Definición de la función f(E) = E - e*sin(E) - M\n",
        "def kepler_eq(E):\n",
        "    return E - e * np.sin(E) - M\n",
        "\n",
        "E = np.linspace(0, 2*np.pi, 100)\n",
        "plt.plot(E, kepler_eq(E), label = '$E - 0.6 \\\\sin E = 1$')\n",
        "plt.axhline(y=0, color='m', linestyle = '--')\n",
        "plt.xlabel('E')\n",
        "plt.ylabel('f(E)')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "# Resolución usando el método de Brent\n",
        "sol = newton(kepler_eq, x0 = 1.0)\n",
        "print(\"Anomalía excéntrica E:\", sol)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 467
        },
        "id": "RlOfeWSKR3cd",
        "outputId": "be4ebb6d-0703-4c09-958d-daf44f6a5303"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Anomalía excéntrica E: 1.599748548227517\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Métodos Numéricos para Encontrar Raíces de Funciones en Python\n",
        "\n",
        "Una raíz de una función $f(x)$ es un valor $x = r$ tal que $f(r) = 0$. En general, muchas funciones no admiten una solución analítica exacta para sus raíces, por lo que se utilizan **métodos numéricos**.\n",
        "\n",
        "En Python, las siguientes librerías permiten resolver raíces de manera eficiente:\n",
        "\n",
        "- `scipy.optimize`\n",
        "- `numpy`\n",
        "\n",
        "Usando los siguientes métodos:\n",
        "\n",
        "- Métodos clásicos: Bisección, Newton-Raphson, Secante\n",
        "- Métodos disponibles en `scipy.optimize.root_scalar`\n",
        "- Método `fsolve` para sistemas no lineales\n",
        "- Método `np.roots` para polinomios\n"
      ],
      "metadata": {
        "id": "uX7qwKQYMsTt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.optimize import bisect, newton, root_scalar, fsolve"
      ],
      "metadata": {
        "id": "41h9gafbKn2p"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def f(x):\n",
        "  '''\n",
        "  función a la que queremos encontrar la raíz\n",
        "  x^3 - 2*x^2 - 5 = 0\n",
        "  '''\n",
        "  return x**3 - 2*x**2 - 5"
      ],
      "metadata": {
        "id": "BKBRCMkPNLv1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.linspace(-4, 4, 100)\n",
        "plt.plot(x, f(x), label = '$f(x)=x^3-2x^2-5$')\n",
        "plt.legend()\n",
        "plt.axhline(y=0, color='m', linestyle = '--')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('f(x)')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "VnqwxMmNNXLp",
        "outputId": "a9baa7ff-be9d-4e9c-f2d9-49a58f095f67"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Método de Bisección\n",
        "\n",
        "Requiere un intervalo $[a, b]$ tal que $f(a)f(b) < 0$. Divide el intervalo iterativamente hasta alcanzar la raíz con la precisión deseada."
      ],
      "metadata": {
        "id": "XvVgd0KtNFru"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "raiz_biseccion = bisect(f, 2, 3)\n",
        "print(\"Raíz (Bisección):\", raiz_biseccion)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uPxsT5RBM-OC",
        "outputId": "57d92b19-75a0-480d-fcc9-66b876cc771e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Raíz (Bisección): 2.6906474480292673\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Método de Newton-Raphson\n",
        "\n",
        "\n",
        "El método de Newton-Raphson utiliza una estimación inicial $x_0$ y la derivada de la función $f'(x)$ para iterar mediante la fórmula:\n",
        "\n",
        "$$\n",
        "x_{n+1} = x_n - \\frac{f(x_n)}{f'(x_n)}\n",
        "$$\n",
        "\n",
        "Este método converge rápidamente si la función es suficientemente suave y $x_0$ está cerca de la raíz.\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "OzfRMz3UNxpE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def f(x):\n",
        "    return x**3 - 2*x**2 - 5\n",
        "\n",
        "def df(x):\n",
        "    return 3*x**2 - 4*x\n",
        "\n",
        "# Usando derivada explícita\n",
        "raiz_newton = newton(f, x0=2.5, fprime=df)\n",
        "print(\"Raíz (Newton-Raphson):\", raiz_newton)\n",
        "\n",
        "# Usando derivada aproximada (diferencias finitas)\n",
        "raiz_newton_aprox = newton(f, x0=2.5)\n",
        "print(\"Raíz (Newton sin derivada explícita):\", raiz_newton_aprox)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TVIgTHNuNU8v",
        "outputId": "0fc11352-122c-43f4-8ab7-f0f16ce08f3e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Raíz (Newton-Raphson): 2.6906474480286136\n",
            "Raíz (Newton sin derivada explícita): 2.6906474480286136\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Método de la Secante\n",
        "\n",
        "La secante es un método similar a Newton-Raphson pero no requiere conocer la derivada. Utiliza dos aproximaciones iniciales \\$x\\_0\\$ y \\$x\\_1\\$ para estimar la raíz:\n",
        "\n",
        "$$\n",
        "x_{n+1} = x_n - f(x_n) \\cdot \\frac{x_n - x_{n-1}}{f(x_n) - f(x_{n-1})}\n",
        "$$"
      ],
      "metadata": {
        "id": "IgXL3CTdOgEF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Método de la secante: se especifican dos valores iniciales\n",
        "raiz_secante = newton(f, x0=2, x1=3)\n",
        "print(\"Raíz (Secante):\", raiz_secante)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RTcV2UVYOUiM",
        "outputId": "896413ff-eb4a-4cb9-bb33-537c76bc1aa2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Raíz (Secante): 2.6906474480286136\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Método fsolve (Raíces de funciones no lineales)\n",
        "\n",
        "`fsolve` resuelve sistemas de ecuaciones no lineales $f(x) = 0$, usando un método iterativo similar a Newton-Raphson multidimensional.\n",
        "\n"
      ],
      "metadata": {
        "id": "ehE1bjypP8if"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "raiz_fsolve = fsolve(f, x0=2.5)\n",
        "print(\"Raíz (fsolve):\", raiz_fsolve[0])\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5vCxxzrNQOVX",
        "outputId": "ae4c924a-1ab8-41f8-8a56-a62bcde39b5a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Raíz (fsolve): 2.6906474480286136\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def sistema(vars):\n",
        "    x, y = vars\n",
        "    return [x**2 + y**2 - 4, x*y - 1]\n",
        "\n",
        "solucion_sistema = fsolve(sistema, [1, 1])\n",
        "print(\"Solución del sistema:\", solucion_sistema)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-G0cgHO6QTiU",
        "outputId": "45fdc3ef-5a55-4247-9e61-0e5b9d9d6e19"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Solución del sistema: [1.93185165 0.51763809]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Método `numpy.roots`\n",
        "\n",
        "\n",
        "El método `numpy.roots` permite encontrar todas las raíces (reales y complejas) de un polinomio cuyos coeficientes se conocen.\n",
        "\n",
        "Para polinomios de la forma:\n",
        "\n",
        "$$\n",
        "P(x) = a_n x^n + a_{n-1} x^{n-1} + \\cdots + a_1 x + a_0\n",
        "$$\n",
        "\n",
        "Se representa en Python como una lista o array de coeficientes ordenados desde el mayor grado al término independiente:\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "2L_m7tNUQP_U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Polinomio: x³ - 2x² - 5\n",
        "coeficientes = [1, -2, 0, -5]\n",
        "\n",
        "raices = np.roots(coeficientes)\n",
        "print(\"Raíces del polinomio:\", raices)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NEVaZVeSQzAo",
        "outputId": "773e49c6-b50e-46c4-9f94-e0a56701dd6a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Raíces del polinomio: [ 2.69064745+0.j         -0.34532372+1.31872678j -0.34532372-1.31872678j]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Convergencia y Errores Comunes en Métodos de Búsqueda de Raíces\n",
        "\n",
        "## 1. Método de Bisección\n",
        "\n",
        "### Convergencia\n",
        "\n",
        "- **Orden**: Lineal\n",
        "- **Condiciones**: $f(a)\\cdot f(b) < 0$ (cambio de signo)\n",
        "- **Garantía de convergencia**: Siempre que $f$ sea continua en $[a, b]$ y cumpla la condición anterior.\n",
        "\n",
        "### Fórmula del error:\n",
        "\n",
        "$$\n",
        "|r - x_n| \\leq \\frac{b - a}{2^n}\n",
        "$$\n",
        "\n",
        "### Errores comunes\n",
        "\n",
        "- Elegir un intervalo $[a, b]$ sin cambio de signo.\n",
        "- Aplicarlo a funciones discontinuas.\n",
        "- Lentitud si se requiere alta precisión (convergencia lenta).\n",
        "\n",
        "---\n",
        "\n",
        "## 2. Método del Punto Fijo\n",
        "\n",
        "### Convergencia\n",
        "\n",
        "- **Orden**: Lineal (en general).\n",
        "- Requiere reescribir $f(x) = 0$ como $x = g(x)$.\n",
        "- Si $g$ es continua y derivable en un entorno de la raíz y $|g'(x)| < 1$, el método converge localmente.\n",
        "\n",
        "### Criterio de convergencia:\n",
        "\n",
        "$$\n",
        "|x_{n+1} - r| \\leq |g'(r)| \\cdot |x_n - r|\n",
        "$$\n",
        "\n",
        "### Errores comunes\n",
        "\n",
        "- Escoger una función $g(x)$ inadecuada que no cumpla $|g'(x)| < 1$ cerca de la raíz.\n",
        "- Oscilaciones o divergencia.\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "## 3. Método de Newton-Raphson\n",
        "\n",
        "### Convergencia\n",
        "\n",
        "- **Orden**: Cuadrático si $f \\in C^2$ y $f'(r) \\ne 0$.\n",
        "- Muy eficiente si se inicia cerca de la raíz.\n",
        "\n",
        "### Fórmula de iteración:\n",
        "\n",
        "$$\n",
        "x_{n+1} = x_n - \\frac{f(x_n)}{f'(x_n)}\n",
        "$$\n",
        "\n",
        "### Errores comunes\n",
        "\n",
        "- Derivada $f'(x_n) \\approx 0$ causa división por número pequeño o cero.\n",
        "- Raíz múltiple: la convergencia se vuelve lineal.\n",
        "- Malas estimaciones iniciales pueden llevar a divergencia.\n",
        "- Costoso si se evalúa simbólicamente la derivada.\n",
        "\n",
        "---\n",
        "\n",
        "## 4. Método de la Secante\n",
        "\n",
        "### Convergencia\n",
        "\n",
        "- **Orden**: Superlineal, aproximadamente $\\varphi = \\frac{1+\\sqrt{5}}{2} \\approx 1.618$\n",
        "- No requiere derivada.\n",
        "\n",
        "### Fórmula de iteración:\n",
        "\n",
        "$$\n",
        "x_{n+1} = x_n - f(x_n) \\cdot \\frac{x_n - x_{n-1}}{f(x_n) - f(x_{n-1})}\n",
        "$$\n",
        "\n",
        "### Errores comunes\n",
        "\n",
        "- Si $f(x_n) \\approx f(x_{n-1})$, se produce división por número pequeño.\n",
        "- Sensible a malas estimaciones iniciales.\n",
        "- Convergencia más lenta que Newton, pero mejor que bisección.\n",
        "\n",
        "---\n",
        "\n",
        "## Comparación de Órdenes de Convergencia\n",
        "\n",
        "| Método         | Orden de Convergencia | Derivada requerida |\n",
        "|----------------|------------------------|---------------------|\n",
        "| Bisección      | Lineal                 | No                  |\n",
        "| Punto Fijo     | Lineal                 | Implícitamente sí   |\n",
        "| Newton-Raphson | Cuadrático             | Sí                  |\n",
        "| Secante        | Superlineal ($\\approx 1.618$) | No         |\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "4yezcsodPpzh"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "nxe1j9r5RHgk"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}