sistema de ecuaciones lineales.ipynb

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      "source": [
        "<div align=\"center\">\n",
        "    <h1>Sistema de Ecuaciones Lineales</h1>\n",
        "    <p>\n",
        "        Autores:</br>\n",
        "        Sergio Andrés Majé Franco</br>\n",
        "        Marleny Rojas Gómez</br>\n",
        "    </p>\n",
        "    <p>\n",
        "        Docente:</br>\n",
        "        Dr. Jesús Emilio Pinto Lopera</br>\n",
        "    </p>\n",
        "    <p>\n",
        "        Universidad de la Amazonia</br>\n",
        "        Facultad de Ingeniería</br>\n",
        "        Programa Ingeniería de Sistemas</br>\n",
        "        Florencia - Caquetá</br>\n",
        "        2022</br>\n",
        "    </p>\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kpvvwgsbB0GN"
      },
      "source": [
        "## Tabla de Contenido\n",
        "\n",
        "1. Introducción\n",
        "2. Desarrollo Metodológico\n",
        "    1. Desarrollo Teórico\n",
        "        1. Método de Eliminación Gauss\n",
        "            1. Eliminación Gaussiana con pivote\n",
        "        2. Método de de Gauss-Jordan\n",
        "            1. Eliminación Gauss-Jordan con pivoteo\n",
        "        3. Descomposición LU\n",
        "        4. Inversión de Matrices\n",
        "        5. Método de Gauss-Seidel\n",
        "    2. Desarrollo Computacional\n",
        "        1. Método de Eliminación Gauss\n",
        "        2. Método de de Gauss-Jordan\n",
        "        3. Descomposición LU\n",
        "        4. Inversión de Matrices\n",
        "        5. Método de Gauss-Seidel\n",
        "3. Resultados\n",
        "    1. Ejercicios con los métodos\n",
        "        1. Eliminación Gaussiana\n",
        "        2. Eliminación Gauss-Jordan\n",
        "        3. Descomposición LU\n",
        "        4. Inversión de Matrices\n",
        "        5. Método de Gauss-Seidel\n",
        "    2. Benchmarking\n",
        "4. Conclusiones\n",
        "5. Referencias"
      ]
    },
    {
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      "metadata": {
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      },
      "source": [
        "## Tabla de Fórmulas"
      ]
    },
    {
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      "metadata": {
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      },
      "source": [
        "1. Fórmula 1. Eliminación Gaussiana con pivote - Eliminación hacia adelante\n",
        "2. Fórmula 2. Eliminación Gaussiana con pivote - Sustitución hacia atrás\n",
        "3. Fórmula 3. Método Gauss-Jordan - Transformación de la fila pivote - Matriz A\n",
        "4. Fórmula 4. Método Gauss-Jordan - Transformación de la fila pivote - Matriz b\n",
        "5. Fórmula 5. Método Gauss-Jordan - Transformación de la filas no pivote - Matriz A\n",
        "6. Fórmula 6. Método Gauss-Jordan - Transformación de la filas no pivote - Matriz b\n",
        "7. Fórmula 7. Descomposición LU - Descomposición de la Matriz A\n",
        "8. Fórmula 8. Descomposición LU - Matriz LU de la matriz A\n",
        "9. Fórmula 9. Descomposición LU - Igualdad de LU con y\n",
        "10. Fórmula 10. Inversion de Matrices - Matriz identidad\n",
        "11. Fórmula 11. Inversion de Matrices - Despejar x\n",
        "12. Fórmula 12. Método Gauss-Seidel\n",
        "13. Fórmula 13. Método Gauss-Seidel - Criterio\n",
        "14. Fórmula 14. Método Gauss-Seidel - Convergencia\n",
        "15. Fórmula 15. Método Gauss-Seidel - Generalización"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nLNllt9FCRFc"
      },
      "source": [
        "## Tabla de Tablas"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uzznFlHkzRXG"
      },
      "source": [
        "1. Tabla 1. Gauss - Matriz 2x2\n",
        "2. Tabla 2. Gauss - Matriz 3x3\n",
        "3. Tabla 3. Gauss - Matriz 4x4\n",
        "4. Tabla 4. Gauss - Matriz 5x5\n",
        "5. Tabla 5. Gauss-Jordan - Matriz 2x2\n",
        "6. Tabla 6. Gauss-Jordan - Matriz 3x3\n",
        "7. Tabla 7. Gauss-Jordan - Matriz 4x4\n",
        "8. Tabla 8. Gauss-Jordan - Matriz 5x5\n",
        "9. Tabla 9. Gauss-Seidel - Matriz 2x2\n",
        "10. Tabla 10. Gauss-Seidel - Matriz 3x3\n",
        "11. Tabla 11. Gauss-Seidel - Matriz 4x4\n",
        "12. Tabla 12. Gauss-Seidel - Matriz 5x5\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KtwblzvpCbh8"
      },
      "source": [
        "## Tabla de Gráficos"
      ]
    },
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      "metadata": {
        "id": "AqI2ghoKzTZk"
      },
      "source": [
        "1. Gráfica 1. Gauss – tiempos\n",
        "2. Gráfica 2. Gauss-Jordan – tiempos\n",
        "3. Gráfica 3. Descomposición LU – tiempos\n",
        "4. Gráfica 4. Inversión de Matrices\n",
        "5. Gráfica 5. Gauss-Seidel - tiempos\n",
        "5. Gráfica 6. Benchmarking - tiempos\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_sVT6ah2Ce_U"
      },
      "source": [
        "## 1. Introducción\n",
        "\n",
        "Un sistema de ecuación lineal es todo aquel que representa un conjunto de ecuaciones lineales, que, por medio de una estructura, al encontrar los valores deseados de las respectivas variables, generan un óptimo resultado para las ecuaciones implementadas, es un sistema con n incógnitas, m ecuaciones y el cual puede ser interpretado con la notación matricial desarrollada. Tiene distintas ventajas las cuales nos permiten destacarlo en algún fenómeno de la vida real, poder probarlo, implementarlo, ejecutarlo, logrando resolver variedad de problemas y así el interés de encontrar la solución esperada.\n",
        "\n",
        "Durante el proceso que se implemento para cada uno de los métodos, se desea obtener un aprendizaje de gran escala, por lo tanto, saber el paso a paso en cada uno de ellos, donde por medio de los ejercicios anexados podemos encontrar múltiples respuestas y procedimientos según el método. El método de Gauss, Gauss-Jordan, Descomposición LU, inversión de matrices y el método de Gauss-Seidel, nos permitieron realizar un recorrido para conocer su estructura y que compone cada uno de ellos.\n",
        "\n",
        "Lo que se pretende para con el presente documento, es realizar un análisis de los tiempos que se manejan en las diferentes dimensiones de cada método, cual es el cambio que se presenta de acuerdo con el tiempo, variables y estimaciones como resultado."
      ]
    },
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      },
      "source": [
        "## 2. Desarrollo Metodológico"
      ]
    },
    {
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      "metadata": {
        "id": "zeInco2SGqHg"
      },
      "source": [
        "### 2.1. Desarrollo Teórico"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8yyWoKfkHERd"
      },
      "source": [
        "#### 2.1.1. Método de Eliminación Gauss"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_R0oETczHnI2"
      },
      "source": [
        "La eliminación gaussiana también se conoce como el método de reducción de filas. Es un algoritmo comúnmente utilizado para resolver problemas lineales. El algoritmo implica una serie de operaciones de fila en una matriz de coeficientes extraídos de las ecuaciones lineales hasta que la matriz se reduce a la forma escalonada.\n",
        "\n",
        "Las siguientes tres operaciones se realizan cuando se transforma una matriz en una forma escalonada. Éstos incluyen:\n",
        "\n",
        "* Multiplicar una fila por un escalar y sumarlo o restarlo de otra fila.\n",
        "* Intercambio de filas.\n",
        "* Multiplicar filas con un escalar.\n",
        "\n",
        "Una matriz está en forma escalonada de filas si el primer elemento de cada fila, también conocido como la entrada inicial, es un cero; la entrada inicial de cada fila está una columna a la derecha de la entrada inicial de la fila anterior. Además, las filas con elementos cero deben estar debajo de los elementos que tienen filas distintas de cero.\n",
        "\n",
        "Las operaciones de fila se clasifican en gran medida en dos. La eliminación directa implica reducir una matriz a forma escalonada para determinar si existe una solución viable y si es finita o infinita. Por otro lado, la sustitución hacia atrás reduce aún más la matriz a la forma escalonada reducida por filas."
      ]
    },
    {
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      "metadata": {
        "id": "aCaO__eCHpsc"
      },
      "source": [
        "##### 2.1.1.1 Eliminación Gaussiana con pivote"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rr8K33I-H2kZ"
      },
      "source": [
        "$$ A_k = A_k - A_i \\cdot \\frac{a_{k, i}}{a_{i, i}} $$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 1. Eliminación Gaussiana con pivote - Eliminación hacia adelante\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bEBwHPhRH5bE"
      },
      "source": [
        "$$ x_i = \\frac{b^{(i - 1)}_{i} - \\sum^{n}_{j = i + 1} A^{(i - 1)}_{i, j} \\cdot x_j}{A^{(i - 1)}_{i, i}} $$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 2. Eliminación Gaussiana con pivote - Sustitución hacia atrás\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0VZ5E5AVIB3V"
      },
      "source": [
        "Pivotar es el intercambio de filas y columnas para obtener el elemento de pivote adecuado. Un elemento de pivote adecuado debe ser distinto de cero y significativamente grande pero más pequeño en comparación con las otras entradas de la fila.\n",
        "\n",
        "El pivote se clasifica en pivote parcial y pivote completo. Bajo el algoritmo de pivote parcial, el elemento más grande se considera el elemento pivote para minimizar los errores de redondeo.\n",
        "\n",
        "Por otro lado, el pivoteo completo incluye el intercambio de filas y columnas para obtener el mejor elemento de pivote, aumentando así la precisión.\n",
        "\n",
        "Un conjunto de ecuaciones se considera lineal si ninguna variable tiene un exponente de más de uno. La eliminación gaussiana implica una serie de pasos; el primer paso consiste en crear una matriz de coeficientes.\n",
        "\n",
        "Una matriz de coeficientes es simplemente una matriz de coeficientes extraídos de un conjunto de ecuaciones lineales. El siguiente paso consiste en crear una matriz aumentada que luego se somete a una serie de operaciones que la reducen a una forma escalonada.\n",
        "\n",
        "Sin embargo, en los casos en que el elemento pivote sea cero o de muy pequeña magnitud, tenemos que intercambiar la fila pivote con una fila inferior.\n",
        "\n",
        "Luego podemos leer el contenido de la matriz aumentada, aplicar el método de eliminación, sustitución hacia atrás y finalmente mostrar la respuesta."
      ]
    },
    {
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      "source": [
        "#### 2.1.2. Método de Gauss-Jordan"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "54g9EEBmGL9N"
      },
      "source": [
        "El método de Gauss-Jordan se basa en transformar una matriz, utilizando operaciones para resolver sistemas de ecuaciones de n número de variables. El uso de este método consiste en saber aplicarlo en cada operación que se vaya a realizar, implementándose en toda la fila o a toda la columna según el ejercicio.\n",
        "\n",
        "Tiene como objetivo principal, tratar de convertir lo que conlleva en la matriz, los coeficientes de las variables en una matriz de identidad o matriz de escalón reducida, y todo se logra a partir de las distintas operaciones como la eliminación, escalamiento e intercambio de filas y columnas."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RgoBQXoKW_xj"
      },
      "source": [
        "##### 2.1.2.1. Eliminación Gauss-Jordan con pivoteo"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bLYsW-veXJq3"
      },
      "source": [
        "$$\n",
        "a^{*}_{k, j} = \\frac{a_{k, j}}{a_{k, k}}\n",
        "\\left\\lbrace\n",
        "\\begin{array}{ll}\n",
        "k = 1, ..., n\\\\\n",
        "j = k, ..., n\n",
        "\\end{array}\n",
        "\\right.\n",
        "$$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 3. Método Gauss-Jordan - Transformación de la fila pivote - Matriz A\n",
        "</div>\n",
        "\n",
        "$$\n",
        "b^{*}_{k} = \\frac{b_{k}}{a_{k, k}}\n",
        "\\left\\lbrace\n",
        "\\begin{array}{ll}\n",
        "k = 1, ..., n\n",
        "\\end{array}\n",
        "\\right.\n",
        "$$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 4. Método Gauss-Jordan - Transformación de la fila pivote - Matriz b\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q3eJ4Tp_XWcq"
      },
      "source": [
        "$$\n",
        "a^{*}_{i, j} = a_{i, j} - a_{i, j} \\cdot a^{*}_{k, j}\n",
        "\\left\\lbrace\n",
        "\\begin{array}{ll}\n",
        "k = 1, ..., n\\\\\n",
        "i = 1, ..., n, i \\neq k\\\\\n",
        "j = k, ..., n\n",
        "\\end{array}\n",
        "\\right.\n",
        "$$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 5. Método Gauss-Jordan - Transformación de la filas no pivote - Matriz A\n",
        "</div>\n",
        "\n",
        "$$\n",
        "b^{*}_{i} = b_{i} - a_{i, k} \\cdot b^{*}_{k}\n",
        "\\left\\lbrace\n",
        "\\begin{array}{ll}\n",
        "k = 1, ..., n\\\\\n",
        "i = 1, ..., n, i \\neq k\n",
        "\\end{array}\n",
        "\\right.\n",
        "$$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 6. Método Gauss-Jordan - Transformación de la filas no pivote - Matriz b\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q3M-3VSnXbwK"
      },
      "source": [
        "Al igual que el proceso de pivote para la eliminación Gaussiana, en la eliminación Gauss-Jordan es muy simular en la serie de pasos a aplicar.\n",
        "\n",
        "El primer paso consiste en crear una matriz de coeficientes y de constantes.\n",
        "\n",
        "El siguiente paso consiste en crear una matriz aumentada que luego se somete a una serie de operaciones iterativas que la reducen a una forma escalonada.\n",
        "\n",
        "Sin embargo, en los casos en que el elemento pivote sea cero o de muy pequeña magnitud, tenemos que intercambiar la fila pivote con una fila inferior.\n",
        "\n",
        "Luego podemos leer el contenido de la matriz aumentada, aplicar la división del pivote descrito en la formulas 3 y 4, el método de eliminación descrito en la formulas 5 y 6, y finalmente mostrar la respuesta."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "my46JnzZYk-p"
      },
      "source": [
        "#### 2.1.3. Descomposición LU"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aCep-myTsBsV"
      },
      "source": [
        "Este método sirve para resolver sistemas de ecuaciones lineales debido a que consiste, como lo su nombre lo indica, en la descomposición de la matriz de coeficientes ($ A $) en dos matrices diferentes ($ L $ y $ U $).\n",
        "\n",
        "$$ A = L \\cdot U $$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 7. Descomposición LU - Descomposición de la Matriz A\n",
        "</div>\n",
        "\n",
        "La matriz $ L $ va a ser una matriz triangular inferior de $ A $.\n",
        "\n",
        "La matriz $ U $ va a ser una matriz triangular superior de $ A $ con la diagonal igual a $ 1 $.\n",
        "\n",
        "$$ L \\cdot U \\cdot x = b $$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 8. Descomposición LU - Matriz LU de la matriz A\n",
        "</div>\n",
        "\n",
        "Para el desarrollo de este método se igualan las matrices $ LU $ con una variable para facilitar su implementación.\n",
        "\n",
        "$$\n",
        "U \\cdot x = y\n",
        "\\hspace{1cm}\n",
        "L \\cdot y = b\n",
        "$$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 9. Descomposición LU - Igualdad de LU con y\n",
        "</div>\n",
        "\n",
        "Una vez igualadas las matrices $ LU $ a una variable se debe ampliar la matriz $ L $ con el sistema de nuevas variables e igualarlas a las constantes de la matriz $ A $, luego se convierte a un sistema de ecuaciones lineales y se resuelven las incógnitas.\n",
        "\n",
        "Obtenidas las incógnitas del nuevo sistema de variables se halla $ U \\cdot x = y $ ampliando la matriz con el sistema de variables de la matriz $ A $ y reemplazando las constantes de $ A $ por las incógnitas halladas en el sistema de variables nuevo. luego, al igual que en el paso anterior se debe convertir a un sistema de ecuaciones lineales y resolver las incógnitas.\n",
        "\n",
        "El resultado de las incógnitas del paso anterior serán el resultado del sistema de ecuaciones lineales original ($ A \\cdot x = b $).\n",
        "\n",
        "Se debe tener presente que, al momento de resolver la matriz, y es $ 2 x 2 $ se hace con $ 1 $ iteración, $ 3 x 3 $ con $ 2 $ y así sucesivamente con el resto."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8nfoI5FSrWHp"
      },
      "source": [
        "#### 2.1.4. Inversión de Matrices"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X-XzHurVrcyu"
      },
      "source": [
        "Partimos de lo siguiente: si una matriz $ n * n $ es una matriz cuadrada de dimensión $n$, pero si el número de filas y columnas no son lo mismo es una matriz rectangular. Por lo tanto, A una matriz cuadrada de dimensión $n$, entonces $B$ es una matriz inversa de $A$ si se cumplen.\n",
        "\n",
        "$$ A \\cdot B = I_n = B \\cdot A $$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 10. Inversion de Matrices - Matriz identidad\n",
        "</div>\n",
        "\n",
        "Donde, $I_n$ es la matriz de identidad con dimensión $n$.\n",
        "\n",
        "Se considera que la dimensión $B$ también debe ser nxn para llevar el calculo del contenido matricial por ambos. En el transcurso de las definiciones conoceremos que en realidad solo existe una matriz inversa donde si se cumple una de las dos igualdades se cumplirá la otra, para eso es necesario llevar detalladamente le procedimiento y los pasos a seguir para cada matriz, por lo tanto, dicha matriz es única, se denota como $A - 1$ y esto se lee la inversa de $A$.\n",
        "\n",
        "• Para conocer un poco se debe tener presente que no todas las matrices cuadradas tienen inversa\n",
        "• Por ejemplo, si la matriz $A$ tiene inversa, de deduce que es regular o invisible sino entonces es singular\n",
        "• Para multiplicar por uno y otro, se debe tener en cuenta que las dimensiones deben ser las apropiadas.\n",
        "\n",
        "La inversa de una matriz es única: sea A una matriz de dimensión n, por lo tanto solo tiene una matriz inversa y se le puede asignar un nombre propio.\n",
        "\n",
        "Para la obtención de una matriz inversa nos presenta que existen diversos métodos para los cuales se puede llevar a cabo el calculo de la matriz y entre los más utilizados están matriz inversa por Gauss y a partir de la matriz adjunta.\n",
        "\n",
        "La grata conclusión que se puede obtener una vez vista los parámetros, como y para que sirve la inversa de una matriz, podemos deducir que representa una herramienta importante para toda solución de sistemas de ecuaciones lineales, que es el tema principal abordado en este documento y que cada matriz conlleva un procedimiento de acuerdo con su método.\n",
        "\n",
        "$$\n",
        "A \\cdot x = b\\\\\n",
        "x = A^{-1} \\cdot b\n",
        "$$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 11. Inversion de Matrices - Despejar x\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uOEZl0l7OnR0"
      },
      "source": [
        "#### 2.2.5. Método de Gauss-Seidel"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qS2UjAlyXEgm"
      },
      "source": [
        "El método de Gauss-Seidel surgió de una mejoría al método Jacobs, acelerando su convergencia, por medio de iteraciones a partir de un vector inicial encuentras los respectivos valores de las incógnitas hasta poder encontrar la tolerancia estimada.\n",
        "\n",
        "En punto es que cada vez que se estima encontrar un nuevo valor de una $ x_i $, usando los valores anteriores de las $ x $ también se puede utilizar los que actualmente se encuentran para con las $ x $, desde $ x_0 $ hasta $ x_i - 1 $.\n",
        "\n",
        "Para ello se presenta la siguiente ecuación:\n",
        "\n",
        "$$ x^{k}_{i} = \\frac{b_i - \\sum^{i - 1}_{j = 1}) a_{i, j} \\cdot x^{k}{j} - \\sum^{n}_{j = i + 1} a_{i, j} \\cdot x^{k - 1}}{a_{i, j}}$$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 12. Método Gauss-Seidel\n",
        "</div>\n",
        "\n",
        "Este método permite esencialmente recortar cierto número de iteraciones para lograr obtener el resultado esperado, los criterios que maneja son similares al método Jacobs.\n",
        "\n",
        "El siguiente criterio es aplicado en varias dimensiones, ecuaciones lineales que al resolverlas se espera un óptimo resultado, que no solo se resuelven con el método de Gauss-Seidel, también con el Punto Fijo y Jacobs. Al aplicarlo y evaluarlo se arroja la siguiente expresión:\n",
        "\n",
        "$$\n",
        "\\lvert \\frac{a_{2, 1}}{a_{2, 2}} \\rvert < 1\n",
        "\\hspace{1cm}\n",
        "\\lvert \\frac{a_{1, 2}}{a_{1, 1}} \\rvert < 1\n",
        "$$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 13. Método Gauss-Seidel - Criterio\n",
        "</div>\n",
        "\n",
        "Para asegurar la convergencia, en la ecuación el valor absoluto de las pendientes debe ser menos que la unidad.\n",
        "\n",
        "$$\n",
        "\\lvert a_{2, 2} \\rvert > \\lvert a_{2, 1} \\rvert\n",
        "\\hspace{1cm}\n",
        "\\lvert a_{1, 1} \\rvert > \\lvert a_{1, 2} \\rvert\n",
        "$$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 14. Método Gauss-Seidel - Convergencia\n",
        "</div>\n",
        "\n",
        "El elemento diagonal debe ser mayor al que está afuera de la diagonal, para ello la generalización seria:\n",
        "\n",
        "$$\n",
        "\\lvert a_{i, i} \\rvert > \\sum^{n}_{j = i} \\lvert a_{i, j} \\rvert\n",
        "\\left\\lbrace\n",
        "\\begin{array}{ll}\n",
        "j \\neq i\n",
        "\\end{array}\n",
        "\\right.\n",
        "$$\n",
        "\n",
        "<div align=\"center\">\n",
        "    Formula 15. Método Gauss-Seidel - Generalización\n",
        "</div>\n",
        "\n",
        "En el transcurso del trabajo implementado sobre este método, se puede deducir que el método de Gauss-Seidel utiliza la misma transformación que el método de jacobi, dando una mejoría y ambos aportando gran equivalencia para la solución de los sistemas de ecuaciones lineales llevándolo a la aproximación sucesiva en la solución de estas ecuaciones."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hDsWGY-ZG4FJ"
      },
      "source": [
        "### 2.2. Desarrollo Computacional"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O_OF93tAIXgE"
      },
      "source": [
        "Para el desarrollo de computacional relacionado a este informe se uso el lenguaje de programación Python 3.10.7 y las siguientes librerías:\n",
        "\n",
        "* timeit - librería especializada en el manejo del tiempo con mayor precisión.\n",
        "* matplotlib - permite graficar los resultados de los procesos.\n",
        "* numpy - se especializa en el cálculo, transformación y análisis de datos numéricos.\n",
        "* pandas - permite la manipulación y análisis de datos sobre tablas numéricas y series temporales."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "B11KEtOyITad"
      },
      "outputs": [],
      "source": [
        "from timeit import default_timer as timer\n",
        "\n",
        "%matplotlib inline\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PFY2zPeQIeGb"
      },
      "source": [
        "Para medir el tiempo transcurrido de los algoritmos y funciones que se implementan en este informe se empleo la función decorador ```count_elapsed_time()```."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "y4MPttHxIi8N"
      },
      "outputs": [],
      "source": [
        "def count_elapsed_time(func):\n",
        "    '''\n",
        "    Decorador.\n",
        "    Ejecuta la función y calcula el tiempo transcurrido.\n",
        "    Retorna el resultado de la función y el tiempo transcurrido.\n",
        "    '''\n",
        "    def wrapper(*args, **kwargs):\n",
        "        start_time = timer()\n",
        "        ret = func(*args, **kwargs)\n",
        "        elapsed_time = timer() - start_time\n",
        "        return (ret, elapsed_time)\n",
        "\n",
        "    return wrapper"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aAhfnKrUIqV0"
      },
      "source": [
        "El método ```solve``` dará solución al sistema de ecuaciones $ A \\cdot x = b $ mediante el método de desarrollo especificado."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XqD3vEaPIvFG"
      },
      "outputs": [],
      "source": [
        "@count_elapsed_time\n",
        "def solve(A: np.array, b: np.array, method, table: list, *args, **kwargs) -> np.array:\n",
        "    '''Resuelve un sistema de ecuaciones Ax = b, por medio del método dado.\n",
        "\n",
        "    Args:\n",
        "        A (np.array): Matriz A.\n",
        "        b (np.array): Matriz b.\n",
        "        method (function): Método para resolve el sistema de ecuaciones.\n",
        "        table (list): Recolección de datos del procedimiento.\n",
        "\n",
        "    Raises:\n",
        "        ValueError: Las filas y columnas de la matriz A deben ser iguales.\n",
        "        ValueError: El tamaño de la matriz b debe coincidir con el de la matriz A.\n",
        "\n",
        "    Returns:\n",
        "        np.array: Matriz x. Solución del sistema de ecuaciones.\n",
        "    '''\n",
        "    m, n = A.shape[-2:]\n",
        "    if m != n:\n",
        "        raise ValueError('Las filas y columnas de la matriz A deben ser iguales.')\n",
        "\n",
        "    if len(A) != len(b):\n",
        "        raise ValueError(f'El tamaño matriz b debe ser de {len(A)}')\n",
        "\n",
        "    return method(A, b, table=table, *args, **kwargs)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GunOnimGI03M"
      },
      "source": [
        "#### 2.2.1 Método de Eliminación Gauss"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pvPAXxI4P-_e"
      },
      "source": [
        "El método ```gauss``` provee una implementación de la eliminación Gaussian con pivote para resolver sistema de ecuaciones lineales $ A \\cdot x = b$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kHJRa2ByJMYc"
      },
      "outputs": [],
      "source": [
        "def gauss(A: np.array, b: np.array, table: list) -> np.array:\n",
        "    '''Implementación del método de eliminación de Gauss con pivote\n",
        "    para la resolución de sistemas de ecuaciones lineales Ax=b.\n",
        "\n",
        "    Args:\n",
        "        A (np.array): Matriz A.\n",
        "        b (np.array): Matriz b.\n",
        "        table (list): Recolección de datos del procedimiento.\n",
        "\n",
        "    Returns:\n",
        "        np.array: Matriz x. Solución del sistema de ecuaciones.\n",
        "    '''\n",
        "    n = len(b)\n",
        "    x = np.zeros(n, np.float64)\n",
        "    A_aux = np.copy(A)\n",
        "    b_aux = np.copy(b)\n",
        "\n",
        "    for k in range(n - 1):\n",
        "        # Intercambio de filas\n",
        "        if np.fabs(A_aux[k, k]) < 1.0e-12:\n",
        "            for i in range(k + 1, n):\n",
        "                if np.fabs(A_aux[i, k]) > np.fabs(A_aux[k, k]):\n",
        "                    A_aux[[k, i]] = A_aux[[i, k]]\n",
        "                    b_aux[[k, i]] = b_aux[[i, k]]\n",
        "\n",
        "                    table.append([k, 'Intercambio', i, None, None])\n",
        "\n",
        "                    break\n",
        "\n",
        "        # Eliminación hacia adelante\n",
        "        for i in range(k + 1, n):\n",
        "            if A_aux[i, k] == 0:\n",
        "                continue\n",
        "\n",
        "            factor = A_aux[k, k] / A_aux[i, k]\n",
        "\n",
        "            A_aux[i, k:] = A_aux[k, k:] - A_aux[i, k:] * factor\n",
        "            b_aux[i] = b_aux[k] - b_aux[i] * factor\n",
        "\n",
        "            table.append([k, 'Eliminación', i, factor, None])\n",
        "\n",
        "    # Sustitución hacia atrás\n",
        "    x[n - 1] = b_aux[n - 1] / A_aux[n - 1, n - 1]\n",
        "\n",
        "    table.append([None, 'Sustitución', n - 1, None, None])\n",
        "\n",
        "    for i in range(n - 2, -1, -1):\n",
        "        sum_ax = sum(A_aux[i, j] * x[j] for j in range(i + 1, n))\n",
        "        x[i] = (b_aux[i] - sum_ax) / A_aux[i, i]\n",
        "\n",
        "        table.append([None, 'Sustitución', i, None, sum_ax])\n",
        "\n",
        "    return x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r03d6maGxRvk"
      },
      "source": [
        "#### 2.2.2. Método de Gauss-Jordan"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CZ92M36FFo1O"
      },
      "source": [
        "El método ```gauss_jordan``` provee una implementación de la eliminación Gauss-Jordan con pivote para resolver sistema de ecuaciones lineales $ A \\cdot x = b$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VO7gOp2cBObC"
      },
      "outputs": [],
      "source": [
        "def gauss_jordan(A: np.array, b: np.array, table: list) -> np.array:\n",
        "    '''Implementación del método de eliminación de Gauss-Jordan con pivote.\n",
        "\n",
        "    Args:\n",
        "        A (np.array): Matriz A.\n",
        "        b (np.array): Matriz b.\n",
        "        table (list): Recolección de datos del procedimiento.\n",
        "\n",
        "    Returns:\n",
        "        np.array: Matriz x. Solución del sistema de ecuaciones.\n",
        "    '''\n",
        "    n = len(b)\n",
        "    A_aux = np.copy(A)\n",
        "    b_aux = np.copy(b)\n",
        "\n",
        "    for k in range(n):\n",
        "        # Intercambio de filas\n",
        "        if np.fabs(A_aux[k, k]) < 1.0e-12:\n",
        "            for i in range(k + 1, n):\n",
        "                if np.fabs(A_aux[i, k]) > np.fabs(A_aux[k, k]):\n",
        "                    A_aux[[k, i]] = A_aux[[i, k]]\n",
        "                    b_aux[[k, i]] = b_aux[[i, k]]\n",
        "                    table.append([k, 'Intercambio', i, None, None])\n",
        "                    break\n",
        "\n",
        "        # División del pivote\n",
        "        pivot = A_aux[k, k]\n",
        "        A_aux[k, k:] /= pivot\n",
        "        b_aux[k] /= pivot\n",
        "\n",
        "        # Eliminación\n",
        "        for i in range(n):\n",
        "            if i == k or A_aux[i, k] == 0:\n",
        "                continue\n",
        "\n",
        "            factor = A_aux[i, k]\n",
        "            A_aux[i, k:] -= A_aux[k, k:] * factor\n",
        "            b_aux[i] -= b_aux[k] * factor\n",
        "\n",
        "            table.append([k, 'Eliminación', i, pivot, factor])\n",
        "\n",
        "    return b_aux"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qe1V6ySoYsJJ"
      },
      "source": [
        "#### 2.2.3. Descomposición LU"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8W_oQ5GOkaWC"
      },
      "source": [
        "El método ```LU_decompose``` provee una implementación con pivote del método numérico descomposición LU para resolver sistema de ecuaciones lineales $ A \\cdot x = b$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GlyK-LymkbLL"
      },
      "outputs": [],
      "source": [
        "def lu_factor(A: np.ndarray):\n",
        "    '''Factorización LU con pivote parcial.\n",
        "\n",
        "    Args:\n",
        "        A (np.ndarray): Matriz A.\n",
        "\n",
        "    Returns:\n",
        "        np.ndarray, np.ndarray: Matriz LU y pivote.\n",
        "    '''\n",
        "    n = A.shape[0]\n",
        "    A = np.copy(A)\n",
        "    piv = np.arange(0, n)\n",
        "    for k in range(n - 1):\n",
        "        # pivote\n",
        "        max_row_index = np.argmax(abs(A[k:n, k])) + k\n",
        "        piv[[k, max_row_index]] = piv[[max_row_index, k]]\n",
        "        A[[k, max_row_index]] = A[[max_row_index, k]]\n",
        "\n",
        "        # LU\n",
        "        for i in range(k+1, n):\n",
        "            A[i, k] = A[i, k] / A[k, k]\n",
        "            for j in range(k + 1, n):\n",
        "                A[i, j] -= A[i, k] * A[k, j]\n",
        "\n",
        "    return A, piv\n",
        "\n",
        "\n",
        "def forward_substitution(L: np.ndarray, b: np.ndarray) -> np.ndarray:\n",
        "    '''Sustitución hacia adelante para resolver Ly = b.\n",
        "\n",
        "    Args:\n",
        "        L (np.ndarray): Matriz L.\n",
        "        b (np.ndarray): Matriz b.\n",
        "\n",
        "    Returns:\n",
        "        np.ndarray: Matriz y.\n",
        "    '''\n",
        "    b = np.copy(b)\n",
        "\n",
        "    for i in range(L.shape[0]):\n",
        "        for j in range(i):\n",
        "            b[i] -= L[i,j] * b[j]\n",
        "\n",
        "    return b\n",
        "\n",
        "\n",
        "def backward_substitution(U: np.ndarray, y: np.ndarray) -> np.ndarray:\n",
        "    '''Sustitución hacia atrás para resolver Ux = y.\n",
        "\n",
        "    Args:\n",
        "        U (np.ndarray): Matriz U.\n",
        "        y (np.ndarray): Matriz y.\n",
        "\n",
        "    Returns:\n",
        "        np.ndarray: Matriz x.\n",
        "    '''\n",
        "    y = np.copy(y)\n",
        "\n",
        "    for i in range(U.shape[0] - 1, -1, -1):\n",
        "        for j in range(i + 1, U.shape[1]):\n",
        "            y[i] -= U[i, j] * y[j]\n",
        "        y[i] = y[i] / U[i, i]\n",
        "\n",
        "    return y\n",
        "\n",
        "\n",
        "def LU_decompose(A: np.ndarray, b: np.ndarray, *, table: list) -> np.ndarray:\n",
        "    '''Implementación de la descomposición LU.\n",
        "\n",
        "    Args:\n",
        "        A (np.ndarray): Matriz A.\n",
        "        b (np.ndarray): Matriz B.\n",
        "        table (list): Recolección de datos del procedimiento.\n",
        "\n",
        "    Returns:\n",
        "        np.ndarray: Matriz x. Solución del sistema de ecuaciones.\n",
        "    '''\n",
        "    LU, piv = lu_factor(A)\n",
        "    b = b[piv]  # intercambio de filas\n",
        "    y = forward_substitution(LU, b)\n",
        "    return backward_substitution(LU, y)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qq0TmI7Ysb9g"
      },
      "source": [
        "#### 2.2.4. Inversión de Matrices"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iqH35j0gsl55"
      },
      "source": [
        "El método ```inversion``` provee una implementación de del método numérico inversion de matrices para resolver sistema de ecuaciones lineales $ A \\cdot x = b$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "m2OMCeMHtBOy"
      },
      "outputs": [],
      "source": [
        "def inversion(A: np.ndarray, b: np.ndarray, *, table: list) -> np.ndarray:\n",
        "    '''Implementación del método de inversión de matrices.\n",
        "\n",
        "    Args:\n",
        "        A (np.ndarray): Matriz A.\n",
        "        b (np.ndarray): Matriz b.\n",
        "        table (list): Recolección de datos del procedimiento.\n",
        "\n",
        "    Raises:\n",
        "        ValueError: determinante de A es igual a cero.\n",
        "\n",
        "    Returns:\n",
        "        np.ndarray: Matriz x.\n",
        "    '''\n",
        "    if np.linalg.det(A) == 0:\n",
        "        raise ValueError('La sistema de ecuaciones no tiene solución por medio de este método')\n",
        "\n",
        "    A_inv = np.linalg.inv(A)\n",
        "\n",
        "    return A_inv.dot(b)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_w206X5UOc9J"
      },
      "source": [
        "#### 2.2.5. Método de Gauss-Seidel"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h2rWMo6FOp4-"
      },
      "source": [
        "El método ```gauss_seidel``` provee una implementación de iterativa del método numérico Gauss-Seidel para resolver sistema de ecuaciones lineales $ A \\cdot x = b$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hj_47K_GOqac"
      },
      "outputs": [],
      "source": [
        "def gauss_seidel(\n",
        "    A: np.array,\n",
        "    b: np.array,\n",
        "    *,\n",
        "    max = 50,\n",
        "    error_total: float = 1.0e-4,\n",
        "    table: list\n",
        ") -> np.array:\n",
        "    '''\n",
        "    Implementación del método de Gauss-Seidel.\n",
        "\n",
        "    Args:\n",
        "        A (np.array): Matriz A.\n",
        "        b (np.array): Matriz b.\n",
        "        error_total (float): Error permitido.\n",
        "        table (list): Recolección de datos del procedimiento.\n",
        "\n",
        "    Returns:\n",
        "        np.array: Matriz x. Solución del sistema de ecuaciones.\n",
        "    '''\n",
        "    error = np.ones(len(b))\n",
        "    x = np.zeros(len(b))\n",
        "    aux = np.zeros(len(b))  # x_i-1\n",
        "    L = np.tril(A)\n",
        "    U = A - L\n",
        "    i = 0\n",
        "\n",
        "    while any(error > error_total) and max > i:\n",
        "        x = np.dot(\n",
        "            np.linalg.inv(L),\n",
        "            b - U.dot(x)\n",
        "        )\n",
        "\n",
        "        error = x - aux\n",
        "        aux = x\n",
        "\n",
        "        i += 1\n",
        "        table.append([i, x, error])\n",
        "\n",
        "    return x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rdEeatLUJcht"
      },
      "source": [
        "## 3. Resultados"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yft1QBqPBGqa"
      },
      "source": [
        "Las siguientes matrices $2x2$, $3x3$, $4x4$, $5x5$; serán empleadas en la elaboración de los ejercicios del presente informe."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HXNVScotBd6h"
      },
      "outputs": [],
      "source": [
        "matrices = {\n",
        "    2: {\n",
        "        'A': np.array([[3, 5],\n",
        "                       [2, 1]], np.float64),\n",
        "        'b': np.array([3, 1], np.float64)\n",
        "    },\n",
        "    3: {\n",
        "        'A': np.array([[1, -1, 2],\n",
        "                       [2, 1, 0],\n",
        "                       [3, 1, 4]], np.float64),\n",
        "        'b': np.array([6, 7, 18], np.float64)\n",
        "    },\n",
        "    4: {\n",
        "        'A': np.array([[1, 2, -1, 1],\n",
        "                       [2, -1, 2, 3],\n",
        "                       [-1, 3, 3, -2],\n",
        "                       [3, -2, 1, 1]], np.float64),\n",
        "        'b': np.array([0, 7, 17, -2], np.float64)\n",
        "    },\n",
        "    5: {\n",
        "        'A': np.array([[2, -1, 4, 1, -1],\n",
        "                       [-1, 3, -2, -1, 2],\n",
        "                       [5, 1, 3, -4, 1],\n",
        "                       [3, -2, -2, -2, 3],\n",
        "                       [-4, -1, -5, 3, -4]], np.float64),\n",
        "        'b': np.array([7, 1, 33, 24, -49], np.float64)\n",
        "    }\n",
        "}\n",
        "\n",
        "\n",
        "times = []\n",
        "benchmarking = []"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yhMLjRFIaKmo"
      },
      "source": [
        "### 3.1. Ejercicios con los métodos"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "waCAFhqZaRzK"
      },
      "source": [
        "#### 3.1.1. Eliminación Gaussiana"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UtuMVcC_afdD"
      },
      "source": [
        "Ejercicio con la matriz $2x2$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "ChBMJCu4araJ",
        "outputId": "a87a1c39-f0a2-4f68-f757-d5bbb32d175f"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000217s'"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[2]['A'],\n",
        "    matrices[2]['b'],\n",
        "    gauss,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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        "outputId": "fcae2d61-aac0-48ed-fbf2-79b351d28c41"
      },
      "outputs": [
        {
          "data": {
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            "text/plain": [
              "'El resultado de la operación es: x: 0.28571428571428575, y: 0.42857142857142855'"
            ]
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          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
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      "source": [
        "f'El resultado de la operación es: x: {x[0]}, y: {x[1]}'"
      ]
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    {
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      "execution_count": null,
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          "height": 143
        },
        "id": "HxnoHWdBeCCX",
        "outputId": "80a9d885-9acd-4460-fb83-0ad32cbef198"
      },
      "outputs": [
        {
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              "  Iteración    Operación Índice factor   sum(Ax)\n",
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              "2      None  Sustitución      0   None  2.142857"
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        "    Tabla 1. Gauss - matriz 2x2\n",
        "</div>"
      ]
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    {
      "cell_type": "markdown",
      "metadata": {
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        "Ejercicio con la matriz $3x3$."
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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          "base_uri": "https://localhost:8080/",
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        "id": "RlgsgewmfqQR",
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              "'Time: 0.002253s'"
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          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
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      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[3]['A'],\n",
        "    matrices[3]['b'],\n",
        "    gauss,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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        "id": "EmVabmJwfqQR",
        "outputId": "eae6c1f7-a359-4920-a202-31b32abc7dc9"
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        {
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            "text/plain": [
              "'El resultado de la operación es: x: 3.0, y: 1.0, z: 2.0'"
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          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
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      "source": [
        "f'El resultado de la operación es: x: {x[0]}, y: {x[1]}, z: {x[2]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
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          "height": 238
        },
        "id": "rXWDLgfCfqQS",
        "outputId": "15722abe-424d-4496-8236-8b4dd3e5fb03"
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              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
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              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
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              "  "
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              "  Iteración    Operación Índice    factor sum(Ax)\n",
              "0         0  Eliminación      1       0.5    None\n",
              "1         0  Eliminación      2  0.333333    None\n",
              "2         1  Eliminación      2     1.125    None\n",
              "3      None  Sustitución      2      None    None\n",
              "4      None  Sustitución      1      None     4.0\n",
              "5      None  Sustitución      0      None     3.0"
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          "execution_count": 15,
          "metadata": {},
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      "metadata": {
        "id": "FamObHPRh3dM"
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        "<div align=\"center\">\n",
        "    Tabla 2. Gauss - matriz 3x3\n",
        "</div>"
      ]
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nEP8Swf2gGer"
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      "source": [
        "Ejercicio con la matriz $4x4$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "K1jZ4i-SgGer",
        "outputId": "42ba6fc3-000a-4fa0-e991-eba870a264b9"
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        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
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            "text/plain": [
              "'Time: 0.000297s'"
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          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[4]['A'],\n",
        "    matrices[4]['b'],\n",
        "    gauss,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
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    {
      "cell_type": "code",
      "execution_count": null,
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        {
          "data": {
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              "'El resultado de la operación es: w: -1.0, x: 2.0, y: 4.0, z: 1.0'"
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          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
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      "source": [
        "f'El resultado de la operación es: w: {x[0]}, x: {x[1]}, y: {x[2]}, z: {x[3]}'"
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    },
    {
      "cell_type": "code",
      "execution_count": null,
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        "id": "ykCtel0jgGes",
        "outputId": "626ba9c9-8f26-47ac-cd0b-98650a3bd8ce"
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        {
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Iteración</th>\n",
              "      <th>Operación</th>\n",
              "      <th>Índice</th>\n",
              "      <th>factor</th>\n",
              "      <th>sum(Ax)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>1</td>\n",
              "      <td>0.5</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>2</td>\n",
              "      <td>-1.0</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>3</td>\n",
              "      <td>0.333333</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>2</td>\n",
              "      <td>0.5</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>3</td>\n",
              "      <td>0.9375</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>2</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>3</td>\n",
              "      <td>4.0</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>None</td>\n",
              "      <td>Sustitución</td>\n",
              "      <td>3</td>\n",
              "      <td>None</td>\n",
              "      <td>None</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>None</td>\n",
              "      <td>Sustitución</td>\n",
              "      <td>2</td>\n",
              "      <td>None</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>None</td>\n",
              "      <td>Sustitución</td>\n",
              "      <td>1</td>\n",
              "      <td>None</td>\n",
              "      <td>-8.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>None</td>\n",
              "      <td>Sustitución</td>\n",
              "      <td>0</td>\n",
              "      <td>None</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-4cc9b088-5979-4a38-8612-b22d596386f8')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
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              "\n",
              "    .colab-df-convert {\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
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              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
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              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-4cc9b088-5979-4a38-8612-b22d596386f8 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-4cc9b088-5979-4a38-8612-b22d596386f8');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "  Iteración    Operación Índice    factor sum(Ax)\n",
              "0         0  Eliminación      1       0.5    None\n",
              "1         0  Eliminación      2      -1.0    None\n",
              "2         0  Eliminación      3  0.333333    None\n",
              "3         1  Eliminación      2       0.5    None\n",
              "4         1  Eliminación      3    0.9375    None\n",
              "5         2  Eliminación      3       4.0    None\n",
              "6      None  Sustitución      3      None    None\n",
              "7      None  Sustitución      2      None     0.0\n",
              "8      None  Sustitución      1      None    -8.5\n",
              "9      None  Sustitución      0      None     1.0"
            ]
          },
          "execution_count": 18,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table), columns=['Iteración', 'Operación', 'Índice', 'factor', 'sum(Ax)'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h_gB7L-8h7X-"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 3. Gauss - matriz 4x4\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FtFxGyZJgy2m"
      },
      "source": [
        "Ejercicio con la matriz $5x5$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "GMKAPhI-gy2m",
        "outputId": "343fe5a3-176d-4643-f71a-8e456b146106"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.005944s'"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[5]['A'],\n",
        "    matrices[5]['b'],\n",
        "    gauss,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "RrZ8wemNgy2n",
        "outputId": "fbb437b4-7018-4e3b-cf93-38767cc4a1c1"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: v: 1.0000000000000004, w: -1.9999999999999993, x: 2.9999999999999996, y: -4.0, z: 4.999999999999999'"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: v: {x[0]}, w: {x[1]}, x: {x[2]}, y: {x[3]}, z: {x[4]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 520
        },
        "id": "pRjGY1X1gy2o",
        "outputId": "72986731-5b90-4fcd-816d-7e2eccbc11d0"
      },
      "outputs": [
        {
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              "      <td>-0.593284</td>\n",
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              "      <th>10</th>\n",
              "      <td>None</td>\n",
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              "      <td>4</td>\n",
              "      <td>None</td>\n",
              "      <td>None</td>\n",
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              "      <th>11</th>\n",
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              "      <td>3</td>\n",
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              "      <th>12</th>\n",
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              "      <td>-43.142857</td>\n",
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              "      <script>\n",
              "        const buttonEl =\n",
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              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-d74d5f9b-d68c-4f9a-a3bb-cc50bd960ed2');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
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              "  "
            ],
            "text/plain": [
              "   Iteración    Operación Índice    factor    sum(Ax)\n",
              "0          0  Eliminación      1      -2.0       None\n",
              "1          0  Eliminación      2       0.4       None\n",
              "2          0  Eliminación      3  0.666667       None\n",
              "3          0  Eliminación      4      -0.5       None\n",
              "4          1  Eliminación      2 -3.571429       None\n",
              "5          1  Eliminación      3      15.0       None\n",
              "6          1  Eliminación      4 -3.333333       None\n",
              "7          2  Eliminación      3    -0.125       None\n",
              "8          2  Eliminación      4       2.0       None\n",
              "9          3  Eliminación      4 -0.593284       None\n",
              "10      None  Sustitución      4      None       None\n",
              "11      None  Sustitución      3      None       20.0\n",
              "12      None  Sustitución      2      None -43.142857\n",
              "13      None  Sustitución      1      None       19.0\n",
              "14      None  Sustitución      0      None        5.0"
            ]
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table), columns=['Iteración', 'Operación', 'Índice', 'factor', 'sum(Ax)'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8BlZ4dADiEX2"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 4. Gauss - matriz 5x5\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "7s7jQbrmiQ5O",
        "outputId": "87ef783d-92ce-4f75-a6ae-5fb6e6f1f6f6"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "benchmarking.append([times, 'Gauss'])\n",
        "\n",
        "plt.plot([2, 3, 4, 5], times, linewidth=2.0)\n",
        "plt.plot([2, 3, 4, 5], times, 'o', linewidth=2.0)\n",
        "\n",
        "plt.xlabel('dimensiones (n x n)')\n",
        "plt.ylabel('tiempos (s)')\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hdpWnyHVlA9y"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 1. Gauss - tiempos\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "484qiDTcl7oa"
      },
      "source": [
        "#### 3.1.2. Eliminación Gauss-Jordan"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ujCa4eTkl7oa"
      },
      "source": [
        "Ejercicio con la matriz $2x2$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "hpN4E-0ul7oa",
        "outputId": "aea02b01-818d-4379-d8ff-59558fa6302c"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000180s'"
            ]
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[2]['A'],\n",
        "    matrices[2]['b'],\n",
        "    gauss_jordan,\n",
        "    table\n",
        ")\n",
        "\n",
        "times = [t]\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "AuU0MUZql7ob",
        "outputId": "cb870c08-a22b-44f1-9d3a-6a0e3a6c608d"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: x: 0.2857142857142857, y: 0.42857142857142855'"
            ]
          },
          "execution_count": 24,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: x: {x[0]}, y: {x[1]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 112
        },
        "id": "y7Q_W4l_l7ob",
        "outputId": "11934fa2-3b68-429e-acfa-ec877464db7e"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-2275835e-a66f-466c-8631-6a1587d99829\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>Iteración</th>\n",
              "      <th>Operación</th>\n",
              "      <th>Índice</th>\n",
              "      <th>pivote</th>\n",
              "      <th>factor</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>1</td>\n",
              "      <td>3.0</td>\n",
              "      <td>2.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
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              "\n",
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              "          document.querySelector('#df-2275835e-a66f-466c-8631-6a1587d99829 button.colab-df-convert');\n",
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              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-2275835e-a66f-466c-8631-6a1587d99829');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
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              "        }\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "  Iteración    Operación Índice               pivote              factor\n",
              "0         0  Eliminación      1                  3.0                 2.0\n",
              "1         1  Eliminación      0  -2.3333333333333335  1.6666666666666667"
            ]
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table), columns=['Iteración', 'Operación', 'Índice', 'pivote', 'factor'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PmsHub9Xl7ob"
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      "source": [
        "<div align=\"center\">\n",
        "    Tabla 5. Gauss-Jordan - matriz 2x2\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tlDfKApPl7ob"
      },
      "source": [
        "Ejercicio con la matriz $3x3$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "DrHAYJIhl7ob",
        "outputId": "4131266a-717c-4b3d-ed4e-3bea7320af94"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000220s'"
            ]
          },
          "execution_count": 26,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[3]['A'],\n",
        "    matrices[3]['b'],\n",
        "    gauss_jordan,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "FCJJYBt0l7oc",
        "outputId": "74ab75bd-a73d-4c69-ca61-68552b9a30d7"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: x: 2.999999999999999, y: 1.0000000000000002, z: 2.0000000000000004'"
            ]
          },
          "execution_count": 27,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: x: {x[0]}, y: {x[1]}, z: {x[2]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 238
        },
        "id": "nWNt5OqSl7oc",
        "outputId": "c9b33684-fa85-43af-a8d3-be265c02fc04"
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              "                                                     [key], {});\n",
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              "  Iteración    Operación Índice             pivote               factor\n",
              "0         0  Eliminación      1                1.0                  2.0\n",
              "1         0  Eliminación      2                1.0                  3.0\n",
              "2         1  Eliminación      0                3.0                 -1.0\n",
              "3         1  Eliminación      2                3.0                  4.0\n",
              "4         2  Eliminación      0  3.333333333333333   0.6666666666666667\n",
              "5         2  Eliminación      1  3.333333333333333  -1.3333333333333333"
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          "metadata": {},
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        "<div align=\"center\">\n",
        "    Tabla 6. Gauss-Jordan - matriz 3x3\n",
        "</div>"
      ]
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ki0IkEb3l7oc"
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      "source": [
        "Ejercicio con la matriz $4x4$."
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    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
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        "id": "YS2maKDZl7oc",
        "outputId": "3ca369db-c85c-471c-b4ca-29ee2eca8cc1"
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        {
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              "type": "string"
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            "text/plain": [
              "'Time: 0.000288s'"
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          },
          "execution_count": 29,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[4]['A'],\n",
        "    matrices[4]['b'],\n",
        "    gauss_jordan,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
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    {
      "cell_type": "code",
      "execution_count": null,
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        {
          "data": {
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              "'El resultado de la operación es: w: -0.9999999999999996, x: 2.0, y: 4.0, z: 0.9999999999999993'"
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          "execution_count": 30,
          "metadata": {},
          "output_type": "execute_result"
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      "source": [
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        "id": "iWDmu16ul7oc",
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              "      <th>8</th>\n",
              "      <td>2</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>3</td>\n",
              "      <td>6.0</td>\n",
              "      <td>-2.4000000000000004</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>3</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>0</td>\n",
              "      <td>-3.6</td>\n",
              "      <td>1.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>3</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>1</td>\n",
              "      <td>-3.6</td>\n",
              "      <td>-0.2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-978f0736-7495-4fad-80e6-947c6f1e234c')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
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              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
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              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-978f0736-7495-4fad-80e6-947c6f1e234c button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-978f0736-7495-4fad-80e6-947c6f1e234c');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   Iteración    Operación Índice pivote               factor\n",
              "0          0  Eliminación      1    1.0                  2.0\n",
              "1          0  Eliminación      2    1.0                 -1.0\n",
              "2          0  Eliminación      3    1.0                  3.0\n",
              "3          1  Eliminación      0   -5.0                  2.0\n",
              "4          1  Eliminación      2   -5.0                  5.0\n",
              "5          1  Eliminación      3   -5.0                 -8.0\n",
              "6          2  Eliminación      0    6.0   0.6000000000000001\n",
              "7          2  Eliminación      1    6.0                 -0.8\n",
              "8          2  Eliminación      3    6.0  -2.4000000000000004\n",
              "9          3  Eliminación      0   -3.6                  1.4\n",
              "10         3  Eliminación      1   -3.6                 -0.2"
            ]
          },
          "execution_count": 31,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table), columns=['Iteración', 'Operación', 'Índice', 'pivote', 'factor'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "13akJcmLl7od"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 7. Gauss-Jordan - matriz 4x4\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "44iComFKl7od"
      },
      "source": [
        "Ejercicio con la matriz $5x5$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "wdrzAKb7l7od",
        "outputId": "8216e88c-4d35-424b-b9ac-2c6e47421444"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000274s'"
            ]
          },
          "execution_count": 32,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[5]['A'],\n",
        "    matrices[5]['b'],\n",
        "    gauss_jordan,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "LuAvNZfRl7od",
        "outputId": "b4582979-bdcf-42f7-e18e-b6490811b1a5"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: v: 1.0, w: -1.9999999999999996, x: 3.000000000000001, y: -4.0, z: 5.0'"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: v: {x[0]}, w: {x[1]}, x: {x[2]}, y: {x[3]}, z: {x[4]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 645
        },
        "id": "IXdQKxnfl7od",
        "outputId": "6b5ff3a0-1244-4907-ba26-0aa73cfe0a5c"
      },
      "outputs": [
        {
          "data": {
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              "      <th>Iteración</th>\n",
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              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>1</td>\n",
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              "      <td>3</td>\n",
              "      <td>2.5</td>\n",
              "      <td>-0.5</td>\n",
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              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>1</td>\n",
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              "      <td>2.5</td>\n",
              "      <td>-3.0</td>\n",
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              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>2</td>\n",
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              "      <td>-7.0</td>\n",
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              "      <th>9</th>\n",
              "      <td>2</td>\n",
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              "      <td>-7.0</td>\n",
              "      <td>-8.0</td>\n",
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              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>2</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>4</td>\n",
              "      <td>-7.0</td>\n",
              "      <td>3.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>3</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>0</td>\n",
              "      <td>3.028571428571428</td>\n",
              "      <td>-1.2571428571428571</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>3</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>1</td>\n",
              "      <td>3.028571428571428</td>\n",
              "      <td>-0.2</td>\n",
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              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>3</td>\n",
              "      <td>Eliminación</td>\n",
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              "      <td>3.028571428571428</td>\n",
              "      <td>0.8285714285714285</td>\n",
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              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>3</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>4</td>\n",
              "      <td>3.028571428571428</td>\n",
              "      <td>1.9142857142857146</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>4</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>0</td>\n",
              "      <td>-5.622641509433963</td>\n",
              "      <td>1.528301886792453</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>4</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>1</td>\n",
              "      <td>-5.622641509433963</td>\n",
              "      <td>0.8113207547169812</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>4</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>2</td>\n",
              "      <td>-5.622641509433963</td>\n",
              "      <td>-1.0754716981132078</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>4</td>\n",
              "      <td>Eliminación</td>\n",
              "      <td>3</td>\n",
              "      <td>-5.622641509433963</td>\n",
              "      <td>1.0566037735849059</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-6c073474-a4d3-46f6-9738-2ae627730337')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
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              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
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              "      </button>\n",
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              "    .colab-df-container {\n",
              "      display:flex;\n",
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              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
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              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-6c073474-a4d3-46f6-9738-2ae627730337 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-6c073474-a4d3-46f6-9738-2ae627730337');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
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              "          const docLink = document.createElement('div');\n",
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              "          element.appendChild(docLink);\n",
              "        }\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   Iteración    Operación Índice              pivote               factor\n",
              "0          0  Eliminación      1                 2.0                 -1.0\n",
              "1          0  Eliminación      2                 2.0                  5.0\n",
              "2          0  Eliminación      3                 2.0                  3.0\n",
              "3          0  Eliminación      4                 2.0                 -4.0\n",
              "4          1  Eliminación      0                 2.5                 -0.5\n",
              "5          1  Eliminación      2                 2.5                  3.5\n",
              "6          1  Eliminación      3                 2.5                 -0.5\n",
              "7          1  Eliminación      4                 2.5                 -3.0\n",
              "8          2  Eliminación      0                -7.0                  2.0\n",
              "9          2  Eliminación      3                -7.0                 -8.0\n",
              "10         2  Eliminación      4                -7.0                  3.0\n",
              "11         3  Eliminación      0   3.028571428571428  -1.2571428571428571\n",
              "12         3  Eliminación      1   3.028571428571428                 -0.2\n",
              "13         3  Eliminación      2   3.028571428571428   0.8285714285714285\n",
              "14         3  Eliminación      4   3.028571428571428   1.9142857142857146\n",
              "15         4  Eliminación      0  -5.622641509433963    1.528301886792453\n",
              "16         4  Eliminación      1  -5.622641509433963   0.8113207547169812\n",
              "17         4  Eliminación      2  -5.622641509433963  -1.0754716981132078\n",
              "18         4  Eliminación      3  -5.622641509433963   1.0566037735849059"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table), columns=['Iteración', 'Operación', 'Índice', 'pivote', 'factor'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K8zH3DE9l7od"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 8. Gauss-Jordan - matriz 5x5\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "owKgfxDrl7oe",
        "outputId": "4f0b204c-0a10-4fee-a2a3-3b1db63ef1c6"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "benchmarking.append([times, 'Jordan'])\n",
        "\n",
        "plt.plot([2, 3, 4, 5], times, linewidth=2.0)\n",
        "plt.plot([2, 3, 4, 5], times, 'o', linewidth=2.0)\n",
        "\n",
        "plt.xlabel('dimensiones (n x n)')\n",
        "plt.ylabel('tiempos (s)')\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CxTSoQH0l7oe"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 2. Gauss-Jordan - tiempos\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2cxU3HBlox2I"
      },
      "source": [
        "#### 3.1.3. Descomposición LU"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0LdGxmeFox2I"
      },
      "source": [
        "Ejercicio con la matriz $2x2$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "9SNBlGb_ox2J",
        "outputId": "f0080a22-fbe6-421d-c3d3-ab25db7f3ce9"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000244s'"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x, t = solve(\n",
        "    matrices[2]['A'],\n",
        "    matrices[2]['b'],\n",
        "    LU_decompose,\n",
        "    []\n",
        ")\n",
        "\n",
        "times = [t]\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "kXXFexSlox2J",
        "outputId": "288042ea-1bd8-4533-9f7f-94f87cd3ae67"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: x: 0.2857142857142856, y: 0.4285714285714286'"
            ]
          },
          "execution_count": 37,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: x: {x[0]}, y: {x[1]}'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0WrOcRO-ox2K"
      },
      "source": [
        "Ejercicio con la matriz $3x3$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "l4QyHzwDox2K",
        "outputId": "3f7e5e23-0b82-4b88-b7e3-f1242b654e03"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000283s'"
            ]
          },
          "execution_count": 38,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x, t = solve(\n",
        "    matrices[3]['A'],\n",
        "    matrices[3]['b'],\n",
        "    LU_decompose,\n",
        "    []\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "xEPPBtUOox2K",
        "outputId": "e14ac644-eae8-499f-e784-191b25dbc1cc"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: x: 3.0, y: 1.0000000000000002, z: 2.0'"
            ]
          },
          "execution_count": 39,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: x: {x[0]}, y: {x[1]}, z: {x[2]}'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AL8q85DDox2L"
      },
      "source": [
        "Ejercicio con la matriz $4x4$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "pzrQ5APNox2L",
        "outputId": "3d59e6a0-8fa1-42df-d3d0-db443261a069"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000407s'"
            ]
          },
          "execution_count": 40,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x, t = solve(\n",
        "    matrices[4]['A'],\n",
        "    matrices[4]['b'],\n",
        "    LU_decompose,\n",
        "    []\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "ZN-PGLcWox2L",
        "outputId": "597d75af-8fdf-49d0-b301-7587eca7f640"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: w: -1.0, x: 2.0, y: 4.0, z: 1.0000000000000002'"
            ]
          },
          "execution_count": 41,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: w: {x[0]}, x: {x[1]}, y: {x[2]}, z: {x[3]}'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "auM3I68aox2M"
      },
      "source": [
        "Ejercicio con la matriz $5x5$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "kVfLeBExox2M",
        "outputId": "fa2ba9f7-3590-461a-978c-68764f05fbf0"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000330s'"
            ]
          },
          "execution_count": 42,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x, t = solve(\n",
        "    matrices[5]['A'],\n",
        "    matrices[5]['b'],\n",
        "    LU_decompose,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "vjht--Wcox2M",
        "outputId": "85b09118-8c6c-4583-d7f7-8ecdb0eec036"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: v: 1.0000000000000009, w: -1.9999999999999998, x: 2.999999999999999, y: -4.0, z: 4.999999999999999'"
            ]
          },
          "execution_count": 43,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: v: {x[0]}, w: {x[1]}, x: {x[2]}, y: {x[3]}, z: {x[4]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "RJlM88NOox2M",
        "outputId": "cc5b25cf-9f63-4e1c-82b2-bbfd1767ed7a"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "benchmarking.append([times, 'LU'])\n",
        "\n",
        "plt.plot([2, 3, 4, 5], times, linewidth=2.0)\n",
        "plt.plot([2, 3, 4, 5], times, 'o', linewidth=2.0)\n",
        "\n",
        "plt.xlabel('dimensiones (n x n)')\n",
        "plt.ylabel('tiempos (s)')\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "37e1Ylygox2N"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 3. Descomposición LU - tiempos\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BI4iJIsjq5yg"
      },
      "source": [
        "#### 3.1.4. Inversión de Matrices"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mwgbzdXpq5yn"
      },
      "source": [
        "Ejercicio con la matriz $2x2$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "dXH4JJvcq5yn",
        "outputId": "967006ae-2665-4b35-d173-2a749ccf367d"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.002998s'"
            ]
          },
          "execution_count": 45,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x, t = solve(\n",
        "    matrices[2]['A'],\n",
        "    matrices[2]['b'],\n",
        "    inversion,\n",
        "    []\n",
        ")\n",
        "\n",
        "times = [t]\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "JmPeR3qWq5yo",
        "outputId": "67c82f1d-e87f-40a3-8fd3-da16325322ad"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: x: 0.28571428571428603, y: 0.4285714285714285'"
            ]
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: x: {x[0]}, y: {x[1]}'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RBDGBmTLq5yp"
      },
      "source": [
        "Ejercicio con la matriz $3x3$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "OGVPQb9Zq5yq",
        "outputId": "a011e944-66e9-46c3-a495-b553de184b8c"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000300s'"
            ]
          },
          "execution_count": 47,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x, t = solve(\n",
        "    matrices[3]['A'],\n",
        "    matrices[3]['b'],\n",
        "    inversion,\n",
        "    []\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "EAQo5LkDq5yq",
        "outputId": "f82b5706-5177-4309-e11c-70361cd9eb7a"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: x: 2.999999999999999, y: 0.9999999999999991, z: 2.0'"
            ]
          },
          "execution_count": 48,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: x: {x[0]}, y: {x[1]}, z: {x[2]}'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SOQ99sRCq5yr"
      },
      "source": [
        "Ejercicio con la matriz $4x4$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "wqnAZHFvq5yr",
        "outputId": "a0b6efad-1967-498b-f805-8cb59d443f7c"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000209s'"
            ]
          },
          "execution_count": 49,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x, t = solve(\n",
        "    matrices[4]['A'],\n",
        "    matrices[4]['b'],\n",
        "    inversion,\n",
        "    []\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "gjAYSe1Rq5yr",
        "outputId": "1bea83da-b9dd-4a31-ff38-391166ce19ed"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: w: -0.9999999999999998, x: 1.9999999999999998, y: 3.9999999999999996, z: 0.9999999999999996'"
            ]
          },
          "execution_count": 50,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: w: {x[0]}, x: {x[1]}, y: {x[2]}, z: {x[3]}'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n1JP3eP8q5yr"
      },
      "source": [
        "Ejercicio con la matriz $5x5$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "Eq-iJ1V7q5yr",
        "outputId": "acec53be-9e87-4b44-f311-4a1c548f2292"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.000998s'"
            ]
          },
          "execution_count": 51,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x, t = solve(\n",
        "    matrices[5]['A'],\n",
        "    matrices[5]['b'],\n",
        "    inversion,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "PQ4K3umlq5ys",
        "outputId": "dd616c56-5179-457e-d47f-41fff0d823f5"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: v: 0.9999999999999982, w: -2.000000000000001, x: 3.0, y: -3.9999999999999982, z: 5.0'"
            ]
          },
          "execution_count": 52,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: v: {x[0]}, w: {x[1]}, x: {x[2]}, y: {x[3]}, z: {x[4]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "hRwVda1kq5ys",
        "outputId": "0f465064-da01-4119-9a57-576aaadd03d9"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "benchmarking.append([times, 'Inversa'])\n",
        "\n",
        "plt.plot([2, 3, 4, 5], times, linewidth=2.0)\n",
        "plt.plot([2, 3, 4, 5], times, 'o', linewidth=2.0)\n",
        "\n",
        "plt.xlabel('dimensiones (n x n)')\n",
        "plt.ylabel('tiempos (s)')\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_9vyicK4q5ys"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 4. Inversion de Matrices \n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MaUkoMKm1tbd"
      },
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6wQt6Tj61w7H"
      },
      "source": [
        "#### 3.1.5. Método Gauss-Seidel"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KwGWhpjK1w7H"
      },
      "source": [
        "Ejercicio con la matriz $2x2$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "Qk5f_n2Y1w7I",
        "outputId": "ad048052-c621-4a7d-8e14-53911e4cf480"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.019888s'"
            ]
          },
          "execution_count": 54,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[2]['A'],\n",
        "    matrices[2]['b'],\n",
        "    gauss_seidel,\n",
        "    table,\n",
        "    max=200\n",
        ")\n",
        "\n",
        "times = [t]\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "2PBL7R2Y1w7I",
        "outputId": "901a802c-3763-481b-f8be-216a71d30b6d"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: x: 8.067561320569263e+103, y: -1.6135122641138526e+104'"
            ]
          },
          "execution_count": 55,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: x: {x[0]}, y: {x[1]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 478
        },
        "id": "AWnNh7Gw1w7I",
        "outputId": "82ee1ca6-1ad9-486b-d9d4-2b9b521fdfd5"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:1: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
            "  \"\"\"Entry point for launching an IPython kernel.\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-7ee795f4-7884-4a4a-9628-41d3144d896e\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>Iteración</th>\n",
              "      <th>x</th>\n",
              "      <th>error</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>[1.0, -1.0]</td>\n",
              "      <td>[1.0, -1.0]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>[2.6666666666666665, -4.333333333333333]</td>\n",
              "      <td>[1.6666666666666665, -3.333333333333333]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>[8.222222222222221, -15.444444444444443]</td>\n",
              "      <td>[5.555555555555555, -11.11111111111111]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>[26.740740740740737, -52.481481481481474]</td>\n",
              "      <td>[18.518518518518515, -37.03703703703703]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>[88.46913580246913, -175.93827160493825]</td>\n",
              "      <td>[61.72839506172839, -123.45679012345678]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>195</th>\n",
              "      <td>196</td>\n",
              "      <td>[6.534724669661107e+101, -1.3069449339322214e+...</td>\n",
              "      <td>[4.574307268762775e+101, -9.14861453752555e+101]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>196</th>\n",
              "      <td>197</td>\n",
              "      <td>[2.178241556553702e+102, -4.356483113107404e+102]</td>\n",
              "      <td>[1.5247690895875913e+102, -3.0495381791751827e...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>197</th>\n",
              "      <td>198</td>\n",
              "      <td>[7.260805188512339e+102, -1.4521610377024678e+...</td>\n",
              "      <td>[5.082563631958638e+102, -1.0165127263917275e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>198</th>\n",
              "      <td>199</td>\n",
              "      <td>[2.4202683961707793e+103, -4.840536792341559e+...</td>\n",
              "      <td>[1.6941878773195454e+103, -3.388375754639091e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>199</th>\n",
              "      <td>200</td>\n",
              "      <td>[8.067561320569263e+103, -1.6135122641138526e+...</td>\n",
              "      <td>[5.6472929243984835e+103, -1.1294585848796967e...</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>200 rows × 3 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-7ee795f4-7884-4a4a-9628-41d3144d896e')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
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              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
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              "\n",
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              "    .colab-df-convert:hover {\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-7ee795f4-7884-4a4a-9628-41d3144d896e button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-7ee795f4-7884-4a4a-9628-41d3144d896e');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "    Iteración                                                  x  \\\n",
              "0           1                                        [1.0, -1.0]   \n",
              "1           2           [2.6666666666666665, -4.333333333333333]   \n",
              "2           3           [8.222222222222221, -15.444444444444443]   \n",
              "3           4          [26.740740740740737, -52.481481481481474]   \n",
              "4           5           [88.46913580246913, -175.93827160493825]   \n",
              "..        ...                                                ...   \n",
              "195       196  [6.534724669661107e+101, -1.3069449339322214e+...   \n",
              "196       197  [2.178241556553702e+102, -4.356483113107404e+102]   \n",
              "197       198  [7.260805188512339e+102, -1.4521610377024678e+...   \n",
              "198       199  [2.4202683961707793e+103, -4.840536792341559e+...   \n",
              "199       200  [8.067561320569263e+103, -1.6135122641138526e+...   \n",
              "\n",
              "                                                 error  \n",
              "0                                          [1.0, -1.0]  \n",
              "1             [1.6666666666666665, -3.333333333333333]  \n",
              "2              [5.555555555555555, -11.11111111111111]  \n",
              "3             [18.518518518518515, -37.03703703703703]  \n",
              "4             [61.72839506172839, -123.45679012345678]  \n",
              "..                                                 ...  \n",
              "195   [4.574307268762775e+101, -9.14861453752555e+101]  \n",
              "196  [1.5247690895875913e+102, -3.0495381791751827e...  \n",
              "197  [5.082563631958638e+102, -1.0165127263917275e+...  \n",
              "198  [1.6941878773195454e+103, -3.388375754639091e+...  \n",
              "199  [5.6472929243984835e+103, -1.1294585848796967e...  \n",
              "\n",
              "[200 rows x 3 columns]"
            ]
          },
          "execution_count": 56,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table), columns=['Iteración', 'x', 'error'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bPkUj_221w7J"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 9. Gauss-Seidel - matriz 2x2\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o4Is07OU1w7J"
      },
      "source": [
        "Ejercicio con la matriz $3x3$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "b7CTpLGj1w7J",
        "outputId": "238d7634-2eaa-4a81-b72a-e08ecb183d7b"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.022288s'"
            ]
          },
          "execution_count": 57,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[3]['A'],\n",
        "    matrices[3]['b'],\n",
        "    gauss_seidel,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "rB9-44Qq1w7J",
        "outputId": "cfc09fa7-f63c-45a1-ff3b-0d596d8e1c6d"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: x: -1275242997.4280949, y: 2550486001.8561897, z: 318810752.1070238'"
            ]
          },
          "execution_count": 58,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: x: {x[0]}, y: {x[1]}, z: {x[2]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "wtuhkrOH1w7J",
        "outputId": "081343b9-a6d7-4cd7-d093-f65779c49a1b"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:1: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
            "  \"\"\"Entry point for launching an IPython kernel.\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-891c07d9-e9ac-4b5c-b135-045103fd73b8\">\n",
              "    <div class=\"colab-df-container\">\n",
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              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "    .dataframe thead th {\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Iteración</th>\n",
              "      <th>x</th>\n",
              "      <th>error</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>[6.0, -5.0, 1.2499999999999996]</td>\n",
              "      <td>[6.0, -5.0, 1.2499999999999996]</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>[-1.4999999999999991, 9.999999999999998, 3.125]</td>\n",
              "      <td>[-7.499999999999999, 14.999999999999998, 1.875...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>[9.749999999999998, -12.499999999999996, 0.3125]</td>\n",
              "      <td>[11.249999999999996, -22.499999999999993, -2.8...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>[-7.1249999999999964, 21.249999999999993, 4.53...</td>\n",
              "      <td>[-16.874999999999993, 33.749999999999986, 4.21...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>[18.187499999999993, -29.374999999999986, -1.7...</td>\n",
              "      <td>[25.31249999999999, -50.62499999999998, -6.328...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>6</td>\n",
              "      <td>[-19.781249999999986, 46.56249999999997, 7.695...</td>\n",
              "      <td>[-37.96874999999998, 75.93749999999996, 9.4921...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>7</td>\n",
              "      <td>[37.17187499999998, -67.34374999999996, -6.542...</td>\n",
              "      <td>[56.953124999999964, -113.90624999999993, -14....</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>8</td>\n",
              "      <td>[-48.257812499999964, 103.51562499999993, 14.8...</td>\n",
              "      <td>[-85.42968749999994, 170.8593749999999, 21.357...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>9</td>\n",
              "      <td>[79.88671874999994, -152.7734374999999, -17.22...</td>\n",
              "      <td>[128.14453124999991, -256.28906249999983, -32....</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>10</td>\n",
              "      <td>[-112.33007812499991, 231.66015624999983, 30.8...</td>\n",
              "      <td>[-192.21679687499986, 384.4335937499997, 48.05...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>11</td>\n",
              "      <td>[175.99511718749986, -344.9902343749997, -41.2...</td>\n",
              "      <td>[288.3251953124998, -576.6503906249995, -72.08...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>12</td>\n",
              "      <td>[-256.4926757812498, 519.9853515624995, 66.873...</td>\n",
              "      <td>[-432.48779296874966, 864.9755859374993, 108.1...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>13</td>\n",
              "      <td>[392.23901367187466, -777.4780273437493, -95.3...</td>\n",
              "      <td>[648.7316894531244, -1297.4633789062489, -162....</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>14</td>\n",
              "      <td>[-580.8585205078119, 1168.7170410156239, 147.9...</td>\n",
              "      <td>[-973.0975341796866, 1946.1950683593732, 243.2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>15</td>\n",
              "      <td>[878.7877807617178, -1750.5755615234357, -216....</td>\n",
              "      <td>[1459.6463012695299, -2919.2926025390598, -364...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>16</td>\n",
              "      <td>[-1310.6816711425768, 2628.3633422851535, 330....</td>\n",
              "      <td>[-2189.4694519042946, 4378.938903808589, 547.3...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>17</td>\n",
              "      <td>[1973.522506713865, -3940.04501342773, -490.63...</td>\n",
              "      <td>[3284.2041778564417, -6568.408355712883, -821....</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>18</td>\n",
              "      <td>[-2952.783760070797, 5912.567520141594, 740.94...</td>\n",
              "      <td>[-4926.3062667846625, 9852.612533569325, 1231....</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>19</td>\n",
              "      <td>[4436.675640106196, -8866.351280212391, -1106....</td>\n",
              "      <td>[7389.459400176993, -14778.918800353986, -1847...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>20</td>\n",
              "      <td>[-6647.513460159293, 13302.026920318585, 1664....</td>\n",
              "      <td>[-11084.189100265488, 22168.378200530977, 2771...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>21</td>\n",
              "      <td>[9978.770190238938, -19950.540380477876, -2491...</td>\n",
              "      <td>[16626.283650398233, -33252.567300796465, -415...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>22</td>\n",
              "      <td>[-14960.655285358407, 29928.310570716814, 3742...</td>\n",
              "      <td>[-24939.425475597345, 49878.85095119469, 6234....</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>23</td>\n",
              "      <td>[22448.482928037607, -44889.965856075214, -560...</td>\n",
              "      <td>[37409.138213396014, -74818.27642679203, -9352...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>24</td>\n",
              "      <td>[-33665.22439205641, 67337.44878411281, 8419.0...</td>\n",
              "      <td>[-56113.707320094014, 112227.41464018803, 1402...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>25</td>\n",
              "      <td>[50505.33658808461, -101003.67317616922, -1262...</td>\n",
              "      <td>[84170.56098014102, -168341.12196028203, -2104...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>26</td>\n",
              "      <td>[-75750.5048821269, 151508.0097642538, 18940.3...</td>\n",
              "      <td>[-126255.84147021151, 252511.68294042302, 3156...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>27</td>\n",
              "      <td>[113633.25732319034, -227259.51464638067, -284...</td>\n",
              "      <td>[189383.76220531724, -378767.5244106345, -4734...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>28</td>\n",
              "      <td>[-170442.3859847855, 340891.771969571, 42613.3...</td>\n",
              "      <td>[-284075.64330797584, 568151.2866159517, 71018...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>29</td>\n",
              "      <td>[255671.07897717826, -511335.1579543565, -6391...</td>\n",
              "      <td>[426113.46496196376, -852226.9299239275, -1065...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>30</td>\n",
              "      <td>[-383499.11846576736, 767005.2369315347, 95877...</td>\n",
              "      <td>[-639170.1974429456, 1278340.3948858911, 15979...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>30</th>\n",
              "      <td>31</td>\n",
              "      <td>[575256.177698651, -1150505.355397302, -143811...</td>\n",
              "      <td>[958755.2961644183, -1917510.5923288367, -2396...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>31</th>\n",
              "      <td>32</td>\n",
              "      <td>[-862876.7665479764, 1725760.5330959528, 21572...</td>\n",
              "      <td>[-1438132.9442466274, 2876265.888493255, 35953...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>32</th>\n",
              "      <td>33</td>\n",
              "      <td>[1294322.6498219646, -2588638.299643929, -3235...</td>\n",
              "      <td>[2157199.416369941, -4314398.832739882, -53929...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>33</th>\n",
              "      <td>34</td>\n",
              "      <td>[-1941476.4747329466, 3882959.949465893, 48537...</td>\n",
              "      <td>[-3235799.124554911, 6471598.249109822, 808949...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>34</th>\n",
              "      <td>35</td>\n",
              "      <td>[2912222.21209942, -5824437.42419884, -728052....</td>\n",
              "      <td>[4853698.6868323665, -9707397.373664733, -1213...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>35</th>\n",
              "      <td>36</td>\n",
              "      <td>[-4368325.81814913, 8736658.63629826, 1092084....</td>\n",
              "      <td>[-7280548.03024855, 14561096.0604971, 1820137....</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>36</th>\n",
              "      <td>37</td>\n",
              "      <td>[6552496.227223694, -13104985.454447389, -1638...</td>\n",
              "      <td>[10920822.045372825, -21841644.09074565, -2730...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>37</th>\n",
              "      <td>38</td>\n",
              "      <td>[-9828736.840835541, 19657480.681671083, 24571...</td>\n",
              "      <td>[-16381233.068059236, 32762466.13611847, 40953...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>38</th>\n",
              "      <td>39</td>\n",
              "      <td>[14743112.761253312, -29486218.522506624, -368...</td>\n",
              "      <td>[24571849.602088854, -49143699.20417771, -6142...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>39</th>\n",
              "      <td>40</td>\n",
              "      <td>[-22114661.64187997, 44229330.28375994, 552866...</td>\n",
              "      <td>[-36857774.40313328, 73715548.80626656, 921444...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>40</th>\n",
              "      <td>41</td>\n",
              "      <td>[33171999.96281995, -66343992.9256399, -829299...</td>\n",
              "      <td>[55286661.60469992, -110573323.20939983, -1382...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>41</th>\n",
              "      <td>42</td>\n",
              "      <td>[-49757992.444229916, 99515991.88845983, 12439...</td>\n",
              "      <td>[-82929992.40704986, 165859984.81409973, 20732...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>42</th>\n",
              "      <td>43</td>\n",
              "      <td>[74636996.16634487, -149273985.33268973, -1865...</td>\n",
              "      <td>[124394988.61057478, -248789977.22114956, -310...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>43</th>\n",
              "      <td>44</td>\n",
              "      <td>[-111955486.74951729, 223910980.49903458, 2798...</td>\n",
              "      <td>[-186592482.91586214, 373184965.8317243, 46648...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>44</th>\n",
              "      <td>45</td>\n",
              "      <td>[167933237.62427592, -335866468.24855185, -419...</td>\n",
              "      <td>[279888724.37379324, -559777448.7475865, -6997...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>45</th>\n",
              "      <td>46</td>\n",
              "      <td>[-251899848.93641388, 503799704.87282777, 6297...</td>\n",
              "      <td>[-419833086.5606898, 839666173.1213796, 104958...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>46</th>\n",
              "      <td>47</td>\n",
              "      <td>[377849780.90462077, -755699554.8092415, -9446...</td>\n",
              "      <td>[629749629.8410347, -1259499259.6820693, -1574...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>47</th>\n",
              "      <td>48</td>\n",
              "      <td>[-566774663.8569311, 1133549334.7138622, 14169...</td>\n",
              "      <td>[-944624444.7615519, 1889248889.5231037, 23615...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>48</th>\n",
              "      <td>49</td>\n",
              "      <td>[850162003.2853966, -1700323999.5707932, -2125...</td>\n",
              "      <td>[1416936667.1423278, -2833873334.2846556, -354...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49</th>\n",
              "      <td>50</td>\n",
              "      <td>[-1275242997.4280949, 2550486001.8561897, 3188...</td>\n",
              "      <td>[-2125405000.7134914, 4250810001.426983, 53135...</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-891c07d9-e9ac-4b5c-b135-045103fd73b8')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
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              "    .colab-df-convert:hover {\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-891c07d9-e9ac-4b5c-b135-045103fd73b8 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-891c07d9-e9ac-4b5c-b135-045103fd73b8');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   Iteración                                                  x  \\\n",
              "0          1                    [6.0, -5.0, 1.2499999999999996]   \n",
              "1          2    [-1.4999999999999991, 9.999999999999998, 3.125]   \n",
              "2          3   [9.749999999999998, -12.499999999999996, 0.3125]   \n",
              "3          4  [-7.1249999999999964, 21.249999999999993, 4.53...   \n",
              "4          5  [18.187499999999993, -29.374999999999986, -1.7...   \n",
              "5          6  [-19.781249999999986, 46.56249999999997, 7.695...   \n",
              "6          7  [37.17187499999998, -67.34374999999996, -6.542...   \n",
              "7          8  [-48.257812499999964, 103.51562499999993, 14.8...   \n",
              "8          9  [79.88671874999994, -152.7734374999999, -17.22...   \n",
              "9         10  [-112.33007812499991, 231.66015624999983, 30.8...   \n",
              "10        11  [175.99511718749986, -344.9902343749997, -41.2...   \n",
              "11        12  [-256.4926757812498, 519.9853515624995, 66.873...   \n",
              "12        13  [392.23901367187466, -777.4780273437493, -95.3...   \n",
              "13        14  [-580.8585205078119, 1168.7170410156239, 147.9...   \n",
              "14        15  [878.7877807617178, -1750.5755615234357, -216....   \n",
              "15        16  [-1310.6816711425768, 2628.3633422851535, 330....   \n",
              "16        17  [1973.522506713865, -3940.04501342773, -490.63...   \n",
              "17        18  [-2952.783760070797, 5912.567520141594, 740.94...   \n",
              "18        19  [4436.675640106196, -8866.351280212391, -1106....   \n",
              "19        20  [-6647.513460159293, 13302.026920318585, 1664....   \n",
              "20        21  [9978.770190238938, -19950.540380477876, -2491...   \n",
              "21        22  [-14960.655285358407, 29928.310570716814, 3742...   \n",
              "22        23  [22448.482928037607, -44889.965856075214, -560...   \n",
              "23        24  [-33665.22439205641, 67337.44878411281, 8419.0...   \n",
              "24        25  [50505.33658808461, -101003.67317616922, -1262...   \n",
              "25        26  [-75750.5048821269, 151508.0097642538, 18940.3...   \n",
              "26        27  [113633.25732319034, -227259.51464638067, -284...   \n",
              "27        28  [-170442.3859847855, 340891.771969571, 42613.3...   \n",
              "28        29  [255671.07897717826, -511335.1579543565, -6391...   \n",
              "29        30  [-383499.11846576736, 767005.2369315347, 95877...   \n",
              "30        31  [575256.177698651, -1150505.355397302, -143811...   \n",
              "31        32  [-862876.7665479764, 1725760.5330959528, 21572...   \n",
              "32        33  [1294322.6498219646, -2588638.299643929, -3235...   \n",
              "33        34  [-1941476.4747329466, 3882959.949465893, 48537...   \n",
              "34        35  [2912222.21209942, -5824437.42419884, -728052....   \n",
              "35        36  [-4368325.81814913, 8736658.63629826, 1092084....   \n",
              "36        37  [6552496.227223694, -13104985.454447389, -1638...   \n",
              "37        38  [-9828736.840835541, 19657480.681671083, 24571...   \n",
              "38        39  [14743112.761253312, -29486218.522506624, -368...   \n",
              "39        40  [-22114661.64187997, 44229330.28375994, 552866...   \n",
              "40        41  [33171999.96281995, -66343992.9256399, -829299...   \n",
              "41        42  [-49757992.444229916, 99515991.88845983, 12439...   \n",
              "42        43  [74636996.16634487, -149273985.33268973, -1865...   \n",
              "43        44  [-111955486.74951729, 223910980.49903458, 2798...   \n",
              "44        45  [167933237.62427592, -335866468.24855185, -419...   \n",
              "45        46  [-251899848.93641388, 503799704.87282777, 6297...   \n",
              "46        47  [377849780.90462077, -755699554.8092415, -9446...   \n",
              "47        48  [-566774663.8569311, 1133549334.7138622, 14169...   \n",
              "48        49  [850162003.2853966, -1700323999.5707932, -2125...   \n",
              "49        50  [-1275242997.4280949, 2550486001.8561897, 3188...   \n",
              "\n",
              "                                                error  \n",
              "0                     [6.0, -5.0, 1.2499999999999996]  \n",
              "1   [-7.499999999999999, 14.999999999999998, 1.875...  \n",
              "2   [11.249999999999996, -22.499999999999993, -2.8...  \n",
              "3   [-16.874999999999993, 33.749999999999986, 4.21...  \n",
              "4   [25.31249999999999, -50.62499999999998, -6.328...  \n",
              "5   [-37.96874999999998, 75.93749999999996, 9.4921...  \n",
              "6   [56.953124999999964, -113.90624999999993, -14....  \n",
              "7   [-85.42968749999994, 170.8593749999999, 21.357...  \n",
              "8   [128.14453124999991, -256.28906249999983, -32....  \n",
              "9   [-192.21679687499986, 384.4335937499997, 48.05...  \n",
              "10  [288.3251953124998, -576.6503906249995, -72.08...  \n",
              "11  [-432.48779296874966, 864.9755859374993, 108.1...  \n",
              "12  [648.7316894531244, -1297.4633789062489, -162....  \n",
              "13  [-973.0975341796866, 1946.1950683593732, 243.2...  \n",
              "14  [1459.6463012695299, -2919.2926025390598, -364...  \n",
              "15  [-2189.4694519042946, 4378.938903808589, 547.3...  \n",
              "16  [3284.2041778564417, -6568.408355712883, -821....  \n",
              "17  [-4926.3062667846625, 9852.612533569325, 1231....  \n",
              "18  [7389.459400176993, -14778.918800353986, -1847...  \n",
              "19  [-11084.189100265488, 22168.378200530977, 2771...  \n",
              "20  [16626.283650398233, -33252.567300796465, -415...  \n",
              "21  [-24939.425475597345, 49878.85095119469, 6234....  \n",
              "22  [37409.138213396014, -74818.27642679203, -9352...  \n",
              "23  [-56113.707320094014, 112227.41464018803, 1402...  \n",
              "24  [84170.56098014102, -168341.12196028203, -2104...  \n",
              "25  [-126255.84147021151, 252511.68294042302, 3156...  \n",
              "26  [189383.76220531724, -378767.5244106345, -4734...  \n",
              "27  [-284075.64330797584, 568151.2866159517, 71018...  \n",
              "28  [426113.46496196376, -852226.9299239275, -1065...  \n",
              "29  [-639170.1974429456, 1278340.3948858911, 15979...  \n",
              "30  [958755.2961644183, -1917510.5923288367, -2396...  \n",
              "31  [-1438132.9442466274, 2876265.888493255, 35953...  \n",
              "32  [2157199.416369941, -4314398.832739882, -53929...  \n",
              "33  [-3235799.124554911, 6471598.249109822, 808949...  \n",
              "34  [4853698.6868323665, -9707397.373664733, -1213...  \n",
              "35  [-7280548.03024855, 14561096.0604971, 1820137....  \n",
              "36  [10920822.045372825, -21841644.09074565, -2730...  \n",
              "37  [-16381233.068059236, 32762466.13611847, 40953...  \n",
              "38  [24571849.602088854, -49143699.20417771, -6142...  \n",
              "39  [-36857774.40313328, 73715548.80626656, 921444...  \n",
              "40  [55286661.60469992, -110573323.20939983, -1382...  \n",
              "41  [-82929992.40704986, 165859984.81409973, 20732...  \n",
              "42  [124394988.61057478, -248789977.22114956, -310...  \n",
              "43  [-186592482.91586214, 373184965.8317243, 46648...  \n",
              "44  [279888724.37379324, -559777448.7475865, -6997...  \n",
              "45  [-419833086.5606898, 839666173.1213796, 104958...  \n",
              "46  [629749629.8410347, -1259499259.6820693, -1574...  \n",
              "47  [-944624444.7615519, 1889248889.5231037, 23615...  \n",
              "48  [1416936667.1423278, -2833873334.2846556, -354...  \n",
              "49  [-2125405000.7134914, 4250810001.426983, 53135...  "
            ]
          },
          "execution_count": 59,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table), columns=['Iteración', 'x', 'error'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "csKDNex61w7J"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 10. Gauss-Seidel - matriz 3x3\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M9FUz-Aw1w7K"
      },
      "source": [
        "Ejercicio con la matriz $4x4$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "EiTFfNx91w7K",
        "outputId": "0a37b38f-1dbe-4a61-faa8-2f24e7c7d4da"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.009198s'"
            ]
          },
          "execution_count": 60,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[4]['A'],\n",
        "    matrices[4]['b'],\n",
        "    gauss_seidel,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "ohmwykfS1w7K",
        "outputId": "c5c34ca5-ff2e-4854-edea-b6e71e801714"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: w: 4.588885377855392e+40, x: 7.535908930869659e+40, y: -6.83508210634873e+40, z: 8.14024383452187e+40'"
            ]
          },
          "execution_count": 61,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: w: {x[0]}, x: {x[1]}, y: {x[2]}, z: {x[3]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "WFzAYF0N1w7K",
        "outputId": "eab572c0-3134-4240-bd6c-a01ed83d4992"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:1: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
            "  \"\"\"Entry point for launching an IPython kernel.\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-fb0f68bf-5285-434c-932c-7213c449fc84\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Iteración</th>\n",
              "      <th>x</th>\n",
              "      <th>error</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>[-2.8363554891018876e-15, -7.000000000000006, ...</td>\n",
              "      <td>[-2.8363554891018876e-15, -7.000000000000006, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>[55.33333333333334, 43.00000000000003, -38.000...</td>\n",
              "      <td>[55.33333333333334, 50.000000000000036, -50.66...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>[-80.00000000000021, -375.0000000000004, 324.6...</td>\n",
              "      <td>[-135.33333333333354, -418.00000000000045, 362...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>[1911.3333333333344, 1955.000000000002, -1870....</td>\n",
              "      <td>[1991.3333333333346, 2330.0000000000023, -2194...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>[-5824.00000000001, -15263.000000000018, 13356...</td>\n",
              "      <td>[-7735.333333333345, -17218.000000000022, 1522...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>6</td>\n",
              "      <td>[70295.3333333334, 88059.00000000012, -82230.0...</td>\n",
              "      <td>[76119.33333333342, 103322.00000000013, -95586...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>7</td>\n",
              "      <td>[-305808.00000000047, -633703.0000000008, 5634...</td>\n",
              "      <td>[-376103.33333333384, -721762.0000000009, 6456...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>8</td>\n",
              "      <td>[2744215.3333333363, 3875059.0000000047, -3569...</td>\n",
              "      <td>[3050023.3333333367, 4508762.000000006, -41326...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>9</td>\n",
              "      <td>[-14406080.00000002, -26690511.00000004, 23946...</td>\n",
              "      <td>[-17150295.33333336, -30565570.000000045, 2751...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>10</td>\n",
              "      <td>[111436407.3333335, 168438155.00000033, -15403...</td>\n",
              "      <td>[125842487.33333352, 195128666.00000036, -1779...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>11</td>\n",
              "      <td>[-647507536.0000014, -1133281751.0000024, 1021...</td>\n",
              "      <td>[-758943943.3333349, -1301719906.0000026, 1175...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>12</td>\n",
              "      <td>[4634295095.333343, 7274622147.000017, -662711...</td>\n",
              "      <td>[5281802631.3333435, 8407903898.000019, -76489...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>13</td>\n",
              "      <td>[-28449832512.000072, -48333473407.00012, 4369...</td>\n",
              "      <td>[-33084127607.333416, -55608095554.00014, 5032...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>14</td>\n",
              "      <td>[195382752727.33383, 313113979291.0009, -28466...</td>\n",
              "      <td>[223832585239.3339, 361447452698.00104, -32836...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>15</td>\n",
              "      <td>[-1235635952528.004, -2066368657095.0063, 1870...</td>\n",
              "      <td>[-1431018705255.3376, -2379482636386.0073, 215...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>16</td>\n",
              "      <td>[8300538579543.358, 13452602884883.045, -12216...</td>\n",
              "      <td>[9536174532071.363, 15518971541978.05, -140879...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>17</td>\n",
              "      <td>[-53342729665600.18, -88457722305455.31, 80157...</td>\n",
              "      <td>[-61643268245143.54, -101910325190338.36, 9237...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>18</td>\n",
              "      <td>[354117067676856.5, 577415184785453.2, -524072...</td>\n",
              "      <td>[407459797342456.7, 665872907090908.5, -604229...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>19</td>\n",
              "      <td>[-2295454446350937.5, -3789398937961030.0, 343...</td>\n",
              "      <td>[-2649571514027794.0, -4366814122746483.0, 395...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>20</td>\n",
              "      <td>[1.5141796153359666e+16, 2.4771006825827404e+1...</td>\n",
              "      <td>[1.7437250599710604e+16, 2.856040576378843e+16...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>21</td>\n",
              "      <td>[-9.860974360218352e+16, -1.623940592501632e+1...</td>\n",
              "      <td>[-1.1375153975554318e+17, -1.871650660759906e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>22</td>\n",
              "      <td>[6.482515323877093e+17, 1.062374138597288e+18,...</td>\n",
              "      <td>[7.468612759898929e+17, 1.2247681978474511e+18...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>23</td>\n",
              "      <td>[-4.232270747216232e+18, -6.960796059343018e+1...</td>\n",
              "      <td>[-4.880522279603941e+18, -8.023170197940306e+1...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>24</td>\n",
              "      <td>[2.7771461049633993e+19, 4.555603794120067e+19...</td>\n",
              "      <td>[3.2003731796850225e+19, 5.251683400054369e+19...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>25</td>\n",
              "      <td>[-1.815573030038695e+20, -2.9839776061325666e+...</td>\n",
              "      <td>[-2.093287640535035e+20, -3.4395379855445734e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>26</td>\n",
              "      <td>[1.1901717325686637e+21, 1.9533463289289905e+2...</td>\n",
              "      <td>[1.3717290355725333e+21, 2.2517440895422473e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>27</td>\n",
              "      <td>[-7.786448169860213e+21, -1.279257493333934e+2...</td>\n",
              "      <td>[-8.976619902428877e+21, -1.474592126226833e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>28</td>\n",
              "      <td>[5.101576162531807e+22, 8.375170397857137e+22,...</td>\n",
              "      <td>[5.880220979517828e+22, 9.654427891191071e+22,...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>29</td>\n",
              "      <td>[-3.338900426557535e+23, -5.484464602592305e+2...</td>\n",
              "      <td>[-3.849058042810716e+23, -6.321981642378018e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>30</td>\n",
              "      <td>[2.1869771103374858e+24, 3.59085514438746e+24,...</td>\n",
              "      <td>[2.5208671529932393e+24, 4.13930160464669e+24,...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>30</th>\n",
              "      <td>31</td>\n",
              "      <td>[-1.4316419450000791e+25, -2.35135369249825e+2...</td>\n",
              "      <td>[-1.6503396560338277e+25, -2.710439206936996e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>31</th>\n",
              "      <td>32</td>\n",
              "      <td>[9.375800897921764e+25, 1.5395601164390244e+26...</td>\n",
              "      <td>[1.0807442842921844e+26, 1.7746954856888495e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>32</th>\n",
              "      <td>33</td>\n",
              "      <td>[-6.138292040257601e+26, -1.0081048268071631e+...</td>\n",
              "      <td>[-7.075872130049778e+26, -1.1620608384510655e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>33</th>\n",
              "      <td>34</td>\n",
              "      <td>[4.019625330807263e+27, 6.600737719175445e+27,...</td>\n",
              "      <td>[4.633454534833023e+27, 7.608842545982608e+27,...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>34</th>\n",
              "      <td>35</td>\n",
              "      <td>[-2.6317891914579357e+28, -4.322107697622174e+...</td>\n",
              "      <td>[-3.033751724538662e+28, -4.982181469539719e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>35</th>\n",
              "      <td>36</td>\n",
              "      <td>[1.7233353545197784e+29, 2.8300018463242504e+2...</td>\n",
              "      <td>[1.9865142736655722e+29, 3.2622126160864675e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>36</th>\n",
              "      <td>37</td>\n",
              "      <td>[-1.1283647176094579e+30, -1.8530478537743214e...</td>\n",
              "      <td>[-1.3006982530614357e+30, -2.1360480384067465e...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>37</th>\n",
              "      <td>38</td>\n",
              "      <td>[7.388525898913596e+30, 1.2133332815344048e+31...</td>\n",
              "      <td>[8.516890616523054e+30, 1.398638066911837e+31,...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>38</th>\n",
              "      <td>39</td>\n",
              "      <td>[-4.837768976010457e+31, -7.944714762063266e+3...</td>\n",
              "      <td>[-5.576621565901817e+31, -9.158048043597671e+3...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>39</th>\n",
              "      <td>40</td>\n",
              "      <td>[3.1677276464565505e+32, 5.2020322968673634e+3...</td>\n",
              "      <td>[3.6515045440575965e+32, 5.99650377307369e+32,...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>40</th>\n",
              "      <td>41</td>\n",
              "      <td>[-2.0741457046632437e+33, -3.4062013730903344e...</td>\n",
              "      <td>[-2.390918469308899e+33, -3.926404602777071e+3...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>41</th>\n",
              "      <td>42</td>\n",
              "      <td>[1.3581225595260961e+34, 2.230312568550444e+34...</td>\n",
              "      <td>[1.5655371299924206e+34, 2.5709327058594776e+3...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>42</th>\n",
              "      <td>43</td>\n",
              "      <td>[-8.892678591791726e+34, -1.4603686809931539e+...</td>\n",
              "      <td>[-1.0250801151317823e+35, -1.683399937848198e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>43</th>\n",
              "      <td>44</td>\n",
              "      <td>[5.8227839965161846e+35, 9.56221021464546e+35,...</td>\n",
              "      <td>[6.712051855695357e+35, 1.1022578895638614e+36...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>44</th>\n",
              "      <td>45</td>\n",
              "      <td>[-3.812637357996586e+36, -6.261159948523836e+3...</td>\n",
              "      <td>[-4.3949157576482045e+36, -7.217380969988382e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>45</th>\n",
              "      <td>46</td>\n",
              "      <td>[2.4964490817850014e+37, 4.099687661765408e+37...</td>\n",
              "      <td>[2.87771281758466e+37, 4.725803656617792e+37, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>46</th>\n",
              "      <td>47</td>\n",
              "      <td>[-1.6346251253638126e+38, -2.6843994346783073e...</td>\n",
              "      <td>[-1.884270033542313e+38, -3.094368200854848e+3...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>47</th>\n",
              "      <td>48</td>\n",
              "      <td>[1.0703231415621406e+39, 1.757693782494748e+39...</td>\n",
              "      <td>[1.2337856540985219e+39, 2.0261337259625785e+3...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>48</th>\n",
              "      <td>49</td>\n",
              "      <td>[-7.008268245209301e+39, -1.1509050799551018e+...</td>\n",
              "      <td>[-8.078591386771441e+39, -1.3266744582045766e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49</th>\n",
              "      <td>50</td>\n",
              "      <td>[4.588885377855392e+40, 7.535908930869659e+40,...</td>\n",
              "      <td>[5.289712202376322e+40, 8.686814010824762e+40,...</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-fb0f68bf-5285-434c-932c-7213c449fc84 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-fb0f68bf-5285-434c-932c-7213c449fc84');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   Iteración                                                  x  \\\n",
              "0          1  [-2.8363554891018876e-15, -7.000000000000006, ...   \n",
              "1          2  [55.33333333333334, 43.00000000000003, -38.000...   \n",
              "2          3  [-80.00000000000021, -375.0000000000004, 324.6...   \n",
              "3          4  [1911.3333333333344, 1955.000000000002, -1870....   \n",
              "4          5  [-5824.00000000001, -15263.000000000018, 13356...   \n",
              "5          6  [70295.3333333334, 88059.00000000012, -82230.0...   \n",
              "6          7  [-305808.00000000047, -633703.0000000008, 5634...   \n",
              "7          8  [2744215.3333333363, 3875059.0000000047, -3569...   \n",
              "8          9  [-14406080.00000002, -26690511.00000004, 23946...   \n",
              "9         10  [111436407.3333335, 168438155.00000033, -15403...   \n",
              "10        11  [-647507536.0000014, -1133281751.0000024, 1021...   \n",
              "11        12  [4634295095.333343, 7274622147.000017, -662711...   \n",
              "12        13  [-28449832512.000072, -48333473407.00012, 4369...   \n",
              "13        14  [195382752727.33383, 313113979291.0009, -28466...   \n",
              "14        15  [-1235635952528.004, -2066368657095.0063, 1870...   \n",
              "15        16  [8300538579543.358, 13452602884883.045, -12216...   \n",
              "16        17  [-53342729665600.18, -88457722305455.31, 80157...   \n",
              "17        18  [354117067676856.5, 577415184785453.2, -524072...   \n",
              "18        19  [-2295454446350937.5, -3789398937961030.0, 343...   \n",
              "19        20  [1.5141796153359666e+16, 2.4771006825827404e+1...   \n",
              "20        21  [-9.860974360218352e+16, -1.623940592501632e+1...   \n",
              "21        22  [6.482515323877093e+17, 1.062374138597288e+18,...   \n",
              "22        23  [-4.232270747216232e+18, -6.960796059343018e+1...   \n",
              "23        24  [2.7771461049633993e+19, 4.555603794120067e+19...   \n",
              "24        25  [-1.815573030038695e+20, -2.9839776061325666e+...   \n",
              "25        26  [1.1901717325686637e+21, 1.9533463289289905e+2...   \n",
              "26        27  [-7.786448169860213e+21, -1.279257493333934e+2...   \n",
              "27        28  [5.101576162531807e+22, 8.375170397857137e+22,...   \n",
              "28        29  [-3.338900426557535e+23, -5.484464602592305e+2...   \n",
              "29        30  [2.1869771103374858e+24, 3.59085514438746e+24,...   \n",
              "30        31  [-1.4316419450000791e+25, -2.35135369249825e+2...   \n",
              "31        32  [9.375800897921764e+25, 1.5395601164390244e+26...   \n",
              "32        33  [-6.138292040257601e+26, -1.0081048268071631e+...   \n",
              "33        34  [4.019625330807263e+27, 6.600737719175445e+27,...   \n",
              "34        35  [-2.6317891914579357e+28, -4.322107697622174e+...   \n",
              "35        36  [1.7233353545197784e+29, 2.8300018463242504e+2...   \n",
              "36        37  [-1.1283647176094579e+30, -1.8530478537743214e...   \n",
              "37        38  [7.388525898913596e+30, 1.2133332815344048e+31...   \n",
              "38        39  [-4.837768976010457e+31, -7.944714762063266e+3...   \n",
              "39        40  [3.1677276464565505e+32, 5.2020322968673634e+3...   \n",
              "40        41  [-2.0741457046632437e+33, -3.4062013730903344e...   \n",
              "41        42  [1.3581225595260961e+34, 2.230312568550444e+34...   \n",
              "42        43  [-8.892678591791726e+34, -1.4603686809931539e+...   \n",
              "43        44  [5.8227839965161846e+35, 9.56221021464546e+35,...   \n",
              "44        45  [-3.812637357996586e+36, -6.261159948523836e+3...   \n",
              "45        46  [2.4964490817850014e+37, 4.099687661765408e+37...   \n",
              "46        47  [-1.6346251253638126e+38, -2.6843994346783073e...   \n",
              "47        48  [1.0703231415621406e+39, 1.757693782494748e+39...   \n",
              "48        49  [-7.008268245209301e+39, -1.1509050799551018e+...   \n",
              "49        50  [4.588885377855392e+40, 7.535908930869659e+40,...   \n",
              "\n",
              "                                                error  \n",
              "0   [-2.8363554891018876e-15, -7.000000000000006, ...  \n",
              "1   [55.33333333333334, 50.000000000000036, -50.66...  \n",
              "2   [-135.33333333333354, -418.00000000000045, 362...  \n",
              "3   [1991.3333333333346, 2330.0000000000023, -2194...  \n",
              "4   [-7735.333333333345, -17218.000000000022, 1522...  \n",
              "5   [76119.33333333342, 103322.00000000013, -95586...  \n",
              "6   [-376103.33333333384, -721762.0000000009, 6456...  \n",
              "7   [3050023.3333333367, 4508762.000000006, -41326...  \n",
              "8   [-17150295.33333336, -30565570.000000045, 2751...  \n",
              "9   [125842487.33333352, 195128666.00000036, -1779...  \n",
              "10  [-758943943.3333349, -1301719906.0000026, 1175...  \n",
              "11  [5281802631.3333435, 8407903898.000019, -76489...  \n",
              "12  [-33084127607.333416, -55608095554.00014, 5032...  \n",
              "13  [223832585239.3339, 361447452698.00104, -32836...  \n",
              "14  [-1431018705255.3376, -2379482636386.0073, 215...  \n",
              "15  [9536174532071.363, 15518971541978.05, -140879...  \n",
              "16  [-61643268245143.54, -101910325190338.36, 9237...  \n",
              "17  [407459797342456.7, 665872907090908.5, -604229...  \n",
              "18  [-2649571514027794.0, -4366814122746483.0, 395...  \n",
              "19  [1.7437250599710604e+16, 2.856040576378843e+16...  \n",
              "20  [-1.1375153975554318e+17, -1.871650660759906e+...  \n",
              "21  [7.468612759898929e+17, 1.2247681978474511e+18...  \n",
              "22  [-4.880522279603941e+18, -8.023170197940306e+1...  \n",
              "23  [3.2003731796850225e+19, 5.251683400054369e+19...  \n",
              "24  [-2.093287640535035e+20, -3.4395379855445734e+...  \n",
              "25  [1.3717290355725333e+21, 2.2517440895422473e+2...  \n",
              "26  [-8.976619902428877e+21, -1.474592126226833e+2...  \n",
              "27  [5.880220979517828e+22, 9.654427891191071e+22,...  \n",
              "28  [-3.849058042810716e+23, -6.321981642378018e+2...  \n",
              "29  [2.5208671529932393e+24, 4.13930160464669e+24,...  \n",
              "30  [-1.6503396560338277e+25, -2.710439206936996e+...  \n",
              "31  [1.0807442842921844e+26, 1.7746954856888495e+2...  \n",
              "32  [-7.075872130049778e+26, -1.1620608384510655e+...  \n",
              "33  [4.633454534833023e+27, 7.608842545982608e+27,...  \n",
              "34  [-3.033751724538662e+28, -4.982181469539719e+2...  \n",
              "35  [1.9865142736655722e+29, 3.2622126160864675e+2...  \n",
              "36  [-1.3006982530614357e+30, -2.1360480384067465e...  \n",
              "37  [8.516890616523054e+30, 1.398638066911837e+31,...  \n",
              "38  [-5.576621565901817e+31, -9.158048043597671e+3...  \n",
              "39  [3.6515045440575965e+32, 5.99650377307369e+32,...  \n",
              "40  [-2.390918469308899e+33, -3.926404602777071e+3...  \n",
              "41  [1.5655371299924206e+34, 2.5709327058594776e+3...  \n",
              "42  [-1.0250801151317823e+35, -1.683399937848198e+...  \n",
              "43  [6.712051855695357e+35, 1.1022578895638614e+36...  \n",
              "44  [-4.3949157576482045e+36, -7.217380969988382e+...  \n",
              "45  [2.87771281758466e+37, 4.725803656617792e+37, ...  \n",
              "46  [-1.884270033542313e+38, -3.094368200854848e+3...  \n",
              "47  [1.2337856540985219e+39, 2.0261337259625785e+3...  \n",
              "48  [-8.078591386771441e+39, -1.3266744582045766e+...  \n",
              "49  [5.289712202376322e+40, 8.686814010824762e+40,...  "
            ]
          },
          "execution_count": 62,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table), columns=['Iteración', 'x', 'error'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hVgRKdqD1w7K"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 11. Gauss-Seidel - matriz 4x4\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vx-71oi-1w7K"
      },
      "source": [
        "Ejercicio con la matriz $5x5$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "s3N95eJT1w7K",
        "outputId": "107e2d45-0a85-423b-fde2-af97fed93113"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'Time: 0.010041s'"
            ]
          },
          "execution_count": 63,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "table = []\n",
        "\n",
        "x, t = solve(\n",
        "    matrices[5]['A'],\n",
        "    matrices[5]['b'],\n",
        "    gauss_seidel,\n",
        "    table\n",
        ")\n",
        "\n",
        "times.append(t)\n",
        "\n",
        "f'Time: {t:.6f}s'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "cdrtJ1KO1w7L",
        "outputId": "11b3bfae-7cde-4763-d381-43e0ac54a185"
      },
      "outputs": [
        {
          "data": {
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            },
            "text/plain": [
              "'El resultado de la operación es: v: 1.6629981614884656e+27, w: 6.489548691596904e+26, x: -9.284357707879191e+27, y: 6.783388429574996e+27, z: 1.4867751578251848e+28'"
            ]
          },
          "execution_count": 64,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f'El resultado de la operación es: v: {x[0]}, w: {x[1]}, x: {x[2]}, y: {x[3]}, z: {x[4]}'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "k_33TSYv1w7L",
        "outputId": "b491403f-4f00-4591-f55b-c2717c33c460"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:1: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
            "  \"\"\"Entry point for launching an IPython kernel.\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-d2a50084-23f6-44b8-ac46-c1c2bef57780\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>Iteración</th>\n",
              "      <th>x</th>\n",
              "      <th>error</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>[3.500000000000001, 1.5, 4.666666666666666, -1...</td>\n",
              "      <td>[3.500000000000001, 1.5, 4.666666666666666, -1...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>[-2.197916666666665, 3.170138888888887, -1.233...</td>\n",
              "      <td>[-5.697916666666666, 1.670138888888887, -5.900...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3</td>\n",
              "      <td>[18.6454716435185, 0.25286940586419515, -55.50...</td>\n",
              "      <td>[20.843388310185166, -2.917269483024692, -54.2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>[138.28198794769148, -42.956597054773205, -158...</td>\n",
              "      <td>[119.63651630417297, -43.2094664606374, -102.8...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5</td>\n",
              "      <td>[269.8268679430017, -163.95412648565377, 196.6...</td>\n",
              "      <td>[131.5448799953102, -120.99752943088058, 355.0...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>6</td>\n",
              "      <td>[-842.5354671241574, -27.025704436412013, 2786...</td>\n",
              "      <td>[-1112.3623350671592, 136.92842204924176, 2590...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>7</td>\n",
              "      <td>[-6460.8074778108885, 2031.9193450818202, 7211...</td>\n",
              "      <td>[-5618.272010686731, 2058.9450495182323, 4424....</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>8</td>\n",
              "      <td>[-11580.596792242868, 7446.082149997246, -1117...</td>\n",
              "      <td>[-5119.78931443198, 5414.162804915426, -18386....</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>9</td>\n",
              "      <td>[43971.91106239002, -531.0728704950106, -13339...</td>\n",
              "      <td>[55552.50785463289, -7977.155020492257, -12222...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>10</td>\n",
              "      <td>[305361.22860074457, -99256.09077556073, -3207...</td>\n",
              "      <td>[261389.31753835455, -98725.01790506572, -1873...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>11</td>\n",
              "      <td>[493739.26684346446, -340475.329683207, 622000...</td>\n",
              "      <td>[188378.0382427199, -241219.23890764624, 94271...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>12</td>\n",
              "      <td>[-2265274.12375732, 106334.38213641057, 637126...</td>\n",
              "      <td>[-2759013.3906007847, 446809.71181961754, 5749...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>13</td>\n",
              "      <td>[-14385446.249443762, 4824750.14359469, 141654...</td>\n",
              "      <td>[-12120172.125686442, 4718415.76145828, 779414...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>14</td>\n",
              "      <td>[-20725212.624253113, 15496171.383334208, -337...</td>\n",
              "      <td>[-6339766.374809351, 10671421.239739519, -4790...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>15</td>\n",
              "      <td>[115588046.44475417, -8859003.294411436, -3033...</td>\n",
              "      <td>[136313259.06900728, -24355174.677745644, -269...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>16</td>\n",
              "      <td>[675597976.0535307, -233659431.03549594, -6204...</td>\n",
              "      <td>[560009929.6087766, -224800427.74108452, -3171...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>17</td>\n",
              "      <td>[853002737.7622929, -701961574.7118251, 179538...</td>\n",
              "      <td>[177404761.70876217, -468302143.6763292, 24158...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>18</td>\n",
              "      <td>[-5849655534.3577, 598813070.259795, 143980672...</td>\n",
              "      <td>[-6702658272.119993, 1300774644.97162, 1260268...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>19</td>\n",
              "      <td>[-31629215064.949028, 11275832737.786518, 2691...</td>\n",
              "      <td>[-25779559530.591328, 10677019667.526724, 1251...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>20</td>\n",
              "      <td>[-34203927115.623955, 31634766543.051495, -940...</td>\n",
              "      <td>[-2574712050.6749268, 20358933805.264977, -121...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>21</td>\n",
              "      <td>[293919036578.6679, -36737970373.20715, -68129...</td>\n",
              "      <td>[328122963694.2919, -68372736916.25865, -58720...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>22</td>\n",
              "      <td>[1476031632765.2295, -542290697383.1816, -1154...</td>\n",
              "      <td>[1182112596186.5615, -505552727009.9744, -4727...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>23</td>\n",
              "      <td>[1322408019279.2607, -1417591774724.4194, 4870...</td>\n",
              "      <td>[-153623613485.96875, -875301077341.2378, 6024...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>24</td>\n",
              "      <td>[-14674465282662.363, 2130236550002.3164, 3213...</td>\n",
              "      <td>[-15996873301941.625, 3547828324726.736, 27268...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>25</td>\n",
              "      <td>[-68655040613452.766, 25994586455114.83, 48795...</td>\n",
              "      <td>[-53980575330790.41, 23864349905112.51, 166560...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25</th>\n",
              "      <td>26</td>\n",
              "      <td>[-48388324113878.69, 63123576198303.17, -24951...</td>\n",
              "      <td>[20266716499574.08, 37128989743188.34, -298312...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>26</th>\n",
              "      <td>27</td>\n",
              "      <td>[728481777716847.6, -119011908271953.94, -1511...</td>\n",
              "      <td>[776870101830726.2, -182135484470257.12, -1261...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27</th>\n",
              "      <td>28</td>\n",
              "      <td>[3182513795325153.5, -1242050069635028.8, -202...</td>\n",
              "      <td>[2454032017608306.0, -1123038161363074.8, -515...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>28</th>\n",
              "      <td>29</td>\n",
              "      <td>[1612119864289641.0, -2790828509049113.0, 1.26...</td>\n",
              "      <td>[-1570393931035512.5, -1548778439414084.2, 1.4...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>29</th>\n",
              "      <td>30</td>\n",
              "      <td>[-3.597714024332239e+16, 6475028228294264.0, 7...</td>\n",
              "      <td>[-3.758926010761203e+16, 9265856737343376.0, 5...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>30</th>\n",
              "      <td>31</td>\n",
              "      <td>[-1.4700386265454518e+17, 5.916013430042594e+1...</td>\n",
              "      <td>[-1.1102672241122278e+17, 5.268510607213167e+1...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>31</th>\n",
              "      <td>32</td>\n",
              "      <td>[-4.402419656665865e+16, 1.2238471494213659e+1...</td>\n",
              "      <td>[1.0297966608788653e+17, 6.322458064171066e+16...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>32</th>\n",
              "      <td>33</td>\n",
              "      <td>[1.76837024723695e+18, -3.453213817302856e+17,...</td>\n",
              "      <td>[1.8123944438036086e+18, -4.6770609667242214e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>33</th>\n",
              "      <td>34</td>\n",
              "      <td>[6.765086629722298e+18, -2.8091338985401866e+1...</td>\n",
              "      <td>[4.996716382485348e+18, -2.463812516809901e+18...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>34</th>\n",
              "      <td>35</td>\n",
              "      <td>[5.52010563640492e+17, -5.316092555453881e+18,...</td>\n",
              "      <td>[-6.213076066081806e+18, -2.5069586569136947e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>35</th>\n",
              "      <td>36</td>\n",
              "      <td>[-8.653898231864694e+19, 1.8130199799093846e+1...</td>\n",
              "      <td>[-8.709099288228743e+19, 2.344629235454773e+19...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>36</th>\n",
              "      <td>37</td>\n",
              "      <td>[-3.1010835825756386e+20, 1.329780034703356e+2...</td>\n",
              "      <td>[-2.235693759389169e+20, 1.1484780367124175e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>37</th>\n",
              "      <td>38</td>\n",
              "      <td>[4.633161233551491e+19, 2.2832820430062354e+20...</td>\n",
              "      <td>[3.564399705930788e+20, 9.535020083028794e+19,...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>38</th>\n",
              "      <td>39</td>\n",
              "      <td>[4.217632594454056e+21, -9.398754799160284e+20...</td>\n",
              "      <td>[4.171300982118541e+21, -1.1682036842166519e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>39</th>\n",
              "      <td>40</td>\n",
              "      <td>[1.4155952040889788e+22, -6.275579176460517e+2...</td>\n",
              "      <td>[9.938319446435732e+21, -5.335703696544488e+21...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>40</th>\n",
              "      <td>41</td>\n",
              "      <td>[-5.610160403779325e+21, -9.673433750878344e+2...</td>\n",
              "      <td>[-1.9766112444669114e+22, -3.3978545744178273e...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>41</th>\n",
              "      <td>42</td>\n",
              "      <td>[-2.0476150815123805e+23, 4.821211164131398e+2...</td>\n",
              "      <td>[-1.9915134774745874e+23, 5.788554539219232e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>42</th>\n",
              "      <td>43</td>\n",
              "      <td>[-6.433048774042327e+23, 2.9524924827548365e+2...</td>\n",
              "      <td>[-4.385433692529946e+23, 2.4703713663416965e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>43</th>\n",
              "      <td>44</td>\n",
              "      <td>[4.261983074107584e+23, 4.02884146827779e+23, ...</td>\n",
              "      <td>[1.0695031848149911e+24, 1.0763489855229537e+2...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>44</th>\n",
              "      <td>45</td>\n",
              "      <td>[9.904586886608654e+24, -2.451040748370069e+24...</td>\n",
              "      <td>[9.478388579197895e+24, -2.853924895197848e+24...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>45</th>\n",
              "      <td>46</td>\n",
              "      <td>[2.9092744638461248e+25, -1.3847480434556093e+...</td>\n",
              "      <td>[1.9188157751852594e+25, -1.1396439686186024e+...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>46</th>\n",
              "      <td>47</td>\n",
              "      <td>[-2.7702540892118753e+25, -1.6412944627286512e...</td>\n",
              "      <td>[-5.679528553058e+25, -2.565464192730419e+24, ...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>47</th>\n",
              "      <td>48</td>\n",
              "      <td>[-4.7742286243729275e+26, 1.2364582380031154e+...</td>\n",
              "      <td>[-4.49720321545174e+26, 1.4005876842759805e+26...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>48</th>\n",
              "      <td>49</td>\n",
              "      <td>[-1.30871379400211e+27, 6.474063825254925e+26,...</td>\n",
              "      <td>[-8.312909315648173e+26, 5.23760558725181e+26,...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>49</th>\n",
              "      <td>50</td>\n",
              "      <td>[1.6629981614884656e+27, 6.489548691596904e+26...</td>\n",
              "      <td>[2.9717119554905757e+27, 1.5484866341978346e+2...</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-d2a50084-23f6-44b8-ac46-c1c2bef57780')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-d2a50084-23f6-44b8-ac46-c1c2bef57780 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-d2a50084-23f6-44b8-ac46-c1c2bef57780');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   Iteración                                                  x  \\\n",
              "0          1  [3.500000000000001, 1.5, 4.666666666666666, -1...   \n",
              "1          2  [-2.197916666666665, 3.170138888888887, -1.233...   \n",
              "2          3  [18.6454716435185, 0.25286940586419515, -55.50...   \n",
              "3          4  [138.28198794769148, -42.956597054773205, -158...   \n",
              "4          5  [269.8268679430017, -163.95412648565377, 196.6...   \n",
              "5          6  [-842.5354671241574, -27.025704436412013, 2786...   \n",
              "6          7  [-6460.8074778108885, 2031.9193450818202, 7211...   \n",
              "7          8  [-11580.596792242868, 7446.082149997246, -1117...   \n",
              "8          9  [43971.91106239002, -531.0728704950106, -13339...   \n",
              "9         10  [305361.22860074457, -99256.09077556073, -3207...   \n",
              "10        11  [493739.26684346446, -340475.329683207, 622000...   \n",
              "11        12  [-2265274.12375732, 106334.38213641057, 637126...   \n",
              "12        13  [-14385446.249443762, 4824750.14359469, 141654...   \n",
              "13        14  [-20725212.624253113, 15496171.383334208, -337...   \n",
              "14        15  [115588046.44475417, -8859003.294411436, -3033...   \n",
              "15        16  [675597976.0535307, -233659431.03549594, -6204...   \n",
              "16        17  [853002737.7622929, -701961574.7118251, 179538...   \n",
              "17        18  [-5849655534.3577, 598813070.259795, 143980672...   \n",
              "18        19  [-31629215064.949028, 11275832737.786518, 2691...   \n",
              "19        20  [-34203927115.623955, 31634766543.051495, -940...   \n",
              "20        21  [293919036578.6679, -36737970373.20715, -68129...   \n",
              "21        22  [1476031632765.2295, -542290697383.1816, -1154...   \n",
              "22        23  [1322408019279.2607, -1417591774724.4194, 4870...   \n",
              "23        24  [-14674465282662.363, 2130236550002.3164, 3213...   \n",
              "24        25  [-68655040613452.766, 25994586455114.83, 48795...   \n",
              "25        26  [-48388324113878.69, 63123576198303.17, -24951...   \n",
              "26        27  [728481777716847.6, -119011908271953.94, -1511...   \n",
              "27        28  [3182513795325153.5, -1242050069635028.8, -202...   \n",
              "28        29  [1612119864289641.0, -2790828509049113.0, 1.26...   \n",
              "29        30  [-3.597714024332239e+16, 6475028228294264.0, 7...   \n",
              "30        31  [-1.4700386265454518e+17, 5.916013430042594e+1...   \n",
              "31        32  [-4.402419656665865e+16, 1.2238471494213659e+1...   \n",
              "32        33  [1.76837024723695e+18, -3.453213817302856e+17,...   \n",
              "33        34  [6.765086629722298e+18, -2.8091338985401866e+1...   \n",
              "34        35  [5.52010563640492e+17, -5.316092555453881e+18,...   \n",
              "35        36  [-8.653898231864694e+19, 1.8130199799093846e+1...   \n",
              "36        37  [-3.1010835825756386e+20, 1.329780034703356e+2...   \n",
              "37        38  [4.633161233551491e+19, 2.2832820430062354e+20...   \n",
              "38        39  [4.217632594454056e+21, -9.398754799160284e+20...   \n",
              "39        40  [1.4155952040889788e+22, -6.275579176460517e+2...   \n",
              "40        41  [-5.610160403779325e+21, -9.673433750878344e+2...   \n",
              "41        42  [-2.0476150815123805e+23, 4.821211164131398e+2...   \n",
              "42        43  [-6.433048774042327e+23, 2.9524924827548365e+2...   \n",
              "43        44  [4.261983074107584e+23, 4.02884146827779e+23, ...   \n",
              "44        45  [9.904586886608654e+24, -2.451040748370069e+24...   \n",
              "45        46  [2.9092744638461248e+25, -1.3847480434556093e+...   \n",
              "46        47  [-2.7702540892118753e+25, -1.6412944627286512e...   \n",
              "47        48  [-4.7742286243729275e+26, 1.2364582380031154e+...   \n",
              "48        49  [-1.30871379400211e+27, 6.474063825254925e+26,...   \n",
              "49        50  [1.6629981614884656e+27, 6.489548691596904e+26...   \n",
              "\n",
              "                                                error  \n",
              "0   [3.500000000000001, 1.5, 4.666666666666666, -1...  \n",
              "1   [-5.697916666666666, 1.670138888888887, -5.900...  \n",
              "2   [20.843388310185166, -2.917269483024692, -54.2...  \n",
              "3   [119.63651630417297, -43.2094664606374, -102.8...  \n",
              "4   [131.5448799953102, -120.99752943088058, 355.0...  \n",
              "5   [-1112.3623350671592, 136.92842204924176, 2590...  \n",
              "6   [-5618.272010686731, 2058.9450495182323, 4424....  \n",
              "7   [-5119.78931443198, 5414.162804915426, -18386....  \n",
              "8   [55552.50785463289, -7977.155020492257, -12222...  \n",
              "9   [261389.31753835455, -98725.01790506572, -1873...  \n",
              "10  [188378.0382427199, -241219.23890764624, 94271...  \n",
              "11  [-2759013.3906007847, 446809.71181961754, 5749...  \n",
              "12  [-12120172.125686442, 4718415.76145828, 779414...  \n",
              "13  [-6339766.374809351, 10671421.239739519, -4790...  \n",
              "14  [136313259.06900728, -24355174.677745644, -269...  \n",
              "15  [560009929.6087766, -224800427.74108452, -3171...  \n",
              "16  [177404761.70876217, -468302143.6763292, 24158...  \n",
              "17  [-6702658272.119993, 1300774644.97162, 1260268...  \n",
              "18  [-25779559530.591328, 10677019667.526724, 1251...  \n",
              "19  [-2574712050.6749268, 20358933805.264977, -121...  \n",
              "20  [328122963694.2919, -68372736916.25865, -58720...  \n",
              "21  [1182112596186.5615, -505552727009.9744, -4727...  \n",
              "22  [-153623613485.96875, -875301077341.2378, 6024...  \n",
              "23  [-15996873301941.625, 3547828324726.736, 27268...  \n",
              "24  [-53980575330790.41, 23864349905112.51, 166560...  \n",
              "25  [20266716499574.08, 37128989743188.34, -298312...  \n",
              "26  [776870101830726.2, -182135484470257.12, -1261...  \n",
              "27  [2454032017608306.0, -1123038161363074.8, -515...  \n",
              "28  [-1570393931035512.5, -1548778439414084.2, 1.4...  \n",
              "29  [-3.758926010761203e+16, 9265856737343376.0, 5...  \n",
              "30  [-1.1102672241122278e+17, 5.268510607213167e+1...  \n",
              "31  [1.0297966608788653e+17, 6.322458064171066e+16...  \n",
              "32  [1.8123944438036086e+18, -4.6770609667242214e+...  \n",
              "33  [4.996716382485348e+18, -2.463812516809901e+18...  \n",
              "34  [-6.213076066081806e+18, -2.5069586569136947e+...  \n",
              "35  [-8.709099288228743e+19, 2.344629235454773e+19...  \n",
              "36  [-2.235693759389169e+20, 1.1484780367124175e+2...  \n",
              "37  [3.564399705930788e+20, 9.535020083028794e+19,...  \n",
              "38  [4.171300982118541e+21, -1.1682036842166519e+2...  \n",
              "39  [9.938319446435732e+21, -5.335703696544488e+21...  \n",
              "40  [-1.9766112444669114e+22, -3.3978545744178273e...  \n",
              "41  [-1.9915134774745874e+23, 5.788554539219232e+2...  \n",
              "42  [-4.385433692529946e+23, 2.4703713663416965e+2...  \n",
              "43  [1.0695031848149911e+24, 1.0763489855229537e+2...  \n",
              "44  [9.478388579197895e+24, -2.853924895197848e+24...  \n",
              "45  [1.9188157751852594e+25, -1.1396439686186024e+...  \n",
              "46  [-5.679528553058e+25, -2.565464192730419e+24, ...  \n",
              "47  [-4.49720321545174e+26, 1.4005876842759805e+26...  \n",
              "48  [-8.312909315648173e+26, 5.23760558725181e+26,...  \n",
              "49  [2.9717119554905757e+27, 1.5484866341978346e+2...  "
            ]
          },
          "execution_count": 65,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "pd.DataFrame(np.array(table), columns=['Iteración', 'x', 'error'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_LZQn5631w7L"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Tabla 12. Gauss-Seidel - matriz 5x5\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "T_jKgvA11w7L",
        "outputId": "adf2cc04-7e14-433a-ca87-ec6ad420e70f"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "benchmarking.append([times, 'Seidel'])\n",
        "\n",
        "plt.plot([2, 3, 4, 5], times, linewidth=2.0)\n",
        "plt.plot([2, 3, 4, 5], times, 'o', linewidth=2.0)\n",
        "\n",
        "plt.xlabel('dimensiones (n x n)')\n",
        "plt.ylabel('tiempos (s)')\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6d8gtqHT1w7L"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 5. Gauss-Seidel - tiempos\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7dNags_BFCcY"
      },
      "source": [
        "### 3.2. Benchmarking"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "pxgFnAxAFOKl",
        "outputId": "876f8896-1000-4d7f-bea0-266c57e7d7f1"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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MiPQB3gR+ZYz5pKGwMWYXUCYiJ4t1WtL3gP92dsXvHDaIeFvTs57ibcKdwwZ19lupGBs6ZDaDB8+ieOuT7Nj571hXR/VCTz31FFdeeWWrO/ueKmqBwxjjB27DOiNqHfCSMWaNiMwRkf8JFnsO6Ccim4CfAL8Kzr8NGAHcLSIrg4+GsTV+CPwF2ARsJgpnVF2SlsIjozPJcDkRDBkuJ4+MzuSStJ497LhqqWEo9n4pZ1BUdBcHDnwU6yqpXuaWW25h7dq1nHdeh4+4d1tRzXEYY97COmU2fN7dYdM+4LJW1rsfaDU8G2OWAeM7t6YtXZKWwiVpKdZx21Pyov12KoZsNgfjw4Zinzr133iSxsS6Wkp1WzrwkVKAw5HExJxncTiSKCi4AV/w2hylVEsaOJQKcrsHMTHnL/j95RQU3ITff3QD0inV22ngUCqMx3MCE8b/icrKIlavuYNAIHoXUSnVU2ngUKqZfv1mMHrUfRw48AEbNt5HjIdCU71EUlLTG4kVFxczfnzTdO29997LI4880pXVOird+gJApWIlPf1Kqn0lbN36FPHuTIYOnR3rKinVbWjgUKoNw4f9lOrq7WzaPBd3fIYOxa5UkAYOpdpgDcX+sA7F3st89NIG9m9v/8SHjg6r3j8zidMvH3WsVesxNMehVDusodifwuUaRGHhzVRVFce6SqqXaOuePD3hXj3a41DqCHQo9t4lkp5BVwyr3q9fPw4dOtRk3sGDB0P35OjOtMehVAQSErLJmfAUNTU7KSi8hfr6mlhXSfVwSUlJDBo0iMWLFwNW0HjnnXc47bTTYlyzI9PAoVSE+vTJZewJj1Bauox1636BMYFYV0n1IFVVVWRkZIQejz76KC+88AK/+93vmDRpEmeddRb33HMPw4cPj3VVj0gPVSnVAamp38LnK2HT5odwx2cyQodiVxEKBFr/obFkyZIursmx08ChVAcNGTKb6urtbN36JPHuDNLTZ8W6Skp1KQ0cSnWQiDBq1L34fDso2nA3bvdg+vU7I9bVUqrLaI5DqaPQMBR7YuIoVq2+nfLydbGuklJdRgOHUkfJ4Uhi4sS/WEOxF96oQ7Gr44YGDqWOgduVxsSJz+H3V1BQcKMOxa6OCxo4lDpGnqQxwaHYN7B69e06FLvq9TRwKNUJ+vU7g9Gj5nDg4IcUbbhHh2JXLTQfVr0n07OqlOok6emzgkOxP0lC/BCGDr051lVSx5GODsx4LLTHoVQnGj7sJ6QOvJBNmx9iz543Y10d1Q3l5+eTl5fHpZdeypgxY7j66qsxxvDOO+9w2WWXNSl34YUXAvDee+8xffp0pkyZwmWXXUZFhZVLy8rK4pe//CVTpkzh5Zdf5vHHH2fs2LHk5OQwa5Z1fdHSpUuZPn06kydP5pRTTqGoqOiY26A9DqU6kYiNE054CF/Nbtau+5k1FHuf3FhXS4U5vGAztTsr2y1TX++n2h757jFucCJ9Lop8qJCvvvqKNWvWMHjwYE499VQ++eQTzjnnHGbPnk1lZSWJiYn8+9//ZtasWezfv5/777+fhQsXkpiYyNy5c3n00Ue5++67AWuwxBUrVgAwePBgvv76a1wuF4cPHwZgzJgxfPTRRzgcDhYuXMivf/1rXn311Yjr2hrtcSjVyex2FxNznsLlGkzhqlt0KHbVwkknnURGRgY2m41JkyZRXFyMw+Hg/PPPZ8GCBfj9ft58801mzpzJ559/ztq1azn11FOZNGkSf/vb39i6dWtoW1dccUVoOicnh6uvvpp//OMfOBxW4CstLeWyyy5j/Pjx/PjHP2bNmjXHXH/tcSgVBU5n3+BQ7JeysuB6cqe+QlxcSqyrpSCinkG0h1V3uVyhabvdjt9vnYk3a9Ys5s2bR0pKCrm5uXg8HowxnHvuufzrX/9qdVuJiYmh6TfffJMPP/yQBQsW8MADD/Dpp59y1113ceaZZ/L6669TXFxMXl7eMddfexxKRUlCQhY5OU9TU7OLwlU6FLs6shkzZrBixQqeffbZUI7i5JNP5pNPPmHTpk0AVFZWsmHDhhbrBgIBtm/fzplnnsncuXMpLS2loqKC0tJS0tPTAfjrX//aKfXUwKFUFPXxTmXs2P9Laely1q77uQ7Frtplt9u58MILefvtt0OJ8QEDBvDXv/6VK6+8kpycHKZPn8769etbrFtfX893v/tdJkyYwOTJk7njjjvo06cPv/jFL7jzzjuZPHlyqGdzrPRQlVJRljrwAnzDS9i0eS6b4zMZMfznsa6SioGGM6Hy8vKaHC6aN29ek3Lz5s1rMe+ss87iyy+/bLHN4uLi0LTT6eTjjz9usry8vJzp06c36aHcf//9R9uEEA0cSnWBIUNuotq3na1bnwoOxX5lrKuk1FHTwKFUFxARRo28JzgU+z3BodhnxLpaSh0VzXEo1UVsNgfjxz1OYuJoHYpd9WgaOJTqQtZQ7M/icHgoKLwRYw7GukpKdZgGDqW6WPhQ7AHzGH5/eayrpFSHaOBQKgasodjnATtZtfp2AoG6WFdJqYhp4FAqRvr1Ox2Razh48CMdiv048MADDzBu3DhycnKYNGkSX3zxRZtl7777bhYuXNhifvjAh22JpMyx0rOqlIohm5xB5pAEirc+SXz8ULJ0KPZe6bPPPuONN95gxYoVuFwu9u/fT21tbZvl58yZ04W167io9jhE5HwRKRKRTSLyq1aWu0Tk38HlX4hIVnB+PxFZIiIVIjKv2Tr5wW2uDD4GRrMNSkXbsGE/ITX1IjZvfog9e96IdXVUFOzatYv+/fuHxqjq378/gwcPZvny5cyYMYOpU6fyjW98g127dgFw3XXX8corrwDwzjvvMGbMGKZMmcJrr70W2mZlZSXXX389J510EpMnT+a///1vl7Unaj0OEbEDTwDnAiXAlyIy3xizNqzYDcAhY8wIEZkFzAWuAHzAXcD44KO5q40xy6JVd6W6koiNsSfMxefbxdp1P8flStOh2KNow4bfUV7R/qnQ9fV+7B0YVt2TdAKjRt3V5vLzzjuPOXPmMGrUKM455xyuuOIKTjnlFG6//Xb++9//MmDAAP7973/zm9/8hueffz60ns/n46abbmLx4sWMGDGiyUi4DzzwAGeddRbPP/88hw8f5qSTTuKcc86JuM7HIpo9jpOATcaYLcaYWuBFYGazMjOBvwWnXwHOFhExxlQaYz7GCiBK9Xo2W/Oh2L+OdZVUJ0pKSmL58uU888wzDBgwgCuuuIKnn36a1atXc+655zJp0iTuv/9+SkpKmqy3fv16srOzGTlyJCLCd7/73dCy9957jwcffJBJkyaRl5eHz+dj27ZtXdKeaOY40oHtYa9LgGltlTHG+EWkFOgH7D/Ctv+fiNQDrwL3m1ayiiIyG5gNkJqaSn5+/tG0gYqKiqNet7vpLW3pLe2Alm0xZjYB83/47POrsMmvEYne0N6drTt/L16vl/Jy67TnQYP+l0FHKH80t2Ft2H57pk6dytSpUxkxYgTPPvssY8aMYdGiRS22U1dXR3V1NZWVldTX14e2XV1djd/vp7y8nPr6el544QVGjhzZZP2vv/66SZlI6gVW7ybS768nJsevNsbsEOsv6lXgGuCF5oWMMc8AzwDk5uaaox2DvuE2j71Bb2lLb2kHtN6W0tKRrPjqajyeF5g86R/Y7a7WV+5muvP3sm7dug7dX6Oz78dRVFSEzWYL7eSLiooYP3487733HqtXr2b69OnU1dWxYcMGxo0bh9PpJD4+nqlTp7J9+3b27t3L8OHD+c9//oPD4cDj8fDNb36T559/nj/96U+ICF999RWTJ08mISEhVKYj7XC73UyePDmistE8VLUDyAx7nRGc12oZEXEAXuBAexs1xuwIPpcD/8Q6JKZUr+H1TmHs2EcpLV3B2nU/06HYe4GKigquvfba0P3A165dy5w5c3jllVf45S9/ycSJE5k0aRKffvppk/XcbjfPPPMM3/rWt5gyZQoDBzaeC3TXXXdRV1dHTk4O48aN46672s6xdLZo9ji+BEaKSDZWgJgFXNWszHzgWuAz4FJgcWuHnRoEg0sfY8x+EXECFwItT3ZWqodLHfhNfCN+xaZND7LZncmIEb+IdZXUMZg6dWqLoADW2VUffvhhi/nhN1w6//zzW73/Rnx8PE8//XSL+c2HbY+GqAWOYM7iNuBdwA48b4xZIyJzgGXGmPnAc8DfRWQTcBAruAAgIsVAMhAnIt8GzgO2Au8Gg4YdK2g8G602KBVLQzJvpLp6O1u3PY07PoOM9Oa/u5SKjajmOIwxbwFvNZt3d9i0D7isjXWz2tjs1M6qn1LdmTUU+934fDvYsOFe3O7B9O+XF+tqKaVDjijVnTUMxZ6UOIbVq++gvHztkVdSrdIhXdrW0c9GA4dS3ZzDkdg4FHvBjfh8u2JdpR7H7XZz4MABDR6tMMZw4MAB3G53xOsc8VCViNiAicBgoBpYbYzZe9S1VEp1mMuVyqSJz7Ns+eUUFN7I1Ckv4nD0nGs8Yi0jI4OSkhL27dsXUXmfz9ehHWl3FWk73G43GRkZEW+3zcAhIsOBXwLnABuBfYAbGCUiVcDTwN+MniuoVJdIShrNhAlPUFBwA6tW387EnGex2ZyxrlaP4HQ6yc7Ojrh8fn5+xNc0dGfRakd7h6ruB/4BDDfGfMMY811jzKXGmBzgf7Cuubim02uklGpTv5TTGDP6d9ZQ7EV366EXFRNt9jiMMVe2s2wv8Meo1Egp1a7Bgy+nuno7xVv/bA3FnnVLrKukjjNHTI6LyGXB4T0QkbtE5DURmRL9qiml2hIain3Lw+zesyDW1VHHmUjOqrrLGFMuIqcBZ2NdtPdkdKullGqPiDD2hLn08Z7IunW/4PBhvcuA6jqRBI764PO3gGeMMW8CcdGrklIqEjabi5ycJ3G70ykovFmHYlddJpLAsUNEnsa6wdJbIuKKcD2lVJQ5nX2ZmPMcIjZWFlxPbW27Y4Qq1SkiCQCXY4039Q1jzGEgBfh5VGullIpYQsJQJuY8TU3NHgoLb6a+Xu9/pqKrzcAhIkkAxpgqY8xrxpiNwde7jDHvhZdRSsWW1zuFcWMfpbRsJWvX/VyHYldR1V6P478i8n9F5AwRSWyYKSLDROQGEXkXOD/6VVRKRWLgwPMZMeJX7N37Fps3Pxzr6qherL3rOM4WkQuAm4FTRaQv4AeKgDeBa40xu7ummkqpSAzJvCE4FPszuOMzdSh2FRXtjlXV2rDoSqnuyxqK/S58vh0UFd2D2zWI/v3PjHW1VC+jZ0cp1ctYQ7E/hifpBFavuYPy8jWxrpLqZTRwKNULNQ7F7qWg4CZ8vp2xrpLqRTRwKNVLWUOxP4e/vpKCghvx+8tjXSXVS0QyVtXw4EV/iEieiNwhIn2iXzWl1LFKShpNzoQ/U1m1mVWrbycQqIt1lVQvEEmP41WgXkRGAM8AmcA/o1orpVSnSUk5lTGj79eh2FWnOeIdAIGAMcYvIt8B/mSM+ZOIfBXtiimlOs/gwZdRXb1Nh2JXnSKSwFEnIlcC1wIXBefpbceU6mGGDfsJ1b4SNm95GHd8OmmpFx15JaVaEcmhqu8D04EHjDFfi0g28PfoVksp1dmsodgfpI/3RNau1aHY1dE7YuAwxqwFfgasEpHxQIkxZm7Ua6aU6nTWUOxPER+foUOxq6MWyVlVecBG4Angz8AGETkjyvVSSkWJ09mHSRN1KHZ19CI5VPV/gfOMMTOMMWcA3wD+EN1qKaWiKT5+CBNzntGh2NVRiSRwOI0xRQ0vjDEb0OS4Uj2e1zu5cSj2tT/TodhVxCIJHMtE5C/Bi//yRORZQLNqSvUCAweez8gRd7J339ts2vxQrKujeohITsf9AXArcEfw9UdYuQ6lVC+QmXk91dXb2bbtWeLdmWRkXB3rKqlu7oiBwxhTIyLzgEVAACgyxtRGvWZKqS4hIowc+VtrKPYN9+J2D9ah2FW7Ijmr6lvAZuAxYB6wSUS+Ge2KKaW6js3mYNy4P+Lx6FDs6sgiPavqTGNMnjFmBnAmelaVUr2Ow5HIxJy/4HB4WVlwow7FrtoUSeAoN8ZsCnu9BdDxmZXqhVyugUya+Bz19VWsLLhBh2JXrYr0rKq3REzBycMAACAASURBVOQ6EbkWWAB8KSIXi8jFUa6fUqqLNQzFXlW1hVWrbtOh2FULkQQON7AHmAHkAfuAeKwBDy+MWs2UUjFjDcX+AAcPfaxDsasWIjmr6vtdURGlVPcyePClVPu2UVz8BPHxQ8jK+kGsq6S6iUjOqsoWkUdF5DURmd/wiGTjInK+iBSJyCYR+VUry10i8u/g8i9EJCs4v5+ILBGRiuCpwOHrTBWRVcF1HhcRiaypSqmOGpb9Y1JT/4fNWx5h9+6I/uxVN/Dq7oPkfrqGK42X3E/X8Orug526/UguAPwP8BxWbiPiMQlExI41MOK5QAlWXmR+cLTdBjcAh4wxI0RkFjAXuALwAXcB44OPcE8CNwFfAG8B5wNvR1ovpVTkGoZir6nZzdp1v8TlHkTfPifGulqqHa/uPsjPirZTHTCAUFJTx8+KtgNwSVpKp7xHJIHDZ4x5/Ci2fRKwyRizBUBEXgRmAuGBYyZwb3D6FWCeiIgxphL4OHi72hARGQQkG2M+D75+Afg2GjiUihqbzUXOhCdZtvwyCgtvIXfqyyQmDot1tY4rxhjq6yuoqztEXd3hVp4bp+8t/T7Vpk+T9asDht9v2dWlgeMxEbkHeA+oCWvIiiOslw5sD3tdAkxrq0zw9rSlQD9gfzvbLGm2zfTWCorIbGA2QGpqKvn5+UeobusqKiqOet3upre0pbe0A3pWW4yZTcA8wOdfXIVNfoOIp8nyntSWI4lmW4zxA5VARfBRiWmYNtZ8E5xP6LkSqG9nqwlAEpDEPrzQygH8HTW1ndamSALHBOAa4CwaD1WZ4OtuyxjzDPAMQG5ursnLyzuq7eTn53O063Y3vaUtvaUd0PPaUlo6khVfXUVS0t+YMvkf2O3u0LKe1pb2RNKWxl5A67/86/ytzKs7TCBQ0eY2bbY4nI6+OJ19cDhTcDqH43T2wensG3wOm3Y0zPNiZQYsGZ+uoaSm5SnU6a448k5pv02RiiRwXAYMO4rxqXYAmWGvM4LzWitTIiIOwAu0d1eZHcHttLdNpVSUeL2TGDf2D6xafStr1v6UCeP/hEgkZ/V3b4FAHXX+0tAO3pgV7Ny5t42A0DBdijFtX+PicCSHdvRxcf1ITBjRcuff7Nlmi+dYz/e5c9igsByHJd4m3Dls0DFtN1wkgWM10AfY28FtfwmMDN6jfAcwC7iqWZn5wLXAZ8ClwGLTzgnjxphdIlImIidjJce/B/ypg/VSSh2DgQO/wcgRv2bjpgfYtHkuI0fcGesqhVi9gMqWeQB/81/+TQNCfX3LXsC69dazSFyTHX5CwrA2fvk3znM4vNhskexeO19DHuP3W3axo6aWdFccdw4b1Gn5DYgscPQB1ovIlzTNcfxPeysFcxa3Ae8CduB5Y8waEZkDLDPGzMc6W+vvIrIJOIgVXAAQkWIgGYgTkW9j3YVwLfBD4K9YFyG+jSbGlepymZnfp9q3jW3b/kJ+7XiePjyMHcZL+qdrOm0nFQj48Yd2+K3t9FsLCKW0d3DE4fCEdvRxzr4kJgzD0cqhoMKCzZx88jk4nX2w2xOOuRfQ1S5JS+GStBTrkFsnHZ4KF0nguOdoN26MeQvrlNnweXeHTfuwDoW1tm5WG/OX0fIUXaVUFxIRRo28i7cOJ/CH3QOolTraOvXT6gVUNTvu3/QXv7/5PP+hdsfJEnE26wVk43S0fQiosRcQ2c1LRfzEx7d63o0isivHPxCRocBIY8xCEUnA6kEopY5jInb+4b+AWvE3mV8dMNy7fhXpWx8MBYL2egF2e1KTHXx8QlazQ0EtA4HdntjjegG9yREDh4jchHVaawowHOv016eAs6NbNaVUd7ezxt/q/P0mmYT4oTiTJ7U8/h8eBDrQC1DdRySHqm7FupjvCwBjzEYRGRjVWimleoR0l7PNUz9zcp6KQY1UV4jkPLqa8FNxg6fN6lCZSinuHDaIeFvTQ0adfeqn6n4iCRwfiMivgXgRORd4GWvcKqXUce6StBQeGZ1JhsuJYMhwOXlkdGannvqpup9IAsevsO7BsQq4Gessqd9Gs1JKqZ7jkrQUlp0yjn9JKctOGadB4zgQyVlVAeDZ4EMppdRxrs3AISIvGWMuF5FVtJLTMMbkRLVmSimluqX2ehw/Cj7r7WGVUkqFtJnjMMbsCk7+0BizNfyBNeyHUkqp41AkyfFzW5n3zc6uiFJKqZ6hvRzHD7B6FsNEpDBskQf4JNoVU0op1T21l+P4J9bIs7/HOiW3QbkxpnPvfK6UUqrHaDNwGGNKgVLgyq6rjlJKqe6u59+6SymlVJfSwKGUUqpDNHAopZTqEA0cSimlOkQDh1JKqQ7RwKGUUqpDNHAopZTqEA0cSimlOkQDh1JKqQ7RwKGUUqpDNHAopZTqEA0cSimlOkQDh1JKqQ7RwKGUUr1N4Uvwh/HMyP82/GG89boTtXc/DqWUUj1N4Uuw4A6oq0YASrdbrwFyLu+Ut9Aeh1JK9SaL5kBdddN5ddXW/E6igUMppXoRU1rS+oK25h8FDRxKKdUL7DhczW//s4qdpl/rBbwZnfZemuNQSqkerORQFX/O38zLy7YDMGHYD7ls18PY/GGHq5zxcPbdnfaeGjiUUqoHKjlUxRNLNvPKcitgXJ6byQ/PHEF6nwugMBMWzcGUliDeDCtodFJiHDRwKKVUj7L9YBV/zt/EK8tLEIQrTszkB3kjSO8T31go53LIuZwP8vPJy8vr9Dpo4FBKqR5g+8EqnlhiBQybCLNOHMIP8oYzODxgdJGoBg4ROR94DLADfzHGPNhsuQt4AZgKHACuMMYUB5fdCdwA1AN3GGPeDc4vBsqD8/3GmNxotkEppWJp2wErYLy6wgoYV02zAsYgb9cHjAZRCxwiYgeeAM4FSoAvRWS+MWZtWLEbgEPGmBEiMguYC1whImOBWcA4YDCwUERGGWPqg+udaYzZH626K6VUrG07UMW8JRt5dcUO7Dbh6mlDuCXGAaNBNHscJwGbjDFbAETkRWAmEB44ZgL3BqdfAeaJiATnv2iMqQG+FpFNwe19FsX6KqVUzBXvr2Tekk28/pUVMK45eSg/yBtOarI71lULiWbgSAe2h70uAaa1VcYY4xeRUqBfcP7nzdZND04b4D0RMcDTxphnWntzEZkNzAZITU0lPz//qBpRUVFx1Ot2N72lLb2lHaBt6a5i0ZY9lQHmb67js11+7AJnZTq4INtJX/c+1q3Yx7qj2Ga02tETk+OnGWN2iMhA4H0RWW+M+bB5oWBAeQYgNzfXHO2ZBflROishFnpLW3pLO0Db0l11ZVu+3l/JnxZv5L8rd+KwCdedks0tM4YxsBN6GNFqRzQDxw4gM+x1RnBea2VKRMQBeLGS5G2ua4xpeN4rIq9jHcJqETiUUqo727KvgnmLN/GflTuIc9i47pQsbp4xjIGe7nNIqi3RDBxfAiNFJBtrpz8LuKpZmfnAtVi5i0uBxcYYIyLzgX+KyKNYyfGRwFIRSQRsxpjy4PR5QOeN3KWUUlG2ORgw/hsMGNefms3sHhIwGkQtcARzFrcB72Kdjvu8MWaNiMwBlhlj5gPPAX8PJr8PYgUXguVewkqk+4FbjTH1IpIKvG7lz3EA/zTGvBOtNiilVGfZtLeCeYs3Mr9gJ3EOGzecls3sM4YzwOOKddU6LKo5DmPMW8BbzebdHTbtAy5rY90HgAeazdsCTOz8miqlVHRs2lvO44s2saBwJ26HnZtOH8ZNZwyjf1LPCxgNemJyXCmlur2Ne8p5fPEm3ggGjNlnDOOm03t2wGiggUMppTrRhj3lPL5oI2+u2kW8087NZwznptOz6dcLAkYDDRxKKdUJinaX8/jijby1ahcJTju3zBjOTacPIyUxLtZV63QaOJRS6hgU7W7sYSTG2fnBjOHc2EsDRgMNHEopdRTW7y7j8UUbeWvVbpJcDm49czg3njaMvr04YDTQwKGUUh2wbpcVMN5ebQWM288awQ2nZdMnofcHjAYaOJRSKgJrdpby+KKNvLtmDx6XgzvOGsH1x1nAaKCBQyml2rFmZymPLdzIe2uDAePskdxwajbeBGesqxYzGjiUUqoVq3eU8tiijby/dg8et4MfnT2S64/zgNFAA0cbCgsLWbRoEaWlpXz11VecffbZ5OTkxLpaSqkoW72jlMdW+PjqnY/xuB387zkj+f6p2XjjNWA00MDRisLCQhYsWEBdXR0ApaWlLFiwAECDh1K91KqSUh5btIGF6/aS4IAfnzOK607N0oDRCg0crVi0aFEoaDSoq6tj4bvvM2HceMRui1HNlFKdrbDkMI8t3Mii9Xvxxjv56bmjGB4o4YJzRsa6at2WBo5WlJaWtjq/rKKcnfd+RtzQZFxZycRleYkb4sEWZ+/iGiqljtXK7Yd5bOEGlhTtwxvv5GfnjeLaU7LwuJ3k5ze/dZAKp4GjFV6vt9XgkZyQRMKYVGqLyyhbtM26ia1NcKYn4cpKxpXlJS4rGXuidm2V6q6+2naIxxZtJL9oH30SnPz8G6P53vSheNz6dxspDRytOPvss5vkOACcTifnfPM8+uaMACBQ7admWxm1X5dRU1xKxac7qfjI+pXiGJiAKzsYSLKTcfTpOTdoUaq3WrHtEI8t3MgHG/bRNxgwrj0liySX7gY7Sj+xVjQkwBvOqvJ6vS3OqrLFO4gfnUL86BQATF2A2pJyaopLqfm6jKqV+6j8YjcAdq+LuGAgcWUn4xiQgNik6xvW0xW+BIvmMKO0BL7KgLPvhpzLY10r1c0t32r1MD4MBoxfnD+a703XgHEs9JNrQ05ODjk5ORHf7F2cNlzZXlzZXjgTTMBQt7uS2q9LqSkuo2bzYapX7gPAluCw8iTZ1qGtuPQkTbgfSeFLsOAOqKtGAEq3W69Bg4dq1fKtB/njwo18tHE/KYlx/PL8MXxv+lASNWAcM/0Eo0RsQtzgJOIGJ5F0ajrGGOoP+EI9ktriUnzrDlplnTbiMj3EZXutpPuQZGwuTbg3sWgO1FU3nVdXbc3XwKHCLCs+yGOLGgPGnd8cw3dP1oDRmfST7CIigqN/PI7+8STmpgFQX15LTXFpKE9Svngb5QawgXNwUujQVtzQZOxJx894OPUBw9YDlazfXc76XWWs213O06UltNYnC5SWcOs/ljMq1cPoNA+jUj1k9UvAoT24486XxQf548INfLLpAP0S4/j1BVbASIjT3Vxn0080huyeOBImDCBhwgAAAj4/tVvLrENbX5dS8flOKj4OJtwHxIcObbmyvNj7uhDp+XmSQ5W1rNtdRtHuctbvKmf97jKK9pTjqwsAYBMYNiCJQ46B9PPvabm+YwDrdpXxzprdGGPNi3PYGDEgKRRIRqclMSrVQ3qf+F7xmammln5tBYxPNx+gf1Icv7ngBK4+eYgGjCjST7YbsbkduEen4G5IuPsbEu5l1H5dSlXhPiqXNiTc44gL9khcWV4cA7t3wr3WH2DL/grW7ypn3e6yUJDYU1YTKpOSGMcJgzxcPW0oY9I8nDAomREDk3A77VB4fyjHEeKMp99FD5CfcybVtfVs2ltB0Z5yNuwpp2h3OZ9vOcDrXzWej5/kcjAqNSygpHoYlebpFfeAPh59vuUAjy3cyGdbDtA/ycVvv3UCV08bSrxeVxV1Gji6MXHYrMNVWV7Iy2xMuBeXBXMlpVQXWAl3iXfgGppsHdrK8loJd0fXH64xxrC3vIZ1u4K9iN3lrNtVxuZ9FdTVW12COLuNEQOTOHV4f8YM8jAmLZkxgzwMSGqnF9WQx1g0B1NagnibnlUVH2dnQoaXCRneJquVVtWxYa8VSBoCyturd/OvpdtDZfolxoUOdTUElVGpSXpefzf12eYDPLZoA59vOagBI0Y0cPQgTRLupwy2Eu4HfaFDW7XFZfjWN0u4ZwXP3hri6fT6VNfWs3FveYtexKGqxutfBnndjEnzcOaYgaFeRHb/RJxHk4PIuRxyLueDCM90A/AmODkxK4UTs1JC84wx7KuoYcPuCtbvLrMCyp4KXlq2nara+lC59D7xjEpNYlSa1TsZneZh+IBgD0h1uc82H+CPCzfwxdcHGeBxcdeFY7nqpCEaMGJAA0cPJiI4+sXj6BdP4tRUoCHhbp21VVNcRvmS7ZQv3g42yEiycbh8cyhXEmnC3RhDyaHqULJ6/W4rUBTvryQQzCvEO+2MTvPwjXFpjEnzMGZQMmPSPN3yJjciwkCPm4EeN6eN7B+aHwgYdhyupmh3eZNDXh9v2h/qLdkEsvonWoe5NCEfdcYYK2As2sjSrw8y0OPinovGcuVJQzSAx5AGjl7GSrj3J2GCtUMM1Pip3WpdmFj91TYqvthNxSc7gWDCPash4Z6MPcVNRY2fot3lrAsLEkW7y6mo8YfeY2i/BMakebgoZzAnBA81DUlJwNaNcyyRsNmEzJQEMlMSOGdsamh+XX2A4v2VVjAJBpX1u8s1IR9Fxhg+3WzlMJYWWwHj3ovGMksDRreggaOXs7kcuEf1xT2qL1/FFTPjtNOo3VGB7+tSDm84iG/lXhxfWgn3g2JYYfwU4qeAeva7bIwenMzFU9JDeYjRqZ7j7nx4p93GyFQPI1M9EDaqvibkO58xhk82WTmML4sPkZbs5r7/GccVJ2ZqwOhGjq89wHHqYGUt63eV8W5xHW/uW8X6YKK4xh9AgBFi58zEeHIdcZxabeecGispLGLH5UomzpuMKzWZuMGemCTcu6s2E/LVdWzcY/VMina3n5BP9NewK2HbcZ+QN8bw8ab9/HHhRpZvtQLGnJnjuDxXA0Z3pIGjF6n1B9i8z0r4Wglr63DT3vLGU177J+1jTJqHa04eGspDhE55xfoDrj9UY12YGEy6NyTccdiIy2y4MDE4pLxb/wk15413kpuVQm4bCfnwQ14rdvpZuG1VqNzxlpA3xvDRxv38ceEGVmw7zCCvm9/NHMflJ2bicvTONneFaN/BVP/qeyBjDHvKapqcybR+Vzmb91XgDzSe8joyNYnTRw4I5SEObFnFzG+c2e62RQRHihtHipvEKcGEe0Vt8BTg4BXuH2ynfMl2kIYr3JMbL0z0dL9keHfQVkJ+8ZIljJw47bhLyBtj+DAYML7adpjBXjf3f3s8l+VmaMA4RoWFhSyYv4A6f/TuYKqBo5urrq1nwx4rOKxrCBK7yzkcdsprep94Rqd5OPuEgYwZlMwJaR6yWjnlNX/H0SVp7UlxxI/vT/z4hoR7PbXbykIXJlYuDUu4948PBRFXtpVw1+Rw22zSdkK+YdiV3pSQN8aQv2Efjy3cyMrtVsB44DvjuXSqBozmjDGYmnoCVX4C1X4CVXXWc7U/OK/Oeg4uN8HX79UsoU5a3sF00aJFGjh6m0DAOuW1SS9idznFBypDO4qEOOuU12+OHxTqRYxO9eBN6Nrj4jaXHffIvrhH9gWCV7jvrAiNuVW95gBVy6zhQWyeuMZ7k2Ql40xL7NZXuHcXTruNEQM9jBjYMiG/eV9FqIfSVkJ+ZGpS6FBXd0jIG2PIL9rHHxdtpGD7YdL7xPN/vjOBS6dmENfL82amPtBshx8WBKr8mLaCQrUfAm1vV5w2bPEOJN6BLcGBPSUeZ4aDitW+Vsu3dWfTo6GBIwbKfHXBsZnKQnmIot3lVAYvPhOBoSkJjElLZuakwYxJS+aEQR4y+3bPU17FYcM1JBnXkGQ8MzIwAYN/XxU1wUBS+3UZ1YX7rbJuO66hyaHhUuIyNOHeEfFxdsanexmf3nZCvqGH8u6a3bz4ZWyvkDfGsKRoL48t3EhBSSnpfeL5/cUTuGRKzwoYxhhMXaBxx15VZ+3wm//6rw4LDA09gZr6drctbmvHbwsGAGcfF7YEp/U6vmGZs0kZW7wDaSPv5d3e+h1MvV5vK6WPjgaOKPLXByg+UNl4iGmXdbhhx+HG8Za88U7GpHm4LDczdOHcqNSkHj1Am9gEZ2oiztREkk4eBID/kC90aKumuAxfUbFV2CHEZXise5lkWSMBa8K94zqSkO/sK+TXfbSEj158gfL9+9jw8t84fdb3GHNaHovX7+WxRRspLCklo288D148gYtjHDBMwGB8bf/6b3g9aLuNvesLmgQFgjmnVtkkbMfuxJ7swpmWGLbzb9zxS8Pr4LLO7oG3dQfTs88+u9PeQ4xp58PoJXJzc82yZcs6tE74H4On/wBOn/U9Tji97cTy/ooa68K54EVz1lAWFdT6rb6m3SYMH5AYuh7ihOBzWnLX5QAivSlVV6ivrGscc6u4jLodFRAwVsI9LbFxJODsxoT7Oy+9yJerVlNvs2MP1HPihPGcf/msGLfk2MTiO2m4Qn5DMG/SkJAPH08s0oT8uo+W8O6fH6U+0LgfsYmweuSFLKrLIDMlntvOHMHFUzKObpiZNhh/oI2dfhu//hsOC/n80M4uT+Js2OKdVAV8JA/oE/q1LwnNfv03TDcsj7N1q7zSfx9+kIJDpQSccdjqapnY18vMn/+qw9sRkeXGmNwW8zVwtNTaH4PdJnzjhz9h2PQz2LS3okkeYt2ucvZXNJ7yOsDjCo3LNCbNykUMH5gY8+RfdwoczQVqgwn3r8uo3Wo9THBodUc/N2tkCx+XrcWE/zoLBDh5/NhOCx7GGOsXqbF+mQbCpq1lYfObLbPmhW0jOB0IGDCGQHDdhvUx1g589arVjB07Luw9gmVbq0v4e4SXbV6/ZuuG3tcAoeVhy4J1CQQCVPnqqfD5qaqxHtW19dTW1SMIAtgAt8OG22HHZbdRu/0JfElx1A5IxzjjkLpa4vbtwFVeQ0LW7SS7rV/UIgJiHYYVERr2sXYBpwGngCNgcAAOY3CYsOeAwW6M9Rywnm3t7LYMELAJ9Xah3m4j4BACdhv1diHgsDV5GIeNgNMqYxx2xGFVctu2rWRlZQXrLMF6A6Fpabas+es2ytqw7mDZMB38IKT5a1vzdcM+t7DttvY+6198jhXLFxEIi9P2QIDTTz+HqXf8pEN/EzEJHCJyPvAYYAf+Yox5sNlyF/ACMBU4AFxhjCkOLrsTuAGoB+4wxrwbyTZb09HA8fT3vkNFTV2L+SIuPh08m4AxiAGH3caApLjgaZYuUj0u+ntcJAYPMzV8tsYQ/JVjCP+4rfmmYVHYfGvH0jjfhG2jYVbYegZMaIWw5Sa48zAGg2Hnzl0MHjTImodpfJ+Geobeu3HbDdsIvkNwu43vZ5q1q7HN4W1obXl4Gxrfv+E9xRgS/YbkOvD64X35mEpbY3BukBCI4zt1p4Xeq+FjNOHbazJtgu1s/A6avG5tG+0sb/zcGl6b9uvQTh3D5zUp22J902J5QIJLxGAkWKbhGYOxBdsdKmMIYEAMATGN8wm+loC1A5YAAQz11OM3geCjnjoC1JsA3kNLKUtLA1vjXkoChvSDtST3nYrL2HAZB25jJw578LUdF3Zc2LDR9q/0egw1BKgNPmqMCU4bao2xnglQZww1BuqC8+oMiAlu1wRDniH0DBJabj1LsJxVvrEMSKu3D+vefKXPQqC8xfz4+gA/fOWtDm2rrcARtYPJImIHngDOBUqAL0VkvjFmbVixG4BDxpgRIjILmAtcISJjgVnAOGAwsFBERgXXOdI2j1mFr5bQT6IwxtRwZlWzRGJlAPZUUU8VO4Gdx/C+wT/l0Cuk6W7IBHcOwVeNz9J0Tvj85uvv2rahyfrh22363qbFOzX8jTfugmhSrnHt8PcOLpVmy0Pv3Xx3S7P3tqacCT5oZSdTJbV8bYIjAgfXJaxk8EdYcFnYNA3TEjbdMF9CrxunI3kOmzZN59sano0Q/l97O86YCY9S7RF4MW0/2JqexWNswuEUL+fXWqcX+xy1+Jy1+Jw1VDlrOeiopdpZQ7WzFl9o2npd7ajF57Cm62z+xn9zprV/P83+3TSZbKN8W9tp9gP6cOlh+nj70PiDTDABEww+EvwlEfqDaAw8gYZ/BVaRxsBkgus1riOIVaYhoIW2ExbUgq+NCX9vQstD64e2IYx5v7y1PxWqOzGXEs0s5EnAJmPMFgAReRGYCYTv5GcC9wanXwHmidVXmwm8aIypAb4WkU3B7RHBNo+Zu86PL67lmSbuWj/bL1kU3AFZ3e/QDinU5bT+F1oe/K6saQFMaFloO7aw8g3/aBq2R7Nl0nRe+I5HpGnZ5uWLi4sZlj2s5fbDyjef39Z0i/Jt1beVenWkfQ3/ffL0FgJx7hbfia3OR+LtA8I+b7F+x4a9p01sYZ+XLVROaLqszdcRLGu+7fbqEL6tD/I/YMaMGU26LSa8G9TQM2t4HWj2uvny8O0ETNvbDRzhfdqpT/h2KxYspLW9VIVUM+i306zkbw+8SLE7H9Y9kj+/ewHVrXzm8WGH3o9VNANHOrA97HUJMK2tMsYYv4iUAv2C8z9vtm56cPpI2zxmYw8dZOWAAQTCut+2QICxhw5w67kPdPbbdZn8Q/nk5eTFuhpHZd+251g/bDjYwvJEgXpGbdvGqemnxq5ix0oIO6tGwv7fM3jegvJWrjXw2Il42H7VuaadcQ4ffbSQ+rD9lz0QYNoZ53Tae/Ta8x5FZDYwGyA1NZX8/PyI1009ZTw5+atYn9oPn9OBu87PmD0HSM2b0KHtdDcVFRU9tv5ZEyZRv/QzNo8eTcDpwlZXw/CiIrJOmt5j2wQ9+zsByBg9lg1r11AvYTspEyBj9Lge3a4e/b3kTGFYyQ62b16Lz27DXR8gc/hYynOmdFqbohk4dgCZYa8zgvNaK1MiIg7Ai5Ukb2/dI20TAGPMM8AzYCXHO9TtzMsj/YnfMOT/vYa/wuBIEgZ+/2K8tz7A2Mi30u305O43eXmcsGABe//wR+p27sQ5eDADf/y/eC+6KNY1OyY9+jsJCh9Qz+v1dvqAerHQ47+XYN2j1Y5oBo4vgZEiko21c58FXNWszHzgWuAz4FJgsTHGiMh84J8i8ihWcnwksBSrQ01ynQAACJpJREFUF3+kbXYK760P4L31gZ7/D6gX8V50Ed6LLtLvpJvJyckhJydHv5fjSNQCRzBncRvwLtaps88bY9aIyBxgmTFmPvAc8Pdg8vsgViAgWO4lrKS3H7jVGFMP0No2o9UGpZRSLUU1x2GMeQt4q9m8u8OmfcBlbaz7ANAiE93aNpVSSnWdnneenFJKqZjSwKGUUqpDNHAopZTqkONikEMR2QdsPcrV+wP7O7E6sdRb2tJb2gHalu6qt7TlWNsx1BgzoPnM4yJwHAsRWdbaIF89UW9pS29pB2hbuqve0pZotUMPVSmllOoQDRxKKaU6RAPHkT0T6wp0ot7Slt7SDtC2dFe9pS1RaYfmOJRSSnWI9jiUUkp1iAYOpZRSHaKBAxCRTBFZIiJrRWSNiPyolTIiIo+LyCYRKRSRKbGoa3sibEeeiJSKyMrg4+7WthVrIuIWkaUiUhBsy32tlHGJyL+D38kXIpLV9TU9sgjbcp2I7Av7Xm6MRV0jISJ2EflKRN5oZVmP+E4aHKEtPek7KRaRVcF6Lmtleafuv3rtjZw6yA/81BizQkQ8wHIReb/Zvcy/iTW8+0isuw4+SRTuPniMImkHwEfGmAtjUL+OqAHOMsZUiIgT+FhE3jbGhN8ZstV71seiskcQSVsA/m2MuS0G9euoHwHrgORWlvWU76RBe22BnvOdAJxpjGnrYr9O3X9pjwMwxuwyxqwITpdj/UNKb1ZsJvCCsXwO9BGRQV1c1XZF2I4eIfg5VwRfOoOP5mdyzAT+Fpx+BThbGm5m3o1E2JYeQUQygG8Bf2mjSI/4TiCitvQmnbr/0sDRTLBrPRn4otmi1u6h3m13yu20A2B68LDJ2yIyrksr1gHBwwgrgb3A+8aYNr8TY4wfaLhnfbcTQVsALgkeRnhFRDJbWd4d/BH4BfD/27u3WDumOI7j359LqEqQutW1DxUVSrXRVEofRJuGtiEkiKJ4KBFCaBQvCHENWgQhSnpJSdrKoUmVatyJtEIbFddGgqRuLU0R2p+HtXaNsc85e3rZZ+9z/p+kOXP2rJm1VufsWXvWnvn/62QaB9romNB9X6A9jgmkDyJLJa3IabPLduj5KwaOAkl7AwuAa23/2tPt2Vbd9GMlKf7MCcDDwAvNbl+jbG+2PYyUInikpON6uk3bqoG+vAgMsn088Ar/fmpvGZImAOtsr+jptmyvBvvS8sek4BTbw0lTUldJGrMzK4uBI8tzzwuAubYX1inSSA71HtddP2z/Wps2yUmxdpe0f5ObWYnt9cByYHxp1dZjov/mrG9ZnfXF9k+2/8y/PgWMaHbbGjAamCRpLTAfOE3SnFKZdjkm3falTY4JALa/zT/XAYuAkaUiO/T8FQMH6Y4DUhrbNbYf6KRYB3BxvjthFLDB9vdNa2QDGumHpINrc86SRpL+BlrujS3pAEn75uV+wFjg01KxWs56KOSsb14rG9NIX0rzzZNI30+1FNs32T7M9iBSmufXbE8uFWuLY9JIX9rhmABI6p9vhkFSf2AcsLpUbIeev+KuqmQ0cBGwKs9DA9wMHAFg+3FSutozgC+ATcClPdDO7jTSj3OBKyX9DfwOnN+Kb2xgIPCspF1Jg9vztl9SAznrW1AjfblG0iTSnXE/A1N6rLUVtekxqatNj8lBwKL8eXA3YJ7tJZKugJ1z/oqQIyGEECqJqaoQQgiVxMARQgihkhg4QgghVBIDRwghhEpi4AghhFBJDByh15B0q6Qb8vLtkk7vgTZMkjS92fXmuh/a2U8Ml+p7VdJ+zaovtI64HTf0GpJuBTbavr+n29JskgYAi22PamKdlwCH2b6zWXWG1hBXHKGtSbpF0meS3gKOLrz+jKRz8/JaSXfVchVIGi7pZUlf1h6SyuWmSfogB7W7Lb82SNIaSU8q5dJYmp/+RtI1SrlPPpY0P782RdIjhW1fy+uXSTqi0LaZkt6R9FWtnV20ob+kxUqBKVdLqhem/BxgSWE/ayXdJmmlUp6GIXX+766T9HReHpr3vVepzBRJCyUtkfS5pHsLqzuACxo6UKFXiYEjtC1JI0hPJg8jPRV7UhfFv8lBBt8EniE9QT8KqJ2cx5FyFYzM+xtRmPY5CnjU9rHAetJJGmA6cGIOgrd1ACp4GHg2r58LzCysGwicAkwA7u6mDeOB72yfYPs4CgNEwWigHLDvxxz47jHghjrbzAAGSzobmAVMtb2pTrlhpJwaQ4HzlKPE2v4F2CNf7YQ+JAaO0M5OBRbZ3pSjAHd0Uba2bhXwvu3fbP8A/JnjSI3L/z4kRRAeQjqJA3xtuxbCZQUwKC9/DMyVNJkUlqLsZGBeXp5NGihqXrC9JSfZOii/1lkbVgFjJd0j6VTbG+rUNRD4ofRaLchlsc1b2d5CCqMxG3jd9tt19guwzPYG238AnwBHFtatAw7pZLvQS0WsqtBX1KKcbiks137fDRBwl+0nihsp5TUplt8M9MvLZwJjgInALZKGbkN7yHXXfv6vDbkdw0lXVXdIWmb79lKR34E9O6ljM52/148CNtL1yb/c/+K+9sx1hz4krjhCO3sDOEtSvxwddOJ27Otl4DKlXCZIOlTSgZ0VlrQLcLjt5cCNpPDhe5eKvcO/Qf4uJE2TVW6DpEOATbbnAPcB9fJFrwEGd7P/ch/2IU2fjQEGFL9raXB7AQcDa6tsF9pfXHGEtpVzqz8HfESaMvlgO/a1VNIxwLs5yuhGYDLpE3Y9uwJz8slXwEzb6/XfLKlXA7MkTSNNI3UZkbSLNgwG7pO0BfgLuLLO5ouBqVRLg/og6bubzyRdDiyX9EbO6dCIEcB7OdNf6EPidtwQeol8Z9mEnCyqGfXNADpsL2tGfaF1xFRVCL3H9eTcK02yOgaNvimuOEIIIVQSVxwhhBAqiYEjhBBCJTFwhBBCqCQGjhBCCJXEwBFCCKGSfwDFC787bihYRgAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "for bench in benchmarking:\n",
        "    plt.plot([2, 3, 4, 5], bench[0], label=bench[1])\n",
        "    plt.plot([2, 3, 4, 5], bench[0], 'o')\n",
        "\n",
        "plt.xlabel('dimensiones (n x n)')\n",
        "plt.ylabel('tiempos (s)')\n",
        "plt.grid()\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vgeI6zIUFCQN"
      },
      "source": [
        "<div align=\"center\">\n",
        "    Gráfica 6. Benchmarking - tiempos\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w5cbzI-FJkt9"
      },
      "source": [
        "## 4. Conclusiones"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OddkHgNZTOhi"
      },
      "source": [
        "Si algo se debe tener en cuenta en este informe es el error, y como este se correlaciona este con el tiempo y el performance.\n",
        "\n",
        "Analizando cada uno de los cinco métodos empleados en este informe, nos damos cuenta de las similitudes y diferencias que existen entres sus respectivos algoritmos, algunos de estos usan técnicas de pivote, de recorridos forward y backward, incluso hasta el uso de ambos o como otros que emplean el uso del error.\n",
        "\n",
        "Así el error no se calcule en la mayoría de este método, no significa que exentos de este, ya que sus resultados por muy aproximados que sean a sus valores esperado poseen un grado mínimo de error.\n",
        "\n",
        "De los cinco métodos empleados, Gauss fue el más aproximado al resultado esperado, pero con performance muy pobre comparado con los otros métodos, ya que en tiempo es uno de los que más tarde y en cantidad de pasos empleado puede llegar a usar el doble de pasos que usa el método Gauss-Jordan en el peor de los casos, aunque esa cantidad se va estandarizando entre estos dos métodos a medida que aumenta la dimensión de la matriz a calcular.\n",
        "\n",
        "El método Gauss-Jordan mostró tener un performance en tiempo relativamente mejor a los otros métodos, pero es el método que en sus resultados da la aproximación más lejana, aunque mínima esta.\n",
        "\n",
        "El método de descomposición LU también demostró ser muy eficiente en términos de tiempo y su resultado tienen la aproximación muy cercana, después de Gauss, también se caracterizó porque su aproximación fue por la derecha del resultado y no por la izquierda como es regular en los otros métodos.\n",
        "\n",
        "Respecto al método de Gauss-Seidel, sus parámetros de tolerancia de error y máximo de iteración se manipularon múltiples veces para buscar la convergencia del sistema de ecuaciones dado, pero no fue posible llegar a ese punto deseado, lo que nos hace pensar que el algoritmo usado no es conveniente y debería no solo modificarse, sino reemplazarse por uno apropiado.\n"
      ]
    },
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      "source": [
        "## 5. Referencias"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xCrvsgArJsvV"
      },
      "source": [
        "* [Gaussian Elimination Using Pivoting in Python](https://www.delftstack.com/howto/python/gaussian-elimination-using-pivoting/)\n",
        "* [Gauss Jordan Method Python Program (With Output)](https://www.codesansar.com/numerical-methods/gauss-jordan-method-python-program-output.htm)\n",
        "* [Gauss-Jordan Method Tutorial - Step-By-Step Theory & Coding | Numerical Computing with Python](https://youtu.be/xOLJMKGNivU)\n",
        "* [Python Programming - Gauss Seidel Method | Linear Algebra](https://youtu.be/c6Ng-_Kf2KM)\n",
        "* [Python : Décomposition LU](https://youtu.be/lhPh5Gp2RNg)\n",
        "* [How to implement LU decomposition with partial pivoting in Python?](https://stackoverflow.com/questions/28441509/how-to-implement-lu-decomposition-with-partial-pivoting-in-python)\n",
        "* [Resolución de sistemas de tres ecuaciones por matriz inversa](https://youtu.be/DnLfqXGgEtw)"
      ]
    }
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